To make it easier to explain, I will illustrate the suggestions by an example. Let us suppose that the human time-binding capacities or energies in the organic chemistry correspond to radium in the inorganic chemistry; being of course of different dimensions and of absolutely different character. It may happen, for it probably is so, that the complex time-binding energy has many different stages of development and different kinds of “rays” A, B, C, ... M....
Let us suppose that the so-called mental capacities are the M rays of the time-binding energy; the “spiritual” capacities, the A rays; the “will” powers, the B rays; and so on. Psychological truths will then be a function of all rays together, namely A B C ... M ... or f (A B C ... M ...), the character of any “truth” in question will largely depend upon which of these elements prevail.
If it were possible to isolate completely from the other rays the “mental” process—the “logos”—the M rays—and have a complete abstraction (which in the present could only be in mathematics), then the work of M could be compared to the work of an impersonal machine which always gives the same correctly shaped product no matter what is the material put into it.
It is a fact that mathematics is correct—impersonal—passionless. Again, as a matter of fact, all the basic axioms which underlie mathematics are "psychological axioms"; therefore it may happen that these "axioms" are not of the αinfinity type but are of the f (A B C ...) personal type and [pg 215] this may be why mathematics cannot account for psychological facts. If psychology is to be an exact science it must be mathematical in principle. And, therefore, mathematics must find a way to embrace psychology. Here I will endeavor to outline a way in which this can be done. To express it correctly is more than difficult: I beg the mathematical reader to tolerate the form and look for the sense or even the feelings in what I attempt to express. To make it less shocking to the ear of the pure mathematician, I will use for the “infinitesimals” the words “very small numbers,” for the “finite” the words “normal numbers” and for the “transfinite” the words “very great numbers.” Instead of using the word “number” I will sometimes use the word “magnitude” and under the word “infinity” I will understand the meaning as “limitless.” The base of the whole of mathematics or rather the starting point of mathematics was “psychological truths,” axioms concerning normal numbers, and magnitudes that were tangible for the senses. Here to my mind is to be found the kernel of the whole trouble. The base of mathematics was f (A B C ... M ...); the work, or the development, of mathematics is f (M); this is the reason for the “ghosts” in the background of mathematics. The f (M) evolved from this f (A B C ... M ...) base a wonderful abstract theory absolutely correct for the normal, the very small, and for the very great numbers. But the rules which govern the small numbers, the normal, or psychological numbers, and the great numbers, are not the same. As a matter of fact, in the meantime, the physical world, the psychological world, is composed exclusively of very great numbers and of very small magnitudes (atoms, electrons, etc.). It seems to me that, if we want really to understand the world and man, we shall have to start from the beginning, from 0, then take the next very small number as the first finite or “normal number”; then the old finites or the normal numbers would become very great numbers and the old very-great [pg 216] numbers would become the very great of the second order and so on. Such transposed mathematics would become psychological and philosophic mathematics and mathematical philosophy would become philosophic mathematics. The immediate and most vital effect would be, that the start would be made not somewhere in the middle of the magnitudes but from the beginning, or from the limit “zero,” from the “0”—from the intrinsic “to be or not to be”—and the next to it would be the very first small magnitude, the physical and therefore psychological continuum (I use the words physical continuum in the way Poincaré used them) would become a mathematical continuum in this new philosophic mathematics. This new branch of philosophic, psychological mathematics would be absolutely rigorous, correct and true in addition to which, maybe, it would change or enlarge and make humanly tangible for the layman, the concept of numbers, continuum, infinity, space, time and so on. Such a mathematics would be the mathematics for the time-binding psychology. Mathematical philosophy is the highest philosophy in existence; nevertheless, it could be changed to a still higher order in the way indicated here and become philosophic or psychological mathematics. This new science, of course, would not change the ordinary mathematics for ordinary purposes. It would be a special mathematics for the study of Man dealing only with the “natural finites” (the old infinitesimals) and great numbers of different orders (including the normal numbers), but starting from a real, common base—from 0, and next to it very small number, which is a common tangible base for psychological as well as analytical truths.
This new philosophic mathematics would eliminate the concept of “infinitesimals” as such, which is an artificial concept and is not as a concept an element of Nature. The so-called infinitesimals are Nature's real, natural finites. In mathematics the infinitesimals were an analytical—an “M”—time-binding—necessity, [pg 217] because of our starting point. I repeat once again that this transposition of our starting point would not affect the normal mathematics for normal purposes; it would build rather a new philosophic mathematics rigorously correct where analytical facts would be also psychological facts. This new mathematics would not only give correct results but also true results. Keeping in mind both conceptions of time, the scientific time and the psychological time, we may see that the human capacity of “Time-binding” is a very practical one and that this time-binding faculty is a functional name and definition for what we broadly mean by human “intelligence”; which makes it obvious that time (in any understanding of the term) is somehow very closely related to intelligence—the mental and spiritual activities of man. All we know about “time” will explain to us a great deal about Man, and all we know about Man will explain to us a great deal about time, if we consider facts alone. The “ghosts” in the background will rapidly vanish and become intelligible facts for philosophic mathematics. The most vital importance, nevertheless, is that taking zero as the limit and the next to it very small magnitude for the real starting point, it will give us a mathematical science from a natural base where correct formulas will be also true formulas and will correspond to psychological truths.
We have found that man is an exponential function where time enters as an exponent. If we compare the formula for organic growth y==ekt, with the formula “P RT,” we see that they are of the same type and the law of organic growth applies to the human time-binding energy. We see, too, that the time-binding energy is also “alive” and multiplying in larger and larger families. The formula for the decomposing of radium is the same—only the exponent is negative instead of positive. This fact is indeed very curious and suggestive. Procreation, the organic growth, is also some function of time. I call “time-linking” for the sake of difference. [pg 218] Whether the energy of procreation or that of “time-linking” can be accounted for in units of chemical energy taken up in food, I do not know. Not so with the mind—this “time-binding,” higher exponential energy, “able to direct basic powers.” If we analyse this energy, free from any speculation, we will find that this higher energy which is somehow directly connected with “time”—no matter what time is—is able to produce, by transformation or by drawing on other sources of energy, new energies unknown to nature. Thus the solar energy transformed into coal is, for instance, transformed into the energy of the drive of a piston, or the rotary energy in a steam engine, and so on. It is obvious that no amount of chemical energy in food can account for such an energy as the time-binding energy. There is only one supposition left, namely, that the time-binding apparatus has a source for its tremendous energy in the transformation of organic atoms, and—what is very characteristic—the results are time-binding energies.
This supposition is almost a certainty because it seems to be the only possible supposition to account for that energy. This supposition, which seems to be the only supposition, would bring us to face striking facts, namely, the transformation of organic atoms, which means a direct drawing upon the cosmic energy; and this cosmic energy—time—and intelligence are somehow connected—if not indeed equivalent. Happily these things can be verified in scientific laboratories. Radium was discovered only a few years ago and is still very scarce, but the results for science and life are already tremendous because scientific methods were applied in the understanding and use of it. We did not use any zoological or theological methods, but just direct, correct and scientific methods. There is no scarcity in “human radium,” but, to my knowledge, physicists have never attempted to study this energy from that point of view. I am confident that, if once they start, there will be results in which all the so-called [pg 219] “supernatural, spiritual, psychic” phenomena, such as are not fakes, will become scientifically understood and will be consciously utilized. Now they are mostly wasted or only played with. It may happen that the science of Man—as the science of time-binding—will disclose to us the inner and final secrets—the final truth—of nature, valid in infinity.
It is very difficult to give in such a book as this an adequate list of the literature which may help to orient the reader in a general way in the great advance science has made in the last few years. This book is a pioneer book in its own way, and so there are no books dealing directly with its subject. There are two branches of science and one art which are fundamental for the further development of the subject; these two sciences are (1) Mathematical philosophy and (2) Scientific biology, the art is the art of creative engineering.
In mathematical philosophy there are to my knowledge only four great mathematical writers who treat the subject as a distinct science. They are two English scientists, Bertrand Russell and A. N. Whitehead; one Frenchman, Henri Poincaré (deceased); and one American, Professor C. J. Keyser. Messrs. Russell and Whitehead approach the problems from a purely logical point of view and therein lies the peculiar value of their work. Henri Poincaré was a physicist (as well as a mathematician) and, therefore, approaches the problems somewhat from a physicist's point of view, a circumstance giving his philosophy its particular value. Professor Keyser approaches the problems from both the logical and the warmly human points of view; in this is the great human and practical value of his work.
These four scientists are unique in their respective elaborations and elucidations of mathematical philosophy. It is not for me to advise the reader what selections to make, for if a thorough knowledge of the subject is desired the reader should read all these books, but not all readers are willing [pg 220] to make that effort toward clear thinking (which in the meantime will remain of the highest importance in science). Some readers will wish to select for themselves and to facilitate their selection I will lay out a “Menu” of this intellectual feast by giving in some cases the chapter heads.