LaRouche's Method and the Physical Sciences
Axiomatics, Science and Physical Economy, A Case Study:

[dodecahedron]Dmitri Mendeleyev and the Discovery of the Periodic Law

Conference Speech by Jonathan Tennenbaum, February 19, 1994

Printed in the The American Almanac, February, 1994

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Jonathan Tennenbaum, of the Fusion Energy Foundation in Germany, addressed the second panel of the Schiller Institute's Presidents' Day conference on February 20.

The subject I wish to address this afternoon, is reflected in the seeming paradox of the existence of two very different, mutually exclusive (or contradictory) definitions of truth. The first definition or criteria is that exemplified by the schoolboy idea of ``getting the right answer'' in school or equivalent classroom, the right answer relative to some system of textbook knowledge, so that nothing can be accepted as true that contradicts the basic assumptions of that textbook knowledge. So this is the notion of truth expressed, for example, in the practice of cheating at examinations, or learning how to do the experiment so you get the answer which is in the textbook. It's the notion of so-called truth expressed by so-called political correctness, that children should engage in polymorphous sexual perversion in order to demonstrate their acquiescence to what have been defined as the latest axioms of acceptable behavior.

In each case, the truth is defined by non-contradiction to some collection of assumptions, either explicit or implicit, which are regarded as completely evident, unassailable, and beyond suspicion.

The second conception of truth--the true one, I should argue--is truth as measured against man's continuing existence on this planet, truth measured in the great laboratory of human history, past, present, and future. We test the relative truthfulness of our thinking by the success or failure of societies employing that mode of thinking to maintain and expand their existence--of course, with the proviso that what may appear to be successful in the short term, may be the surest road to destruction further down the line.

Now these two definitions or criteria for truth stand in ironic contradictory relation to each other. For it is historically demonstrated, that in order for man to have existed up to this point, he had to constantly revise, often in a revolutionary way, his knowledge. So, what was at one time defined as true or as the right answer, becomes later the wrong answer. Entire chapters of accepted classroom knowledge are eliminated or overthrown. And demonstrably, without that, man could not have progressed to more successful ways of existing on this planet.

Considering these historically demonstrated revolutions (I will speak of an example), we should beware of a trap, of the fallacy of British empiricism. British empiricism admits generally, that knowledge does change, but limits the development of knowledge to adding new facts or correcting facts on the basis of sense perception. So the British idea of truth, is to get your facts right, according to the latest authoritative edition of Encyclopedia Britannica and The New York Times.

I said that there's a trap there. What is the trap? Well, there's a fallacy underlying this idea of adding facts on the basis of perception, which people often miss.

First, in British empiricism, there is no change in the underlying assumptions, the axioms adopted for knowledge. Secondly, there is no such thing as a fact determined by sense perception. The fact is, that all sense perception is evaluated by the human mind on the basis of certain ideas in the mind; and those ideas do not come from sense perception, nor are they changed by perception per se.

In fact, I may shock you by saying no idea ever came into anyone's mind from the outside, but all ideas are created from inside the mind. Therefore, no progress of knowledge comes as a reaction to sense perception. Progress of knowledge of the sort upon which our existence depends, comes uniquely through the process of changing the basic assumptions upon which everything is based, including the way we evaluate so-called facts.

We have historical proof that such changes are necessary for human existence. Every society, we can document historically, which comes to rely on schoolboy notions of corrections of knowledge, on the equivalent of the Encyclopedia Britannica, is doomed to collapse.

This second, truer criteria of the truth of the development of human knowledge which I indicated, presents us with a number of apparent paradoxes. One of these paradoxes might come up in the following sort of question: How can you prove a form of new knowledge which contradicts the basic assumptions of existing knowledge or maybe your own assumptions? People will ask, ``Well, this new knowledge or these new hypotheses: what can we check them against?'' Because people habituated to British empiricism and similar modes of schooling, always want to check a proposition against something, as a reflex--to check whether it's the ``right answer.''

Then you have another question or paradox. How can I check an idea to find out whether it agrees with human existence on this planet or not?

Well, things are not quite so simple, and the problem lies other than where the person formulating the question thinks it lies. The problem is the question of the way of thinking.

Let me intensify this paradox with the kind of example which I think will be familiar to many of you. We have someone in front of us, and we want to organize that person. And we say, ``Look, the United States is becoming a pure British colony.'' And the person jumps up and says, ``That's the most ridiculous thing I ever heard! What could be more ridiculous than the proposition that the United States is being made into a plantation, a British-controlled financial system, and that we're all being made slaves to that?''

So, what do we do? We try to prove what we said, by going through the obvious selection of recent events, the clear evidence, to prove it. But our friend doesn't see it that way. He or she interprets events in his or her own way. The same facts, the same perceptions are read in a different way, so as not to arrive at the forbidden conclusions which his or her adopted assumptions forbid him or her to accept.

So we see that no collection of empirical facts, no matter how large, are going to do any good in this case. So we appreciate now the meaning of the statement that the British Empire, like the Venetian one, is an ``empire of the mind.''

Of course, there exists a remedy; otherwise, we wouldn't exist. Man was not born to be a British empiricist.

To find the answers, or to get on the most fruitful path, I propose that we focus on the most crucial phenomenon called fundamental scientific discovery and its relationship to the desired effect of advancing human existence, that subject matter which is the center of Lyn's work. In order to do that, I want to discuss a case study and use it as a kind of Archimedean lever. In that way, I hope we'll be able to spring ourselves progressively upward to higher levels of insight....

I've chosen for this discussion the case of the great Russian scientist Dmitri Mendeleyev, born in 1834, and died in 1907, and who is known primarily for his discovery of what he called the Periodic Law of the Chemical Elements, or perhaps more accurately, the Natural System of Chemical Elements, which is not quite the same thing as the Periodic Table, which is a simple formal presentation of a result of that Natural System.

One reason for choosing this particular example, is that this discovery of Mendeleyev's is central to the whole vast increase of the productive powers of human labor over the period of the last 100 years, and that Mendeleyev as a fascinating personality displays, in a very high degree, the universal qualities of a scientist in the positive sense, in a sense of a scientist devoted to building his nation, to building the world.

I'm not giving a presentation on chemistry here, and I'm not aiming at being precise in details of chemistry. I want to be as precise as I can about something else, that is, the internal process of discovery or some crucial features of that process of discovery, which is our experimental data here. Not the chemistry, but the process in the mind.

Axioms of Physical Chemistry

I have to say, however, a few words about the field of physical chemistry to introduce this. At the time Dmitri Mendeleyev began his scientific work in 1855, the central axiomatic assumption of chemistry was the notion of a chemical element. This notion is associated with the idea, that we cannot differentiate or divide substance down indefinitely, without encountering some kind of a limit, boundary or, as we say, singularity.

In the specific practice of chemistry up to the time of Mendeleyev, the exploration of this area took the form mainly of what are called chemical separation methods, which some of you know if you were fortunate or perhaps unfortunate enough to do school laboratory work in chemistry--things such as distillation, precipitation, electrolysis, centrifugation, and so forth. Generally speaking, we start with any kind of stuff, and we do various things to it, to see if we can induce a separation or differentiation of the original stuff into two or more new ones, each having clearly distinct characteristics. So in electrolysis, out of water, we produce hydrogen and oxygen, for example. And then we take those new substances which we produced by the separation of the first one, and try to do the same thing with each of those two. We keep doing that, trying to push the process to its most extreme differentiation of matter.

Through this kind of playful exploration, chemists in fact did arrive at a limit, as expected, in the form of what were sometimes called ``simple bodies'' or elements--substances which seemingly could no longer be caused to differentiate further. From ancient times a number of such elements had been identified: iron, copper, tin, lead, mercury, gold, silver, sulphur, and carbon. About five more elements were added in the period called the Middle Ages, and then, under the influence of Leibniz's work in launching the Industrial Revolution, there occurred during Leibniz's time, from about the 1740s, an explosive development of physical chemistry, so that, at the time Mendeleyev graduated from the Main Pedagogical Institute of St. Petersburg, about 64 chemical elements were known.

I should note, however, before going further, that there are different, opposing types of hypotheses associated with the term chemical element. British empiricism has insisted, for example, on the supposedly self-evident axiom or idea which is still repeated unfortunately in much of our elementary education, that the elements represent unbreakable, ultimate ``building blocks'' of matter, whose supposed quality of reality is borrowed from the baby's earliest years in the playpen. The great French chemist Lavoisier, on the contrary, adopted the more adult view that the chemical elements are singularities, are moments of change, in a search not for ultimate building blocks, but for what he called the ``principles'' of matter, the principle of generation of matter. Lavoisier emphasized that the separation methods of chemistry, and the result of so-called simple bodies, depends on technology. It's relative; something that may appear to us to be an element or an indivisible substance, later may become divisible through a revolution in technology, which actually occurred through, in large degree, the work of Mendeleyev.

I just want to note to you, in reference to what I said before, that this British idea of the building blocks, of the unbreakable hard balls, or however it's represented, has the form of an axiomatic assumption. You can't refute it by any experiment or any so-called experimental fact. Because if you succeed in separating what appeared to be an element, then they will simply say, ``Oh yeah, we just made a mistake in our facts, and this element is actually made up of smaller hard balls which are irreducible, and which are building blocks.'' By this process you get to quarks and other things, and you're led down the path toward insanity, which has actually occurred to the majority of physicists following this kind of idea, in the endless search for those blocks which they haven't had since they were babies.

But Lavoisier's conception raises itself a very fruitful paradox. And in the practice of science we should never try to run away from paradoxes, because where there's a paradox, there's a potential discovery. At the point where we try to define a set of distinct, individual principles apparently governing a domain, say the domain of chemistry, we can no longer account for the existence of these principles, for their multitude, and for the relationships between them by the principles themselves. So we can have the elements, but we can't account for why they exist, why they have the properties they have.

And exactly the success of the chemists in discovering more and more elements, ironically underlined that paradox. If we look at the development of chemistry up until 1860, we see an explosion of an accumulation of empirical material, which became what Cantor called a ``bad infinity.'' A group of chemists around the circles of the great German chemist Justus Liebig and Kekule organized in Karlsruhe in Germany in 1860, a conference to put an end to this bad infinity, and to introduce new hypotheses for chemistry. So conceptions that had been developed by Ampère and others, in particular a concept of species of singularities, were introduced into chemistry in a broad way, from 1860. Mendeleyev was at that conference.

Mendeleyev's Discovery

Mendeleyev's discovery of the Periodic System was provoked by his work as a teacher. In teaching, he was irritated and provoked by the state of chemistry and asked himself the question: Is what we're doing here really a science? Can I present this as a science? Mendeleyev wrote the following:

``The mere accumulation of facts, even an extremely extensive collection, ... does not constitute scientific method; it provides neither a direction for further discoveries nor does it even deserve the name of science in the higher sense of that word. The cathedral of science requires not only material, but a design, harmony ... a design ... for the harmonic composition of parts and to indicate the pathway, by which the most fruitful new material might be generated.''

Thus, from the very beginning, Mendeleyev is not looking for some mere classification or systematization of data, as some have often tended to presented this, but for a principle and method of discovery, for a method of organizing the progress of science and technology, and looking for it in the direction of what we call a hereditary principle.

What was ironically distinct about the way Mendeleyev approached this problem, was his insistence on the individuality of each element. And I should just add, for those who might want to consider this point, that there is a crucial difference underlined by Mendeleyev between the notion of discreteness, which is really a mathematical notion, and the notion of individuality, which is associated with the Leibniz monad. In any case, Mendeleyev emphasized that there is no simple continuity of the sort we associate with continuous motion in visual space; that chemistry, as an experimental domain, reflects the action of something which modifies the ordinary properties of space and imposes a characteristic of what appears to be discontinuous ``jumps'' in the manifest properties as we go from one element to the next.

That means that we cannot use an ordinary smooth mathematical function or any of the usual type of mathematical functions for this, but we have to use what Leibniz called the method of analysis situs. It's exactly the knowledge of the individuality of the chemical elements, that is, the discontinuity between them, which permits the discovery of the Periodic Law.

Very briefly, how did this happen? Before Mendeleyev, chemists had concentrated on similarities or analogies between the elements [Figure 1].

Figure 1: Groups of Elements

HalogensAlkali Metals

I'll give you an example. There were discovered groups of elements which have similar or analogous properties, for example the group of the chemical elements which we call halogens, which are called fluorine, chlorine, bromine, and iodine. They all have similar chemical properties. We have another group called the alkali metals: sodium, potassium, rubidium, which are also very similar. But these two groups--the group of halogens and the group of alkali metals--are completely dissimilar, have completely different properties. You have to be plunged into the process of developing chemistry, for the notion of the individuality of these elements to mean anything to you.

Now, what did Mendeleyev do? Well, he had already begun in his earlier work, looking at the notion of the natural groups of elements from a geometrical standpoint. He studied what is called isomorphism of crystals, the fact that one can replace in a crystal elements of a similar group, maintaining the form of the crystal. Then one can consider the jumps or changes of crystal structure, as you go from one group of elements to another.

So what Mendeleyev did, which had not really been done before that, is not to look at the similar things alone, but to juxtapose the dissimilar in the manner of Leibniz's analysis situs. He compared that with the relative ranking or ordering of elements by means of what is called the atomic weight, which gives a very ironic and paradoxical ordering of the elements according to increasing atomic weight.

When you do that, you don't get a clean, algebraic mathematical relationship. But Mendeleyev found what he was looking for. What occurred, is that he made a shift in his thinking to say it's not the chemical elements themselves, but it's the system, the totality, which is elementary. It's the ordering of the system as a whole, which is the actual element or which we should replace as a notion of elementarity. This is the crucial shift in thinking of the notion of elementarity. And after that shift, which is his insight, comes the Periodic System.

It's a shift toward what we would call today in modern language, a negentropic quantum field.

Mendeleyev at Work

We have the testimony of a friend who witnessed Mendeleyev in the middle of the struggle to work up the vast material of chemistry into an explicit law. One day the friend stops by to visit Mendeleyev in his office. He sees immediately that Mendeleyev (who had very long hair, he was sort of a Beethovian-type figure), is in a state of agony and exhaustion. ``What are you working on?'' he asks Mendeleyev. Mendeleyev explains that he had discovered the existence of a periodic system of elements, but had not yet been able to formulate the law and table. He exclaimed, ``Everything is coming together in my head, but I can't express it.''

Soon afterwards, following three days and nights of continuous, unbroken concentration, Mendeleyev finally produced his periodic law and the famous table of elements which bears his name. He wrote later about the whole process:

``The thought was born involuntarily, that there must be a connection between mass and the chemical elements; and since the mass of material bodies, although it is not an absolute magnitude, but only a relative one, which expresses itself ultimately in the form of atoms--for these reasons it was necessary to search for a functional relationship between the individual characteristics of the individual elements, and their atomic weights. When you are searching for something--whether you are looking for mushrooms or for some kind of law--there is no other way, than to look and keep trying again. So I wrote down on a collection of cards, the names of the elements with their atomic weights and crucial properties, and started to group them according to similar elements and neighboring atomic weights. As soon as I did that, I came to the conclusion, that the properties of the elements must be a periodic function of the atomic weight; although I had doubts about many unclear details, I did not doubt for a minute that the general conclusion was correct.''

This last comment of Mendeleyev is crucial. What Mendeleyev now did was to take these groups where you have jumps from one group to the other and order them, showing the periodic relationship.

So what Mendeleyev now did, was to use his discovery as a yardstick for completely reorganizing and correcting the data of chemistry. In other words, it's the act of discovery, not its literal form, which constitutes the elementary, superior fact or axiom for reorganizing all of knowledge.

So Mendeleyev accordingly insisted that this new elementarity of the system as a whole, must be universal. All of chemistry must obey it, with respect to all existing and all future chemical elements. He tolerated no exceptions.

I mentioned that Mendeleyev did not find a clean mathematical fit for his law. On the contrary, a great part of the best experimental data of his time, completely contradicted his periodic law. In about two dozen cases, the atomic weights given for the elements indicated that the elements were in the wrong place in the table, that they contradicted the system.

So what did Mendeleyev do? He could say, oh, my law does not obey the data. No. He said, I have made a discovery. This data is wrong. So he took these two dozen elements, with the best measurements of the best chemists of his time, and he simply changed their atomic weights, and put them where they should be, according to the law. This created an uproar in the chemist community. But Mendeleyev was right in every single case. Furthermore, if you look at Mendeleyev's original layout of the Periodic Table [Figure 2], you will see two question marks there, just to the right of aluminium and silicon.

Figure 2: Mendeleyev's Organization of the Periodic Table by Atomic Weight

H = 1
Be = 9
B = 11
C = 12
N = 14
O = 16
F = 19
Li = 7
Mg = 24
Al = 27
Si = 28
P = 31
S = 32
Cl = 35
K = 39
Zn = 65
? = 68
? = 70
As = 75
Sc = 79
Br = 80
Rb = 85
Cd = 112
Ur = 116
Sn = 118
Sb = 122
Te = 128
I = 127
Cs = 133

There was a third one, near boron. These were just holes--anomalies--in the table. So Mendeleyev predicted that there must be, given the universality of the law, elements which will be discovered with the characteristics indicated by their place in the ordering expressed by the table. And Mendeleyev used the Sanskrit word eka, which means ``the next one,'' and gave names to the undiscovered elements, in the first case eka aluminium and in the second case, eka silizium, or silicon. And less than ten years after Mendeleyev published detailed prognoses of the properties of these three elements, they were found. In 1875, eka aluminium was found by a Frenchman, so he called it Gallium; in 1879 eka bor was found by a Swede so he called it Scandium; and then finally, in 1886, a German found Germanium.

But there's more. As we follow this process of unfolding the implications of Mendeleyev's discovery, we begin to develop the astrophysical implications, which are already implicit in the universality of the law which he claimed. That is, what we're looking at implicitly, is a process of generation of the elements. Not a British evolutionary scheme, a Darwinian evolution, but we can say in retrospect a Vernadskyian evolution.

For example, if we look at the modern form of the Periodic System, you will see that I've circled a number of squares there [Figure 3].

Figure 3: Periodic Table of the Elements

One Version Second Version Third Version List of Science Tables

Those are elements which were not known at the time of Mendeleyev, including the whole right-hand column of the so-called Noble Gasses. And also, I've indicated radioactive elements. In fact, the discovery of radioactivity was an immediate consequence of Mendeleyev's work, and in particular the work done by Pierre and Marie Curie....

Now we start to generate more and more anomalies, and a whole new world opens up. The dimension of the isotopes, where the Periodic System is expanded but in a coherent way. This also led to the discovery of nuclear fission, in a very lawful way. For example, the question why the Periodic System seems to end at uranium, which was the heaviest element known up until the 1930s. That's an anomaly of the system. Efforts were made to generate elements heavier than uranium. What happened? Well, the Periodic System responded with fission. It reacted to that attempt with fission. So we got nuclear fission.

However, we can generate heavier elements. We can expand the system in different ways. However, when we do that, we get into new modes. We can't expand it in one mode, but we must go to a new mode of expansion, a new mode of technology. So the Periodic System, in Mendeleyev's intention, becomes not a scheme of classification of elements, but a method of discovery and continuous expansion.

So now let me look back from what I've said, at the axiomatics of what Mendeleyev did, and emphasize a few very crucial points.

The Method

First, Mendeleyev did not arrive at his hypothesis through some kind of inductive reasoning from empirical data. He didn't start by noticing a ``pattern,'' as the typical fraudulent British empiricist account of scientific discovery would have it. Quite the contrary, the discovery originated with a deliberate, willful act of negating the central axiomatic assumption which had prevailed in the teaching and practice of chemistry at his time: the assumed elementarity of the elements. Instead, he located elementarity in something higher, which was later explicitly embodied in his periodic law, but implicitly involves a notion of a principle of generation of all the elements, including undiscovered ones.

Second observation: It was only after the original act of insight, that Mendeleyev threw himself into the chaos of incomplete and contradictory data and, through a Promethean effort, forced into the light of day the principle he knew must be there.

Third point: The result of his discovery was, in effect, a new system of scientific knowledge regarding physical chemistry and, implicitly, everything else. If we compare the new, Mendeleyev system of knowledge, with the one which existed at his time, before his discovery, we find a relationship which is characteristic of fundamental scientific discovery in general.

Firstly, Mendeleyev's new system contains everything which was useful in the then-existing chemical knowledge, but from a vastly more powerful point of view. We don't throw away anything, really, of substance, except our own clinging to a false assumption. We redefine what we thought we knew, from a higher standpoint; and we correct it from that higher standpoint. Then we can look back at the old system and understand many anomalies in that system, from the higher standpoint.

At the same time, there is no way to go from the earlier, inferior system to the superior system by some mere deductive or inductive procedure, such as merely filling out the gaps or adding data successively to the older system. The change from the lower to the higher, involves throwing out the central axiom and replacing it with a new one, which means an absolute break or discontinuity with the old system of knowledge. The authority of the old system is broken, as Mendeleyev clearly acts upon that, and a new authority is created. Thus, so to speak, in this business, you can't be half-pregnant. You either make the jump or you don't. This point is demonstrated in a very instructive way by the case of Lothar Meyer, a German chemist, who is often regarded as having independently discovered the periodic system but who actually missed, as far as I can tell, the revolutionary kernel of Mendeleyev's discovery.

Meyer at about the same time had arrived at a superficially similar periodic table by essentially inductive reasoning, without challenging the axiomatic assumptions of the old system. Consequently, he neither corrected the wrong values of the atomic weights, nor predicted the existence of new elements. In fact, Meyer publicly criticized Mendeleyev for what appeared to him to be--but was not--unwarranted speculation. Meyer could not understand what was the source of Mendeleyev's internal authority, in going beyond what was provable in Meyer's deductive/inductive terms of reference. He did not understand the reason why Mendeleyev insisted that there could not be any exceptions to the natural system.

So although Meyer's and Mendeleyev's periodic tables are formally similar, the explosion of new scientific discoveries which ensued in the subsequent period, flows unambiguously from Mendeleyev, and not from Lothar Meyer's more timid, half-pregnant approach.

This poses the question: How did Mendeleyev know that he was right before he proved it from the data? What was his internal authority? That defines the next paradox which I want to address.

It's a paradox also in the sense that we can't solve it by reference only to the immediate circumstances of Mendeleyev's discovery. We have to turn our attention to the long waves in the history of science, and juxtapose what Mendeleyev did, to other fundamental discoveries which display the kind of common, underlying principle or equivalence.

In other words, we shift from looking at the individual fundamental discovery as elementary, to a different notion, a notion of higher hypothesis, as relatively the more elementary reality of human thought, an evolutionary unity of acts of fundamental discovery.

Fundamental Discoveries

For this purpose, I propose to just briefly turn our attention to the following series of fundamental discoveries. I don't have time to elaborate them, but most of them have been dealt with, at least to a certain extent, in published materials of the Schiller Institute.

First in this historical series, is Nicolaus of Cusa's insight into the character and implications of the singularity separating the circle, and the higher world of circular action, from the inferior, linear world of its inscribed polygons [Figure 4].

Figure 4: The Separation of the Circle (Circular Action) from Its Inscribed Polygons (Linear Action).

Cusa's discovery was crucial to launching the Renaissance. There we see an attempt to arrive at a circle by a process of building polygons with more and more sides (this is familiar to most of you). You build a polygon with more and more sides and try to fill out, so to speak, the circle. But it doesn't work.

The second discovery, the discovery underlying the work of Leonardo da Vinci and Pacioli, is that of conceptualizing the geometrical ordering of living processes and defining the irreducible distinction between living and non-living processes.

Third, Johannes Kepler's founding of a comprehensive physics and astrophysics based on the same notion of what we call today a quantum field, and exemplified by his discovery of a universal ordering principle of the planetary orbits--and, most notable, Kepler's prediction of a missing planet in a gap, in a lawfully determined order in his system, which is entirely similar to what Mendeleyev did himself.

Fourth, Christiaan Huygens' insight into the implications of a relatively constant speed of light, and the closely related development of the geometrical domain of nonalgebraic functions by Huygens, Leibniz, Bernoulli, and others.

Fifth, the work of Ampère in developing insight into what are called force-free geometries, launching modern electrodynamics and a technological revolution which Gauss and Weber followed through, something which fed directly into, as I mentioned, the 1860 conference at Karlsruhe and the work of Mendeleyev.

Mendeleyev's discovery itself in this series; and I might mention, as a last example, the discovery by Max Planck, a daring and revolutionary hypothesis at that time, of the quantum of action.

I would like to assert, that if we look into each case in the way I indicated in the case of Mendeleyev, we shall find, that there is a kind of congruence of each and every one in this series of discoveries, even though each one is a highly individual, unrepeatable event. Furthermore, there is an ordering between these events.

We can come to that very readily through Cusa's discovery, which I'll just reference in following what I said before. The world of the polygons inscribed in the circle is externally bounded by something--the circle--which can't be reached from the lower world, even in the hypothetical bad infinity elaboration of that lower world. Instead, we have to challenge the axioms of the world of polygons, rework them from the standpoint of circular action as the elementarity.

So what is then primary, is what is, so to speak, located in this region between the polygons and the circle. It's very lawful that each of these discoveries involves an irony which is reflected in each case by geometries consistent with circular action and the great circle divisions of the sphere, so-called Golden Mean harmonics. You have a recurring theme of the expression of this irony in a similar way, reflecting what you might call the natural language of God's own universe.

I might mention that my esteemed colleague Lawrence Hecht began to rework, together with the late Dr. Robert Moon, some years ago, Mendeleyev's discovery, and its further implications from the standpoint of this geometrical expression, of the underlying irony, the underlying cause of these discoveries, and made a preliminary but very important discovery. Unfortunately, Larry is presently hindered from continuing his work in the way he would have liked to, because he has been thrown into jail for 39 years for supporting the presidential campaigns of Lyndon LaRouche. I would just point out that Mendeleyev, at the time he made his discovery, became a national hero in Russia. At the moment, it seems that here in the United States, if someone discovers something, they throw him in jail! We have to change that.

However, it is not enough to simply describe, let us say, or point to this congruence between scientific discoveries from the outside, so to speak. That only identifies an ironically placed location within which the actual substance of the process is located. To get at what the substance of the discovery is, we have to relive the ``flash of insight'' of the discovery which inhabits, so to speak, the space between Cusa's circle and the inferior world of the polygons.

If we look at the great discoverers of the past, we find in fact, among them, invariably, a special type of what one might call apprenticeship. I don't mean necessarily apprenticeship to a living person, but a relationship of reliving, through a kind of internalization, the activity of fundamental discovery of more than one great scientist or thinker of the past. It is in reliving this process that something is caused to be evoked, to be synthesized in our own minds, which is, from generation to generation, the immediate cause of fundamental scientific discovery, something we call higher hypothesis.

In the case of Mendeleyev, I don't know exactly how this apprenticeship came about. Certainly an important role was played by his studies at the Main Pedagogical Institute in Saint Petersburg, which was founded in 1804, and which we have reason to believe was strongly influenced by the ideas of Leibniz, the Ecole Polytechnique, and the Humboldts. This Main Pedagogical Institute, which trained teachers for the Gymnasia in Russia, grouped together some of the most extraordinary scientific thinkers in Russia at that time, particularly Mendeleyev's teacher, the chemist A.A. Voskresensky. Voskresensky focused his pedagogy on what he called the battle of ideas in science.

There is, however, another crucial piece of evidence demonstrating the higher hypothesis underlying Mendeleyev's work, which is the way he reacted to a typical British operation against continental science. This is the case of the well-known British physicist Crookes, who in 1886 gave speeches and circulated writings about his supposed hypothesis on the existence of a primordial form of matter, which he called protila, out of which all elements are supposedly formed. This was nothing more than a warmed-over version of Aristotle's old ``first matter,'' a shapeless, featureless goo which generates a kind of foam out of which everything is supposed to come. Crookes made two arguments which, unfortunately, were plausible to some people at that time. He argued that the periodic law of Mendeleyev pointed to the unity of all forms of matter, and also to a process of evolution of matter paralleling the evolution of animal species. Since--watch out--evolution proceeds from the simpler to the complex, everything must originate from a single form of the simplest matter, something that has no features whatsoever.

Many in Russian scientific circles were attracted by this idea. Mendeleyev hit the ceiling. He was furious, and he attacked Crookes violently for reasons which many of colleagues, unfortunately, did not comprehend. Here is a quote from a colleague of Mendeleyev: ``It is strange, that Dmitri Mendeleyev protested against this approach of Crookes, which was based on Mendeleyev's own periodic law. I remember vividly how, after a very lively meeting of the Physical Society, we three--Dmitri Ivanovich, Stoletov and I--argued into late at night over this question, which at that time everyone was thinking about, thanks to brochures by Crookes. Throwing forward all his objections, Dmitri Ivanovich, whose familiar wide modulations of voice from the lowest bass to almost unsingable high notes, signaled to those who knew him that he was becoming angry, began to turn his arguments literally ad hominem: `Alexander Grigorevich! Klementi Arkadyevich! I beg your pardon! Surely you are able to recognize your own individual identity. Please permit also the elements cobalt and nickel to have their own personalities!' We looked at each other and changed the subject.''

What is the point here? It is the Parmenides Paradox. You cannot solve the problem of reconciling the One and the Many, you can't explain the existence of individuality, except from the standpoint of higher hypothesis, that is, from the standpoint of that action which carries us through a series of fundamental scientific revolutions, each of which involves an axiomatic discontinuity, a ``jump'' of the sort we have indicated. Nothing less than this type of action can qualify to be considered as a candid ate for primordial substance or for substance at all.

If you introduce into science, a species of fundamental substance which is representable as an object of sense imagination--as tiny hard balls, building blocks, or the primordial goo of Crookes, or any other notion which is compatible with a fixed formal axiomatic system--if you do that, then you automatically collapse the process of scientific discovery. Because the mind of the scientist becomes stuck in the axiomatic system of that quality, and he's lost his grip on the higher hypothesis....

The Question of Proof

How did Mendeleyev know that his hypothesis was a truthful one in advance, before it was elaborated? The answer in essence is simple, that the truthfulness of an individual discovery resides essentially in the higher hypothesis which generated it, which is actualized in this flash of insight that we described. A true or relatively true higher hypothesis, is proved not by any individual laboratory experiment, or an individual discovery, but by physical economy, by its effect in providing the basis for a physically negentropic development of human society into the potentially indefinite future.

So the history of the last 550 years since Cusa, has demonstrated, in the great burst of human productivity and creativity, relative to any other period, the superiority or relative truth of the higher hypothesis from which Mendeleyev and others derived their discoveries.

Mendeleyev's life work is completely coherent with this relationship to physical economy. His life spans the period between the Russian-American alliance of the 1860s to the period of Sergei Witte, the period of the relatively successful initial industrialization of Russia. And Mendeleyev was really the dynamo of the industrial development of Russia in collaboration with Europe. His early work was in agricultural chemistry, continuing the work of Liebig. He ran experimental farms and other activities. He played a crucial role in developing the petrochemical industry in Baku. He made an official visit to the United States in 1876, to the Philadelphia Centenary celebration. He had a close relationship to the American chemical school leading to Harkins. He developed the industrial region of the Urals. He collaborated with Witte. He wrote on economics, particularly a 700-page treatise on the tariff, showing his studies of List and so forth....

So Mendeleyev represents a kind of Promethean scientist, a nation-builder, of a similar sort perhaps, as Benjamin Franklin. It would be important to investigate carefully what happened to the scientific tradition exemplified by Mendeleyev in Russia and Ukraine and so forth, over the last 100 years. Scientific institutions of Russia and Ukraine continue to produce a great number of brilliant and excellent scientists and engineers rivalling certainly anything abroad in that period. Particularly I would mention Vernadsky, another universal scientific mind, and figures such as Alexander Gurwich and so forth.

But at the same time, we see, especially in the last 25 years, a clear decline. We see a corrupting influence of an overemphasis on mathematical formalism and sterile classroom and textbook forms of education, and a competitive examination system, as opposed to the kind of apprenticeship education which apparently Mendeleyev had. There's also the influence of systems analysis as a formal doctrine of the kind of economic theory of Von Neumann. And on the other side, particularly into the 1950s, the injection of Hegelian ideas exemplified by the promotion of the so-called law of transformation of quantity into quality, which is a complete mystification of Mendeleyev's method.

So we see that the scientific and intellectual leadership has been crippled in the East, by mainly British influence parallel to what happened in the West.

So what we most urgently need, I think, is the emergence of a new leadership in Russia and in other nations, which understands the kinds of things we've been discussing. Might we not imagine, in the not-too-distant future, a revival of the alliance between Russia, America, and continental Europe, against the evil represented by the British empire of the mind, a revival of the Russian-American alliance of the 1860s against Britain, which was essential to the environment in which Mendeleyev worked, of which he was a part?

... By counterposing the notion of Platonic higher hypothesis to the different varieties of British empiricism now destroying the world, we realize that there's a higher level of mental activity which generates the change, the improvement of the method by which we exist, a movement toward a more perfect higher hypothesis, in a sense toward an intellectually and morally more perfect human race in practice. That is hypothesizing the higher hypothesis, the kind of activity which Lyndon LaRouche exemplifies.

The possibility of defeating the empire of the mind and of saving the human race, rests on that kind of Socratic knowledge, the kind of knowledge which Lyn has given us. So, as thankful apprentices, we want to end by wishing Lyn many more years of fruitful and productive life.


``Mendeleyev was looking for a principle and method of discovery, for a method of organizing the progress of science and technology, and looking for it in the direction of what we call a hereditary principle.''

Nauka Publishers, Leningrad
Dmitri Mendeleyev in the 1890s.

``The second conception of truth--the true one, I should argue--is truth as measured against man's continuing existence on this planet, truth measured in the great laboratory of human history, past, present, and future.''

``It is historically demonstrated, that in order for man to have existed up to this point, he had to constantly revise, often in a revolutionary way, his knowledge. So, what was at one time defined as true or as the right answer, becomes later the wrong answer.''

Creative thinkers behind fundamental scientific discoveries: Clockwise from top left: Nicolaus of Cusa, Johannes Kepler, Gottfried Leibniz, and André Ampère.

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The preceding article is a rough version of the article that appeared in The American Almanac. It is made available here with the permission of The New Federalist Newspaper. Any use of, or quotations from, this article must attribute them to The New Federalist, and The American Almanac

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