Chapter 4

Direction and purpose

This allows us to see what is "pointed to" by the term "direction." Since instability is self-contradictory, and a body cannot exist as unstable, and since equilibrium is a state in which there is no internal contradiction, then obviously we can draw this conclusion:

Conclusion 5: The direction of any change is always and only from instability to equilibrium.

This needs a bit of discussion. First of all, what about the transition from equilibrium to instability; isn't that a change? In one sense, I suppose you could say it is, but in another, it isn't. Clearly the energy-level of the changing body is different when it is unstable from what it was an instant ago before it absorbed the energy; and so in that sense, there has been a change "toward" instability.

But that is not really an accurate way of looking at it. As soon as the body absorbs the energy, and even while energy is being forced into it, it is getting rid of it. Consider what happens as you press your foot on the accelerator of the car, making the engine run faster and faster. You are feeding energy into this system, and feeding more and more, making it more and more unstable, and so making it give off more and more energy. But it is not tending toward being more and more unstable; as soon as you feed any fuel to it, it begins to run, which is its way of getting rid of the excess energy; and the more fuel you feed, the greater the contradiction between the instability it now has, and the more work it does to get rid of this excess energy. Hence, from the very beginning, the tendency of the changing body is to return to its ground state, not to become more unstable; it is just that it keeps being "attacked," as it were, by more and more of this outside energy, and so it looks as if it is in a process toward greater instability, when in fact its own process is in the other direction.

Similarly, when you cook your soup, the heat of the pan makes the soup hotter--which is an instability, as can be seen from the fact that if you take the pan off the burner, the whole system cools down. What is going on is that the electricity in the burner excites the molecules of metal, giving them too much kinetic energy; they get rid of this by hitting the molecules of the pan, which then get too much energy, and start hitting the molecules of the soup (and the air outside the pan too, of course, as you can feel if you put your hand near it), which then become unstable and bang into each other harder and harder as more and more energy gets bumped into them. But these collisions get rid of this excess energy by hitting the air, which carries off the excess; and once you take the system off the stove and stop feeding energy into it, the energy is rather quickly dispersed out of the soup.

Something else goes on, however, in the soup, if you're actually cooking it and not simply warming it up. Some of the bodies you put into it are just not there afterwards; they have got combined into new bodies by the heat that is applied to them. That is, there has been a chemical change, and new chemical substances have been formed out of the substances that were the raw ingredients. Baked bread, for instance, tastes different from the raw dough, because in fact it is a different kind of body after it is baked.

But we will see this distinction shortly. For now, let us note that the change as such starts from the instability and goes toward equilibrium.

Direction means a change insofar as it is going from instability to equilibrium.

The direction is the "towardness" of the change (or its "fromness" if you want to look at it the other way). Notice that "direction in space" insofar as it is a direction and not just a space relation involves (at least an implicit) movement from the beginning-point to the end-point. Of course, the "directions" from the origin in coordinate systems are just mental devices that do not correspond to anything in reality, as I said earlier when talking about distance and position.

Direction, of course, is what "vector quantities" have in mathematics. In the non-technical sense that physicists learn, vectors are numbers that have "magnitude (quantity) and direction"; in rather purer mathematics, they are "ordered pairs of numbers," where it makes a difference which one comes first. This latter is an abstraction of the notion of "from" and "to," which of course is what we were just talking about when we spoke of direction. Hence, every vector contains an implicit change from the first number toward the second, usually illustrated by an arrow pointing from the first to the second (or a little arrow written over the number itself, if there is only one, in which case, you are supposed to know where the beginning and the end are).

Notice that energy itself in physics is a scalar (non-vector, ordinary) quantity, while force is a vector. And this fits with what we have been saying. Energy as such is equilibrium and is not headed anywhere; it has no direction, but just is. Force, on the other hand, is, like acceleration (also a vector) the causality of energy, its tendency to produce a change in what is affected (the accelerating body); and so it will have a direction.

In physics, when you integrate the force equations, you come up with work on the left-hand side; which as a "dot-product" or scalar product turns into a scalar (because the work is just the amount of energy used, and obviously as used up it is not headed anywhere); while on the right-hand side, you get the square of the velocity in the kinetic energy; and so even if there is velocity there, this product is also a scalar (because what you are interested in is the amount of energy, not where the body is moving to).

But the fact that the change always points to some equilibrium allows us to define another important term:

Purpose is the equilibrium that a change is directed towards.

First, distinguish the purpose clearly from the direction. The direction is "to get to the purpose"; the purpose is the end itself, the goal where the change stops. It is equilibrium, of course, because every body changes because it is unstable, and every instability implies an equilibrium it is directed towards; and once this equilibrium is reached, then that change stops--though, of course, if the body is unstable in different ways at the same time (which is not only possible, but usually happens), it still might be changing in other directions.

For instance, a body might be falling and also getting colder; as unstable gravitationally, its direction is downward, and its purpose is the lowest place it can be in that field (the closest to the center of the other body it can get to); as getting colder, it has an excess of heat energy, which it is dissipating into its surroundings, and the purpose of that change is the temperature which is the same as that of the surroundings ("thermal equilibrium"). This same body might also be reading this book while falling and cooling off, and the purpose of that change is the knowledge acquired by it; and it might be digesting food while all this is going on, and the purpose of that change is the biological equilibrium of having the "right" total internal energy. And so on.

The point is that, while a body might be constantly changing, you can still define a given change in terms of a given instability; and that particular instability always implies a given equilibrium which stops that particular change, and toward which that particular change is directed.

Hence, we can draw the following conclusion:

Conclusion 6: Every change has a purpose.

A body cannot change unless it is unstable; but since to be unstable is to be in self-contradiction, unable to exist as such, then the instability necessarily has an equilibrium that it is directed toward. And this equilibrium is its purpose.

In principle, the purpose of any change could be known, provided you knew what the instability was; but in practice it is not quite so simple.

Actually, one of the things that makes physics and chemistry so powerful as sciences is precisely that, since these two sciences deal with inanimate bodies, and since the instability in inanimate bodies is always an excess of energy, and since the equilibrium of an inanimate body will always be the minimum energy-level for the configuration in question, and since inanimate bodies of a given type in equilibrium are indistinguishable from each other, then by knowing "the initial conditions" (how much excess energy there is in this instability, and so on), and by watching what happens a couple of times to a body in these initial conditions, you know what the purpose of this change is, and you can predict that it will be the purpose of any body of this type under these conditions.

Physicists, however, don't like to talk in terms of purposes, even though they are constantly talking about predictable results--and "purpose" in the sense I defined it is nothing but the (in principle) predictable result of a change. The reason they don't is that it sounds as if the bodies "have a motive" while they are changing and "choose" to be at the purpose--or that somebody (God) is choosing for them--when in fact all that is going on is that a strain in the internal structure is righting itself, or excess energy is being got rid of.

This reluctance to look on changes "teleologically" (with reference to their end or purpose) is legitimate, given the history of the concept of purpose.

Actually, the original notion of "purpose" was more or less like what our definition states: the one the scientists have no use for: the human sense of purpose, which is the end chosen in making a given choice, as when I say, "I am going to finish writing this book," and then have as my purpose the finished book.

Aristotle gave the term "purpose" the purely metaphysical (or mechanical, if you will) meaning I defined it to have above, as simply the end of a change (or in his terms, the end of "being in potency," which, as you recall, meant the body's having its end "outside" it in some sense). And he pointed out that this was the primary meaning of the term, and human purpose (implying knowledge of the end and a deliberate choosing to get there) was a derived sense.

I think he was basically right. In my terms, this is what the relation between the two senses is: The purpose is always the equilibrium toward which some instability is directed. What happens in human beings, however, is that, because they can conceive by using imagination states of affairs (either in themselves or in other bodies) that are not the same as the way things are--as we saw in the section dealing with truth and goodness-- 1.5 then they can take this imaginary ideal and use it to cause an instability within themselves, which instability now has as its purpose that ideal(1).

That is, when you make a choice as opposed to simply evaluating a situation (and complaining, for instance, that it's not good), you use the ideal, which doesn't exist, as the basis for rearranging the internal energy you have (which is too high anyway for physical equilibrium) and making yourself unstable with an instability that has the ideal now as its (physical) purpose.

So the human sense of purpose is not really in itself different from the metaphysical (or, if you will, the "physical") sense I defined above; the only difference between human beings that "act for a purpose" and other changing bodies is how the instability got there; once it's there, the whole thing occurs automatically. This can be seen from the fact that if you choose to put your hand up to your face, your choice just creates the instability of your hand's not being at your face; but how your body goes about removing this instability is something your mind, really, has nothing to do with. In general, you don't even know how it happens at all; it just happens.

Hence, human purpose in the sense of "having a motive or goal" merely deals with how you become unstable by means of your internal energy, and not with what your body does with this instability and how it reaches the goal; so that the main sense of "purpose" is just what Aristotle said it was: (to use my terminology) the equilibrium implied in any instability.

However, since "purpose" does have these two senses, and since everyone before Hume thought that "goodness" was something objective; and since Aristotle muddied the waters (as we saw in discussing goodness in Chapter 10 of Section 5 of the first Part 1.5.10) by saying that the "end" or purpose was "the good" (because, after all, things naturally tended toward the end), then it wasn't surprising that Christian thinkers should confuse the two senses of purpose and bring "God's purpose" into the picture.

The argument, begun by Augustine and developed further by St. Thomas, went something like this: Bodies tend to act in predictable ways when they change; they do not change at random, but given instabilities have always the same purpose for the same kind of body. Hence, changes tend toward an end in an intelligible way (because predictable and not random). But the end is the good. Hence, bodies tend toward their good in an intelligible way. But unintelligent bodies cannot know what is good for them or do anything in an intelligent way; as unintelligent, they would act randomly. Therefore, they must be directed from outside themselves toward these purposes which are their good. But whatever is doing the directing, if it is not intelligent, must be directed ultimately by something which is intelligent, or the effect is greater than its cause. Therefore, what directs unintelligent beings toward rational goals must be some intelligent being. But since these bodies are directed to their goals by their nature (and not some outside force), then this "outside intelligent director" must be the Being which causes them to have this nature; and since this is the cause of their (finite) existence, this Being is God. Therefore, God directs all bodies toward their goal, which is their good.

There are, unfortunately, several flaws in this reasoning. First of all, it does not follow that an unintelligent being cannot act in an intelligible way. What "intelligent" means (certainly in this context) is "capable of seeing a state that does not exist and causing an instability whose purpose is that state"--or "knowing and choosing goals for a body," if you prefer.

But what is intelligible is "what can be understood" or in this case, "what is constant and not random." Now there is no effect in what is constant that says that it is inexplicable unless produced by something which can know ideals. All "constant" means is "the same all the time."

Hence, all we have to do to assume that a given instability in a given body has a given purpose is assume (a) that the body's structure (i.e. its parts and the form of the unifying energy) remains the same; and (b) that the "initial conditions" for the change are the same in all the cases in question (i.e. that the amount of internal energy over the equilibrium is the same in all cases). If we assume that the same type of body with the same excess energy will get rid of it in the same way, then we have all we need to account for the predictability and constancy of the change, without assuming that some being had to "choose for" it what its "purpose" was (i.e. that it had to have a purpose in the human sense in whatever was making it change)(2).

That is, suppose an inanimate body had no intelligent being directing it. Then it would either act randomly (as some do, such as dice) or constantly. What I was saying above is that (a) there is no reason for saying that it must always act randomly and that (b) if you assume that it is identifiable as the same body throughout the change, then this implies a constancy, which would lead you to expect a constancy in the change--which would make constancy of purpose intelligible without resorting to anything intelligent being its director.

The example of dice is instructive in this regard. The die when thrown operates randomly, because there is nothing in the throw making a given face appear on top as the purpose of the throw. But we know that in the long run, any given face will appear on top one-sixth of the time simply because the die has six faces and the instability is such that the minimum-energy state for a moving die is to be at rest with a face on the bottom(3). Hence, the purpose of the throw (because of the shape of the die) is being at rest with a face on the bottom (and its opposite uppermost). But there is no purpose that tells you which face it will be (or the throw was precisely not random). That is, you could throw the die in such a way that you started with the "one" on top in your palm and it rolled over four times and wound up with the "one" on top when it came to rest. But that would be cheating, of course, because the throw now is not random.

So we now have a change that is purposeless in some respect--which calls into question the notion that the Maker is "directing" every change toward its purpose, which is its good. True, you could argue that if you knew all about the initial conditions, you could predict what face would wind up on top, and so the purpose is there, but just not knowable. But while this may apply to the die, there are indications from quantum mechanics and catastrophe theory that there are changes where this determination of the purpose from the initial conditions is in principle impossible.

But notice that, even not knowing the purpose of any given throw, we know that in the long run the "one" will appear on top a sixth of the time simply because we know that the die has six faces all the time.

Hence, the purpose of a whole disconnected series of changes is known because of the knowledge of a constancy in the body, without our assuming that God is actually directing this body to make the "one" come up a sixth of the time for throws that have no connection with each other.

And so the point of the predictability is simply the constancy of the operating body, and does not of itself have anything to do with "being directed toward a goal by something that chose the goal."

Hence, the fact that changes in a given type of body lead toward predictable goals does not imply that they are directed toward their goals by what is intelligent and chooses the goal for them.

Secondly, if the goal is "the good," then we get into all the difficulties we saw in Section 5 of the first Part of "hidden goodnesses" in destructive changes, and in the contradiction implied in reversible changes, where what is better (the new goal) is what was worse (because it is what existed before the change in the opposite direction).

From all of this it follows that you can't argue (as St. Thomas did in his "fifth way" to demonstrate God's existence) that the constancy of changes in unintelligent bodies imply an intelligent director, who wills them to achieve their "good."

And what soured physicists ever since Galileo on this notion of teleology was precisely this dragging of God into the picture; because no matter how something changed, the "teleologist" would say, "Well, obviously God willed it to be this way, and if he did, then he had a reason for it, and the reason means that it's better this way."

True, if a change happens, then it means that God wills it to happen as it happens, because a change is obviously a finite act, and as such it must be caused to be what it is by God. But the only "reason" God has for any finite act is that it be what it is. He can't have any purpose for it beyond this, because this would mean that he would be dependent on its becoming whatever it became; and God can't be dependent on anything finite. Hence, God does not "want" the change to happen "because it is better this way." As we saw in Section 5, "better" and "worse" are meaningless except from a human point of view; and so all that God's causing the change to happen means is that it happens as it happens (and this implies as dependent for its specification on its structure and its instability). It's just the fact that the change is finite that brings God into the picture; anything else about it necessarily would have to have a different cause, because it would be a different effect from finiteness as such, and different effects necessarily have different causes.

So yes, there is something about changes and their teleology that involves God: the fact that the change is a finite act, and the structure and instability are also finite acts.

I should mention here, however, that there is something other than constancy or predictability in changes in the world that would lead one to say that God has got something to do with them. The Second Law of Thermodynamics says that inanimate bodies tend toward lower-energy states; and it also says as interpreted in physics that this means that things go from more organized toward less organized. But if you look at evolution, even the evolution of inanimate bodies, the basic direction is toward more organized bodies--exactly the opposite of what you would expect from looking at things "by themselves." This deviation from the "natural" direction needs explaining somehow.

We will see more of this in the next Part when we include living bodies in our look at evolution; but the point I am making is that while any given change is perfectly consistent with the Second Law of Thermodynamics, it is still true that the basic direction of evolution is the reverse of what you would expect from that Law. It is as if a die were thrown a million times and came up with the "one" on top every time. It could happen; but anybody who had any sense would tend to look at the die to see if someone had loaded it.

Hence, there is very strong evidence in evolution that the dice have been loaded; and since this tendency is in the universe as a total system, then it sounds as if the one who caused it to be what it is is the one who did the loading.(4)

With that out of the way, let me now draw another conclusion based on the notion of purpose as I defined it:

Conclusion 7: Equilibrium has no purpose.

Any body in equilibrium does not have a "goal" or purpose. It just is. Equilibrium sometimes is a purpose, if it is the equilibrium that ends a change; but it never has one; it is complete in itself; it is simply finite existence; it is what it is, and it stays what it is; it has no direction or "tendency"; it just is.

Well, but everything has a purpose, doesn't it? No. This is obviously false. Even those who hold it (those who talk about "God's purpose" for everything and say, "You wouldn't be here if God didn't have a purpose for putting you here") don't think that God has a purpose. He just is, even if, for them, he is the purpose of everything else.

No, what has a purpose, presumably, has not achieved its purpose, and so is incomplete until it has achieved its purpose. But this means that it is unstable. What else could it mean? But then, of course, it is precisely not in equilibrium; and once it achieves its purpose, then it (in that respect) has no further purpose and is intelligible in itself (or if you want to get picky is as finite intelligible in itself and through God as the cause of its finiteness).

Hence, all changes have purposes, and only changes have purposes. Equilibrium has no purpose and needs none.

Having discussed what instability implies with respect to the equilibrium to follow it, what about what it implies with respect to its preceding equilibrium?

It would seem that we could immediately draw another conclusion, that every change needs some external cause to get the body from instability into equilibrium; but it turns out that things aren't quite that simple.

This external cause putting something into instability is, of course, what has historically been called the "efficient cause," and is for practical purposes the only thing that anyone is referring to nowadays by the term "cause" itself.

The argument, which we find in St. Thomas's Second Way to demonstrate God's existence, is that no being can put itself into "potency," because "being in potency" means to lack an act, and only a being "in act" can cause something; therefore, any being "in potency" has to have an external cause for its being in potency.

And even in our terms this seems obvious; because if the being has too much energy to exist in this form, then obviously it couldn't have given itself this excess of energy; and so it needs an external cause.

This is true. And since inanimate bodies are unstable only when they have too much energy, we can in fact draw this conclusion:

Conclusion 8: Any instability in an inanimate body has to have been introduced from outside it.

If this efficient cause is itself energy from a body--the efficient causer (it doesn't need to be, notice, because a spiritual act, as active, can cause changes)--then obviously, this causer will have to be a body which is giving off energy, and so is going from a higher to a lower energy state--or in other words, it has to be a body which is itself unstable, or is changing.

And this is especially true if the efficient causer is an inanimate body, because the same argument applies.

Note, as St. Thomas says in his first way, that it is perfectly true that this retrogression cannot involve an infinite number of causers like this, because if you look at just the effect (unstable because of too much energy) and its immediate causer (unstable because of too much energy) then the combination of the two has an excess of energy over equilibrium, and therefore, the combination is not explicable.

If there were an infinite number of these unstable causers, then the whole infinite set would be unstable with an excess of energy over its equilibrium, and so would be impossible (because instability, remember, is a self-contradictory condition, and contradictions can't exist by themselves). Hence, there has to be a "first causer" of any series of unstable inanimate bodies causing (by their sloughing off of excess energy) instability in other unstable inanimate bodies.

It sounds, then, as if St. Thomas' first and second ways of demonstrating God's existence were valid. Then why did we bother to go through the elaborate rigmarole in Section 4 of the first Part?

Because the argument does not in fact lead to the existence of an infinite being, but only to one that (a) can cause a change, and (b) is not causing it by its instability.

But living bodies exist in equilibrium at a high energy state, which is unstable from the point of view of the physics and chemistry of the body (i.e. the biological equilibrium is above ground-state equilibrium). Hence, they can, while still in equilibrium, rearrange this "physical excess" of energy within themselves, and so can initiate their own changes, and so do things which give off energy--which they then recoup by actively "sucking it in" from the environment.

Hence, although it seems that St. Thomas' argument leads to the existence of God, all it does is lead to the existence of a living being(5). And, in fact, when I decide to type at my keyboard, I set in motion (by my choice) a series of electrical impulses to my finger muscles, which then tap out the letters, and these instabilities in the keys create instabilities in the contacts below them, which then make the circuits unstable, which put letters on the screen and onto the disk. My choice is the "first mover" of this series of changes, and as soon as I say, "Enough for one day! I'm tired!" the whole series stops, because the excess energy is not being poured into the computer, and it falls back to its ground state.

Now you could argue that the whole universe (if its evolution even remotely resembles what astronomers say it was) was once inanimate (because stars are too hot for living bodies to exist, and there had to be stars before planets); and if it all began in a Big Bang, then obviously what "banged" was an unstable inanimate body, and something or other had to get it into that condition.

But this is still no proof, because of two possibilities: First, what got it into its initial instability could be a living being--or even an unstable body--beyond it (after all, our argument for God's existence does not rule out the possibility that we might have begun to exist as the product of some super-body beyond the Einsteinian curved space, and so nowhere with respect to it). Secondly, depending on the total mass of the universe, it may be that the universe is alternately expanding and contracting cyclically, and the Big Bang is just one of its phases of internal trade-off of the same amount of energy. In this second case, the universe is in equilibrium, not unstable, and so needs no efficient cause.

Still, if the universe as a whole is unstable, then obviously something beyond the universe either "made it from nothing" or got what was in equilibrium out of equilibrium by pouring an excess of energy into it. The point is that you can't automatically call that being God, because such a being does not need to be infinite to do the job.

Now then, the only thing left to mention before taking a look at the actual act of changing is to make explicit something I have already referred to: that there are two different kinds of changes.

A substantial change is a change in which the body afterwards is a different kind of body.

An accidental change is a change in which the body afterwards, while different, is still the same kind of body.

Obviously, in the case of an accidental change, the form of the unifying energy is such that its excess quantity does not split the body apart; the body is able to get rid of the excess energy and return to its ground state (or as nearly as possible, given that some energy is coming at it all the time) while keeping the same basic configuration of the body.

In the case of the substantial change, the instability is such that the unifying energy cannot cope with the amount, and so the body must be reconfigured, with a structure that can deal with the amount of energy in question. Thus the body becomes one or more different kinds of bodies, with a different kind of unifying energy; and very often, this new body (or these new bodies) exist at a very different energy-level from the original unstable body; but the restructuring is able to get rid of the excess--and we have something like an explosion.

For instance, the very first experiment in chemistry I performed was to heat mercuric oxide in a test tube. The first thing that happened was that the powder got hotter: an accidental change. The energy added to the molecules was not great enough so that they couldn't release it by moving and hitting each other more and more vigorously; which is what the heat was.

But when a critical temperature was reached, the molecules added so much energy to each other as they hit each other that it was no longer possible for them to exist as mercuric o

xide; and so the molecules "broke apart" into mercury and oxygen; and oxygen, of course, as a gas, can handle much more heat, and so can mercury as a metal.

Note that a given interaction between bodies can be a substantial change on the part of one of the bodies and an accidental change on the part of the other. When you eat an oyster, say, and it gets into your digestive system, the oyster stops being organized as an oyster (and so it undergoes a substantial change); but the parts of the oyster and a good deal of its energy is absorbed into your body, replacing worn-out parts and increasing your total energy up to (let us hope) your biological equilibrium level; and this is an accidental change for you, since you obviously are still a human being throughout the process of increase of energy.

Observe that, since you are a unit, the oyster (or parts of it) become you. You do not "have" an oyster "inside" you except for that brief time before it gets digested (or really the briefer time before it dies). Once it is assimilated, there is only one body there, and that is you. You are not, as I have stressed, what you are made of; you are parts united with the special unifying energy that is your unique unification of material.



1. The idea here, as you will see in the next Part, is that living bodies, as existing at a super-high energy level (above their physico-chemical "ground state"), have some excess internal energy that they can "play around with." The human spirit uses this residual energy in the brain and directs it into certain motor nerves, setting up instabilities in them which lead to action of various organs of the body; and thus, a living body can initiate changes in itself, as Aristotle saw. So the goal you conceive for yourself, insofar as it is such as to produce this instability, turns out to be the purpose of the (physical) change you set up as the purpose in the sense of the "motive."

2. Of course, whatever accounts for its finite existence (i.e. God) would also account for its structure as finite (since the "structure" is, in the last analysis, the complex limitation of existence which it "has"); in which case, the stable structure and the "initial conditions" are built into it; and so its tendency toward this equilibrium under these conditions was in fact caused by God. In this sense, the Scholastics are right. The problem I have with this is that it doesn't explain why it has this tendency and no other, since God is the cause of finiteness as such, and only secondarily of the specific finiteness things have (which definiteness is also caused by other creatures).

3. This preservation from total randomness, by the way, is not a logical necessity. There is no reason why, if a die has six sides, it cannot operate totally randomly, so that in the long run it is not predictable that the one-spot will appear on top one-sixth of the time. The reasoning goes this way: There is no reason why the one-spot should be the one to appear on the first throw (obviously). But the first throw is not in any way connected with the second, and so there is no reason for it to appear on the second, and the same goes for the third, the fourth, the fifth, and so on to infinity. There is no reason, therefore, given even an infinity of throws, why the one-spot should ever appear on top. For those who say, "Given an infinity of throws, all possibilities will eventually have to be realized," I answer that the one-spot's appearing not at all, or only once, or whatever number of times, is, as I just showed, a real possibility; but if it appears not at all, this contradicts its appearing once or one-sixth of the time. That would mean that contradictory possibilities would have to be realized, which of course is a violation of the Principle of Contradiction--on which logic and mathematics, by the way, is based.

The point is that, however much it might "stand to reason" that the one-spot in the long run will appear one-sixth of the time (because the die always has six and only six faces) you can't say that there's mathematical necessity in the laws of probability; it's just that the material universe is so constructed that they work (and the "law of averages" where a run of three hundred one's in a row means that it "stands to reason" that its coming up on the next throw is extremely unlikely--because three hundred one appearances of the one on top is much more unlikely than three hundred--doesn't work. Why? Both "stand to reason," but the universe is just constructed that way. So, interestingly, the laws of probability are empirical laws, not strictly mathematical ones.

4. I should mention that physics counters that we don't know of this tendency in the universe as a whole, because we don't know if stars with planets are scattered through the universe, or whether our earth is unique; and with so many billions of stars, it is not unlikely that by chance this anomalous reversal of the basic tendency of evolution would appear in some small pocket. This is true, and is why the argument I gave is no "proof" for God. But it should be said that there really shouldn't even be stars, if the universe began with an explosion; the detritus of that Big Bang should have distributed itself evenly throughout space, with perhaps only a very few stars, which would then burn themselves out. So the case is by no means closed.

5. Actually, this is not quite true, since non-human living beings only have acts which are in some sense energy (though surpassing the limitations of their quantity, as we will see). But human choices are spiritual acts, having no quantity in themselves; and yet the clearly can initiate the rearranging of energy in the brain, which then causes the change in the body. Unlike God, however, they cannot directly initiate changes outside their own body.