The modern physico-mathematical discoveries become very simple when explained on the Anthropometer. Einstein simply refused to copy Fido, and objectify higher abstractions such as "space" and "time" (Minkowski) and "matter" (Whitehead).
AS SHOWN before, the meaning of a label must be given by a definition. This fact gives us the means to investigate the structure of all human knowledge.
Whenever and wherever we start, we must start with a set of words which are undefined, because we have, by assumption, no more words to define them. This means that human knowledge, at every stage, presupposes knowledge of these few undefined words. This is called, in logical terms, the circularity of human knowledge.
We have never before faced this issue candidly, and it has ever been responsible, as it is today, for most of all intellectual gloom and skepticism. This inherent structure of human knowledge was called the "weak spot" of knowledge, which, of course, it is not.
It cannot be theoretically denied that human knowledge is a faculty such that the son can start where the father ended; therefore it always should start from the latter-end (1924) and not from the beginning. This fact, as yet entirely ignored theoretically, shows that the naturalistic philosophies should be reversed as to logic and order when they tackle the problem of man.
The gross empiricists, overwhelmed with horror against the old metaphysics, went to the other extreme, into a mythology equally false to facts.
When we inquire indefinitely, "What do you mean?" accidentally we spoil every nice "talky-talk"; but we also come to a set of undefined terms, which are postulates. All the rest of our vocabularies (not names for things) are theorems, logical necessities of the starting set of terms strictly interwoven with the metaphysics of the maker of the vocabulary. It may be mentioned that a babe, before he begins to understand anything and to revise his feelings about the world around himself, has already his metaphysics aggravated by the metaphysics of his parents, teachers, etc., away back to our savage ancestors. Of course, these metaphysics are false to facts, but just the same it is first as to order.
We see that all human knowledge is geometrical in structure (I might say mathematical, but for serious reasons, I prefer to say geometrical). Somewhere at the border line there is the metaphysics. The system is strictly interdependent and bound up by "Logical Destiny," to use this beautiful expression of Professor Keyser.
The expression "circularity of human knowledge," was used here in its logical sense, which is misleading if taken literally. We must start somewhere, somehow, anywhere, anyhow, with a set of undefined terms, then go ahead, come back, revise our base (a) for (b), go ahead again, revise our base (b) for (c), go ahead again, and so on endlessly. Human knowledge is inexhaustible. No set is undefined absolutely, but only relatively so.
In practice, things are much more complicated because we seldom, if ever, have one vocabulary. But we must untangle first the simplest theoretical issue. The vocabularies (silent postulates) imply the theorems, the theorems imply the postulates. He who accepts uncritically the vocabulary made by X, accepts unwillingly and unbeknowingly X's metaphysics. This fact is of very great importance. If we accept the vocabulary made by X and the metaphysics made by Y, we are lost in inconsistency, the world is an ugly mess, unknown and unknowable. This mess, which is nearly always followed up by rampant pessimism, is the necessary consequence of the misunderstanding of what is here explained. With understanding, our troubles vanish, the world remains unknown (because the Fidos have so long persecuted science) but it becomes knowable.
With all of this permanently in mind, it is easy to understand anybody else, just as a mathematician when he hears a theorem, he knows usually from which geometry it is taken.
If we do not understand the above, we are slaves; if we know it, we are free, because we can select our master (Keyser, Poincaré).
The geometrical structure of human knowledge shows that man is extremely logical, if we grant him his conscious and unconscious premises (language). Whoever has any doubts about all of the mentioned issues should visit an asylum, where he would see the working of this general theory in its nakedness. In daily life and in semi-insane cases the issues are veiled by customs, habits, overlapping vocabularies, and other doctrinal complications. It is known that "insane" people are extremely logical. In many instances "insanity" is cured by making the unconscious premises conscious. Psychiatry, as yet, has no preventive methods. The Anthropometer is such a preventive educational method against many cases of insanity and different unbalanced states, due to inherited or inhibited false doctrines. A man full of false doctrines cannot be a perfectly normal, healthy and useful man; neither can he copy Fido in his thinking processes without somehow registering it to the detriment of society and himself.
When someone claims to be a "Napoleon" we lock him up. How about the majority of us? Do we not fancy that we are what we are not? That is rather a serious question.
The psychiatrists have all the time to fight "absolutism" and "dogmatism," which in many instances are responsible for different forms of insanity. They do so without the full understanding of the mechanism of it.
The whole advancement of science and civilization shows that this theory is true, but as we did not know explicitly the structure of human knowledge, every revision from (a) to (b) and from (b) to (c) (see page 21) etc., was always painful and slow. We see that, as the structure of the atom is reflected in a grandiose manner in the structure of the universe, so is the structure of the knowledge of the individual man reflected in the collective knowledge of mankind called science, and vice versa.
IV. Consequences and Applications
AT THE present stage of our inquiry it is impossible to foresee all the consequences and applications of this general theory by means of the Anthropometer, but some of them are manifest from the beginning, and are manifold and weighty. I will summarize them, roughly only, as material for thought and further analysis.
It must be emphasized again that merely talking about the Anthropometer will not help much. This prototype of the event and the object and the label must be shown. The moment we point our finger at them and say "this," it cannot be covered by words, and it economizes thousands of words at once. Whoever disregards this positive condition and misses the benefit of it, should not blame the theory and the Anthropometer, but his disregard of a vital condition and issue. The old Fido-way is so deeply rooted in our theories, practice, habits, systems, etc., that although I have had it on my desk for more than a year, my own Fidoism shocks me far too often. In a century or so, of course, we shall not need it, but such is not the case at present.
Some of the consequences are educational and scientific, some are suggestions for activities. We will start with the educational and scientific ones.
The inherent circularity and geometrical structure of human knowledge proves the interconnection of our vocabularies with our metaphysics. We see, that if we want humans to be humans and think as humans, we must start our education from the latter-end (1924) by beginning with modern "metaphysics" of Planck, Einstein, Whitehead, Russell, Keyser, etc., made possible by the understanding of the Anthropometer and the structure of human knowledge.
We would then find, at once, the interest of the masses aroused, and thinking would start on an unprecedented scale, with all its beneficial results. The "scientific temper" would overrun mankind in a few years, facts and correct symbolism would count, and the exponential law PRt would begin to work properly.
Man is ultimately a doctrinal being. Even our language has its silent doctrines, and no activity of man is free from some doctrines, so that the kind of metaphysics a man has, is not of indifference to his world outlook and his behaviour.
We cannot expect when we force a dynamic being into the patterns of Fido static doctrines, that we will get anything else but an unbalanced being in an unbalanced civilization.
The Anthropometer should be introduced into elementary schools and we should start our education with it, everywhere. We must teach a small modern scientific vocabulary and train our children to think habitually in these new terms; which automatically carry with them a new non-absolutistic world conception. Such simple and mechanical means (they must be mechanical and simple if we hope to give them to the masses) would impart to all mankind, not the knowledge, but the cultural results of university training. Such methods, the complete reversal of the old, would stop Fido-ways in theory and practice.
The language of "concepts" is very difficult because that is an elementalistic, absolutistic term (as auxiliary it may be useful) and will not do as our fundamental term. This doctrine is very difficult to teach even to university students, to say nothing of the masses. The language of "abstractions of different orders" is not an elementalistic term; it is a "joint-phenomenon," "organism-as-a-whole" modern new term; it is natural to man, it can be shown to him, and is easily grasped by children and people of very low mentality when shown on the Anthropometer.
We see that modern philosophers have heavy duties and responsibilities toward mankind; heavier, perhaps, and more important than the duties and responsibilities of engineers and doctors. With the modern physico-mathematical discoveries and mathematical discoveries, as those of Whitehead, Russell, the "doctrinal function" of Keyser, etc., "philosophy" has ceased to be a divertisement of the few, it has become as vital an inherent factor in all human life, as air, water, and sunshine. There are communities who have very little to do with engineers or doctors, but no community in the world is free from some kind of "philosophy." Among savage tribes we see how doctrines have prevented entirely any progress at all. The more civilized races have advanced simply because they were more rebellious, and never could stick to an unrevised doctrine for too long.
This is why we have had this semblance of civilization at all! It is not enough to discard philosophy entirely, on the ground that most of it is foolish. Granted our old philosophies were foolish enough, whoever thinks he can discard them entirely without supplanting them by others, sometimes equally foolish, deludes himself. The problems at hand require philosophy, and ignorant vagaries will not do. It is about time that mankind should hold the philosophers responsible. Ignorance is not an excuse.
It may as well be admitted that our old educational methods would have to be reversed. Babies should start their education playing more with microscopes than toys. Before they learn to spell they should firmly feel, at least, the structure of "matter," the structure of human knowledge, and the mechanism of human symbolism. Then they would be equipped to be humans.
Science is not a luxury for the few, but as it leads to the consciousness that we abstract, science and scientific method is precisely that, which makes man think and behave as man.
Non-scientific, half-education (in the sense of 1924, which we could, maybe, consider "scientific education" in the sense of 300 B.C.) is not a boon to mankind in 1924, far from it. That is very natural in the meantime. The conditions, environment, social inheritance, racial experience, other complications, with all accompanying and novel nervous and mental pressure upon man in 1924, are entirely different from these in 300 B. C. Is his mental, nervous resistance and health properly taken care of? Are our educators and doctors themselves modern men? Sad to say the answer is NO. We still educate man, drug him with doctrines thousands of years old, doctrines which are inconsistent and false to facts. We still keep him in a savage-made universe. This deep discrepancy must unbalance him, and periodically unbalance his institutions. The sooner we understand this and modernize the antiquated branches of knowledge, the better for all of us. There is hope for us, if we stop folly. Our old doctrines do not work even with savage tribes, as practice shows. From the modern point of view the savage tribes do not gain anything by passing from one kind of savage-made doctrines to another set of savage-made doctrines. Experiments should be made, by taking some newly-born from different savage tribes, placing such children in highly cultured scientific families and give them full scientific education, and see what would happen. The new doctrines would work maybe, where the old failed.
The Anthropometer presents a synthesis of modern scientific strivings in a form ready for application.
In the old way we delude ourselves talking about the "education of the masses," and in the old way it is hopeless. What we need most at present and what could be accomplished very quickly is the re-education of the educated. A proper insistence by the scientists, and a few books for this purpose would perform the task. The understanding of the Anthropometer shifts the center of gravity from something which is impossible to something which is possible.
With a re-educated educated class the world would soon become a different place to live in.
The benefits of new terms are that occasionally they throw a new light on old problems, or quite often they help in settling, in a positive way, old controversies. When some controversial questions are settled the world accepts them quickly. What was roughly known but ignored, because veiled by the old language is brought by the new language to a sharp focus. After the results are obtained, they may be explained in any language, but the results, in most cases, could not be gotten in another way.
As a matter of fact, civilization has advanced in the shape of the diagram given on page 21, but as we did not know that this was the inherent structure of human knowledge, every revision of our assumptions was slow and accomplished with great suffering and bewilderment. The creative scientists and teachers were persecuted and
hampered, mankind has paid a hideous price. The new understanding will stop persecution and propaganda of any kind.
The popular introduction of the Anthropometer would also prevent the publication of nine-tenths of books and the delivery of the majority of speeches, inasmuch as most of them are based on Fido-ways. Such elimination would relieve us of a great amount of useless ballast.
We must repeat here that the theories of relativity have a still more general underlying theory, namely, the general theory of time-binding. As this theory is so general it is therefore easy to grasp and teach, even to children. It explains the refusal to accept high-order abstractions, such as "matter," "space," and "time," for first order abstractions, which they are not. This is the minimum of science (1924) with which each babe should start its education.
There are a few interesting points about "matter," "space" and "time." Taken separately they are abstractions of high order and not objects, or abstractions of first order. If we objectify the high abstraction, we get a fanciful universe, self-contradictory, a nature which is against human nature. Being logical, we invent something supernatural to account for a nature against human nature. If "time" is an object, if it has objective existence, then, obviously, it must have, as all objects have, a beginning and an end; then the universe was made, it must have a "beginning of the beginning" (old "essences"), etc., etc., and the whole old anthropomorphic mythology follows, by a purely logical process.
But if "time" is an abstraction of high order and not an object (first order abstraction), otherwise, if it does not exist as an object, then, obviously, something which does not exist cannot have a "beginning," or a "beginning of the beginning," the universe was not "made," etc. It just was, is, and will be. Obviously the "primal substance" may quite happily be a myth in such a universe of transformation; we cannot exhaust it in either direction.
Our universe is timeless. In another language, it is eternity in time, or, still in another language, infinity of times (this is a generalization of experimental time). When times are very rapid we nervously summarize times, and feel "time," a "duration." The "infinity of times" is nothing else, when translated in still another language, than the law of conservation of energy. Incidentally it proves the existence of actual infinity.
The above explanations were given because the old Fido-ways are omnipresent. In a way they permeate all mankind, and they must lead us to most acute mental disorders, reflected in behaviour. I do not know any other phase of science in the whole history of civilization which would have a more profound and beneficial influence upon the daily life of the man on the street, than the modern advancement of mathematical and physico-mathematical sciences, when given to the masses and applied in education.
This understanding clears up another old fallacy. We are accustomed to hear that the old mythologies are somehow "primary" with man. We see clearly that it is not true. Those mythologies are "secondary" with man. What was primary is the objectification of high abstractions, the Fido-ways in our thinking processes. Once this is eliminated by the Anthropometer, all the old vicious fictions automatically vanish.
If we confuse the orders of abstractions; if we fancy that the high abstractions are first-order abstractions, which they are not, then we get "absolute matter," "absolute space," and "absolute time." If the world is made up of "absolute matter," "absolute space," "absolute time" then of course such a structure cannot account for "mind" and what not. The number of possibilities in such a universe are too limited, etc., etc., and all the rest follows. But if the world is made up of "quanta," "fields," etc., then all we see, we feel, we know and can know are averages, summaries, abstractions of different orders, etc., etc. Only a language of processes, transformations, variables, functions, integration, abstractions of different orders, probabilities, etc., etc., can account for such a universe. Mathematics considered as an activity of the human organism, reflects in its structure and form the structure and form of the universe. Being a language, it is the universal tongue.
In such a universe all we deal with are combinations of high orders ("Matter" made up of molecules, molecules of atoms, atoms of electrons, and so on, probably).
How the combinations of high order grow, as to numbers of possibilities, an instance taken from the Principles of Science by Jevons will show. This simplest possible case which is far, far away from any "simplicity" in nature, will show.
"The successive orders of the powers of two have, then, the following values, so far as we can succeed in describing them:
First order ...................................................... 2
Second order ..................................................... 4
Third order ..................................................... 16
Fourth order ................................................ 65,536
Fifth order number expressed by 19,729 figures.
Sixth order number expressed by figures, to express the number of which figures would require about 19,729 figures."
By way of contrast Jevons gives us "that the almost inconceivably vast sphere of our stellar system if entirely filled with solid matter, would contain more than about 68•1090 atoms, that is to say, a number requiring for its expression 92 places of figures. Now, this number would be immensely less than the fifth order of the powers of two."
Due to the modern knowledge of the structure of the world we see that practically everything becomes possible, and may be understood, no matter when. The feeling of these issues, with the lack of understanding of the simple law of growth of the higher order combinations, gives, I think, the base for mystical feelings, which vanish as such, once these issues are understood. We can know, never mind when; all the rest is a matter of method and science. In this way the unknowable becomes knowable. Correct symbolism covers all these facts, also, and leads to the same conclusions.
The concept of order is fundamental, not only because it underlies all mathematics but, also, because it is easily and obviously translated in terms of senses. This gives a base for a scientific vocabulary.
The savage-made language of "cause" and "effect" has also order in it, only it is a very short series—it is a two-term relation. Yet, in the world around us, there is no such thing in existence as a two-term relation, and therefore when we use a two-term relation, cause-effect, these two terms are overloaded with non-crystallized "thought" (emotion), hence metaphysics of the wildest kind. Science expands the series into an indefinite number of members. Old ignorance and metaphysics go.
The expansion of this series is the coefficient of our knowledge.
The theory, as expounded in this paper, seems to suggest directions in which some activities could be started.
There seems to be no doubt that the recent physico-mathematical and logic-mathematical advancement of science is affecting all branches of human knowledge in many unexpected directions. It seems without question, that the scientists could not deal with these problems without the help of professional mathematicians. If the mathematicians refuse to cooperate with other branches of science, Human Engineering included, it will probably take one or more generations before the whole beneficial effect of modern discoveries would be felt in education and life.
The situation today is such that, in many serious instances, naturalists who know "facts" speak nonsense quite happily, about them. The mathematicians who alone speak sense, know very little or nothing about facts. The results are: slow advance, groping in the dark, thousands of false doctrines, and endless arguments in vacuo. Science is a joint phenomenon of logic and "facts"; as there are no "facts" free from some doctrine, therefore science should be carried on as a joint phenomenon. Experimentalists, for example, should have very able and creative mathematicians who would work at logic and language, and they should work together, jointly. Life is too short for one to be a specialist in several lines at once; science has outgrown the individualistic epoch, it must become a group activity.
All our doctrines should be revised and correct symbolism should be applied to facts. The old philosophy is dead in disgrace, the world is without co-ordinating guidance. To be fair to philosophers, no single person nowadays could perform this co-ordinating work alone. It again must become a group activity.
If we want to avoid complete mental anarchy, which must be followed up some day by grave disturbances in our behaviour, this problem of revision and co-ordination must be our urgent and immediate task. The people of the world have lost the old faiths in their theories, their leaders, and themselves; this state, again is another phase of other creeds as yet not crystallized. Only heroic measures can save us from still worse turmoils.
When, for instance, biologists make statements about mathematics, or mathematicians make statements about biology, such statements are always short somewhere on knowledge, they never are competent. Statements should be made by biologists on biology, but with the full understanding of other branches of knowledge; by mathematicians on mathematics, but also with full understanding of other achievements.
Such work could be done only and exclusively by a permanent body of the world's best scientists being relieved from all other duties who, after getting acquainted with each other's specialities, would work together on the revision of language and doctrines, and would prepare this co-ordination of knowledge. Such a permanent body could issue a yearly or quarterly journal which would give to mankind the revised and co-ordinated doctrines of each "present" day.
Such a method would allow mankind to start every generation where the last one left off, and the progress of civilization would follow the exponential law PRt. A copy of this general doctrinal summary should be placed in the hands of every teacher throughout the world, by legislation if need be. There is no doubt that if scientists themselves insist upon some such plan, mankind would accept it. After all, a united opinion of those who, in the major part, are the driving force of civilization, is irresistible. Scientists would start with such an institution a new period of human history which would be called the "scientific era." This body might be called the "Senate of Humanity" (this name was suggested to me by Professor A. Vasiliev, and I gratefully acknowledge it).
If the peoples of the world were told that the best scientists of the world are working on their problems they would settle down and wait, some hope would be restored, otherwise they will not wait. The publications of the "Senate of Humanity" would be stripped of technicalities so that the general public would understand them. They would save an enormous amount of work to scientists and laymen by giving short, yet reliable, informations in an already co-ordinated and revised form. With these budgets of knowledge, not of paradoxes, mankind would come gradually out of the Fido era, into the scientific era.
We need not delude ourselves. The most important hindrances, in the old ways, are found in language and the logics; these problems would remain the most important for a long time to come, and the mathematicians would have to play nolens volens, a most conspicuous rôle, a rôle worthy of their science.
It follows from the geometrical structure of human knowledge, that the solution of all human problems lies in frankly putting all branches of human endeavor upon a postulational base. Postulational treatment gives us unique benefits, among others, it facilitates inspection, gives clarified systems of doctrines, and unifies all other methods. Our debates would become limited to experimental testing of our sets of postulates.
It may be mentioned that such a library is being established in New York City under the name of "International Library of Human Engineering" (Principia Scientiæ Hominis), which will originate a deductive science of man, and deductive natural and other sciences.
This library will be at present under the editorship of one mathematician and one engineer, with an advisory board of scientists from all countries in all branches of science. For geographical and linguistic reasons, local national boards of co-editors will also be formed.
Until the Senate of Humanity is organized, this library with its international scientific boards, will be the research and organizing center for the future permanent international body of scientists. Its publications would be the handbooks for the future chairs of Human Engineering which sooner or later must be established in all important universities of the world. Human Engineering, as every other branch of engineering, would be based on mathematical methods.
Such is the outline of immediate constructive steps which could be taken. The problems at hand are manifold, weighty, and difficult, beyond the power of any single man to deal with. A great deal of responsible preparatory work must also be accomplished. Such work of course must be a group activity, and it is hoped that the international advisory boards of the library will be able to accomplish a good deal of this preparatory work.