TIME-BINDING:
The General Theory
BY
ALFRED KORZYBSKI
Presented in abstract before
the
International Mathematical Congress, August, 1924.
Toronto, Canada.
NEW YORK
E. P. DUTTON & COMPANY
681 Fifth Avenue
Copyright, 1924 by
ALFRED KORZYBSKI
Warsaw, Poland, and New York City
All international rights reserved.
Printed by the
Graphic Press, 39 W. 8th St., N. Y. C.
Photographs by the Fernand Studios, N. Y. C.
TIME-BINDING: The General
Theory
by ALFRED KORZYBSKI
Presented in abstract
before the International
Mathematical Congress, August, 1924, Toronto, Canada.
(This paper
is a summary of a larger work on Human Engineering soon to be
published.)
I
ALL HUMAN knowledge
is conditioned and limited, at present, by the properties of light
and human symbolism. The solution of all human problems depends
upon inquiries into these two conditions and limitations.
Einstein's theory
is a fundamental inquiry and application of the known properties
of light; the irrefutable minimum of his theory results in
an entirely new world conception, as beautiful and cheerful as the
old ones were gloomy and despairing.
The minimum of our
inquiry into the structure of human knowledge and symbolism is also
irrefutable, and this beginning, imperfect as it may be, has already
enormous beneficial consequences.
Einstein's theory
was the application of modern scientific methods to the universe,
man excluded. The present inquiry includes man in the field of modern
science. As a result, both theories meet on a common ground.
The theory presented
here is broader than Einstein's. It may be proved that the whole
of the theory of relativity can be deduced from the application
of correct symbolism to facts; so that the general theory of Time-binding
includes the general theory of relativity as a particular case.
For a full understanding
this essay should be read twice, at least, because the beginning
presupposes the end, and vice versa. This theory is built
upon the minimum of the best ascertained scientific facts of 1924.
Its scientific soundness has to be judged on theoretical grounds
(1924). Its working cannot be judged by arguments, only by application.
Fortunately, it works with the reader who has understood it. If
it does not work, the reader has not understood.
(5)
We
cannot argue as to whether the sun is shining, we must go and
see. In the case here presented, arguments alone are
also not legitimate.
Statements containing
variables are called "propositional functions"; they are neither
true nor false. When values are assigned to such variables the expressions
become propositions, which are either true or false. (Russell.)
Many words are names
for stages of processes and are therefore variables, as for instance,
"civilization", "science", "humanity", "mathematics", etc., etc.
To generate a proposition with such words, we must assign to them
a value through the use of co-ordinates. For our purpose, it will
be sufficient to use only the time-co-ordinate, which will be indicated
by the year in parenthesis, such as "science (1924)."
Obviously "science
(1924)" is a different affair from "science (1500)," or "science
(300 B. C.)." In the field of this investigation the term "science"
means, for the majority, "science (300 B. C.)," or, at best, "science
(1800 A. D.)." For such readers, this inquiry will be incomprehensible.
Most, not all, of
the details of this general theory are vaguely known; it seems that
the main novelty consists in the building up of an autonomous system.
Such systems, if scientific, are useful; they economize thought
and bring to light truths as well as fallacies. In a deeper sense
fallacies, if scientific, are often as useful as truths, because
they open new and unexpected fields for inquiry. Probably no system
is true, although this statement does not include mathematics which
does not claim to be true but to be correct.
The scientific revolution
started with Geometry, and, in a deeper sense, it is carried on
by Geometry. Until Gauss, Lobachevski, Bolyai, Riemann, etc., the
Euclidean Geometry, being unique, was theologically believed
to be the geometry of the space. The moment a second
geometry was produced, "just as good," self-consistent, yet contradictory
to the old one, the geometry became a geometry. None
was unique. One absolute was dead. Until Einstein (roughly) the
universe of Newton was for us the universe. With Einstein
it became a universe. The same happened to man. A new "man"
was produced, "just as good" and a trifle better, yet contradictory
to the old one.[1] The man became a man, otherwise
a conceptual construction, one among the infinity of possible ones.
(6)
Granting,
for the time being, all that mathematicians say about mathematics
(1924), there are two aspects of mathematics which have been
neglected.
That which has symbols
and propositions is a language. This aspect must be taken
into account.[2] Besides, if we free mathematics entirely from theology,
mathematics may be viewed as an activity of these bags of
protoplasm called "Smith," "Brown," etc. This aspect makes mathematics
a form of behaviour of man. No psychology of man can ever
be valid so long as we disregard entirely this most characteristic
behaviour of man. It explains the utter failure of the old
mythological psychologies, and the failure of those contemporary
students of psychology whose scientific standards and mental age
are somewhere B. C.
Lately the natural
sciences have firmly established the fact that an organism should
be treated "as-a-whole" (Loeb, Ritter, etc.). The theory of relativity
has established another fact, that all we know and may know is a
"joint phenomenon" of the observer and the observed. Indeed there
is no such thing as an "observer," without something to observe,
neither such thing as the "observed," without somebody making the
observation.
Any inquiry into the
affairs of man with any pretense of being scientific (1924), must
take into account these two fundamental principles or fail.
Our daily language,
and, in most cases, our so-called scientific language together with
its logic, originated mostly in a pre-scientific epoch and are largely
elementalistic and absolutistic; which must hamper successful reasoning
and solutions.
It has been known
for some years that we cannot speak sense about man in the old language.
Although Wittgenstein has proved this point, he did not show us
the way out. The way out is simple. We must form a new vocabulary,
which would be in accord with the above-mentioned principles.
Some authors have
already used new terms successfully, yet they did not explain the
importance of these new terms. For instance the late J. Loeb introduced
the term "Tropism" to cover the forced movements of the organism
"as-a-whole"; the present writer introduced the term "Time-binding"
to cover all the factors "as-a-whole" which made man, a man. We
may agree that man differs somehow from ani-
(7)
mals
by the capacity for building this accumulative affair called
civilization. In the old way we could argue endlessly about
"what made civilization possible." Some say that "thinking"
made it, others say that "speech" is responsible (Watson), or
writing, etc., etc. As a matter of brute fact, all such statements,
taken separately, are false, because civilization is
a joint affair of all of them and an infinity of others, as
yet not abstracted.
The new words do perform
the task, because they do not split what, for our purpose, should
not be separated (Poincaré). This explains why the language of this
paper is not our usual one.
The old subject-predicate
language and logic veil the inter-relatedness of nature (Whitehead);
the new, brings these relations to a sharp focus (Korzybski).
There is a profound
difference, indeed, between a man-made green leaf and a non-man-made
green leaf. In the first, green color was added, it is a
"plus" affair, it was "made." In the second, color was not added,
it is a functional affair, it was not made, it "happened,"
"became."
Quite obviously, a
subject-predicate "plus" language and logic can cover man-made "plus"
affairs, but cannot cover functional affairs, "happenings,"
"becomings"—where, for instance, the natural greenness of the leaf
is inherent in the leaf itself, which is not the case with a man-made
leaf.
Only a functional
logic and language can cover functional natural phenomena (Korzybski).
Such logic and language have been built by modern mathematical discoveries
(Whitehead, Russell, Keyser, etc.). To treat man at least as fairly
as we treat a green leaf, the same methods must be used.
Universal Peace—(be
it family, school, industrial, economic, political, scientific,
personal, international and what not) depends ultimately on Universal
Agreement.
Universal Agreement—is finally based on Rigorous Demonstration.
Rigorous Demonstration—absolutely depends on Definitions.
Definitions—are ultimately conditioned by
Correct Symbolism.
So, if we want universal
agreement, we must start with correct symbolism. Before a
theory of correct symbolism may be written down it must already
have started with correct symbolism. It must be felt instinctively.
A prototype of correct symbolism we may find in mathematics.
(8)
A
word is a symbol. Before a sign may become a symbol something
must exist for this sign to symbolize, else the sign
has no meaning; it is not a symbol, not a word, but a noise.
For our purpose we may speak, in the rough, of two kinds of
existence, namely, the physical existence, somehow connected
with persistence, and logical existence. By logical existence
we mean in this case a thinkable thought, otherwise free from
self-contradiction (Poincaré). A "word" which labels a self-contradictory
"idea" is not a word, not a symbol, because it symbolizes nothing;
if spoken, it is a noise, or if written, a blot of black on
white; it is meaningless, no matter how many thousands of volumes
have been written about it.
If we use such noises
as significant words, it is a fraud played on the other fellow.
Such acts should and will be some day, listed in the criminal codes
of civilized countries as among the most harmful crimes against
civilization.
With this introduction
permanently in mind we may proceed, provided we agree that we will
try to talk sense about "man." If this unusual request is granted,
our task is not difficult; without it, it is impossible.
Let us imagine a genetic
series, father-son-grandson, etc. We start with "Amoeba I" (A1),
and end the series with "Albert Einstein" (AE). Somewhere near the
end there is an individual, "Adam" (A). All individuals are very
"real," and every one of them is different. According to
one of the important rules of correct symbolism we label every individual
with a different name, so that every individual has one and
only one name.
We wish, (it
is only our pleasure) to produce two other words "man" and "animal."
I said "We wish"; it is so because there is no such thing in
the world as "a man" or "an animal." These labels are names for
abstractions of high order, for "ideas" and not things. Smith,
Brown, Jones, etc., are "realities," objects, but they all are different,
and the collective name "man" is given to an idea and not a thing.
This point is extremely important, and I would suggest to the reader
to be entirely convinced on this point before he proceeds, otherwise
he will not be able to follow the rest.
Incidentally we see
that the naturalistic, as well as anti-naturalistic creeds are false,
because both are based on the false assumption that "a man" or "an
animal" is a thing.
If we want to talk
sense about the ideas "man" and "animal", we must have them
sharply defined, otherwise confusion must fol-
(9)
low.
We do not want to produce unnecessary new words; we inquire
whether the old terms in which we used to speak about the terms
"man" and "animal" will serve our purpose, which is to talk
sense. There is one condition, among others, which must be fulfilled,
namely the terms must be sharp. We pick any of the old
terms, let us say, for instance, the term "thinking."
How do we get this
term? We find that we watched the behaviour of Smith, Brown, Jones,
etc.; we passed through a mental process of abstraction, generalization,
assumption, inference and what not, and in this way we got our term
"thinking." We do the same with, let us say, "Fido" (I select Fido
because the majority of us know and like dogs). We watch the behaviour
of different dogs, Fido I, Fido II, Fido III, etc.; we pass
through the same processes of abstraction, etc. and we conclude,
"Fido thinks." Obviously the term "thinking" is not sharp,
and because it is not sharp, we must abandon it as useless. We may
retain this term for family use, but science is a public activity,
and for public use nicknames will not do.
The problem now is
such that we want to keep the useful terms "man" and "animal"
and we have no terms in which we could talk sense about them. There
is only one way out, namely, to produce new terms which will
be sharp. As "man" and "animal" are not things but logical
entities, the finding of those sharp definitions is a problem of
ingenuity only.
We observe again our
genetic series; we note that "man" is an accumulative class of life
with a special high rate, in that the son may start where
the father ended, and that "animals" are not accumulative, or, if
accumulative, they are so with a different and slower rate.
With Korzybski we label these two different rates of accumulation
"Time-binding" for "man," and "Space-binding" for "animals."
| Amoeba I |
Adam |
Albert Einstein |
| I........................................................ |
I......................... |
I........................... |
|
————animal————
|
——————man—————
|
Non-accumulative
class of life or
if accumulative, with a different
and slower rate, which we label:
"Space-binding"
| accumulative
class of life, with
a rapid rate, which we label:
"Time-binding" |
These differences
are sharp.
The foundation for
a deductive science of man is thus laid down.
(10)
If
we inquire into the mechanism of this rapid accumulation (Time-binding,
PRt) we should be entitled to expect that we will
strike the very core of our problem. This actually happens with
most unexpected results.
We must stop here
to emphasize, and it cannot be over-emphasized, namely, the power
of the method. We cannot talk sense in the old "psychological"
terms, therefore we deliberately avoid such terms; we carry on our
inquiry in a "queer" engineering way and language, yet the results
are deeply psychological. This inquiry unravels to us the deepest
secret of man as man, a secret which neither psychology nor philosophy
had ever disclosed and capitalized (the last three words
represent one idea). The explanation is simple: This could
not be done before the physico-mathematical revolution of modern
science.
II
THE reader is warned
about an extremely important principle entirely disregarded in practice,
namely, that what can be shown cannot be said (Wittgenstein). If
we show something which we call "a pencil," it is an entirely
different affair than when we speak of "a pencil." The content
of the first is inexhaustible, the second is a concept, with
finite content, fixed by a definition.
The following applies
to things, and therefore the actual thing should always be
shown.
We take something
(anything) let us say a pencil; we show it and ask, "What is this?"
This is a process, a chunk of nature, a clog of electricity, a mad
dance of electrons; this is something acted upon by everything else,
and reacting upon everything else; this is something which is different
all the time, something which we can never recognize, because
when it is gone, it is gone, etc.
This something which
we can never recognize we call an event (Minkowski, Lorentz,
Einstein, Whitehead, Planck, Millikan, etc.). The number of characteristics
an event has, is infinite.
Yet in this event
which we cannot recognize there is something fairly permanent which
we can recognize. This we call an object (Whitehead). We
label our object with a special symbol which we call a word.
The accompanying picture
represents the Anthropometer, a plastic diagram to illustrate what
has been said. C represents the "event"; it is a broken-off paraboloid
which indicates extension to infinity, while the holes represent
characteristics, infinite in number.
(11)
(12)
B is the object of
finite size with a large, yet finite, number of characteristics.
A is the label—a word.
The holes, also, represent characteristics.
What is an
object? An object is a first abstraction, a first
rough summary, a first integration, etc., of the infinite number
of characteristics of the event, into the few characteristics of
the object. This process of abstracting is indicated by lines F.
What is the label?
The label is a symbol. A symbol for what? For an abstraction
of first order
In the history of
mankind two, and only two, answers have been given to this all-important
question; one was that the symbol was for a "percept," the other
that for a "concept." Both of these answers are elementalistic,
and therefore fallacious. Our positive answer settles one of the
most troublesome and important problems of the theory of knowledge,
as to the meaning of the symbol. We see that I cannot
know what YOU abstract, unless YOU tell ME. Otherwise the meaning
of the symbol MUST be given by a DEFINITION
We get the meaning
of our symbol by defining it, that is by abstracting a second
time (F1) from the many characteristics of the object
into the still fewer characteristics of the label. The symbol is
a second order abstraction. Then follow abstractions of higher
orders.
How about Fido? We
defined objects in terms of recognition, therefore "who recognizes
has objects." It means, by definition, that Fido "has objects."
Are his objects the same as ours? Similar, but not the same (D).
For instance, we can not recognize our own gloves among a thousand
of gloves, but Fido can. Has Fido "symbols"? Yes, he barks at a
cat and another Fido "knows" somehow, something. But his symbols
are not articulate (E).
We see that Fido's
objects (D) are first-order abstractions; what he lacks is the second
and higher-order abstractions. It must be remembered that the new
language of orders of abstractions has the flexibility and exactness
of number series. We could ascribe to Fido many orders of abstractions,
but man would have still higher. I take here the simplest case;
the other refinements would not alter the method, and this
is important.
We see that the difference
between "Fido" and "Smith" is in the order of abstractions,
and this difference is sharp.
Here a crucial question
arises. No doubt Fido did the abstracting; does Fido
know, and can Fido know that he abstracts? The answer is
positive (due to the method): Fido does not know
and cannot know
(13)
that
he abstracts, because it takes science to know that we abstract,
and Fido has no science, as a matter of brute fact.
This faculty for
building higher and higher abstractions is the mechanism of the
characteristic rapid accumulation, which makes man a man.
If, for instance,
we could see an electron in its flight, the world would be a maze;
no law, no order, no intelligence would be possible.
The first nerve, the
first dynamic gradient (Professor Child) (a) was not stimulated
by all of (b) but only by a small part (c). (a) got the experience
of (b) by exploring, summarizing, abstracting the (c's), and so
it goes all through life, man included.
Life and "intelligence"
and abstracting start together, this being the result of
the physico-chemical structure of living organisms. The function
builds the organ (Professor Child). The mechanism of the rapid human
accumulation is the faculty for higher and higher abstractions,
which accelerate its progress at a permanently increasing rate.
The term "abstracting"
is used here in the "organism-as-a-whole" way, where "senses" and
"mind" are not divided; we know that the old elementalistic methods
are not valid.
The complexities of
life and of the organism become intelligible in terms of orders
of abstractions, and it must be repeated again, that it is immaterial
how many orders of abstractions we ascribe to an organism—the method
remains the same.
We may illustrate
what was said by a simple experimental fact. We all know an electric
fan. When the fan is rotating rapidly we do not see the separate
blades (a) but we see a disk, a shield (b). "Matter" and "objects"
are such shields or disks; in other words a "joint phenomenon"
of the rotating blades and our abstracting organism. We cannot
put our finger through the disk, although it
(14)
is
a fiction, because the rotation of the blades is much more rapid
(for one of the reasons) than the velocity of our finger. Similar
reasons explain why we cannot put our finger through a table;
it takes an X-ray to be able to do so, in some instances.
The Anthropometer
shows to the physical eye, that in human economy (A) is not
(B) and (B) is not (C) (this must be shown on the Anthropometer);
in animal economy (A) is (B) and (B) is (C); in other words, the
animal does not discriminate between the three. If man omits to
discriminate, he copies the animals in thinking.
This simple fact is
the solution of practically all human troubles. The reader should
not be misled by the childish simplicity of this all-important issue.
As a matter of fact we nearly all, until this day copy Fidos
in our thinking, by not being conscious that we abstract. This habit
so permeates our old theories and practice, that one has to have
the Anthropometer before him for some time to overcome this pernicious
habit. Those who copy Fido must be dogmatists, categorists,
absolutists, "know-alls"; they must be fanatics, intolerant; when
they meet others of their kind, a fight must follow, etc. They do
not want to think, they are not interested to investigate, for why
should they? They "know it all," they are self-satisfied in their
ignorance, they "know" that they "know all," which is all there
is to know about it. They will persecute others who think. For them
thinking and science are crimes, or, at best, unnecessary waste
of time; and, if forced to think, it is a serious pain to them.
They take everything for granted, critical thought and the spirit
of inquiry is entirely foreign to their makeup.
Man to be a man and
think as a man must be a relativist, which is an inevitable consequence
of the application of correct symbolism to
(15)
facts.
He knows that he does not know, but may know indefinitely
more, that his knowledge is only limited by his own ingenuity
and nothing else. This feeling liberates his creative faculties,
arouses his interest, his energy, builds up his character and
puts his strivings on a very high level. His sporting spirit
is aroused; he wants to know more; he wants to inquire
and think; in fact, with the understanding of the Anthropometer
he must think, there is no escape for him, and thinking
becomes a pleasure to him as well as a necessity.
This explains, also,
the well-known fact that with the Fido-way imposed upon mankind,
it was impossible to make a man think. But with the Anthropometer
introduced into homes and elementary schools, it is impossible
to stop man from thinking.
A man who understands
and applies the Anthropometer will never take a word for
granted; instead, he will ask indefinitely, "What do you mean?"
and this, ultimately, leads to inquiry into facts, correct symbolism,
and universal agreement. The important thing is to get
the feeling that we abstract, firmly rooted into the minds
of the children.
This achieved, the
rest follows automatically.
All disputes such
as the fight between the vitalists and the mechanists; the modernists
and the fundamentalists; naturalists and anti-naturalists; the Newtonians
and the relativists, etc., evaporate, since these are mostly due
to the objectification of higher abstractions, the Fidoism in our
thinking processes.
The elimination of
the Fido-ways would affect, in an extremely beneficial manner, our
old economic system; it would bring sanity where, at present, there
is none.
What is money? Money
is a symbol. A symbol for what? For all human Time-binding faculties;
animals have it not. No doubt bees produce goods—honey, but
these goods of the bees are not wealth until man puts his
hands on them. Money is not edible or habitable, it is worthless
if the other fellow refuses to take it. The reality behind
the symbol is human agreement, or else the value behind the
symbol is doctrinal. Fido does not discriminate between A
and B, and B and C (see the Anthropometer). He worships the symbol
alone. "In Gold we trust" is his motto, with all its destructive
consequences. Man must not forget the reality which is behind the
symbol. It is amusing to see how the so-called "practical man" deals,
mostly, with fictitious values, for which he is willing to live
and die. When he has the upper-hand and ignorantly plays with symbols,
dis-
(16)
regarding
the realities behind the symbols, of course, he drives
civilization to disasters. Life is full of them.
We see also the utter
folly of anyone making a race to accumulate symbols, worthless
in themselves, destroying the mental and moral values which are
behind them. For it is useless to own a mentally disorganized
world, such "ownership" is a fiction, no matter how stable it may
look on paper. Commercialism, as a creed, is such a folly.
Some day even economists,
bankers and merchants will understand that such "impractical" works,
as the present one, for instance, on the stabilization of doctrinal
values, are directly working toward the stabilization of an economic
system; which the former, in their ignorance, do their best to keep
unscientific and, therefore, unbalanced.
But such thoughts
are beyond the Fidos, and the world is drifting rapidly toward further
catastrophes.[3]
We may outline a few
more, important consequences. The understanding and the training
with the Anthropometer would help scientists in all lines of
research, for there are no "facts" free from some "doctrine." There
are only "facts" with bad logic and facts with good logic. Gross
empiricism is a delusion, and he who professes it as a creed is
probably more mistaken than the old metaphysicians were.
|
|
| Deduction works
relatively until we bump our nose on these particulars
left out. |
Deduction works
absolutely, if correct. We never can bump our nose, because
no particular is left out. |
(17)
Mathematical abstractions
differ from our daily abstractions by the fact that mathematical
abstractions include the particulars, in mathematics we go
by remembering (Lambert, Cassirer); the opposite is the case
with our daily language, wherein abstractions leave the particulars
out. We go by forgetting, until we bump our nose in our deductions
on some particular left out.
The majority of our
disasters is due to the not knowing or neglecting of this
all important issue. The Anthropometer, giving the consciousness
that we abstract, brings these issues forcibly home.
We mostly all (mathematicians
included) objectify our high abstractions, which is a confusion
of order of abstractions. But mathematics is unique in this
respect, that mathematical abstractions have all particulars included,
and therefore these objectifications are not dangerous. This
explains why mathematicians very seldom show "practicality" in life;
they objectify daily abstractions with great assurance in the same
way they do with mathematical abstractions, and disasters must
follow.
The objectification
of high abstractions is a terrible danger, because of these particulars
left out, but the moment we realize this, we are conscious of it,
the danger is over.
If the event has an
infinity of characteristics, then, obviously, from an event we can
build up an infinity of higher-order abstractions. Because of it
the old "negative facts" become a much more fundamental source of
knowledge than the old "positive facts" (conventional). Einstein's
theory is a brilliant example. When we speak about something, what
we actually do, is to exhibit the behaviour of a system of symbols,
rather than to say much about this world (Ogden). When the system
misbehaves, then we learn something important about this world.
The realization of
it, the feeling of it, gives us these wings Couturat was
speaking of, and Poincaré was laughing at. It sets man free. The
Anthropometer releases man from the old limitations of Fidoism,
when shown (not only said. A "knowing class of life"
begins with "knowing," therefore, scientific method and science
is not a luxury for the privileged few; it is the very thing which
differentiates "Smith's" "thinking" from Fido's "thinking." The
consciousness of abstracting which is so fundamental for man, is
the awareness of a faculty, and in this special case we can
use this faculty only when we are aware that we have it.
The Anthropometer
shows that the event is an absolute variable, different all
the time; the object is a relative variable, different for
(18)
every
observer, the label is a constant, when posited by a
definition. It follows that we cannot agree (theoretically)
about an object, and cannot disagree on the label.
These undeniable facts
lay down the foundation for a positive theory of universal agreement,
inherent in the structure of human knowledge. From an event we can
abstract an infinite number of abstractions of first and higher
orders. Only folly can make us fight for these abstractions, which
are only poor selections among the infinity of possible ones. We
do not need to doubt human reason, we should distrust our language.
There is a world of difference between these two conceptions and
attitudes.
The Anthropometer
is built upon two fundamental primitive feelings, namely: that we
abstract, showing on the Anthropometer "This (A) is not this (B),
and this (B) is not this (C)"; while for Fido "This (A) is this
(B) and this (B) is this (C)"; all three are one. And that of difference
and of counting the differences (we do not need actually
to count them, the feeling is there just the same). Exactness
here is not required, although it is always desirable; the feeling
that we abstract is all that is needed. This feeling, I repeat
again, is the awareness of a circular faculty, and is, therefore,
necessary for its exercise.
As a result, universal
agreement becomes a possibility. We can give the "scientific temper"
to the masses in a very short time. The dreams of Bertrand Russell
may become true.
The modern physico-mathematical
discoveries become very simple when explained on the Anthropometer.
Einstein simply refused to copy Fido, and objectify higher abstractions
such as "space" and "time" (Minkowski) and "matter" (Whitehead).
III
AS SHOWN before, the
meaning of a label must be given by a definition. This fact
gives us the means to investigate the structure of all human knowledge.
Whenever and wherever
we start, we must start with a set of words which are undefined,
because we have, by assumption, no more words to define them. This
means that human knowledge, at every stage, presupposes knowledge
of these few undefined words. This is called, in logical terms,
the circularity of human knowledge.
We have never before
faced this issue candidly, and it has ever been responsible, as
it is today, for most of all intellectual gloom and
(19)
skepticism.
This inherent structure of human knowledge was called the "weak
spot" of knowledge, which, of course, it is not.
It cannot be theoretically
denied that human knowledge is a faculty such that the son can start
where the father ended; therefore it always should start from the
latter-end (1924) and not from the beginning. This fact, as yet
entirely ignored theoretically, shows that the naturalistic philosophies
should be reversed as to logic and order when they tackle the problem
of man.
The gross empiricists,
overwhelmed with horror against the old metaphysics, went to the
other extreme, into a mythology equally false to facts.
When we inquire indefinitely,
"What do you mean?" accidentally we spoil every nice "talky-talk";
but we also come to a set of undefined terms, which are
postulates. All the rest of our vocabularies (not names for
things) are theorems, logical necessities of the starting set of
terms strictly interwoven with the metaphysics of the maker of the
vocabulary. It may be mentioned that a babe, before he begins to
understand anything and to revise his feelings about
the world around himself, has already his metaphysics aggravated
by the metaphysics of his parents, teachers, etc., away back to
our savage ancestors. Of course, these metaphysics are false to
facts, but just the same it is first as to order.
We see that all human
knowledge is geometrical in structure (I might say mathematical,
but for serious reasons, I prefer to say geometrical). Somewhere
at the border line there is the metaphysics. The system is strictly
interdependent and bound up by "Logical Destiny," to use this beautiful
expression of Professor Keyser.
The expression "circularity
of human knowledge," was used here in its logical sense, which is
misleading if taken literally. We must
(20)
start
somewhere, somehow, anywhere, anyhow, with a set of undefined
terms, then go ahead, come back, revise our base (a) for (b),
go ahead again, revise our base (b) for (c), go ahead again,
and so on endlessly. Human knowledge is inexhaustible. No set
is undefined absolutely, but only relatively so.
In practice, things
are much more complicated because we seldom, if ever, have one vocabulary.
But we must untangle first the simplest theoretical issue. The vocabularies
(silent postulates) imply the theorems, the theorems imply the postulates.
He who accepts uncritically the vocabulary made by X, accepts unwillingly
and unbeknowingly X's metaphysics. This fact is of very great importance.
If we accept the vocabulary made by X and the metaphysics made by
Y, we are lost in inconsistency, the world is an ugly mess, unknown
and unknowable. This mess, which is nearly always followed
up by rampant pessimism, is the necessary consequence of the misunderstanding
of what is here explained. With understanding, our troubles vanish,
the world remains unknown (because the Fidos have so long persecuted
science) but it becomes knowable.
With all of this permanently
in mind, it is easy to understand anybody else, just as a mathematician
when he hears a theorem, he knows usually from which geometry it
is taken.
If we do not understand
the above, we are slaves; if we know it, we are free, because we
can select our master (Keyser, Poincaré).
The geometrical structure
of human knowledge shows that man is extremely logical, if
we grant him his conscious and unconscious premises (language).
Whoever has any doubts about all of the mentioned issues should
visit an asylum, where he would see the working of this general
theory in its nakedness. In daily life and in semi-insane cases
the issues are veiled by customs, habits, overlapping vocabu-
(21)
laries,
and other doctrinal complications. It is known that "insane"
people are extremely logical. In many instances "insanity" is
cured by making the unconscious premises conscious. Psychiatry,
as yet, has no preventive methods. The Anthropometer is such
a preventive educational method against many cases of insanity
and different unbalanced states, due to inherited or inhibited
false doctrines. A man full of false doctrines cannot be a perfectly
normal, healthy and useful man; neither can he copy Fido in
his thinking processes without somehow registering it to the
detriment of society and himself.
When someone claims
to be a "Napoleon" we lock him up. How about the majority of us?
Do we not fancy that we are what we are not? That is rather a serious
question.
The psychiatrists
have all the time to fight "absolutism" and "dogmatism," which in
many instances are responsible for different forms of insanity.
They do so without the full understanding of the mechanism of it.
The whole advancement
of science and civilization shows that this theory is true, but
as we did not know explicitly the structure of human knowledge,
every revision from (a) to (b) and from (b) to (c) (see page 21)
etc., was always painful and slow. We see that, as the structure
of the atom is reflected in a grandiose manner in the structure
of the universe, so is the structure of the knowledge of the individual
man reflected in the collective knowledge of mankind called science,
and vice versa.
IV.
Consequences and Applications
AT THE present stage
of our inquiry it is impossible to foresee all the consequences
and applications of this general theory by means of the Anthropometer,
but some of them are manifest from the beginning, and are manifold
and weighty. I will summarize them, roughly only, as material for
thought and further analysis.
It must be emphasized
again that merely talking about the Anthropometer will not
help much. This prototype of the event and the object and the label
must be shown. The moment we point our finger at them and
say "this," it cannot be covered by words, and it economizes thousands
of words at once. Whoever disregards this positive condition and
misses the benefit of it, should not blame the theory and the Anthropometer,
but his disregard of a vital condition and issue. The old Fido-way
is so deeply rooted in our theories, practice, habits, systems,
etc., that although I have had it on my desk for more than a year,
my own Fidoism shocks me far too often. In a
(22)
century
or so, of course, we shall not need it, but such is not the
case at present.
Some of the consequences
are educational and scientific, some are suggestions for activities.
We will start with the educational and scientific ones.
The inherent circularity
and geometrical structure of human knowledge proves the interconnection
of our vocabularies with our metaphysics. We see, that if we want
humans to be humans and think as humans, we must start our education
from the latter-end (1924) by beginning with modern "metaphysics"
of Planck, Einstein, Whitehead, Russell, Keyser, etc., made possible
by the understanding of the Anthropometer and the structure of human
knowledge.
We would then find,
at once, the interest of the masses aroused, and thinking would
start on an unprecedented scale, with all its beneficial results.
The "scientific temper" would overrun mankind in a few years, facts
and correct symbolism would count, and the exponential law PRt
would begin to work properly.
Man is ultimately
a doctrinal being. Even our language has its silent doctrines, and
no activity of man is free from some doctrines, so that the kind
of metaphysics a man has, is not of indifference to his world outlook
and his behaviour.
We cannot expect when
we force a dynamic being into the patterns of Fido static
doctrines, that we will get anything else but an unbalanced being
in an unbalanced civilization.
The Anthropometer
should be introduced into elementary schools and we should start
our education with it, everywhere. We must teach a small modern
scientific vocabulary and train our children to think habitually
in these new terms; which automatically carry with them a
new non-absolutistic world conception. Such simple and mechanical
means (they must be mechanical and simple if we hope to give them
to the masses) would impart to all mankind, not the knowledge, but
the cultural results of university training. Such methods,
the complete reversal of the old, would stop Fido-ways in theory
and practice.
The language of "concepts"
is very difficult because that is an elementalistic, absolutistic
term (as auxiliary it may be useful) and will not do as our fundamental
term. This doctrine is very difficult to teach even to university
students, to say nothing of the masses. The language of "abstractions
of different orders" is not an elementalistic term; it is a "joint-phenomenon,"
"organism-as-a-whole" modern new term; it is natural to man, it
can be shown to him, and is easily
(23)
grasped
by children and people of very low mentality when shown on
the Anthropometer.
We see that modern
philosophers have heavy duties and responsibilities toward mankind;
heavier, perhaps, and more important than the duties and responsibilities
of engineers and doctors. With the modern physico-mathematical discoveries
and mathematical discoveries, as those of Whitehead, Russell, the
"doctrinal function" of Keyser, etc., "philosophy" has ceased to
be a divertisement of the few, it has become as vital an inherent
factor in all human life, as air, water, and sunshine. There are
communities who have very little to do with engineers or doctors,
but no community in the world is free from some kind of "philosophy."
Among savage tribes we see how doctrines have prevented entirely
any progress at all. The more civilized races have advanced simply
because they were more rebellious, and never could stick to an unrevised
doctrine for too long.
This is why we have
had this semblance of civilization at all! It is not enough to discard
philosophy entirely, on the ground that most of it is foolish. Granted
our old philosophies were foolish enough, whoever thinks he can
discard them entirely without supplanting them by others, sometimes
equally foolish, deludes himself. The problems at hand require philosophy,
and ignorant vagaries will not do. It is about time that mankind
should hold the philosophers responsible. Ignorance is not an excuse.
It may as well be
admitted that our old educational methods would have to be reversed.
Babies should start their education playing more with microscopes
than toys. Before they learn to spell they should firmly feel, at
least, the structure of "matter," the structure of human knowledge,
and the mechanism of human symbolism. Then they would be equipped
to be humans.
Science is not a luxury
for the few, but as it leads to the consciousness that we abstract,
science and scientific method is precisely that, which makes man
think and behave as man.
Non-scientific,
half-education (in the sense of 1924, which we could, maybe,
consider "scientific education" in the sense of 300 B.C.)
is not a boon to mankind in 1924, far from it. That is very
natural in the meantime. The conditions, environment, social inheritance,
racial experience, other complications, with all accompanying and
novel nervous and mental pressure upon man in 1924, are entirely
different from these in 300 B. C. Is his mental, nervous resistance
and health properly taken care of? Are our educators and
(24)
doctors
themselves modern men? Sad to say the answer is NO. We still
educate man, drug him with doctrines thousands of years old,
doctrines which are inconsistent and false to facts. We still
keep him in a savage-made universe. This deep discrepancy must
unbalance him, and periodically unbalance his institutions.
The sooner we understand this and modernize the antiquated branches
of knowledge, the better for all of us. There is hope for us,
if we stop folly. Our old doctrines do not work even with savage
tribes, as practice shows. From the modern point of view the
savage tribes do not gain anything by passing from one kind
of savage-made doctrines to another set of savage-made doctrines.
Experiments should be made, by taking some newly-born from different
savage tribes, placing such children in highly cultured scientific
families and give them full scientific education, and
see what would happen. The new doctrines would work maybe, where
the old failed.
The Anthropometer
presents a synthesis of modern scientific strivings in a form ready
for application.
In the old way we
delude ourselves talking about the "education of the masses," and
in the old way it is hopeless. What we need most at present
and what could be accomplished very quickly is the re-education
of the educated. A proper insistence by the scientists, and a few
books for this purpose would perform the task. The understanding
of the Anthropometer shifts the center of gravity from something
which is impossible to something which is possible.
With a re-educated
educated class the world would soon become a different place to
live in.
The benefits of new
terms are that occasionally they throw a new light on old problems,
or quite often they help in settling, in a positive way, old controversies.
When some controversial questions are settled the world accepts
them quickly. What was roughly known but ignored, because veiled
by the old language is brought by the new language to a sharp focus.
After the results are obtained, they may be explained in any language,
but the results, in most cases, could not be gotten in another way.
As a matter of fact,
civilization has advanced in the shape of the diagram given on page
21, but as we did not know that this was the inherent structure
of human knowledge, every revision of our assumptions was slow and
accomplished with great suffering and bewilderment. The creative
scientists and teachers were persecuted and
(25)
hampered,
mankind has paid a hideous price. The new understanding will
stop persecution and propaganda of any kind.
The popular introduction
of the Anthropometer would also prevent the publication of nine-tenths
of books and the delivery of the majority of speeches, inasmuch
as most of them are based on Fido-ways. Such elimination would relieve
us of a great amount of useless ballast.
We must repeat here
that the theories of relativity have a still more general underlying
theory, namely, the general theory of time-binding. As this theory
is so general it is therefore easy to grasp and teach, even to children.
It explains the refusal to accept high-order abstractions, such
as "matter," "space," and "time," for first order abstractions,
which they are not. This is the minimum of science (1924) with which
each babe should start its education.
There are a few interesting
points about "matter," "space" and "time." Taken separately they
are abstractions of high order and not objects, or abstractions
of first order. If we objectify the high abstraction, we
get a fanciful universe, self-contradictory, a nature which is against
human nature. Being logical, we invent something supernatural
to account for a nature against human nature. If "time" is an object,
if it has objective existence, then, obviously, it must have,
as all objects have, a beginning and an end; then the universe was
made, it must have a "beginning of the beginning" (old "essences"),
etc., etc., and the whole old anthropomorphic mythology follows,
by a purely logical process.
But if "time" is an
abstraction of high order and not an object (first order
abstraction), otherwise, if it does not exist as an object,
then, obviously, something which does not exist cannot have a "beginning,"
or a "beginning of the beginning," the universe was not "made,"
etc. It just was, is, and will be. Obviously the "primal substance"
may quite happily be a myth in such a universe of transformation;
we cannot exhaust it in either direction.
Our universe is timeless.
In another language, it is eternity in time, or, still in another
language, infinity of times (this is a generalization of
experimental time). When times are very rapid we nervously
summarize times, and feel "time," a "duration." The "infinity
of times" is nothing else, when translated in still another
language, than the law of conservation of energy. Incidentally
it proves the existence of actual infinity.
(26)
The
above explanations were given because the old Fido-ways are
omnipresent. In a way they permeate all mankind, and they must
lead us to most acute mental disorders, reflected in behaviour.
I do not know any other phase of science in the whole history
of civilization which would have a more profound and beneficial
influence upon the daily life of the man on the street, than
the modern advancement of mathematical and physico-mathematical
sciences, when given to the masses and applied in education.
This understanding
clears up another old fallacy. We are accustomed to hear that the
old mythologies are somehow "primary" with man. We see clearly that
it is not true. Those mythologies are "secondary" with man. What
was primary is the objectification of high abstractions,
the Fido-ways in our thinking processes. Once this is eliminated
by the Anthropometer, all the old vicious fictions automatically
vanish.
If we confuse the
orders of abstractions; if we fancy that the high abstractions are
first-order abstractions, which they are not, then we get "absolute
matter," "absolute space," and "absolute time." If the world is
made up of "absolute matter," "absolute space," "absolute time"
then of course such a structure cannot account for "mind" and what
not. The number of possibilities in such a universe are too
limited, etc., etc., and all the rest follows. But if the world
is made up of "quanta," "fields," etc., then all we see, we feel,
we know and can know are averages, summaries, abstractions of different
orders, etc., etc. Only a language of processes, transformations,
variables, functions, integration, abstractions of different orders,
probabilities, etc., etc., can account for such a universe. Mathematics
considered as an activity of the human organism, reflects
in its structure and form the structure and form of the universe.
Being a language, it is the universal tongue.
In such a universe
all we deal with are combinations of high orders ("Matter" made
up of molecules, molecules of atoms, atoms of electrons, and so
on, probably).
How the combinations
of high order grow, as to numbers of possibilities, an instance
taken from the Principles of Science by Jevons will show. This simplest
possible case which is far, far away from any "simplicity" in nature,
will show.
"The successive orders
of the powers of two have, then, the following values, so far as
we can succeed in describing them:
First order ......................................................
2
Second order .....................................................
4
(27)
Third
order .....................................................
16
Fourth order ................................................
65,536
Fifth order number expressed by 19,729 figures.
Sixth order number expressed by figures, to express the number
of which figures would require about 19,729 figures."
By way of contrast
Jevons gives us "that the almost inconceivably vast sphere of our
stellar system if entirely filled with solid matter, would contain
more than about 68•1090 atoms, that is to say, a number
requiring for its expression 92 places of figures. Now, this number
would be immensely less than the fifth order of the powers of two."
Due to the modern
knowledge of the structure of the world we see that practically
everything becomes possible, and may be understood, no matter when.
The feeling of these issues, with the lack of understanding of the
simple law of growth of the higher order combinations, gives, I
think, the base for mystical feelings, which vanish as such, once
these issues are understood. We can know, never mind when; all the
rest is a matter of method and science. In this way the unknowable
becomes knowable. Correct symbolism covers all these facts,
also, and leads to the same conclusions.
The concept of order
is fundamental, not only because it underlies all mathematics but,
also, because it is easily and obviously translated in terms
of senses. This gives a base for a scientific vocabulary.
The savage-made language
of "cause" and "effect" has also order in it, only it is a very
short series—it is a two-term relation. Yet, in the world around
us, there is no such thing in existence as a two-term relation,
and therefore when we use a two-term relation, cause-effect, these
two terms are overloaded with non-crystallized "thought" (emotion),
hence metaphysics of the wildest kind. Science expands the
series into an indefinite number of members. Old ignorance and metaphysics
go.
The expansion of this
series is the coefficient of our knowledge.
The theory, as expounded
in this paper, seems to suggest directions in which some activities
could be started.
There seems to be
no doubt that the recent physico-mathematical and logic-mathematical
advancement of science is affecting all branches of human knowledge
in many unexpected directions. It seems without question, that the
scientists could not deal with these problems without the help of
professional mathematicians. If the
(28)
mathematicians
refuse to cooperate with other branches of science, Human Engineering
included, it will probably take one or more generations before
the whole beneficial effect of modern discoveries would be felt
in education and life.
The situation today
is such that, in many serious instances, naturalists who know "facts"
speak nonsense quite happily, about them. The mathematicians who
alone speak sense, know very little or nothing about facts. The
results are: slow advance, groping in the dark, thousands of false
doctrines, and endless arguments in vacuo. Science is a joint
phenomenon of logic and "facts"; as there are no "facts" free from
some doctrine, therefore science should be carried on as a joint
phenomenon. Experimentalists, for example, should have very
able and creative mathematicians who would work at logic and language,
and they should work together, jointly. Life is too short for one
to be a specialist in several lines at once; science has outgrown
the individualistic epoch, it must become a group activity.
All our doctrines
should be revised and correct symbolism should be applied to facts.
The old philosophy is dead in disgrace, the world is without co-ordinating
guidance. To be fair to philosophers, no single person nowadays
could perform this co-ordinating work alone. It again must become
a group activity.
If we want to avoid
complete mental anarchy, which must be followed up some day by grave
disturbances in our behaviour, this problem of revision and co-ordination
must be our urgent and immediate task. The people of the world have
lost the old faiths in their theories, their leaders, and themselves;
this state, again is another phase of other creeds as yet not crystallized.
Only heroic measures can save us from still worse turmoils.
When, for instance,
biologists make statements about mathematics, or mathematicians
make statements about biology, such statements are always short
somewhere on knowledge, they never are competent. Statements should
be made by biologists on biology, but with the full understanding
of other branches of knowledge; by mathematicians on mathematics,
but also with full understanding of other achievements.
Such work could be
done only and exclusively by a permanent body of the world's best
scientists being relieved from all other duties who, after getting
acquainted with each other's specialities, would work together on
the revision of language and doctrines, and would prepare this co-ordination
of knowledge. Such a permanent body could
(29)
issue
a yearly or quarterly journal which would give to mankind the
revised and co-ordinated doctrines of each "present" day.
Such a method would
allow mankind to start every generation where the last one left
off, and the progress of civilization would follow the exponential
law PRt. A copy of this general doctrinal summary should
be placed in the hands of every teacher throughout the world, by
legislation if need be. There is no doubt that if scientists themselves
insist upon some such plan, mankind would accept it. After all,
a united opinion of those who, in the major part, are the driving
force of civilization, is irresistible. Scientists would start with
such an institution a new period of human history which would be
called the "scientific era." This body might be called the "Senate
of Humanity" (this name was suggested to me by Professor A. Vasiliev,
and I gratefully acknowledge it).
If the peoples of
the world were told that the best scientists of the world are working
on their problems they would settle down and wait, some hope would
be restored, otherwise they will not wait. The publications of the
"Senate of Humanity" would be stripped of technicalities so that
the general public would understand them. They would save an enormous
amount of work to scientists and laymen by giving short, yet reliable,
informations in an already co-ordinated and revised form.
With these budgets of knowledge, not of paradoxes, mankind would
come gradually out of the Fido era, into the scientific era.
We need not delude
ourselves. The most important hindrances, in the old ways, are found
in language and the logics; these problems would remain the most
important for a long time to come, and the mathematicians would
have to play nolens volens, a most conspicuous rôle, a rôle
worthy of their science.
It follows from the
geometrical structure of human knowledge, that the solution of all
human problems lies in frankly putting all branches of human endeavor
upon a postulational base. Postulational treatment gives us unique
benefits, among others, it facilitates inspection, gives clarified
systems of doctrines, and unifies all other methods. Our debates
would become limited to experimental testing of our sets of postulates.
It may be mentioned
that such a library is being established in New York City under
the name of "International Library of Human Engineering" (Principia
Scientiæ Hominis), which will originate a deductive science of man,
and deductive natural and other sciences.
(30)
This
library will be at present under the editorship of one mathematician
and one engineer, with an advisory board of scientists from
all countries in all branches of science. For geographical and
linguistic reasons, local national boards of co-editors will
also be formed.
Until the Senate of
Humanity is organized, this library with its international scientific
boards, will be the research and organizing center for the future
permanent international body of scientists. Its publications would
be the handbooks for the future chairs of Human Engineering which
sooner or later must be established in all important universities
of the world. Human Engineering, as every other branch of engineering,
would be based on mathematical methods.
Such is the outline
of immediate constructive steps which could be taken. The problems
at hand are manifold, weighty, and difficult, beyond the power of
any single man to deal with. A great deal of responsible preparatory
work must also be accomplished. Such work of course must be a group
activity, and it is hoped that the international advisory boards
of the library will be able to accomplish a good deal of this preparatory
work.
A SHORT BIBLIOGRAPHY
SCIENCE, METHOD
BROAD, C. D. Scientific
Thought. London & N. Y.
CASSIRER, E. Substance and Function and Einstein's Theory of
Relativity. Chicago.
CAMPBELL, N. R. Physics, The Elements. Cambridge.
ENRIQUES, FEDERICO. Problems of Science. Chicago.
JEVONS, W. S. The Principles of Science. London.
MACH, E. Science of Mechanics. Chicago. Conservation of
Energy. Chicago. Scientific Lectures. Chicago. Space
and Geometry. Chicago. The Analysis of Sensations. Chicago.
OGDEN, C. K. The Meaning of Meaning. London & N. Y.
POINCARE, H. The Foundations of Science. New York.
MATHEMATICS, MATHEMATICAL
PHILOSOPHY, LOGIC
BALDWIN, J. M. Thought
and Things, 3 Vols. London, New York.
BONOLA, R. Non-Euclidian Geometry. Chicago.
BOOLE, GEORGE. Laws of Thought. Chicago.
BRUNSCHVIC. Les Etapes de la Philosophie Mathématique.
CAJORI, F. A History of Mathematics. London, New York.
CANTOR, G. Contribution to the Founding of the Theory of Transfinite
Numbers. Chicago.
COUTURAT, L. The Algebra of Logic. Chicago.
DEDEKIND, R. Essay on Number. Chicago.
HUNTINGTON, E. V. The Continuum. Harvard Press.
KEYNES, J. M. .A Treatise on Probability. London, New York.
KEYSER, C. J. The Human Worth of Rigorous Thinking. Columbia
Univ. Press.
KEYSER, C. J. Mathematical Philosophy. E. P. Dutton, N. Y.
LEIBNIZ. The Early Mathematical Manuscripts of Leibniz. Chicago.
LEIBNIZ. New Essays Concerning Human Understanding. Chicago.
LEWIS, C. I. .A Survey of Symbolic Logic. Univ. of California
Press.
LOBACHEVSKI, N. The Theory of Parallels. Chicago.
MANNING, H. P. Geometry of Four Dimensions. New York.
RUSSELL, B. The Principles of Mathematics. Cambridge. Scientific
Method in Philosophy. Chicago. The Problems of Philosophy.
New York. Mysticism and Logic. New York. Introduction
to Mathematical Philosophy. London, New York.
SHAW, J. B. Lectures on the Philosophy of Mathematics. Chicago.
SOMMERVILLE, D. M. Y. Non-Euclidian Geometry. London, Chicago.
WEATHERBURN, C. E. Elementary Vector Analysis. London, Chicago.
Advanced Vector Analysis. London, Chicago.
(35)
WHITEHEAD,
A. N. and B. RUSSELL. Principia Mathematica. Vol. 1.
Cambridge.
WHITEHEAD, A. N. An Introduction to Mathematics. New
York. The Organization of Thought Educational and Scientific.
London. An Inquiry Concerning the Principles of Natural Knowledge.
Cambridge. The Concept of Nature. Cambridge. The Principle
of Relativity. Cambridge.
WINDELBAND, W. (Editor). Logic. London, New York.
WITTGENSTEIN, L. Tractatus Logico-Philosophicus. London,
New York.
YOUNG, J. W. A. (Editor). Monographs on Topics of Modern
Mathematics. London and New York.
YOUNG, J. W. Lectures on Fundamental Concepts of Algebra
and Geometry. New York.
THE THEORIES OF
RELATIVITY.
BIRD, J. M. Einstein's
Theories of Relativity and Gravitation. New York.
BIRKHOFF, G. D. Relativity and Modern Physics. Harvard University
Press.
BOLTON, L. An Introduction to the Theory of Relativity. New
York.
CARMICHAEL, R. D. The Theory of Relativity (postulational)
2nd Edition. London, New York.
CARR, H. W. The General Principle of Relativity (Philosophical).
London, New York.
CUNNINGHAM, E. Relativity, The Electron Theory and Gravitation.
London, New York.
EDDINGTON, A. S. Space, Time and Gravitation. Cambridge.
The Mathematical Theory of Relativity. Cambridge.
EINSTEIN, A. Relativity. N. Y. The Meaning of Relativity.
Princeton Univ. Press. Sidelights on Relativity. N. Y.
FREUNDLICH, E. The Foundation of Einstein's Theory of Gravitation.
N. Y. The Theory of Relativity. N. Y.
KOPFF, A. The Mathematical Theory of Relativity. N. Y.
MOSZKOWSKI, A. Einstein, the Searcher. N. Y.
NORDMANN, C. Einstein and the Universe. N. Y.
NUNN, T. P. Relativity and Gravitation. London and N. Y.
SCHLICK, M. Space and Time. Oxford Univ. Press.
WEYL, H. Space-Time-Matter. N. Y.
WHITEHEAD, A. N. The Principle of Relativity. Cambridge.
WILSON, E. B. The Space-Time Manifold of Relativity. Proceedings
of the American Academy of Arts and Science.
VASILIEV, A. V. Space, Time, Motion. (Historical). N. Y.
THE NEWER PHYSICS.
BORN, M. The Constitution
of Matter. London. New York.
COMSTOCK, D. E. and L. T. TROLAND. The Nature of Matter and Electricity.
New York.
GRAETZ, L. Recent Developments in Atomic Theory. New York.
HAAS, A. The New Physics. New York.
KAY, G. W. C. The Practical Application of X-Rays. New York.
LORING, F. H. Atomic Theories. New York.
(36)
PLANCK,
M. The Origin and Development of the Quantum Theory. Oxford.
REICHE, F. The Quantum Theory. New York.
RUSSELL, B. The A B C of Atoms. London. New York.
SOMMERFELD, A. Atomic Structure and Spectral Lines. New
York.
STOCK, A. The Structure of Atoms. New York.
PSYCHIATRY
ADLER, A. Organ Inferiority
and its Psychical Compensation. Washington.
The Neurotic Constitution.
DANA, C. L. Psychiatry in its Relation to Other Sciences. N.
Y.
FREUD, S. Totem and Taboo. New York. General Introduction
to Psychoanalysis. New York.
FOREL, A. Ants and some other Insects. Chicago.
GRASSET, J. The Semi Insane and the Semi Responsible. New York.
VON HUG HELLMUTH, H. A Study of the Mental Life of the Child.
Washington.
JELLIFFE, S. E. Diseases of the Nervous System (with Dr. Wm.
A. White). Technique of Psychoanalysis. Washington. The
Symbol as an Energy Container, J. of N. and M. D. Vol.
50, No. 6. Emotional and Psychological Factors in Multiple Sclerosis.
Ass. for Research in Nerv. and Ment. Dis. 1921. The Parathyroid
and Convulsive States. N. Y. Med. J., Dec. 4, 1920. Multiple
Sclerosis and Psychoanalysis. A. J. Med. Sc. May, 1921. Paleopsychology.
Psychoanalytical Review. Vol. X, No. 2.
MEYER, A. Objective Psychology or Psychobiology. J. A. Med.
Ass. Sept. 4, 1925. The Contribution of Psychiatry to the Understanding
of Life Problems. Address. What do Histories of Cases of Insanity
Teach Us Concerning Preventive Mental Hygiene During the Years of
School Life. The Psychological Clinic Press. Philadelphia. Inter-Relations
of the Domain of Neuropsychiatry. Archives Neur. and Psychiatry.
Aug. 1922. The Philosophy of Occupation Therapy. Arch. of Occup.
Therapy, Vol. 1, No. 1.
KEMPF, E. The Autonomic Functions and the Personality. Washington.
WHITE, Wm. A. Outlines of Psychiatry. Washington. Foundations
of Psychiatry. Washington. Mechanism of Character Formation.
New York. Principles of Mental Hygiene. New York. Insanity
and the Criminal Law, New York. The Mental Hygiene of
Childhood. Boston. Thoughts of a Psychiatrist on the War and
After. New York. The Modern Treatment of Nervous and Mental
Diseases (2 Vols.). (With Dr. Jelliffe.) Text-book of Diseases
of the Nervous System. (With Dr. Jelliffe.) An Introduction
to the Study of the Mind. Washington. Contribution of Modern
Psychiatry to General Medicine. Mental Mechanism. Washington.
The Behavioristic Attitude. Reprint 101. Nat. Comm. For Mental
Hygiene. New York. The New Functional Psychiatry. Archives
of Diagnosis, Oct., 1910. Principles Underlying The Classification
of Diseases of the Nervous System. J. A. Med. Ass., March 11,
1916. Psychoanalysis and the Practice of Medicine. J. A. Med.
Ass. June 2, 1917. Underlying Concepts in Mental Hygiene. Reprint
4 Nat. Comm. for Mental Hygiene. New York. The Meaning of the Mental
Hygiene Movement. Publ. No. 17. Massachusetts Soc. for Mental
Hygiene. Existing
(37)
Tendencies,
Recent Developments and Correlations in the Field of Psychopathology.
J. Ner. Men. Dis. July, 1922. The Meaning of "Faith Cures"
and other Extra-Professional "Cures" in the Search for Mental
Health. A. J. Publ. Health, Vol. 4, No. 3. Psychoanalytic
Parallels. Psychoan. Review. April, 1915. Symbolism.
Psychoan. Review. Jan., 1916. Individuality and Introversion
(as above). Jan., 1916. The Significance for Psychotherapy
of Child's Developmental Gradients and the Dynamic Differentiation
of the Head Region (as above). Jan., 1917. The Autonomic
Functions of the Personality (as above). Jan., 1919.
MISCELLANEOUS.
CANNON, W. B. Bodily
Changes in Pain, Hunger, Fear and Rage, New York.
CHILD, C. M. Individuality in Organisms. Chicago. Senescence
and Rejuvenescence. Chicago. The Origin and Development of
the Nervous System. Chicago.
CONKLIN, E. G. Heredity and Environment. Princeton.
D’HERELLE, F. The Bacteriophage. Baltimore.
HERRICK, C. J. Introduction to Neurology. London, Philadelphia.
JENNINGS, H. S. Life and Death, Heredity and Evolution in Unicellular
Organisms. Boston. Behavior of the Lower Organisms. New
York.
JOHNSTONE, J. The Mechanism of Life. London.
LOEB, J. The Mechanistic Conception of Life. Chicago. Comparative
Physiology of the Brain and Comparative Psychology. New York.
The Organism as a Whole. New York. Forced Movements, Tropisms,
and Animal Conduct. Philadelphia. Proteins and the Theory
of Colloidal Behavior. New York.
MORGAN, T. H. The Physical Basis of Heredity. Philadelphia.
McCOLLUM, E. V. The Newer Knowledge of Nutrition. New York.
PATON, S. Education in War and Peace. New York.
ROBACK, A. A. Behaviorism and Psychology. Cambridge.
ROBERTSON, T. B. The Chemical Basis of Growth and Senescence.
Philadelphia.
RITTER, W. E. The Unity of the Organism. Boston.
SHERRINGTON, C. S. The Integrative action of the Nervous System.
London.
WATSON, J. B. Behaviour. An Introduction to Comparative Psychology.
New York.
WHEELER, W. M. Social Life Among The Insects. New York.
HUMAN ENGINEERING
CARMICHAEL, R. D. Logic
of Discovery. (Forthcoming book.)
KEYSER, C. J. Mathematical Philosophy. E. P. Dutton. New York.
KORZYBSKI, ALFRED. Manhood of Humanity, The Science & Art of
Human Engineering. E. P. Dutton. New York. Time-Binding: The
General Theory. (Forthcoming book.)
POLAKOV, W. N. Man and his Affairs. (Forthcoming book.)
RUEFF. Des Sciences Physiques aux Sciences Morales. Paris.
(English translation forthcoming.)
[1] See my "Manhood
of Humanity." The Science and Art of Human Engineering. E. P. Dutton
& Co., N. Y. C.
[2] See my "Fate and
Freedom," in Mathematics Teacher, May, 1923.
[3] See the chapter
on "Wealth" in my "Manhood of Humanity".
