This essay is also available in two eBook formats:
.epub for most e-readers
.mobi for Kindle
If clicking the links above doesn't download the files,
you may need to right-click the link and choose
"Download Linked File" or
"Save Linked File"

What Is This Stuff?!?

A study of the concepts of body, matter and substance.



By Carl Aron

Senior Essay for St. John’s College, Annapolis, MD, 1986

File written by Adobe Photoshop® 4.0
Comix by Vaughn Bode



Imagine for a moment the first human consciousness, awakening, looking about in wonder, touching and feeling things which were ... other than itself.  It found that each of these bodies was a thing like its own self, yet might also be broken into many smaller pieces, each a thing in its own right.  These things were hard or elastic or liquid like water.  This first mind might at that point form the question "What is Body?".  Still pursuing this question today, mankind has found that whether body turns out to be atoms or waves or energy, the question "What is Body?" inevitably leads to the question "What is Matter?".  But to return to our primeval mind, all these well phrased questions tend to hide that first childlike, perhaps even outraged, wondering of "What Is This Stuff?!?"

At first glimpse, this question might seem to be rather silly.  Physical objects seem to be the simplest things around.  They just are.  They take up space, they're heavy, they resist invasion of their space, whether it be by moving them or by altering their shape or size.  But what about body makes it take up space?  If a body is truly hard, why would it ever break down into smaller pieces?  If it is made of smaller pieces, how does it acquire its power to resist destruction at all?   And just why are some of them so determined to fall to the ground?  Our primeval inquiring mind might begin to wonder if there were something behind these apparently simple facts.  The science of physical bodies has been, for the most part, the search for what it is that underlies the things that our experience tells us of bodies.  The beginning of Aristotle's Physics would in some ways serve as a definition of the study of the physical world for hundreds of years:

Since understanding and knowing in every inquiry concerned with things having principles or causes or elements results from the knowledge of these (for we think we know each thing when we know the first causes and the first principles and have reached the elements), clearly, in the science of nature too we should first try to determine what is the case with regard to the principles.

(Physics, Bk I, sec.1) 

Long before Aristotle, the Greeks were seeking to understand nature by asking about its underlying principles.  Many of them were seeking entirely different sorts of things as principles.  Some, looking for some ultimate material, argued for either atoms or for some one homogeneous material, without trying to picture it as made of small particles.   The endless variations on these themes made for endless arguments over their advantages and disadvantages.  Some, of a more metaphysical bent, sought principles of a different kind, causes and forms, which might explain the world in terms other than material makeup. Yet they were all looking for some clear unambiguous source which would explain the physical world as they experienced it, and which would need no source or explanation of its own.  They soon found that each answer brought new questions and difficulties. 

Many centuries later, in the time of Descartes, Newton, and Leibniz, the focus of physics shifted away from the seemingly bottomless pit of questions about first principles.  It soon became clear that while the question "why?" led to terrible puzzles and paradoxes, the question "how?" led to clearer, more easily tested answers.  Mathematics proved to be very adept at describing the "how" of bodies and their motions.  Great progress seemed to be underway, and the question "why?" took a back seat as answers and equations began to show that even if explanations could not be found, there was great order and clarity in the phenomena themselves.  But the human mind cannot resist trying to picture some underlying mechanism or structure to explain these beautifully simple laws.  Leibniz, although he was modern-style scientist who was convinced of the importance of understanding the mathematical description of nature, felt even stronger that there had to be reasons, metaphysical underpinnings, to all of the phenomena which were being very neatly described and classified. 

Some of the newly discovered phenomena (or more correctly the mathematical details of the description of the phenomena) were quite simple on the surface, but attempting to describe principles which would explain that simplicity would lead to questions as unanswerable as those of the Greeks.

Despite the fact that no completely coherent explanation could be found for the "Laws" of nature being discovered, the new way of exploring nature was so encouraging, so mathematically self-consistent, and so technologically useful, that the "march of science" continued to gain momentum, scarcely worried about its foundations, until the beginning of the twentieth century.  At that point, modern physics, proceeding in its own "scientific" manner, began to find that it was producing results which could not possibly be reconciled with each other.  After so much "progress", we found ourselves face to face with paradoxes at least as deep and irreconcilable as those of the Greeks.  In some ways the paradoxes were made clearer and less deniable.  The vague, sometimes poetic talk of the Greeks could gloss over and sometimes almost heal the great rifts between contradictory ideas which must both be true at once.

If one examines the various answers to the question "What is this stuff?", which have been formed by men from the earliest Greek physicists and philosophers to modern quantum physicists, one finds the same sorts of problems all along.  There are certain contradictory aspects of our conception of bodies and matter which cause us difficulty regardless of the particulars of our theory.  All material bodies must be conceived of as being both a part of some all-pervading whole, and yet as separate and distinct.  We find that the material world cannot be simply dead, inactive matter.  The distinctions between matter and the forces which move it are blurred.  Finally, all bodies can be seen as being in some sense alive and, in a very strange way, conscious.


When we ponder the nature of physical bodies, several phenomena catch our attention immediately, without the need for complex experiments or tests.  Lucretius, in his poem De Rerum Natura discusses them very clearly.  The first is that they are solid and take up space:

For nothing can touch or be touched, unless it possesses body.

(De Rerum Natura, ln. 304)

... that which is the function of body, to hinder and obstruct, ...

(De Rerum Natura, ln. 336)

The next is that they are heavy: is matter's property to press things downwards, ...

(De Rerum Natura, ln. 362)

But next, one notices that not all things are completely hard, and the hardest, most impenetrable bodies are not altogether solid:

Besides, however solid things may seem to be, here is proof that nothing can be really solid:  water seeps and trickles into rocky caverns... Food is dispersed through the body of every living creature... And noises pass through walls and fly into closed houses. And freezing cold can penetrate our very bones.

(De Rerum Natura, ln. 346...355)

Next, one finds that bodies of the same size often have very different weights.  The first two obeservations give us important properties of bodies:  solidity and weight.  The second two show that these properties are not absolute, and hint that bodies as we experience them cannot be made solely of solidity and weight.

The almost immediate answer is that large sensible bodies are made of small, absolutely solid, absolutely weighty bodies, along with empty void.  Again, Lucretius offers us a succinct description of this theory:

All of nature as it is in itself consists of two kinds of things:  bodies and vacant space...

(De Rerum Natura, ln. 419)

This seems to answer many questions about bodies.  Solidity is possible because the atoms themselves are solid, but it is not absolute, because there may be more or less void in between them.  Differing density can be explained in a similar manner.  There are also some other benefits to the atomist's theory.  The first is that motion, something evident to our senses, is possible, since there is void to provide elbow room for motion to begin.  We thus avoid the trap of Parmenides' argument against the possibility of motion.  The second benefit is that decay and destruction are explained, yet the world is safe from utter dissolution, because we have stated that the atoms are indestructible.  The converse of this is that bodies need not be built from infinitely small parts - an unthinkable task - but from atoms of definite size and weight.  This is a very convincing argument for atomists like Lucretius:

And besides, if matter were not everlasting, by this time all things would have been reduced to nothing, and everything we see would have been reborn from nothing.

(De Rerum Natura, ln. 540-542)

It would seem that the theory of atoms and void just about has things wrapped up, with no need of anything other than those two principles — atoms and void — to explain the physical world.  If something can affect others and/or be affected by others, it must be matter; if it cannot affect or be affected, it must be void.

There are several problems here, however.  Some of them are mechanical in nature, and might be explained away by an imaginative atomist, but some of them are more serious.  To begin with, a theory of atoms and void assumes that the atoms be separated in order to form soft and liquid bodies.  Yet there is nothing in this theory (certainly not the empty void) which could prevent the solid atoms from becoming tightly packed against one another when bodies came together, and so eventually making all bodies absolutely hard, a compacted ball of all the attoms inthe universe.  Also, if these atoms are separate, as in soft bodies they must be, there is again no reason that they should stay together at all, rather than flying apart at the first bump, not being in contact with one another so as to be held together by hooks or hoops or velcro.  And as Lucretius hinted in our earlier quote, even stone and iron are not to be considered as totally hard.

Even more troubling, however, is that the theory of atoms and void merely begs the question of "What is body?":

The atoms, therefore, are of solid singleness, for in no other way could they have been preserved, from time immemorial, to make new things.

(De Rerum Natura, ln. 548-550)

These bits of "solid singleness" are simply absolute bodies.  They are presumably of definite extension, and that extension is presumably continuously full of matter or bodyness or something.  By what infinite power is this continuous magnitude of stuff held in one indivisible piece?  Our mind tells us that any magnitude can be divided, and, as Aristotle points out, if it is continuous, then it can be divided infinitely.

...for the continuous is infinitely divisible.

(Physics, Bk I, sec.2)

What is it about the continuous material of atoms that makes it stick together?  It is simply not a satisfactory answer to the question "What is body?" to say "lots of little bodies".

The imaginary process of breaking bodies into little bodies and these into still smaller bodies seems to have no end.  Indeed, our minds can find no reason why it should ever end.  The atomists argue that eventually matter would be destroyed into nothing, if there is no end to the division of bodies, and that no thing could be made from nothing.  However, the intellect can discover no material principle which might cause this process to stop at some arbitrary finite size.

Thoughts like these caused many presocratic thinkers , such as Thales and Anaximander, to posit a non-atomic, infinitely divisible substance as the primary element.  Since water, air, and fire are, to our level of perception, continuous and fluid, they were often taken as examples.  Since we have only a few fragments from most of those thinkers, and most of those fragments appear only as quotes in commentaries by other writers, it is difficult to say whether any of the original thinkers actually posited water or air or fire as the primary element. It is possible that they only used those materials as analogies for a formless and fluid element from which all things might be made.  Anaximander, at least, seems clearly to have posited something other than the four common elements of earth, air, water and fire:

It is clear that he [Anaximander], seeing the changing of the four elements into each other, thought it right to make none of these the substratum, but something else besides these...

(Simplicius, writing on Anaximander)

And this element he called the "apeiron":

Of those who say that it is one, moving and infinite, Anaximander, son of Praxiades, a milesian, the successor and pupil of Thales, said that the principle and element of all things was the apeiron [indefinite or infinite] ,  being the first to introduce this name of the material principle.

(Simplicius, writing on Anaximander)

"Apeiron" literally means "boundless".  If it is taken as meaning boundless in extent or quantity, it would correspond to "infinite".  But there is another possible meaning.  If it is taken as meaning qualitatively boundless or without defining limits, it would mean "indeterminate" or "indefinite".  Aristotle later assumes that Anaximander meant only "infinite", thus making the idea muddled and easy to refute.  But if the meaning is taken as primarily "indefinite", Anaximander is clearly referring to a formless substratum, something which Aristotle himself talked of as the "underlying nature" in his Physics, and which is often referred to as Prime Matter.  This Indefinite element, being completely without specific characteristics, could become any specific object.  The only thing it lacked was a power to give it specific characteristics, such as solidity, which the atomists gave to their atoms by assumption.  A hint as to what Anaximander might have answered to this difficulty is given in this commentary on his ideas:

...and he produces coming-to-be not through the alteration of the element, but by separation of the opposites through the eternal motion.

(Simplicius, writing on Anaximander)

What is meant by "separation of the opposites" in something supposedly indefinite (i.e. having no characteristics) is unclear.  Perhaps it means that any part of the Indefinite might be originally both hot and cold, for example, and thus neither, because of the balance of their effects.  It might become either hot or cold by a separation of one or the other characteristic to another part of the Indefinite, causing the Indefinite to be locally defined in that one respect.

This is pretty vague, and does not totally satisfy our desire for an original principle that could cause the distinct, solid world of phenomena we experience.

We have now seen that the most obvious answer to the question "What is this stuff?!?" — atoms and void — is not completely satisfactory.  It is necessary that there be some homogeneous, non-atomic substance which is prior to bodies, whatever their size.  But this opens questions about the principle by which such a substance might come to be the distinct bodies we live among.


This difficulty in finding a cause for the "solid singleness" of bodies, for their definiteness and concreteness, whether they be atoms or not, moved Aristotle and Plato to take an approach to the question of body radically different from that of materialist scientists.  For them, solidity could not simply be taken as a given.  Solidity was an attribute predicated of a body, and if that attribute was brought about by the solidity of the constituent matter or bodies of that body, then they sought a cause for the solidity of that constituent matter or bodies.  As mentioned earlier, the mind can find no material principle for limiting the divisibility of matter.  Hence, Plato and Aristotle sought a principle of another type.  For them, the something which was capable of giving "solid singleness" was Form.

For Plato and Aristotle, Form is more concrete than matter.  Form is not some ghostly, arbitrary order that our minds superimpose over existence to make sense of it. Form is inherent in the things we see, and actually brings about the bodies we experience every day.  Odd as this may sound, there are some very good reasons for thinking about bodies in this way.  When we look about, it is apparent that bodies are constantly undergoing change.  Alteration, growth, decay, generation, destruction, and locomotion are all readily apparent phenomena.  The atomists recognize this and make accommodation for it by interspersing their solid matter with empty void.  But since their atoms are permanent bits of "solid singleness", the only kind of change they recognize was locomotion.  Atoms do not change in any way except in position relative to each other.  Because the atomists considered all change to be locomotion of particles whose material existence was eternal and unchangeable, Form for them was only structure or shape.  It did not need to have any power or be a principle, since it was only a fact about atoms and their arrangements.

Aristotle, on the other hand, thinks of some kinds of change as being actual changes in the being or "whatness" of a body.  At the same time, he does not believe there are any material atoms whose whatness is unchangeable.  This being so, we are amazed to find any lasting bodies at all.  With all bodies capable of continual change, we are on the verge of admitting the old saying of Heraclitus:

All things flow; Nothing stands still.

But while all things do seem to change, a certain degree of stability is apparent in the world.  For Plato and Aristotle, the source of  this stability is the fact that Form is more than structure or shape.  Form is that which gives an object its whatness, and in some way holds its existence together in the midst of the flux of existence.  Aristotle argues that the nature of a thing is its form, and not its matter, since its matter is only potentially that thing, while the object comes to be only when matter has the form of that object.  For example, gold is potentially a coin, or a statue, or powder in a physician's potion, but it is actually one or the other of them when it has that form:

Indeed, the form is a nature to a higher degree than the matter; for each thing receives a name when it exists in actuality rather than when it exists potentially.

(Physics, Bk II,sec.1)

That which we experience of bodies is not their matter, which is now existing in one form and now another, but rather their form. 

An understanding of the concept of Form begins with shape and attributes, but it must go further.  A man is a man, not because of the material of which he is made, but because he has the form of a man.  On the surface, this may mean that matter is organized in such and such a way in each of his limbs and organs, and that his limbs and organs are arranged in such and such a way, but Form must imply much more.  A man is a man, one man, because he has one Form, which is a whole, and which comprehends all that it means to be that man.  Form may include all of the particulars of structure, but if it does not impart a unity to those particulars, then we are no better off than the atomists, who can offer no explanation for the union of many atoms into one whole, nor for the "solid singleness" of their atoms.

I have been speaking of this new concept of Form as a principle of bodies, as if it were necessitated by the inadequacy of matter to explain bodies.  But we can just as well reason in the other direction, since the two ideas are bound closely together and arise at the same time, making it difficult to say which leads to which.  While we can now see that Form is the cause of an object's being what it is, we find it hard to imagine Form, except as being in some matter:

Now in things which are being generated, one of these[two natures] is an underlying joint cause with form...

(Physics, Bk I, sec.9)

While a statue may be what it is in virtue of its form, it would not be at all, unless that form were in some material.  For this seems to be a situation in which the ancient adage "nothing from nothing" seems to be applicable.  But if that material is bronze or stone or any other material we are familiar with, it too has a Form which makes it bronze or stone or whatever, rather than primal, indeterminate matter.  Earlier, when we critiqued atoms, we broke down matter in a quantitative way, dividing and dividing it until we could no longer imagine it as being a useful building block for bodies.  Now, if we realize that the bronze too is not an elemental material, and that the Form of bronze must be embodied in some other,simpler, material, we find that this process of separating out Form from underlying matter will not stop until matter is completely without characteristics or Form of any kind.  It will be very similar to Anaximander's Indefinite Principle.  Aristotle says of it that it cannot be known directly, but only by extrapolation from thoughts like the ones about bronze mentioned above:

As for the underlying nature, it is knowable by analogy.  Thus, as bronze is to the statue ar wood is to the bed or matter or the formless object prior to receiving form is to that which has form, so is this [underlying nature] to a substance or to a this or a being.

(Physics, Bk I,sec.7)

Plato, in the Timaeus, describes the material principle in this way:

This, more than anything else:  that it is the Receptacle-as it were, the nurse-of all Becoming.

(Timaeus, 49a)

Matter has been stripped of all its active powers and remains only in order to embody form.  Later in the same dialogue, he compares it to a mass of plastic, moldable, material.  But as he goes on, it becomes clear that since the Receptacle must be able to take on any form, it must be free from all forms which might interfere with its moldability, and that it must be much more like Anaximander's Indefinite:

For this reason then, the mother and Receptacle of what has come to be visible and otherwise sensible, must not be called earth or air or fire or water, nor any of their compounds or components; but we shall not be deceived if we call it a nature invisible and characterless, all-receiving, partaking in some way of the intelligible, and very hard to apprehend.

(Timaeus, 51a-b)

Matter is in fact so invisible that in this description of the three main principles of nature, Timaeus calls it "space", since its function is only very subtly different from that of the atomist's void:

This being so, we must agree that there is, first, the unchanging Form, ungenerated and indestructible, which neither receives anything else into itself from elsewhere nor itself enters into anything else anywhere, invisible and otherwise imperceptible; that, in fact, which thinking has for its object.  Second is that which bears the same name and is like Form; is sensible; is brought into existence; is perpetually in motion, coming to be in certain places and again vanishing out of it; and is to be apprehended by belief involving perception.  Third is Space, which is everlasting, not admitting of destruction; providing a situation for all things that come into being, but itself apprehended without the senses by a sort of bastard reasoning, and hardly an object of belief.

(Timaeus ,52b)

It is important to realize the difference between the atomists’ void and Timaeus' Receptacle, as similar as they may seem.  The void is complete emptiness, nothing but a place to be filled.  Timaeus' Receptacle, Space, the Indefinite, or Prime Matter, are, on the other hand, empty only of Form, but full of a power to make Form tangible and physical.  If our formless matter were no different from the void, we could be rightly accused of making something from nothing, but as Aristotle puts it in his Physics:

  Now we too maintain, as they do, that nothing is generated from unqualified non-being, yet we do maintain that generation from non-being in a  qualified sense exists, namely with respect to an attribute; for from privation, which in itself is a not-being, something which did not exist is generated.

(Physics, Bk I,sec.8)

We are not generating something from nothing.  Our prime matter is formless, but not devoid of existence.  Aristotle distinguishes Prime Matter from absolute nothingness as follows:

Now we maintain that matter is distinct from privation and that one of these, matter, is non-being with respect to an attribute but privation is non-being in itself, and also that matter is in some way near to substance but privation is in no way such

(Physics, Bk I,sec.9)

Aristotle talks of prime matter as "potentially" this or that specific body or object, while the Form completed that "potential", and made it an actuality.  A piece of gold has the potential to be either a statue or a coin.  The word "potential" is from the Greek "dunamis" or "dynamis", meaning power, or ability.

In spite of, or because of, being almost nothing, this Indefinite matter is full of power to be.  It is not power to be this thing or that thing, but an indiscriminate power towards being.  It is in one sense empty and in another it is full, containing all opposite properties which nullify each other, and therefore produce nothing because they are not organized.  It is seething with the possibility of being, yet because its power is not directed or limited in any way, it remains intangible and immaterial.

Form, too is intangible, as hinted in the first part of Timaeus' description of the three principles.  As we mentioned before, Form without matter is as hard to imagine as matter without Form.  They are each removed from the sensible in different ways, and neither alone could be responsible for bodies as we know them.

Now let these two intangible and ghost-like things come together.  Matter might be coaxed by Form to try certain attributes for a moment, in order to be in a more definite way.  Then, its boundless will to be feeling limited, it would break that form and plunge back towards indefiniteness and infinitude.  Yet fearing to lose all hold of being, in the nothingness of complete chaos, it would again be coaxed into another form for an instant.  Thus, continually flirting with this form and that, it would flicker and seethe on the border between unlimited, formless nothingness, and finite stasis and permanency.  Pure Form or eidos, on the other hand would flirt with dissolution, imperfection and disorder, so that its beauty and perfection could exist solidly even for a fleeting moment.

Another picture of this continuous generation and decay is given in this commentary on Anaximander,concerning his Indefinite principle:

...And the source of coming to be  for existing things is that into which destruction too, happens 'according to necessity;  ...  for they pay penalty and retribution to each other for their injustice according to the assessment of Time',  ... as he describes it in these rather poetical terms.

(Simplicius, writing on Anaximander)

Here, physical existence in any particular form is portrayed as somehow being an injustice, perhaps to the limitless number of other forms which have yet to live their moment in the dance of nature, or to the infinite "dynamis" or "apeiron", which is unjustly bound and limited.

This is a strange marriage between two intangibles to produce the tangible world of bodies!  But it explains much.  The world we see is made up of many bodies, each of which has a certain identity and hint of permanence.  Yet the world is also in constant flux, and any body, given enough time, will almost certainly cease to exist. 

Matter and Form each contribute to both parts of reality - generation and destruction.  Form is clearly at work in the generation of definite bodies from indefinite matter, and of more complex bodies from those bodies.  But Form could never generate even one atom without matter, despite the fact that matter is constantly throwing off its form and changing.  It is in fact this very resistance to form which makes matter capable of taking on form at all.  Consider a piece of wax.  If you press it with your finger, it takes on and holds the form of your finger.  Yet if you do this to the air, or to water, no form will be left in them.  It is only because wax resists your finger that it is able to make a solid or even semi-solid representation of it at all.  In this way, the very tendency of matter to resist form makes it capable of holding form even fleetingly.

In dissolution or destruction, the work of matter's unbridled power is clear to see.  Its indiscriminate will-to-be constantly destroys its present form, so that it may embody a new one.  But destruction is also the work of form.  The chief role of form is to limit, to set definite boundaries to the unlimited existence of matter.  Perhaps it is necessary, in order for bodies to exist physically, with finite boundaries in space, that they also have a boundary in time and thus a natural end.

We have come to some very strange answers in our investigation of body.  When we began, body seemed the simplest of all things, something we might investigate quickly, and dismiss on the way to more challenging mysteries.  Instead, we have found that matter is anything but simple.  In order to explain even its most basic traits, we have had to resort to almost mystical substances and powers.

We find that the "stuff" of our world must be determinate and finite, for, as Aristotle shows, an object exists in the fullest sense for us when it exists actually, defined and separated from the rest of the world by its form:

This [underlying nature] then, is one of the principles, though it is not one nor a being in the manner of a this; another [principle] is the formula; then there is the contrary of the latter, and this is the privation.

(Physics, Bk I,sec.7)

But the "stuff" of our world is not completely unitized and individual like the atoms.  It must exist as part of the fluid whole of indefinite matter, since it is this, not the specific beings which abide permanently.  As Plato points out in the Timaeus:

Only in speaking of that in which all of them are always coming to be, making their appearance and again vanishing out of it, may we use the words 'this' or 'that';  we must not apply any of these words to that which is of some quality-hot or cold or any of the opposites-or to any combination of these opposites.

(Timaeus ,49e-50a)

Thus the bodies we experience must be a dynamic balance of flux and stasis. While Aristotle and Plato felt that their talk of Form and underlying matter belonged to the study of physics, it seems to modern minds more like metaphysics or philosophy.  It's general way of investigating detours us from many interesting aspects of bodies, whatever their metaphysical foundations may be.  We will now move on to some thoughts about matter made possible through a more specific study of its properties.


Our recent investigation leaves us with some very powerful ideas about bodies and their changes in general, but our curiosity about the specific properties of bodies is not slaked.  We find that by doing more than simply observing, by performing experiments and measuring carefully, and then applying mathematics to the values in these experiments, we can discover much knowledge that is useful and fascinating about bodies. 

Descartes, one of the earliest leaders in what I will call mathematical physics, thought that all bodily phenomena could be explained by simple geometry and locomotion.  In his Le Monde, he makes a claim that sounds something like that of the atomists:

Indeed, unless I am mistaken, not only these four qualities [heat, cold, moistness, and dryness], but also all the others (indeed all the forms of inanimate bodies) can be explained without the need of supposing for that purpose anything in their matter other than the motion, size, shape, and arrangement of their parts. (Le Monde, chp.5)

This is very much like the atomist's assertion that the only change is change in location, except that he wishes to treat these facts mathematically.  He wants to limit the principles of bodies to these, because he believes that the principles should be those things which are most clearly understood and apparent to us.  For this reason, he posits extension as the primary property of bodies:

Nor should they find it strange if I conceive of its extension, or the property it has of occupying space, not as an accident, but as its true form and its essence.  For they cannot deny that it is quite easy to conceive of it in that way. (Le Monde, chp.6)

Leibniz disagrees with this simple version of mathematical physics violently.  He feels that there must be more to bodies than extension:

We have suggested elsewhere that there is something besides extension in corporeal things; indeed that there is something prior to extension, namely a natural force everywhere implanted by the Author of nature ....Indeed, it must constitute the inmost nature of the body, since it is the character of substance to act, and extension means only the continuation or diffusion of a resisting substance.  So far is extension itself from comprising substance! (Specimen Dynamicum, Part I)

Indeed, extension alone seems no more capable of explaining the real presence of bodies - their solidity and weight - than the atoms which simply assumed these properties .  Descartes would have done better to pay a bit more attention to this method of study prescribed by Aristotle in his Physics:

The natural way to proceed is from what is more known and clearer to us to what is by nature clearer and more knowable; for what is known to us and what is known without qualification are not the same.  So we should proceed in this manner, namely, from what is less clear by nature, though clearer to us, to what is by its nature clearer and more known.  Now the things that are at first plain and clear to us are rather mingled, and it is later that their elements and principles become known to those who distinguish them. (Physics, Bk I, sec.1)

Extension, while very simple, is not enough to explain one body's action on another.  Extended solidity, while it may seem very apparent, is not really so clear.  Leibniz feels that bodies must have something more, something active which fills that extension.  In his essay Specimen Dynamicum, he lays out a rather complex system of the forces which he feels make up body.  We will not at this time go into the details of his theory, but it will be useful to discuss the basics of it.  He says that bodies consist of two main forces, "Active" and "Passive", and that each of these forces has two types, "Primitive" and "Derivative".  The primitive forces, active and passive, correspond respectively to Aristotelian Form and Prime Matter.  While these are important to understanding bodies fully, they are too general and not as useful as the derivative forces for understanding phenomena:

[Active] Primitive force, which is nothing but the first entelechy, corresponds to the soul or substantial form, but for this reason it relates only to general causes which cannot suffice to explain phenomena.  Therefore I agree with those who deny that forms are to be used in investigating the specific and special causes of sensible things. ....

But having set aside these general and primary considerations, and having established the fact that every body acts in virtue of its form and suffers in virtue of its matter, we must now proceed to the doctrine of derivative forces and resistances and discuss the question of how bodies prevail over or resist each other in various ways by their varied impulses.  For to these derivative forces apply the laws of action, which are not only known by reason but also verified by sense itself through phenomena.  (Specimen Dynamicum, part I)

These derivative forces are the ones by which we see bodies acting upon one another, and Leibniz considers them to be quantitative.  Derivative forces, therefore, are what is to be studied by mathematical physics.

While most physicists are not quite so closely linked with their metaphysics, the method of investigation since Leibniz's time can be described as primarily the study of what he called derivative forces.  We have already mentioned the properties of hardness and weight, which are examples of derivative forces, but we have not investigated these forces in detail.  For example, we have not examined weight to see if any law governs its strength.

Leibniz always considered the metaphysical foundations of his physics to be crucial to their proper understanding.  For this reason, his descriptions of physics are in some ways more fully thought out and have the questions of "What is body?" and "What is matter?" always close at hand.  Newton, however, states many of the phenomena in a much clearer manner, since he is not so worried about the underlying causes of them .  We will refer to Newton and other less metaphysical physicists when we discuss the phenomena themselves, and we will refer to Leibniz, Faraday, and other more philosophical physicists when we wish to investigate the import of those phenomena.

To begin our discussion of mathematical physics, we will examine several phenomena which became clearer in themselves under the piercing light of experimentation and mathematical analysis.  These phenomena are : the collision of bodies, action at a distance , and the propagation of light.  These properties at first seem to be explained most simply by an account of matter much like that of the ancient atomists.

Collision between bodies does not seem to need any fancy explanation of matter, and gravitation between two bodies is easiest to visualize if those two bodies are simple, and light would certainly be easy to understand if it was made of streams of particles.  Indeed, despite the difficulties we found with atoms, our theory of Form as the origin of material solidity does not really deny the possibility of small particles which come to be in the manner we described yet serve as building blocks in the manner of atoms.

 After we describe these phenomena, we will discuss how these phenomena affect our understanding of bodies and substance, and it will become clear that these easily visualized theories are not really so clearly understood.

When two bodies collide, they each act on each other to change their motions.  The simplest example of this is two bodies of equal weight, body 'A' moving, body 'B' at rest.  After they collide, 'A' will be at rest, and 'B' will be moving at the same speed that 'A' had when it approached.  They each have changed the other's motion by the same amount that their own motion was changed.  Newton called this the Law of Equal Action and Reaction.  He describes this law in his Principia:

To every action there is always an equal and opposed reaction:  or, the mutual actions of two bodies on each other are always equal, and directed toward contrary parts.

Whatever draws or presses upon another is as much drawn or pressed by that other.  If you press a stone with your finger, the finger is also pressed by the stone.  If a horse draws a stone tied to rope, the horse ( if I may so say) will be equally drawn back towards the stone; (Principia, Law III)

This power of bodies, not only to prevent other bodies from entering within their boundaries, but also to resist a change in their state of motion is called inertia, and the property of bodies which is its source is called inertial mass.  Newton, in his definition of inertia or "vis insita" notes that this force may be seen as both active and passive:

The vis insita, or innate force of matter, is a power of resisting,by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly in a right line.

This force is always proportional to the body whose force it is and differs nothing from the inactivity of the mass, but in our manner of conceiving it.  A body, from the inert nature of matter, is not without difficulty put out of its state of rest or motion. Upon this account, this vis insita may, by a most significant name, be called inertia (vis inertiaæ) or force of inactivity.  But a body only exerts this force when another force, impressed upon it, endeavors to change its condition; and the exercise of this force may be considered as both resistance and impulse; it is resistance so far as the body, for maintaining its present state, opposes the force impressed; it is impulse so far as the body, by not easily giving way to the impressed force of another, endeavors to change the state of that other.  Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest, which are commonly taken to be so. (Principia, Def. III)

This inertia is the first of the new properties we will find in bodies.  It is set into action through the solidness of bodies, since, unless the bodies were at least a little bit solid, they would not affect each other or try to move one another.  But inertia is quite different from solidity, because it is not a force preventing their boundaries from overlapping but rather a force resisting change of motion.  Inertia is also proportional to weight, but is different from it because weight is an actual tendency to move downwards at an ever increased rate of speed.

The next derivative force of bodies is actually one which we have noticed all along but have never really understood.  Weight seems to be a very simple tendency to go down if unimpeded.  But if we examine it closely, that motion down has a very definite rule.  As Galileo showed, all bodies, regardless of their heaviness, accelerate downward at the same rate, contrary to many people's belief that heavier objects must accelerate faster.

Newton, by rigorous mathematical analysis, shows several interesting things about the force that causes heaviness and falling.  First, he unravels the connection between force, inertial mass, and acceleration.  The force necessary to accelerate a mass M (i.e. change its state of motion, contrary to its inertia) at a rate of acceleration A will be proportional to the product M*A.  If the units of Force 'F' are chosen correctly, F=M*A.  This means that if all falling bodies have the same rate of acceleration, the force moving them must not be equal for all bodies, since that would cause objects to accelerate in inverse proportion to their mass, but rather it must be proportional to the mass.  Thus, a double mass must be affected by a double force, and so on, resulting in the same acceleration for all falling bodies.  This is the first clue to gravitation as a property of all bodies. 

By further math, Newton shows us that the moon revolves about the earth, and the earth and all the planets around the sun, as if they were drawn by the same force, or one similar, to that which draws stones towards the ground.  This force he proves to be inversely proportional to the square of the distance between the centers of the two masses, and proportional to their mass.

Here at last we have a very clear law of the force by which each and every mass is drawn towards every other one.


The mathematics by which we understand this force treat it as if it were acting across empty space from one center of mass to another.  Soon after gravity was analyzed, static electricity and magnetism were discovered to have force laws identical to the one for gravitation, and they too were posited by some physicists as action at a distance.  Of course this idea of action at a distance goes against some very strong prejudices we have about bodies and force.  It seems quite sensible to say that a body cannot act where it is not.  To remedy this problem many physicists posited some sort of intervening substance or Aether, by which the force might be transmitted.  We will discuss this difficulty and some of the "solutions" later.  Now we will move on to the next new phenomenon.

Light is a very interesting phenomenon.  It definitely has physical existence of some kind.  It warms us when we stand in the sunlight, it causes growth in plants, and it reflects much in the same way as a hard projectile.  But light seems too insubstantial to say it exists in the same way as a baseball bat.  Just what is light?  Around the time of Newton's explanation of gravity, this question was being very hotly debated.  There are two possibilities.  Light could be streams of very small particles, which by bouncing off of things and hitting our eyes produce images and give us sight.  If not particles, then light might be waves, much like waves in water or like sound waves.  If light is waves, then its travel would not be the travel of any body, but rather the travel of a disturbance in some medium.

For most phenomena involving light, neither theory is superior, but in the phenomenon of diffraction, the spreading and bending of light when it passes through very small openings, the particle theory has no explanation at all, while the wave theory has a very simple and clear one.  Diffraction involves the patterns made by light when it is sent through very narrow slits.  The patterns have light and dark bands which are neatly explained in the wave theory by reinforcement and cancellation of waves, such that light areas represent the coincidence of matching crests, and the dark regions represent coincidence of opposing crests.

Mathematical analysis of experiments reveals that the relations between the width of the openings, the angle of diffraction, and the length of the hypothetical waves are exactly as predicted.  The particle theory is stumped completely at this point, since two particles cannot be conceived to cancel each other in the way that waves can.  Diffraction, therefore, makes an irrefutable argument for light as a wave.

This is very interesting to note because it represents a new kind of entity which is recognized as having physical existence and being able to act on bodies.  Waves are simply moving areas of tension or force in some medium.  However, waves must be waves in some medium.  Again, physicists imagined some very fine, elastic medium which they called an Aether. 

Now that we have briefly introduced three of the main phenomena which are unveiled by our new method of studying nature, we will examine how they affect our thoughts about bodies and the world we experience.

When we first begin thinking about it, collision seems like a pretty straightforward occurrence, from which no earthshaking ideas might come.  What could be simpler than the action of bodies on one another by immediate contact?  Unfortunately, immediate contact is not such a simple idea.  The laws of collision apply most correctly to bodies which are hard, and less accurately to other bodies in proportion to their lack of hardness.  But this idea of hardness, aside from the difficulties raised in the earlier section, brings new problems with it to the phenomenon of collision.

For Leibniz and Boscovitch, the difficulty with absolute hardness was that it would necessitate a violation of what they called the law of continuity.  This meant that it would cause an instantaneous change in velocity, which they considered impossible.  For example, if the bodies in our first example were perfectly hard, then one of the bodies would instantly change from rest to a finite velocity, without going through all of the intermediate velocities.  Similarly, the other body would go from motion to rest without taking any time to slow down.  It seems that this would require that the bodies exert an infinite force upon each other to produce even the slightest instantaneous change.  The conclusion seems obvious.  Even the hardest bodies must be to some degree elastic, slowing down as they compress and speeding up as they restore their shape.  Leibniz writes in Specimen Dynamicum:

There follows also from these matters the view which Descartes attacked in his letters and which some great men are even now unwilling to admit - that all rebound arises from elasticity, and a reason is given for many brilliant experiments which show that a body is bent before it is propelled;...(Specimen Dynamicum, Part II)

This elasticity does not seem to be such a terrible fate for matter, and one might wonder why anyone would resist it.  But when we try to imagine how it might be so, this elasticity in matter turns out to dissolve matter completely.  First, we might think that a body might be elastic if it was made of many small particles, like atoms, which might rearrange themselves when the body was compressed.  But would not these particles also break the law of continuity when they collided, if they were absolutely hard?  Boscovitch describes the fallacy in making elasticity by building large bodies from small ones:

Now in the first place this reply cannot be used by anyone who, following Newton, & indeed many of the ancient philosophers as well, admit the primary elements of matter to be absolutely hard & solid, possessing infinite adhesion & a definite shape that is perfectly impossible to alter.  For the whole force of my argument then applies quite unimpaired to those solid and hard primary elements... (A Theory of Natural Philosophy, Part I)

If we wish then, to make those particles elastic by composing them of smaller parts, this process continues indefinitely.  Leibniz states the situation quite succinctly:

Finally, there follows also that most admirable principle of all - that there is no body, however small, which has no elasticity and is not thus penetrated by a still subtler fluid; and thus that there are no elementary bodies, nor any most fluid matter, nor any solid globes of some second element, I know not what; but that analysis proceeds to the infinite. (Specimen Dynamicum, Part II)

Ultimately matter is again destroyed completely, much as it was in our earlier discussion on the divisibility of atoms.  This time, however, we see that atoms not only can be but must be infinitely divisible.  Again, we would be forced to build tangible bodies from an intangible substance.

Perhaps matter can be saved by the next new phenomenon - action at a distance.  Is it possible that there are absolutely solid particles somehow suspended by a repulsive force of some kind between them?  If the force could create the elasticity necessary to maintain continuity we might still be able to save solidity.

But first, action at a distance brings up its own questions.  How can it be that a body acts where it does not exist?  Even Newton, who in a sense pioneered the mathematics of action at a distance, thought that the idea of two bodies acting on each other through a complete void, without any medium to communicate their action, was absurd.

Of course, we have many examples of actions which appear to be at a distance only because the medium is not apparent to the eye.  When we hear a sound, a person not familiar with the properties of air might believe that this was a case of action at a distance.  Is it not possible that all cases of what we believe to be action at a distance are only normal actions through an Aether, a  medium which is too fine for us to perceive?

But such a medium is very hard to conceive.  It must be elastic, so that it may contract or expand, and so cause attraction and repulsion between bodies. Also, if it is not elastic, it will violate the law of continuity.  We saw earlier the difficulty in imagining an elastic substance, and we saw that it cannot have any smallest particles.  What then is this Aether?  It is as nebulous as Plato's receptacle or Anaximander's Indefinite Principle.  If gravity or magnetism is visualized as being accomplished through the action of such an immaterial Aether, would it not be a tension in something completely immaterial?  How is it really any different from action at a distance, except in its semantics ?

Finally, light, which seems clearly to be wave motion, needs to have some medium through which its waves might travel.  Since light travels just as well through the airless tracts from the sun to the earth as from the lamp to my paper, this medium is not air, as it is for sound.  Light also travels through glass and water, so its medium must permeate these bodies.  It must be a medium similar to the Aether by whose tension action at a distance might be visualized as being transmitted.  But we have already seen that such Aethers cannot be thought of as being tangible in any way.

Thoughts like these lead one to question the existence of simple material bodies altogether.  Large bodies are quite evident to our senses, and their effects can be seen constantly on all sides, but in no case can any of these affects be attributed to any simple dead matter, if there be any, which makes them up.

  Boscovitch posits, as the elements of material bodies, unextended points which have forces linked to them, both attractive and repulsive, by which they produce the appearance of solid matter.  These forces have laws relating to the distance from the unextended center point, by which the repulsive force rises very sharply and increases toward infinity within a certain distance, as one approaches the center.  This gives the impression of a definite edge, such as a solid atom might have, but also provides for elasticity, so that the law of continuity will not be broken. In his view, there is not matter, only forces.

Faraday holds a similar belief about the nature of bodies.  In an essay on the nature of matter, he criticizes the common conception of bodies as being made of atoms of matter.  To do this he cites the fact that some materials are conductors and some are insulators.  He argues that in the common view of atoms they must be considered as being far apart, and not in contact with each other.  If this is so, then space must be the only continuous element in matter, separating all of the atoms from each other.  The insulating or conducting properties of any material must therefore be derived from the space in that material.  He points out that this causes a contradiction:

But if space be a conductor, how then can shell-lac, sulphur, etc., insulate?  for space permeates them in every direction.  Or if space be an insulator, how can a metal or other similar body conduct? (Faraday, A Speculation Touching Conduction and the Nature of Matter)

In the normal atomic view, the atom contains all of its attributes, and the space surrounding the atom is supposed to be indifferent to the presence of the atom.  But this example clearly shows that space has different properties when it is in a metal than it does when it is in an insulator.

For this reason, Faraday considers matter to consist of the forces and properties of space, since the solid atom itself does not seem to contribute at all to the properties of matter.  His description of matter is much like this;  he designates the atom away from its powers of attraction, repulsion, etc., "a", and those powers, apart from the atom, he designates "m".  In his interpretation of Boscovitch's theory, therefore, the “a” disappears.  This makes a lot of sense, as he argues, since the atom is nothing without those powers:

Thus, referring back to potassium, in which as a metal the atoms must, as we have seen, be, according to the usual view, very far apart from each other, how can we for a moment imagine that its conducting property belongs to it, any otherwise than as a consequence of the properties of the space, or as I have called it above, the  m?  so also its other properties in regard to light or magnetism, or solidity, or hardness, or specific gravity, must belong to it, in consequence of the properties or forces of the  m, not those of the  a, which, without the forces, is conceived of as having no powers.  But then surely the  m is the  matter of the potassium,... (Faraday, A Speculation Touching Conduction and the Nature of Matter)

Such an idea has some very powerful consequences.  A particle of matter is no longer an isolated piece of dead material.  We no longer have the difficulty of a body acting where it is not, since a body's ability to act will define the limits of its existence:

The view now stated of the constitution of matter would seem to involve necessarily the conclusion that matter fills all space, or, at least, all space to which gravitation extends (including the sun and its system); for gravitation is a property of matter dependent on a certain force, and it is this force which constitutes matter.  In that view matter is not merely mutually penetrable, but each atom extends, so to say, throughout the whole of the solar system, yet always retaining its own center of force. (Faraday, A Speculation Touching Conduction and the Nature of Matter)

These particles are very strange, almost like waves.  They are, in a sense, an area of tension in space which somehow originates from a center.  In this they are different from waves, which are not associated with any center point which locates them as being primarily in any one spot.

All this talk of the properties or powers of space is very reminiscent of Timaeus' Receptacle and Anaximander's Indefinite principle, which were almost, but not quite, empty void.  Once again, matter as a solid thing, similar to our experience of large bodies, has dissolved into an almost nonexistent substratum, which is yet full of power and tension.  By the limitation and direction of that tension, definition and form enter into the world, creating the objects of our experience.  Each body may be conceived of as being omnipresent, and as overlapping with every other body, yet particles maintain some vestige of identity and separateness, since they have a center which locates the origin and concentration of their existence.

Leibniz' ideas on this subject are even stranger, but they lend some additional power to our understanding of matter.  His theory of monads is far too long and complex for me to present it here, but a look at some of the basic parts of it will be very instructive.  He conceives of the world as made up of indivisible points, much like those of Boscovitch, but they are endowed with what can best be described as a very simple consciousness.  This consciousness consists of a sense of identity, a certain amount of perception of the world about them, and certain tendencies or “appetites”.

 In # 19 of the Monadology, he says that while this might be called a soul, he prefers to reserve that name for such things in which perception is clearer and accompanied by memory.  He would consider the forces which surround Boscovitch's centers to be derivative from the monad’s perceptions and appetites, which might correspond to the passive and active primitive forces mentioned in the Specimen Dynamicum.  This theory even offers us an explanation of the inertia of bodies:

It also follows that creatures receive their perfections from the influence of God but that their imperfections are due to their own nature, which is incapable of being limitless.  For it is in this that they differ from God.  This original imperfection of creatures is noticeable in the natural inertia of the body.  (Monadology, #42)

Since it is necessary, in order to exist as a particular being, to be limited, the monads have a strong sense of self which separates them from the world.  Extrapolating from what Leibniz says, we might create this story.  Inertia might be seen as the effect of a body's egoism.  Imagine our simple collision of body 'A' and body 'B', as viewed from within body 'A', which is moving before the collision.  As far as 'A' is concerned, it is motionless, and 'B' and the rest of the universe is barreling toward 'A' in an effort to cause it to move.  'A' hunkers down, vowing not let this inferior moving body move it from its perfect motionless state.  After the collision, 'B' is travelling away from 'A' at the same rate at which it approached.  By a supreme act of self assertion, 'A' has managed to completely ward off the attempt to make it move!  Of course 'B' at the same time has a similar opinion of the conflict, except that it believes it has managed to maintain its immovable position against the attack of 'A'.  And this can be the case in all collisions, since relative velocity is always preserved.  Thus inertia might be seen as being caused by each particle's firm and unshakable belief that it is the immovable center of the universe.  Granted, this is a rather fantastic story to explain what Newton calls the inactivity of the mass, but since that "inactivity" very evidently acts on other bodies, this myth lends something to our understanding of inertia.

The world of "inorganic" bodies is now alive with perception and intelligence.  And this perception and intelligence is not simply tacked onto dead inert matter.  The hardness, inertia, and weight, of bodies consists of this perception and intelligence, and its derivative forces:

Compounds, or bodies are multitudes; and simple substances, lives, souls, spirits are unities.  And there must be simple substances everywhere, because without simple substances there would be no compounds; and consequently all nature is full of life. (Principles of Nature and Grace, # 1)

Nature is transformed from a collection of atoms flying about in the void to an organic being.  This image is beautiful and moving, but it is certainly not what one would expect when first setting out to investigate matter.

We now continue for a brief examination of the discoveries of quantum theory to see the extremes to which our imagination must go to begin to express the mystery of "What is this stuff?!"



We have arrived at some very odd conclusions about the "stuff" of the world we live in.  Even if we dismiss the ideas about consciousness in monads as an imaginative myth, our atoms of "solid singleness" have taken quite a beating.  Yet they do still have their "singleness" to some degree.  They are still particulate in that respect.  Bodies are made of particles, and light consists of waves.  We do not fully understand the Aether or "field" in which the light waves exist, but we do know that it is the same field in which electric and magnetic forces are propagated, and we have laws about wave motion which help us understand and predict what light will do.  By the same token, we may have trouble visualizing particles with mass but no extension, but Newton's laws still work to understand the interaction of these centers of force.

Quantum physics breaks down these last vestiges of a simple understanding of nature. In what has gone before, I have assumed a sort of innocence, in order to bring out the wonder in this investigation of matter, and to assure that nothing was taken for granted without being examined.  In the coming section, I wish to examine several concepts which have arisen with the beginning of quantum physics.  It would be impossible to go into all of the developments which have led up to the ideas which I will examine in this section, without making this essay more unwieldy than it already is.  Therefore, I assume quite a bit of knowledge which I denied myself in the previous section.  I will for the most part only mention those things which I feel throw light on our question "What is this stuff?!?"

The first hint of problems with our old way of thinking come from a paper of Einstein's about an experiment measuring the energy imparted to electrons by shining light of various frequencies and intensities on a metal plate.  This phenomenon is called the photoelectric effect.  The exact details of the experiment may be read elsewhere, but the results are very disturbing.  The energy imparted to electrons by light turns out to be proportional to the frequency of the light, and not to the intensity (which is the amplitude of the wave).  Classical physics expects that the amplitude of the waves of light should be proportional to their energy.( Imagine sea waves.  Their strength has nothing to do with how close together they are, but rather with their height.)  The experiments showed that increased intensity would eject more electrons, but that these electrons would not have greater energy unless the frequency of the light was increased!  Einstein proposes that this could be explained if light came in little packets, whose energy E was proportional to their frequency.  The constant of proportionality he posits is h, a constant called Planck's constant for a man who studied another phenomenon involving the emission of light from heated bodies.  Planck discovered that the light was emitted in a way that suggested that some mechanism only allowed it to be emitted in packets whose energy E was equal to h*l  , where l was the frequency of the light.  Einstein goes one step further and suggests that light not only is emitted but actually exists in packets of energy E=h*l .  This is ridiculous!  Diffraction proves that light must be a wave, yet this experiment proves that it must be a particle!  The equation itself reveals the contradictory nature of this hypothesis.  The energy of the light particle is proportional to its frequency?  What frequency?!?  The frequency it would have if it were a wave!  Strange as this idea is, the theory still stands today, and no purely wave theory has ever been able to explain the photoelectric effect.

Next, we find evidence that electrons, one of our new atoms (so to speak), or ultimate particles, is behaving like a wave!  When X-rays, a type of light radiation with very high frequency (whatever that means anymore), strike a polished face of a crystal of nickel , they are reflected in a selective way.  Only certain frequencies are reflected for a given angle.  This can be explained quite neatly, assuming the X-rays are waves (note that we must now assume this), as a variation of the phenomenon of diffraction (I omit the details here for the sake of brevity).  The problem is that electrons are also selectively reflected from a crystal of nickel .  Only electrons with specific velocities will be reflected at a given angle, as if their velocity were somehow analogous to the frequency of a wave.  Well, our poor particles have been so problematic, why don't we just give in, admit we were wrong, and say that electrons really are waves?  This won't work because we have too many good reasons for believing that they are particles.  The entire framework of chemistry and its laws of definite proportion depend on particles.  The same goes for the beautiful structures of crystals.  To say that electron diffraction would be explained if they were waves is not helpful at all.  Davisson, in an essay on this problem describes the dilemma:

This observation though true is not a very valuable one.  It is rather as if one were to see a rabbit climbing a tree, and were to say, "well, that is rather a strange thing for a rabbit to be doing, but after all there is really nothing to get excited about.  Cats climb trees- so that if the rabbit were only a cat, we would understand its behavior perfectly." (Are Electrons Waves?)

And we cannot escape the dilemma by claiming that we were wrong in believing that it is a rabbit, for we have very good evidence that it is a rabbit.

Even before these experiments confirmed the wave nature of electrons, while thinking about spectral lines of hydrogen atoms, De Broglie derived an equation parallel to Einstein's E=h*l , for calculating the wavelength of electrons.  This equation is l =h/mv.  Again, this equation immediately shows its contradictory nature.  The wavelength is equal to h over the mass times the velocity?  The mass of a wave?  The mass it would have if it were a particle!

We have certainly made a mess of nature now.  All things - light and bodies - must be finite discrete particles, and infinite continuous waves.  They must even be both at once.  There is a marvelous experiment in which light is shown from a very weak source onto a two slit diffraction grating.  The source is so weak that it theoretically emits one light particle at a time.  If one places a light sensitive screen on the other side of the grating, the screen is exposed in discreet little spots, as if it were being hit by single particles of light.  But if the screen is left for a long time, the overall pattern of light is just as if there were full waves of light diffracting and canceling.  How does one particle cancel itself?  Or if cancellation is not the cause of the pattern, then how does that lone particle know where to go?  Further, if one of the slits is closed, the pattern changes accordingly.  One particle can only go through one slit, yet it "knows" whether the other slit is open or not!

One possible way of visualizing this dual existence is to imagine that the particle is the sum of many different wave patterns, which cancel each other almost completely except in one limited region.  The tighter and more distinct this packet of waves is, the more component waves will be needed to produce it, and therefore its frequency will be less distinct.  If its frequency is more distinct, it will tend to spread wider, and if its frequency is perfectly uniform, it will be a sine wave and therefore infinite in size.  This idea, expressed in more mathematical terms, is Heisenberg's Uncertainty principle.  By playing with De Broglie's equation we find that momentum (m*v) is directly proportional to frequency.  Therefore, in the above picture of a wave packet, if we wish to know an object's momentum or velocity, we must know its frequency.  But if its frequency becomes uniform, so that its momentum can be known, the object becomes less particle-like and more wave-like.  Thus its position becomes less defined.  Alternately, if it manifests its particle-like attributes and its position is well defined, its momentum becomes unclear.  When stated mathematically, this concept becomes:


The uncertainty in the position times the uncertainty in the momentum must always be equal to or greater than planck's constant.

When we consider the world around us, it is very difficult to imagine that these objects which seem so clear as to their position and motion should be made up of such a strange flux of beings which are either moving somewhere specific, but existing in no clear place, or visa versa.

Finally, we should look at one more idea about bodies which comes up in the light of all this strangeness, but which looks somehow familiar.  For a long time, scientists have wondered what force could hold all of the protons in a nucleus together, against their repulsive force for each other.  It is a very mysterious force.  It must be very strong, yet it does not act for any appreciable distance outside the nucleus.  The proposed solution is that the protons act on each other through a field much like the electromagnetic field.  Because of the wave-particle duality, the disturbances in this field should also be to some degree particulate.  According to calculation these particles, called Pi Mesons, in order to have the energy to accomlish their job, should have a mass several hundred times that of the electron.  Particles roughly fitting their theoretical description have been detected.  But if these particles really existed, the nucleus, being full of such particles, would have to have a much greater mass than it does.  Physicists solve this difficulty by using Einstein's principle of the equivalence of mass and energy, and assume that these particles must be momentarily created out of energy, and then reabsorbed.  Of course the next question is "where does all that energy come from?".  The answer to this question is at once a stroke of genius and of madness.  If we multiply both sides of Heisenberg's equation by velocity (V) and again isolate Planck’s constant on one side, it can be altered to this form:


This is to say that the conservation of energy/mass  is only precise to a certain point.  The energy in any system may fluctuate by small amounts DE, with a duration of Dt.  The greater the fluctuation, the smaller the duration may be.  These pi mesons are thus created out of such energy fluctuations.  Calculations can be made, which show that given the energy they must require, their duration is just as long as it would take to traverse the diameter of the nucleus at near to the speed of light.  In this way, they exists just long enough to do their job, and then cease to be.  This is very reminiscent of beings which come to be from Anaximander's Indefinite and then disappear:

...  for they pay penalty and retribution to each other for their injustice according to the assessment of Time',  ... as he describes it in these rather poetical terms. (Simplicius, writing on Anaximander)

The greater their mass/energy, the more severe their penalty "according to the assessment of time."  They come to be from almost nothing, and are destroyed by the natural tendency of space to be formless.  We might say that Space is full of a tension or power, which enables it to be an underlying principle of material bodies.  This tension is ordinarily balanced and not directed in any way.  If it becomes unbalanced and directed, its tendency is to return to a balanced state.  This tension can only be stretched so far before it snaps back toward indeterminateness.  Planck's constant can be seen as being a measure of the limits beyond which Space will not allow itself to be made determinate.  This is of course only another myth which contains part of the truth but certainly not all of it.

This brief tour of quantum physics should be enough to show the further mysteries that lie beneath the question "What is this stuff?!?".  We have found that even the singleness of our centers of force is not absolute, but it is not altogether false either.  Mathematical physics has showed us in its clear and undeniable way, that the stuff of our world is stranger than any myth of the Greeks.


Our questioning has brought us a long way from solidity and weight.  Looking back, we seem to have followed what Aristotle called the natural way to proceed.  We went from what is most obvious to us, but not truly understood, to something which is clearer in itself, though strange on first thought.  But the clarity we have reached is one of perplexity.  We are very certain that we cannot understand the world in the simple way we understand everyday things.  If we break up any object around us, we find smaller pieces, not Space and Form.  Baseballs do not spread out over the entire universe when we measure their momentum.  And if that baseball hits you on the head, it certainly doesn't feel as if it were barely clinging to existence, through the action of ephemeral particles like Pi Mesons.

The amount of solidity, determinateness, and intelligibility in the world is startling when you consider the liquid, indeterminate, formless foundations on which it stands.  As Einstein once put it:

The most incomprehensible thing about the world is that it is comprehensible.


Let us return to that awakening human mind with which we began.  Imagine that it has learned and thought about all that we have discussed.  It may have begun by thinking "Matter is simple.  First I will understand it, and then I will move on to the difficult problems of life, death, and the soul."  Imagine its suprise to find that matter is far from simple, and that the question "What is this stuff?!?" contains within it the questions of life, death, and the soul.  We live because matter itself is full of life, and we die because all things, even the matter we are made of, is only fleetingly stolen from Indefinite Space.  We too, must "pay penalty and retribution... according to the assessment of Time."

It seems that the more our primeval mind might learn, the more it would wonder "What is this stuff?!?"

File written by Adobe Photoshop® 4.0
Comix by Vaughn Bode


·      All references to Presocratic thinkers except those quoted from Aristotle, are from The Presocratic Philosophers,    2nd Ed., by G.S.Kirk, J.E.Raven, and M.Schofield,   Cambridge University Press, 1983

·      Lucretius references are from the Mantinband translation, Fredrick Ungar Publishing Co, 1965

·      Timaeus references are from the Cornford translation, Bobbs/Merrill Educational Publishing, 1959

·      Aristotle references are from the Apostle translation, Peripatetic Press, 1980

·      Descartes references are from the St. John’s Junior Lab Manual, or from the old Lab Readings Manual.

·      Leibniz references are from Leibniz : Philosophical Papers and Letters, University of Chicago Press, 1956

·      Newton references are from the Principia, Motte's translation, Revised by Cajori, Univ. of Calif. Press, 1962

·      Boscovitch references are from the old Lab Readings Manual

·      Faraday        "       "    "   "   "   "     "       "

·      All references to ideas in quantum theory are from the Senior Lab Manual.

·      Information on Pi Mesons is from a handout written by our Assistant dean, Malcolm Wyatt

·      Einstein Quote found in Gravitation, by Charles W. Misner, Kip S. Thorne, And John A. Wheeler, W.H. Freeman & Co, 1971

·      Illustations from The Man, by Vaughn Bode, Printmint, 1972