God & the Laws of Physics
Beginning with the concept of deterministic chaos, which describes immeasurably small forces magnifying into a large effect, coupled with insights drawn from quantum mechanics involving probability distribution, Thompson examines Eugene Wigner’s analysis of the conscious observer and the laws of physics. He then expands upon this discussion by considering several natural systems such as butterfly wing diffraction gratings, E. coli flagella, and DNA gyrase, that suggest complexity in light of contemporary evolutionary theory. Thompson proposes the evidence could intimate that the influence of consciousness “is being exerted starting from a sub-microscopic level, and this is then amplified in a natural way.”
TRANSCRIPT: God & the Laws of Physics. Santa Fe College: Gainesville, FL – March 3, 1997 / (529)
Actually, this is a solution of the famous three-body problem. Suppose you have three gravitating masses and you have them moving according to Newton's laws, how will they move? This was a famous prize problem back in the 19th century. People were challenged to give a general solution for the motion of the objects. No one could ever do it and maybe from this diagram you could get an idea of why, because this is one possible solution to the three-body problem and it was just worked out numerically with the computer. In fact, everybody could understand these things analytically.
So, this illustrates something called deterministic chaos. And deterministic chaos is something that turns out to be quite common and its existence was really only appreciated in fairly recent years with the development of computers. Another example where you have deterministic chaos is turbulence. If you have the flow of a fluid, this is a computer simulation of airflow past a barrier and you see the formation of vortices go behind the barrier. This is also an example of deterministic chaos and there are many other examples. So, what I'd like to do is give… hmm, where did my next transparency go… give a brief idea of how deterministic chaos works. So, here's a simple illustration:
Suppose we have a pinball machine. So, these little circles represent the pins. You're looking down on the pinball machine from above and imagine another little ball that is bouncing from one pin to another. Now, you know that in a pinball machine, the balls tend to bounce in unpredictable directions. This is also an example of deterministic chaos and the reason for it is fairly easy to understand. If the ball is coming along and it hits a pin, if you slightly changed the direction of the ball, due to the curvature of the pin the change gets magnified; and you can adjust it, for example, so that it's magnified by a factor of 10, let's say. It's a question of how big the pins are and what their spacing is. So, let's say a ball is coming along and you change its direction of motion by a hundredth of a degree. Well after one bounce, the direction change amounts to a 10th of a degree and after the next bounce, it amounts to one degree and then after the next bounce, it becomes 10 degrees. So what started out as a very tiny change in the direction of the ball in three bounces, becomes a substantial change. And after that, the ball would just go hit a different pin and follow a completely different path. And likewise, you can see... let's say you changed the direction of the ball by a millionth of a degree. Well, that's six tens multiplied together so six bounces, will bring that up to one degree. So, what it amounts to is that motion is unpredictable because extremely tiny changes in the motion of the object can produce big effects.
Now, in physics, you could ask, well, how closely can you measure the direction in which an object is going? There has to be some limit to that. Let's, say you can't measure it more accurately than a billionth of a degree in either direction. Well, if in nature, some process changes the direction by an amount smaller than what you can measure, that means that it becomes impossible in principle for you to predict what the system is going to do because things that are immeasurably small can magnify and produce a big effect. Now, let us suppose then that on the level of the immeasurably small, changes are made in a deliberate way so as to control the motion of the bouncing ball. Well, in that case, this would be something that would be beyond what you can measure or directly deal with scientifically, but yet the motion of the ball could be controlled in that way.
So, I've drawn a straight line here and show the ball bouncing in such a way that it keeps going pretty much along the straight line, although it bounces back and forth on either side of it to some extent. So, by making very tiny adjustments in the motion of the ball, it is possible to control the motion so that it moves in a systematic way. In fact, if you imagine a very big array of pins, you could have the ball moving so as to spell out somebody's name or anything that you wanted. In fact, the ironic thing is that chaos allows for the possibility of control. Whereas if things were really deterministic, then there is no possibility of control.
An example of something that's really deterministic would be a pendulum. Say a simple pendulum used in clocks that just swings in a certain way, and there's no opportunity to control that unless you really hit it hard, you give a massive jolt to it and then you would change the motion of the pendulum. But in the case of a system that has this feature of deterministic chaos, it's possible to control it on a sub-microscopic level beneath what you could hope to measure. So, there is a possibility that on the one hand things are following the laws of physics to the full degree that you can verify that by measurement, but on the other hand intelligent control is being exerted starting from a sub-microscopic level and this is then amplified in a natural way. I should note by the way, that some researchers have experimented with methods of controlling deterministic chaos and in fact, you can do it by just making slight bumps to a chaotic system in the right way you can guide it in any way that you like. So that's the first point, and that deals with classical physics, with Newton's laws.
So, let's try another slide. Oh, well, that's a picture of what the world is like if it were purely Newtonian. These springs represent forces, not literal springs, but basically, you have a lot of particles and forces between them. Next slide please.
So, now what I want to turn to is quantum mechanics. So, of course, Newtonian physics is no longer considered to be the last word regarding the laws of nature. Another fundamental theory has come to basically replace classical physics – this is called quantum mechanics. Quantum mechanics agrees with classical physics on the scale of large objects, but on the atomic scale, it gives a fundamentally different picture of nature. So, I thought I would say a little bit about that. Here is a classical picture of a hydrogen atom with the nucleus and an electron spinning around in orbit. In quantum mechanics, you replace this with a picture that looks kind of like this. Basically, the electron becomes something fuzzy and smeared out; and it becomes what is called in quantum mechanics a wave pattern. So, I'd like to say a little bit about these wave patterns. Next slide.
What I need to do is talk about a thing called a probability distribution. That sounds a bit formidable, but it's a very simple concept. Consider a horse race, let's say you have several different horses that are going to run in this race and you have a probability for each one to win the race. This is a very practical thing for people who gamble on horse races. So, for horse A, it might be you can estimate 20% probability that it's going to win and for Horse B it might be 35% and so on. And for all the horses, the percentages have to add up to a hundred percent because you know some horse is going to win for sure. So, this series of probabilities represents partial knowledge concerning which horse will win. You don't know for sure, but you do know something. So, probability then is a kind of way of representing partial knowledge.
But now when the race is actually run, one horse wins and now you know for sure this one won and there's zero probability that any of the other ones won. So at that point, you erase your old probability distribution, and now you have 100% for one of the horses and zero for all of the others. So this is a reasonable procedure because your knowledge now has increased because now you know which horse won and so the probability distribution representing partial or imperfect knowledge is replaced by one representing perfect knowledge in this case. Well, this isn't too surprising because the probability distribution is just something we write down, but in quantum mechanics, we find a very unusual situation. There we find that the probability distribution is something real that is out there in nature. So instead of having a particle that's in a particular position, we have a bunch of probabilities for the particle to be in various locations.
So, let's say it's more probable to be here and not at all probable here, but it has some probability of being over here; and instead of saying that this is a representation of our imperfect knowledge of where the particle is, we say that in nature this is really what we have. The probability distribution is out there in nature. Next slide please.
I'm going to illustrate a classical experiment that shows the paradox here. Actually, the physicist Richard Feynman said that this is the fundamental mystery of quantum mechanics. All the other mysteries follow from this one. So in this experiment, you send electrons through a little slit and then they come to a place, a barrier where there are two slits and then finally they'd come to a screen and when each electron hits the screen, it makes a little flash of light that you can see. So you keep sending electrons through.
Now, what happens is, if you would do the next slide, electrons in quantum mechanics are represented by a wave. Now the wave is something you can experiment with in classical physics also. If you have a wave of the right wavelength and it hits two slits, then two little waves start out from the two slits on the other side of the barrier and they combine together to form what's called an interference pattern. So in certain places, the waves cancel out and you get zero intensity and in other places, the waves add together and you get a greater intensity and so on. So, this is something that waves do and you can do this with water in a tank. If you have water and you have a barrier with two little openings in it and you have a vibrating paddle, waves will go up to the barrier and then little ripples will come through the two holes in the barrier and they'll form a pattern like this, if you can see. So, the interesting thing is that in quantum mechanics, these waves are actually probability distributions. That's the mysterious point. So if we go to the next slide, it turns out that if you send a lot of electrons through the system and they hit the screen, they bunch together in bands like this, which correspond to the interference pattern, which has places where the waves build up and places where they cancel out, alternating, and that's how you'd expect waves to behave, but if you send one or two electrons and individually, each electron just makes a single little flash.
Now, the idea in quantum mechanics is when an electron goes through, it's a wave that is spread out over the whole space of the system, but that's a probability wave. And when it hits the screen, you observe it and it's just like knowing the outcome of the horse race. Now you know that, whereas it could have hit the screen at any point, it did hit right here. So, the wave collapses to a point, and this seems a little bit unusual for a physical thing, but that's what happens in quantum mechanics. It's called the collapse of the wave function. So, this is the basic situation. Next slide please.
I'm going to... Well, first of all, I should comment that the founders of quantum mechanics deliberated on this for quite a long time and tried to understand what is going on here. And many of them introduced the idea of consciousness and knowledge into physics because after all, if a probability distribution represents knowledge and it's also physically real, then physics becomes somehow a science of knowledge and that in fact was the viewpoint of Werner Heisenberg. This is Werner Heisenberg right here, he's a very famous physicist. This is Niels Bohr. He's also a pioneer of quantum mechanics.
So, how does this relate to the basic theme of God and the laws of physics? Well, a number of points can be made. First of all, this creates problems if one wants to think that God in some way intervenes in nature and directs things. Because I just explained how deterministic chaos provides a loophole whereby God could control things without making a really drastic change of the kind that Leibniz criticized Newton for proposing. But if we go back to this picture again showing the path of the bouncing ball, it turns out in quantum mechanics, you don't get deterministic chaos, at least not as easily as you do in classical physics. There are situations where you can obtain deterministic chaos, but generally, you don't. And that's because instead of having a particle here bouncing along and following a definite path, you have this wave that spreads out in more or less continuous fashion. And so what happens when the wave hits this round pin is it just spreads out into broadband and each time it hits a pin, another segment of the wave spreads out more but this very great sensitivity to slight changes in initial conditions no longer exists.
So, how does that then agree with classical physics? Because I said quantum mechanics and classical physics should agree basically. And what happens is that if you observe the particle according to quantum mechanics, since it's a probability wave, Bingo! It collapses to a certain point and that's where the particle is. Now, it collapses by chance. This is another mysterious thing in quantum mechanics. Before quantum mechanics came along, when people said something happens by chance they really mean, or they really meant, well, it happened for some definite cause but we don't know the cause and so, therefore, we estimate probabilities. It's back to the idea of a probability distribution representing imperfect knowledge. But with quantum mechanics, you say in nature it happened literally by chance. So now, chance becomes a cause, so to speak. It becomes something that makes things happen in nature.
So, it turns out there are laws of chance and this is something people at insurance companies and gambling casinos study very carefully, because if something is occurring in a random way, like spinning a roulette wheel and waiting for the little marker to come upon a certain number, if you do it once or twice, you can't predict what's going to happen; but if you do it many times, it becomes very predictable and that's the basis by which gambling houses make their money. They adjust the odds so that they know that if people run through these gambling games many times, the house is going to make a steady profit.
So, the laws of probability are actually quite stringent. So now, if you want to have God intervening in the laws of physics, you have a problem. The quantum wave spreads out according to an equation called Schrodinger's equation, which is deterministic. There's no room there for God to intervene unless you want to say, well God just changes the equation. At the same time, things that happen by chance provides some leeway for random unpredictable motion, but the laws of chance in the long run very strongly restrict things so that if you wanted to say that God, let us say, introduces changes so as to spell out somebody's name, as I was saying in this example, that would violate the laws of probability; and you would really be saying, we're not following quantum mechanics anymore – we're following some different theory. So quantum mechanics creates a problem. And basically, if one is going to have God intervening to control matter, quantum mechanics would have to be altered in some fundamental way. So that's one development that has taken place. Well, let's go back to the slides. Next slide please. There we go.
Well, as it turns out, as I was saying before, quantum mechanics is also quite mysterious and people have wondered about how it can be that we have a theory of physics, which also involves knowledge which seems to have something to do with consciousness and observation and so forth. So, I put in this picture. This is an idea put forward by a physicist named John Wheeler, he was a very famous physicist who's thought a lot about quantum mechanics. And he deliberately introduced an almost solipsistic picture here in which he said that by our conscious observations, we brought the universe into existence. That's what this picture shows. Here... this is the universe and there are galaxies and here is the observer sitting on the planet earth, let's say, observing through his scientific knowledge, the Big Bang that created the universe; and that's what brought it into being. Now, how can a very famous physicist at Princeton University say something like that? Why would he say that?
Well, let's go onto the next slide. It turns out that ideas like that are more or less inherent in the framework of quantum mechanics and we do have quite a curious situation. Here, we have an example to illustrate this. We have a man looking through some kind of microscope at an object. So you could say, the microscope plus object, if you like, is the observed system and the man is the observer. So, there's a barrier here indicating the division between the observer and the observed, and this is important in quantum mechanics because I said, when you make an observation, that's when the wave function collapses – the probabilities collapse representing your observation. Next slide. Well, why not put the barrier here between the observer and the observed? We include the eyeball and the telescope or microscope and the object as the observed system. And basically, the brain and optic nerve connection here becomes the observer. After all, the eye is supposedly a physical instrument and you could describe this by quantum mechanics as well as anything else in principle. But then, of course, you see we have a problem here because then you could move the barrier further and further back until everything is on the side of the observed. In that case, what is the observer? This is the problem.
Now, John Von Neumann, a very famous mathematician and physicist, commented on this. In fact, this illustration comes from his work. He said in particular, we saw that the observer in this sense needs not to become identified with the body of the actual observer. Now, what did he mean? Well, he came out and said it. There's a non-physical observer and it's curious that from quantum mechanics, you should be led to the idea that there could be a non-physical observer of the physical system. Now, this becomes quite a problem if you look at quantum cosmology. Now, John Wheeler tried to turn things around in a circle. He said, “Okay, well, later in the universe we have observers. They're observing the universe and somehow their observation causes the collapse of the probabilities for all possible potential universes to create the universe that actually exists.” But this circle is a bit of a problem; cause and effect work out a lot better when it goes from A to B to C and it doesn't link around in a circle. You get into all kinds of paradoxes and problems if you allow that. So what do you do in the case of cosmology?
Physicists such as Stephen Hawking and Steven Weinberg and others, have openly admitted that it's a real problem if you want to apply quantum mechanics to the entire universe, because then what is the observer that collapses the wave function and determines what's going to happen? So then there's the thought, well, maybe God is the observer, after all. But as I pointed out, the problem of quantum mechanical probabilities means that we really have to look here at some modification of quantum mechanics and there are different possibilities.
I could mention, on the one hand, there is a Nobel prize-winning physicist named Eugene Wigner who proposed that when the collapse of the wave function occurs, that's where we need to introduce some new equations and those new equations would involve life. He said that, well, up till now in physics, we've had no reason to introduce life into the picture and certainly biologists and chemists following physics have thought that life just reduces down to a physical system of particles. So life is just reducible to physics. But Eugene Wigner said, well, it seems that life in the form of the conscious observer plays a fundamental role. So perhaps we need a new physics, a new theory of quantum mechanics, which will introduce life in a more explicit way and resolve these difficulties.
Now, going at it from another side, there's a physicist named David Bohm, who introduced… well what he did was show that you can go back to classical physics and still have quantum mechanics. It's something called the "hidden variable" theory. But basically, by doing that, he re-introduced the possibility of control through deterministic chaos. I won't go into the details of how that worked out. So, next slide please.
So, what I'd like to turn to now is this topic of consciousness. Wigner was trying to propose that something non-physical, some non-physical principle of consciousness, would have to be introduced in order to solve the problems of quantum mechanics. Now, in modern science, the general viewpoint is that consciousness is a product of the brain. Of course, this comes back to physical reductionism. So, you have a lot of nerve cells connected together with synapses and all kinds of complicated chemical reactions are occurring in all of these cells – there are about 50 billion nerve cells in the cerebral cortex – so the idea is that with all these nerve cells interacting, sending impulses back and forth on the level of 50 billion of them all going on at once, that produces consciousness. And all our thoughts, our feelings, our perceptions, and so on are simply caused by the interaction of those neurons.
Recently, Francis Crick wrote a book that he called the "Astonishing Hypothesis" and this was his hypothesis that we're nothing but a bunch of nerve impulses, but even Crick admitted that there is a problem. Let's see... the problem is, "how do you explain qualities of perception?" It seems innocuous at first, but here we have something that is red. Everyone can see that it's red. Pretty much, I presume. Now, as far as physics goes, you would explain this in terms of some wave given by some equations and the redness depends on the wavelength of the light. But looking at it from the physical viewpoint, what does this have to do with our perception of red? Now, we perceive that in a certain way blue would be a different perception, the sound of a violin that's another perception, a feeling when you touch something is another perception. What accounts for the perception? You can talk about the equations to be sure, but that doesn't explain the redness of red. Philosophers have a word for this, they speak of qualia. How can we account for qualia? And Francis Crick openly said in his book, “Well, I've brushed aside the idea of qualia, the redness of red, for example, because I really have no idea what to say about that.” So, we have a fundamental problem involving consciousness, namely that our physical descriptions in terms of electrons or whatever we may postulate in the physical system – that description really says nothing about the perception of something, and that's quite a mystery.
Going back to those neurons, why is it that some neurons firing nerve impulses produce the sound of the violin, and other neurons firing impulses give you the perception of the sunset? It's a bit mysterious. Next slide please. This is another slide illustrating the same thing, different colors in different wavelengths, but the suggestion here is that there may be a non-physical conscious entity, something that is real that is in nature but which is conscious, it perceives, it experiences the qualities of perception, and it does so through linkage with the material system in which for example, you have different wavelengths of light and so forth, but then one has to account for this linkage. What would the nature of that linkage be? So next slide.
So, now, I'd like to change course slightly and turn to another topic, which is related to the whole question of God and the laws of physics. And that is the whole controversy of creation versus evolution, because of course, many people who would argue that God directly influences nature also say that God is somehow responsible for the origin of living species. That was the whole topic of the discussion that I started out with. Julian Huxley was a great advocate of the position that everything that you see in the biological world has come about purely by chance and natural selection. Natural selection, or survival of the fittest, is simply the culling process by which things compete with one another and some survive, others die out, some reproduce more, some reproduce less, and so on and then chance, once again, is the process by which new things are introduced. So Huxley's viewpoint, which is the orthodox scientific position, is that chance is throwing up possibilities, natural selection is weeding them out, and that explains everything that we see in the biological world, including ourselves. So, I'd like to make a few observations concerning this.
By the way, Shapely was referring to the pope accepting evolution, but of course that refers to a concept called directed evolution. The idea is that God manipulates the process of evolution so that things will come out in the desired way, but of course, that means God has to be introducing a lot of information into nature, directing things and shifting things and so forth.
So, the first observation that I'd like to make is that the Darwinian process of evolution does work in some cases. I picked an illustration which is kind of interesting. There's a kind of trilobite that lived about 400 million years ago. It had eyes with lenses distributed like this, and it's rather amazing that these lenses are preserved in the fossil record because they're made of calcite, which is a mineral, and you can take photographs through them. People have done that. And the interesting thing – next slide – is these lenses are corrected for spherical aberration, which is a problem that lenses have. I won't go into how it's done in detail, but basically, you have a two-part lens with different refractive indices and you have a strange little curve, which was actually discovered by René Descartes, theoretically. And this scheme focuses light very nicely – it avoids spherical aberration. So, how did that come into being? Could it be a product of evolution? Well, in this case, the answer is, well, yes, it could. Next slide please.
I made a mathematical model on a computer in which you start out with a curve that doesn't work very well for correcting spherical aberration and you make random changes in it and if the changes improve the focus, you keep them and if they make the focus worse, you throw them out. You keep doing this and what you find – this is the number of trials – is the curve approaches the theoretical optimum curve. So this is the case where evolution works. Next slide please. The problem is that in a lot of cases, it's very difficult to see how evolution could work. We can understand why it works in the cases where it does, you have a fairly simple system which is being nudged into an optimum position. But there are many things in the world of biology that are a little bit hard to evolve. Some of them seem intuitively so, for example, iridescent butterflies that produce a rainbow of color have refraction gratings built into their wings. And if you look with a microscope, you find a series of very fine parallel grooves set up in this fashion in the butterfly wing, which acts as a diffraction grating. Now, how did that come about by chance? Because for natural selection to select it, it has to come up by chance. Well, one could debate that. Next slide.
There are a lot of complicated examples. This is a structure whereby cells communicate. This is one cell membrane, this is another, this is a system of pores made of specially shaped molecules. Next slide. This is a more complicated version of cellular plumbing. Our bodies are made up of millions and millions of cells and each cell has plumbing arrangements in it like this. Actually, they are a lot more complicated than this, and one could wonder how this can all come about just by chance and natural selection. Next slide. One can debate all these things, but if you get down to the molecular level, you can see some examples where it really becomes difficult for chance and natural selection to work.
This is an illustration of a DNA molecule with some protein enzyme attached to it. Next slide. This shows the amount of DNA in a little virus particle. This is a virus particle that burst and the DNA came flying out which is strewn all over the place. Basically, the DNA is very long compared to the organism and this is true in general of living cells. There's a huge amount of DNA, which is a long strand which carries the genetic information of the cell and it's coiled up very tightly inside the cell. Now, when cells reproduce... [unclear]... is represented by this yellow object here, what it will do is grab a DNA strand in two places. Next slide. Holding on to one strand, it slits the other – next slide – then it pulls this one up, puts these two pieces together, and reconnects them, and it keeps doing this all the time. Now, the effect that this has is it can untie knots. Suppose the DNA gets all knotted up? Well, by doing this enough times, you can untie all the knots without having to do what we do when we untie knots, and it's very effective. This is how cells are able to divide. They have this kind of apparatus.
Now, my observation would be... I made this drawing, I don't know what the molecule was really like, but I would suggest this is a pretty complicated molecule. Just think of a molecule that can do that. Grab the strand, break it, pull another strand through, and put it back together. So unless that is there, the cell can't reproduce. It's not possible because it's DNA would get all tangled up. So how did that come into being? That is the question. Next slide.
So, here's another example that I've always found kind of interesting. This is a motor built into the side of a bacterium called E. coli. These bacteria live in your intestines all the time. The bacterium is like this and it has little flagella which are in the spiral form and the bacterium can rotate the flagellum and it acts like a little propeller that it enables the bacteria to swim through the fluid in which it's living. The propeller is driven by a motor, which is a kind of turbine. This motor runs by the flow of hydrogen ions through the membrane of the cell. Cell metabolism builds up a hydrogen ion difference between the inside and the outside and so it runs hydrogen ions through a turbine and this powers a little motor.
Now, not only do these motors work nicely, but they self-assemble. Let's say, the cell keeps dividing. It has to keep making new motors. Next slide please. This is something which I made a study of one time. This is an example of a model of this motor. It's been studied in very great detail by some biologists. So I considered the question of, well, how can the molecular pieces of this motor assemble together inside the cell? So this thing here represents a piece of the cell membrane and this is the central axis of the motor made of molecular units. Next slide. There's a whole series of steps, which I won't go through, but basically, different molecular subunits combine with a very particular order, next slide, and they keep combining, next slide, until finally you have the completed mechanism. This is actually a working model according to reasonable rules for the biochemical interactions. Next slide. Here, you see it from the top and the next slide after that will give you a bottom view. This is where the flagellum would come down.
So, to make a model like this that works, it's quite a design problem. There are all kinds of things that have to work just right and it's a fairly complex system. Now my question then is, well, how would that evolve by chance and natural selection? What good to the cell is half of a motor or a quarter of a motor? Or, if you say it's not half a motor, it's something else that does some other function, what function would that be?
So, in recent years, a biochemist named Michael Behe wrote a book called Darwin's Black Box in which he goes into the whole subject of molecular biology. He's a molecular biologist himself. And by the way, he says very prominently, he's not a creationist. But he says that basically, molecular biology has made a tremendous case against the theory of evolution, but scientists haven't really noticed. And he goes into very great detail giving case after case, in which we really can't explain how different things came about by chance and natural selection. So, if not chance and natural selection, how did they come about?
Another possibility, of course, is there is some intelligent design and direction in nature. That does not rule out the possibility that chance and natural selection has some role in nature but, it is certainly possible that systems like this can be designed through intelligence. So perhaps, there's some intelligence in nature. After all, every cell in our bodies contains complex systems, far beyond any supercomputer that human beings have yet built, and one wonders if it's just a product of chance. So, let's see. Next slide please.
So, what I wanted to do in the remainder of the lecture is give a few observations about historical views concerning how God might control nature. So, I'm going to start out by going back to the Renaissance period in Europe. This is a fellow named, Robert Fludd. He made a number of nice illustrations of medieval and renaissance cosmology. This is a picture showing the earth in the center. Fludd by the way, didn't think this was to scale, but you have the earth and oceans and atmosphere, a region of fire, this is Aristotle's philosophy actually. And then the spheres in which the different planets are orbiting. Here is the sun and the moon and you have the sphere of the fixed stars, and beyond that, you have a region of angels and beyond that, you have the Kingdom of God. Next slide.
This is another diagram illustrating his idea. Here, he's emphasizing the concept of an earthly realm, here, with earthly qualities diminishing as you go up and spiritual qualities increasing. Here beyond the region of the sun, he has different regions of angelic beings and so forth and this triangle, of course, represents the trinity.