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Why Human Exploration of the Solar System

2011-10-20T00:01:00.000-04:00

There is a debate within our country on whether we should pursue human exploration of the solar system. I think we should aggressively pursue human exploration of the solar system for the following reasons:

Exploration is a fundamental part of who humans are. Robotic exploration is not enough. Humans going to other parts of the solar system captures the human imagination and aspirations in a deeper way than just robotic exploration. The solar system is within reach for human exploration. Pushing the human exploration solar system addresses that deep aspiration. This is a deep story of human struggle, with its tragedies and triumphs, that will grip people around the world.

Human exploration of the solar system provides focused and well defined challenges for humans to overcome. We need to push our knowledge, technical ability, to keep growing as a civilization with really challenging problems that have reasonable chances for success. This kind of problem solving keeps us sharp. This spills over into other endeavors, not as direct "spinoffs" per se, but it expands our horizons, gives us different ways of thinking and solving problems, which helps in so many other fields and endeavors.

Solar system exploration is a constructive adventure that diverts human resources from other more destructive enterprises. National pride is better expressed in cooperative space exploration rather than military conquest and might. Space exploration requires tremendous allocation of resources that compete with the voracious requirements for an advanced technological military. While much of the technology for space could be used for the military, cooperative space exploration shares the technological expertise for space with other nations and lessens the chance of it being developed for military use.

Knowledge. Human exploration of the solar system will expand our knowledge of the solar system more deeply than just robotic exploration. The paradox is that per dollar spent, robotic exploration is more cost effective for gaining knowledge. However, the public will be more captivated by human exploration and lavish money on human exploration while being stingy on just robotic missions, hence the more expensive human exploration will achieve more knowledge because the public will be willing to spend the money to accomplish it.

There are a number of poor reasons to explore the solar system. These are reasons I've heard offer that are not realistic, in my opinion.

Provide raw mineral and other mined resources from asteroids, comets, moons and planets for use on earth. The energy in fuel, costs in mining, and the costs in returning raw materials from celestial objects in the solar system are prohibitively expensive to be cost effective for centuries.

Develop alternative homes for humans if a disaster or war wipes out human life on earth. This is unrealistic for the human settlement of the solar system since human settlements will be precarious outside of the hospitable environment of the earth. Perhaps over many centuries, or even millennia, if humans ferry out to the stars and set up independent colonies on habitable worlds this might be possible, however this does not make for a practical reason, in my opinion, to explore the solar system now.

Finally, exploring the solar system glorifies God. Exploring space reveals the diverse creative ways God created the universe. It reveals God's lavish creativity, power, beauty, long patience that unfolds over billions of years, and the awe inspiring forces that shape the solar system and the universe. As the Psalmist says:

The heavens declare the glory of God,
and the sky above proclaims his handiwork.

Transcendence and Immanence in the Game of Life

2011-10-17T00:01:00.000-04:00

Two theological words: transcendence and immanence. These two words describe certain aspects about God. I'll explore just a few aspects of these words using analogies with the Game of Life that I described in an earlier blog post (see Simulation and Life). The word transcendence refers to something being in a transcendent state. Wikipedia speaks of the original definition of transcendent as:

"transcendent means that God is completely outside of and beyond the world, ..."

Theopedia defines the transcendence of God this way:

"It means that God is above, other than, and distinct from all he has made"

Paired with transcendent in Christian theology is the word immanent. Theopedia has a good working definition:

"The literal meaning of the immanence of God is “to be within” or “near” in relation to God’s creation."

In Christian theology, both of these words are essential to understanding God. Theopedia states why this is important:

"To affirm God’s transcendence and deny his immanence is to arrive at deism. To deny his transcendence and affirm his immanence is to arrive at pantheism."

Deism is the view that God initially set the conditions to create the universe and then has not intervened in any way since, having the universe run on its own through natural laws. In deism, there is no supernatural activity of God in the universe since its initial creation. Pantheism is the view that God is the sum of all things in the universe. Everything and everyone make up what God is.

Considering the immensity of the universe (the observable universe is 92 billion light years in diameter -- see blog entry How Big is the Universe?), how can God be above and beyond (transcendent) and near (immanent)? There are many ways to answer this, but I will give an feasibility analysis of this through an analogy. In stating this as a feasibility analysis I am not saying this is how God relates to the world through transcendence and immanence, but there exists at least one approach that shows that the concepts of transcendence and immanence are not impossible.

Consider the expanse of the universe. As we look out into the night sky, especially if we are standing on the peak of a tall mountain, we are aware of three dimensions: (1) the sky to the left and right of us, (2) the sky to the front and back of us, and (3) the sky above us and the universe that is beneath our feet on the other side of the world. Since Einstein, we like to talk about a fourth dimension: time. Time is interwoven with the other three dimensions, but for the moment we will consider just the three spacial dimensions of left/right, front/back, and up/down. One of the interesting things that many physicists propose is that the universe around us may have more than three spacial dimensions. Some versions of String Theory, M-Theory in particular, proposes 11 spacial dimensions. Granted, the dimensions of String Theory outside of the 3 we are familiar with are curled in microscopic, very tight and complicated ways -- but physics does not rule out (and in some cases, proposes) there are other large dimensions than the 3 we know about. How can such a universe with extra dimensions exist? How can we imagine such a thing? Here is where Conway's Game of Life comes in, along with a small book written in 1864 entitled, Flatland: A Romance of Many Dimensions by Edwin Abott Abott (see Wikipedia for a description). Flatland is a simple story of how higher dimensions can interact in a two dimensional world.

The important thing to remember about Conway's Game of Life is that everything happens on a 2-dimensional surface. Think of a sheet of graph paper where we draw the dots for square that are alive. All that the dots on the graph paper are aware of are the squares to the left/right and in front/behind them. There is no concept of up and down. The universe in the sheet of paper is 2 dimensional. We are ignoring that real sheets of paper under a microscope has a thickness to it -- we are considering the idealized example of a 2-dimensional sheet of paper.

Now, consider a cube that approaches the 2 dimensional sheet from above as shown in the illustration to the right. The cube is separate from the sheet of paper and illustrates that it is in some sense transcendent from the live cells on the sheet of paper and from the paper itself. But the cube can move extremely close to the cells and the sheet of paper without even entering it. It can get so close to each of the dots that it is closer to each dot than the other dots are to each other. In this sense the cube is immanent to the dots while being transcendent. But this looks like a small cube, it is not equally immanent to the entire 2-D surface. This is easily remedied by enlarging the cube to have the same or larger breadth and width of the 2-D surface of the Life universe. In this way we can see that both transcendence and immanence are possible in a 2 dimensional universe. In a similar way, God could exist in other dimensions around our universe and thus be transcendent and immanent to all of us and the entire universe.

Again, I am not saying this is how God is actually transcendent and immanent to us and the universe. There are many other ways to explain this that are more accurate statements about these two properties. However, what I have shown is that the properties of God's transcendence and immanence are not necessarily contradictory since there is at least one way of analyzing it that shows no contradictions.

This is certainly not the final word on the topic of transcendence and immanence. This does not even scratch the surface. Much has been written on the topic in religion, philosophy, and in particular in Christian understanding.

299,297,458 Meters/Second -- A Mere Suggestion

2011-09-26T00:01:00.000-04:00

This past week European scientists published the results of an experiment where neutrinos appeared to travel faster than the speed of light. Neutrinos, subatomic particles, that were created in CERN outside of Geneva, Switzerland, traveled 730-kilometers in 2.43-milliseconds to to a cavern underneath Gran Sasso in Italy. If you do the math, 730,000 meters/0.000243 seconds = 300,411,522.6 meters/second. Light speed in a vacuum is 299,792,458 meters/second.

This is not a final word on overturning the speed of light as the ultimate speed limit. More experiments by other scientists over the next few years will either confirm this or invalidate this experiment. If it turns out that these neutrinos do travel faster than light, what are we to make of this? It should be noted I am not a physicist nor a scientist of any sort, but I like to follow these kind of things.

Many in the popular media said this could overturn Einstein's Special Relativity, which is one of the pivotal foundations that scientists have about knowing the universe. Special Relativity had its roots in the 1800s from the work of Scottish physicist and mathematician James Clerk Maxwell. He developed the elegant equations that unified electricity, magnetism, and light. One of the implications of Maxwell's work was that the speed of light was constant. In the early 1900s, Albert Einstein took this observation about the speed of light, which was puzzling at the time, and made two proposals:

The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity),

The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light. (from Wikipedia article on Special Relativity)

Uniform motion means traveling at a constant speed without speeding up or slowing down. There are a number of surprising results

When viewing someone else who is traveling at a different speed than you are you will see that their clocks are running slower than your clocks. Everything about them is running slower. The differences at speeds we are used to are very small so that we don't notice them. However, when you observe someone traveling faster than you at almost the speed of light, the difference is very noticeable.

When viewing the same person traveling at a different speed from you, you will see that their lengths aligned in the direction of motion are shorter. A yard stick or a meter rod will be shorter if held parallel to the direction of their motion. Again, this is not noticeable to our senses at speeds we are used to, but when the other person's speed is close to the speed of light, it is very noticeable.

For a variety of reasons, nothing can go faster, relative to you, than the speed of light in a vacuum. There are some known exceptions to this -- the most notable where space itself is expanding causing distant objects to move away from each other faster than the speed of light. It is even impossible to accelerate an object to the speed of light because to push an object to the speed of light would cause their clock relative to you to stop, their length to contract to zero, and their mass to become infinite.

Mass is a fundamental property of matter, the stuff that things are made of. In gravity, the force that pulls you down to the ground on earth, mass results in weight. Photons, the particles of light, have a "zero" rest mass, meaning that if a photon could stand still, it would have zero mass. Photons can go at the speed of light as a result. In fact, all massless particles travel at the speed of light. Neutrinos, on the other hand, have a very slight mass. Therefore, according to Special Relativity, they should travel slower than the speed of light.

So, what does it mean that the neutrinos in the CERN experiment were going slightly faster than the speed of light? I don't know and don't have the background to make an educated guess, but I'm going to do it anyway.

Special Relativity, and the theory that builds on it, General Relativity, will not be completely disregarded. Special and General Relativity have proved to be so useful in predicting things will see experimentally. It is used on some of our everyday technology, such as GPS satellites. Without the corrections made by the software in the GPS satellites, would GPS devices would not be accurate enough to be useful. What may happen is a revision of the underlying equations, the way General Relativity changed Newton's equations on gravity. General Relativity applied to objects traveling at "normal" speeds gives almost identical results to Newton's equations. In fact, NASA uses Newton's equations for all their spacecraft calculations, whether orbiting around earth, or going from earth to mars or elsewhere in the solar system. In a similar way, new theories and equations would probably under "normal conditions" give almost identical results as Einstein's equations.

We may find that neutrinos going faster than light only in limited circumstances. In 1987, a supernova was observed in an irregular galaxy that is close to our own Milky Way Galaxy (that is, compared to other galaxies). Supernovas generate a huge burst of neutrinos. About 3 hours before the light of the supernova reached us, a burst of neutrinos was detected. These neutrinos came when the central core of the star collapsed before the visible star explosion is seen. If CERN's experiential observations of the speed of the neutrinos is correct, and that speed holds under all circumstances, that neutrino burst would have been seen 4 years earlier. Warning, here is an Earl speculation: neutrinos may travel faster in a gravity field. I don't know why. Speculation: in gravity fields there are extra physical dimensions that provide a slightly shorter path for neutrinos to travel. Along that path, neutrinos travel slightly less than the speed of light, but the distance is shorter under stronger gravity fields. This might be a reason neutrinos don't interact with regular matter much. Neutrinos can happily travel through a light-year of lead and not be bothered but it because there are traveling in another dimension where the lead atoms don't reside. Perhaps neutrinos travel in this extra dimension and leak out to the regular 3 dimensions very infrequently. These extra dimensions would act like a "worm hole," a shortcut from our regular 3 dimensional space (4 dimensional when including time in space-time), but without some of the problems of true worm holes.

Earl Speculation: If we could measure time on the neutrinos at their point of interception in Gran Sasso, we would see that their time is negative from before the time they were generated near Geneva. From our point of view, these are neutrinos with times before they were generated. The clock in the neutrinos say they arrived in Italy before they left Switzerland. From the perspective of the neutrino, however, the neutrino would arrive in Italy after it was created in Switzerland.

Those are some of my thoughts for now. Take them with a grain of salt and consider the source.

Does Anybody Really Know What Time Is?

2011-09-19T00:01:00.000-04:00

Continuing the series on Conway's Game of Life, simulation, and theology -- consider the pattern called a glider in Life. It consists of five live cells. As we step through the each sequence in Life, the glider pattern changes. It morphs from the initial pattern over a sequence of steps to back to its original pattern, shifted down one square and to the right one square. Each of these steps is a step in time. Five steps of time are shown above, from Tick 0 to Tick 4. Notice that these increments of time are referred to as ticks.

Ticks are the smallest units of time in Life in any practical sense. It might be possible to consider the underlying computer program that might run it and the program steps it takes, or the rules that are applied to each step by the human that plots the next set of live and dead cells as smaller steps -- but these "smaller steps" don't manifest itself in the diagrams shown above. In fact, the 4 basic rules of Life can be applied simultaneously or sequentially in any order. All that counts is the final result of the step. So, in considering Tick 0 and the next tick, Tick 1, all that matters is the resulting pattern from Tick 0 that shows up in Tick 1.

Time in Life, using the language of mathematics, is not continuous. This means that the passage of time can be divided up to individual ticks, but no further. Another word for this is that time in Life is discrete, composed of indivisible time ticks.

Time in Life is also independent, at least to some degree, of time that we humans experience. We can run life on a computer where hundreds, even thousands of Life ticks occur in a second of human time. We can also slow down the time ticks in Life to where a tick happens once a minute, or one an hour. We can also speed up and slow down the ticks in comparison to our time.

These speedups and slowdowns of Life ticks to our human time does not effect the world inside the Life game. In fact, nothing inside the world of Life can tell is there is a speedup or slowdown in the application of ticks in the world of Life. Time inside Life is governed by the Life tick and nothing else.

There is more that can be discussed about time in Life. But I'll end this post by noting that time steps in Life is something that is bound to the Game of Life universe and is distinct from the universe we live in. In a similar way, time for us is a feature that is part of the fabric of our universe. Even the ancient theologian Augustine noted that before the world was created time did not exist because it is a feature of our universe. When we think of God and time, we must note that God is not within the realm of our time, just as we are not within the realm of time in the Game of Life. Whether there is a time associated with God is something for another discussion. The Apostle Peter notes this separateness of God's time from our time when he wrote, "But do not overlook this one fact, beloved, that with the Lord one day is as a thousand years, and a thousand years as one day." (2 Peter 3:8, ESV) Looking at the Game of Life in relationship to us and our world we can more easily understand Peter's statement.

The Shape of Space

2011-09-18T00:01:00.000-04:00

The next series of blog posts will explore some theological connections with Conway's Game of Life (see previous blog entry). What does does single-cell automata have to do with theology -- especially Christian theology? I'll explore that. First I need to lay out some concepts.

The previous blog entry introduced the "Game of Life" by the mathematician John Conway. It's not really a game in the typical every-day usage of the word, but it is a game in the sense a solitaire card game is a game, only that the human player sets up the initial conditions of the game by determining where the live cells are and then generates the resulting sequences of "moves" that automatically spring forth from the rules.

John Conway initially described the surface of playing area as an infinitely extending graph paper, extending in infinite directions left and right and up and down. Most computer implementations of the game don't follow that, instead having a limited number of grid lines extending up and down and left and right and then joining the right edge with the left edge and the bottom edge with the top edge of the graph paper. When a graph paper grid is joined in this way it geometrically (or topologically) describes a torus. A doughnut is an example of a torus. A torus is pictured above to the left. Pictured on this torus is a standard configuration of live cells known as a glider.

Life on a torus has some subtle differences from Life on an infinitely extending graph paper grid (or in geometrical terms, an infinite plane). Initially for the glider, the difference between the two surfaces is not readily apparent. Each cell has eight adjacent neighboring cells. Rates of travel in each kind of surface is the same. The space in the immediate area looks the same. However, differences show up over longer distances. A glider launched on an infinite flat plan or graph paper will travel in one direction over time, never to return or cross its path. A glider launched on a torus, like the one above, will circle from the outside of the torus into the inner circle and back around, repeating this cycle and eventually crossing where it once was before. The glider, which lives on the 2-dimensional surface of the torus cannot visualize the 3-dimensional doughnut shape of the torus, but can get a clue that it is on surface that wraps onto itself when it detects it has crossed where it has traveled before.

Believe it or not, astronomers and cosmologists have asked the question of whether our 3-dimensional universe we live in extends infinitely everywhere (the equivalent of the 2-dimensional infinite plane or graph paper), or if it wraps around itself like a sphere or torus. The universe could also "wrap away" from itself. All of these considerations means that the universe has a forth dimensional curve or shape to it (that is different from the idea of time being a dimension as in General Relativity). Like the glider on the torus, we cannot physically see this fourth dimensional curve since we are creatures of three dimensions living in three dimensional space and don't have the wherewithal to look at the fourth dimension.

To sound like a late night cheap TV commercial -- but wait, there's more. There are lots of reasons to think we live in a universe with more than three, four, five and more dimensions. But that is another topic for another time.

The point I want to make here is that both the glider in the Game of Life and ourselves in our world have our sight and imagination limited in great part to the dimensions and world we live in. There is a lot more to our world and universe than what we might initially think.

Simulation and Life

2011-09-14T00:01:00.000-04:00

Back in 1970, Scientific American published in Martin Gardner's Mathematical Games a little "game" that is done on graph paper. The game, known as Life, was developed by British Mathematician John Horton Conway. I loved it. It went viral. Several of us played with it in the back corner of our high school Calculus class during the lecture. The rules, copied from the Wikipedia article on Life, are as follows:

"The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, alive or dead. Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

Any live cell with fewer than two live neighbors dies, as if caused by under-population.
Any live cell with two or three live neighbors lives on to the next generation.
Any live cell with more than three live neighbors dies, as if by overcrowding.
Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

The initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed—births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick (in other words, each generation is a pure function of the preceding one). The rules continue to be applied repeatedly to create further generations."

I have included a Google Gadget that runs life on a small grid. Each side of the grid connects the the opposite side of the grid. So if you move down beyond the bottom of the grid you move into the top. If you move off the right of the grid you are placed into the left side.

To play, click on the grid squares, it will generate a live cell. If you don't like it, click again and it will erase the live cell. When you have the pattern you want, click start. You will see patterns develop. Some will completely disappear, some will grow large, others will end in a static pattern.

In the next few postings on this blog I will draw some ideas to continue the thread I started on simulations based on Conway's Game of Life.

Reality Versus Simulation

2011-09-09T00:01:00.000-04:00

I am not advocating that you and I are simulations. Neither are any group of physicists, at least in the mainstream of physics (not that I know any personally or am trained or practice in the field). We are not imaginary simulations of God, figments of God's fanciful imagination.

However, I do like to play around with different wonder-if scenarios.Why can't we play around with our imaginations and explore different situations and imagine what it would be like? Why leave the speculative fun to others? So, a wonder-if question I have is: what if we were simulations and are unaware of it?

A related question is what is the true nature of reality? Leaving the question aside of whether we have non-physical spirits that are not governed by the known laws of physics, there is a lot about our appearance and the world around us that is misleading. Over the last few hundred years our understanding of our composition, what we are made of, has changed considerably. We discovered that we are made of up of thousands of billions of individual units of life called cells. The cells are made up of a lot of structures, such as membranes, proteins, and long curled strands that encode our genetics. These are composed of atoms -- which in turn are composed of smaller particles and forces. If we were to see the actual particles themselves at the smallest level and see how much space it all takes up -- we'd discover the vast majority of the volume of space we occupy is nothing! We we look at the person sitting next to us, or a rock, or a mountain -- we are seeing the result of light and the electromagnetic force giving the appearance of solidity. But in reality, over 99.9999 percent of us is made up of nothing.

So, what if God made a simulation of our world, the universe, and us based on ephemeral mathematical formulas or patterns? How much different would we be in the simulation from us in the real world? Already we see that us in the real world is made up of the vast majority of nothing. How much worse would a simulation be? And if the simulation was really good, would it matter? When does a simulation stop being a simulation and cross into reality? What is absolutely crucial in our reality that is not captured in a simulation? And if that or those crucial elements about reality can be identified, would it be possible for God to simulate those to perfect fidelity? And if it were possible, what is the difference between the simulation and reality that is important?

Creation Ex Nihilo and Mathematics

2011-09-07T00:01:00.000-04:00

As I exercise, I listen to books on my iPod Touch. I had the pleasure of listening to The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos by Brian Greene. While I don't necessarily buy into what the book proposes, multiple kinds of infinite parallel universes, the book is delightful in expanding my imagination -- to lift it into other areas I never considered. Several topics explored in the book included the notion of simulated universes (exploring whether we are living in a simulated universe) and pure mathematical parallel universes.

The idea of a simulated universe can be thought of along the lines of philosopher Nick Bostrom's thoughts reported in Wikipedia:

i. It is possible that an advanced civilization could create a computer simulation which contains individuals with artificial intelligence (AI).

ii. Such a civilization would likely run many, billions for example, of these simulations (just for fun, for research or any other permutation of possible reasons).

iii. A simulated individual inside the simulation wouldn’t necessarily know that it is inside a simulation — it is just going about its daily business in what it considers to be the "real world."

What is the likelihood that we are living inside a simulation?

Now, let's add the speculative idea of mathematics forming real universes -- that mathematics is the real ground in which we exist. Max Tegmark of MIT has postulated:

All structures that exist mathematically also exist physically. That is, in the sense that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world". (See the Wikipedia article on the Mathematical Universe Hypothesis).

One of the directions this takes is an ultimate form of reductionism. All of reality can be traced to mathematical forms and expressions. Yours and my thoughts, our consciousness, etc., as well as the rest of the universe can be explained in mathematical expressions and states -- and that is the essence of life, the universe, and everything.

Now, the question of how could the universe come into existence out of nothing, ex nihilo, takes an interesting twist. Imagine a sufficiently complex entity that exists independently of our space/time realm. This entity has always been. Mathematics is part of this entity's core. Personality and intelligence make up this entity -- and this entity makes the ultimate simulation by uttering, "Let there be light... ." The simulated universe springs into existence. It is so real to the inhabitants of this universe that there is no reason to take the universe as anything but real.

One of the interesting things about simulated universes is that it is possible in sufficiently rich and complex simulations for beings from the outside to enter into the simulation. It so happens, the simulation's creator sends his beloved Logos into the simulation (that in reality can be called the real universe). But the creator of the simulation and the Logos has, in a real ontological sense, a greater reality than all the inhabitants that live within the created universe.

299,792,458 Meters Per Second. Not Just a Good Idea, It's The Law!

2011-01-01T00:01:00.007-05:00

Einstein discovered the speed limit of the universe -- the velocity of light. It is pegged exactly at 299,792,458 meters per second, no more, no less. Admittedly there is a little bit of fudging on this. The length of the meter is defined to be so that when light travels exactly one second in a vacuum, it will traverse 299,792,458 meters. Einstein didn't fudge the kilometer to get the exact size, scientists and engineers did this later. They did this based on the discovery that the velocity of light is constant, no matter how refined your measurements are, and the desire to have a precise definition for the metric meter.
Last month I was in a couple of conversations that explored question could something go faster than light. The particular idea explored was a moving beam of light. Imagine a beam of light from a flashlight aimed into the night sky. If you move that beam around, how fast is the distant part of light beam moving? To illustrate the issue I'll tell you about a dance routine I saw. My wife's parents are very accomplished square dancers and perform in a square dance company. One of their signature performances is dance where they form a line, side-by-side, link arms, and rotate their line. There is couple in the center, with linked arms rotating slowly. Each couple attached to them outwardly must move faster and faster to keep the straight line, with the last ladies at theends of this line are moving so fast that their feet are off the ground. Imagine this with a beacon of light, extending out from a flashlight. How fast is that beam moving as the beam of light stretches millions of miles out into space.

This leads me to propose a thought experiment. Thought experiments have a noble position in investigating questions. Of course they can be done wrong and lead to all sorts of fallacious notions. But if done right, a thought experiment can lead to critical insights about these kind of problems. In this thought experiment I have set up the parameters so that they can be diagrammed and illustrated in an animated gif.

Imagine you are in a clear section of outer space (in a good spacesuit). Around you is a spherical shell and you are in the very center of it. The sphere has a diameter of 10,792,528,488 meters, or 6,706,166 miles. This size is chosen so that a beam of light traveling across the diameter of the sphere will cross it in 36 seconds. The circumference of the sphere is 33,905,728,212 meters, or 21,068,042 miles, or 113.1 light seconds (it takes 113.1 seconds for light to travel the circumference of the sphere).

I am using three different units of length: Imperial system miles (commonly used in the United States); the metric system meters (used by the rest of the world); and light seconds -- the unit of measurement being the distance spanned by light traveling in a vacuum for one second. Each of these can be used interchangeably as long as you use them consistently.

You are at the center of the sphere holding a marvelously engineered laser flashlight. It will send out a perfectly aligned, straight beam of light that won't disperse or spread out. The nice thing about thought experiments is that you can construct all sorts of expensive gadgets, such as this precision laser flashlight and giant sphere. In the diagrams the flashlight will not be drawn to scale.

We will rotate this beam of light at one revolution per minute. The light hitting the sphere will trace a circle in one minute. Tracing the circle is tracing the circumference of the circle, which is 113.1 light seconds (10,792,528,488 meters, or 6,706,166 miles). Tracing the circle at light speed would mean it would complete the revolution in 113.1 seconds -- but in this experiment it will trace it in 60 seconds -- faster than the speed of light!

Is this a violation of the light speed limit? To help see if this is, we need to add one more feature to our laser flashlight. We can change the light to strobe mode so it will emit one photon each second. A photon is a "particle" of light; the smallest unit of light. In this experiment, all the photons will travel from the center of the sphere to the shell of the sphere. The photons will be represented by little yellow circles in the diagram. As with the flashlight, the photons are not drawn to scale, but they will provide a good picture of how the photons travel.

The animation seen on the right runs for two minutes and then repeats itself (If you do not see the animation move, click on it so that the image shows up alone in your browser). All during this time the laser flashlight in the middle rotates around at one revolution per minute. During the first minute it starts emitting a stream of photons, one per second. As the flashlight turns you see the path of the photons as the move away from the flashlight. At 30 seconds a red arrow traces the path of one photon so you can see how an individual photon travels and so see that all the photons travel in a straight line out from the flashlight to the rim of the sphere. The photons appear to form a spiral that moves out from the flashlight, but each individual photon travels in a straight line away from the flashlight.

A few observations follow. First, it takes 18 seconds for each photon to travel from the flashlight to the rim of the sphere, all traveling at light speed of 299,792,458 meters per second. The beam starts sweeping the rim of the sphere at 18 seconds after the first photon is emitted from the flashlight. Secondly, the last photon hits the rim 18 seconds after the completion of the first revolution, which is 18 seconds into the second revolution when the flashlight is not emitting photons any more. Accounting for the delay at the start and at the end, the beam does a complete sweep of the rim in one minute. Finally, the thing I want to note is that the sweeping motion of the beam on the rim of the sphere is only an apparent motion. There are no photons that actually take a path around the rim of the sphere. Photons are hitting the rim in rapid succession in during one minute, but each photon that hits the rim, traveled at light speed traveling on a straight line from the flashlight to the rim. This demonstrates that a rotating beam of light does not violate the speed limit 299,792,458 meters per second, or 186,282 miles per second, or 1 light second per second.

Okay, some might say this is well and good for emitting one photon per second, but what about a laser flashlight emitting a continuous beam of light? Imagine our laser flashlight emits a photon every half second. The animation would look much the same, only the photon dots would be tighter together showing a more continuous spiral. Each photon still travels in a straight line from the flashlight to the rim. Now imagine a photon every tenth of a second, still the animation would be much the same. The dots would overlap, but it is still doing the same thing, each photon travels in a straight line from the flashlight to the rim. The sweeping motion on the rim is still only an illusion of a spot of light traveling around the rim, because it is still a succession of individual photons hitting the rim that traveled from the flashlight. No matter how small we make the interval of time between the photons, the overall principle holds true. All the photons are traveling from the flashlight to the rim in a straight line going only at light speed, no more, no less.

Gliese 581

2010-12-09T00:01:00.003-05:00

Gliese 581 is a dry clinical name of a diminutive star that's captured the imagination of many. Gliese 581 is the number 581 in German astronomer Wilhelm Gliese's first star catalog of approximately 1000 stars within 20 parsecs of earth. Gliese 581 is 20.3 light years away from earth. The star has a diameter that is 29% of the Sun and a mass that is 31% of the Sun [1].

Gliese 581 is a Type M Red Dwarf star. It is much cooler and dimmer than the Sun. In the visual spectrum the star's luminosity is 0.2 % of the Sun. Considering the overall spectrum of the star, which has its greatest peak in the near infrared, its luminosity is 1.3% of the Sun.

What has captured the imagination of many is that Gliese 581 has as little as 4 planets orbiting it, and as many as 6 or more planets orbiting it. Among these planets are some near earth-sized planets orbiting in the so-called habitable zone or "Goldilocks" zone. This zone is where surface water can exist as a liquid. Inside the zone, surface water can only exist as a vapor while outside the zone the surface water can only exist as ice. In the 4-planet solution proposed in 2009[2] there are planets (in relative distance from the star going out) e, b, c, and d. All the planets appear to be in the zone where tidal locking occurs, meaning that the planets are tidally locked to face one way to the star. Planet e, estimated to be 1.94 – 3.1 earth masses, orbits just over 3 days. Planet b, 15 to 30 times the mass of the earth, orbits over 5 days. Both of these planets are too hot for liquid surface water. Planet c is near the inner zone of the habitable zone. It is 5 to 10 earth masses and orbits every 13 days. It is thought that runaway greenhouse effects makes the atmosphere too hot for liquid water. Planet d at 7.09 to 13.8 times the mass of the earth orbits almost 67 days. This planet swings into the middle of the habitable zone to outside of it.

In 2010 another group proposed a 6-planet solution [3]. The diagram on the left shows the first five planets in this configuration. Planet e has a minimum mass of 1.7 earth masses. It orbits a little over 3 days. Planet b is at least 15.6 earth masses and orbits 5.3 days. Planet c is at least 5.6 earth masses and orbits nearly 13 days. The planets mentioned so far are too close to the star to be in the habitable zone, although c is close to the inner boundary of the zone, but again greenhouse effects are thought to prevent liquid surface water.

Planet g, on the other hand, is at least a 3.1 earth mass planet, orbiting in 36.56 days well inside the habitable zone. However, tidal locking means one side of the planet is hot while the other side is cold, with a narrow "temperate" zone at the terminator where there is a permanent "sunrise" or "sunset" for the star on the planet.

Planet d in this arrangement is at least 5.6 earth masses and orbits in a near circular orbit just inside the outer boundary of the habitable zone with a period of 67 days.

Planet f, not shown in the diagram, is at least 7.0 earth masses with an orbital period of 433 days.

Planets g and f are disputed and are thus considered not confirmed [4].

We should note how these planets were discovered. These were discovered using a very fine resolution spectrograph of Gliese 581 over a period of time. In these spectral pictures, the absorption lines for the various elements show up as very thin lines. The position of these lines change every so slightly over time indicating that the star is being tugged by planets. This shift is a "Doppler shift," analogous to hearing the pitch change of a fire-engine approaching and going away from us. Performing an analysis on this leads to the proposed models. The planets orbital plane is assumed to be nearly on edge to us -- but it is not completely on edge because no transits of the planets (where the planet crosses between us and the star) have been observed. Because there are no transits, we cannot find more precise masses and sizes of the planets. Neither can we perform spectral analysis of the planet atmospheres as we can with planets of other stellar systems that transit their star. So there is little more we can find out about these planets.

One of the big questions is the question of whether there is life on any of the planets of Gliese 581. The most likely planets would be g and d of the six-planet model, and d of the four-model. Assuming that life could develop readily on a planet with water, it is possible that planet g could have some primitive forms of life. It is estimated [2] that Gliese 581 is at least 2 billion years old. Type M Red dwarfs are unstable the first 1.2 billion years, with massive stellar winds that would sterilize the surface of the planet. Further, with the planet being tidally locked, there is very little motion that would dynamically add to generating magnetic fields that could shield the nascent life developing on the planet. While it is known that life on earth can exist in all kinds of harsh conditions, little is known about what is required for life to initially develop. So, at best, it is speculated that primitive life might exist, but it could be likely that no life does exist on the planets of Gliese 581. Further, there is little that can be done to improve on the information we have on the stellar system to make a better determination. Our chances for more information are with stellar systems whose planets transit the star in our line of sight. In those systems we can make better determination of planet size and masses and also some of the chemical composition of the planetary atmospheres. If, for instance, we detect oxygen and carbon-dioxide in similar scales that exist on earth for a planet orbiting another star in its habitable zone, we would have an argument for life on that planet because oxygen in that abundance cannot be maintained by any geological mechanism we know of. It would be a probable marker for life. In the next few years we may have opportunity to analyze a dozen or more near earth-sized planets to see if these markers exist.

1. Much of the information comes from the Wikipedia article on Gliese 581.

2. Mayor, M.; et al. (2009). The HARPS search for southern extra-solar planets.

3. Vogt, Steven S.; et al. (2010). The Lick-Carnegie Exoplanet Survey: A 3.1M⊕ Planet in the Habitable Zone of the Nearby M3V Star Gliese 581

4 Cowen, Ron (Science News, November 6, 2010). Existence of habitable exoplanet questioned

A Framework Hypothesis

2010-07-17T00:01:00.011-04:00

In the previous post I mentioned the existence of a couple of approaches in interpreting the days of Genesis other than six consecutive 24-hour days. I briefly mentioned the day-age theory. Now I will discuss the so-called "Framework" approach. For this I am using information gathered from Lee Irons and Meredith Kline (Kline is a major developer of the hypothesis) from the book The Genesis Debate, and Wikipedia.

There are several observations that can be made about Genesis chapter 1. The first I'll note is that there are parallels between the first six days in Genesis. In day 1 God creates light and in day 4 God creates the lights in the heavens. In day 2 God separates the waters from the heavens and in day 5 God populates the waters with fish and the heavens with birds. With day 3 God brings plants from the earth and in day 6 God brings animals from the earth. These parallels make two groups of three. The groups of three (days 1-3, days 4-6) are referred to as triads. The chart below illustrates the two triads and shows the parallels of the days within the triads, each parallel having the same color (my apologies to people with color visual disabilities). You can click on the diagram to enlarge the image.

What could these parallel arrangements of the days of each triad mean? When I saw this pointed in Meredith Kline's presentation, I could see immediately where he was headed. This is a form parallelism is a recapitulation, where day 4 revisits the activities of day 1, day 5 recapitulates the activities of day 2, and day 6 revisits the activities of day 3. This kind of recapitulation is seen elsewhere in the Bible. One prime example is the last book of the Bible, the book of Revelation, where there are a series of sevens, the seven seals, seven trumpets, seven bowls, etc. While one popular approach in Revelation is to view each of those sevens as sequential, but the literary structure that makes the most sense is that the sevens in Revelation are recapitulations of each other. They describe the same sequence of time, from Christ's first advent until his second coming, examining different facets or aspects of the same periods.

Genesis, the first chapter, and Revelation, the last book, are both displaying a style or framework of recapitulation make that style of writing bookends to the Bible, where the Holy Spirit displayed an artistic style through the human authors, Moses of Genesis, and John for Revelation. This framework opens the door that the primary meaning of the days in Genesis are not to be thought of as 24-hour days, but a framework for which the creative acts of God are described. It is possible that the days in this framework hypothesis are 24-hour days, but it is also possible that these days are not tied to any earthly 24-hour periods. Since the days are literary devices to display God's activity, so are the beginning and ending descriptions, evening and morning. Further, these beginnings and endings don't have physical realities in the first days in a literalistic reading of the days of Genesis, since the sun and moon are created in along with day and night in day 4.

The whole sequence marches to the climax for the seventh day. This is the day that God rested from his creative activity. But the book of Hebrews indicates that the seventh day did not end, it continues and will continue into all eternity (Hebrews 4). It is ultimately an eschatological rest that all of God's people will participate in with God in the new heavens and earth.

There is much more to be said in the framework hypothesis, perhaps as time permits I will explore some of the other avenues -- but I have other things I need to prepare for in August, so I will not be devoting much time to the topic in the next couple of months. I recommend The Genesis Debate, it provides an excellent description of the framework hypothesis.

I've heard several objections to not taking the days of Genesis 1 as 24-hour days:

1. Numbers assigned to days are only done to literal 24-hour days in the Bible. In the Bible, numbers can be assigned to periods of time that do not refer to an actual literal period of time. For instance, the book of Daniel in the Old Testament there is a non-literal use of the concept of week.

Seventy weeks are decreed about your people and your holy city, to finish the transgression, to put an end to sin, and to atone for iniquity, to bring in everlasting righteousness, to seal both vision and prophet, and to anoint a most holy place. (Daniel 9:24, ESV see the passage to 9:27)

The seventy weeks are a period of time from Daniel to when the Messiah comes and the destruction of the Jerusalem, the Temple, and possibly to the end of history. This is a period longer than a literal 490 years.

2. Exodus 20:8-11 -- the commandment of working six days and resting on the seventh only makes sense if Genesis creation days are 24-hour days. If you consider that the language God uses the language of resting and working in a highly analogous human descriptions, then this objection does not have any force. Consider the following passage:

14 You shall keep the Sabbath, because it is holy for you. Everyone who profanes it shall be put to death. Whoever does any work on it, that soul shall be cut off from among his people. 15 Six days shall work be done, but the seventh day is a Sabbath of solemn rest, holy to the Lord. Whoever does any work on the Sabbath day shall be put to death. 16 Therefore the people of Israel shall keep the Sabbath, observing the Sabbath throughout their generations, as a covenant forever. 17 It is a sign forever between me and the people of Israel that in six days the Lord made heaven and earth, and on the seventh day he rested and was refreshed. (Exodus 31:14-17, ESV)

This passage describes God's rested to refresh himself. The Hebrew word for refresh is used in two places, Exodus 23:12:

Six days you shall do your work, but on the seventh day you shall rest; that your ox and your donkey may have rest, and the son of your servant woman, and the alien, may be refreshed. (Exodus 23:12, ESV)

and 2 Samuel 16:14:

And the king, and all the people who were with him, arrived weary at the Jordan. And there he refreshed himself. (2 Samuel 16:14, ESV)

Here you see in these passages, and particularly in 2 Samuel, that people need to be refreshed because they are weary. However, God in Exodus 20:11 is not weary in a literal sense. That Exodus 20 passage makes sense even when we understand we do not take it the part of it saying that God was refreshed in a literalistic fashion. In the same way the week in Genesis need not be a consecutive series of seven, 24-hour days for it to make sense. Considering that the seventh day in Genesis 1 continues from what Hebrew says, we see that tying our hands to only reading the Genesis days as only 24-hour days makes no sense with other passages (e.g., Hebrews) in the Bible.

I will take up the discussion further, time permitting, in a couple of months. For now other pressing commitments are demanding my time. I welcome comments. If these series of blog entries do not make sense, don't pursue this. I personally think this makes a lot of sense, but I certainly understand if you don't think so.

The Day the Universe Became Huge

2010-07-16T00:01:00.075-04:00

100 years ago, the entire universe was thought to consist of just the Milky Way galaxy. There was speculation by some that the faint spiral nebulae seen in telescopes might be galaxies like the Milky Way -- but the majority of astronomers did not think so. Then it was possible to think of the universe spanning only thousands of light years. A recently created universe was reasonable in that historical setting. Light from the other side of the Milky Way could reach us in tens of thousands of years -- and we didn't really know the size of the Milky Way yet. But our view of the universe then was going to explode. The gentleman on the upper left, Dr. Edwin Hubble, along with other pioneering astronomers, rocked astronomy with discoveries about the size of the universe. January 1, 1925, Hubble announced that the Andromeda spiral nebula was in fact a galaxy, with stars like the Milky Way, that was more than a million light years away. In 1929, Hubble published his red-shift observations, demonstrating that the universe was larger than billions of light years and expanding.

We know that the universe is huge because astronomers can estimate the distance of remote galaxies via certain kinds of stars and exploding stars (supernova) are known to have certain inherent brightnesses, like the supernova pictured in the galaxy on the right (see the bright star on the lower left of the galaxy). When this supernova's brightness is seen here on earth through a telescope, astronomers note how bright it appears here in the telescope. Using the brightness we see here and the actual known brightness of the supernova in a standard formula, the distance can be calculated.

So, the universe is HUGE. It takes light from distant galaxies billions of years to reach earth. That alone indicates the universe is billions of years old. It is certainly possible for God to have created the universe with photons (light) in motion, just as it would be if they originated from the various galaxies stretching across the universe. But there are so many things that fit with an old universe that it would take volumes to list. If the universe actually was created mere thousands of years ago, the conditions we see of the universe all around us then perfectly simulate a universe that is 13 to 14 billion years old.

For Christians, we must make a judgment call on the evidence. For many, the perfect simulation of the old universe is not a problem. Certainly an omnipotent God described in the Bible can do that -- create a universe thousands of years ago that looks so consistently billions of years old. But the Bible also uses language and descriptions that put the earth at the center of the universe and we dismiss that today without even a thought In my mind, it is more easy to believe that we live in an earth centered universe that simulates the earth going around the sun than to believe that the universe is only a few thousand years old -- that is how strong the evidence is for an old universe. I know there are Christians who will say I put science ahead of the Bible. By that same reasoning, they put science ahead of the Bible when they adopt a sun centered solar system. These Christians part company with John Calvin and Martin Luther, who firmly believed the earth was the center of the universe because the Bible said so. But, those who are convinced that anyone who factors in and is convinced of the evidence for an old universe is selling out on biblical authority -- I would strongly urge them to stay the course and hold to an young universe. It is if first importance not to sell out on biblical authority.In fact, if these blog posts are troubling, by all means stop reading them.

I believe the Bible is inerrant. How can that be? Genesis uses the word days -- six days to describe the creation of the heavens and the earth -- occurring thousands of years ago. Is it possible that the language of creation, the days of creation, can be understood in a way outside of six consecutive 24-hour days, just as we understand the language describing the earth at the center of the universe is not to be taken "literally"? I think so, and I will mention a couple of plausible approaches that theologians I respect have discussed, but concentrate on one approach that makes the most sense to me.

The first approach I mention is the day-age theory. This is probably the one I am exposed to the most simply because I enjoy listening to the podcasts of Reasons to Believe, a ministry of Christian astrophysicist Hugh Ross and others. They have a variety of podcast series you can get from iTunes, searching for Reasons to Believe. They observe that the Hebrew word for "day" in Genesis has other uses than simply a 24-hour day, just as "day" does in the English language. How I used "day" in the title of this post is an example of using "day" in other than a 24-hour sense. Reasons to Believe propose that days in Genesis refers to long epochs of time in God's creative activity.

Personally, I have reservations in how Reasons to Believe interpret Genesis, reading in a whole lot of detailed scientific theory in the Genesis narration of creation that just doesn't make sense to me in that I don't think late twentieth/twenty-first century scientific theory was purposely inspired by God into the Bible. Read some of Reasons to Believe books or listen to their podcasts and you decide if it makes sense.

However, I find Reasons to Believe (RTB) podcasts useful because I enjoy reading and listening to perspectives different from my own (I also listen to young earth creationists), and RTB discusses all sorts of science and theological issues that illuminate in so many ways -- without the agenda of a young earth creationist which, I'm sorry to say, often skews the science and doesn't present the whole picture. RTB topics range from radiometric dating, multiple parallel universes, the philosophical and theological problems of evolution, and the list goes on and on.

The next post I will examine another approach to Genesis days.

Virtual Reality

2010-07-08T00:01:00.002-04:00

This is another thought experiment. There are two premises to this experiment:

1. The earth was created 6000 years ago in six 24-hour days, as outlined in the first two chapters of Genesis. Each of the days is 24 hours and they sequentially describe what happened each day.

2. It appears that the universe is on the order of 13 to 14 billion years old. This appearance is so striking that in all the careful scientific analysis, everything is consistent with an old universe. Sometimes there seems to be anomalies, inconsistencies with what is observed and the age of the universe, but as measurements and observations are refined, these too fall in line with being consistent with a 13 to 14 billion year old universe.

I do not know if anyone is advocating this view. Ken Ham of Answers in Genesis certainly is not. Neither do the people at the Institute for Creation Research. They would disagree with premise 2. Scientists who believe that the universe is 13 to 14 billion disagree with premise 1. Let's note how people differ with the premises but move on with the thought experiment and run with these two premises.

Oh -- as a parenthetical note, it is possible that Tim Challies was reporting this viewpoint in his blog about the Ligonier Ministries’ annual conference. This is the position I take whenever I take the young earth/universe view the third month of every prime number year (that makes March of 2011 my young universe/earth viewpoint month).

So, back to the premises. So, according to this thought experiment model, the universe/earth were created 6000 years ago, but all the empirical evidence looks as if the universe sprang into existence 13.74 billion years ago.

So,we live in the reality of a 6000 year old universe, but a virtual reality of a 13 to 14 billion year old universe. It is as if this is a simulation, an extremely good simulation, of an old universe.

In this thought experiment you can see why scientists fall for believing we are in an old universe. It really looks old. You can also see why many Christians, like me, also fall for thinking the universe is old -- it really looks old. The only ones who aren't fooled are the ones who read Genesis literally, taking the days as six, 24-hour sequential days. But those other Christians, like me, see that the evidence for the old universe is analogous to once held view of the earth centered universe -- that even my heroes Martin Luther and John Calvin mistakenly believed in. They, after all, simply took the Bible literally when it said that God made the sun stand still (implying it when around the earth) and that the earth is unmoved (implying the earth stands still and everything moves around the earth). Since theologians and the church did this once before without ill effects, shouldn't it be done again because of the strong evidence? -- or so would Christians like me think.

Some questions assuming these premises:

1. Suppose the study of the solar system as if it were billions of years old showed a pattern that it appears that every 10,000 years comets would bombard earth from a certain direction, and the last bombardment appears to be 10,000 years ago. Should we ignore this study because nothing existed prior to 6,000 years ago?

2. Given that reality is the universe is only 6,000 years old, even though the overwhelming evidence is that it looks like its billions of year old, why should we give up the earth centered universe since the language of the Bible seems to imply the earth is at the center it while the scientific evidence points the other way?

Thought Experiment 1

2010-07-06T00:01:00.000-04:00

Imagine, for a moment, that the earth is actually at the center of the universe. The sun, the planets, and the stars revolve actually around the earth. Newton's laws, modified by Einstein's General Relativity, computationally compute orbits around the sun. They are very useful in providing simple, accurate approximations for all the spacecraft we send to other planets. But in reality, the sun, Mars, and everything else revolves around the earth.

Now consider that it is actually possible to develop a version of Newton's laws of motion and Einstein's General Relativity that would actually describe accurately the motions of spacecraft going to Mars where everything revolves around the earth. It would be much more complicated than the orbital dynamics equations that are currently used, but it would just as accurately give the results needed to send spacecraft to Mars.

So, here is the reality in our thought experiment, everything revolves around the earth. When planets go through complicated retrograde motion, where they appear to go backwards in the sky -- they actually are, instead of the earth's orbit around the sun passing the more distant planet in the same orbital segment.

So, in our thought experiment, the earth is the center of the universe. It only appears that the earth is orbiting around the sun with the rest of the planets of our solar system. In fact, the appearance of the sun being at the center of the solar system is so striking that there is no way to tell, experimentally and mathematically, that the sun is not at the center of the solar system.

Now suppose that much of the world is deluded into believing the sun is the center of the solar system, even though the earth is actually at the center. In fact, many scientists are also deluded in believing the sun is the center of the solar system.

Here are some questions based on the thought experiment where the earth is actually at the center of the universe.

Questions:

1. Is there any scientific validity to discuss the solar system as if the sun is at the center of the solar system, even if earth is really at the center?

2. Is it okay to use the mathematics of a sun centered solar system to calculate spaceship paths, because it is simpler to do, rather than using the much more complicated (but physically correct and real) earth centered orbital dynamics?

3. How much effort should be given to correct the delusions of others who believe the sun is the center of the solar system rather than the earth?

Starting Points

2010-07-02T00:01:00.026-04:00

This continues a series of posts on the idea of the old universe. I want to thank Jared for his good comments and critique on my previous post for it is providing a springboard for this series of articles.

The previous article stated some of my views of why I view the universe to be old, on the order of billions of year old, even though I am a Christian who holds to the inerrancy of the Bible. This is in contrast to many other Christians, and what was the majority view in the history of the Christian church for 2000 years that viewed the universe and earth were created in the span of six twenty-four hour days. I know that many in the Christian community view that those who hold to an old universe/old earth position start with the speculations of the dominant view of science and twists the Bible to fit with those speculations.

Before I continue, first I will say that I have the greatest respect for Christians who believe that the universe and earth were created in the span of six twenty-four hour days. I have some reservations in discussing this. First, I believe that overall those who believe in the young universe, along with the understanding that the Triune God is actively involved in history drawing his specially called people to himself through the death and resurrection of Jesus, the second person of the Trinity (this activity of God through Jesus is commonly referred to as the gospel) -- have a more accurate view of the important features of the universe (even though in my opinion they get the young universe part of it wrong), than those who correctly see the age of the universe but do not believe that God is at work through Jesus. Secondly, if those who hold to a young universe were persuaded to abandon that view and this were to weaken their faith in the gospel -- I would rather they not be persuaded to an old universe/old earth view at all. The gospel is the core of everything, everything else pales to it. Thirdly, I think there are more important discussions inside and outside the Christian community than the age of the universe. The gospel itself, the work of God in history through Jesus Christ, and its ramifications, are far more important than debating the age of the universe.

So why engage in this discussion at all? Here are a few thoughts:

1. God, first and foremost, has disclosed who he is and who we are through the Bible. In theological terms, this is referred to as special revelation. Special revelation gives the most detailed and comprehensive understanding of God, his activity, who we are, and how God, humanity, and all of the universe interact with God. God also discloses information about himself and his creation through the world and universe around us. Theologically this is referred to as general revelation. It's called general revelation because this is information open to all people, regardless of whether they have been exposed or not to the special revelation contained in the Bible. Both forms of revelation, when properly understood and interpreted, give an accurate picture of reality, of truth, of the way the universe is, who God is, and the relation of everything to God. Both forms of revelation, when properly understood, do not contradict each other. Rather,they complement each other in understanding the truth.

2. Special revelation, the Bible, is to be given the priority over everything else, including general revelation. However, special revelation is not given in a vacuum. Foundational is the work of the third person of the Trinity, the Holy Spirit, in convicting and convincing people of the truth contained in the special revelation. General revelation provides insights into understanding special revelation.

Consider the following passage written by King David thousands of years ago:

The heavens declare the glory of God,
and the sky above proclaims his handiwork.
(Psalm 19:1, ESV)

King David knew that the heavens were immense. He knew whenever anyone looked at the heavens above they saw it declared the glory of God. The sun, the moon, the planets, the stars, especially in the dark skies of that time, would take their breath away.

The English Standard Version (ESV) quoted above hides some interesting features of the passage. The King James Version (KJV) says:

The heavens declare the glory of God;
and the firmament sheweth his handywork.
(Psalm 91:1, KJV)

In particular, notice the word firmament used in the KJV instead of sky in the ESV.

The word for sky or firmament comes from the Hebrew vault of heaven. According to the Jewish Encyclopedia:

The Hebrews regarded the earth as a plain or a hill figured like a hemisphere, swimming on water. Over this is arched the solid vault of heaven. To this vault are fastened the lights, the stars. So slight is this elevation that birds may rise to it and fly along its expanse. (The Jewish Encyclopedia)

One way of reading the descriptions of the sky and the heavens in the Old Testament is that the sky consists of a sold arched vault. For us Christians this doesn't even enter our minds as a possibility in large part because we've grown up in a global culture where advances in science, and in particular, astronomy, aeronautics and space endeavors, have demonstrated that the sky is not a solid vault. Our collective understanding of what the Bible is saying about the sky changes accordingly. Whether or not King David, or Moses for that matter, had the opinion that the sky consisted of a solid vault is immaterial to us. In turn this gives an even greater appreciation of how that heavens declare the glory of God. The sheer size of the heavens is almost infinitely greater than the early Hebrews and possibly David and Moses and the impact of Psalm 19 is greater as a result. What we correctly observe in general revelation corrects some of our misunderstandings about special revelation. There are numerous areas where general revelation provides feedback to special revelation.

It is not a one way street where general revelation clarifies special revelation. For example, special revelation in the Bible unequivocally states that God created the heavens and the earth and all of creation is moving according to God's eternal plan towards a climax. Any interpretations of general revelation which say that the universe and all the is contained in it are brought about by impersonal, undirected events, is rejected by special revelation. There is a feedback cycle between special and general revelation, with the clear principles of special revelation taking the priority over the interpretation process. Nevertheless, general revelation does provide feedback. When general revelation is interpreted correctly, the feedback corrects our misunderstandings of special revelation that we may have when reading our Bibles.

3. Suppose for a moment, that the universe and the earth is truly old, on the order of billions of years old. Then those who correctly surmise that the universe is old through general revelation can have an unneeded intellectual impediment for embracing the Christian Faith and the gospel when they are informed that the correct Biblical view is that the earth and universe is no more than thousands of years old.

This is not an argument that the universe is billions of years old. Neither am I denying the power of the Holy Spirit to draw people to himself even with intellectual impediments. What I am arguing for is being careful not to introduce impediments to the gospel. I recognize I could be wrong that the universe is old and so that a young universe viewpoint would not a true impediment to the gospel. But are we absolutely sure that the old universe is wrong? Is there room for error, and if there is, can we be so certain in the young universe that is becomes part of the package of the gospel we present to others outside the Christian faith?

4. That the universe has a beginning in the Big Bang theories can be used to point to God. There are non-Christians who are convinced that the universe and earth are old and who are curious about Christianity. While many Christians may disagree with the Big Bang Theory (the theory that the universe came into existence in an instant some 13 to 14 billion years ago and started expanding from a small region), the theory itself does point to the universe having a beginning. Since the universe has a beginning, it is reasonable to conclude there was a "Big Bang Beginner". While that does not necessarily imply the Christian God, it certainly opens the door for the possibility. Some Christian philosophers, such as William Lane Craig, follow the example of the Apostle Paul on Mars Hill in the book of Acts in the New Testament. This is where Paul noted the objects of worship of the people of Athens. Paul saw an alter to "the unknown god" and and took that inscription to introduce to them the God of the universe. This is taking a concept from our culture and pointing to God. Dr. Craig has refined a version of the cosmological argument and presents this to university campuses around the world.

5. There are Christians who see that the universe is old and struggle with their faith thinking that holding to a young universe is required in the Christian faith. These believers need to know that belief in a young universe is not required for faith in Christ and walking in the Christian life. Just as I do not want to wound those who believe in a young universe/young earth, who would have their faith hindered in adopting an old universe viewpoint -- I do not want to see those believers who are intellectually convinced that the universe is old be forced into holding a young creation view that makes them feel that Christianity is intellectually compromised.

5. Finally, there are examples of well known and respected theologically conservative Christian theologians who hold to the possibility of an old universe and earth. Examples of other Christians who hold to at least the possibility of an old universe include:

Charles Hodge (see The Protestant Rule Of Faith, Part 2 under the section labeled Objections, number 4).
B.B. Warfield (B.B. Warfield, Wikipedia),
C.S. Lewis (C. S. Lewis, Wikipedia),
Alvin Plantinga (Alvin Plantinga, Wikipedia),
William Lane Craig (William Lane Craig's website),
Nancy Pearcey (Pearcey's review of Michael Behe's Darwin's Black Box),
Hank Hanegraaff (See the Christian Research Institute's statement on the topic.)
Tim Keller (Tim Keller at www.monergism.com),
Francis Schaeffer (Wesite dedicated to the works of Schaeffer )

So, am I starting with some popular speculations of science and then warping the Bible around those views? Perhaps it depends on who you are asking. Ken Ham of Answers in Genesis would say I am. Astrophysicists Max Tegmark of MIT and Sean Carroll of Cal Tech would say I'm not, that instead I start with a faith position from the Bible and bend science around that.

I would say I fit more in the thinking of Charles Hodge, Francis Schaeffer, Tim Keller and others on the list I mentioned who allow for an old universe. These people do not start with science and then bend the Bible to their view. Rather these people are taking the Bible as their foundation and recognizing that the facts from general revelation will not contradict what the Bible genuinely teaches. These people will carefully weigh the various theories being proffered in the scientific community, and those, in their opinion, that have strong evidence, they will use to correct possible misinterpretations they have about the Bible. Again, most every Christian engages in this activity, often without realizing it, including Ken Ham. For instance Mr. Ham does not believe the the sun revolves around the earth whenever he reads about a sunrise or sunset in the Bible. What he has done is find compelling from the scientific community that feeds back to interpreting the Bible. Specifically, Mr. Ham finds that evidence for a spherical type of earth, rotating and orbiting the sun to be very compelling, which in turn he uses to guide his interpretation of the Bible. Various theories and evidence from the scientific community is not equally compelling to all Christians. Many Christians do not find the spectrum redshift of stars and galaxies, along with the cosmic background radiation and other evidences for the Big Bang billions of years ago, to be very compelling. For those who don't find it compelling, don't budge from a young earth perspective. But for those who do find it compelling, it is worthwhile to explore the ramifications. For both camps, we need to exercise patience with each other.

There are theological questions about an old universe. This will be covered in upcoming posts.

Why Does the Universe Look So Old?

2010-06-23T00:13:00.000-04:00

Tim Challies recently posted in his blog a summary of a talk presented at the Ligonier Ministries’ annual conference on why does the universe look so old. I have a very high regard for Tim Challies and for all the people at Ligonier Ministries. Challies gave a stab at an answer by saying:

"... the universe looks old because the Creator made it whole. When he made Adam, Adam was not a fetus but a man. By our understanding this would have required time. But for God it did not. He put Adam in the garden, which was not merely seeds, but a fertile, mature garden. God creates and makes things whole. And secondly, it looks old because it bears the effects of sin, the flood, catastrophe. Creation is groaning and in its groaning it looks old and worn, giving us empirical evidence of the reality of sin."

Implicit in Challies' position is that the earth and universe is young -- on the order of thousands of years old. Challies reported the contents of the Ligonier talk which dealt strictly with theological questions. He left the scientific questions untouched. I am very sympathetic to the theological issues. I hold to biblical inerrancy, as outlined in the Chicago Statement of Biblical Inerrancy. But there is a compelling argument for an old universe following this line of evidence:

1. The universe is expanding. Everywhere astronomers look at any distance beyond our local galaxy cluster, the objects we see are moving away from us. There is a telltale indication, light that arrives in the telescopes and is analyzed by their constituent color spectrum is shifted to a "redder" color, a lower frequency. It is analogous to hearing a police or fire engine siren dropping in pitch as it moves away from us. Actually, it is not the objects themselves that are speeding away from us, it is space itself that is expanding, making those objects recede from us.

2. There is a uniform rule to describe the expansion of the universe based on the distance of the observed objects. This is known as "Hubble's Law," named after the 20th century astronomer that first published the rule. The greater the distance, the greater the rate the universe that the object we see is receding from us.

3. The natural question to ask is if we were to imagine "running the universe backwards" -- what would we see? It is the same kind of question a physicist would ask upon seeing a ball hitting the pavement. If you know the velocity and motion of the ball at impact, you can derive where the ball would have been dropped and concluded it came out of an open window of a nearby building 4 seconds prior to impact.

4. Using the known motions of the galaxies around us, plugging in the values observed at all the galaxies' rate of receding away from us, astronomers can identify a time when the entire observed universe would be lumped together at a "big bang" moment. This time is on the order of billions of years, sometime between 12 to 14 billion years ago.

5. Just because the universe is expanding and we can imagine running the expansion backwards does not necessarily mean the universe had a big bang creation moment billions of years ago. However, there is other evidence of the big bang moment some 13.75 billion years ago. I will mention two lines of evidence. This first is a microwave background radiation that bathes the universe all around us. For reasons that I will not get into here, this is consistent with a hot big bang moment billions of years ago. The second is the ratios of hydrogen and helium (along with other elements) observed in the universe. This also fits nicely with a hot big bang moment.

Tim Challies wrote that God creates and makes things whole. So God created the universe to look as if it had a beginning 13.75 billion years ago. It's not just a few things that make the universe look 13.75 billion years old, but it is the web of everything that is observed in the universe that makes it look 13.75 billion years old. While it is possible that God created the universe thousands of years ago, if God did that, why did he make it look so thoroughly consistently look 13.75 billion years old? Would God make a young universe that looked so old -- or is it an indication that God did create the universe a long time ago? I opt for the latter, because I think it is more consistent with God's character of displaying truth and not being deceptive.

Faith and Parasailing

2009-11-09T00:01:00.004-05:00

How do you like to go up in a swing,
Up in the air so blue?
Oh, I do think it the pleasantest thing
Ever a child can do!
(The Swing, Robert Louis Stevenson)

Last month my wife and I were in Puerto Vallarta, Mexico. In the back of my mind I thought it might be fun to parasail. I've seen people parasail in Florida, saw videos of people doing it, it looked like the pleasantest thing that ever a guy could do! But would I actually do it? It could be expensive. Perhaps it was dangerous.

The moment of decision came one morning as we were relaxing on the beach. I short Mexican guy (who called himself "Shimp") stood on the beach near us flying a small parachute kite indicating he was selling parasailing rides. I then pondered whether or not to do it. Lots of thoughts raced through my mind. Was it too expensive? No -- I asked Shimp and he quoted a price that was a lot lower than I expected. The weather was nice, no storm, no winds, no lightning to fry me while up in the air. The parachute looked big. The boat that would pull me liked tiny -- but the engine looked big. Wait, I'm overweight, is the engine big enough? I looked again, yes maybe the engine was big enough. This was going to be a beach takeoff and landing. Could they do it? I saw Shrimp's crew pull someone else in a parachute -- but wait, did I? I saw the parasailing the previous day from my hotel balcony and I don't know if these were the same people. Could I do it? Land on the beach. I gulped and decided I could.

As I took that step off the beach, I thought of Kierkegaard's "leap of faith." In many ways I had put my life into the hands and equipment of a guy I knew only for only 10 minutes, a crew I never meet before, a boat and equipment I wasn't sure I'd seen do this before.

Was I warranted to put my trust in these people and their equipment? Considering the risk of my life and limb, was I justified in putting my faith in them?

Faith in the Christian life is often modeled in the way I approached parasailing. I look at the world around me. I have some basic beliefs about this world. I look at the possibility of placing my faith in Christ. I marshal the evidence, reason it out and then make my leap of faith. Is that how it works? Am I warranted in developing beliefs about Christ? Am I justified to do so?

The model I used for faith in parasailing does not fit with what actually happens in a Christian's life when she turns to Christ with faith. I need to explore a few more issues to narrow in on a model that better describes what happens when a Christian places her faith in Christ.

Cold Pizza and Basic Beliefs

2009-11-02T00:01:00.002-05:00

In the previous post on faith I wrote that there were some inadequacies with what I wrote. What was incomplete? I'll get to that, but first I want to explore the idea of basic beliefs that Alvin Plantinga writes about in various books.

Imagine that I am walking on a beach in Florida and musing over some thoughts.

Okay, I don't normally stroll on the beach thinking the thought 1+2=3, but these thoughts in this contrived example illustrate the concept of basic beliefs. Normally, basic beliefs fall into the following categories:

A priori -- self evident beliefs that are always true. The basic facts of arithmetic, such as 1+2=3, 5x4=20, or modus ponens (if a then b, so given a is true, then b must be true).

Senses -- belief of things derived from the senses. When I am walking on the beach, I sense I am walking in water, on sand and feel the warmth of the Sun shining on me.

Memory -- belief in things or events that I recall from my memory. Let's say I ate some left over cold greasy pizza slices for breakfast that morning. My memory presents the events to me of what I did and I simply believe it.

Internal -- Belief in the things I feel about internally about myself. If my stomach is out of sorts I feel sick.

Basic beliefs are not a fixed set of beliefs. The self evident beliefs can change and grow in time. When I was 5 years old, I knew 1+2=3, but 4x5=20 was not a basic belief yet. As I grew older, my set of self evident beliefs grew. There is much more to say about basic beliefs. For instance, when I look out the front window of my house I see a tree. That is a basic belief based on what my sight presents me. How I grew as an infant to learning the properties of treeness from my parents and others can be an interesting discussion that I will not get into this series.

The next post will explore using basic beliefs to build other beliefs.

Faith, a Traditional but Inadequate View

2009-10-28T00:01:00.004-04:00

My wife and I vacationed the previous two weeks of October. This was a time of physical relaxation and a time I finally read Alvin Plantinga's Warranted Christian Belief. This entry will start with some basic traditional thoughts about faith I posted sometime ago. It follows some thoughts of the late John Murray of Westminster Seminary in Philadelphia. In upcoming entries I'll get to some interesting insights that Dr. Plantinga discussed in his book. There is an interesting distinction between the typical traditional discussion of faith that Dr. Murray presents and the insight Plantinga presents (or to be fair and probably more accurate, my take on what Dr. Murray said). Plantinga has thought deeply on what justification or warrant a Christian has in her beliefs. His treatment is not novel, it has a firm foundation in the history of the Christian Church, such as Augustine, Aquinas and Jonathan Edwards -- but I think aspects of the enlightenment philosophy of the past few hundred years has subtly influenced my view on faith.

If you hang around religious people, you'll sooner or later come across the word faith. What exactly is faith? This entry will introduce the concept of faith used in the Christian faith. Faith is defined in various ways¹. This discussion will use the term faith as defined in historical Protestant Christianity that has its roots in the German, Swiss, English and Scottish Reformation. Originally when I wrote this article I said, faith means being satisfied to the reality of something because of certain reasons. If we use the word faith with respect to a certain event, we mean we believe that the event has occurred. If we use faith with respect to an object, we are saying we believe that the object is trustworthy for the purpose we have in view. I now think this definition of faith is inadequate in some ways. I will continue in this vein for the rest of this post and point out some issues in following entires.

This judgment about the reality of something may be the result of deliberate, careful and conscious reasoning. It may also be the result of very quick reasoning that appears spontaneous and intuitive. This judgment may also come from a very long process where we are unable to reconstruct the series of steps that caused us to arrive at that judgment. The judgment can be based on good, sufficient evidence, or be based on poor and unjustified evidence.

Another characteristic of faith is that it is compelling. Faith is forced consent². The evidence is judged by the mind to be so sufficient that belief or faith is the inevitable outcome. We may will to the contrary, have a desire to the contrary, even an overwhelming interest to the contrary, but it cannot make us believe to the opposite of our judgment with respect to the evidence.

Faith, specific to the Christian faith, has by its nature, three elements that compose it. These elements are not a time ordered sequence, but all are present in what is called saving faith.

Notita

Knowledge -- this is the cognitive foundation. Faith has as its base the knowledge of the content of the Christian faith. It understands that the content of this knowledge is propositional truth about the Christian faith. Elements of this propositional truth include: the perfection and holiness of God, the fallen and rebellious nature of every living human, the just results of the fallen and rebellious nature is eternal judgment and death, and that Jesus' death paid for the punitive eternal judgment for all who depend on Jesus.

Assensus

Assent -- this is (a) the intellectual or cognitive conviction that all the knowledge that one has acquired about Christ is indeed factually true, and (b) that this applies exactly to one's spiritual needs.

Intellectual knowledge and assent to the propositions of truth is not sufficient for saving faith.

Fiducia

Trust -- this consists of entrustment to Christ. "In faith there is the engagement of person to person in the inner movement of the whole man to receive and rest upon Christ alone for salvation. It means the abandonment of confidence in our own or any human resources in a totality act of self-commitment to Christ."³

Roman Catholic theologians have historically defined saving faith as notitia (knowledge) and assensus (assent). The Protestant Reformers put an emphasis on faith as fiducia in opposition to Rome, which taught that faith was assent.

Perhaps an example will help illustrate the difference with these three aspects. When my wife and I had small children, we had a difficult time leaving our children with baby-sitters (partly because of some terrible experiences people we knew had with some baby-sitters). When we got to know some mature teenage girls, we intellectually got to know their character (notitia). When we knew them well enough, we knew that they would be good baby-sitters and that they would fit in the needs of our family when we needed to go someplace without our children. However, we were still reluctant to leave our children with the potential baby-sitters. Even though we intellectually knew the baby-sitter and agreed in our minds that the baby-sitter could do the job and provide the needed service, we could not entrust our very precious children to her. Finally, there came a time when we felt we could entrust our children to the baby-sitter. This is when intellectual assent passed into entrustment (fiducia) with our children.

Even though this discussion divides faith into three parts, these parts are so intermingled together that we really cannot conceive of saving faith without any one of these components. Neither is saving faith a process of walking through one of the parts chronologically into another. All of these parts work together. Murray writes:

"There is an interpermeation of these various ingredients. Even in assent there is incipient trust. And in trust there is the full assent to the veracity of God's promise and to the word of Christ. But what we need to appreciate in connection with these elements is that faith, however simple it is as an act of trust, is a complex act and that diverse factors enter into its constitution. The trust that the infant may be said to be simple but, after all, it is complex, and we soon find out if we try to substitute for the mother."⁴

Finally, there is diversity in the individual temperament with respect to faith. For some the intellectual aspect is more predominant, in others feeling, in others will. So as various people come to initial faith, some will see the outstanding feature in their act of faith as the intellectual understanding where they came to see the light of understanding in their reasoning. Another person may have had an emotional crisis that is prominent in their coming to faith. In each of these people, no matter what the temperament, these "coalesce to make faith the proper exercise of intelligent, confident, loving trust."⁵

Footnotes:

1 In this discussion I am summarizing insights of John Murray, in the chapter, "Faith", in Collected Writings of John Murray, Vol 2: Systematic Theology.

2 Murray, p. 237

3 Murray, p. 258

4 Murray, p. 260

5 Murray, p. 261

Evangelical Confessions

2009-08-20T00:01:00.003-04:00

This is a first draft of Creeds, Confessions, and Catechisms used by Protestant Evangelical churches over the centuries. Not all Evangelical churches use these documents, but many have found these useful in outlining what they believe the Bible is teaching. Some denominations have moved away from officially endorsing their historic confessions, while others have kept to these confessions.

Early Confessions and Creeds

The Apostle's Creed

The Nicene Creed
- The Nicene Creed Text
- Wikipedia Article on the Nicene Creed

The Athanasian Creed
- The Athanasian Creed Text
- Wikipedia article on the Athanasian Creed

The Definition of Chalcedon
- The Definition of Chalcedon Text
- Wikipedia article on Chalcedon

The Second Council of Constantinople

The Canons of Orange (529 AD)

Lutheran Confessions

The Book of Concord

Wikipedia article on the Book of Concord

An introduction to the Book of Concord

Reformed Confessions

Continental Europe

Three Forms of Unity
- The Heidelberg Catechism
  - The Heidelberg Catechism Text
  - Background of the Heidelberg Catechism
- The Belgic Confession
  - Belgic Confession Text
  - Background of the Belgic Confession
- Canons of Dort

The First Helvetic Confession

The Second Helvetic Confession

The French Confession of Faith. A.D. 1559

Presbyterian

The official documents of historical Presbyterianism are the Westminster Confession of Faith, the Westminster Larger Catechism, and the Westminster Shorter Catechism. The Scots Confession was the original confession of the Church of Scotland (Presbyterian) but was superseded by the Westminster Confession and Catechisms. The Children's Catechism does not have official standing but is a useful document to teach young children the basics of the faith.

Scots Confession

Westminster Confession of Faith

Westminster Shorter Catechism
- The Westminster Shorter Catechism Text
- The Westminster Shorter Catechism with Scripture Annotation

The Westminster Larger Catechism

Catechism for Young Children

Modern Statements

The Chicago Statement of Biblical Inerrancy

Chicago Statement on Biblical Hermeneutics

Hazards of Being a Software Engineer

2009-07-27T00:01:00.000-04:00

I know computer languages C++, C, Java, Fortran, Lisp, Perl, and JavaScript exceptionally well. I know databases, currently most familiar with Oracle programming and DBA management, but am also comfortable with PostgreSQL and MySQL. I know various flavors of UNIX operating systems, especially Linux, IBM AIX, Sun Solaris. I am on call 24 hours a day, 7 days a week, 365.4 days a year (got to get that leap day in) to fix our on-line systems when the first levels of support and trouble shooting cannot deal with the problem.

But I do not know Microsoft Windows, Microsoft Vista, the machinations of Microsoft Word. I am passable on Blogger, but I don't do nearly a quarter of the features others in the household do. However, I am considered an expert, and when I shrug my shoulders at a problem, being perplexed at it, I get the perception that the others think I am lazy and just want to blow them off.

This other side of the software world, Microsoft, Windows, Vista, Word, Blogger, Facebook -- I find mystifying. It took years of long days of working with the technology I am an expert in to gain that expertise. I haven't had the time -- and frankly the inclination to spend inordinate amounts of time -- to learn this other world.

So, if you have a UNIX problem, trouble with C++ or Java -- I'm your guy to help you through that world.

Windows? Word? Google Blogger? Well, I might be able to give you some help, but you might know more than I do on those subjects.

Happy Aphelion!

2009-07-04T00:01:00.000-04:00

July 4th, at 10am Eastern Daylight Time in the USA, the earth will be at its furthest point away from the sun as it orbits around the sun. The technical term for this position of the earth is aphelion. In six months the earth will be at its closest point to the sun in its orbit -- and that is called perihelion. The picture on the left shows the difference in size the sun appears to us on earth at perihelion (left side of the picture) and aphelion (right side of the picture). Tom Lindholtz, an Internet friend, humorously suggested as we reach and pass the aphelion:

If you REALLY want a thrill, hold your hands up as we go over.

Aseity

2009-07-03T00:01:00.002-04:00

Geek word for today: Aseity -- The word comes from the Latin, "a" from, and "ity" self. It is the description of an entity being underived from anything else. This is in contrast to being derived from other things. In Christian theology, only God has the attribute of aseity.

"Let There Be Light"

2009-06-28T00:01:00.002-04:00

And God said, “Let there be light,” and there was light.

This is a picture of the entire sky taken of microwave light at a very specific frequency. It is an absolutely amazing picture. It is a picture of the universe at an extremely young age, at less than 0.003% of its present age. The universe is estimated to be 13,740,000,000 years old, and this recorded light comes from the universe when it is 379,000 years old. Why 379,000 years old? This is the time the universe cooled in its expansion so that light was not trapped anymore in the hot plasma and gas. Prior to that the universe was a hot fog of protons and electrons, among other particles, which was opaque to light. At the fog cooled, the electrons attached to the protons, forming hydrogen atoms which allowed the light to be emitted from the fog. This happened at the same period of time all over the universe and we see first emission of light from that universe that was emitted over 13 billion years ago. Because the actual time/space has expanded since that time, we see the bright white light "red-shifted" down to the microwave range. What was thousands of degrees 13 billion years ago, through this red shift, is cooled down to just a few degrees above absolute zero, the theoretical coldest temperature possible. (Technically absolute zero is not possible, but it is possible to get very close to it.)

What's so exciting about this? It is evidence the universe had a beginning. It fits with the Christian world view that God created the universe.

Fuzzball

2009-06-27T00:01:00.000-04:00

Geek work for today: Fuzzball -- Einstein's General Relativity predicted black holes, areas in space where huge things (like a huge dying star) collapses on itself, forming a region where nothing can escape, not even light. The problem is that the stuff squeezes within this region to a zero sized point. String Theory, on the other hand, predicts a fuzzball of strings in the black hole where nothing can escape.

Eight Is Enough (for this week)

2009-06-25T21:58:00.002-04:00

Born this week, my second grandchild. Pictured is the moment my first grandchild saw his new brother. This makes our household eight. It's lots of fun for us (the grandparents). For my daughter and son-in-law, I'm sure its great joy but it is also an exercise in sleep deprivation. I remember those days.

While I Was Away

2009-06-09T07:31:00.004-04:00

I have not been posting to this blog lately. Much of it is due to the fullness of life, enjoying being a grandfather, but also the pressing work of a greatly underestimated software project.

Also while I was away from blogging I was working in my role as an elder in helping a family in crisis. I was bewildered when I initially stepped in, but soon I started to see, only by the grace of God, the broad outlines of the problem and issues. At times I have been flummoxed at how evil can be so insidious, beguiling, and deep -- not from inside that family, but coming from outside of it.

By God's grace I have seen things turn around. There is significant healing but there is much undone. Evil explosions like this are never just contained to a small area. I grieve over those I could not help, where I don't see healing coming yet.

I have given considerable time, attention, and prayer to this -- and gladly so and will continue to do so very gladly. I am honored that these dear people would let me into their lives and honored that God lets me serve in this way.

The Irony of Good Friday

2009-04-10T00:01:00.002-04:00

This day remembers the worst atrocity in history, the puppet trial and killing of God himself. How can that be good? But as I think how awful, another irony is that I am a pivotal cause of the killing just as much as the Romans nailing Jesus on the cross or the religious authorities arranging the sham trial. But just as I am the cause, I am a beneficiary of the killing. Good Friday, Bad Friday, Good Friday.

On Being an Elder

2009-04-07T07:44:00.004-04:00

It is a great honor to serve my church as an elder. I feel very unworthy of the calling. I am a very fallen man. As I walk further in my life I sense more that I miss the mark of who I should be. This is no pious platitude, but a deep seated gut realization of the untamed jungle of me inner being. As I see this within me I realize more of my need to cling to Jesus, his death pays for and covers the deep insurrection in my heart, my rebellion that I struggle to subdue and at times relish. His perfect life covers my imperfection. Without Jesus, being an elder would be a hopeless chore, a joyless duty that I can never begin to fulfill. Jesus, who is the reason for my life, is also the reason of my being an elder. I am nothing without Jesus.

Writer's Block

2009-04-06T22:22:00.002-04:00

I haven't posted for a while. Partly this is due to all the other activities, preparing personal income tax, bookkeeping in preparing for corporate taxes, a very tight project, and other activities. I've also discovered the waste of time on Facebook. Facebook is easy to use, and easy to waste time on. There are oodles of stupid little applications, quizzes that mean nothing. Not all of it is a waste. Connecting with friends and family can be very useful. But it has drained what little creativity I have these days. But I'll get back. There are several topics that I've been thinking of that are interesting (to me).

My Nobel Prize Acceptance Speech, Take 2

2009-02-11T00:01:00.114-05:00

In the previous blog entry I wrote about an acceptance speech that Earl Flask gives for the Nobel Prize in Literature in another part of the infinite multiverse. It was a whimsical look at what would happen if the universe we observed was just a piece of an impersonal, chaotic, infinite multiverse.

One of my favorite science fiction writers is Arthur C. Clark. He had three interesting laws about prediction:

1. When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.

2. The only way of discovering the limits of the possible is to venture a little way past them into the impossible.

3. Any sufficiently advanced technology is indistinguishable from magic.

Let add the observation that these laws work for a infinite multiverse. We don't even have to have an infinite multiverse. In the immortal words of many calculus teachers, given a sufficiently large multiverse, these things, if not absolutely impossible, would happen somewhere in the multiverse. Michael Shermer has reparaphrased Clark's last law as: "Any sufficiently advanced ETI is indistinguishable from God." where an ETI is an extraterrestrial intelligence. In a sufficiently large multiverse, there are corners where the bizarre happens, and that can be indistinguishable from the activity of God. Here is another variation of Earl Flask giving a Nobel Prize acceptance speech, this time it is not for Literature, but the even more prestigious Peace Prize.

Your Majesty, members of the Nobel Committee, gentle women and gentle men. I cannot tell you how surprised and humbled I was when I received the phone call from the Nobel Committee that I had won the Nobel Prize for peace. But I also, like you all, am surprised by the amazing turn of events in the last few years. I remember the phone call from the Iranian President, President Mahmoud Ahmadinejad asking me to be the opening speaker to the first General Assembly Meeting of the Iranian Presbyterian Church and that the day before the Iranian Parliament had adopted the Westminster Confession and Catechisms as the official state religion. All of this, from reading my blog, Metaschema. But that was just the beginning. That same week I received calls from the Royal Family in Saudi Arabia, the Swedish Parliament, the Norwegian Parliament, all informing me of their adoption of the Westminster Confession. All wanted me to speak to their newly formed General Assemblies. All from reading my humble blog, Metaschema. These remarkable events continued. A year ago today, I got phone calls from three people, emissaries from Osama bin Laden, the Pope of the Roman Catholic Church, and the Patriarchs of the Orthodox Church, each telling their conversion or adoption of the principles of the Westminster Confession of Faith. From all these surprising events, it is no wonder that peace broke out in the world.

Because these series of events culminating in this award are so unlikely, especially considering abysmal words that I wrote, I am now convinced more than ever of the hand of God in governing human affairs. This thought humbles me. With this I rededicate my life to the betterment of humankind and the glory of God.

This award is giving me great courage to continue my work. I will, with God's help, rise to the occasion. Again, thank you all for giving me this award.

This speech got a 30 minute standing ovation in this particular part of the infinite multiverse (or sufficiently large multiverse).

Unlikely, absurd? Absolutely. Is it impossible? Perhaps as unlikely as one chance in 10^{100,000,000,000,000,000,000} (you add the zeros in the exponent to express the unlikeliness). But given a sufficiently large multiverse, it would happen. This raises the question -- how can we tell what is the cause of anything in an infinite multiverse? Do remarkable or unique events mean anything at all? If Earl is deluded to the cause of the remarkable course of history in his part of the multiverse, how do we know we are not deluded in our thoughts about the universe around us? The concept of an infinite multiverse, or a sufficiently large multiverse, has the seeds of its own defeat in the universe of ideas.

My Nobel Prize Acceptance Speech

2009-02-10T00:01:00.005-05:00

This didn't happen in this universe. But, if there are an infinite number of universes, in other words, an infinite multiverse, then no matter how unlikely this event is, as long as it is absolutely not impossible, then in some universe far, far, away, Earl Flask gets up to deliver the following acceptance speech for his Nobel Prize in literature.

Your Majesty, members of the Nobel Committee, gentle ladies and gentlemen. I cannot tell you how surprised I was when I received the phone call from the Nobel Committee that I had won the Nobel Prize for literature. I thought there was a big mistake, that the committee confused me with someone else, because I had not published anything except for a few technical articles in some obscure software conferences. But when the committee member told of my articles in my blog, MetaSchema, and the Adventures of Erlenmeyer Flask, I was speechless. Never in my mind did I think I was writing anything worthwhile for humanity to read. These were just a few amusing things I wrote to keep myself entertained.

Because this award is so unlikely that I would ever get it, especially considering what I wrote, I am now convinced we live in an obscure corner of a vast multiverse. I can think of no other conceivable reason to get this great award. This thought humbles me. Mediocrity can truimph in this obscure corner of the multiverse. There is no rhyme or reason to what happens here. As a result I am walking away from my Calvinism and embracing the random meaningless of it all.

This award is giving me the courage to continue to write meaningless and pointless prose. I liked my previous life better, but what the heck. I'll take the award money and run. Besides, my sitemeter is skyrocketing, I'm number one in the New York Times Best Seller List with my brand new book, "MetaSchema and Other Worthless Insights", and I am getting multi-million dollar book contracts. Who would have thought this could happen to me?

Again, thank you all for giving me this award.

...and this speech got a 20 minute standing ovation in this particular part of the infinite multiverse.

Sperm Whales and Boltzmann Brains

2009-02-06T00:01:00.005-05:00

It is important to note that suddenly, and against all probability, a Sperm Whale had been called into existence, several miles above the surface of an alien planet and since this is not a naturally tenable position for a whale, this innocent creature had very little time to come to terms with its identity. This is what it thought, as it fell:

Ahhh! Woooh! What's happening? Who am I? Why am I here? What's my purpose in life? What do I mean by who am I? Okay okay, calm down calm down get a grip now. Ooh, this is an interesting sensation. What is it? Its a sort of tingling in my... well I suppose I better start finding names for things. Lets call it a... tail! Yeah! Tail! And hey, what's this roaring sound, whooshing past what I'm suddenly gonna call my head? Wind! Is that a good name? It'll do. Yeah, this is really exciting. I'm dizzy with anticipation! Or is it the wind? There's an awful lot of that now isn't it? And what's this thing coming toward me very fast? So big and flat and round, it needs a big wide sounding name like 'Ow', 'Ownge', 'Round', 'Ground'! That's it! Ground! Ha! I wonder if it'll be friends with me? Hello Ground!
[splat!] -- The Hitchhiker's Guide to the Galaxy

This is one of my favorite scenes from the Hitchhiker's Guide to the Galaxy (you can watch the video clip here). The whale suddenly appears our of nothing but thin air when the spaceship, the Heart of Gold, activated its main propulsion engine, the Infinite Improbability Drive. Strange things happened when that drive was activated -- very improbable things -- like a intelligent whale contemplating its brief life.

Funny fiction. Of course such things would never happen, only in the mind of Douglas Adams. But there is an interesting twist. Some astrophysicists speculate our universe is one of or part of an infinite number of universes -- or an infinite multiverse. While a spontaneously generated intellectual sperm whale is next to impossible to happen in our universe, in a infinite multiverse, whatever is highly improbable but strictly not absolutely impossible-- happens, somewhere in the infinite multiverse -- an infinite number of times.

In the infinite span of the multiverse, there will be an infinite number of observers. Let me step back and explore what is meant in an infinite number of universes there are an infinite number of observers. Infinity comes in many varieties. Some infinities in some sense is greater than other infinities. Establishing a mapping from one infinite set to another, a rule to map each element in one infinite set to another uniquely in the other infinite set, is a way of determining whether one infinite set is greater than the other, or equal. In a strict sense we are not counting the infinite sets. We are determining ways to pair one element from one set to another.

One of the things to ask is what kinds of observers exist in all the multiverses? We know that one kind exists -- humans. If we take the path of evolutionary and cosmological big bang, it appears it took 13.7 billion years with current span of 92 billion light years across (see How Big is the Universe) -- this seems to be a rather inefficient and even unlikely process to produce observers. At the risk of quoting out of context, Sean Carroll of Cal Tech writes,

Cosmologists have contemplated the idea of baby universes for many years, but we do not understand the birthing process. If quantum fluctuations could create new universes, they could also create many other things—for example, an entire galaxy. For a scenario like ours to explain the universe we see, it has to predict that most galaxies arise in the aftermath of big bang–like events and not as lonely fluctuations in an otherwise empty universe. If not, our universe would seem highly unnatural. (Sean M. Carroll, Does Time Run Backward in Other Universes?, Scientific American on the Web, May 2008, p. 5)

While Dr. Carroll is not saying that other kinds of universes are more likely than ours, his statement does seem to say that given our current information (or lack thereof), our universe is more improbable than many other kinds of universes. Considering entropy alone, our universe came into existence in an extremely low entropy state and an extremely tight configuration to ignite inflation, the engine that drove the incredibly huge expansion that took moments, inflating our universe in size faster than the speed of light.

This brings us to the concept of the Boltzmann Brain. Our universe, which has at least the billions of human observers, is huge and highly unlikely to arise out of a random fluctuation, even the kind that Dr. Carroll speculates arising from a near zero entropy de Sitter Space. Instead, much smaller configurations that does not require such small entropies would seem to be much more typical. Quantum fluctuations could give rise to a single observer organism, such a single brain -- a brain with false memories that would exist for moments, like the sperm whale in the Hitchhikers' Guide. These brains require much less entropy to come into existence from the quantum fluctuations. It means over the vast span of the infinite multiverse, these single brains would be more likely because of their modest entropy requirements than the universe that spans over 90 billion light years across that requires the passage of nearly 14 billion years to produce observers to note and contemplate the universe.

Let me make two observations (these observations are courtesy of Dr. Jeff Zweerink in a podcast I listened to recently):

1. Boltzmann brains would most likely observe a chaotic universe. A Boltzmann brain that has false images and memories that makes it consistently think it is in a large universe with regular laws would be a very unusual brain.

2. A universe that is huge, stable, and gives rise to many observers in the course of billions of years is extremely unlikely compared to the number of probable Boltzmann brains spanning the vast multiverse.

If we observe that we live in a huge, old universe with many observers, then given these two observations it is unlikely that we live in a spontaneously generating multiverse. This is because it is much more likely for each of us as an observer to be an isolated Boltzmann brain seeing the universe chaotically, which we do not observe.

For a rebuttal to this argument, see this Discovery Magazine blog article.

A Favorite Defintion

2009-01-30T15:23:00.002-05:00

recursion: see recursion.

Interpreting Matthew 24

2009-01-09T08:26:00.004-05:00

Jesus left the temple and was going away, when his disciples came to point out to him the buildings of the temple. But he answered them, “You see all these, do you not? Truly, I say to you, there will not be left here one stone upon another that will not be thrown down.” (Matthew 24:1, ESV)

Matthew chapter 24 is an interesting chapter. Jesus says some very interesting things that different groups interpret in basically four different ways:

Futurist: All Jesus describes in Matthew 24 happens in the future.
Preterist: All Jesus describes in Matthew 24 happened in the past, circa 70 AD.
Failed Preterist: Jesus and the Gospel authors meant the words to fit within the disciples' generation, but one or more of the prophecy failed.
Eclectic (Amillennialism): Some of what Jesus said happened in 70 AD. Some of it continues to happen. Some of it will happen with Jesus' second coming, which has not occurred yet.

Each of these views have issues. I am assuming that Matthew was written prior to 70 AD, although I will note some things if it was written after 70 AD. The plain reading of the passage seems to suggest the following to the first audience reading/hearing the passage.

The events were going to start within the normal life span of the disciples (v. 34).
The gospel will be preached to the whole world before the end happens (v. 14).
There will be birth pangs that will signal that the end is coming, but the end is not here yet (v. 6-7). These birth pangs include:
- False Christs.
- Wars.
- Famine.
- Earthquakes.
Terrible tribulation accompanying the abomination of desolation. Those who are alert will be able to see the signs and flee (v. 15-20).
The comming of Christ will be sudden and visible to all (v. 27). It will have the following properties:
- All nations and tribes will see (v. 30).
- It will be unmistakable, accompanied by loud trumpet, great glory (v. 31).
- All the elect is seperated from the non-elect and gathered at this time (v. 31).
- Accompanied by abrupt changes in the heavens (v. 29).
No one knows the time of Christ's return (v. 36), and it seems this will be the case until just before Christ's return.
The events seem to all take place in quick succession (v. 29).
All that is described will absolutely occur (v. 35).

None of the various views (Futurist, Preterist, Failed Preterist, Eclectic) fits the list of observations perfectly. I'll walk through each of these and discuss these observations. I'll look at the strengths and weaknesses of each view.

Futurist

There are two types of Futurists: Historical Premillennialists and Dispensational Premillennialists. Dispensational by far is the most popular view today, although it is a a relatively young view. Historical Premillennialism had supporters for it dating almost all the way back to the "apostolic fathers". Historical does not have the concept of the rapture of the church.

Strengths -- The strengths include:

Recognizes the gospel goes to the entire world (2).
Recognizes the birth pang aspects of many of the signs (3).
Recognizes the terrible tribulation accompanying the abomination of desolation (4).
Recognizes the coming of Christ will be visible to all (part of 5).
Recognizes the events take place in quick succession, in the span of less than a decade.
Commitment to these prophecies being true and will come to pass.

Weaknesses -- The problems with this view are:

The events happen in the distant future for the disciples, violating (1). None of that generation will be alive for these events. There has to be some creative exegesis to get around this issue.
For Dispensational Premillennialists, there will be a seven year warning when Christ's second coming will occur, violating (6). When the secret rapture of Christ happens, there will be a seven year count down to when Christ will come again in visible glory. Historical Premillennialists do not have this problem, because there is no secret Rapture for them.

Preterist

Preterists' greatest strengths are their serious commitment to the prophecy being fulfilled within the same generation of the disciples.

Strengths -- The Preterists have a number of strengths:

The events were going to complete by 70 AD, well within the normal life span of the disciples (1).
The recognition of birth pangs (3). Preterists recognize that there would be wars and rumors of wars, earthquakes and famine that would point to the future return of Christ, but would not mean it would happen immediately. That said, the birth pangs and relatively short, historically speaking, only lasting a few decades from when Christ made his prophetic statements.
Recognizing the terrible tribulation accompanying the abomination of desolation (4).
The coming of Christ is sudden -- but not visible to all (5).
No one could predict when Christ return until the Roman army blockaded Jerusalem (6).
The events take place in quick succession (7).
The Preterist view asserts that all the Christ predicted did come true (8).

Weaknesses -- Preterism has a couple of major weaknesses:

The gospel was not close to being preached to the whole world in 70 AD (2). The gospel did not reach the northen european tribes, extend throught Africa, throughout Asia, the Americas, and Australia. Preterists claim that peoples from all the known world were present at Pentecost and so that was the intent of the preaching prophecy.
The coming of Christ was not visible to all in the world in 70 AD (5). R.C. Sproul and Gary DeMar claim that Christ made the appearence that was talked about in Matthew 24. However, the appearance was not accompanied by great glory for all the world to see. It was not loud (with trumpet call). Sproul talks about how Josephus writes that there were signs in the clouds around Jerusalem at the destruction of the temple. Even if Josephus' signs in the sky are to be taken as the manifestation of Christ coming in the clouds, it was not visible outside the environs of Jerusalem. The rest of the world did not take note of it that day.

Failed Preterist

The major weakness of the Failed Preterist view is their low view of scripture. Usually this view is the position of radical skeptics to the Christian faith.

Strengths -- The primary strengths of this view is that it holds that Christ and the very early Christians believed in all that Christ is said to have predicted in Matthew 24.

Weaknesses -- The major weakness of this view is that while Jesus might have gotten the destruction of the temple right, he did not get his second coming correct. Thus people holding this view believe that Jesus failed in his prophecy.

Eclectic (Amillennialism)

Eclecticism is almost a middle ground between Futurism and Preterism. It picks the strengths of Futurism and Preterism while trying to avoid the major weaknesses of either.

Strengths -- The strengths of this view include:

This recognizes Matthew 24 predicts the destruction of the temple that happened in 70 AD. The destruction occurred well within the normal lifespan of the disciples (1).
This recognizes that the gospel will be preached to the whole world before Christ returns (2).
Recognizes there will be birth pangs that will signal that the end is coming (3). For the Eclectic view, the birth pangs are recognized as a long process, spanning millennia. They argue that these pangs remind us that we are to be ready at all times.
Recognizes there will be a terrible tribulation accompanying the abomination of desolation (4). With the Preterist, the Eclectic view recognizes that Jesus was referring to destruction of the temple in Matthew 24.
Recognizes that the coming of Christ will be sudden and visible to all (5).
Recognizes that no one will know the time of Christ's return (6).
Affirms that all that is described will absolutely occur (8).

Weaknesses -- The weaknesses of this view are:

The biggest weakness of this view is that there is a very long interval from the start of the great tribulation to the time that Christ returns (violating 7).

As I evaluate the various perspectives, I immediately rule out Failed Preterism because I believe that all of Christ's words will happen. Secondly, I rule out Futurism because it is very obvious to me that Jesus was referring to the destruction of the temple in 70 AD in Matthew.

I am left with Preterism and Eclectism. I greatly respect both views. Between these two, I think Eclectism is the stronger position because Preterism fails to see how that the appearance of Christ in Matthew 24 is the second coming of Christ that everyone will see. Christ's appearance is described in such strong terms, in Matthew 24, and elsewhere, that I cannot see any real corresponence to the events of 70 AD to Christ's appearance as described in the passage. Further, I do not see the advance of the gospel to all the world in Preterism that is told in Matthew 24.

So I am left with Eclictisim. But what about its major weakness, the huge discontinuity between the tribulation of the destruction of the temple and the second coming of Christ? I admit this is not easily dismissed, but compared to the problems of Preterism with Matthew 24, this is not nearly as huge of a problem in my mind. Breifly, I see this as an aspect of "telescoping" in biblical prophecy, where one aspect of prophecy is fulfilled but the other is fulfilled later. Many of the Old Testament prophecies of the Messiah show this. The Messiah was described in some ways as a suffering messiah, but also in other ways a victorious ruler. Christ's first coming showed more strongly the suffering nature of the prophecies. Christ's second coming will show the victorious aspects of the prophecies. Think of it as looking across a valley to a moutain range. As you survey the vista all the mountains look like one chain. However, if you drive to the range you discover what looked like one range is actually a series of mountain ranges, one after another, seperated by many miles. A similar thing is going on with the prophecy of Matthew 24. From the initial perspective of the disciples, the destruction of the temple and the end of the world looked one and the same to them. A careful examination of Jesus' words actually show these are seperate concepts. Our experience of two thousand intervening years show the expansion of this prophecy.

This is my initial look at Matthew 24. It makes the most sense to me. As I have discussed this topic with others I've seen people are place different weights on the strengths and weaknesses I've listed above. There is much more analysis that needs to be done than what I spent in this brief blog entry.

Millennial Charts

2009-01-04T00:43:00.002-05:00

Then I saw an angel coming down from heaven, holding in his hand the key to the bottomless pit and a great chain. And he seized the dragon, that ancient serpent, who is the devil and Satan, and bound him for a thousand years, and threw him into the pit, and shut it and sealed it over him, so that he might not deceive the nations any longer, until the thousand years were ended. After that he must be released for a little while. (Revelation 20:1-3, ESV)

Revelation 20 speaks of a one thousand year period. There are several ways to classify major view of Revelation. One of the ways is identifying when the millennium of Revelation 20 occurs. I taught a series on Revelation and I put together these charts which outline the various views of the Millennium. I would love feedback on these, particularly where I am getting the information wrong.

Postmillennialism. The great tribulation occurs soon after Christ's ascension into heaven. The hermeneutic is the nearness of the events. The tribulation gives way to a period of God's kingdom advancing on earth. This period is known at the millennium, which may or may not last a literal 1000 years. Here is where I can use some help from my Postmillennial friends. It seems that most Postmillennialists today are partial preterists, believing that the fulfillment of the bulk of Revelation occurred around 70 AD with the fall of Jerusalem with a "visitation" of Christ at that time in judgement -- not to be confused with the actual second coming of Christ, which is yet to happen. At the close of the millennium, some Postmillennialists believe there will be a great falling away, others do not. Christ's second coming occurs at the end of the millennium, upon which there is a general resurrection, the judgment, and then the eternal kingdom.

Amillennialism. Amillennialism is really a form of Postmillennialism. The millennial age (where 1000 is symbolic of the long sovereign reign of Christ but not a literal 1000 years) begins with Christ's first advent where he binds the strong man Satan and plunders his house. With Satan being bound, gospel goes to all nations, tribes, and peoples. During the same time the tribulation, the persecution of the church, is going on. The tribulation is spoken of as a short time (time, times, and half a time -- or three and a half years) to indicate in comparison to the millennium, Satan is bound and Christ is ruling. The hermeneutic is the kingdom of God is both now (the events will come to pass quickly) and not yet. God's kingdom is advancing now but it is not consummated. It is also known as the inaugurated eschatology. This age between Christ's first coming and his second are the latter days. The saints are victorious through the ironic suffering, persevering, and martyrdom. The symbols of Revelation refer to the times throughout the church age and are not tied to one specific historical event, except those that refer to Christ's first and second coming and the establishment of the new heavens and new earth. At Christ's second coming, there is the general resurrection, the judgment, and the establishment of the eternal kingdom.

A little before 1900, there was no distinction between Postmillennialism and Amillennialism, they were considered part of the same group. However, developments in eschatology during the 1800s started pushing the "two wings" of Postmillennialism apart so that one group in the Postmillennial camp needed to distinguish themselves from the other group. Abraham Kuyper coined the term "amillennialism" -- which is unfortunate because this view recognizes the millennium as much as the Postmillennialists do.

Dispensational Premillennialism. This is the most popular form of premillennialism. Beale summarizes the essential views are (G.K. Beale, The Book of Revelation, Eerdmans, 1999, p. 47) as:
- The restoration of ethnic Israel to its land.
- The church is raptured into heaven.
- After the rapture there is a seven year tribulation.
- During the tribulation there is the reign of the antichrist.
- Christ's second coming.
- Christ's millennial reign.
- Satan's final rebellion.
- Christ's eternal reign with the saints in a new heaven and new earth.

Historic Premillennialism. Unlike Dispensational Premillennialism, Historical Premillennialists views that the church as the true Israel. Hence there is no rapture of the church prior to Christ's second coming. Christians will pass through the final period of trial prior to Christ's second coming. Upon Christ's second coming, Christ sets up his millennial reign, followed by Satan's final rebellion, the final judgment, and the eternal reign of Christ with his saints in the new heaven and earth.

Full Preterism. The preterist view has two forms. The first sees Revelation as largely a prophecy of the fall of Jerusalem in 70 AD (G.K. Beale, pp. 44-45). Babylon the Great is apostate Israel. Both Israel and Rome oppress the Christians. The judgment is limited to apostate Israel. Another form of preterism views Revelation is about the fall of Rome.

In Full Preterism, the fall of Jerusalem is accompanied by Christ's second coming. The new age is setup, the New Heaven and New Earth is ushered in. Full Preterism, for me, is hard to understand because in looking at the world around me I do not see anything approaching what the Bible describes as victory over death and the new heaven and earth.

Partial preterism views that Christ did not return with either the fall of Jerusalem or the fall of Rome. The preterist view associated with the fall of Jerusalem has several interesting issues. One is that is requires Revelation to be written prior to AD 70 (say AD 67). This form of preterism falls if Revelation is written after 70 AD, which even most conservative scholars and ancient tradition believes (such as the history passed down via Eusebius). Secondly, the symbols of Babylon the Great has not been used for Israel in other parts of scripture, and the judgment does not include all the godless nations such as Rome.

The second form of preterism tends to be, in my opinion, more viable. The godless nations are judged with the fall of Rome. The date of Revelation is not critical (for either an early or the later traditional date of the 90s AD).

666: What's in a Number?

2009-01-03T00:51:00.005-05:00

This calls for wisdom: let the one who has understanding calculate the number of the beast, for it is the number of a man, and his number is 666. (Revelation 13:18 ESV)

Many of you know that there are New Testament manuscript families. When the original New Testament letters and books were written, and gathered together, possibly around the end of the first century, it appears that copies went to different regions. In those regions, copies of those manuscripts were made with some distinctive variations. The variations were not major changes. Many were copiest mistakes. Some changes were made to correct perceived grammatical errors. Other changes were made to smooth-out the reading of hard passages. Out of these regions, copies were made of these manuscripts that incorporated the changes. An excellent book on the topic by a world renown expert is Bruce Metzger's The Text of the New Testament.

Two of the major manuscript lines are the Alexandrian and the Byzantine. The Alexandrian family of manuscripts tends to be more polished than the Byzantine family. Scholars have made a discipline of trying to figure out what the original text was of the New Testament was. They have made tremendous contributions which are reflected in all our modern Bibles, from the Revised Standard, the NIV, New American Standard, New King James, ESV, etc. One of the rules of thumb when you have variant readings in two manuscript families, like we have with the Byzantine and Alexandrian families, is to take the more primitive style of text. Here is how Revelation 13:18 is preserved in these two families (taken from the Parallel Greek New Testament Website):

Byzantine Majority
wde h sofia estin o ecwn noun yhfisatw ton ariqmon tou qhriou ariqmoV gar anqrwpou estin [kai] o ariqmoV autou [estin] cxs

Alexandrian
wde h sofia estin o ecwn noun yhfisatw ton ariqmon tou qhriou ariqmoV gar anqrwpou estin kai o ariqmoV autou exakosioi exhkonta ex

The number 666 is written differently in these two manuscript families.

Byzantine Majority
cxs

Alexandrian
exakosioi exhkonta ex

The Byzantine follows the ancient Greek way of writing numbers (cxs -- where c is the letter for 600, x is the letter for 60, and s is letter for 6). For a good discussion of the Greek numbering system, see the Ancient Greek Mathematics website of the University of St. Andrews, Scotland. Go to the paragraph that has "second ancient Greek number system" towards the middle of the page. The Alexandrian family writes the number in a long form, exakosioi exhkonta ex, where exakosioi literally means 6-hundreds, exhkonta literally means 6-tens, and ex is 6.

The left image shows a photograph of the Sinaticus, a very important Alexandrian family manuscript that is currently on display in the British Library (I saw it when it was housed in the British Museum). I have retouched the image to show the long form of the 666.

The oldest existing fragment of Revelation 13:18 is shown on the right. It is the P¹¹⁵ manuscript fragment (the picture is taken from the Wikipedia article on Papyrus 115). It was collected in the early 20^th century, but it was only examined and cataloged at the end of the 20^th century. The interesting thing about the manuscript is the number of the beast is 616, shown next to the red arrow -- an interesting variant to 666 which is in the vast majority of the other ancient Revelation manuscripts. While 616 is in the earliest Revelation manuscript, it does not necessarily mean that 616 was written by John in the original manuscript of Revelation. Most of the other manuscripts have 666, which could have been copied correctly from previous copies that were accurate in their copying of 666. P¹¹⁵, while copied early, the scribe could have made a mistake.

Beale has an interesting theory on the variation from 666 in P¹¹⁵. If the scribe producing P¹¹⁵ was working with a "Byzantine" manuscript with the number written as cxs, the central "digit" x (ksi) could have been written sloppily in the manuscript the scribe was copying from, it could have looked straight to him, like i (iota). The scribe would write cis in his copy, which is literally 616.

One further note on P¹¹⁵. Scholars consider this fragment to be Alexandrian in style, even though it inserts the number in the Byzantine way.

So what are we to make out of the 666? Here are some possibilities:

The beast is Roman Emperor Nero. R.C. Sproul writes in The Last Days According to Jesus (pp. 186-189) that during the first century there was a game of making numbers out of people's names by summing up the digits associated with the letters in their name. We saw this above in how the number 666 was written in the short Byzantine style using the Greek letters. The same kind of number was practiced in Hebrew. Nero was known to be a brutal tyrant who killed many Christians in Rome. If you transliterate Emperor Nero from Greek into Hebrew, there is no clean fit because Hebrew does not have vowels. There are a variety of ways to fudge the name. One documented way that was found from the first century was "Nrwn Qsr" (pronounced Neron Kaiser). If you add the numbers represented by the letters Nrwn Qsr you get 666. The argument is that many first century Hebrew readers would have made that connection and identified the beast as Nero. However, according to G.K. Beale, Charles Hill, Vernon Poythress, it is not a slam dunk that the original readers associated Nero with the number of the beast. Many of the original audience of Revelation spoke Greek or Latin as their first language, and many did not know Hebrew. Further, Nrwn Qsr is just one of several "fudged" ways to transliterate the Greek Nero into Hebrew, and those other variations do not add up to 666. G.K. Beale writes: "None of the many solutions using gematria is ultimately satisfactory because there are so many names, ancient and modern, that come to 666. There are so many proposals because it is easy to turn a name into a number but hard to deduce the right name from a number." (G.K. Beale: The Book of Revelation, A Commentary on the Greek Text, Eerdmans, 1999, p. 721)

R.C. Sproul also wrote about a possible other reason that 616 showed up in some manuscripts, which he got from the very respected scholar Bruce M. Metzger of Princeton (Sproul: The Last Days According to Jesus, p. 188): "Perhaps the change was intentional, seeing that the Greek form Neron Caesar written in Hebrew characters (nrwn qsr) is equivalent to 666, whereas the Latin form Nero Caesar (nrw qsr) is equivalent to 616." In other words, the scribe copying the manuscript "updated" the text to his audience who were no longer Greek speaking, but spoke Latin instead. By transliterating the Latin Caesar Nero into Hebrew you get a spelling change that results in 616. An interesting theory, but I wonder why the scribe who created P¹¹⁵, copying a manuscript in Greek for obviously Greek readers, would use this kind of reasoning. Beale's reasoning above about how one letter can be mistaken for another is a simpler and more reasonable explanation.

The number is symbolic of an unholy trinity. We can see this easily with our modern numbering system: 666. It is three sixes. Three in Revelation often was a symbolic reference to the Trinity. Seven is symbolic of perfection and completion (e.g. the seven spirits refers to the perfect Holy Spirit, seven days in a week). Six falls short of completion or perfection. In this section of Revelation John reveals a trinity of evil beings, the Dragon, the sea beast, and the false prophet. The 666 can play on that unholy trinity idea. The problem with this view is that 666 is a modern representation of the number. We can see in the short way of writing 666 in Greek is cxs. There is no repeated digits of six in this. This would seem to rule out this possible interpretation of 666.

However, Irenaeus, in the second century, noted that cxs was 6 hundereds, 6 tens, and 6 ones -- which is similar to our view today. While cxs is not just thee sixes strung together, there is enough commonality in their viewpoint in looking at the number for them in the long "polished literary" way (exakosioi exhkonta ex) to see three sixes strung together, in much the same way we would today. So, it is very possible they could have seen that pattern. How were the Dragon, the sea beast, and the earth beast (the false prophet) counterfeits to the Trinity?
- The Dragon wears crowns, claiming authority that does not belong to him.
- The Dragon summons the Sea Beast in a way that mimics the Father calling the Son.
- The Sea Beast has a fatal wound that mimics Christ's death and resurrection.
- The Sea Beast summons the Earth Beast in a distorted imitation of Christ and the Father calling the Holy Spirit.
- The Earth Beast causes people to worship the Sea Beast, in a distorted way that the Holy Spirit causes believers to worship Christ.

666 is visually a corrupted Christ Type. Tony Sisk wrote this as a comment in one of my blog entries in MetaSchema in a blog series where I was initially exploring the idea of 666 (It's All Greek to Me):

I have enough knowledge of Greek to make me a danger to myself and the rest of Christendom, so to that I will not appeal.

I would like to offer the view of my NT professor, Dr. Maurice Robinson, from seminary who holds to Byzantine priority. (This view certainly is not original!)

The number '666' when written in Greek letters is Chi+Xi+Final Sigma, with a bar drawn over it to indicate it is a numeral. Elsewhere, certain “sacred names” like God, Jesus, Christ, Spirit, etc. are also abbreviated by their first and last letters with a bar over them.

So Christ is abbreviated Chi+Final sigma. The only difference between the number abbreviation '666' and the abbreviation for Christ is the presence of Xi in the middle, and Xi is the most twisted and convoluted letter in the Greek alphabet, thus within the numeral '666' picturing someone who appears to be Christ outwardly, but who within is a serpent, thus the Antichrist in league with the devil.

So, rather than a name of the beast that has to be calculated, the concept of “the number of his name” more accurately reflects his character.

You can go here, scroll down to the eighteenth verse, and look under the heading "Byzantine Majority", though the line indicating it is an abbreviation of a sacred name is not present, it does plainly show the order of the letters.

It is a compelling argument and one I have provided as I have taught through Revelation as a viable explanation. Just something else to chew on!

Nero was a prototype of the Beast. In this view, it is recognized that Nero fit the 666 pattern in the ears and minds of the first audience to hear Revelation being read. But as many prophecies in the Old Testament spoke of a particular event and was echoed in other following events (such as some of the prophecies which ultimately referred to Christ but were initially fulfilled by a prior event), so this description of Nero sets the pattern of the type of person (or the government and state he ran) of the beasts to come.

666 refers to a beast in the future. Many Premillennialists, including many Historical Premillennialists (to be defined in a future entry) and all Dispensational Premillennialists (also to be defined in a future entry) believe this passage refers to a time a great future persecution by an entity or person in the future.

All of the above. There is some truth to all of the above observations.

The last option is what I prefer. Revelation is a vastly rich book full of deep imagery inspired by the Holy Spirit for all of the age the church. To identify Nero as the period of the great persecution with no others to follow is to insult the Christians in the 20^th century who were martyred in numbers much greater than ever before.

Trying to find a particular name that adds up to 666 and identify that person as the Beast misses what the text of Revelation is saying. Revelation is using symbolism. The number 666 itself is very suggestive as shown above.

Searching for the one Anti-Christ beast sometime in the future, or even in the past, misses that the spirit of Beast is present among us now. We live in a fallen world and the culture of this world is not to be identified with God's precepts. Sometimes the situation is very obvious. Hitler in Nazi Germany was very much a beast, an anti-Christ, as was Stalin. These people took the honor and glory reserved only for God. Each reflected the beast in some form, and Revelation is referring to these kind of people and oppressive governments. However, that is not the only story. Revelation 13:17 says, "no one can buy or sell unless he has the mark." We, in our Western culture, often sell ourselves to the consumer mentality. We desire more and more stuff and get addicted to buying and going into debt. How many people, Christians and otherwise, have huge credit card debt? How many foolishly borrow on cars, homes (with crazy sub-prime loans)? People who borrow become slaves to the lender. Perhaps the credit number is the mark of the beast for these people.

Looking for one person to be the 666 beast, either in the future, or in the past, is closing the eyes to the anti-Christs that are around us today. Anything that draws your heart away from fully serving Christ is a form of the anti-Christ. It can be blatant, like the Islamic countries that persecute and kill those who convert to Christianity. It can be much more subtle as not wanting to be thought of as an "intolerant" fundamentalist Christian. It can be allowing yourself to be enslaved to consumerism, debt, and not using your resources for advancing God's kingdom. As Revelation says, "Here is a call for the endurance of the saints, those who keep the commandments of God and their faith in Jesus." (Revelation 14:12, ESV).

But also know this, if you are in Christ, you have been sealed by God. God's name is written on your forehead. You will be singing a new song before the throne of God that no one can learn except God's redeemed and elect. Because of that, you will heed the call to endure, not to enslave yourselves to the Beast, in whatever form it takes, and keep the commandments of God and your faith in Jesus.

Dancing in the Aisle at Christmas Eve

2008-12-24T23:59:00.000-05:00

I love the Christmas Eve service at my church. I recognize most of the people attending because we're not a huge church. It is a time where I see families together, infants to grown children returning to visit. It is a time were I see the the family nature of the church. The Christian faith is not rugged individual with God facing the world. It is people inside families among friends who help nurture each other in the faith.

Tonight, my grandson attended the service. He turned one year old at the beginning of December. He loves music and dances to it. He danced in the center aisle during most of the service, wondering down the aisle to the front and danced next to the pastor. The choir members watched and smiled along with much of the other church.

We also heard the news friends were going to become grandparents and enjoyed sharing their joy as well as their daughter's excitement.

Worshiping God is not an individual experience. It is sharing our joys and tribulations with families and close friends, who act as Christ to us in all our experiences. They help us worship the Lord of the universe who became a man to suffer and die on our behalf. That is a great reason to dance in the aisles -- even for us Presbyterians.

Merry Christmas!

2008-12-24T09:37:00.003-05:00

The news this Christmas season is bad. We are going through the worst economic crash in a generation. Christmas this year means with doing with less for many people. Many are out of work and prospects for the new year look bleak. How can Christmas this year be merry?

An interesting Biblical passage for this time of year is Revelation 18.

Fallen, fallen is Babylon the great!

But Christmas is a time of looking back to Christ's first coming. What do the troubled times of Revelation have to do with the advent of Christ? What does it have to do with us now?

Jesus' birth in Bethlehem ushered in the last days -- we are living in the end times of Revelation. God paints the picture rich in metaphors of what we are living through. Babylon in Revelation is the metaphor of all that is rich and mighty in the eyes of the people on earth, but it is corrupt. Babylon shows its face in history over and over. The wealth and power of Rome was a prime type of Babylon. The modern Western world in its wealth and power is another reoccurrence of Babylon. In the past few months a lot of wealth has vanished. I see it in my own retirement account, down 30% since September. Revelation speaks of the downfalls of the Babylons in history, including ours this day.

And the merchants of the earth weep and mourn for her, since no one buys their cargo anymore...

The current economic crisis that made its visible appearance with with bad loans has crashed throughout the world. The price of oil has dropped dramatically, sales of cars has dropped off so dramatically that the large US automakers are shutting down their factories for months. Even the popular Toyota will report a loss this year. The problems echo thoughout industries around the world.

Christians are in the world but in some fundamental sense we are not part of the world. Revelation speaks of this:

Come out of her, my people,
lest you take part in her sins,
lest you share in her plagues

We are not to depend on and participate in the evils of our present age. There is much in the western world, in the United States, that is evil. Not all is evil, God works through governments he institutes to accomplish his plans.

So, as we see the global economy crash, we can rejoice with the angels in Revelation 19 that our safety, security, salvation does not depend on the economy, our savings accounts, or what governments can do.

Hallelujah!
Salvation and glory and power belong to our God,
for his judgments are true and just...

Hallelujah!
For the Lord our God
the Almighty reigns

So while times look troubling to us now we can take great comfort this Christmas season that God is working out all the details of history for his glory and our good.

God entered history as a little babe in Jesus in Bethlehem two thousand years ago. History has never been that same since as God reigns bring history to its fulfillment.

Merry Christmas!

Circumcision and Baptism Similarities

2008-11-21T00:01:00.002-05:00

The previous post looked at the broad outline of the history of the church. The story of the church is the story of God's promise to be the God of his people, referred to as God's covenant people. From the time of the first humans, God bound himself to his people. God introduced through Abraham the special rite of circumcision that signified belonging to God. Along with belonging to God, circumcision signified:

Salvation by faith. The Apostle Paul in Romans tells us that Abraham received the sign of circumcision that was a seal his righteousness obtained through faith.
Inner Cleansing. In the Old Testament circumcision is portrayed as a cutting away of sin, resulting in a purified life.
Death of the past and new life for the future. Circumcision was applied to the Israelites as the left Egypt to show their death to their past life of slavery and new life for the Promised Land.
Union with Christ. Jeremiah says to "circumcise yourselves to the LORD". In doing this, the Israelites were uniting with Christ.
Regeneration. Paul says in Romans that circumcision represented an act of regeneration by Spirit of God in the heart.
Sign of belonging to God's visible covenant community. Circumcision was applied to all who participated in the life of God's visible covenant community. Not only was circumcision to be applied to Israelite families, but to the foreigner and strangers who come to the covenant community and wish to join it.
Applied to the household. Circumcision was applied to the males of the whole household. Infants, at eight days, were circumcised.

There are many questions that could be asked about circumcision. One question is if circumcision was a sign of salvation by faith, why was it applied to infants?

Circumcision shows how salvation is at the initiative of God. Before the infant can make a decisive choice one way or another, God extends his covenant blessing and promise to the family and to the infant. Circumcision was not an act on the part of the infant, or the adult for that matter, to show their devotion to God. Rather, circumcision is an act by God showing the infant, and whoever takes on circumcision, that God has included that person into God's covenant family. No one is automatically or magically saved in circumcision. Salvation in Old Testament times was by God's grace through faith. That faith, if not ever present, would mean that person is forever lost, even if he was a circumcised man.

An important thing to note is that whatever is signified by circumcision is also signified by baptism.

Church Timeline

2008-11-17T00:01:00.001-05:00

Inside the Protestant Christian communities there are many debates, one of the debates is when the sacrament (or ordinance) of baptism may be applied to the children of Christian parents. One side believes that baptism should only be applied to those who profess faith in Christ. I shall refer to those who hold that viewpoint as credobaptists (where credo comes from the Latin meaning "I believe"). I use the term paedobaptist (from the Greek pais meaning "child") to those who hold to the view that Bible teaches that children, including infants, of believing parents should be baptized.

To start the series, we will look at the big picture of church history. The word "church" refers to the visible community of God's people throughout the ages. There is an important distinction in the concept of God's community -- the visible and invisible community of God's people. The invisible community are those who have true faith in God. Because we cannot see into the heart of a person, we cannot identify with absolute certainty who is in the community of God and who is not. This aspect of not being able to see the heart of a person, that only God sees the heart, is what makes this class of people invisible to use. The visible community of God are all those who publicly profess faith in God and visibly attach themselves to the visible community of God in operation where they live.

As we look with the broadest brush strokes of church history, we see the church began with Adam and Eve, the first humans. As we develop the timeline, Abraham is recognized as a special recipient of God's promised blessing. Abraham and his male decedents were to receive the sign of belonging to God, circumcision. Later, Moses was instructed by God to teach the Children of Israel that they were not only to practice circumcision on all converts and newborn children in the homes of God's community of people, but also to celebrate the ceremonial dinner of Passover.

Jesus Christ ushers in the new phase in God's community. Christ replaced Passover with the Lord's Supper and replaced circumcision with baptism. In this transition of the community, a remnant of faithful Jews along with a huge in grafting of non-Jewish (Gentile) believers now comprises the visible community of God, or the church.

This broad view of the history of God's visible community of people, the church, is where we begin examining the issue of baptism.

Baptism Series

2008-11-15T16:59:00.002-05:00

Today I taught a class for prospective elders and deacons in my church on the Presbyterian view of baptism and the Lord's Supper. Some of the questions reminded me when I was first investigating infant baptism. I had grown up in a church and denomination that permitted both infant baptism and believers baptism. For those of us who believed in "credo baptism" we had the option to dedicate our babies. I did that with all three of our children -- against the objections of my wife, particularly on the last two of our children. As I would come to learn, my wife lead the way in my family in spiritual insight and theological understanding. She was a Calvinist -- ah, er, ah, Reformed, before I adopted that viewpoint.

So I was a credo baptist when we moved to Georgia. Our pastor back in Colorado suggested we try a "Perimeter" Church. I had no idea that Perimeter churches were Presbyterian -- and that there were several kinds of Presbyterian denominations. When we came to our present church sixteen years ago, I discovered that Presbyterians believed in infant baptism -- and the thing that looked like a baptistery behind the pulpit and choir area was merely an air conditioning air flow return. It took a couple of years or searching the Scriptures and talking with others before I finally became convinced that the Bible taught that we should baptize our children. That is when our family joined the church and all our children were baptized.

Why I Am Not A Calvinist

2008-10-14T00:01:00.004-04:00

Okay, what gives? I have published before that I am a Calvinist. But I recant all that today. Here is why.

Have you ever been pigeonholed? When I was a kid, I made the mistake of saying my favorite color was green. So did my wife. We each grew up being handed green lollipops -- yuk! Strawberry, cherry, or grape tasted so much better than the nasty green flavor. We were given green things, such as green clothes, green paintings, etc. Admittedly, we brought some of this on ourselves for vocally identifying a color as a favorite (which is such an in color these days). This kind of pigeonholing was very minor compared to what others have endured. I think of the terrible racial and ethnic pigeonholing that so many people have suffered through.

When I first stumbled into Calvinism 16 years ago, I was taken aback by some of the doctrine. But, as I interacted with various Presbyterians, I discovered that Calvinism presented a view of God's glory, power, majesty and overwhelming grace that I had never seen before or anywhere else since. But a lot of people, a lot of Christians have a dislike for Calvinism. The dislike varies from the normal "I don't think it makes sense" (which is normal) to an intense hatred. Often those who oppose Calvinism tell me what Calvinists believe, and that's where things get a little interesting. The beliefs are often things I don't recognize. Here are a few:

1. Calvin taught that God favors rich people because God predestined them to have riches.
2. Calvin taught people are saved by works.
3. Calvinists believe that infant baptism saves you.
4. Calvin taught that God hates everyone except a very few elect people.
5. Calvinists believe that you cannot have an assurance that you are saved because you must work to stay in the faith until the end, or else you are lost.
6. Calvinists believe that John 3:16 really says, "For God so loved the elect that he have his only Begotten Son..."
7. Calvinists don't believe in sharing their faith with others because it is up to God to save people.

...the list goes on and on.

Often, these statements are made with supporting quotes from Calvin's Institutes. One time I responded to one set of quotes claiming that Calvin did not believe in assurance. After showing my point, the person did not even acknowledge he had misquoted Calvin. That is somewhat typical of those who quote Calvin's Institutes. I have never come across someone quoting Calvin against Calvinism who has completely read the Institutes. There are plenty of websites and books which takes snippets used by the detractors.

Calvinism, as defined by these other people does not resemble the Calvinism I know. But often they refuse to believe me, a practitioner of over 14 years. What do I know -- the other websites are the true authorities on the topic. So, if Calvinism is defined in those ways, then I am certainly not a Calvinist. I stand in good company. The late John Gerstner, a theology professor and mentor of R.C. Sproul, was often asked in his classes if he was a Calvinist. Dr. Gerstner would ask, what do you mean by Calvinist? The student would respond with some of the usual misunderstandings, and Gerstner would reply, no, I'm not a Calvinist.

To be fair -- this does not happen just to Calvinism. Any position that is well defined and articulated in one of the Christian traditions, particularly those that run against the grain of default views of culture, face similar biases.

So, what theological position do I take? Often, when presented a distorted Calvinist picture, I'll reply that I am Reformed, as defined by the Westminster Confession of Faith and the Westminster Larger and Shorter Catechisms.

So, if you have an issue with Calvinism, don't take it up with me. I'm not a Calvinist -- at least not the sort you're probably thinking of. If you have an issues with Reformed Theology, then take a look at the Westminster Confession and Catechisms. See what they say. If you don't like it, then I'd be happy to discuss it with you.

Did the Universe Cause Itself?

2008-10-13T00:01:00.002-04:00

Could the universe have been its own cause?

Let's assume that if we were to watch the universe "run backwards" we would see it contract to a point at about 13.7 billion years ago. The question is, could that single point caused itself to come into existence?

Part of the problem in discussing this is that space/time itself presumably did not exist prior to the singularity. When we speak of cause and effect, there is an implicit assumption that a cause to some effect, the effect being the singularity of the start of the universe, is something in the local proximity of the singularity just prior, temporarily speaking, to the existence of the single point that started the expansion of the universe. But if the point did not exist, neither did space nor time exist, and so the notion of temporal prior-ness is difficult to make sense of.

Secondly, if we could assume that a temporal period did exist before the singularity, we have an interesting contradiction. If the single point (which the universe expanded from) was the cause of that same single point, then there was a moment in which the point did not exist, but at that same moment the point had to exist in order to be the cause of that point to exist. In other words, the point had to exist and not exist at the same moment for it to be a cuase of its existence -- which is a contradiction.

From this brief analysis, if the universe did not exist at some point, then we cannot offer a logically consistent theory that the universe was the cause of its own existence. Something else had to be the cause for the universe to come into existence.

Does Mathematics Cause Anything?

2008-10-09T00:06:00.013-04:00

Why is 6 afraid of 7? Because seven ate (eight) nine.

My blog article, Taking Temperatures of Black Holes, is my most viewed article. The reason is that I linked a simulated picture of a black hole from Wikipedia and for some reason, Google image searches puts that image and article fairly high in the search list -- and a lot of people are interested in black holes these days (particularly on September 10, the start up of the LHC at CERN).

Recently someone posted a comment to the article:

Causality [is] a source of order upon the chaotic randomness of the ingredients of the universe... mathematics are the foundation for that causality, a moment in time that had various factors within it's space to lead to a further moment in time where those factors acted upon each other in various ways based on factors that created those factors and so on and so forth.

The commenter is attributing to mathematics the power to cause things to happen in the physical universe. If you stop to think about it for a moment, the idea is absurd. It can be illustrated in this way.

Think of the concept of the number 7. Don't think of the number as seven apples, but just as the abstract concept of 7. Imagine a billiard table with a white cue ball. Does the abstract number 7 have the ability to be the cause of moving the cue ball? A cue stick can be a cause, another ball can be a cause, any number of things can serve as a cause. However, the abstract number 7 does not have the ability to cause the cue ball to move.

The commenter was trying to make a point that mathematics provided a sufficient cause to start the universe and as a result that God was unnecessary for a causal explanation for the universe. However, the commenter came up with a proposal for an abstract concept to be the initial cause for the universe, like the unmoved mover. The problem is that mathematics is an abstract category that is completely unable to serve as a cause for physical things.

Can Every Logical Statement be Proven?

2008-09-27T00:01:00.009-04:00

Kurt Gödel is the mystery man of the previous post.

Before Gödel, mathematics had undergone an interesting change in its foundations. During the nineteenth century it became more abstract, developing a notation and language that expressed great power. Georg Cantor developed set theory which gave ways of expressing and working with infinities. Logic, which was largely unchanged since the days of the Aristotle (384 BC – 322 BC). Gottlob Frege in 1879 extended logical to deal with concepts of "All" and "Some", which were not possible with Aristotelian logic. Frege's concepts were major breakthroughs, but his notation was difficult to work with. In 1885, Charles Peirce developed the notation that is largely used today[1].

At the beginning of the twentieth century, mathematics and logic were progressing so well that the great German mathematician David Hilbert (1862 – 1943) predicted that there would be ways to automate the mathematical theorem discovery along with their proofs. But cracks were beginning to appear on the road to the promised land.

Gottlob Frege was working on a monumental multi-volume opus, "Basic Laws of Arithmetic". He had published the first volume, and wrote the second volume and was publishing it as his own expense, when he got a letter from the British philosopher, Bertrand Russell. Russell had found ways to construct contradictions (which became known as Russell's paradox[3]) in Frege's first volume and was hoping that Frege would make some relatively minor corrections to eliminate the problem. Frege was, in his own words, was thunderstruck. He attempted to fix it, but ran out of steam and abandoned the project[2].

Another interesting paradox is the "Liar's Paradox" that is illustrated above. In one of its simplest forms:

This statement is false.

The interesting thing about the statement is trying to determine whether it is true or false. If the statement is true, then we must take what it says to be true, which is an assertion that the statement is false -- so the statement must be false, but that is a contradiction. So, if we assume to statement to be false, then what it asserts about itself is false, namely that this statement is false, which means the statement is true -- another contradiction.

Here is where Kurt Gödel enters the picture. In 1931, Gödel proved two theorems in logic that are known as his incompleteness theorems. Basically, Gödel constructed a version of the Liar's Paradox using the axiomatic Arithmetic system of the mathematician Peano. The statement referred to itself in a special way using numbering. At the time, the process was revolutionary because people did not think of describing statements as numbers. Today, with computers, which use numbers as their bottom layer of existence (binary numbers), this whole blog article can be assigned a number in various ways. One is simply the numbers that encode each of the letters in this article[4][5].

When Gödel constructed such a self referential statement, he was able to demonstrate that complex mathematical systems could be one or the other, but not both: (1) the system is complete and inconsistent, or, (2) that it was not complete and consistent.

If a system is complete, it means that all that statements you can construct within that system can be proved. However, you will get statements like the Liar's Paradox which are both true and false. In other words, there are logical contradictions in a complete system of mathematics.

If a system is incomplete, it means there are statements you can state within the system that you cannot in principle prove to be either true or false.

An example is the Liar's Paradox for us. If we have a complete system, then we can prove that Liar's Paradox -- the problem is that it is both true and false, and hence our system has contradictions. The alternative is to say we cannot deal with the Liar's Paradox. In other words, we cannot prove it to be either true or false. This means our system is incomplete.

What does this mean for us? I think it means in our pursuit of knowledge, there are going to be gaps of knowledge that we cannot know, in principle, whether something is true or false. In theology, the study of God, who is eternal and infinite, we will come across many things that we cannot know about God, in principle. In some of our discussions and debates, we need to leave room for the mystery about God. Indeed, Gödel has shown us in mathematics there are an infinite number of theorems that we cannot know in principle to be true or false. God, who is greater than mathematics, has an infinite number of logical statements about him that we cannot in principle answer as true or false.

As we study God, we need the humility to realize that we cannot know, in principle, an infinite number of things about him. This does not mean that God is unknowable. Mathematics has an infinite number of unknowable things, yet we can study and know many things about mathematics. The same is true with God, but we need to recognize out limits.

Notes/Sources:

[1] History of Logic, Wikipedia.

[2] Gottlob Frege, Internet Encyclopedia of Philosophy.

[3] See Russell's Paradox, Internet Encyclopedia of Philosophy.

[4] See Kurt Gödel in the Stanford Encyclopedia of Philosophy.

[5] See Kurt Gödel in Wikipedia.

Who Is This Man?

2008-09-21T00:01:00.000-04:00

Who is this man? He shook the foundations of his field of study during the twentieth century.

Earl's Conjecture Answered

2008-09-19T00:01:00.002-04:00

A month ago I made a conjecture -- Calvinism is a subset of Molinism[1]. I made the conjecture without examining the subject in detail, not really caring if I was right or wrong. This provided a springboard for some discussion -- probably a frustrating discussion for some of the participants. The conjecture is illustrated in the following diagram:

A proponent of Molinism is the contemporary Christian philosopher William Lane Craig[2][3]. He has written a number of articles on the topic. I have included links to some of these in the notes below. The definition of Calvinism I am using is common beliefs specified in the Westminster Confession of Faith[4] and the London Baptist Confession of 1689[5].

The answer to my conjecture is that Calvinism is NOT a subset of Molinism. There are elements in common between Calvinism and Molinism -- but each makes propositional statements that fall outside of the other viewpoint. The following diagram illustrates the relationship between the two views:

William Lane Craig provided a description of Molinism and its relationship to Calvinism in an interview with Hugh Ross' Reasons to Believe[6]. In that description, Dr. Craig outlined how Molinism was an attempt by 16th Century Spanish Roman Catholic Jesuit theologian, Luis de Molina, to respond to the rise of theologies of Martin Luther and John Calvin[7]. Jacobus Arminius (1560-1609) was the first Protestant to embrace Molinism in his protest against Dutch Calvinism. The interview was very helpful because some of the Reasons to Believe team were familiar with Reformed Theology (Calvinism) and pressed Dr. Craig on the distinctions. For instance, Dr. Craig specifically stated he did not hold to the idea of irresistible grace, the idea that when the Holy Spirit calls one of the elect, that call will always result in the person becoming a believer. Presumably then, on the famous "five points" of Calvinism, which came out of the Synod of Dort in response to the Arminian protesters, Molinism sides with Arminianism in denying each of the five points.

Sources/Notes

1. For a very brief description of Molinism, see Wikipedia's article on Molinism.

2. William Lane Craig, "No Other Name": A Middle Knowledge Perspective on the Exclusivity of SalvationThrough Christ.

3. See William Lane Craig's scholarly section of his website for more papers on Molinism. You will need to register, but it is free.

4. See the Westminster Confession of Faith for the content of the confession.

5. See the London Baptist Confession of 1689 for the content of that confession. This particular one had some minor modifications by Spurgeon.

6. Reasons to Believe.

7. Podcast: September 9, 2008 interview with William Lane Craig.

Spike in Readership

2008-09-14T00:01:00.000-04:00

This blog normally gets about 40 people a day from around the world that come to one of the past articles I've posted. On September 10, 2008, over 350 people came to my blog, the most ever in one day.

The reason? September 10 was the day the the Large Hadron Collider (LHC) of CERN in Geneva was fired up. It made the news around the world -- with some fear mongerers speculating that it would generate black holes that would gobble up the earth. I had several hundred come to my entries on black holes and CERN.

We're still here. I should tell you that the LHC did not run on full power on September 10 -- that will come later.

In the meantime, I might publish in this blog a fictional short story of something going amiss with the LHC. The story cannot happen for a variety of scientific reasons -- but it will be fun, if I get around to publishing it.

How Big is the Universe?

2008-09-12T00:01:00.010-04:00

How big is the universe? That is an interesting question that is not necessarily obvious. First, let me state some initial assumptions because there are a lot of religious people like me who visit this blog. I think the universe is old. Those who hold to a young universe (thousands of years old instead of billions), if the universe was created with an appearance of age (that is, the universe appears to be billions of years old) -- then these assumptions will work for you too.

(1) The universe is 13.73 billion years old[2] (using the short-scale billion vs. the long-scale billion of continental Europe, the number 13.73 billion is 13,730,000,000 years old).

(2) The universe is expanding.

The second assumption is not to be viewed as objects (galaxies) simply moving further out into space, but that space itself is expanding. The galaxies themselves have an average relative motion in the local space they occupy of zero, but the space itself is expanding. Imagine two people, George and Bob, standing in two different locations on earth, George at Trafalgar Square in London, next to Nelson's Column, and Bob is standing next to the Big Chicken in Marietta, Georgia northwest of Atlanta. The distance is 4,193 miles or 6,748 kilometers. Imagine that something dreadfully wrong and completely unanticipated happened at the Large Hadron Collider at CERN in Geneva, and the surface of the earth is expanding 1 kilometer per hour (don't worry, that will not happen). That means if Bob is 1 kilometer from home, in one hour his home will be 2 kilometers away. Bob is just standing there, and his house is not on a trailer moving around -- it is just earth expanding that is causing that change in distance. Now, think of that one hour period where the surface of the earth expanded at 1 kilometer per hour all over the planet. It means that Bob and George are now an additional 6,748 kilometers, so they are now 13,496 kilometers apart. Bob and George have not taken a step, they are standing still, but the distance has grown between them.

That analogy is actually what is happening in the universe. While there would be problems with the earth expanding (it would open cracks and fissures and make a huge mess of the planet) -- this does not happen with space. Space just expands, taking us along for the ride. We don't notice it because the expansion is so slight, we would not be able to see it with our five senses. Further, any expansion that occurs around us is does not pull us apart, nor the earth, nor the solar system because gravity and the atomic and molecular binding energy compensates for it. But, over the huge distances of space, the expansion really shows up.

So, getting back to the question, how big is our universe? Part of the problem is that we do not know how much of the universe there is beyond what we see. We could be seeing only a small fraction of the universe, limited by age and expansion rate of the universe. In fact, if we were standing on the Andromeda Galaxy right now, we would see into a region of space that we cannot see from our own Milky Way Galaxy. The vast majority of what is seen from either Andromeda or the Milky Way Galaxies is the same, but each one sees some part of the universe that the other cannot see. So, we need to add one more assumption:

(3) Limit the measurement to the universe we observe.

(4) The actual universe is at least as large as what we see.

It is possible that the universe is much smaller than what it appears to be. In that case, light could be traveling around once or twice or more times. It would mean that one of the galaxies we see our there is our Milky Way Galaxy, at a much younger age -- or there are several versions of the Milky Way we can see, where we see the Milky Way at successively younger ages. There are a whole variety of reasons why astrophysicists do not believe the universe is smaller than what we appear to see. One is that there would be repeating patterns that should be observed about the universe that are not seen.

One final assumption:

(5) The velocity of light is constant throughout the lifetime of the universe.

Again, how big is the observable universe? One possibility:

(a) 27,460,000,000 light years in diameter (13,730,000,000 light years x 2). If the universe were static, not expanding or contracting, this would be the size of the observable universe based on the age of the universe times the velocity of light. Because this does not take into account the expansion of the universe, this answer is wrong.

We need to remember that when a photon leaves a distant object, the space behind the photon expands so that when it arrives at earth, the distant region can be much further. In fact, the most distant objects will be about three times further[3]. Taking that into account, we arrive at:

(b) 92 billion (92,000,000,000) light years in diameter[4][5]. This is the correct answer according to the assumptions listed.

A span of 92 billion light years in diameter! It seems strange that two points could travel 92 billion light years in 13.7 billion years. In one sense they are moving relative to each other faster than the speed of light. Didn't Einstein put a cosmic speed limit of the speed of light? Yes, the Special Theory and General Theory of Relativity forbids light and other things that start at rest to go faster than the speed of light, relative to local space (hmmm -- I've got to watch how I say this). But Relativity does not prohibit space expanding relative to each other faster than the speed of light.

There is something else that is interesting and rather strange. At about 16 billion light years from us[6], space expansion makes our region and that region of space to move faster than the speed of light. Photons emitted from galaxies at 16 billion light years or greater will never reach earth, if all the above assumptions continue to hold on into the indefinite future. That means that very distant galaxies that can be seen from earth now cannot be seen from earth in the future. Over vast scales of time, distant galaxies will fade out of the view from earth.

Sources/Notes

[1] Image at the top left is The Cosmic Microwave Background temperature fluctuations from the 5-year Wilkinson Microwave Anisotropy Probe data seen over the full sky. It was taken from Wikipedia, who took it from NASA and so the image is in the public domain.

[2] Gary F. Hinshaw, et al., p. 2 and p. 42, Five-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Data Processing, Sky Maps, & Basic Results, unpublished manuscript submitted to the Astrophysical Journal Supplement Series. No date, but footnotes imply the manuscript was written in 2008.

[3] Charles H. Lineweaver and Tamara M. Davis, Misconceptions about the Big Bang, Scientific American, February, 2005, p. 5.

[4] ibid.

[5] Universe, Wikipedia.

[6] Misconceptions about the Big Bang, p. 5.

The Omnivore’s Hundred

2008-09-07T16:54:00.003-04:00

I don't like the usual meme blogs which ask you to list things and tag someone else, like the 10 most influential books, etc. But this one caught my fancy. It was created by the Very Good Taste blog and has his list of the 100 things an omnivore should have tasted in their lifetime.

Here are the instructions:

1) Copy this list into your blog or journal, including these instructions.
2) Bold all the items you’ve eaten.
3) Cross out any items that you would never consider eating.
4) Optional extra: Post a comment here at www.verygoodtaste.co.uk linking to your results.

The VGT Omnivore’s Hundred:

1. Venison
2. Nettle tea
3. Huevos rancheros
4. Steak tartare
5. Crocodile
6. Black pudding
7. Cheese fondue
8. Carp
9. Borscht
10. Baba ghanoush
11. Calamari
12. Pho
13. PB&J sandwich
14. Aloo gobi
15. Hot dog from a street cart
16. Epoisses
17. Black truffle
18. Fruit wine made from something other than grapes
19. Steamed pork buns
20. Pistachio ice cream
21. Heirloom tomatoes
22. Fresh wild berries
23. Foie gras
24. Rice and beans
25. Brawn, or head cheese
26. Raw Scotch Bonnet pepper
27. Dulce de leche
28. Oysters
29. Baklava
30. Bagna cauda
31. Wasabi peas
32. Clam chowder in a sourdough bowl
33. Salted lassi
34. Sauerkraut
35. Root beer float
36. ~~Cognac with a fat cigar~~
37. Clotted cream tea
38. Vodka jelly/Jell-O
39. Gumbo
40. Oxtail
41. Curried goat
42. Whole insects
43. Phaal
44. Goat’s milk
45. ~~Malt whisky from a bottle worth £60/$120 or more~~
46. Fugu
47. Chicken tikka masala
48. Eel
49. Krispy Kreme original glazed doughnut
50. Sea urchin
51. Prickly pear
52. Umeboshi
53. Abalone
54. Paneer
55. McDonald’s Big Mac Meal
56. Spaetzle
57. Dirty gin martini
58. Beer above 8% ABV
59. Poutine
60. Carob chips
61. S’mores
62. Sweetbreads
63. Kaolin
64. Currywurst
65. Durian
66. Frogs’ legs
67. Beignets, churros, elephant ears or funnel cake
68. Haggis
69. Fried plantain
70. Chitterlings, or andouillette
71. Gazpacho
72. Caviar and blini
73. Louche absinthe
74. Gjetost, or brunost
75. Roadkill
76. Baijiu
77. Hostess Fruit Pie
78. Snail
79. Lapsang souchong
80. Bellini
81. Tom yum
82. Eggs Benedict
83. Pocky
84. Tasting menu at a three-Michelin-star restaurant.
85. Kobe beef
86. Hare
87. Goulash
88. Flowers
89. Horse
90. Criollo chocolate
91. Spam
92. Soft shell crab
93. Rose harissa
94. Catfish
95. Mole poblano
96. Bagel and lox
97. Lobster Thermidor
98. Polenta
99. Jamaican Blue Mountain coffee
100. Snake

Free Will Thought Experiment 1

2008-08-29T00:01:00.002-04:00

I came across an interesting article with a thought experiment I wish to explore[1].

Often, free will is defined as:

(1) An action is free, in the sense of moral responsibility, only if the person could have done otherwise than she actually did.

A corollary is:

(2) An action is free, in the sense of moral responsibility, only if the person could have chosen otherwise than she actually did.

Let us conduct the following thought experiment[2]:

Suppose the subject of the thought experiment is named Sally. She underwent brain surgery by the surgeon Randolf. Randolf is an unethical surgeon who, unknown to Sally, implanted a tiny computer with sensors and electrodes in Sally's brain so that Randolf can control Sally's behavior. One of the things that Randolf monitors is Sally's voting behavior. Randolf has programmed the computer in such a way so that if Sally's brain shows any inclination to vote for John McCain, the computer intervenes so that Sally will vote for Barack Obama. If Sally decides on her own to vote for Barack Obama, the computer will do nothing, not effecting anything inside Sally's brain.

Now, suppose that Sally votes for Barack Obama on her own, just as she would have if Randolf had not inserted the computer in her brain.

Question: Was Sally responsible for her vote for Barack Obama?

The answer is yes, Sally was responsible for her vote for Barack Obama, even though she could not have done otherwise. In this analysis, we see that the two conditions, (1) and (2), listed above are irrelevant in strictly determining if someone acted freely and is responsible for their actions.

This analysis was done by John Fischer, currently a professor of philosophy at the University of California, Riverside[3]. It is one of those thought experiments that eliminates some of the chaff of what people think freedom and responsibility are.

I am going to stop the article here. Feel free to explore the links I have listed below to further explore the topic. All of the people I mention are people I just discovered within the past hour as I write this (August 27, I have scheduled this article for later posting). I don't know where these people take the concepts. It is fascinating and should provide some thought provoking and interesting reading. I love these kind of adventures!

Notes/Sources:

[1] Living Without Free Will, Derk Pereboom, University of Vermont (2001, Cambridge University Press).

[2] ibid, p. 2. This example is derived from Dr. Pereboom's use of John Martin Fischer, "Responsibility and Control," in Moral Responsibility, Fischer, ed. (1986, Cornell University Press), p. 176.

[3] See John M. Fischer webpage at U.C. Riverside, and background information at The Information Philosopher website. Dr. Fischer is a founder and general adviser to the The Garden of Forking Paths group blog on free will and moral responsibility.

...finally, a note to me for a further article to explore.

God Foreseeing

2008-08-28T00:01:00.000-04:00

Question: Is there a difference between the idea of God predetermining everything versus God predetermining based on what God foresaw what someone would do? Would that difference allow for free will to exist in the latter case?

The English language can be very imprecise. Sometimes logic can help. There is a notion in logic known as the general condition and the more specific condition.

Consider the statements:

(1) God determined to permit them to act as He knew beforehand

(2) God determined.

Statement (2) is the more general condition, statement (1) is the more specific condition. This is because statement (1) is a more detailed specification of statement (2). Statement (1) has God's determination which is contained in statement (2), along with the more specific to permit them to act as He knew beforehand.

The word determine means: "to fix conclusively or authoritatively" (see determine in www.m-w.com), the words "to permit them to act as He knew beforehand" is an addition to determine, but the word still implies "to fix conclusively or authoritatively". You'll notice there are other possible definitions of determine, such as "to find out or come to a decision about by investigation, reasoning" -- but the problem with that sense of the definition is that God needed no finding out, he knew from all eternity. Thus the statement God determined to permit them to act as He knew beforehand implies the simple statement that God predetermined.

We can reason further another way. Because (1) happened before the foundation of the world, it means by the definition of predetermined, that God predetermined their actions before they existed. There is no temporal sequence in God's foreknowledge, or in his foreordaining -- because God's foreknowledge and purposes are unchanging (otherwise at one point in time there was knowledge about the future that God did not possess -- which would make him not omniscient at that point, which contradicts God's character and being).

It is possible to logically order God's predeterminations because that is not temporally ordered; logical ordering is true for all eternity. We can say that someone's future activity will imply God's foreknowledge of it and thus imply God's permissive foreordaining. But logical orderings need not be unique, and in most cases they are not unique. Another equally valid logical ordering is that is God's foreordaining necessitates the actions of people in the future.

So, consider the case: God determined beforehand to permit someone to act as He knew beforehand. This implies the action of someone in the future necessitates God's knowledge of the person's action in the future. But the reverse ordering is also true: God's predetermined knowledge necessitates someone to act in a particular way. When it deals with someone's ultimate destination, then that is predestination.

In other words, in all cases, God predetermining and God's predetermining to permit all result in predestining.

Free Will Perspectives

2008-08-27T00:01:00.004-04:00

I have written a number of blog entries on free will before. What I am curious about is what are the differing views on free will. Not only are there the various Christian views on free will, but there are various views on free will in other disciplines. This is an attempt to put together a partial list of different approaches. It is done without deep consideration. I'll gladly take the comments of others. Note: I am biased. You will probably see it show up in the descriptions.

Christian Views:
(1) Augustinian -- God sovereignly ordains all that will be. Human freedom is subordinate to God's sovereignty.
(2) Molinism -- Middle knowledge gives freedom to humans.
(3) Arminian(?) -- This is probably not the best name. God does not ordain human action, but merely foresees all their actions.
(4) Open Theism -- God does not know all the future and so the human will is not constrained by God's foreknowledge.

Evolutionary Biology -- Human free will fits within brain stimuli and neural activity that supports survival of the genome.

Physics -- Human free will is ultimately determined by the physical processes surrounding the human organism, including the random activity at the quantum physical level.

Any other views?

Earl's Conjecture

2008-08-20T00:01:00.004-04:00

I have encountered various people on the Internet who advocate Molinism. My first encounter was back in the mid 1990s with a pastor who had a PhD in philosophy from Notre Dame. We debated Calvinism versus Molinism and that is where I first discovered Molinism.

Molinism is an attempt to reconcile God's omniscience with human free will. It was named after the 16th century Jesuit theologian Luis de Molina[1]. The basic thought is that God knew all the possibilities where he is not the active agent in those activities involving the human will. While God knew what would happen in his creation, he also knew what could have happened in all the various contingencies. It is in this what could have happened that separates God's human freedom from the tyranny of God's foreknowledge. William Lane Craig is probably the most visible modern advocate of Molinism[2][3].

I am going to make a conjecture than can be proved to be true or false with a little bit of work (to see the answer to the conjecture, click here). My conjecture, which I will not-so-humbly call Earl's Conjecture is:

Calvinism is a subset of Molinism.

Diagrammatically, it is illustrated as follows:

In other words, the logical propositions of Calvinism is a subset of the logical propositions of Molinism. This means if you assume Molinism, Calvinism is logical consequence. But it should be noted that the reverse does not follow in my conjecture, that is, if you merely assume Calvinism, you cannot have Molinism as a logical consequence.

Now, let me sharpen this a bit. I will define Calvinism as the set of beliefs that are common to the Westminster Confession of Faith[4] and the London Baptist Confession[5]. This is an arbitrary definition, but it is a concrete definition. For Molinism, I refer you to William Lane Craig's website[3].

Admittedly, the definition of Molinism is not as sharp as Calvinism. There is some gray area in the Molinism definition. If anyone has a set of "confessional" documents for Molinism, let me know.

Please contribute with your thoughts. I will post some of my thoughts in time.

Sources/Notes

1. For a very brief description of Molinism, see Wikipedia's article on Molinism.

2. William Lane Craig, "No Other Name": A Middle Knowledge Perspective on the Exclusivity of SalvationThrough Christ.

3. See William Lane Craig's scholarly section of his website for more papers on Molinism. You will need to register, but it is free.

4. See the Westminster Confession of Faith for the content of the confession.

5. See the London Baptist Confession of 1689 for the content of that confession. This particular one had some minor modifications by Spurgeon.

What Would Pilate Do?

2008-08-19T00:01:00.001-04:00

Rose and John Cole are gracious, hospitable, internet hosts. Rose just recently posed a question asked by a frequent contributer, Colin Maxwell, aka "goodnightsafehome", from a previous discussion,

Yes or No – Answer first and then qualify afterwards, Could Pilate have said “No” to the Jews’ demand to have Christ crucified and let Him go?

Here is how I answer the question.

At one point, only God existed in eternity. God, in all eternity, knew what, how, and why he was going to create the universe along with all the ramifications of it. God's knowledge was complete, perfect, and good -- because God is complete, perfect, and good. Because God's knowledge was complete and perfect, he did not at any point say, I wonder what will happen if..., then muse and ruminate over it, then think, hmmm, how about if I do this..., then ruminate over that, and then pick what the universe would be like and how he would act in its creation and his providential care of it. Because if he did, his knowledge before that point would not be complete. God would not have been omniscient. God's being and character are unchangeable -- thus God was/is/will be always omniscient.

God, being perfect and omnipotent, also had perfectly set his thoughts and plans from all eternity. There are many alternative ways in which God could have planned everything -- but God had perfectly arranged in his mind all that will be.

So, before the foundation of the world, God had arranged in his mind -- to use an anthropomorphic analogy (remember, God is eternal and arranging his mind is tenseless, it is always been arranged as he desired) -- that Adam would fall, that sin would enter the world, that Christ would be arrested, that Peter would deny Christ, that the disciples would flee Christ, that Pilate would pronounce the death sentence on Christ and have him crucified.

These are logical necessities of a perfect, omniscient, omnipotent God. No matter how you dice it and slice it, I don't see how you can get around it, unless you deny some basic feature of the classically known attributes of God -- such as done in Open Theism.

In the past, various theologians have tried to get around the problem -- including Molinism and "Middle Knowledge" -- but that is a theory that the Bible is silent about and really ends up with a predetermined universe anyway -- at least how one of the major Protestant proponents of Molinism, William Lane Craig, presents it.

Others have tried to say that God chooses people who will choose God. However, that is a linguistic convenience -- because God from all eternity had arranged his thoughts so that, by logical necessity, determined who will choose him.

A Calvinist at this point will say that we have no theory of why God chooses, other than in one sense it pleased him (using an anthropomorphic analogy) in his perfect and good will to have things happen this way and that God does things for his glory and the good of his people. Does this mean that God takes delight in punishing people? No. Understanding God requires much more subtle and nuanced thinking than trying to force extremes out these logical results in understanding God.

Asking the question, could Pilate have done anything other than what God had planned? The question actually has multiple senses to it, which makes it an ambiguous question. This is part of the problem with arguments in theology -- people are not precise in what they say AND there is a point where our reasoning cannot take us further.

The question, could Pilate have done anything other than what God had planned? has at least these possible meanings:

(1) Logically speaking, could Pilate have done anything else other than what God had in his mind about Pilate from all eternity?

(2) Physically and emotionally, was there anything that was preventing Pilate from acquitting Christ?

(3) In Pilate's spiritual condition, was Pilate able to do the right thing?

The answer to (1) is no. This follows from God's omniscience and omnipotence in arranging all things so that the answer follows just as you prove a theorem in geometry.

The answer to (2) is no. There is nothing in Pilate's physical nature and condition that made him condemn Christ. Pilate was under pressure from the leaders and people around him, but Pilate was not coerced in some ultimate sense. He was free to do as he wished.

The answer to (3) is no. Pilate was in enmity and rebellion against God. As Romans 3 points out, this is the natural condition of all human kind. This, along with the freedom of coercion, makes all of us guilty before God -- and all of us deserve death. God is not required to intervene to save us from our rebellion -- precisely because we deserve it. This part is hard to understand in today's society, because we don't really believe we all deserve death. We think God owes us a chance -- but if we think in any way like this, then we are saying we don't deserve death.

God was not required to step in and apply grace to Pilate -- just as God was not required to apply grace to your life. You deserve death. That means God did not have to send Jesus to die for you whatsoever.

But blessed are you that you do see, that Jesus did die for you. To you has been given the secret of the kingdom of God. Rejoice and marvel at God being for you and rescuing you -- when you did not deserve it at all.

Another Christian History Series

2008-08-15T00:01:00.000-04:00

I love studying history -- particularly history of the Christian church. Church history reveals people, groups, tribes, and nations in which Christianity spread. History is not orderly. At times it is very messy, with humans who greatly mess up, and others who display amazing sacrifice. There are councils where the orthodox faith is confirmed -- in spite of politics, bloodshed, rancor, and deception.

I just discovered an interesting history series by Dr. Maxie Burch of North Phoenix Baptist Church. If you go to iTunes, got to Podcasts, Audio Podcasts, Christianity, History of Christianity by Dr. Maxie Burch.

There is much that is helpful in this series. Reading and listening to history from multiple sources gives different perspectives that helps understanding history. One helpful notion is that history does not happen in neat logical compartments, but rather it all happens at once and unplanned by the historical participants.

Also -- I heard the helpful reminder that the classic proofs of the existence of God use the word proof in a different way than I often use the word. I have a mathematics background and proof in my mind is a formal logical argument with axioms and premises that result in a necessary logical conclusion. Proof, in the sense Thomas Aquinas used it, is an observation, a suggestion pointing to the existence of God -- not an airtight case.

This is helpful in seeing how to employ these arguments. These are not to be used as a proof beyond all doubt. Instead these paint a picture that suggests it is reasonable that God exists -- that it is just as reasonable as any alternative.

A suggestion, an observation, rather than an earnest formal proof. In conversations these can be employed as a reason when asked why you believe, why you find faith in God compelling against the alternatives. That is the home where these proofs may be the most effective.

Worship and Music

2008-08-14T00:01:00.004-04:00

My church is going through a transition on the worship director. The current worship director is a phenomenal man, gifted in music, not only in leading music, but in composing and arranging. He has written a book on worship that is used in a seminary. Not only is he gifted, but his wife as well. Both contribute substantially to the worship and music of the church. They are leaving soon to go to a church in California.

Our music in the church has been great. The music makes extensive use of electric guitars and drums. My tastes, however, are heavily on the "traditional" side. My heart resonates with hymns. I prefer piano, pipe organ, violin, cello. I like choirs -- if done well, and it is hard for small to medium churches to do it well.

I've always enjoyed classical music since childhood. But I also enjoyed rock to some extent. My musical preferences in worship have changed over the years. Our church has always tended towards contemporary music with a nod in past years to traditional. It was one of the things that drew me to the church -- but my tastes have become much more traditional. However, many in my church prefer contemporary music.

Some people have left our church over the issue of music. These people have preferred traditional music. I have talked with several and encouraged them to stick it out -- to no avail. Why stay if you don't like the style of music? Why do I stay?

First, the gospel of Christ is being proclaimed in the worship service. This is done in the music, the liturgy, the preaching, and in the sacraments. Throughout the service we hear how we fall far short of reaching God's standard of perfection, but we have the sweetness of the gospel of Christ redeeming us.

Secondly, our church is a community of committed believers, working together in Christ. I have submitted myself to this church and am accountable to the body. It is a community that loves and helps my family. I can't tell you how many ways we have been helped, how others have helped in raising our children, how the church has helped me in so many ways.

Thirdly, I am a servant in the community of believers. I am committed to the body. I need to serve the church even more than I am now.

Pulling away from the church means tearing away from a place where the gospel is proclaimed. Sure I can go to another church where the gospel is proclaimed -- but there is a sense where I have been nurtured in a special way at this church with the gospel. In many ways it will not be the same. Also, pulling away tears at the fabric of Christian community, which is a very precious commodity. Finally, I would be shirking my responsibility to the Christian community.

Can I worship God effectively with music I don't like? Absolutely I can. I do struggle with the music, my heart is not fully content. But I realize I need to be more fully engaged in the words in the songs and in worship. While I might not be emotionally carried away as I might be with a pipe organ, I also know that my emotions do not necessarily indicate what is going on in the worship service. God is at work in the congregation. The church service is not about me. It is about God for us, all of us, where God is taking his delight in us, even in our individual struggles, or more pointedly, in spite of my sin.

My struggle with worship is good. I need to go through this to see what is really important. In this, I think I am seeing what worship is more clearly than if I were elevated to the emotional highs of my enjoyment of traditional music

The Utility of Cosmological Arguments

2008-08-13T00:01:00.000-04:00

To review the Kalam Cosmological Argument:


1. Whatever begins to exist has a cause for 
   its existence.

2. The universe began to exist.

3. Therefore the universe has a cause for
   existence.

All the versions of the Kalam arguments I have read are not formal proofs. Usually people will accept point 1. Point 2 is the point of dispute. The persuasiveness of the argument depends on whether those who consider the argument perceive whether the problems with infinities means the universe (or meta-universe) cannot be infinite in its duration. If the meta-universe cannot be infinite in its duration, then the universe began to exist and point 3 follows.

I have talked with people with the concepts of the Kalam argument. All where intelligent non-scientists with technical undergraduate degrees (math, computer science, physics, engineering). Infinity is not a problem with almost all people I talk with. Thus the Kalam argument does not carry much weight.

Does this mean the Kalam argument is useless? I don't think so. I think it has use -- but it cannot be relied upon exclusively. It needs to be part of a full spectrum of presenting the case for God. There are other arguments: the moral argument, the cosmological design argument in its more modern version dealing with fine tuning, historical evidence for Jesus' resurrection, and evidence in changing lives.

So by itself, the Kalam can be persuasive, but not necessarily -- not with a segment of people comfortable with the concepts of infinity. Another point to consider is the persuasive power of the Holy Spirit. Ultimately, it is God's grace that opens the eyes to his presence.

Why Consider Old Universe Arguments?

2008-08-12T00:01:00.002-04:00

Most theologically conservative Protestant or Evangelical Christians believe that the universe was created in the span of six 24-hour days, 6,000 to 10,000 years ago. The Kalam Cosmological Argument for the existence of God, in its modern forms, such as the version employed by William Lane Craig, are assuming the existence of an old universe, with an age in the billions of years old. Perhaps many young universe creationists would dismiss the Kalam argument out of hand because of its old universe assumptions. However, I would advocate considering using the Kalam argument, even if you are a young universe creationist.

The reasons I advocate employing old universe arguments are as follows:

1. Most of the scientific literate people people assume an old universe. Arguing for a young universe adds to the work of a young universe creationist to provide reasonable evidence for a young universe. Depending on the background of the people you are talking to, providing the evidence can be a lot of work.

2. Providing evidence that the universe began to exist is relatively easy. Simply observing that the universe is expanding implies an upper bound to the age of the universe. This is because if you "run the clock backwards" on the current expansion rate, you will arrive at a time where you cannot run the clock backwards any more. The universe is already at an infinitely small point.

3. Using the assumptions of many scientists and showing an absurdity means that the original assumptions were wrong. This is the point of the Kalam argument.

The last point needs a little more explanation. One way to show that an eternal uncaused agent, namely God, created the universe is to assume the opposite and show there is a contradiction that results from that opposite assumption. So, if we assume that the uncaused eternal God did not create the universe, then there must be some other mechanism that created this universe. The mechanism most often used by scientists speculating on this is an infinite series of universes. When we assume such a thing, there results some serious contradictions and problems, such as what I noted in, Meet Yourself, Infinitely Many Times. Therefore an uncaused eternal agent caused the universe to begin to exist. This removes the obstacles for considering the existence of God sooner than if you construct the case for a young universe. When the possibility for God's existence is on the table, then other evidences can be considered, such as the resurrection of Jesus.

In this argument you do not need to surrender the view of a young universe. You can assume, for advancing the argument, an old universe and then look at the evidence for God's existence even in those conditions. This gives breathing room to consider the case for Christ.

The Kalam Cosomological Argument

2008-08-11T00:01:00.006-04:00

The past series of blog entries have loosely presented the Kalam Cosmological Argument for the existence of God. The argument has been popularized by William Lane Craig. Dr. Craig's outline is[1]:


1. Whatever begins to exist has a cause of its
  existence.
2. The universe began to exist.

  2.1 Argument based on the impossibility of an
      actual infinite.

        2.11 An actual infinite cannot exist.
        2.12 An infinite temporal regress of
             events is an actual infinite.
        2.13 Therefore, an infinite temporal
             regress of events cannot exist.

  2.2   Argument based on the impossibility of
        the formation of an actual infinite by
        successive addition.

        2.21 A collection formed by successive
             addition cannot be actually infinite.
        2.22 The temporal series of past events
             is a collection formed by successive
             addition.
        2.23 Therefore, the temporal series of
             past events cannot be actually
             infinite.

3. Therefore, the universe has a cause of its
  existence.

In the approach I am more comfortable with is:


1. Whatever begins to exist has a cause of its
  existence.
2. The universe began to exist.

  2.3 The argument based on the absurdity of an
      infinitely generated series or branching trees
      of universes.

      2.31 All highly improbable non-impossible
           universes will occur infinitely many
           times.
      2.32 The infinite number of improbable universes
           makes scientific understanding of the
           history of any particular universe impossible.
      2.33 Therefore an infinitely generated universes
           is defeats scientific investigation and
           logically impossible.

3. Therefore, the universe has a cause of its
  existence.

The reason I am more comfortable with this approach is because I don't think Dr. Craig's arguments against an actual infinity (argument 2.1) and against the formation of an actual infinity from successive addition (argument 2.2) in his article are strong. Perhaps it is my bias towards my mathematical training going through set theory. In Dr. Craig's argument against an actual infinity, he simply stated the consequences of Hilbert's Hotel are absurd[2].

Simply declaring infinity absurd after discussing the Hilbert Hotel example points out a weakness of argument 2.1. For many people, simply stating the example is grounds enough for rejecting that actual infinity is possible. But there are others, such as astrophysicists at some leading research institutions (such as Caltech and MIT) who do not see it is necessarily impossible. Simply believing something because they are a professor at a prestigious college or university is an unwarranted appeal to authority -- but it does show that infinities are thought possible by intelligent scientists.

Argument 2.2 has some issues too -- which I thought I wrote about in a previous blog, but I don't see it. I will comment on this later[3].

Argument 2.3 is presented in the previous blog, Meet Yourself, Infinitely Many Times.

Notes/Sources:

[1] See William Lane Craig's presentation of the Kalam Cosmological Argument. The outline is copied directly from Dr. Craig's article.

[2] I write about Hilbert's Hotel in Can an Actual Infinity Exist?

[3] Actually I did comment about this in a comment. Alvin Plantigna critiques Immanuel Kant when he makes a similar argument. See p. 25 of Warranted Christian Belief by Alvin Plantinga.

Meet Yourself, Infinitely Many Times

2008-08-06T00:01:00.005-04:00

In a previous series of posts I presented a proposal by some astrophysicists for our universe to be one of a series of spontaneously generated universes. In fact, the proposal is that this universe is one of an infinite number of universes that have been generated spontaneously. I've already given two critiques of that view, and I will give another critique.

Infinite number of universes. Why infinite? Because there is a recognition on the part of these astrophysicists, to quote the highly philosophical movie, The Sound of Music, "nothing comes from nothing." Either you have an uncaused agent that started the who process, which sounds awfully like God, our you have an infinite tree of generating universes, branching into other universes, and so on. In the previous critiques I discussed supertasks and the problem of counting down from infinity. Now I will examine another issue.

Infinite number of universes. Imagine the possibilities. Because there are an infinite number of universes, anything that is extremely unlikely to occur, and I mean extremely unlikely but not absolutely impossible, will have occurred infinitely many times. Is evolution unlikely? Is it extremely unlikely? Well, in an infinite number of universes it occurred infinitely many times.

But, think of this. What is the likelihood that our universe just simply spawned into existence just 10 minutes ago? All the galaxies, everything that we see in telescopes, everything, from the Hubble Telescope, to this planet, to the computer that you are looking at this blog entry from, everything, just 10 minutes ago.

Wait a minute. The Hubble Telescope was blasted in to orbit sometime ago, years ago, and we got all those great pictures. The people in the same room I am sitting in can vouch for that. -- But suppose the universe spontaneously generated just 10 minutes and 3 seconds ago (you can read quickly, can't you? -- from the first time I proposed a 10 minute universe). You were generated 10 minutes ago with memories, along with everyone else you run into. They happen to match -- for the most part. Have you ever noticed that you and your spouse's memory don't quite jibe. You talk about past events, and there are things that don't quite match up? Or you and your boss (or school teacher or professor)? That's because in this spontaneous generated universe the memory "generation" was not quite perfect.

A 10 minute universe? That's impossible -- or is it extremely, extremely unlikely? If it is not absolutely impossible out of the laws of quantum physics, or whatever the physics is at work in the metauniverse we came from (or multiverses), then such a universe, identical to our present universe, did indeed spontaneously generate -- not just once or twice, but infinitely many times.

Infinity is a two edged sword. It allows for fine tuning of the universe and evolution. It also allows for really crazy universes, ones that look identical but are generated differently.

But that isn't all the weirdness with infinitely generating universes.

Okay, you're reading this and you are not buying this blog argument at all. But there are infinitely many universes where you are reading this, and because of some quantum activity in your head, at this point, you're changing your mind and saying this argument is convincing -- an infinite number of you (along with an infinite number that are not changing their minds). This raises the question, how do we know are thinking accurately that reflects the real universe? We are seekers of truth, but how do we know we are grasping the truth? If we are an infinite assemble of universes, with infinite variation that is not ruled out as being absolutely impossible, then there exist an infinite number of us with a staggering number of different views about life, the universe, and everything -- and within each of those infinite numbers for each view, there are an infinite number where each are absolutely sure their view is correct.

Imagine this -- Hillary Clinton leaves Bill and elopes with Rush Limbaugh. Extremely unlikely -- but not theoretically impossible from the physics point of view? Then it happens during August 2008 in an infinite number of other universes. Or try this one, conservative political pundit and adviser Mary Matalin marries arch liberal, rival adviser and pundit James Carville. In infinitely many universes they do not, but in infinitely many universes they do.

David Hume argued that miracles are impossible. But it is recognized today that technically miracles are not absolutely impossible -- just extraordinarily unlikely. Let's say that God doesn't exist, and there are an infinite number of universes that have been spawned. The miracles of Jesus, naturally speaking, are extremely unlikely -- everything from turning water into wine, healing the sick, raising the dead, and his resurrection. Naturally speaking, very, very, very unlikely. But in infinitely generated universes, Jesus lived and did all those things -- in an infinite number of universes.

So, is our universe 12 minutes old, or billions of years old? In infinitely generating universes, there is an infinite set that are 12 minutes old, an infinite set that as 2 hours old, as well as an infinite set that are billions of years old.

Proposing infinitely generating universes saws off the branch we are sitting on, epistemologically. It defeats whether we can know the truth.

There is a simpler, more logically consistent solution. In the beginning, God created the heavens and the earth.

Zeno's Paradox

2008-08-01T00:01:00.003-04:00

Zeno of Elea[1] lived from 490 BC – 430 BC, although the times are not certain[2]. Zeno is noted for several famous paradoxes. I will present one of them from the Stanford Encyclopedia of Philosophy:

Suppose a very fast runner — such as mythical Atalanta — needs to run for the bus. Clearly before she reaches the bus stop she must run half-way, as Aristotle says. There's no problem there; supposing a constant motion it will take her 1/2 the time to run half-way there and 1/2 the time to run the rest of the way. Now she must also run half-way to the half-way point — i.e., a 1/4 of the total distance — before she reaches the half-way point, but again she is left with a finite number of finite lengths to run, and plenty of time to do it. And before she reaches 1/4 of the way she must reach 1/2 of 1/4 = 1/8 of the way; and before that a 1/16; and so on. There is no problem at any finite point in this series, but what if the halving is carried out infinitely many times? The resulting series contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. However it does contain a final distance, namely 1/2 of the way; and a penultimate distance, 1/4 of the way; and a third to last distance, 1/8 of the way; and so on. Thus the series of distances that Atalanta is required to run is: …, then 1/16 of the way, then 1/8 of the way, then 1/4 of the way, and finally 1/2 of the way (of course we are not suggesting that she stops at the end of each segment and then starts running at the beginning of the next — we are thinking of her continuous run being composed of such parts). And now there is a problem, for this description of her run has her travelling an infinite number of finite distances, which, Zeno would have us conclude, must take an infinite time, which is to say it is never completed. And since the argument does not depend on the distance or who or what the mover is, it follows that no finite distance can ever be traveled, which is to say that all motion is impossible. (Note that the paradox could easily be generated in the other direction so that Atalanta must first run half way, then half the remaining way, then half of that and so on, so that she must run the following endless sequence of fractions of the total distance: 1/2, 1/4, 1/8 ….)[3]

Zeno's motivation was to prove that there cannot be a plurality of entities. Instead, everything is one. Motion is an illusion. There have been many attempts to answer this paradox.

One solution came with the advent of Calculus, by Sir Isaac Newton and Gottfried Wilhelm Leibniz. A means was developed to sum an infinite series of diminishing intervals, showing that the sum was finite. Other mathematicians, such as Cauchy, further refined Calculus, putting on a firmer rigorous foundation. However, while Calculus and General Relativity view space and time as a continuum of infinite points between any interval, Quantum Physics assumes a discrete, rather than a continuous, nature to space and time. Ultimately, Quantum Physics might prove to be the ultimate answer to this paradox -- because space and time are not infinitely divisible.

However, there is a related concept, called a supertask[4]. A supertask is an action that takes a finite time to complete. If Atalanta's run has infinite steps with an infinite series of supertasks associated with it, the run will never complete. But since space and time appear to be discrete, not continuous, supertasks do not apply to this particular Zeno paradox. But there are other ways in which supertask analysis gives us interesting insights.

For instance, lets assume that humans that with Christ's second coming, humans who belong to Christ are raised and live forever. Let's further assume that resurrected humans start with a finite amount of knowledge, and that they learn new knowledge incrementally in finite amounts throughout the rest of eternity. While people gain infinite knowledge? The answer is no. Supertasks can be applied to show that humans will never achieve infinite knowledge. This is because to acquire infinite knowledge, people will go through the task of gaining knowledge, which takes some amount of finite, non-zero time. This acquisition of knowledge is a supertask. The activity can never be completed and thus infinite knowledge never achieved.

What about God? God has infinite knowledge in that he is aware of infinite things, as shown in the last post. Did God ever not have infinite knowledge? No. This is because the previous analysis of humans, starting with finite knowledge, shows that humans will never gain infinite knowledge. Thus God's knowledge was always infinite, always complete.

This is an important thing to note about God. God, being eternal, having the unchanging properties of infinite knowledge, is a logically consistent being.

What about the universe? Is it possible for our universe to be part of an infinite succession of universes, that ultimately spawned this universe? Supertasks would suggest not. William Lane Craig frames the argument this way:

One cannot form an actually infinite collection of things by successively adding one member after another. Since one can always add one more before arriving at infinity, it is impossible to reach actual infinity. Sometimes this is called the impossibility of "counting to infinity" or "traversing the infinite." It is important to understand that this impossibility has nothing to do with the amount of time available: it belongs to the nature of infinity that it cannot be so formed[5].

In particular, the reason this infinity cannot be formed is because each spawned universe is a supertask that takes a non-zero amount of time. Further, it is postulated in the "spontaneously generating" universes that this universe is the result from an infinite sequence of universes in the past.

Someone might reply to this argument of supertasks to say that there never was a beginning point. An infinite collection of universes could happened, in which case case our universe arose from that collection. But the solution stated is a mirror reflection of the problem of a person counting to infinity, only you start with zero and count backwards[6].

For example, imagine you come across a man who claims to have been counting down from infinity and just reached zero today. The problem is that the man has been counting down from infinity forever, but yesterday was forever also, and so was the day before, and the year before. Why didn't that man reach zero then at those times? He should have already have been finished by any of those times. Thus there is no time when we would find a man finishing counting down to zero from infinity.

This is another critique of the infinitely spontaneously generating universes. A logical, simpler explanation is that an eternal being, God, created the universe.

But wouldn't God be in a temporal infinity, and don't we find a similar paradox for God's first action in creating the universe? Here is where we find God different from the universe. There was no temporal succession "before" the universe came into existence. Time and space came into existence when the universe began, so there is no infinite regress on the part of God to create the universe.

I am very finite, and so I end this finite post for tonight....

Notes/Sources:

[1] Picture of Zeno of Elea is from MacTutor article on Zeno.

[2] Zeno's Paradoxes, Stanford Encyclopedia of Philosophy.

[3] ibid

[4] ibid, Supertasks.

[5] William Lane Craig, The Existence of God and the Beginning of the Universe.

[6] ibid. This point and the following example are taken from Dr. Craig's article.

God is Infinite

2008-07-31T00:01:00.008-04:00

In the previous blog entry I posed the question, is God's omniscience about events (temporal events) infinite? It turns out it God's knowledge of events is infinite, given the following

(1) Before the creation of the universe there was no time, no events.
(2) The universe is finite.
(3) Time is a series of intervals, possibly the length of Plank time -- (or any small interval of time). This would mean between any two intervals of time, whether it be seconds, years, or millennia, there are a finite number of the smallest possible time intervals between those periods.
(4) In the new heavens and new earth, time continues to be Plank intervals, which continues forever.

We should make some definition of event:
(5) An event is a configuration in the universe that is associated with an individual time interval.

Now, there are some issues with defining events like this, but let's run with this for now.

To get a little formal, we have:

A set of time intervals, T, which contain the smallest consecutive intervals of time, t₁, t₂, t₃, ... . This corresponds to all the time intervals of statements (3) and (4), the time intervals since the creation of the universe on into the new heavens and earth.

A set of configurations, C, which contains configurations c₁, c₂, c₃, ... . A configuration is an arrangement of matter and energy in the universe. The set C contains all the configurations of matter and energy in the universe from its beginning, on into all the future, including the new heavens and earth.

A set of events, E, where each of the elements, e₁, e₂, e₃, ... is a set of pairs of configurations associated with times, such that e₁ = (c₁, t₁), e₂ = (c₂, t₂), e₃ = (c₃, t₃), ... . This set E corresponds to all the events since the creation of the universe on into the future. Each time interval in T, t_j, corresponds with some configuration c_k in C to make the element (c_k, t_j) which is in the set of events E.

Premise: God's omniscient knowledge of events, which is contained in set E, is complete.

An observation. The set of events, E, does not have to have unique configurations for each association with a T (time) element. For instance, configuration c₃₁₃₄ can be associated with time t₁₆₀₃₄ and associated with time t₉₂₀₄₃₁. So (c₃₁₃₄, t₁₆₀₃₄) and (c₃₁₃₄, t₉₂₀₄₃₁) can be valid members of the event set E.

From statement (4), the set T, time intervals, goes on forever.

Definition: Finite Set. One way to define a set A is finite if A is either empty or there is a way to map the elements of set A with a subset of the natural numbers = {1, 2, 3, ..., k}, where k is a specific number in the sequence of counting the numbers in the natural number set and each element of a of A uniquely maps to the numbers 1, 2, 3, ..., k.

Definition: Infinite Set. A set B is said to be infinite if the set is not finite.

So, let's say we have a set of 16 minute intervals -- this is just a goofy example -- of {16, 32, 48, 64}. We can map all the elements to the natural numbers this way:

16 maps to 1

32 maps to 2

48 maps to 3

64 maps to 4

In fact, we can have the rule for each element in the 16 minute interval set, divide it by 16, and that is the element in the natural number set. Because we found we can map the 16 minute interval set to the first four elements of the natural number set, the set is finite.

Our original set of time intervals, T, is infinite. This is because if T was finite, there would be a way to uniquely map all the elements of T to a subset of the natural numbers of size n. But that would violate that the set T goes on forever because it would stop at time corresponding to the natural number n.

What about the set of events, E? All of the events of E are of the form (c_k, t_j), where t_j is an element of T. We have constructed E in such a way that all the elements of T uniquely map into E. We saw that each element of T maps uniquely to the natural numbers in such a way that there is no number in the natural numbers that would be the last number of the mapping. We have a way to maps all the elements of E uniquely onto T, i.e., (c_k, t_j) in E maps to t_j in T, which in turn maps to k in the natural numbers. The set E cannot be finite, because if it were, there would be some number m, such that all the elements of E would map to 1, 2, 3, ..., m. But that would mean that all the elements of T would map uniquely in the same way, making it finite, which contradicts that we saw it was infinite.

Therefore, the set E is not finite, but infinite. Since God's knowledge of set E is complete, there is a unique one to one mapping of God's knowledge to the set of E, thus demonstrating that God's knowledge of events is infinite.

Notes:

The picture is from the Hubble website. It is the Hourglass Nebula.

The definition of infinity is based on one of the definitions from Elements of Set Theory, Second Edition, by Peter W. Zehna and Robert L. Johnson (1972, Allyn and Bacon, Inc, Boston, MA), pp. 101-107.

God Not Infinite?

2008-07-30T00:01:00.008-04:00

John Duns Scotus (1266-1308) was an important medieval philosopher and theologian. Scotus thought deeply about an important attribute about God -- his infinity. Now infinity is something that I studied in college. It was a fascinating topic for me as a kid because of its bizarre, counter intuitive features. I ate up this kind of stuff, it is why I choose to major in mathematics.

Infinity in mathematics deals with an infinite number of parts, known as sets. Scotus wants us to shift from thinking about an actual quantitative infinity to thinking about an actual qualitative infinity[1]:

Think of some quality (say, goodness) as existing infinitely: so that there is, as it were, no more goodness that you could add to that goodness to make it any greater. That's infinite goodness. But notice that you can't think of infinite goodness as in some way composed of little goodness-bits (just an infinite number of them). If I say that an angel is better than a human being, I can't mean that a human being has a certain number of goodness-bits while the angel has that many plus some extras. Rather, the specific degree of goodness of a thing is just an intrinsic, non-quantitative feature of that thing. Infinite being is just like that. Scotus describes it as "a measure of intrinsic excellence that is not finite." This is why the concept of "infinite being" is the simplest concept available to us for understanding God[2].

God's presence is not to be thought of God extending bits and pieces of himself all over the universe, but rather a qualitative presence where God is fully present everywhere:

Where shall I go from your Spirit?
Or where shall I flee from your presence?
If I ascend to heaven, you are there!
If I make my bed in Sheol, you are there!
If I take the wings of the morning
and dwell in the uttermost parts of the sea,
even there your hand shall lead me,
and your right hand shall hold me[3].

Is there an aspect where God can be spoken of quantitatively infinite? How about God's omniscient knowledge about events? It depends on whether there are infinite events. One possible theory is:

(1) Before the creation of the universe there was no time, no events.
(2) The universe is finite.
(3) Time is a series of intervals, possibly the length of Plank time[4]. This would mean between any two intervals of time, whether it be seconds, years, or millennia, there are a finite number of the smallest possible time intervals between those periods.
(4) In the new heavens and new earth, time continues to be Plank intervals, which continues forever.

God comprehends all the time intervals in all the places in the universe for all time, including the new heavens and earth. At any slice of time, there is a finite number of events across all the universe. The number of events is huge, possibly beyond what we can name or fathom, but nevertheless finite. As we add successive time slices, each addition of a time slice with all the events is finite. As time goes on, at no point is there an infinite point of time, or a time slice that is infinite. It will always be finite. The sum of all the time/event points is finite as we go on into eternity. Never, at any time will it achieve infinity.

This last observation means that perhaps God's knowledge does not need to be infinite about events. Infinity, in this case, is a limit concept (as it is in Calculus) that is actually never achieved.

If that is the case, then some logical paradoxes can be avoided about the knowledge of God with events. Some of the issues of Godel's Theorem, that knowledge about infinite sets cannot be both logically complete and consistent. When we speak that God is omniscient and all powerful, those are spoken of in the sense that God can know all that is possible to know and God can do what is not logically forbidden or outside of his character.

It is an interesting speculation -- and that is all it is, a speculation.

But I thought of a simple proof that God's omniscience of events is infinite. Next post...

Notes/Footnotes:

[1] John Duns Scotus, the Stanford Encyclopedia of Philosophy

[2] ibid

[3] Psalm 139:7-10

[4] See Plank Time in Wikapedea.

Can an Actual Infinity Exist?

2008-07-28T00:01:00.001-04:00

Can an actual infinity exist?

I have been recently reading William Lane Craig at his website, Reasonable Faith. I also have the second edition of his book, Reasonable Faith, but he is coming out with his third edition of the book, which significantly expands the material.

One of Dr. Craig's specialties is the Kalam argument for the existence of God. His website, under the scholarly section, has several articles discussing the Kalam argument, along with discussing critiques people have made about the argument. The article I am reading is here.

One of the central arguments in the Kalam argument is that there cannot be an actual infinity. Dr. Craig cites an example of the weirdness of infinity by discussing the Hilbert Hotel.

Imagine a hotel that has an infinite number of rooms. The first room is numbered 1, the second is numbered 2, the third 3, etc. You are a traveler and you come to the hotel and ask for a room. The manager at the desk informs you that all the rooms are occupied, the hotel is full. However, the manager is clever, he says he will make a room available for you. He will have the person in room 1 move to room 2, the person in room 2 move to room three, etc. Thus, without adding any rooms or removing any occupants, the hotel that was once full now has a room.

But it gets stranger. The manager has a sudden insight. I will move each person in each room to 2 times the room number. So the person in room 1 moves to room 2, the person in room 2 moves to room 4, the person in room 3 moves to room 6, the person in room 4 moves to room 8, and so on. Now without adding any rooms or removing any persons, the hotel that was full now has an infinite number of empty rooms -- as well as having an infinite number of occupied rooms.

It is William Craig's contention that such an infinity cannot exist in reality. Part of Dr. Craig's contention is that we have the contradiction of two equal numbers, infinity, being in a contradictory state of where one infinity becomes less to the same identical infinity.

My critique of Dr. Craig's comments is that mathematicians do not speak of an infinite number which can be compared to other infinite numbers in the same way as finite numbers are compared. Otherwise the branches of mathematics which work with infinite sets would have logical inconsistencies in them -- and mathematicians hate logical inconsistencies in their mathematical systems and study hard to remove them.

But Dr. Craig does bring up a point which I have not thought much about. Can an actual infinity exist in the real realm of the universe? I think I am beginning to see his point, that it cannot. But I want to think why it cannot. I have some vague notions and I will sleep on it and continue the discussion later.

3 Years

2008-07-27T21:10:00.002-04:00

This July I have been blogging now for 3 years. Over 300 posts, I don't know how much more than 300.

Its been fun. I have met many delightful people on the Internet. A few people regularly read this blog, which I find amazing, given my tortuous writing style that is in severe need of editing -- and even simple proof reading.

Blogging for me is a form of journaling. I find when I write ideas they become more solidified, concrete, more thought out. That happened when I wrote about Revelation, and recently about Cosmology. In Revelation, it allowed my to explore the different ways the book is interpreted and select an approach that made the most sense to me. With Cosmology, I realized I had not really studied the topic in a number of years. The science had changed so much from when I looked at it before. In cosmology I have not even begun to scratch the surface, there is so much to learn. But I think I am beginning to see the big picture. It has deepened my awe of the universe and even more so the Creator of the Universe.

Critique of Spontaneously Generating Universes, Part 2

2008-07-27T00:01:00.000-04:00

In my blog article, Spontaneously Generating Universes, I discussed a speculative view by some astrophysicists on how our universe could be spawned from another universe. To review, it is assumed that our universe is now expanding into an accelerated phase of expansion caused by dark energy. This dark energy is also assumed to be a special kind of energy, vacuum energy that is the Cosmological Constant. As our universe expands, and it is presumed that the "parent universe" of our universe did the same thing, it is entering a phase which will ultimately bring it into basically empty expanding space that only has the constant dark vacuum energy. While the entropy of the overall universe grows unbounded, any finite regions of the universe will have its entropy drop to exceedingly low values. In these low entropy volumes of space, it is proposed that the quantum fields from the dark energy will at some point in time have a quantum fluctuation, generating a extra low entropy dark repulsive energy, which will suddenly inflate into another baby universe of its own. In a brief moment of time, that tiny region will inflate from a small dense ball of dark energy, less than a millimeter in size, into a volume of space exceeding 100 million light years. At that point, the dark energy will largely "decay" into more common forms of matter and energy -- and a new universe is born. This is illustrated below:

This is a schematic, imagining our universe being a two dimensional universe which is a surface of an expanding cone. In this diagram, several universes are shown to be spawning from other universes.

The diagram is incomplete in several ways. The first is the "vertical funnel" universe is also the result of another universe, which in turn is the result of another universe, which in turn..., well, you get the point.

In this model of cosmology we have an infinite sequence of universes. In fact, it is more than that. It is an infinite sequence of infinite universes, which also have an infinite number of finite universes.

The reason there is an infinite number of universes is because this sequence is proposed by these astrophysicists to have no beginning. Because there is no beginning, there is at least one universe that have been expanding infinitely, spawning an infinite number of universes, which in turn are infinite.

The diagram above, which I made from Google's SketchUp (a really slick tool, and free!), is typical of what some cosmologists also sketch illustrating the principles of this kind of multiverse. However, how would I represent an infinite number of infinite universes? Contemplating this reveals some problems.

The first problem is what will prevent each of the multiverse "cones" from intersecting and interfering with each other. If we simply assume we are lucky in this universe that no other universe has "crashed" into ours, then we are assuming a privileged position, violating one of the major cosmological assumptions known as the Copernican Principle.

An infinite number of universes of infinite size. Yet none of them have been seen interacting with our universe. How can that be? Maybe there are an infinite number of dimensions which those universes occupy. It would mean that each universe would spawn off a completely new dimension. Why would that be the case?

This infinite number of infinite universes,in my opinion, is a fatal flaw of this proposed model of how our universe came into existence. An infinite number of non-intersecting dimensions, which each universe inflates into.

Given the two explanations for the origin of our universe, an infinite number of infinite universes, verses one infinite, uncaused God, bringing our universe into existence, Occam's Razor (the principle of taking the simplest explanation as the real explanation) suggests that God is the cause of our universe.

I will continue this analysis of the spontaneously generating universes in upcoming posts.

Import Excel Tables Into Blogger

2008-07-23T19:05:00.012-04:00

(Alternative title, Export Excel Tables into Blogger) Every once in a while I like to create tables in my blog. Blogger allows you to do this, but you've got to do this in "Edit Html" mode and enter the HTML table codes directly. Those of you in Blogger who do this also realize that simply entering table information the normal way, with carriage returns to break up the table elements, end up with lots of extra lines. There are two ways to eliminate the extra lines: (1) get rid of all the carriage returns, or (2) create a CSS style and put your table inside the style div.

Now I am a lazy sort. I would prefer to make my tables in Microsoft Excel and export the results to Blogger. So, for instance, here is an Excel table just created:

What I want to do is to export the table and put into Blogger that looks like this:

Source	Comments	Extra Info
Original Export Excel Tables	This tells you how to Export Html
Information on Blogger Tables	This tells you how to change the style of blogger tables.	Old Way is Here
More information on Blogger Tables	Another CSS Style.

Well, at first I tried exporting the table from Excel directly. It created HTML table code, but with lots of extra stuff that Blogger was not too happy with. So then I Googled to see if there were Excel utilities that would do what I wanted. I found one here that did 90% of what I wanted (also the first hyperlink entry in my table above). But it missed two things: (1) the CSS style sheet creation, and (2) copying the embedded hyperlinks I had in the Excel Spreadsheet.

So since this was my first VBA program, I followed the information presented in the blog entry, changed the GenerateHTML function to check for the presence of Hyperlinks in the cells and fetch the information. The new GenerateHTML subroutine that replaces the previous one is:



Private Sub GenerateHTML(ByVal sFileName As String, ByVal sTitle As String)
    Dim iFileNum As Integer
    iFileNum = FreeFile
    Open sFileName For Output As iFileNum
    Print #iFileNum, "<HTML>"
    Print #iFileNum, "<TITLE>" + sTitle + "</TITLE>"
    Print #iFileNum, "<BODY>"
    Print #iFileNum, "<P><B><FONT SIZE=5>" + sTitle + "</FONT></B></P>"
    
    Print #iFileNum, ""
    Print #iFileNum, ""
    
    Dim lRowCount As Long
    Dim lRow As Long
    Dim iColCount As Integer
    Dim iCol As Integer
    Dim iCell As Range
    Dim iStr As String
    Dim iCount As Integer
    Dim QUOTE As String
    QUOTE = Chr$(34)
    
    
    Print #iFileNum, "<style type=" & QUOTE & "text/css" & QUOTE & ">.nobrtable br { display: none }</style>"
    Print #iFileNum, "<div class=" & QUOTE & "nobrtable" & QUOTE & ">"
    
    lRowCount = ActiveSheet.UsedRange.Rows.Count
    iColCount = ActiveSheet.UsedRange.Columns.Count
    Print #iFileNum, "<TABLE BORDER=1>"
    For lRow = 1 To lRowCount
        Print #iFileNum, "<TR>"
        For iCol = 1 To iColCount
            Print #iFileNum, "<TD>"
            
            Set iCell = Cells(lRow, iCol)
            iCount = iCell.Cells.Hyperlinks.Count
            If iCount > 0 Then
                iStr = iCell.Cells.Hyperlinks.Item(1).Address
                Print #iFileNum, "<a href=" & QUOTE & iStr & QUOTE & ">" & iCell.Cells.Value & "</a>"
            Else
                Print #iFileNum, CStr(Cells(lRow, iCol).Value)
            End If
            Print #iFileNum, "</TD>"
        Next iCol
        Print #iFileNum, "</TR>"
    Next lRow
    Print #iFileNum, "</TABLE>"
    Print #iFileNum, "</div>"
    Print #iFileNum, ""
    Print #iFileNum, ""
    Print #iFileNum, ""
    Print #iFileNum, ""
    Print #iFileNum, "</BODY>"
    Print #iFileNum, "</HTML>"

    Close iFileNum
End Sub

You create the table you want in Excel, run the macro from inside "tools, Macro, Macros ...". A browser will ultimately pop up and you will see the table in the Browser. It might look a little odd, like this:

But don't worry about it. It will work fine in Blogger. You need to do a "view, Page Source" (Firefox, I don't know what that awful Internet Explorer menu sequence is to view the HTML source -- but you can figure that out), and then cut and paste the table from the source. You will see


<HTML>
<TITLE>Sheet1</TITLE>
<BODY>
<P><B><FONT SIZE=5>Sheet2</FONT></B></P>

At the beginning. Ignore that part, as well as the very last part:


</BODY>
</HTML>

Cut and paste into Blogger (in Edit HTML mode) all the rest. Then you will have a table like what I got -- which was actually how I created the table in this entry.

If you are interested, I could either email or post the Excel macros on a website (any suggestions where?).

One last note: the table in "Preview" mode or in "Compose" mode will look strange. It will look okay when you publish it.

Cosmology Resources

2008-07-23T00:01:00.004-04:00

This is the very beginning of a cosmology resource worksheet. It will be updated as I find more resources. I have yet to enter Intelligent Design sites. I will also cleanup the table format.

Key:
Math -- A Algebra, C Calculus
Difficulty -- 1 the most easy, 10 the most difficult

Resources:

Category	Name	Type	Math	Difficulty	Comments
?	The Universe Is Not Ergodic	Video, Audio		?	Not evaluated.
COS	The Warpings of Spacetime	Video		2	Cosmology Introduction, assumes no prior knowledge
COS	Our Preposterous Universe	Slides		2	Cosmology Introduction, assumes no prior knowledge
COS	Why is the Past Different from the Future?	PDF	A	3	Intro to idea of spontaneously generating universes.
COS	Cosmology Update	Audio		2	NPR interview of 3 astrophysists on expansion.
COS	Universe Timeline	HTML		2	Introduction to the Big Bang Cosmology
COS	Max Tegmark, MIT Astrophysist	HTML		Varies	Various articles by Dr. Tegmark, including parallel universes
COS	Ned Wright's Cosmology Tutorial	HTML		Varies	Dr. Wright, UCLA, tutorial on cosmology
COS	Comic Journey: History of Cosomolgy	HTML		2	Light introduction to the history of cosmology
COS	Cambridge Cosmology Page	HTML		4	Cambridge University Cosmology webpage.
DM/DE	Dark Matter and Dark Energy	PDF		2	Introduction, assumes no prior knowledge
DM/DE	DM/DE Video 1	Video		2	Video for above.
DM/DE	DM/DE Video 2	Video		2	Video for above.
GR	Lecture Notes on General Relativity	PDF	C	6	Introduction, assumes no prior knowledge
GR	General Relativity Primer	Video	C	6	Introduction, 3 hours

Critique of Spontaneously Generating Universes

2008-07-22T00:01:00.004-04:00

This is the first part of a of a first draft of a critique of spontaneously generating universes. Much of what I will discuss is written much better by William Lane Craig's discussion on Contemporary Cosmology and the Beginning of the Universe[1]. These notes capture some initial thoughts that need refinement.

One of the first things to note are the assumptions made by Dr. Sean Carroll[2] about the accelerating expansion of the universe. These include:

1. The accelerating expansion will continue.

2. The accelerating expansion is caused by the dark energy vacuum energy that is the cosmological constant.

That the expansion will continue to accelerate is an assumption based on limited data. There are many possible curves that can fit the data points observed. These can include exponential acceleration, but also other kinds of curves, which could still have the universe eventually collapse, or slow down in its acceleration again. If the further investigation reveals that the future universe would slow down, then there would not be the conditions for a "de Sitter" expansion, a runaway expansion that would setup the low entropy conditions to spawn off other universes. Thus the time associated with the big bang event would be the beginning, not part of an infinite series of beginnings. More detailed observations are required to get a better idea of what is fueling the accelerating expansion.

Assumption number two is not the only possible explanation. The dark energy does not need to be constant in the universe[3][4][7]. It could be a field of energy that varies in time and space. In this case, the universe would not necessarily continue accelerate in its expanding. Further, there is a problem if the dark energy were the cosmological constant. Its constant nature in an expanding universe would violate the Strong Energy Condition[5][6]. Under current understanding of cosmology, this would seem to rule out dark energy as the cosmological constant. In this I must defer to James Sinclair and William Lane Criag who make this point. I am certain Sean Carroll is aware of the problem and I am interested in what he has to say about in his Internet papers and I will search to see what he has to say.

These are a couple of problems with this proposal of spontaneously generating universes. It points to the likelihood that our universe had a unique beginning and was not spawned from an infinite sequence of universes or multiverses. I will continue the discussion later.

Notes/Sources:

[1] William Lane Craig, Q&A Number 48, Contemporary Cosmology and the Beginning of the Universe, from his website, www.reasonablefaith.org

[2] Sean M Carroll and Jennifer Chen, Spontaneous Inflation and the Origin of the Arrow of Time, October 27, 2004,
www.arxiv.org/abs/hep-th/0410270.

[3] Dark Energy, Wikipedia.

[4] p. 15, Sean M Carroll and Jennifer Chen.

[5] William Lane Craig, Q&A Number 48

[6] Wikipedia, Energy condition

[7] HubbleSite, What Is Dark Energy?

Spontaneously Generating Universes

2008-07-21T00:01:00.000-04:00

Our universe had a beginning. Can the beginning be explained by natural causes? Since natural causes and time are tied to the existence of our universe, many scientists say we cannot speak about natural causes before the start of the universe. Others are thinking of possible ways to explain the beginning of the universe through natural causes without involving God.

There are a number of objections that theists, particularly Christians who see God has the agent in the beginning and sustaining of the universe, mention. These include:

1. Nothing comes from nothing (ex nihilo nihil fit). It is a philosophical self evident point that nothing cannot be the cause of something.

2. The universe began with an extremely low entropy. Usual mechanisms for a recreating universe, or for a universe starting from something else, has a high entropy situation giving rise to the extremely low entropy start of the universe.

3. The constants and laws of the universe are unusually well tuned to permit life. It is an extremely low probability that such tuning could happen randomly or naturally.

4. The probability of life occurring on earth like it has is very improbable to have happened by natural causes alone for the universe.

I will look at how some cosmologists answer these objections. An article in the May 2008 issue of Scientific American[1] deals rather creatively with objection 2 and will be the basis of much of this blog entry.

The universe is currently going through an accelerated expansion[2]. It means that after an initial fiery beginning, the observable universe will expand faster and faster forever if left on its own.

As the universe expands, ultimately its density drops while the overall entropy increases. If we follow the progression of any particular region of expanding space, we will see that as space expands, there are less particles, matter, and energy in that region of space.

If we were to examine a cubic meter of space over the long history of the universe's expansion, we would see the entropy drop for that cubic meter. Over a very long time, the cubic meter would have a near perfect vacuum, and its temperature would drop to extremely close to absolute zero. The possible micro states of everything inside that cubic meter would drop extremely close to the lowest possible set of states. In other words, the entropy of that cubic meter would drop extremely close to its theoretical lowest possible value.

An observation to add to this is that a vacuum in the universe is not nothing. The best possible perfect vacuum in the universe is not the absence of everything. First of all, in our universe there is the presence of light known as the Cosmic Microwave Background (CMB) radiation. Currently, the CMB radiation adds a temperature to the vacuum. As the universe expands, the CMB will continue to redshift, and the ambient temperature will drop. But the fact that the universe is acceleratingly in its expansion means there is some vacuum energy that is contributing to the expansion. One possibility is that the vacuum energy is an exceedingly small, but constant value, which corresponds to what is known as the Cosmological Constant[3]. Einstein's General Relativity has within its framework a concept of a cosmological constant, which depending how the equations are solved, predicts an expanding universe or a collapsing universe[4]. If the vacuum energy, which is often referred to as "dark energy" (simply because nothing much is known about it), is constant, even as space expands, it means the universe will expand exponentially in the future. As the universe expands, its density drops. The cubic meter discussed above as approaching a perfect vacuum and an extremely low entropy, that same reasoning can be applied to all finite volumes of the universe -- including the volume of the observable universe, or greater.

If the vacuum dark energy is the cosmological constant (not proven yet), it means in a "perfect" vacuum there is dark energy. This dark energy is subject to quantum fluctuations. Within a vacuum, the Heisenberg Uncertainty Principle means that particles appear and disappear within very brief intervals. These are so quick that they cannot be observed directly. Their effects can be observed indirectly. The electron orbiting around an atom would normally loose energy and fall into the nucleus of the atom, however, as the electron gives up energy as a photon of light, it also absorbs energy from one of the virtual particles that appear from the vacuum. This is very weird stuff. The kind of stuff that will appear in the vacuum has its probability of appearing that is proportional to entropy level.

Dark energy is the stuff that is present everywhere in space, in tiny amounts. When the universe expands infinitely, so that the normal matter and energy density drops to zero, dark energy is still present. While overall entropy increases towards infinity in the universe that has expanded infinitely, the entropy for any particular region drops to an exceedingly low value -- lower than beginning of the universe originally. This means there is an exceedingly small chance that a particular region will fluctuate into a large amount of perfectly configured dark energy that will ignite an expansion of space/time that is distinct from the universe that spawned it. In an extremely brief instant, the new patch of dark energy inflates by 100,000,000 light years, and then the dark energy "decays" (or breaks into) dark matter, regular matter, regular energy, and a residual amount of dark energy.

What would such a fluctuation look like from the universe it inflated out of? It would look like a black hole.

This newly inflated universe would grow and condense into galaxies and stars, and follow the same path as our universe. At some point in that universe's distant future, it would have patches of extremely low entropy dark energy fluctuate into rapidly expanding universes.

How does this model address the original 4 objections to the universe as we know it arising naturally?

1. Nothing comes from nothing (ex nihilo nihil fit). The universe that arises from the Big Bang does not come from nothing. There is a prior existing universe that has a quantum energy field of dark energy that is the cause of the new universe.

2. The universe began with an extremely low entropy. The conditions of the "meta" universe that spawned our universe had an extremely low entropy situation -- lower than the initial start of our universe.

I am combining three and four:

3. The probability of life occurring on earth like it has is very improbable to have happened by natural causes alone for the universe. A meta universe from which our universe inflated out of, is infinitely old and infinite in expanse. It means if there is a slight probability for life to occur in such a universe, no matter how unlikely, it will occur during infinite time.

In the next post, I will critique Dr. Carroll's approach to spontaneously generating universes.

One further note. Dr. Carroll does show a great respect and desire for civil discussion religious people as noted his blog entry, Crakergate. I wish to hold the corresponding same level of respect for the thoughts of scientists who discuss cosmology absent of a belief in God.

Notes/Sources

[1] Sean M. Carroll, Does Time Run Backward in Other Universes? (in the print media it is titled: The Cosmic Origins of Time's Arrow), Scientific American, May 2008.

[2] See previous blog entry about the discovery of the accelerated expansion of the universe.

[3] The discussion is based on Sean M Carroll and Jennifer Chen's paper, Spontaneous Inflation and the Origin of the Arrow of Time, October 27, 2004, www.arxiv.org/abs/hep-th/0410270.

[4] See Sean M. Carroll, The Cosmological Constant, May 2008, Living Reviews in Relativity.

A Dummy's Guide to Cosmology -- by an Idiot

2008-07-20T00:01:00.011-04:00

Those few who read this blog regularly know that I am a Christian -- a theologically conservative Presbyterian Calvinist. I am also not a scientist (hence the title). You may wonder why am I writing about this topic. There is a rich tradition in Calvinism, represented by Abraham Kuyper (29 October 1837 – 8 November 1920), Benjamin Breckinridge Warfield (November 5, 1851 – February 16, 1921), among many others, who championed conservative theology which held the Bible is inerrant and also viewed God has another general revelation in nature that is not inconsistent with the Bible. The ideas I discuss here will follow, philosophically, the approaches of these giants in theology. This is not a "safe blog" -- there will be times where I will mess up on science and theology and get either or both wrong. Sometimes I will not have an answer to some path I am exploring. Part of being a Christian is being a truth seeker. I am interested in finding where the truth goes, and I welcome anyone to discuss these ideas with me, whether they be Christian or infidel, scientist or non-scientist like me. I want the discussion to be open, frank, and friendly.

Articles Written:

A Bad Introduction to Entropy -- A first attempt at writing on entropy. After writing it, I discovered I had some wrong ideas.

A Critique of the Introduction -- Analyzing where I went wrong.

Entropy Take Two -- Trying an introduction to entropy again after I did more reading.

Entropy, Meet Gravity -- Entropy with gravity has a different look than entropy without gravity.

Black Holes -- with an interesting movie of stars orbiting a black hole.

Black Holes, Part 2

Cosmic Odometers and Speedometers, Part 1 -- Trying to find a cosmic yardstick.

Cosmic Odometers and Speedometers, Part 2 -- Proving spiral nebulae are distant galaxies.

Cosmic Odometers and Speedometers, Part 3 -- Research in determining velocity of stars and galaxies.

Cosmic Odometers and Speedometers, Part 4 -- The different forms of redshift, and choosing the surprising option.

The Big Redshift Picture -- Since the end of the 1990s, there has been some remarkable surveys of the sky for galaxies and their distances. These have been plotted and give a fascinating view of the huge structures in the universe.

Redshift,Yawn, So What? -- What does the redshift discoveries mean? How does a Christian approach the topic? There is a discussion with various Christians holding different views on the topic.

Did This Happen? -- A picture of the Antennae Galaxies colliding. For young universe creationists, the standard scientific thought estimates these images happened way before creation by millions of years. There was some discussion with this post.

Cosmological Assumptions -- An initial discussion of the major assumptions made by the scientific community in cosmology.

Isotropic Versus Homogeneous -- A more detailed look at the Cosmological Principle, which are assumptions used in cosmology.

Running the Clock Backwards -- An initial look at the Big Bang Theory.

The Cosmological Surprise of 1998 -- The discovery that the expansion of the universe is accelerating.

Spontaneously Generating Universes -- This is a look at some articles written by the Caltech astrophysicist, Sean M. Carrol. Dr. Carrol answers some classic objections of how an exceedingly low entropy big bang universe could arise following the laws of thermodynamics. Creationists who use the Second Law of Thermodynamics to argue against the Big Bang should understand Dr. Carrol's line of reasoning.

Critique of Spontaneously Generating Universes -- The first part of a critique of the spontaneously generating universes. More to be published shortly.

Critique of Spanteneously Generating Universes, Part 2 -- Examining the consequences of looking back infinitely at universes spawning other universes.

Zeno's Paradox -- Examining an ancient paradox and a related "supertasks" issue with an infinite number of generating universes.

Meet Yourself, Infinitely Many Times -- Some other paradoxes and epistemological issues with infinitely spawning universes.

Just so you know (the truth in advertising part): I favor a form of "old universe/old earth" creationism. The logic behind an old universe is compelling to me. I am open to young earth creationism -- I've held that from time to time in the past. I welcome discussion with all creationists, I greatly respect the reasons for each viewpoint. I also subscribe to the Chicago Statement of Biblical Inerrancy, as well as the Westminster Confession of Faith and Catechisms, with one exception, creation in the "span of six days." While technically, under the PCA's understanding of the Confession, I do not need to take an exception there, I do so so that people know my position.

The Cosmological Surprise of 1998

2008-07-16T00:01:00.007-04:00

In the year 1998, the Monica Lewinsky scandal dominated much of the American news, with the resulting impeachment of President Clinton. 1998 was also the year that Adam G. Riess [1], an astronomer at the University of California, Berkley (now at Johns Hopkins University) announced a cosmic discovery his team made in November of 1997. The universe expansion rate was accelerating. His team was one of two teams studying certain types of supernovas and variable stars[2].

Prior to this time, it was known the universe was expanding. It was assumed the expansion was gradually slowing. The reason this was assumed was because the major forces known by physics were: the strong nuclear force, the weak nuclear force, the electromagnetic force, and gravity. The first three act in close range, while gravity acted over huge distances. Gravity acts in slowing down the expansion of the universe. The question in cosmologist's minds was gravity strong enough to bring the expansion to a halt and ultimately cause the universe to collapse in upon itself. For various reasons, in the 1990s it looked like the universe was close to having just enough matter in the universe to bring the contest of gravity and expansion to a draw -- but scientists weren't sure.

In 1997, two competing teams were researching the expansion of the universe, in part to answer the question of whether the universe would expand or collapse. Both were aware of each other's work. Each of the teams were using the Hubble Space telescope, as well as ground based telescopes, looking at certain types of brilliant supernovae and Cepheid variable stars. They were looking to get an accurate measure of the "Hubble Constant" which is the expansion rate of the universe. In November of 1997, Dr. Riess' calculations indicated that the most distance supernovae were brighter than he expected. There were various possibilities. The most likely one in their minds was that there was dust obscuring the closer supernovae. Another possibility was that the universe had recently sped up its expansion (remember, this is "recent" in astrophysical terms, which means in the past few billion years). This latter possibility needed very careful checking because no one what seen any experimental indication of an acceleratingly universe before. Such unusual possibilities usually meant errors in measurement or in not accounting for much more prosaic possibilities. Only a few years before a couple of scientists had their reputations ruined by rushing to publish their thoughts on cold fusion.

During November and December of 1997 and into January of 1998, Adam Riess checked his results again and again, quietly checking with others at U.C. Berkeley. Dr. Riess knew this was the kind of monumental discovery that few astronomers make in their careers. So far, as far as Dr. Riess could tell, the other competing team had not found the discrepancy in supernovae brightness, but he knew what they were looking at and knew it was only a short time before they would notice the same anomaly. Riess' team sent their paper for publishing in March of 1998[3], just as the other team were also concluding that the expansion rate was accelerating.

In a span of just over a year, the astrophysicists' view of the universe changed drastically. At the start of 1997, it was thought that matter, the stuff you see around you, atoms, cars, baseball bats, and stars, were the dominant stuff of the universe. By the end of 1999, it was realized conventional matter and energy (such as light, gravity), the stuff we see in the universe, made up a small fraction of what there is in the universe. How small? Cosmologists are now saying it is just 4% of the universe. What is the other stuff? No one knows what it is. There is unseen stuff that causes galaxies to form, and unseen negative energy that is driving the accelerating expansion of the universe. Currently the unseen "stuff" that forms the galaxies and other great structures is called "dark matter." The unknown repulsive energy that drives the expansion is called "dark energy." Just because they are both called dark does not mean they are related or tied together in a special dark way. The use of the term "dark" is like "x" for being unknown. Further, dark matter is not really dark per se. Dark matter is transparent to light. We can see dark matter's presence from the gravitational fields it exerts. Dark matter and dark energy make up 96% of the universe.

The previous blog entry briefly explored the cosmologists thoughts of running the clock backwards in the universe. It points to a beginning for the universe. What about running the clock the other way? What will an accelerating expanding universe look like in the extreme future?[4] First, over the course of 100 billion years (7 times what cosmologists think the present age of the universe is), all the galaxies we presently see, outside of the local cluster galaxies we are in, will disappear from view. This is because as space expands, the more distant regions that we currently see will in essence be moving away from as greater than the speed of light. Light emitted from those distant objects will never reach us. Or put another way, the light from the distant objects will redshift so greatly, that we will no longer be able to detect them. Our local galaxy group will not fall out of our sight because gravity is strong enough within the group to counter balance the expansion of space. All the galaxies in our local cluster will collide and merge together into one giant super galaxy. Eventually all the matter in the super galaxy will fall into the super massive black hole that has merged from all massive black holes in the center of the original galaxies. Over a very, very, very long time, the super massive black hole will evaporate, leaving, for practical purposes, an empty space that still is continually expanding.

Overall, in the expansion of the universe, its entropy will continue to increase. As the current universe we see expands infinitely, its entropy will increase infinitely. But the density of the entropy will drop.

I now have covered that background need to discuss Caltech astrophysicist Sean M. Carrol's proposal of how this universe came into existence.[5]

Sources/Notes:

[1] Photograph of Adam Riess taken from his website at the Space Telescope Science Institute.

[2] Adam Riess' story of his discovery is told in the Shaw Prize lecture, My Path to the Accelerating Universe. You can watch the 02/27/98, PBS NewsHour with Jim Lehrer segment's interview of Adam Reiss in Dr. Reiss's FAQ page.

[3] Adam G. Riess, et al., Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, Astronomical Journal, May, 1998

[4] Lawrence M. Krauss and Robert J. Scherrer, The End of Cosmology? Scientific American, February 2008.

[5] Sean M. Carrol, Does Time Run Backward in Other Universes?, Scientific American, May 2008.

Running the Clock Backwards

2008-07-13T00:01:00.003-04:00

The universe is expanding -- so the redshift of the galaxies indicate. That means last year the region of space we see now was closer. Even closer 20 years ago. Let's perform a thought experiment. Suppose we look at the rate of expansion, look at the most distant galaxies, and just run the whole thing backwards, assuming the physical laws of the universe remain the same. Space would shrink smaller and smaller, until it shrinks to an infinitesimal point. how long? Current estimates are 13,730,000,000 years, give or take 12,000,000 years [1].

Virtually all astronomers believe that the universe began 13 to 14 billion years ago. This means virtually all astronomers believe this universe had a beginning. The name of the beginning point is the Big Bang -- a name that was ironically coined by British astronomer Sir Fred Hoyle[2] as a derogatory name for a theory he did not believe in. Hoyle had believed that the universe was eternal and its basic structure always remained the same.

What is thought about the beginning? First, since he universe shows a remarkable degree of homogeneous structure in its distribution of matter and energy, the universe currently has a remarkably low entropy. Since entropy always increases in a large closed system over time, it means at the beginning the universe had an extremely low amount of entropy.

The early universe was a remarkable place. All the particles that make up the universe we currently observe were squeezed into an extraordinarily hot, dense volume. Most important, they were distributed nearly uniformly throughout that tiny volume. On average, the density differed from place to place by only about one part in 100,000. [3]

But an instance before, this extremely low entropy of the hot dense universe was even lower. It is thought by many astrophysicists that early universe when through a brief period of incredible expansion, known as inflation. It is thought extremely dense "dark energy" engaged the inflation. The entropy at the start of the inflation was extremely low:

the ultradense dark energy had to begin in a very specific configuration. In fact, its entropy had to be fantastically smaller than the entropy of the hot, dense gas into which it decayed. [4]

One of the things that many scientists like to do is come up with a natural explanation of why things are the way they are. The universe as we see it is an extraordinarily unusual thing. It's constants (such as the speed of light) and laws are tuned to an incredible degree to support life. Is there a way to explain the beginning of the universe without God, without an intelligent designer? The extremely low entropy at the beginning of the universe is very improbable. It was hoped that String Theory could provide an explanation for the beginning, but the problem is that String Theory has so many unspecified initial conditions that lead to wildly different universes, the vast majority of which could not support life.

Some have proposed that our universe came out of a "quantum" fluctuation. However, it is extraordinarily unusual for low entropy systems to appear in such high entropy fluctuations.

The author of the article that I have quoted from, Sean M. Carrol, has an interesting proposal. I'll examine it in my next post and discuss some problems with that proposal.

Sources/Notes

[1] Gary F. Hinshaw, et al., p. 2 and p. 42, Five-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Data Processing, Sky Maps, & Basic Results, unpublished manuscript submitted to the Astrophysical Journal Supplement Series. No date, but footnotes imply the manuscript was written in 2008.

[2] Wikipedia, Big Bang.

[3] Sean M. Carrol, Does Time Run Backward in Other Universes? p. 2, Scientific American, May 2008.

[4] ibid, p. 3.

Isotropic Versus Homogenous

2008-07-12T17:04:00.007-04:00

Can you image a universe of Energizer Bunnies? Rather frightening. Through the magical world of bloggery, I am taking you there. It's too late, if you try to click away, you've already caught a glimpse. There are two versions of this universe. The first is a homogeneous universe. Its made up of banging bunnies, all facing the same way.

Imagine sitting on the blue ball looking all around. This is a homogeneous universe. The question for an isotropic universe is do all the ways I look at the universe look the same? Looking to the left of the blue ball, you will see bunnies facing you. Looking to the right, you see back of the bunnies. Looking up you see the feet of the bunnies. Looking below, you see the tops of the bunnies. With the first image, you see the universe has a definite orientation. The universe looks differently depending which direction you look at it.

The second image is not so homogeneous, but fits the bill for isotropic.

In this image I ran a program that randomly oriented the bunnies. The result is that there is no particular orientation to this universe of bunnies. Sitting on the blue ball you will see bunnies facing every direction as you look up, down, left, right, and all the directions in between. This is the kind of thing that is meant by an isotropic universe. As we look at any direction, on the large scale (clusters of galaxies and larger distances), we see galaxies oriented in every direction.

This image is from Hubble website.

Finally, the redshift surveys are producing spectacular results. This image is the entire sky from earth showing the Milky Way galaxy, which is the galaxy the solar system resides in, and what can be seen that is not blocked by our view of the Milky Way. Each point in the image represents a galaxy. The galaxies that are closet to us are blue, the furthest ones are shown as red and those at "intermediate" distances are green and other colors. This comes from the internet article, Large Scale Structure in the Local Universe: The 2MASS Galaxy Catalog by Dr. Thomas Jarrett of Caltech.

A detailed listing of the objects in the picture is found here.

This image gives us an idea of the limits of homogeneous and isotropic. If you look at the image carefully, you can see "threads" of galaxies and other large structures. But you also see how all the galaxies spread over the sky in such a way that one area of a sky looks very similar to every other area of the sky.

Cosmological Assumptions

2008-07-11T00:01:00.002-04:00

Remember the Energizer Bunny? I haven't watched TV in years -- any programs I watch are on the Internet -- so I don't know if the bunny is still pounding away at the drum. I am going to use this bunny to illustrate some major assumptions made in cosmology.

The first assumption is that the physics of the universe -- physics of the fundamental forces of electromagnetism, gravity, and a few other forces -- has remained the same throughout all the life of the universe -- or nearly so. The speed of light has not changed over time, forces, properties of matter, the fabric of space and time have remained the same. It is like the Energizer Bunny, the fundamental forces keeps on ticking. The exception is at the very beginning at the universe.

We need to carefully make the distinction between the fundamental forces and physics and that the universe itself was the same all the time -- the latter is known as the Perfect Cosmological Principle. Einstein first assumed that in General Relativity. This is the view that the universe has always existed, forever, in basically its present form. This theory was referred to as the Steady State Theory. Discoveries over the past 50+ years has eliminated the Steady State Theory as a viable theory.

On the large scale, the universe is homogeneous. By large scale, I mean billions of light years. The various redshift surveys show that the universe is somewhat clumpy. There are stars, galaxies, and galaxy clusters. But as you go beyond the super clusters of galaxies, there is a rough evening out of the visible matter in the universe.

On the very large scale, whatever direction you look at the universe, it essentially looks the same way. The diagram I put together for isotropic had a problem, it is not isotropic. Do you see how it is not?

These two assumptions, the universe is homogeneous and isotropic, form what is known as the Cosmological Principle. The universe looks basically the same in every direction it is examined.

There is also another assumption made by cosmologists. There is no special vantage point in the universe. How the universe looks to us in the Milky Way galaxy, looks essentially the same to someone else at a galaxy 10 billion light years away. This principle is known as the Copernican Principle, named after the astronomer that developed the description of the solar system where earth was not at the privileged position of being at the center of the solar system.

The Copernican Principle is a very interesting assumption. When we look at the universe all around us and note how it is expanding, it looks like we're smack in the very center of the universe. Everywhere we look, the universe is expanding (over the large distances) at exactly the same rate. The universe looks like it is growing with earth being the very center point from which all space is expanding away from. The Copernican Principle states if we view the universe this way, so do the observers at a galaxy 10 billion light years away from us. How can that be? There are some straight forward consequences of that assumption that will be discussed later.