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 supernatural or superphysical,
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-inder-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-bindinginvolved 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 (l, 2,
. . . (n).
(2)
Scientific truth (s), 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 l, 2.
. n for the "psychological," "private," or
"relative" truths, between which, for the moment, I will not
discriminate.
sl,s2
. . . sn will be used for scientific truths,
and finally 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 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 O,
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 "O"-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
O, 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=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 it "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 (I) 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:
I.
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 role 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 role 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.
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