[The material of this chapter can be found in Modes of the Finite, Part 2, Section 2, Chapters 1-3.]

5.1. Multiple units

Ordinarily, we do not experience, and in all likelihood cannot experience, a single form of energy in isolation. Energy as we know it always is an act "belonging to" or "produced by" some object, which is what we think of as "really existing." That is, the color of the page is what the page is doing to reradiate (or "reflect") certain combinations of wave lengths of the light falling on it; and it is the page which "really" exists; the whiteness is a kind of way it reveals its existence to us.

Note that we speak of the whiteness of the page; but the "of" here is used in a different sense from that in the last chapter, where we spoke of "experience-of." Experience-of means "experience about or referring to [something other than itself]"; and act "of" means "an act done by [something other than just itself]."

5.1.1. Sets

In any case, energy is experienced as not alone; and there are many different ways of considering multiplicities.

DEFINITION: A SET is many somethings considered together as a unit.

Obviously, if you are going to think of many somethings at the same time, you have to think of them together somehow; and so the most general category is the set.

Note that the "many" of the set don't have even to be real; a set of ten white unicorns is a set, even though there are no white unicorns. Or the many may be real, but there is no real connection among them, such as the set of all red objects. It makes no difference to any of the other objects that a given member of the set exists or is red. That is, if you dye one of the red objects green, then of course the set has one fewer member; but it makes no real difference to any other member that you did this.

A MERE set has no real unification among its members.

Note that the "units" that make up the set are called "members," not "parts" or "elements"; and the members are said to "belong to" the set. A note on why mathematics works

Set theory in mathematics is the logic of the relation "belonging to" and the mathematical set is a mental construct which is the abstraction "whatever is belonged to," and the mathematical member is "whatever belongs to [a set]"; and of course a subset is simply "whatever is belonged to and belongs to."

The "objects" of mathematics are always created by the mathematician from the relationship he is exploring, and so never exist as such, and have only the properties of being related by the particular relation. Mathematicians, then, do not find objects and discover facts about them (relations they have); mathematics starts with a relation and explores the implications of the relationship itself by inventing fictitious "objects" whose sole function is to be related by this relation. This helps the mathematician not clutter up his reasoning by properties of the real objects that have the relation (he simply invents a "causer" which is identical with the "cause"). This, of course, is why mathematics is abstract.

The reason mathematics works in the real world is that real objects are related in the ways mathematicians explore; and so they will follow the logic of these relationships. The reason that real objects don't behave exactly as mathematics says is not that real objects fall short of the mathematically fictitious "objects," but that they have other relationships which usually interfere with the "pure" working of the mathematical laws.

Thus, the angles of a real triangle never add up to exactly 180o, because the real triangle isn't ever exactly on a plane, and the lines definining it are never infinitely thin, and so on. But insofar as the real triangle is a plane figure, then it behaves consistently with the mathematics of triangles.

In other words, what mathematics says about real-world relations is the truth and (if it's doing its job) nothing but the truth, but not the whole truth. Thus, the reason why certain mathematical constants keep popping up where you wouldn't expect them is that the object is actually related by the basic relationship in question, even though it doesn't seem to be, and this is just one of the aspects of the relation.

For instance, pi (the relation between the diameter and circumference of a circle) appears in equations of wave motion. Now mathematically, a wave is describable as the "projection" on the "real plane" of a circle half of which is in the imaginary plane. But waves aren't really going out of space into some never-never land half the time and simply appearing in the real world. Then what is going on?

The relation pi expresses is described mathematically (and was discovered from) the relation between the diameter and circumference of a circle (that is, that the circumference is always 3.14159... times the diameter); but it is actually part of the logic of anything "cyclic" or repetitive. Apparently, when you quantify any deviation from something which is such that it "returns" somehow, this number is connected with the deviation-return sequence. So the circle's internal relations are just a special case of a more general relationship (what goes round in a circle returns to itself, describing the circumference); and so we don't have to pretend that real waves are making funny circles somewhere.

Something similar applies to square roots. They were originally discovered by attempting to measure the diagonals of squares drawn as closely as could be to the "abstract square" of mathematics. But what they express is a more general relationship: one of the aspects of the relation between multiples and the multiplied; it turns out that part of this relationship allows for a "multiplied" that is not itself a unit or multiple of other units--and we find this (or an approximation of it) in the real world; and that is why square roots have applications in physics.

So the key to discovering what "mathematical constants" and so on mean in the real world is to examine what the relationship is that the particular branch of mathematics is exploring; the constant will turn out to be some invariant aspect of that relationship, however it was first discovered historically by mathematicians (who originally thought they were dealing with some kind of "really real" objects in a world better than our own).

5.1.2. Systems

But to return to our multiple units, obviously there are multiplicities we consider together because they are connected together. The solar system is not just the set of the sun and the planets; there is the gravitational interaction of all of the "members" of this set that makes them act together--so that, for instance, the whole solar system moves together round the center of our galaxy, and its gravitational interaction with Alpha Centauri (the next closest star) has the "center of mass" as the center of the whole solar system, not just that of the Sun. There are, then, certain (in this case insignificant) respects in which the solar system behaves as or acts as a unit.

But if it acts as a unit, there is a sense in which it really is a unit, since existence, as we saw, is activity.

DEFINITION: A SYSTEM is many activities that in some respect act together as a unit.

So there is both a real multiplicity and a real unity in a system. In one sense, a system is a special case of a set: sets are multiplicities thought of as a unit; and systems, since they are real multiplicities, are multiplicities, and since there is a real unification among them, would naturally be thought of as units.

But sets as opposed to systems have no real unification among the members; these are the "mere sets" mentioned above.

Note that a system is really very peculiar, when you think about it: it is both really one (it acts as one) and really many (it acts in other respects as many) at the same time. There is a contradiction lurking here, which is a version of the contradiction connected with something's being finite; but we will not pursue it, since that study belongs to the science of metaphysics, not specifically what we are dealing with.

Note also that Immanuel Kant was basically not correct when he put the unification of our experience of systems solely on the side of the perceiver. This would make it impossible to distinguish sets from systems, which we can do. It would also not be possible to account for why we are forced to consider some systems as not parts of others (i.e. why you cannot perceive your hand and the book you are reading as a single unit, while you must perceive your hand and your fingers as a single system).

5.1.3. Bodies

There are systems whose elements are so loosely connected that they are almost independent of each other. Each stone in a pile of stones does act on the others to some extent--so that the ones on the bottom, for instance, hold up the ones on top. But this interaction is less significant even that the one in the solar system. Then there is the interaction among students in a classroom (in not talking out of turn, and so on), though each is really interacting more with the professor than with the other students. Then there is a social group like a band, where the members have to adapt themselves to what the others are doing, or an army, which is supposed to act as a "unit"; and then there are things like tables, where the pieces of wood are so closely united that picking up one piece means picking up the whole table; and then there are things like dogs, in which the parts don't exist except for their "functionality" in the behavior of the whole. That is, it is "really" the dog that bites, not its teeth or mouth.

The point is that the "tightness" of the unification of the elements of the system goes all the way from practically nothing at all to so great that the system is much more obviously "one" than it is "many." And when it reaches this level, we give it a different name:

DEFINITION: A BODY is a system whose unification is so tight that it behaves as a unit more than it does as a multiplicity.

Living bodies are the primary examples of such things; but there are bodies in the world of physics and chemistry as well.

If a system has activities which are not acts of the elements, even when together, but rather has acts that are special to it as a system, then it is a body.

For instance, if you mix hydrogen and oxygen, what do you get? Wrong. You get a mixture of hydrogen and oxygen. If you pass a spark through this mixture, or drop a lighted match into it, however, you get an explosion, and--water, which has properties that are neither properties of hydrogen, nor properties of oxygen, nor properties of the mixed gases.

Water, then, is a body.

This would apply, of course, really only to a single molecule of water; because "a body" of water has no special properties that don't belong to a single molecule--except those that are explainable by many molecules together. Even the liquid character of water (though it appears only when there are many molecules together) is really traceable to the characteristics of the individual molecule (the way it tends to connect itself with other water molecules).

In speaking of "bodies" in physics and chemistry, we are really referring to individual units like atoms or molecules. What we ordinarily call "inanimate bodies" are SYSTEMS of many bodies.

Note that the atoms that make up molecules are NOT bodies (because the molecule is the body), nor are the subatomic consitituents of atoms bodies. A body is always a unit, not a part of another body.

In the realm of living bodies, the living system IS a body, since it has many acts belonging to it as a unit.

So things like tables or even pieces of wood, which we would think of as single units, are not really "bodies" in the strict sense, because they have no real activities that are distinctive to themselves as units as opposed to being simply a sum (or system) of their parts.

With a piece of wood, for instance, if you break it in two, both pieces are still what they used to be; and if you keep doing this, you still get smaller pieces of wood--until you get down to the individual molecule. If you "break" this, however, you get something that isn't wood at all. So this is the body; the piece of wood you can see is a system.

However, if you "break" a dog apart, you get something that isn't a dog at all, and behaves quite differently from a dog. So a dog is a body. So is a plant. If you cut off a branch from a tree, in general it dies, and behaves quite differently from the way it did while a part of the tree; hence, the tree is a body.

DEFINITION: A MEMBER is one of the units in a SET.

DEFINITION: An ELEMENT is one of the units in a SYSTEM.

DEFINITION: A PART is one of the units in a BODY.

There is nothing profound about these definitions; they are simply the way we usually use the terms--and in ordinary speech (and sometimes in science, too) we are apt to use them interchangeably. The reason for this, of course, is that the distinction between a "mere" system and a body has a basis in fact, but is in a sense arbitrary; and when you get into borderline cases, it isn't obvious where the line dividing them is.

I have made the line seem perfectly clear: if there are acts of the unit as a whole that aren't explainable by the parts as connected. But in practice, this doesn't work out so neatly. Is a crystal a body, for instance, or is it a system of molecules? You could argue either way. I incline in the direction of saying that it is a system, myself; but that is really more my preference than any conclusion forced on me.

And in the last analysis, the body is really just a very tightly bound system--and in that sense, it isn't really a different sort of something from a system itself (the way systems, as really unified, are different from "mere" sets that have no real unity). So it isn't surprising that there should be differences of opinion on where "mere" systems end and "true" bodies begin.

But on the other hand, it is silly to make no distinction between the two, and say that there isn't any real difference between a pile of rocks and a dog. The extremes are so extremely different that they don't deserve to be put in the same class; and hence, the difference between systems and bodies is valid.

There is a tendency of physics to consider bodies as systems, whereas chemistry is more apt to consider bodies as units.

This is just a tendency, not something absolute. But physics tends to look at how the parts of a body are connected--the internal forces--while chemistry tends to look at how bodies become different kinds of bodies when certain things happen to them. Chemistry doesn't ignore internal forces, nor does physics pay no attention to the "newness" of a larger unit as a unit; but the basic orientation or focus is as I mentioned, and can explain some of the differences in approach between physics and chemistry.

5.2. The body and its parts

Much that I am going to say from now on will apply both to bodies and to systems. I could treat systems and then bodies; but since they are essentially the same sort of reality, differing only in degree of unification, this would involve either a lot of repetition, or would give the impression that systems are the "primary" sorts of things, and bodies are a kind of "second-class" type of system--when it seems to me that the best description of things is the other way round.

Hence, I am going to talk about bodies, and only mention systems in passing, when there is some need to distinguish what happens in a system from what is going on in a body; in other cases, I leave it to the reader to make the adjustment based on the fact that the body is primarily a unit and secondarily a multiplicity, while the system is the opposite.

Let us first make the a couple of obvious remarks about what is necessary for a body to be a body, and then explore these remarks in detail.

A body has ONE FUNDAMENTAL ACTIVITY making the parts behave together as a unit.

That is, the body, as a real unit, has to have an internal cause of the unity of the many parts. And since existence is activity, then this means that the parts have to act together as a unit.

There have to be MANY parts for something to be a body.

This is obvious. If the "body" is simple (a single act) then it isn't what we are calling a "body" at all, however "material" that act might be, but is simply a single form of "free" energy. Such an act (if there is one) could not be considered a special case of a system, and so would be completely describable in the context of the preceding chapter, and would need no further discussion. What we are considering as "bodies" are multiple units.

The PARTS of a body are not necessarily themselves simple. They may be SUBSYSTEMS.

The "ultimate" parts of a body, perhaps, are single forms of energy; because logically, if the parts are complex and these subsystems (i.e. the parts) are complex, eventually you would have to get down to some subsystem whose elements were not complex--and it would seem reasonable to say that these "ultimate" elements are just single forms of energy. For instance, the parts of a salt molecule are a sodium atom and a chlorine atom; the sodium atom (as a part of a molecule) is a system of a certain number of protons, neutrons, electrons, and so on, unified in a certain way; and the protons are perhaps systems of quarks unified in a certain way; and the quarks (if there are such systems) are unifications of certain forms of energy the "carriers" of the strong force, whatever accounts for "spin" and so on--if indeed these are real forms of energy. When you get down this far into the elements of a subsystem of a body, it is very hard to tell what you are actually dealing with.

In any case, it is not necessary to regard only the "ultimate" parts as the parts of the body. Subsystems interacting in definite ways with each other will do nicely as the parts. Thus, your heart is a part of your body; and it is made up of cells of a certain type unified in a certain way (for a certain function in the body as a whole); and so the cells are "more ultimate" parts, if you will; but even they are very complex systems of molecules, and the molecules are extremely complex systems of atoms, and so on.

It depends on the focus of the investigator what is to be considered a "part" of a body.

There is nothing wrong with considering a body as a unification of various systems of organs, such as the circulatory system, the digestive system, and so on. In this way of considering the body, the systems of organs are the "parts" that make up the body. On the other hand, you can consider the body as made up of the organs themselves: the heart, the veins and arteries, the skin, the stomach, the intestines, the eyes, the brain, and so on; and from this point of view, the organs are the "parts." If you want to consider the body as a unification of cells, then the cells are the "parts," or as a unification of organic chemicals, then the molecules are the "parts." And so on.

No one of these ways of considering your body is "the right way." Your body, for instance, is not "just" a unified collection of chemicals--as if you go from the chemicals (which are the "real" parts) right up to the whole, without passing through the unifications into cells, organs, and systems within the body. On the other hand, there is nothing wrong with considering the chemicals as parts of the body, as if the organs, say, were the "real" parts and the chemicals that make them up were not really there.

The reason that there are disputes about what the "real" parts are (which would seem--and is--silly) is the following fallacy:

The SYSTEM-FALLACY is the consideration of a body as "really" a mere system: considering the PARTS as what it "really is," and the UNIFICATION as "secondary."

In a body, remember, it is the unity which is primary; the parts are secondary to the unit, not the other way round.

This is most obvious in living bodies. The organs and so on in a living body are "functional": that is, they exist for (in some real sense) the activity the body as a whole can perform because of them.

As Aristotle said, "We do not see because we have eyes; we have eyes in order to see." This can be shown by the fact that the living body controls the acts its organs perform; we close our eyes sometimes, preventing them from having their "proper" function, when we think the body as a whole should not be seeing. We even remove parts of the body when they get in the way of the functioning of the body as a whole--such as fingernails when they grow too long. This indicates that the whole is not a kind of "aggregation" of the parts which are what is "really all there is to" the body; but the whole is what is "really there," and the parts are subordinate to it.

This is hard for the "accidentalists" to swallow. Ever since Darwin and the survival of the fittest, there has been the tendency among scientists to consider that evolution has been "explainable" completely by chance--and so the bodies we have are just accidents of natural selection, from which it follows that the parts are what are primary and their unification an accidental accretion. That is, the logic of this way of looking at things is that we see because (in the course of evolution) we acquired eyes, not that we have eyes in order to see. That's old-fashioned unscientific superstition, they think

The trouble with this view is that it supposes that chance can explain something. But, as we saw in discussing the Laws of Probability, the chance element in what behaves probabilistically explains nothing at all about the probabilisitic behavior. It is what is non- random about the system or body in question that gives the rational element to probabilistic behavior.

Hence, evolution is by no means "just chance." It involves chance; but the structure of the evolving organism opens up certain possibilities, which are then realized at some given time by chance. But the possibilities are not realized by chance; they depend on (a) their being realizable in the thing that is evolving and (b) there being a trigger-mechanism in the environment capable of realizing them. The only thing that is "due to chance" is when this trigger will activate the possibility in the evolving body.

On such a flimsy thread does the scientist's materialism hang.

BEWARE, therefore, of considering the parts of the body as what is "really" real about it.

SECOND CAUTION: The forms of energy that are the BEHAVIOR of the body ARE NOT ITS PARTS. These are ways in which the body behaves as a whole, and are not what it is "made up of."

That is, color, mass, shape, motion, elecrical fields, and so on (the things we normally call "properties"--as we will technically call them later) are not parts of the body, but ways in which it acts (as a unit of many parts). We will have to discuss the body and its properties later, after we have considered the body and its parts more closely.

5.2.1. The unifying energy

Let us now look a little bit more closely at the activity that is the cause of the unity of a body. We said that it had to be one activity; and the reason for this is that if there were two of them, they would either be really independent of each other, or they themselves would be connected by some activity. In the latter case, of course, the cause of the unity would be this "connecting" activity; in the former case, the "body" would behave as two independent units, because there would be nothing to give it a real unity. Hence, what makes the body behave as a unit must be one single activity.

The activity that unifies the body is NOT DIRECTLY OBSERVABLE from outside the body.

That is, whatever this activity is, it is not one of the properties (the "behaviors") of the body that you can get at from outside it. Why is this? It is by definition whatever accounts for the unity of the body. Hence, its function is to connect the parts into a unity. If it acted outside the body, then it would obviously be connecting this external thing it acted on into the body--making it part of the body. But this is absurd, since then the external thing would not be external.

Further, since the unifying activity, whatever it is, makes the body a unit, then it follows that it is the activity which is ultimately responsible for EXcluding from the body whatever is "foreign" to it. Hence, it not only keeps the parts together as a single unit; it keeps everything else out of the unity.

Therefore, the activity unifying the body is exclusive to the body, and is not directly observable from outside. You have to argue that it is there from the way the body behaves (i.e. as we did above: that it has properties that belong to it as a unit, and aren't explainable just as a sum of the parts).

The activity unifying the body is a form of ENERGY.

This would naturally be expected, if the parts themselves are bundles of energy and ultimately energies. But you can argue to it this way:

A) Bodies with (for practical purposes) the same parts act as units in different ways, so that we recognize them as different kinds of bodies. Thus, dogs and cats have the same ultimate parts (the same chemicals in the same amounts, more or less, and in the same proportions; or even for practical purposes the same cells; obviously, at the level of the organs there is a difference). Then the difference is not (ultimately) what is unified, but the way in which it is unified.

True, the genetic chemicals determine the way in which the body is ultimately unified; but (1) these chemicals are basically a way in which the atoms are unified; and (2) there are differences which determine only different individual dogs, not different species; and so the differences in chemicals have to determine a different basic kind of unification of the body as a whole in order to determine different species.

So the conclusion from A) is that the activity unifying a body is a FORM of activity.

B) But there are bodies of the same type which are made up of the same ultimate parts, but yet are different from each other.

For instance, there are different dogs, even of the same breed; they have different colors, different degrees of alertness, and so on. Now the form of the activity unifying the body can't account for this; because it accounts for how all the bodies are the same (and different from cats); nor can the parts account for it, because all the dogs have for practical purposes the same parts. Therefore, the form of activity unifying the body must be limited in DEGREE, which means that it is a form of ENERGY.

Conclusions we can draw from this:

The FORM of the unifying energy of the body is what accounts for the KIND OF BODY which the body is.

That is, the form of the body is the form of the unifying energy of the body, not the form of some part or parts.

And since this unifying energy is (as we saw) not observable from outside the body, it follows that there is no direct way to know whether a body is a given kind of body or not. It must be argued to from (a) similarities of substystems (larger parts), and (b) similarities of behavior as a whole.

That is, if an animal has organs that are significantly different from another animal, this argues that it has a different form of unifying energy, and is a different kind of animal. Why else would the organs be different? This would be confirmed if the behavior as a whole were significantly different.

Thus, a cat has different sorts of organs from a dog, and a cat doesn't act (as a whole) like a dog. Since we can't observe the unifying energy directly, we use these two as clues to tell us that cats are different kinds of things from dogs. But note that this means that a caterpillar is a different kind of body from a butterfly, even though the caterpillar turns into a butterfly. Its body has different sorts of parts, and its behavior as a whole (it eats leaves, while the butterfly eats nectar) is significantly different. Hence, the kind of body is not coextensive with the biological species.

[For those interested in the application of this to the abortion question: First, the issue of whether a fetus is or is not a human being will never be settled by direct observation, but can only be got at by inference (since it is the form of the unifying energy of the fetus's body which would make it a human being). Second, the fetus is not part of the mother, since the fetus does not act for the mother's benefit, but its own (it takes nutrients and can make the mother sick, while it develops normally, for example). Third, the fetus is not like a caterpillar as opposed to a butterfly, since it develops organs from the beginning which are not adapted to its life inside the uterus, but its life outside. It also performs very soon (within a couple of months of its nine-month stay) actions which make sense only in its life outside the uterus (breathing, swallowing, thumb-sucking, etc.). But since the parts and the behavior indicate the form of the unifying energy, this means that the fetus is already a human being from the beginning.]

The QUANTITY of the unifying energy of the body accounts for there being DIFFERENT INDIVIDUALS of the SAME FORM of body.

Just as the kind of body depends, not on the parts united, but the form of the unifying energy, so individual differences in bodies of the same type depend, not on the parts united, but on the degree of the unifying energy.

That is, different dogs (of the same breed, say, ignoring whether differences in breed imply different forms of unifying energy) are different, not because they have different parts in their bodies, but because they exist at different energy LEVELS for this kind of unification of body-parts.

To put this another way, what it amounts to is that the form of unifying energy called "dogness" is itself limited, as heat is or mass is, and so on, so that no individual dog exhausts "what it is to be dog"; one dog can always do doggie acts that other dogs can't and vice versa: pit bulldogs can bite and hang on in ways that schnauzers cannot, and greyhounds can run better than other dogs; and so on. There is no such thing as "the absolute dog" any more than there is such a thing as "absolute heat" that is not some temperature of heat.

[It should be noted in this connection, however, that human beings have control over the level of limitation of their humanity to some extent, and can (by choosing) perform activities or refuse to perform activities that make them different from other human beings. This control over one's individual differences from others is called self-determination, and it is different from what you find in the objects that physics and chemistry deals with. Individual differences which are "built in" to the unifying energy by its given quantity are called individuation within the kind of body; individual differences which are due to choices are called individuality of the person in question. The two are similar in results; but the source of the individual characteristics is different.]

5.2.2. Matter

This brings us to a concept that was originally philosophical (the term is Aristotle's) and is used in science, but with a not clearly defined sense: matter.

"Matter," of course, is whatever it is by which things are "material," or are bodies. It is clearly the opposite of "spiritual," from which we can infer that spirits aren't bodies. We usually think of material things as "solid," but there are things like gases which don't fit that notion and clearly are not spiritual. Interestingly, when something is material, it is "there" (i.e. exists in a place), while spiritual things like ideas don't seem to have a location (the idea we share that 2 + 2 = 4 is one idea, and so is not really somewhere "in" my head and yours, let alone "between" it).

In physics, "matter" means either (a) a body (as when the physicist talks about the "propagation of light in matter") or mass (as when he talks about "the conversion of matter into energy). Mass, however, is one of the acts of a body, and a body itself is different from its acts. The two senses of the word are actually incompatible, even if related. Hence, "matter" is not a technical term in physics; it is just one of those words "everyone is supposed to know the meaning of."

If "matter" is what makes a body a body, then it follows that

DEFINITION: MATTER is the name given to the QUANTITY of UNIFYING energy.

[Note: in subsequent treatments of this subject, I stopped using "matter" in this sense, because it only adds to confusion of an already confusing subject; in later works, such as Modes of the Finite I simply speak of the quantity of the unifying energy.]

That is, quantities, as I said in the preceding chapter, are not exactly the same. All are limitations of forms of activity, but the quantities belonging to one form are only analogous to the quantities of another form.

And this is recognized in science by giving the quantities special names depending on the form they are quantities of. Thus, temperature refers to the quantity of heat, charge the quantity of electricity, mass the quantity of gravitational energy, wave length the quantity of electromagnetic energy, and so on. If the energy is unifying energy, its quantity is called matter.

The reason for this is that something is a body if it is (a) not spiritual, and hence has not only the limitation of form, but that of quantity as well, and (b) is a unified multiplicity, implying that it has a unifying activity. But the unifying activity is what defines the thing you are dealing with (its form defines what kind of thing the body is, and its matter defines its individuality within the kind). Hence, the "bodiliness" of the body is due to its unifying activity--and it must be due to the fact that the unifying activity is not spiritual, but has a quantity.

Therefore, the "matter" that makes the body material is precisely the quantity of the unifying energy--which is what our definition says.

This also is consistent with the original usage of the term. Aristotle mentioned that matter is what is responsible for there being different individuals of the same type of thing; which is exactly what matter in the sense above does.

Aristotle, however, thought of matter as some kind of "stuff," (in fact, the word he used for it basically means "stuff") undefined in itself, which acquired a form: as a kind of "ability" to have a form. He was thinking backwards, as can be seen from the fact that he thought that form limited matter, when the facts are the other way round. Matter, as the name for a generic limitation is not itself limited, because it is the abstraction of limitation. Aristotle mistook this abstraction as "non-limit" (as existence is unlimited in itself); and that was why he was fooled.

That is, just as the concept "temperature" does not point to any definite temperature, but applies to any limitation of heat, you can see that, if you wanted to look at temperature in a peculiar way, you could say that temperature was "unlimited" until it "received" a heat, which then made it a definite temperature of heat. Since Aristotle thought of matter as a kind of "stuff" (bodiliness in general), he was thinking of what was actually a limitation in just this peculiar way.

BEWARE, therefore. Matter is NOT some "STUFF"; it is simply the DEGREE of the UNIFYING ENERGY of a body.

That is, matter is nothing more than the strength of the internal force--if you will--uniting the parts; the kind of force is the form of the unifying energy, and the degree of this force is the matter. Bodies are bodies because they are unified to a certain degree as well as in a certain way.

Note that there is NOT just ONE matter. There is one matter (at a given time) per body; but there are an INFINITY of possible matters for any given form of unifying energy.

Again, thinking of matter as one something is thinking of it as a "stuff" out of which material things are "made"; but what it really is is like the temperature of unifying energy; and there isn't a "temperature" that heat is "made of," nor is there just one "temperature"; each case of heat has its own definite temperature, and there are an infinity of possible temperatures for heat. Thus, each form of unifying energy has its own matter, and there are an infinity of possible matters for unifying energy in general.

What Aristotle called "primary matter" (though he did this only once in his writings) and the medieval philosophers referred to often is simply this abstraction of matter analogous to the abstract notion of "temperature." The medievals correctly saw that matter was the limitation of the form of the unifying energy (which they called "substantial form"); but they were so filled with this image of matter as a kind of "stuff" that they didn't see the inconsistency in what they were saying in talking of "prime matter."

So once again: beware! Matter is not a "stuff"; it is simply the degree of the unifying energy; the basic energy level of the body as a unified whole. It is a limitation of something, not a "something."

5.3. The unifying energy and the parts

The body, then, is a number of parts connected by a unifying energy. Having established that the unifier of the parts is energy, and having defined its quantity as matter, let us look at what is happening (so far as we can infer) between this energy and the parts it is connecting.

The unifying energy is nothing more than the interaction of the parts themselves.

That is, the unifying energy is what the parts are doing to each other; it is not something "separate" added to the parts.

Or to put this another way:

From the point of view of one of the parts, the unifying energy is the FORCE this part exerts on the others and the force the others exert on it.

That is, from the point of view of one of the parts of the body, the body "appears" as a system, and the unifying energy appears as a set of forces connecting the different parts. This would have to be the case.

Hence, the form of the unifying energy would appear as the type of force connecting the parts, and the matter would appear as the total strength of these interconnecting forces.

But how can one unifying energy be many forces? Because this one energy is the one that pervades the body, making the parts behave together. Hence, each part is connected to the others by this unifying energy, and so from its point of view, it is a unit connected to others by many forces.

The reason this sounds contradictory is that we are here into the peculiar aspect of the body which is its multiple unity: what makes it a unit appears as a multiplicity to the sub-units within it, while these sub-units are a multiplicity which disappears, more or less, in the unity of the total.

Each of the parts, if it is itself a multiple unit, has its own unifying energy; but this unifying energy is SUBORDINATE TO and GOVERNED BY the unifying energy of the body as a whole.

This must be true, because the body is primarily a unit; if the parts were "really" bodies, and only connected to the other parts, then we would have a "mere" system and not a body.


The unifying energy of the body as a whole is also WITHIN the parts.

Thus, even though the unifying energy appears to a given part as a force connecting it with the other parts, this force makes a difference to its nature, so that it is not the same outside the body as it is in the body.

The part HAS NO REAL IDENTITY except in relation to the whole i.e. as a part of it. It is not the same as it would be if it were a unit in its own right.

Thus, for instance, when two hydrogen atoms and an oxygen atom combine as a water molecule, the oxygen atom no longer exists as such; what exists is the water molecule; the "oxygen atom" is now a part of the molecule, and it has a different configuration from what it would have as a free atom, it has less energy than it would have as a free atom (the water molecule has less total energy than the sum of the atoms taken separately--which is why there is an explosion (energy given off) when they combine. The electrons form a shell of strange shape around the whole molecule now, not the individual "atoms" in it.

The result is that if you were to split this molecule apart, and get two hydrogen atoms and an oxygen atom, you would not get back the same atoms you put in. That is, the atoms would not (in all probability) have the same electrons they had before. You would get "the same" atoms in the sense in which, if you exchange four quarters for a dollar, and then change the dollar back into four quarters, you get "the same" change you started with--but not necessarily the identical quarters you gave in the first place.

The point is that the oxygen as such vanishes or goes out of existence when the oxygen atom becomes a part of a water molecule; the location of its nucleus is identifiable in the molecule, but the oxygen as a "whole" is behaving in a new way, and is not really a whole now; the whole is the water.

The unifying energy can be considered the CONFIGURATION OF THE INTERNAL SPACE of the body.

Remember that the space "around" something is its field, and that space in the other sense is the field-interactions of the bodies in it. But the unifying energy of a system is what the parts are doing to each other; and so it is the relations among the parts as internal to the body; and so it is the body's real internal space.

And this is confirmed by the fact that, say, a proton has an electrical field which extends out to infinity; and so does an electron. But if the proton and the electron interact (and the electron is "bound") what we have is a hydrogen atom, (a body), and the electrical fields change shape, so that they are now a single field internal to the atom. That is, put another electron near the atom, and it has no idea that there is a proton anywhere around--because the proton's positive electrical field has been "neutralized" by the electron it is bound to, and is "tied up inside the atom."

Hence, the unifying energy of the hydrogen atom is in one sense the electrical field; but it is not simply an electrical field; the electrical field in the atom has changed its nature, and is now a different sort of configuration of space: one specific to hydrogen as such.

Physicists are fond of saying that there are three or four "basic forces" of nature (the "strong force" binding the parts of the nucleus, the "electromagnetic force" binding the nucleus to the electrons, the "gravitational force" we all know, and the "weak force" that is quite mysterious), and they talk as if everything is just a kind of accidental summation of these forces as if they are what "really" exists.

This is another version of the fallacy I mentioned above. These "forces" are what they are only if you consider the bodies united by them as systems, not bodies. And the point is that they behave differently depending on what body you are talking about.

For instance, the "electromagnetic force" is the unifying energy of a hydrogen atom; but there is no new force uniting two hydrogen atoms into a hydrogen molecule. But the fact is that the shape of the internal space of the hydrogen molecule is different from that of the atom.

This "shape of space" is not accidental to the "electromagnetic force"; it is that "force." The "force" has no other reality except to be the interaction between things; and so it is the (real) space between things. But this means that the form of the unifying energy of the molecule is different from the form of the unifying energy of the atom; the atom does not behave as an atom any more, but differently; it is not simply "connected" to the other one; it has lost its identity, and what exists is the molecule. The same is true of the electrical interaction of the parts of the molecule; this is different from the electrical interaction of the parts of the atom; and the name "electrical" is an analogous word used to indicate that if you break up the molecule, you get out atoms again.

So what is "really" holding the molecule together is not "really the same" as what is holding its atoms together. The shape of the internal space is the primary aspect of the unifying energy; and it is what makes the body a molecule and not a collection of atoms.

The point here is that a body is not "really" a collection of its parts that happen to be connected (just because you can get bodies like its constituents if you break it up), nor are the "forces" connecting the parts "really" just something external to the parts themselves. The body is primarily a unit, defined by the form of the interaction of the parts; and this form is specific to each type of body, and is the internal space of the body.

5.3.1. Newton and Einstein

It turns out that the argument I just gave applies to a lesser degree even to systems which are not single bodies. One of the major differences, in fact, between Newton's gravitation theory and Einstein's General Theory of Relativity is actually connected with what I have just been saying.

Newton considered the solar system as a system of bodies connected by forces (the gravitational forces) more or less "external" to each body--at least in the sense that the force was a "behavior" of the body towards the other bodies it was connected with. Hence, if you wanted to consider the motion of the earth around the sun, you calculated the strength of the force connecting the two, and supplied the "initial tangential velocity" which made the earth not directly fall into the sun. This give you the basic orbit. Then you calculate the force connecting the earth, say, to Jupiter, and the motion of Jupiter around the sun (so you can see how this force changes as the distance between the earth and Jupiter changes), and you add this to your calculation to get the "perturbation" of the basic orbit. Do this for all the other planets, and you should come up with the actual orbit.

But you don't.

If you look closely at what the General Theory of Relativity is doing, however, you notice that its "warping of space-time" in the presence of massive objects is considering the field, not as a force connecting objects, but as a configuration of space itself, and in this space there are certain "energy levels." The earth, being on one of these "energy levels," follows or stays on this level, which is a kind of "shell" or "path" around the sun. Now the energy level is affected by the massiveness of the other planets, which are at other "energy levels" in the basic "space-warp" of the sun (which, because it is so massive, does most of the "warping"); and you can predict what the orbit of the earth will be because you know what the shape of space has to look like that it travels along.

And this works.

In other words, Einstein was considering the solar system more like what I said is true of a body than of a system of interconnected bodies; and his description of what the "parts" of this "loosely bound body" are doing is more accurate than Newton's description of the same events looked at as a system of bodies that happen to be connected together. And it is not that Newton's numbers were off in calculating the "gravitation constant" of his force. There is no changing the strength of the force known that will give you the exact orbits of the planets; in order to get the exact orbits, you have to take a different point of view, and say that they are like parts of a body which has a certain internal space-configuration.

Now of course, the difference between the two approaches works out to be very very small; Newton is off by an almost unmeasurable amount--because the solar system is a system, and the gravitational interaction of the planets is by no means their most important aspect. But it is significant that even here, you are only perfectly accurate if you consider the shape of space rather than interconnecting forces.

5.3.2. Some predictions

This seems to be an indication that my interpretation of bodies and their unifying energy is on the right track.

I now offer the following prediction from this philosophical view:

The way I described what Einstein was actually doing was not exactly how he would have described it; and it looks suspiciously like certain ways of describing the atom in quantum mechanics. I predict that if this way of looking at things is pursued more closely (i.e. that of considering the solar system as a kind of body with internal "energy levels" on which you find the planets), then there might be fruitful analogies from quantum mechanics, which might possibly explain why the planets are arranged according to Kepler's Third Law (which no one knows what to do with), and why their masses are what they are (because certain masses must be a certain energy-levels in the space, perhaps), and so on.

That is, when the solar-system-atom analogy has been used up to this point, it was the solar system that was the model and the atom was described in terms of it as a kind of little tiny solar system. This didn't work very well. What I am proposing is to turn the analogy back the other way, and use the atom as the model for describing the solar system. I think Einstein has (advertently or inadvertently) made a start on just this; and so my prediction is that if you pursue it consciously, then the results should be fruitful--and it could be that here you would find the long-sought integration of classical, relativistic, and quantum physics.

I would not say that if these hoped-for results fail to materialize, my theory is wrong--because the solar system is a system, not a body (as the atom is); and so the analogy might not work. But if breakthroughs in considering the solar system should occur because of this, I think this would be a confirmation that my philosophical view is really a description of what is really going on.

I offer a second prediction:

Differences in the "basic forces" of nature may very well be describable in terms of different geometries.

People have been recently looking for "magnetic monopoles," (i.e. a "north" pole that doesn't have a south pole attached to it) and have been in a quandary that gravitation doesn't have a repulsive component.

If, as I predicted above, the unifying energies of nature are describable as configurations of space, then it would not be surprising to find that the geometry of a magnetic field and that of an electrical field are different (as they clearly are, because of the "bipolar" aspect of magnetism). My prediction is that each unifying energy is its own special configuration of space, and the differences are to be expected rather than explained away.

That is, what this theory of unifying energy says implies that Einstein was probably on exactly the wrong track in his search for a "unified field" theory; and, if my view here is true, it is not to be wondered at that he couldn't find it. If you will, my view predicts a "diversified field" theory, with Einstein's General Theory of Relativity describing the gravitational field; but a description of electrical field interactions would imply a different non-Euclidean geometry; that of magnetic interactions still a different one; that of the "strong" force its own special geometry, and so on. The hydrogen atom's internal interactions would also be describable in a special geometry of its internal space, the oxygen atom's in its special geometry; and what is called the "chemical bond" would be describable as a new geometry of the internal space of a molecule.

Let us let this be enough for a philosophical description of bodies and the relation of the parts and the unifying energy; but there is still the question of considering the body and the acts it performs as a whole body.