International Catholic University
We ended our last lecture with the notion of powers. We had made the point that powers are distinctive properties of substances that provide a direct insight into their natures. In this lecture we shall continue with this theme, focusing on inorganic or non-living natures. In so doing we shall develop further the concepts of protomatter and natural form. We shall also touch on a few topics relating to quantitative aspects of nature, and how the philosophy of nature relates to the modern sciences of physics and chemistry.
Of all natures in the universe the nature that is most intelligible to us is our own nature, human nature. We have a privileged insight into ourselves, and even before we study the philosophy of human nature -- as treated in Aristotle's De anima, for example -- we have some idea of our own powers and how they operate. Let me start with the powers that are distinctively human, therefore, for these can aid us in understanding the powers of other natures.
I am using graphical aids throughout these lectures that are available to those who are taking the course for credit. Many of the figures are found in my The Modeling of Nature, published by the Catholic University of America Press in 1996. If you have these, Fig. 3.1 (on p. 134 of Modeling) provides a schematic diagram of the six generic powers found in a human being. These are shown in the diagram as parts of a stimulus-response model, with the stimulus represented by the S at the top left of the diagram, and the response by the R directly below it. The three boxes along the top of the figure are known as cognitive powers. They are, from left to right, the outer senses, the inner senses, and the intellect. We have already explained these powers and their operation in our first lecture. At that time we did not go into the other powers with which they are closely connected, which we now show directly beneath them along the bottom line. Known as appetitive powers, they are, from left to right, the motor powers, the sense appetites, and the will. The diagram as a whole, on this account, is entitled "Human Cognitive and Appetitive Powers."
The operations of these powers are indicated in the lower portion of each box. From left to right, when acted on by external stimuli, indicated by the letter S, the outer senses serve to explain our sensations. The outer senses next activate the inner senses, which produce our perceptions, and they in turn activate the intellect, from which come our intellections or thought processes. Then, continuing directly below the intellect but now proceeding in the opposite direction, from right to left, the will produces our volitions or acts of the will, the sense appetites our emotions, and the motor powers the movements of our bodily organs. The bottom line terminates on the right with the letter R, standing for responses and so completing our stimulus-response (S-R) model. These are the many activities we initiate in response to stimuli. And in so initiating them, we act as agents or efficient causes, and we achieve ends or goals that are the final causes of our activities.
From this simple diagram, therefore, we get the point of how powers can serve as efficient causes that have final causes built into their operation. Through the use of powers, therefore, we are able to incorporate both agency and finality in a nature's activities.
We now have enough information to make a synthesis of the three most important concepts we have developed so far, namely, protomatter, natural form, and power. We shall refer to this synthesis as a model, thus introducing the theme of our text, The Modeling of Nature. Now the term "model" is used in science in many different ways. The model we shall be using I refer to as an epistemic model. By an epistemic model I mean an analogue or an analogy that conveys ideas or concepts that are not directly apparent in sense experience. Thus the aim of an epistemic model is to produce intellectual knowledge that is certain, which is what the Greek word episteme means. We have already used one such model in our last lecture when we presented our causal model. This new model is a further development of the causal model. I shall call it a powers model, because it makes use of distinctive powers to characterize the properties of different natures.
It is difficult to display protomatter in a flow chart or a circuit diagram such as we have used up to this point. But in the present day most people realize that there is more to matter than meets the eye. It has been said that matter has been "dematerialized" in our generation. What this means is that the ultimate matter can no longer be thought of little hard balls of stuff. Better to think of it as a matrix, an underlying principle that is conserved throughout all physical change. It is also a source from which all natural forms spontaneously emerge. In itself protomatter is like a kind of potential energy, nothing actual or determinate, but an indeterminate something that grounds every change and motion going on in the universe.
To convey this idea in my model I start with protomatter simply as a mathematical point at its center. Protomatter has no extension, no qualities in terms of which it can be known. Then, because of the intimate relationship between protomatter as a potential principle and natural form as its actualizing principle, I next show a series of concentric circles that radiate out from the center. The concentric circles are meant to suggest that natural form acts as an energizing field. What the field does is "expand" the protomatter, as it were, and form it into a substance of a particular kind. In other words, the natural form is a substancing form, one that determines protomatter to be a particular substance. And it brings with it not only existence, but also extension, bodily parts, and all the qualities proper to that substance.
The natural form, moreover, is a unifying form. It confers a unity on all the parts of a natural body and makes of them a functioning whole. It is a specifying form, making all of the components be and react in a way characteristic of the natural kind to which the substance belongs. And it is a stabilizing form that preserves the identity of the substance and maintains the unity of its components under external influences -- to the extent that this is possible in a changing world.
Thus we have incorporated both protomatter and natural form in our model. What are we now to do with powers? There is a simple solution. Since powers are actually powers of the natural form, we simply locate them as boxes or squares within the energizing field. For the moment I am interested in a generic model that will serve our needs later, and for this purpose four boxes will suffice. Let us now arrange four boxes symmetrically within the field. When we do so we have the powers model shown in Fig. 3.2 (see p. 31 of The Modeling of Nature).
In this figure protomatter is labeled as PM and it occupies the point at the center of the model. The concentric circles or the "field" radiating out from PM we label NF, and this stands predictably for natural form. The four boxes within the field have no labels for the moment. We show them simply as cross-hatched, but later we shall identify them in specific ways. Notice that some of the boxes are fitted with arrows pointing away from the box or toward the box. The arrows represent the actions and reactions that are received from, or are received into, the particular power. They are indicators of efficient causes that act for particular ends, in ways we are about to describe.
If nature, as described in our previous lecture, is the inner dimension, the source of characteristic activities, we can see right away the problem posed when modeling inorganic or non-living substances. As opposed to living things, inanimate objects have little activity that can serve to reveal the natures that are within them. They tend to be inert, and observation alone seems powerless to reveal any of their powers.
With so little to go on, the ancients concentrated on sensible qualities, on the ways substances affect our senses, as primary indicators of basic kinds. The various pairings of active qualities, hot and cold, with passive qualities, wet and dry, led them to regard earth, water, air, and fire as the four basic elements. To these they added the motive powers of gravity and levity to explain up and down motions, as these elements approached or receded from a center of gravity. This, they thought, could explain all the basic changes in the terrestrial region. For the heavenly region they had to add aether as a fifth element, a quintessence or quinta essentia. Its natural motion, for them, was circular, constant movement around a center, for this is how the celestial spheres appeared to move.
For present purposes we can recreate the inorganic powers implied in the Aristotelian system of elements in the diagram shown in Fig. 3.3. The two boxes in the top line took care of the major alterations observed on the earth's surface. That on the left, the active qualities of hot and cold, explained heating and cooling, whereas that on the right, the passive qualities of wet and dry, explained dissolving and melting processes. And the two boxes on the bottom line took care of all the local motions seen in the universe. That on the left, the motive powers of gravity and levity, explained rectilinear motions to and from its center, and that on the right, various aether powers associated with the quintessence, explained the circular motions seen in the heavens.
This theory, primitive though it was, had a long history, lasting over twenty centuries. It was really not replaced until the late eighteenth century, with the birth of modern chemistry. At that time experimentation and measurement was added to simple observation. Of special importance was the study of ways substances react to one another when placed in solution or in close contact. One of the earliest procedures consisted in isolating various substances in the gaseous state. It was found that as gases substances could be made to combine, and then precise measurements could be made of the weights and volumes that entered into combination. Repeated confirmation and analysis of such measurements throughout the nineteenth century led to an important discovery. Over ninety unit atomic weights were found in nature, one for each chemical element. And even vaster numbers of unit molecular weights, one for each chemical compound, were found in nature also. Unit atomic weights, by definition, had their counterparts in atoms, and unit molecular weights had their counterparts in molecules. Thus did the concepts of atom and molecule enter into modern chemistry.
By the end of the nineteenth century the periodic table of the elements had been basically completed. How molecules were structured out of atoms was then well understood. The twentieth century saw the atom broken down into its components, a nucleus surrounded by orbiting electrons. Then the nucleus itself was broken down, first into protons and neutrons, then into the large numbers of nucleons now being studied in high-energy physics. And out of all this work came a startling conclusion. All of the physical and chemical phenomena in the world of the inorganic could be explained in terms of four basic forces. These you have probably heard of in popular media, even if you have not studied them in a science class. They are know as the electromagnetic force, the gravitational force, the weak force, and the strong force.
With this we are in a position to update the Aristotelian model of an inorganic nature and bring it into the twenty-first century. In fact, all we need do is replace the four boxes of Fig. 3.3 with the four basic forces of recent physics. These are the agencies through which elements and compounds, and even subatomic entities, are now known act on each other. All of the forces have potentials and fields associated with them, so it is a simple matter to make the transition to powers when labeling them. (The Latin term for force is vis or virtus, and both terms are usually translated into English as power.) So let us now revise the view presented in Fig. 3.3 and introduce its modern replacement, but incorporated in the context provided by the earlier diagram in Fig.3.2. We then have our next diagram, which we label as Fig. 3.4 (p. 71 of The Modeling of Nature), "A Powers Model of an Inorganic Nature."
In the new diagram we have replaced the cross-hatched boxes of Fig. 3.2 with boxes containing the four forces of recent physics. The labels are now EF, for electromagnetic force, GF for gravitational force, WF for weak force, and SF for strong force. We have retained the F for force rather than using the P for power. But whether F or P is used, the idea is the same. We are attributing to the natural forms of non-living substances powers through which they act, analogous to the vis gravitatis (that is, force of gravity or power of gravity) that was attributed to them from the time of Aristotle.
In our figure, as previously, the protomatter (PM) is shown in the center. The natural form (NF) is the field, the series of concentric circles energizing the protomatter. Notice that the NF now bears the subscript "i" to designate it as inorganic, that is, a natural form of a non-living substance. And arranged symmetrically in the field are the four boxes designating the powers that are operative in inorganic substances.
At the top left, electromagnetic force explains chemical actions and reactions, indicated by the arrows attached to the box, going in both directions. These are associated with the electrons and ions that cause elements and compounds either to enter into combination or to break down into their components. At the bottom left, gravitational force is the associated with the mass of a body. By action and reaction, again indicated by the pair of arrows, it explains most of the phenomena studied in the science of mechanics, including gravitational interactions. At the top right, the weak force, again reciprocating, is useful when explaining various types of radioactive emission and absorption. And finally, at the bottom right, we have the strong force, also reciprocating, that binds nucleons together in the atomic nucleus and serves to explain nuclear reactions.
Inanimate substances with which we ordinarily come in contact, solids and liquids mainly, are characterized by all four forces or powers. In daily experience we notice only weight or other gravitational effects, but with some observation and experiment we can become acquainted with chemical changes and the agencies that produce them. We need more sophisticated equipment to gain knowledge of radioactivity and nuclear reactions. Yet the powers to produce them are present in all sensible substances and so should be regarded as part of their natures.
The four forces or powers give a generic understanding of non-living substance, but they do not provide information at a specific level. To move to this stage we must return to the essential components of substance itself, protomatter and natural form. Let us now do this, concentrating first on the matter and then on the form that determines it to be a particular natural kind.
Thus far we have proceeded on the assumption that atoms and molecules serve as matter for chemical reactions. We have also assumed that electrons, protons, and neutrons, the last two located in the nucleus of the atom, function as material parts when explaining radioactivity and nuclear reactions. These assumptions now require fuller investigation.
A fruitful path to pursue is to pose a question. If chemical substances are composed of atoms and molecules, and these in turn are composed of electrons, protons, and neutrons, what more can be said about the stuff of which all these are made? To push the inquiry further: if subatomic particles such as these are composed of yet smaller and more elementary particles, is there any limit to which one can go in seeking the matter of which everything is ultimately composed? This is the question of the ultimate substrate of natural processes, which we have identified with the protomatter of Aristotle.
Since the discovery of radioactivity at the end of the nineteenth century it has been known that certain chemical substances break down spontaneously into others of lower atomic weight, and in so doing emit particles and radiation of different types. Two of these particles have proved extremely difficult to detect. One of them is the anti-neutrino, a massless and chargeless entity possessing only what is known as "spin," and the other is the W-particle, a massive particle associated with the weak force that holds the neutron together, whence the "W" in its name.
Apart from radioactivity, it has long been realized that a very strong force is required to hold the components of the atom's nucleus, called nucleons, in stable positions. The very strength of this force requires massive equipment to break through it so as to study the structure of the nucleus. The huge particle accelerators of high-energy physics are what are used in this task. But rather than simplify the model of the nucleus, the investigations of nuclear physicists have produced precisely the opposite result. They have led to the discovery of hundreds of new particles and anti-particles, of which protons, neutrons, and electrons are merely special cases. Attempts have been made to cut through all this complexity, but without much success.
The best that can be done, apparently, is to say that there are six ultimate states of matter, three quarks and three anti-quarks, which combine in various ways to produce the particles acted upon by the strong force. Quarks themselves cannot be isolated, since they always recombine to maintain the appearances of known particles. Thus it is meaningless to inquire into their structure or to ask whether they are composed of more ultimate constituents. The search for a fundamental ground to all natural processes seems to end with them. Stated in another way, it ends with a number of conservation principles on which the quark hypothesis is based. These enable us to identify the particular features that will always remain throughout various nuclear reactions.
What I have said is, of course, not proposed as documenting the final stage of nuclear research. It does, however, lend strong support to a view of the ultimate substrate that the famous physicist, Werner Heisenberg, saw as going back to Aristotle's pure potentia, his "first matter." For Aristotle protomatter is not itself a subsistent entity that is already formed. Rather it is an unformed and indeterminate something that it at the base of all substantial change. As the basic material factor, what it contributes to the coming to be of a new substance is its potential. And that potential is merely its ability to be determined by a specifying form to constitute an entity of a particular kind. Somewhat like the quark, protomatter is always "confined" within matter of some kind. It simply cannot exist by itself in isolation from a determining form. Better to think of it as a principle or a cause entering into the composition of a natural substance without being identifiable as a subsistent entity or complete substance itself.
Having said this about protomatter, we can now take a closer look at its correlative principle, natural form. This is also a principle and a cause, but it turns out to be considerably more intelligible than protomatter. I shall approach its intelligibility by first introducing to you a model of a different kind from those we have discussed thus far. This new type of model is an iconic or pictorial model. Being a sensible model it is more easily grasped by us than the epistemic models we have already considered. But an analysis of a few iconic models will show that they themselves are only intelligible in terms of the powers models that actually lie behind them.
The first iconic model we present is the Bohr model of the atom. A simplified version of this model for the first eleven elements of the periodic table is shown in Fig. 3.5 (p. 41 of Modeling). The Bohr model pictures the atom as a solar system in miniature, with the nucleus analogous to the sun and electrons to the planets revolving around it. Bohr's theorizing led him to introduce various circles or shells in which electrons are distributed around the nucleus. Electron orbits of the elements of the first row of the periodic table, hydrogen (H) and helium (He), occupy the first shell in his model, that closest to the nucleus. The orbits of the next eight elements of the table, from lithium (Li) to neon (Ne), then occupy the first and second shells. And after that, the orbits of the next eight elements, from sodium (Na) to argon (Ar), fill the first, second, and third shells.
For understanding chemical reactions, one must focus on the localization of the electrons in the outermost shell of each element, for this serves to explain what chemists call the valence or affinity of that element. Note that we have indicated with an arrow the single valence electrons in the outermost shells of hydrogen (H) and sodium (Na) in Fig. 3.5. We have also pointed with arrows to the missing electrons in the outermost shells of oxygen and chlorine in Fig. 3.5. The basic principle is that one element combines with another element when both elements are able to share or exchange electrons so that each completes its outermost shell. Applying this principle one can explain why chemical elements combine the way they do. One can also visualize chemical bonding, with electromagnetic forces serving to unite the atoms, and so explain the structure of the resulting molecule.
In his theory, Niels Bohr postulated that electrons move in stable orbits within their shells without emitting or absorbing electromagnetic radiation. Under the influence of strong electrical fields or other external energy, however, electrons can make stepwise jumps from one shell to another. When they do so they emit or absorb electromagnetic radiation in precise amounts determined by the energy levels of the shells. Using various rules stating which electron transitions are allowed and which are not, Bohr found that he could explain the emission and absorption spectra of the respective chemical elements.
A refinement of this model by another physicist, Arnold Sommerfeld, replaced Bohr's circles by elliptical orbits. This led to the possibility of the orbits having various orientations in three-dimensional space. Thus it provided additional stable paths or energy states for the electrons within the atom. Another development was the concept of electron spin, that is, the rotation of an electron on its own axis. That gave still more energy states. With each advance, physicists provided a more graphic picture of the structural components of each atom. And, in terms of that picture, they could account for most of the element's chemical properties.
Let us return now to the epistemic, non-pictorial model with which we were earlier concerned. Our aim is to explain how these Bohr-Sommerfeld models may cast light on the nature or inner dimension of an inorganic substance. Of the four causal factors involved in our powers model, we noted that the formal cause, the natural form (NF), is the most intelligible. So that is the point at which we start.
The element sodium was discovered at the beginning of the nineteenth century. It is the sixth most abundant element on earth, found especially in common salt and sea water. It is classified by chemists as an alkali metal, similar to lithium and potassium. It is very active chemically, combining with the oxygen of the air and reacting vigorously with any water with which it comes in contact. When burned in a flame or in a sodium vapor lamp it shines with a strong yellow light. And it has many other properties.
A person who has seen this peculiar metal, and particularly one who has experimented with it, can be said to know the nature of sodium. But what does one know when one knows that nature? Assuming that the nature has a formal and a material component, as already explained, it is difficult to see how one knows the matter directly. At best he can model it as found in the Bohr atom and say that it is formed out of electrons and a nucleus arranged in a special way. This is not too helpful, for the stuff of which these particles are made is not known, and the same material components are found in all the other elements in the periodic table.
Here the Bohr-Sommerfeld model of the sodium atom, which is shown in Fig. 3.6 (p. 46 of Modeling), can be of help. This model differs from that of the simplified electron shells of sodium drawn in Fig. 3.5. The circles of the two-dimensional diagram are now replaced with elliptical orbits having different orientations in space. Each elliptical orbit contains two electrons of opposite spin. And there is still the single valence electron in the third shell, which is pointed out with an arrow as it was in Fig. 3.5.
If this model tells us anything, it is that the organization or formal arrangement of these components, and not the components themselves, makes sodium be what it is. This arrangement occurs in nature and is not an artificial form, like the shape of a chair imposed on pieces of wood that maintain their own identity. None of the electrons in the sodium atom acts simply as an electron. Rather, each functions as a part of sodium. The form that is known and that is modeled in the Bohr-Sommerfeld atom is clearly a natural form, a unifying form that confers a new substantial identity on the parts that make up the composite.
To make more explicit this organizing function of the natural form, two additional features of this atomic model may be pointed out. One is that a "free" electron (one not "bound" within the atom, as are those shown) is completely controlled by its own mass and electric charge. On its own, it would fall directly into the nucleus, attracted by the strong positive charge. When within the sodium atom, however, no electron can do that. It must occupy a unique energy state in the atom that is occupied by no other. Another is this. When, in a sodium vapor lamp, a sodium atom is energized or excited, it directs its single valence electron to a higher energy state, funneling into it all of the absorbed energy. The electron again does not act on its own. Instead it is controlled by the nature of sodium. It returns to its normal energy state by emitting the yellow light produced by a sodium vapor lamp. Again it is sodium as a natural kind, the nature of sodium, that controls this activity and reactivity. The natural form integrates and stabilizes all eleven electrons within the sodium atom. It causes them to function as an integral and natural whole.
Another view of a natural kind is provided by the element chlorine (Cl) and the way it combines with sodium (Na) to form sodium chloride (NaCl) or common salt. Identified as an element only shortly after sodium, chlorine in its natural state is a greenish-yellow gas classified along with fluorine (F) as a member of the halogen group. It is toxic or poisonous and was the first gas used in chemical warfare. It also has more humane uses. It serves as a germicide and disinfectant, is a good bleaching agent, and is widely used in industry.
Like sodium, chlorine can be modeled by the Bohr atom. As already shown in Fig. 3.5, it was pictured with a nucleus surrounded by seventeen electrons -- two in the innermost shell, eight in the middle shell, and seven in the outermost. Since it requires only one electron to complete its outermost shell, it combines easily with elements that can supply its deficit with one valence electron. That is why chlorine has an affinity for sodium and joins with it readily to form common salt.
Those who have seen and smelled chlorine gas know what chlorine is. If they have experimented with it extensively they know its many properties. But, as in the case of sodium, they gain a greater insight into its nature and its properties when they model it with the Bohr atom. In the chlorine model the electrons and the nucleus are like those in the sodium atom. The distinguishing feature of chlorine is not its material composition but rather in the way its components are arranged. Again what is at issue is not merely an artificial arrangement. What is present is a dynamic unity that makes each component behave as a part of chlorine. And we know that unifying factor as the natural form of chlorine. This is what enables us to identify chlorine and classify it among the halogen gases.
Sodium and chlorine unite, as we said, to form a very abundant compound easily recognized as salt. This is usually seen in purified form as small white particles, or under the microscope as translucent cubic crystals. The taste of this substance is distinctive. The facts that it dissolves in water, absorbs moisture from the air, and seasons food are widely known.
Salt obviously has very different properties from both sodium and chlorine, and we may well wonder how it can be formed from those two elements. Fig. 3.7 shows how chemists explain this in terms of the Bohr model, to which we again resort. As indicated in the upper part of the figure, single atoms of sodium and chlorine combine to form one molecule of sodium chloride. The sodium atom transfers its valence electron to the chlorine atom and fills its outermost shell. This leaves both atoms electrically charged within the molecule, the first positively and the second negatively. When a number of salt molecules are present they aggregate under the influence of the resulting electrical forces and align themselves in a regular cubic lattice (see p. 48 of Modeling).
Note again that in this and in the previous cases the model of sodium chloride is not the nature of salt nor is the model known in the same way as the nature. Far more people know what salt is than know anything about sodium and chlorine. The properties of a natural kind such as salt can be grasped quickly on the basis of ordinary experience. But the chemist also knows what salt is. In fact, he possesses a better knowledge of its nature, for he grasps its specifying form in terms of the molecular model shown in the top portion of Fig. 3.7. That gives him a superior insight into its nature, the inner dimension that makes it have the properties it does.
The lower part of Fig. 3.7 now lets us put together what we have learned about protomatter and natural form and gain a more fundamental view of this interaction. Apart from their nucleus and electron components, both sodium and chlorine are essentially composites of a natural form and protomatter. The nature of sodium informs and structures the protomatter of that element, and it acts on the nature of chlorine, which informs and structures its protomatter. In the course of the reaction the substrate is conserved. It carries over all the potentials latent within the elements, many of which can be assigned numerical measures. But at the end of the reaction the two previous natures disappear, to be replaced by a new natural form, that of salt or sodium chloride (see p. 60 of Modeling). This form of salt gives a new unity and structure to the compound. It is now no longer modeled by the atoms of sodium and chlorine but by the molecule of sodium chloride. A new substantial unity has been achieved, a new nature has been produced, with radically different properties. Yet something of the previous substances remains in the protomatter, present as before, still providing the ontological ground for the mass-energy that is conserved in the process.
Now let us return again to Fig. 3.4, "A Powers Model of an Inorganic Nature." The cases of chemical change we have discussed thus far involve the two forces shown on the left side of model, the electromagnetic force and the gravitational force. Elemental transformations also take place through the two forces shown on the right side of the model, the weak force and the strong force. To illustrate how these forces act, we propose a different example of substantial generation, that, namely, of natural radioactivity. The case we shall discuss is the production of the element lead, which occurs in nature, from the radioactive breakdown of uranium, an element that also occurs in nature.
Thus far we have mentioned the atom's nucleus and have noted that it is composed of protons and neutrons. For purposes here we shall use the simplest possible model of the nucleus, one that indicates only the numbers of protons and neutrons it contains. The nucleus itself will be shown as a circle, and in it protons will be indicated by a small circle with a plus (+) inside it, neutrons by a small circle without the plus. Since large numbers of these particles are present in the nuclei of heavy elements, we shall show only one symbol for each type of particle, with a numeral next to it telling how many of each are present.
Fig. 3.8 models the radioactive breakdown of uranium into lead (see pp. 60-62 of Modeling). This process involves changes in the outer shell of electron configurations, as were seen in Fig. 3.7 but are not shown here. It also involves changes within the nuclei, along with the controlled emission of radiation. We have seen that quantitative factors determine the natures that are educed from matter through changes involving gravitational and electromagnetic forces. They do the same through changes involving the weak force and the strong force as well.
Along the top of Fig. 3.8 is written the chemist's formula for what is called the uranium series. Uranium does not turn into lead immediately, but does so through a series of intermediate elements. The sequence reads as follows: Uranium breaks down into thorium, which breaks down into protactinium, which in turn breaks down into radium, which finally breaks down into lead. The atomic number and the mass number is given along with each element, so that one can see that electron structures and mass-energy requirements are changing at each stage. These are accompanied by the emission of radioactive products, which are not shown in the formula.
The close connection between mass-energy and protomatter, which we have spoken of in previous lectures, should now become clear. Protomatter is the ontological substrate that regulates how successive natures emerge in substantial changes. And it regulates these changes in such a way as to satisfy the quantitative needs of mass-energy conservation. Mass-energy is a measure or a metric, but what it measures is really the potentiality of protomatter. That is why we have suggested mass-energy as a surrogate for protomatter when trying to grasp the concept. It itself, as Aristotelians are well aware, is so purely potential that it borders on the unintelligible.
Let me summarize what we have done in this lecture. We may do this by reviewing the various figures in which we presented the major points:
Fig. 3.1 diagrammed the six proper powers of human nature, the three cognitive powers, outer senses, inner senses, and intellect, along with the three appetitive powers, will, emotion, and motor powers, which we know from within, as it were. Fig. 3.2 presented a generic powers model of a nature, showing how matter and form create an "energizing field" in which distinctive powers can be situated. Fig. 3.3 then showed how Aristotle conceived the powers of inorganic substances in terms of active qualities, passive qualities, and two additional powers, one for rectilinear motion, the other for curvilinear motion. Fig. 3.4 replaced Aristotle's powers model for inorganic substances with one suggested by modern physics. Fig. 3.5 showed iconic models of the first eighteen elements of the periodic table. Fig. 3.6 illustrated the Bohr-Sommerfeld model of the sodium atom with elliptical orbits. Fig. 3.7 modeled the generation of sodium chloride from the elements sodium and chlorine. And Fig. 3.8 modeled the natural radioactivity of uranium.
Fig. 3.1 Human Cognitive and Appetitive Powers
Fig. 3.2 A Powers Model of a Nature
Fig. 3.3 Aristotle's Powers Model of an Inorganic Nature
Fig. 3.4 An Improved Powers Model of an Inorganic Nature
Fig.3.5 Iconic Models of Elements in the Periodic Table
Fig.3.6 The Bohr-Sommerfeld Model of the Sodium Atom
Fig. 3.7 The Generation of a Compund: Sodium Chloride