Chapter X: Conclusion (1)

“In Europe we know that an age is dying. Here it would be easy to
miss the signs of coming changes, but I have little doubt that it
will come. A realization of the _aimlessness_ of life lived to
labor and to die, having achieved nothing but avoidance of
starvation, and the birth of children also doomed to the weary
treadmill, has seized the minds of millions.” _Sir Auckland
Geddes, British Ambassador to the U. S. 1920._

In conclusion let me say very briefly, as I said in the beginning, that this little book has aimed to be only a sketch. The Problem of Life is old. I have endeavored to approach it afresh, with a new method, in a new spirit, from a new point of view. The literature of the subject is vast. It displays great knowledge and skill. Much of it is fitted to inform and to inspire such as really read with a genuine desire to understand. Its weakness is due to the absence of a true conception of what human beings are. That is what I miss in it and it is that lack of fundamental and central thought that I have striven to supply. If I have succeeded in that, I have no fear—all else will follow quickly, inevitably, as a matter of course. For a fundamental conception, once it is formed and expressed, has a strange power—the power of enlisting the thought and cooperation of many minds. And no conception can have greater power in our human world than a _true_ conception of the nature of Man. For that most important of truths the times are ripe; the world is filled with the saddest of memories, with gloom, forebodings and fear. Without the truth in this matter, there can be no rational hope—history must go on in its dismal course; but _with_ the truth, there is not only hope but certitude that the old order has passed and that humanity’s manhood dates from the present day. That I have here presented the truth in this matter—the true conception of the human class of life—I have personally no doubt; and I have no doubt that that conception is to be the base, the guide, the source of light, of a new civilization. Whether I am mistaken or not, time will decide. I feel as Buckle felt in writing his _History of Civilization_:

“Whether or not I have effected anything of real value ... is a
question for competent judges to decide. Of this, at least, I feel
certain, that whatever imperfections may be observed, the fault
consists, not in the method proposed, but in the extreme
difficulty of any single man putting into full operation all the
parts of so vast a scheme. It is on this point, and on this alone,
that I feel the need of great indulgence. But, as to the plan
itself, I have no misgivings. Of defects in its execution I am not
unconscious. I can only plead the immensity of the subject, the
shortness of a single life and the imperfection of every single
enterprise. I, therefore, wish this work to be estimated, not
according to the finish of its separate parts, but according to
the way in which those parts have been fused into a complete and
symmetrical whole. This, in an undertaking of such novelty and
magnitude, I have a right to expect, and I would moreover, add,
that if the reader has met with opinions adverse to his own, he
should remember, that his views are, perhaps, the same as those
which I too once held, and which I have abandoned, because, after
a wider range of study, I found them unsupported by solid proof,
subversive of the interest of Man, and fatal to the progress of
his knowledge. To examine the notions in which we have been
educated, and to turn aside from those which will not bear the
test, is a task so painful, that they who shrink from the
sufferings should pause before they reproach those by whom the
suffering is undergone.... Conclusions arrived at in this way are
not to be overturned by stating that they endanger some other
conclusions; nor can they be even affected by allegation against
their supposed tendency. The principles which I advocate are based
upon distinct arguments supported by well ascertained facts. The
only points, therefore, to be ascertained, are, whether the
arguments are fair, and whether the facts are certain. If these
two conditions have been obeyed, the principles follow by an
inevitable inference.”

And why have I sought throughout to follow the spirit of mathematics? Because I have been dealing with ideas and have desired, above all things else, to be right and clear. Ideas have a character of their own—they are right or wrong independently of our hopes and passions and will. In the connection of ideas there is an unbreakable thread of destiny. That is why in his _Mathematical Philosophy_ Professor Keyser has truly said:

“Mathematics is the study of Fate—not fate in a physical sense,
but in the sense of the binding thread that connects thought with
thought and conclusions with their premises. Where, then, is our
freedom? What do you love? Painting? Poetry? Music? The muses are
_their_ fates. Whoso loves them is free. Logic is the muse of
Thought.”

No doubt mathematics is truly impersonal in method; too impersonal maybe to please the sentimentalists before they take the time to think; mathematical analysis of life phenomena elevates our point of view above passion, above selfishness in any form, and, therefore, it is the only method which can tell us genuine truths about ourselves. Spinosa even in the 17th Century had well realized this fact and although imperfect in many ways, his was an effort in the right direction and this quoted conclusion may well be a conclusion for ourselves in the 20th century:

“The truth might forever have remained hid from the human race, if
mathematics, which looks not to the final cause of figures, but to
their essential nature and the properties involved in it, had not
set another type of knowledge before them.... When I turned my
mind to this subject, I did not propose to myself any novel or
strange aim, but simply to demonstrate by certain and indubitable
reason, those things which agree best with practice. And in order
that I might enquire into the matters of the science with the same
freedom of mind with which we are wont to treat lines and surfaces
in mathematics; I determined not to laugh or to weep over the
actions of men, but simply to understand them; and to contemplate
their affections and passions, such as love, hate, anger, envy,
arrogance, pity and all other disturbances of soul not as vices of
human nature, but as properties pertaining to it in the same way
as heat, cold, storm, thunder pertain to the nature of the
atmosphere. For these, though troublesome, are yet necessary, and
have certain causes through which we may come to understand them,
and thus, by contemplating them in their truth, gain for our minds
much joy as by the knowledge of things that are pleasing to the
senses.”

If only this little book will _initiate_ the scientific study of Man, I shall be happy; for then we may confidently expect a science and art that will know how to direct the energies of man to the advancement of human weal.

What else? Many topics have not even been broached. Time-binding energy—what may it not achieve in course of the aeons to come? What light may it not yet throw upon such fundamental phenomena as _Space_, _Time_, _Infinity_, and so on? What, if any, are the limits of Time-binding? In it are somehow involved all the higher functions of mind. Is Time identical with Intelligence? Is either of them the other’s cause? Is Time _in_ the Cosmos or is the latter in the former? Is the Cosmos intelligent? Many no doubt and marvelous are the fields which the scientific study of man will open for research.

Appendix I. Mathematics And Time-Binding

The purpose of this appendix is to give an expression of some new ideas which evolve directly out of the fact that humans are time-binders and which may serve as suggestions for the foundation of _scientific psychology_. The problem is of exceeding difficulty to give expression to in any form and therefore much more difficult to express in any exact or correct form, and so I beg the reader’s patience in regard to the language because some of the ideas are in themselves correct and sometimes very suggestive in spite of the language used. I am particularly interested that mathematicians, physicists and metaphysicians should read it carefully, forgive me the form, and look into the suggestions, because scientific psychology if such a science is to exist, would by necessity have to be a branch of physics. I particularly beg the mathematicians and physicists not to discard this appendix with too hasty a judgment of “Oh! metaphysics,” and also the metaphysicians not to do the same with an equally hasty judgment “Oh! mathematics.” I hope that if this appendix is sympathetically understood, mathematicians and physicists will be moved to investigate the problem. If mathematicians and physicists would be more tolerant toward metaphysics and if metaphysicians would be moved to study mathematics, both would find tremendous fields to work in.

Some scientists are very pedantic and therefore intolerant in their pedantry and they may say “the fellow should learn first how to express himself and then ask our attention.” My answer is that the problems involved are too pressing, too vital, too fundamental for humankind, to permit me to delay for perhaps long years before I shall be able to present the subject in a correct and satisfactory form, and also that the problems involved cover too vast a field for a single man to work it conclusively. It seems best to give the new ideas to the public in a suggestive form so that many people may be led to work on them more fully.

The old word “metaphysics” is an illegitimate child of ignorance and an unnecessary word in the scientific study of nature. Every phenomenon of nature can be classed and studied in physics or chemistry or mathematics; the problem, therefore, is not in any way _super_natural or _super_physical, but belongs rather to an unknown or an undeveloped branch of physics. The problem, therefore, may be not that of some _new_ science, but rather that of a new branch of mathematics, or physics, or chemistry, etc., or all combined.

It is pathetic that only after many aeons of human existence the dimensionality of man has been discovered and his proper status in _nature_ has been given by the definition of “time-binder.” The old metaphysics, in spite of its being far from exact, accomplished a great deal. What prevented metaphysics from achieving more was its use of unmathematical method, or, to be more explicit, its failure to understand the importance of dimensions. Metaphysics used words and conceptions of multi-dimensional meanings which of necessity resulted in hopeless confusion, in “a talking” about words, in mere verbalism. An example will serve to make this clear. If we were to speak of a cow, a man, an automobile, and a locomotive as “pullers,” and if we were not to use any other names in connection with them, what would happen? If we characterized these things or beings, by one common characteristic, namely, “to pull,” havoc would be introduced into our conceptions and in practical life; we would try to milk an automobile or we would try to extract gasoline from a cow, or look for a screw in a man, or we would speculate about any or all of these things. Too obviously nonsensical—but exactly the same thing happens, in a much more subtle way, when we use such words as “life in a crystal” or “memory in animals”; we are thus mentally making a mistake no less nonsensical than the talk of “milking an automobile” would be. Laymen are baffled by the word dimension. They imagine that dimensions are applicable only to space, which is three dimensional, but they are mistaken; a moving object is four-dimensional—that is, it has three dimensions as any object at rest, but, when the object is moving, a fourth dimension is necessary to give its _position_ at any one instant. We see, therefore, that a moving body has four dimensions, and so on. As a matter of fact, scientific psychology will very much need mathematics, but a special _humanized_ mathematics. Can this be produced? It seems to me that it can.

It is a well known fact that experimental sciences bring us to face facts which require further theoretical elaboration; in this way experimental sciences are a permanent source of inspiration to mathematicians because new facts bring about the need of new methods of analysis.

In this book a new and experimental fact has been disclosed and analysed. It is the fact that humanity is a time-binding class of life where the time-binding capacity or the time-binding ENERGY is the highest function of humanity, including all the so-called mental, spiritual, will, etc., powers. In using the words mental, spiritual, and will powers, I deliberately accept and use them in the popular, ordinary sense without further analysing them.

Once the word and concept _Time_ enters, the ground for analysis and reasoning at once becomes very slippery. Mathematicians, physicists, etc., may feel that the expression is just a “well adapted one,” and they may not be very much inclined to look closer into it or attentively to analyse it. Theologians and metaphysicians probably will speculate a great deal about it vaguely, with undefined terms and incoherent ideas with incoherent results; which will not lead us toward a scientific or true solution, but will keep us away from the discovery of truth.

In the meantime two facts remain facts: namely, mathematicians and physicists have almost all agreed with Minkowski “that space by itself and time by itself, are mere shadows, and only a kind of blend of the two exists in its own right.” The other fact—psychological fact—is that _time_ exists psychologically by itself, undefined and not understood. One chief difficulty is always that humans have to sit in judgment upon their own case. The psychological time as such, is our own human time; scientific time as such, is also our own human time. Which one of them is the best concept—which one more nearly corresponds to the truth about “time”? What is time (if any) anyway? Until now we have gone from “Cosmos” to “Bios,” from “Bios” to “Logos,” now we are confronted with the fact that “Logos”—Intelligence—and Time-binding are dangerously near to akin to each other, or may be identical. Do we in this way approach or go back to “Cosmos”? Such are the crucial questions which arise out of this new concept of Man. One fact must be borne in mind, that “the principles of dynamics appeared first to us, as experimental truths; but we have been obliged to use them as definitions. It is by definition that force is equal to the product of mass by acceleration, or that action is equal to reaction.” (_The Foundation of Science_, by Henri Poincaré); and mathematics also has its whole foundation in a few axioms, “self evident,” but _psychological facts_. It must be noted that the time-binding energy—the higher or highest energies of man (one of its branches anyway, for sake of discrimination let us call it “_M_”) when it works properly, that is, mathematically, does _not_ work _psychologically_ but works ABSTRACTLY: the higher the abstraction the less there is of the psychological element and the more there is, so to say, of the pure, impersonal time-binding energy (_M_). The definition of a man as a time-binder—a definition based on facts—suggests many reflections. One of them is the possibility that one of the functions of the time-binding energy in its pure form, in the highest abstraction (_M_), works automatically—machine-like, as it were, shaping _correctly_ the product of its activity, but whether _truly_ is another matter. Mathematics does not presume that its conclusions are true, but it does assert that its conclusions are correct; that is the inestimable value of mathematics. This becomes a very comprehensive fact if we approach and analyse the mathematical processes as some branch (_M_) of the time-binding process, which they are; then this process at once becomes impersonal and cosmic, because of the time-binding involved in it, no matter what _time_ is (if there is such a thing as time).

Is the succession of cosmos, bios, logos, time-binding taking us right back to cosmos again? Now if we put _psychological_ axioms into the time-binding apparatus, it will thrash out the results _correctly_, but whether the results are _true_ is another question.

To be able to talk about these problems I have to introduce three new definitions, which are introduced only for practical purposes. It may happen that after some rewording these definitions may become scientific.

I will try to define “truth” and for this purpose I will divide the concept “truth” into three types:

(1) Psychological, or private, or relative truth, by which I will mean such conceptions of the truth as any one person possesses, but different from other types of truth (α1, α2, ... αn)

(2) Scientific truth (αs), by which I will mean a psychological truth when it is approved by the time-binding faculties or apparatus in the present stage of our development. This scientific truth represents the “bound-up-time” in our present knowledge; and finally,

(3) The absolute truth, which will be the _final definition_ of a phenomenon based upon the final knowledge of _primal causation valid in infinity_.

For simplicity’s sake I will use the signs α1, α2, ... αn for the “psychological,” “private,” or “relative” truths, between which, for the moment, I will not discriminate.

αs1, αs2, ... αsn, will be used for scientific truths, and finally αinfinity for the absolute truth valid in infinity.

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 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 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, 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==e__kt_, with the formula “_P R__T_,” 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. 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 “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 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.

For many temporary reasons I was not able, before going into print, to give a fuller list of the writings of those four unique men; but there is no stroke of their pen but which should be read with great attention—besides which there is a very valuable literature about their work.

(1) The purely mathematical foundation:

RUSSELL, BERTRAND.

“The Principles of Mathematics.” Cambridge University, 1903.

(I am not giving any selections from the contents of this book because this book should, without doubt, be read by every one interested in mathematical philosophy.)

“The Problems of Philosophy.” H. Holt & Co., N. Y., 1912.

“Our Knowledge of the External World, as a Field for Scientific Method in Philosophy.” Chicago, 1914.

“Introduction to Mathematical Philosophy.” Macmillan, N. Y.

Selection from contents: Definition of number. The Definition of order. Kinds of relations. Infinite cardinal numbers. Infinite series and ordinals. Limits and continuity. The axiom of infinity and logical types. Classes. Mathematics and logic.

“Mysticism and Logic.” Longmans Green & Co. 1919. N. Y.

Selection from contents: Mathematics and the metaphysicians. On scientific method in philosophy. The ultimate constituents of matter. On the notion of cause.

WHITEHEAD, ALFRED N.

“An Introduction to Mathematics.” Henry Holt & Co. 1911. N. Y.

“The Organization of Thought Educational and Scientific.” London, 1917.

Selections from contents: The principles of mathematics in relation to elementary teaching. The organization of thought. The anatomy of some scientific ideas. Space, time, and relativity.

“An Enquiry Concerning the Principles of Natural Knowledge.” Cambridge, 1919.

Selection from contents: The traditions of science. The data of science. The method of extensive abstraction. The theory of objects.

“The Concept of Nature.” Cambridge, 1920.

Selection from contents: Nature and thought. Time. The method of extensive abstraction. Space and motion. Objects. The ultimate physical concepts.

“Principia Mathematica.” By A. N. Whitehead and Bertrand Russell. Cambridge, 1910-1913.

This monumental work stands alone. “As a work of constructive criticism it has never been surpassed. To every one and especially to philosophers and men of natural science, it is an amazing revelation of how the familiar terms with which they deal plunge their roots far into the darkness beneath the surface of common sense. It is a noble monument to the critical spirit of science and to the idealism of our time.”

“Human Worth of Rigorous Thinking.” C. J. Keyser.

(2) The physicist’s point of view:

POINCARÉ, HENRI.

“The Foundations of Science.” The Science Press, N. Y., 1913.

Selection from contents: Science and hypothesis. Number and magnitude. Space. Force. Nature. II. The value of science. The mathematical sciences. The physical sciences. The objective value of science. III. Science and method. Science and the scientist. Mathematical reasoning. The new mechanics. Astronomic science.

(3) The human, civilizing, practical life, point of view:

KEYSER, CASSIUS J.

“Science and Religion: The Rational and the Super-rational.” The Yale University Press.

“The New Infinity and the Old Theology.” The Yale University Press.

“The Human Worth of Rigorous Thinking.” Essays and Addresses. Columbia University Press, 1916.

Selection from contents: The human worth of rigorous thinking. The human significance of mathematics. The walls of the world; or concerning the figure and the dimensions of the Universe of space. The universe and beyond. The existence of the hypercosmic. The axiom of infinity: A new presupposition of thought. Research in American Universities. Mathematical productivity in the United States.

“Mathematical Philosophy, the Study of Fate and Freedom. Lectures for Educated Laymen.” Forthcoming Book.

Selection from contents of general interest: The mathematical obligations of philosophy. Humanistic and industrial education. Logic the muse of thought. Radiant aspects of an over-world.—Verifiers and falsifiers. Significance and nonsense.—Distinction of logical and psychological. A diamond test of harmony.—Distinction of doctrine and method.—Theoretical and practical doubt.—Mathematical philosophy in the rôle of critic. A world uncriticised—the garden of the devil. “Supersimian” Wisdom. Autonomous truth and autonomous falsehood. Other Varieties of truth and untruth. Mathematics as the study of fate and freedom. The prototype of reasoned discourse often disguised as in the Declaration of Independence, the Constitution of the United States, the Origin of Species, the Sermon on the Mount.—Nature of mathematical transformation. No transformation, no thinking. Transformation law essentially psychological, Relation function and transformation as three aspects of one thing. Its study, the common enterprise of science. The static and the dynamic worlds. The problem of time and kindred problems. Importation of time and suppression of time as the classic devices of sciences.—The nature of invariance. The ages-old problem of permanence and change. The quest of what abides in a fluctuant world as the binding thread of human history. The tie of comradeship among the enterprises of human spirit.—The concept of a group. The notion simply exemplified in many fields, is “Mind” a group. The philosophy of the cosmic year.—Limits and limit processes omnipresent as ideals and idealization, in all thought and human aspiration. Ideals the flint of reality.—Mathematical infinity, its dynamic and static aspects. Need of history of the Imperious concept. The rôle of infinity in a mighty poem.—Meaning of dimensionality. Distinction of imagination and conception. Logical existence and sensuous existence. Open avenues to unimaginable worlds.—The theory of logical types. A supreme application of it to definition of man, and the science of human welfare.—The psychology of mathematics and the mathematics of psychology. Both of them in their infancy. Consequent retardation of science. The symmetry of thought. The asymmetry of imagination.—Science and engineering. Science as engineering in preparation. Engineering as science in action. Mathematics the guide of the engineer. Engineering the guide of humanity. Humanity the civilizing or Time-Binding class of life. Qualities essential to engineering leadership. The ethics of the art. The engineer as educator, as scientist, as philosopher, as psychologist, as economist, as statesman, as mathematical thinker—as a Man.

Appendix II. Biology And Time-Binding

The life of one man is short, and to very few is it given to achieve much in their lifetime. Extensive achievements are made almost entirely by many men taking up the work done by a discoverer. In such a case, we arrive at a _complete_ “truth,” not by the production of one man but by a chain of men, but the initial discovery not only has to be produced but correctly defined before it can be used and that is the important point to be made. What we do not realize is the tremendous amount of mental work that is lost by an incorrect use of words.

Human thought—that unique, subtle and yet most energetic phenomenon of nature—is in the main wantonly wasted, because we do not use, or take pains to use, suitable language; at the same time, false definitions lead to consequences not merely wasteful but positively harmful. When ideas and facts are falsely defined, they tend to bring us to false conclusions, and false conclusions lead us in wrong directions, and life and knowledge greatly suffer in consequence. Our progress is not a well ordered pursuit after truth, as pure chance plays too large a part in it.

Until lately, logic was supposed to be the science of correct thinking, but modern thought has progressed so far that the old logic is not able to handle the great accumulated volume—the great complicated mass of existing ideas and facts—and so we are forced to look for another instrument much more expedient and powerful. There is no need to establish a new science to replace logic; we simply have to look closer into the sciences at hand and realize the fact, which was with us all the time, namely, that mathematics and mathematical reasoning is nothing else than the true logic of nature—nature’s universal tongue—the one means of expression that is the same for all peoples. This is not a play on words, it is a fact which, after investigation, everybody must admit. Everybody who wants to think logically must think mathematically or give up any pretense of correct thinking—there is no escape and all who refuse to investigate the justice of this statement put themselves outside the pale of logically thinking people. The application of rigorous thinking to life will even revolutionize scientific methods by the introduction of right definitions, correct classifications, just language, and so will lead to trustworthy results. Very probably all our doctrines and creeds will have to be revised; some rejected, some rectified, some broadened; bringing about unanimity of all sciences and thus greatly increasing their effectiveness in the pursuit of truth. This application of mathematics to life will even revolutionize mathematics itself. In App. I it is suggested tentatively how this may be accomplished.

As the seemingly ultimate and highest experimentally known energy is the human time-binding energy, this new concept may lead to a change in our present concepts of matter, space and time, in much the same way as the discovery of radium has affected them. This problem can be solved only by _scientific_ experiments with the _time_-binding energy.

In many, even in most, of the cases, the analysis of these phenomena presents great technical difficulty, but why confuse our minds by being afraid of, or being a slave of words? If instead of calling wine _wine_, we called it by its chemical formula, would this, in any way, change the quality of wine? Of course not. All the “qualities” will remain because they are facts, and cannot be altered by words.

A most pathetic picture of the havoc and chaos which wrong use of words brings into life and science is exhibited in all fields of thought by the endless and bitter fighting over words not well defined. Mathematics has been able to make its most stupendous achievements because of its method of exact analysis of the continuum, dimensions, classes, relations, functions, transfinite numbers, etc., and also of space and time. Hitherto, not all of these conceptions in their sharply defined form have had direct application to our daily life or to our world conception. The thoughts expressed in App. I may suggest this “missing link”—connecting mathematics more intimately with life.

Modern science knows that all energies can be somehow transformed from one kind to another and that all of them represent one type of energetic phenomena, no matter what is the origin of each. For example, a galvanic or chemical battery produces the same kind of electricity as the mechanical process of friction or the interaction of cosmic laws as in the dynamo. In some instances, when our systems are suitably adjusted, the transformations are reversible, that is, the energy results in a chemical process—an accumulator; the chemical process results in electricity—the galvanic battery; motion results in electricity—the dynamo; electricity results in motion—the electric motor; etc. We know all energies are somehow related to each other, in that their transformation is possible. The effects produced by the same type of energy are absolutely the same—no matter what its origin. The marvel of an electric lamp is the same marvel, whether the origin of the electricity be chemical, mechanical or cosmic as in the dynamo. The experiments in scientific biology have proved this to be true in living organisms and just this is the tremendous importance of the discoveries in scientific biology. Light and other energies react on organisms in the same way as the chemical reactions and these phenomena are reversible. More than that, living complex organisms have been produced which grew to maturity through a chemical or mechanical treatment of the egg, and this has been accomplished in the infancy of scientific biology! (See _The Organisms as a Whole_, by Jacques Loeb.)

All phenomena _in nature_ are _natural_ and should be approached as _such_. The human mind is at least an energy which can direct other energies; it is incorrect and misleading to call it _super_natural. It is of course true that we do not fully understand the nature of the human mind and we shall learn to understand it when and only when we acquire sense enough to recognize it as _natural_. If we persist in saying and believing that the “spiritual evidences cannot be explained on a material base,” this statement should be equally applicable to electricity or radium. If this statement is false for these phenomena, it is equally false for the mind or the so-called spiritual and will powers. The scientific understanding of these phenomena will not “degrade” these phenomena, _because that cannot be done. Facts remain facts and no scientific explanation of a phenomenon can lower or degrade that which is a fact._ Electricity is electricity and nothing else, no matter what its origin; human time-binding energies (embracing all faculties) are the highest of the known energies—equally magnificent and astonishing—no matter what the base; and the scientific understanding of them will only _add_ to our respect for them and for ourselves; it will unmistakably help us to develop them indefinitely by mathematical analysis. The _base_ is not the phenomenon—sulphuric acid and zinc _are not_ electricity; time-binding energies _are not_ a pound of beefsteak, although a pound of beefsteak may help to save life and be therefore _instrumental_ in the production of a poem or of a sonata; but by no means can a beefsteak be taken for either of them.

I have attempted, with some measure of success I trust, to solve these problems in science and life; the results are astonishing, as they lead us to a much higher and more embracing ethics than society has ever had. By this analysis I prove that the understanding of this most stupendous but NATURAL phenomenon of human life brings us to the scientifical source of ethics and I prove that the so-called “highest ideals of humanity” have nothing of “sentimentalism” or of the “_super_natural” in them, but are exclusively the _fulfilment_ of the _natural laws_ for the _human class of life_. The recognition of the fact that the phenomena of the human mind are natural and as such conform to natural law has the further advantage over the “supernatural” attitude in that we can no more evade a law of human nature than the law of gravity; in other words, human ethics will have the validity of natural law. With the supernatural attitude, it was simple enough to avoid the issues of life, by a simple statement—“I do not believe”—and that was enough to break all bonds and be free from the “supernatural morale”—but to get away from the “natural morale” and _remain_ HUMAN is IMPOSSIBLE. Whereas, with an artificially formulated morale it was easy enough to break away by a simple mental speculation, and feel perfectly satisfied as long as one escaped the jail; with a morale made clear that it is a NATURAL LAW for the human class of life, the curtain of sophistry and speculation is removed and everyone who breaks away from the NATURAL LAWS FOR HUMANS, WILL KNOW BY HIMSELF, THAT HE IS OUTSIDE THE LAW—FOR HUMANS.

Engineers are not metaphysicians, their field is not one of clever argument but one of proved facts; their work is not to befog the air with cloudy expressions or sophistry, but to create; their method is scientific and their tool is mathematics. It is known that in remote antiquity, in some temples electrical phenomena were known and were used to keep the ignorant masses in awe and obedience. Shall we follow the methods used by those magicians or shall we squarely face facts? Shall we look upon life, and the usually so-called mental, spiritual phenomena, etc., as _super_natural, simply because we do not understand them? It seems evident that everything which _exists in nature, is natural_, no matter how simple or complicated a phenomenon it is; and on no occasion can the so-called “_super_natural” be anything else than a completely natural law, though it may, at the moment, be above or beyond our present understanding. The attitude of mind which admits the _super_natural blinds and frustrates any analysis or any attempt at analysis. The unprejudiced analysis of the so-called “supernatural” does not _alter_ any part of the strange and high functions of it. The phenomena of the human time-binding energy are and will remain the most precious, subtle and highest of known functions, no matter what the origin. _Facts_ may not be _denied_ or _falsified_ if analysis is to arrive at correct conclusions. The high dimensionality of the human mind, the so-called spiritual and will powers, _are facts_ and must be _accepted_ as such. It is about time to establish an exact science to deal with them. The problems of animal life were approached without prejudice, no supernatural “spark” was bothering us in our analysis—an animal was an animal and nothing else—we did not intermix dimensions, therefore we see that the “social structure” of the animals on a farm never breaks down as they are managed on a scientific base with an understanding of _their_ proper standards. Animals to-day live more happily than man. We don’t allow animals to practice the “survival of the fittest,” or “competition,” which is far too destructive. Our present social system imposes these disastrous methods upon man alone, and the result is that the hideous proverb “Homo homini lupus” has become true.

In modern science facts are not wanting, we have first but to know them. If we take, for example, sulphuric acid and zinc and make what we call a galvanic battery, we see that from two chemical substances a third—a salt—is made in addition to which we have a peculiar energy produced called electricity. Who does not know the marvelous properties of this phenomenon?

Scientific biology has made tremendous progress lately; engineers cannot afford to ignore the facts established in laboratory researches. The problem of “life” and of other energies, hitherto considered “_super_natural,” is well in hand, and proves to be none the less astonishing though entirely natural. A number of scientists all over the world are working at this problem and the scientific facts which they have established, and which cannot now be denied, belong to-day to the realm of practical life. Engineers, of course, have to know these facts; mathematicians have to establish correct dimensions in the study of all the sciences and people will have to study mathematical philosophy; only then can the process of integration in any phase of thought be made without mistakes. There is no escape from that, if _truth_ is what we really want. But here one objection may be raised, an objection which for some is a serious one indeed; namely, what will take the place of the old philosophy, law and ethics, if human life is nothing else than a physico-chemical process? To quote Doctor Jacques Loeb from his _Mechanistic Conception of Life_: “If on the basis of a serious survey, this question (_that all life phenomena can be unequivocally explained in physico-chemical terms_—Author) can be answered in the affirmative, our social and ethical life will have to be put on a scientific basis and our rules of conduct must be brought into harmony with the results of scientific biology. Not only is the mechanistic conception of life compatible with ethics, it seems the only conception of life which can lead to an understanding of the source of ethics.”

I hope to have proved in this book that _scientific_ ethics is based on natural laws for the human class of life; that it is based on the experimentally proved fact that Man is a Time-binder, naturally active as such in time; and that this concept or definition of Man is rigorously scientific and accounts for the highest functions of man—the highest of the mental and spiritual perfections—without the need of any “_super_natural” hypothesis.

Scientific biology proves the fact that life and all of its phenomena are the results of some special physico-chemical processes, which manifest themselves in some peculiar energies, of which the human mind is the highest known form. These processes are known to be reversible, in that some of these peculiar energies cause physico-chemical changes in their own base; the process involved I propose to call biolysis, as I propose to call biolyte the substances produced. These phenomena have a parallel analogy in inorganic chemistry—in electricity—the difference being only in the scale or dimension. When an electric current is passed through a special battery called an accumulator or reversible battery, chemical changes occur, in that new compounds are formed which possess a reversible capacity; namely, in reproducing the former materials—that is, electricity is generated. This process of forming chemical substances by the passing of an electrical current is called electrolysis and the product so produced is called electrolyte. At the same time it is a known fact that organic chemistry is infinitely more complicated and variable than inorganic chemistry. The energy produced by the reactions of some organic chemical groups are, therefore, of a more complicated character and of another dimension. One of these energies of organic chemistry which lately has come into the scope of scientific analysis is called life—its physico-chemical base is the protoplasm, which _result_ I call the “time-linking” capacity or energy. This name is important for the consequences it will bring about later on. The time-binding capacity or energy of man (no matter what time is—if it is), which is unique to man, is a most subtle complex; it is the highest known energy and probably has many subdivisions. Ears are sensitive to the vibration of the air. Eyes are sensitive to the more subtle vibrations of light; in a similar way, the time-binding apparatus is sensitive to the most subtle energies; besides which it has the capacity to register not only all of our sensations but also the time-binding energies of other people; and it apparently has the capacity to register the energies of the universe.

Here again we see the same continuity of phenomena; the protoplasm as a complex organic physico-chemical unit which has the peculiarity to “live,” to grow and multiply “autonomously” and this same autonomous peculiarity _applies_ to the _time-binding energy_; it grows and multiplies “autonomously” in its own dimension. The time-binding energy is a complex radiating energy somewhat like the emanations of radium and it probably also has many different subdivisions. _Note that the transformation of the atom_ or the transformation of _radio-active substances after passing different stages, is not complete but probably ends in lead, whereas the transformation which occurs in the production of the time-binding energy probably is complete or nearly complete and is that which I call the time-binding energy. (See _App. I_.)_ All the higher characteristics of man which it is customary to call the “mental, spiritual and will powers,” etc., are embraced in this exact definition of energy—in the capacity of time-binding. A diagram will better explain the continuity, evolution and mechanism of this time-binding energy.

[ A series of circles, connected by lines, the leftmost circle being C1, then next C2, and so on to C7. The first is connected to the second by line T1, the second to the third by T2, etc. Each circle after the first has within it an energy indication, E1, E2, etc. ]

Biology and Time-Binding.