METAGEOMETRICAL NEAR-TRUTHS
Realism is Psychological and Vital--The Impermanence of Facts--On
the Tendency of the Intellect to Fragmentate--The Intellect
and Logic--The Passage of Space, the Kosmometer and Zoometer,
Instruments for the Measurement of the Passage of Space and the
Flow of Life--The Disposal of Life and the Power to Create--Space
a Dynamic, Creative Process--Numbers and Kosmogony--The Kosmic
Significance of the Circle and the Pi-Proportion--Mechanical
Tendence of the Intellect and its Inaptitude for the Understanding
of Life--The Criterion of Truth.
Kosmic truth has many facets. The rays of light which we see darting
from its surface do not always come from the core. Often they are
reflections of rays whose light stops short at the superfice; and
these, in turn, are reflections of deeper realities. Thus the reflected
light may be traced to its source by following the lead of external
reflections. It is now known that moonlight, and perhaps, in many
cases, starlight, are reflections of sunlight, if not of our sun,
some other in the universe. But it is only at certain times and under
certain conditions that we can see the sun which is the source of the
other kinds of light. The stars which owe their light to suns are so
many facets of sunlight. The moon is a facet of sunlight also. Facts
are facets of truth. They are so many faces of eternal truth. They
represent the many ways reality exhibits itself, or rather its effects,
to the consciousness. When we, therefore, become aware of facts we have
not in virtue thereof become aware of the reality which produces the
facts. We have come to know only something of the termini of realism
while the complexities and internal ramifications which lie between
realism itself and these termini altogether elude our cognition.
Let us examine briefly an icosahedron, for instance. An icosahedron is
a figure comprehended under twenty equal sides. These various sides
are so many faces by means of which the figure presents itself to the
consciousness. These faces, however, are not the real object. The
figure may be examined by viewing it from any one of its sides; yet,
by simply examining a single face, or any number of faces, less the
total number, we arrive at no satisfactory knowledge of the magnitude
or its substance. We must first become conscious of all the faces,
holding them in mind as a composite picture, before we can even begin
to have anything like a complete notion of the icosahedron. Then by
continuing the examination we may find that the magnitude is composed
of wood fiber or stone or metal, as the case may be. In this way we
might carry the examination to indefinite limits and finally arrive at
a very comprehensive knowledge of the icosahedron and yet be unaware
altogether of the forces which have been at work in the production of
the magnitude or of the reality which lies back of it.
Realism is psychological and vital. In essence it is mind, spirit,
life. Yet these three are one. Mind is the outward vehicle of life;
spirit is the form or the interior vehicle which life assumes in order
to express itself. Realism, then, is life. Is the logician dealing
with reality when he collects and coördinates the various modes of
interpretation by which we learn to understand the symbolism of life?
Obviously not. The data of logic are simply a collection of rules for
interpreting concepts. It is a compendium of indices for the Book of
Life. It is no more the book itself than a table of contents is a
book. But logic occupies about the same category as does an index to a
volume. A book, however, is more than its conventional contents. It is
the thought that is symbolized therein. The book of life, accordingly,
is the sum total of life's expressions; but it is not life itself. That
is the subtle, evasive something which the contents of the book of life
symbolize. Nature, both in her palpable and impalpable aspects, may be
said to be the book of life wherein are recorded the movements, the
expressions, and the diacritics of life. The whole is a magnitude of
many facets (little faces). We shall have to know all the faces before
we can say that we have a comprehensive knowledge of nature. For so
long as we have only a fragmentary knowledge of the whole, so long even
as we have merely a superficial knowledge of any aspect of nature,
just so long will our knowledge be in vain. Just as it frequently
happens that, on account of the partial view of things, we are led
to make incorrect judgments concerning them, so when we come to make
assertions about life or nature in general, we are apt to fall into the
error of rendering judgments upon insufficient data. And it is not at
all likely that judgments thus arrived at can possess true validity
because it may happen, and undoubtedly does always so happen under the
present limitations of human knowledge, that the very elements which
are ignored or neglected in forming a judgment possess enough of virtue
to alter the intrinsic value of determinations based upon otherwise
insufficient data. Hence it develops not infrequently that our
judgments repeatedly have to be changed in proportion as our data are
made more and more comprehensive. Men searching eagerly for the truth
sometimes allow themselves to be carried away by the enthusiasm of the
moment which arises upon the discovery of a new facet of truth; but
if all searchers were to bear in mind the fact that reality presents
itself to consciousness in myriad ways and that there are innumerable
facets all leading eventually back to the source of all they not so
easily would be induced to jump to the conclusion that they had covered
the entire ground. For when we have discovered a million facts, or many
millions of them, about nature we may say that we have only merely
begun and that what we have found is not to be compared with the
totality even of the directly observable phases of nature.
Logic, therefore, deals with the symbolism existing between and
among facets of truth, and not directly with truth itself, although
the conclusions reached by the logicians may be true enough from
an intrinsic standpoint. Logic is not truth, however; it is merely
the consistence of relations and inter-relations between facts and
among groups of facts. Truth is not established by logic; it stands
in no need of the light of logic for its revelation; indeed, more
apt than not is logic to obscure truth. Truth is its own proof; it
is self-evident. Logic is a mere modeler of facts; it is static,
immobile, fixed. All truly logical processes need a starting point, a
foundation, a premise, a base. Truth, being eternal, mobile, dynamic,
vital, needs no starting point; needs no foundation because it is
itself fundamental; it requires no premise because no premise is
comprehensive enough to encompass it. There is only one way of arriving
at truth and that is not to arrive at all--just to recognize it without
procedure. The fact that facts are, and the fact of their relations and
inter-relations, their sequence and implications, can be arrived at
only by logical processes. Life, in its passage through the universum
of spatiality, carefully diacriticizes between the realm of facts and
the domain of truth, marking each off from the other by unmistakable
signs and barriers. Truth is perceived as an axiomatic, self-evident
principle and no amount of logic could prove or establish its verity.
Facts are intellectual creatures; truth is intuitional, vital. The
intellect conceives the consistence of facts while the intuition
recognizes truth--is truth, and therefore, follows in the wake of life
as consciousness.
There is no permanence in facts and the intellectual recognition of
their consistence. The discovery of a single new fact may destroy the
consistence of a whole mass of previously correlated facts. Thus is
revealed the miracle power of logic over facts. It can take a mass of
facts, related or unrelated, mold them into hypotheses, endow them
with a sort of interior consistency, and make these hypotheses take
the posture of truth. Hence logic is often an effective mask which
the intellect commonly imposes upon its material; but it does so
instinctively and can no more escape the rigorous compulsion of this
instinctive functioning than water can escape its liquidity. Wherefore,
we conclude that true permanence abides alone in truth because truth
is duration itself. For the foundations of the whole structure of
facts in religion, science, art and philosophy which man has toilfully
built up in the last million years might easily be destroyed or
overturned by the discovery of some great fact or by appreciating the
true value of truth. Let us suppose it should suddenly be realized
by men that they are really and truly gods capable of creating and
possessing all the other virtues, powers and capabilities which we are
accustomed to impute to supreme divinity; and suppose that the fact
of their omnipotence and divine omniscience always had been obvious
but that men were so engaged upon details and the non-essentials of
life and matter that they had not noticed nor realized it before,
would not this realization make a vast difference in the character
of our knowledge and the attitude which we would necessarily assume
thereafter towards matter, life and the problems which they present?
Would not it completely revolutionize our arts, our sciences and our
philosophies? How much, then, of the facts of these would be left
when the light of omniscience had been turned on--when truth itself
could be perceived and interiorly realized? Not much, to be sure. We
should undoubtedly have to dispense with the entirety of our fact-mass,
for it should then be entirely useless and meaningless in the light
of the resplendent omniscience of truth. As at present constituted
consciousness is focused upon the material plane for the purposes of
superficial observances. But if the focus of consciousness should be
changed so as to reveal conditions upon what must be a higher and more
interior level, the aspect of things would be entirely changed and the
whole of our theory of knowledge would have to be reconstituted. It
is conceivable, yea obvious, that the stern reality of being is far
removed into the Great Interior of that which is; and there is a point
in the path to the interiority of being where there is no illusion, no
appearance, indeed, nothing but the cold, illuminating body of reality
itself. It must appear also that along the journey interior-ward there
are many apparent levels or planes, each of which requires a new focus.
It is unreasonable, then, to suppose that the conclusions arrived at
as a result of purely logical processes, confined to the lowest levels
of reality, are pertinent and valid for the entirety of realism which
is neither of mathematical nor logical import. For instance, if we
take the purely axiomatic assertion: _x_ equals _x_, the intellect
is at once certain that this is so, and cannot be otherwise, and yet
a proposition of this kind is purely conceptual, conventional and
arbitrary. _x_ may also equal 1, 2, 3, 4, or any other quantity. Then,
if each _x_ in the above equation be replaced, by say, a horse, there
immediately arises a difficulty. For it is not possible to find two
horses which are in all respects mutually equal. So that as soon as
we pass from the conceptual into the actual, whether on the side of
objective reality or that of absolute reality, the validity of the
axiom is immediately exposed to serious questioning. The truth of the
matter is that on both sides of the conceptual it is always found that
there is a variance from the standards set up by the conceptual, this
variance being more marked on the side nearest to absolute reality than
on the side of objectivism. Objectively, the conformity of the sensible
with the conceptual is of such approximation as to lend trustworthy
utility to the conceptual in its application to the sensuous. Thus by
simply eliminating the vital factors from our equations we are enabled
to proceed in a reasonably safe manner with our judgments. Really,
however, no such approximate congruence can be found; for on the side
of reality we are dealing with an indivisible something--something
that is eternally and absolutely unitary in its constitution while
when we transfer the scene of our observations to the objective world
we discover a contrary situation. Here we are everywhere beset by
diversities, multiplicities and dissimilarities. This is so because the
intellect naturally tends toward the objective where it finds a most
comfortable atmosphere for its operations. The conceptual is related to
the objective as a train of cars is related to the railway. That is to
say, the constitution of the intellect is such that it finds its most
facile expression in the objective world and is about as comfortable in
the domain of realism as the same train of cars would be on the ocean.
The intellectuality is designed to deal with facets of truth; it is
made to manipulate segments, parts, fractions, and cannot chart its
way through a continuum such as reality. Being constitutionally a
conventionality of the Thinker's own contrivance, and arising out of
the subtle adaptation of his vehicles to the environment afforded by
the sensuous world, it can only find congruence in that conventionality
which is the instrumentality of a higher intellectuality expressed
in a diversity of forms, into which reality divides itself for
manifestation. The human intellect is, therefore, the bridge over
which is made the passage from the individual consciousness to the
All-Consciousness; simultaneously, the medium whereby the physics
of the brain are converted into the psychics of unconsciousness. It
may be likened to a pair of specially constructed tongs which are so
formed as to fit exactly the objects which a higher intellectuality
has made. It is without the province of the intellect to take note of
what intervenes between physics and psychics; it is always oblivious
of interstices while taking cognizance of objects or things. In this
respect, the intellect is much like a steerage passenger on board an
ocean liner who sees only his port of departure and port of arrival,
knowing nothing in the meantime of what happens during the voyage,
nothing of what the other passengers on the upper decks may experience
and taking no part in any of the passing show until he lands. So
that the passage of the intellect from fact to fact is an altogether
uninteresting voyage; it may as well be made unconsciously, and to all
intents and purposes, is so made.
Accordingly, the advocates of _n_-dimensionality find it quite
impossible to predicate anything whatsoever of the passage, say, from
tridimensionality to quartodimensionality. They find themselves at ease
in tridimensionality and have even contrived to find pleasant environs
in the four-space having made therein such idealized constructions as
will afford ample hospitality to the intellect. But the questions as to
how the passage from the three-space to the four-space is to be made
and how the intellect shall demean itself during the passage have been
completely ignored and, therefore, left unanswered. What, then, shall
be said of an explorer who says he has found a new land and yet can
give no intimation as to how one may proceed to arrive at the new land,
what changes are to be made en route, nor the slightest suggestion
as to the direction one should take in setting out for it? It is not
likely that the report of such an explorer, in practical life, would
be taken seriously; and yet, there are those who, relying utterly
upon similar reports made by certain enthusiastic analysts, dare to
place credence in their asseverations. Not only have they given wide
credence to these reports, but have, indeed, sought to rehabilitate
their own territory in accordance with the strange descriptions given
by unhappy analytical explorers. Now the question of greatest concern,
granting for the nonce that there is such a domain as hyperspace,
is the _passage_. How shall we make the passage? Or, is the passage
possible? In vain do we interrogate the analyst; for he does not know,
nor does he confess to know. Evidently it is impossible for him to know
by means of the intellect alone; for the intellect not being fitted to
take cognizance of the "passage," but only the starts and stops, has no
aptitude for such questions. Hence, what seems to be the most important
phase of the entire question will have to remain utterly inscrutable
until the intellect nourished by the intuition shall be aroused from
its lethargy and brought to a certain high point of illumination where
it, too, may take note of the passage.
Space is the path which life makes in its downward sweep through
all the stages of pyknosis or kosmic condensation by virtue of
which it accomplishes the engenderment of materiality as also the
path marked out by it in its upward swing whereby it accomplishes
the spiritualization of matter. It is the kosmic order which life
establishes by means of its outgoings and incomings. When we look out
into space we perceive that which is a dynamic appearance of life
itself, and not a pure form. Nothing that is a pure form can exist in
nature and in as much as space is not only indissoluble from nature
but partakes of its very essence it cannot be said to be a pure form.
The intellect, however, prone to follow the grooves laid out by pure
logic, never fails to seek to make everything that it contacts conform
to these logical necessities. But, if the analyst were to make careful
discrimination as to the respective categories--that into which life
falls and that in which the intellect is forced by its nature to
proceed--he not so easily would be led into the fault of attempting to
shape realities upon models which being strictly conventional were not
meant for such uses. But neither the logician nor the mathematician can
be condemned for such generosity if such condemnation were justifiable.
For they everywhere and at all times insist upon _realizing_
abstractions and _abstractionizing_ realities, and they do this with
an _insouciance_ that is at times surprising. Yet it is in this very
vagary that is discovered the true nature of the intellect. There is
a sort of dual tendence observed in the method of the intellect's
operation. A polarity is maintained throughout: the abstractive and the
concretional. It vacillates continually between the abstract and the
concrete and no sooner has it found a concrete than it begins to set up
an abstract for it; and _vice versa_--as soon as it is has constructed
an abstract it immediately seeks either its concrete or sets out to hew
some other concrete into such shape as will fit it. And between these
two extremes numerous excuses are found for exercising this peculiar
characteristic, and that too, without regard to consequences. It would
seem that the intellect, in thus functioning, was really engaged at
a sort of sensuous play out of which it derived an intense and not
altogether unselfish pleasure.
Of course, it must be granted that diversity has its specific and
withal necessary uses in that it affords a field for the operation
of human intellectuality and represents the adaptation of the kosmic
intellect to the human for the purposes of evolution. This adaptation
while necessary for the intellectual development is, however, not an
end in itself. It is merely a means to a higher purpose. In fact, if
we regard materiality as a deposit of life, carried by it as a kind of
impedimentum, and consciousness, which _is_ life, as being identical
with the intellectuality which makes these adaptations, there should be
no grounds for the statement that the one is adaptable to the other at
all. And as this is really the view which we assume it would perhaps
be more strict to regard the adaptation as subsisting between the
human intellect and materiality both of which having been constructed
by kosmic intellectuality. Pursuant to the diversity of uses to which
materiality lends itself there arises in the intellect a supreme
tendency to segment, to break up into separate parts, to multiply and
diversify. It is not content unless it is at this favorite and natural
pastime. It delights in taking a whole and dividing it into innumerable
parts. This it will do again and again; because all its muscles, sinews
and nerves are molded in that mold and can no more cease in their
tendency to fragmentation than can the muscles of a dancing mouse
cease in their circular twirling of the mouse's body. Yet, in this
it is but creating a well-nigh endless task for itself--which task
must be performed to the uttermost. But in its performance, that is,
in the intellect's complete understanding of the diversity of parts,
in the knowledge of their relations and inter-relations and in their
synthesis, it may arrive at that one ineluctable something which is
called _unity_. And so doing, become ultimately free.
In view of the foregoing, it is not surprising that the intellect
should have, finally, fallen upon the notion of _n_-dimensionality. It
has come to that as naturally as it has performed its most common task.
Left alone and unhampered in its movements, it has simply followed
the lead of the Great Highway through the domain of materiality. And
now it has arrived at a stage where it thinks it has succeeded in
fractionalizing space. Time has long ago yielded to fragmentation,
been divided into minute parts and each part carefully measured.
Space, not having a visible indicator like time to denote its passage
or parts, suffered a long and tedious delay before it could boast
of a measurer. As the sun-dial measured time in the past and became
the forerunner of the modern clock so _n_-dimensionality measures
space for the mathematician. What more practical instrument for this
purpose may yet be devised is not ours to prophesy; yet it is not
to be despaired of that some one shall find a suitable means for
this purpose. Seriously, however, it is not without possibility that
should some subtle mind devise an instrument for marking the passage
of space as we have for denoting the passage of time a great stride
forward would be accomplished in the evolution of the human intellect.
For the general outcome of the intellect's attention being turned to
the _passage of space_ would undoubtedly be to recognize not only
its dynamism but its _becoming-ness_, as a process of kosmogenesis.
Because such an instrument would have to be so constructed as to take
note of the movement of life, and for this reason, it would have to be
extremely sensitive necessarily and keyed to the subtleties of vitality
and not to materiality. Mathematics shall have failed utterly in the
utilitarian aspects of this phase of its latest diversion if it do not
justify its claims by crowning its work in the field of hyperspace
with a "Kosmometer," an instrument devised for the measurement of
the movement of space or a "Zoometer," an instrument devised for
the measurement of the passage of life. We should like to encourage
inventive minds to turn their attention life-ward and space-ward with
the end in view of constructing such an instrument. When once we have
learned accurately to measure life we shall then be able to dispose of
it--to _create_. It is not doubted that if ever humanity is to arrive
at that point in its evolution where it can understand life; if ever it
is to attain unto the supreme mastery both of vitality and materiality
and to come to the ultimate attainment of divine consciousness (all
of which we confidently believe to be in store for humanity) it must
be accomplished after this manner: first, by syncretizing materiality
with vitality, and then, by intuitionally recognizing the truth of the
implications of the syncretism.
The history of consciousness in the human family is identical with the
history of man's conquest over matter and physical forces. And this
is clearly indicated in the incidentals contingent upon the toilsome
rise of the _genus homo_ from the earliest caveman whose status denoted
a comparatively negligible transcendence of material forces, to the
present-day man who has gained a markedly notable conquest over these
forces. Always consciousness seeks the means of adequately expressing
itself in the sensible world. And to this end it engenders faculties,
organs and processes in the bodily mechanism, and, in matter, devises
instruments of application whereupon and wherewith it may test,
analyze, combine and recombine the forces and materials it finds.
The unlimited range of expressions lying open to the consciousness
makes it necessary continually to devise higher and higher grades of
appliances to meet its needs as it expands. It will not be gainsaid
that the telescope has served actually to lay bare to the consciousness
an immeasurable realm of knowledge nor that the microscope, turning
its attention in an opposite direction, marvelously has enlarged and
enrichened our knowledge of the world about us. And similar declaration
may be made anent almost every invention, discovery and conquest which
man has made over natural phenomena. Thus, by externally applying
mechanical implements to the subject of his consciousness, man has
extended actually his consciousness, his sphere of knowledge; has
greatly enhanced its quality, and, in the process, has urged the
intellect to endeavors that have wrought its present unequaled mastery
of things. Nor have the spiritual aspects of our advance along these
lines been the least notable. For these have enjoyed the essence of all
that has been gained in the process and have, therefore, kept pace with
the onward movement of the intellectual consciousness. But heretofore
no advance has been made as a result of methodic or reflexive
determinations. That is, men did not set out from the beginning,
equipped with foreknowledge of what their efforts would bring, to
develop the present quality of human consciousness. They simply worked
on, their attention being absorbed by the problems that lay nearest and
demanded earliest consideration. So the advance has come as a resultant
of man's close application to his ever-present needs--shelter,
clothing, food, protection and other preservative measures--and it
has come naturally and inevitably and without prepense. Nevertheless,
if man, knowing what to expect from the syncretization of matter and
mind, after this fashion, should set out deliberately to accelerate
the intensification, expansion and growth of his consciousness, there
is no doubt but that the consequence would be most far-reaching and
satisfactory.
But the path that leads to this grand consummation does not lie in the
direction of diversity; it lies in the opposite direction. In vain,
then, does the intellect fractionalize in the hope that by doing so it
shall come to the solid substructure of life; in vain does the analyst
segment space into any number of parts or orders; in vain does he ask
how many and how much; for by answering none of these queries will he
find the satisfaction which he vaguely seeks.
If it be true that it is not by analysis but by synthesis that the true
norm of life, and therefore, of reality shall be found it is futile to
entertain serious hope of finding it in any other way. As a perisophism
or near-truth, then, _n_-dimensionality takes foremost rank. And this
is so for the reason that when we proceed in the direction of multiple
dimensions, that is, one dimension piled upon another dimension or
inserted between two others we are traveling in a direction which, the
more we multiply our dimensions, leads us farther and farther away from
the truth. This is a simple truism. If we take, for instance, a wooden
ball and cut it up into four quarters, and divide each one of these
quarters into eighths, into sixteenths, thirty-seconds, sixty-fourths,
etc., indefinitely, we shall have a multiplicity of parts, each one
unlike the original ball. But from no examination of the multipartite
segments can we derive anything like an adequate conception of the
original ball. Something, of course, can be learned, but not enough
to enable the rendering of a correct judgment as to the nature, size,
shape and general appearance of the ball. But this is precisely what
happens when the analyst divides space into many dimensions. He cuts
it up into _n_-dimensional parts and the more minutely he divides it
into parts the more remote will each part be in its similarity to the
original shape and form of space, and the farther away from the true
conception of the nature of space he is led thereby.
Now, _n_-dimensionality or that phase of metageometry which regards
space as being divisible into any number of dimensions or systems of
coördinates is a direct and inevitable product of that tendency of the
intellect to individuate and to singularize phenomena. Biologically
speaking, it is a peculiarity which harks back to the time when life
was manifested through the cell-colony and when the individual cells
began, because of increasing consciousness, to detach themselves
from the colony and set out for themselves, and thus each intellect
recapitulates in its _modus vivendi_ the salient tendencies of
phylogenesis. Let it suffice, then, to point out that this universal
tendency to segment and fragmentate which rigorously characterizes
intellectual operations upon every phenomenon with which it deals is a
culmination of the primordial tendency among cells to divide, inasmuch
as this phase of cell life must be the work of the kosmic intellect.
The natural inference is that from the extreme of individualization
there shall be a gradual turning, whether of the intellect _per se_
or of the intellect joined to the intuition does not matter, towards
that other extreme of _communalization_. And from this latter shall
grow up, as one of the inevitable and ineluctable tendencies of the
Thinker's consciousness a torrentious movement in human society towards
coöperation, brotherhood, mutuality and union in everything. So that
whereas in the past and at the present time the intellect has been
developing under the dominant note of individuality it will then be
coming gradually under another dominant note--_communality_. The result
of this development will be the unification of all things, and instead
of many dimensions of space, many measures of time, and a general
diversification of all phenomena, we shall come to the only true notion
of these things and realize pragmatically the true value and extent of
unity in the universe.
It is admitted that the intellect, in treating objects singly and
dealing only with the starts and stops of a movement, is withal
loyal to the kosmic order, design and purpose which have priorly
characterized manifested phenomena by segmentation. And in this
loyalty it has been following merely a natural lead which, while
admitting of the widest development and experience, nevertheless at
the same time beneficently obscures the underlying reality in order
that in its adaptation to the sensuous world the intellect might
have the greatest freedom for the development suited to the given
stage of its evolution. But in thus admitting the natural congruence
between the intellectuality and the phenomenal or sensuous we do
not thereby unite with those who already believe that this kosmic
agreement is the _ne plus ultra_ of psychogenesis. On the other
hand, it is maintained that this is merely a phase of psychogenesis
which shall be outgrown in just the same measure as other phases
have been outgrown. And notwithstanding the fact that judgments of
the intellect with respect to inter-factual relations or the ens
of facts themselves are as valid as its judicial determination of
self-consciousness, no more and no less, we are, by the very rigor
and exclusiveness of this logical necessity and inherent limitation,
led to view the intellect's interpretation of phenomena as partial
and fragmentary; for the reason that the necessitous confinement of
its understanding and interpretative powers to fact-relations quite
effectively inhibits the use of these powers for the contemplation
of the deeper causative agencies which have operated to produce the
phenomena. But it is apparent that just as the transmuted results of
other phases of psychogenesis are now being utilized as a basis for the
efficient operation of the intellect in the sensuous world, thereby
enabling the attainment of a very high mastery over matter, so will the
functional dynamism acquired by it in the pursuit and comprehension of
diversity serve well when, in later days, it has acquired the power to
deal directly with reality, to _create_ and dispose of life just as
the kosmic intellect has and is now using it in the execution of the
infinite process of _becoming_ through which creation is proceeding. It
would seem that the necessary prerequisite to the development of any
higher functional capability is that the intellect should be capable of
disposing of innumerable details, indeed the totality of kosmic detail,
before it can come wholly into the power and capacity to understand
and manipulate life. Furthermore, it appears that the acquirement of
this power quite necessarily has been delayed awaiting that time when,
dominated by the intuition, the intellect shall have attained the
requisite managerial ability for marshaling an exceedingly large number
of details.
The supreme tendency of life is expression. And this expression,
singularly enough, reaches its most perfect phenomenalization by means
of that movement which results in the multiplication of forms. Despite
the fact, therefore, that the comprehension of reality involves a
gradual turning away from the exclusive occupation of organizing a
multitude of separate and apparently unrelated facts to a monistic
view which at once recognizes the unitariness and co-originality of
all things, of life, mind and form, the intellect will need the
training and development which come from the mastery of diversity. It
is, then, not difficult to perceive the wise utilitarianism of the
present schematism of things as shown in the universal tendency in the
intellect to devote itself exclusively to parts or segments of truth.
Whenever an individual intellectuality, on account of prolonged
thought and the consequent inurement of the mind to higher and higher
vibrations of the kosmic intellect, brings itself to such a high point
of sensitiveness that it can receive so much as an intimation of some
great truth, it begins to sense, in a more or less vague way, something
of the substance and general tendence of the underlying reality of that
which foreshadows its appearance. Then, confounded by the multiformal
characteristics of kosmic truth because of the fact that it presents
itself in such numerous ways and forms, men often are induced to
attempt the reformation of all facts, or a great mass of kindred
facts, in accordance with the newly-found fact or principle. They
forget evidently that no fact in the universe can be at variance with
any other fact and still be a fact. So that in the totality of facts
every separate and distinct fact must be congruent with every other
fact forming a beautiful, harmonious and symmetrical whole; but often
the whole is made to suffer in the attempt at making it conform to the
substance of a mere intimation. Moreover, it is conceivable that even
the totality of facts may lack a rigid conformity with reality in all
its parts and that having compassed the entire mass of facts one may
fall short of the understanding of realism.
This is practically what has happened in the mind of the
metageometrician who having received an intimation as to the real
nature of space as that whose center is everywhere and yet nowhere
and whose nature is psychological and vital rather than mathematical
and logical, misses the great outstanding facts and clings to the
intimations which he experiences as to the nature of space. He,
therefore, concludes that the form of space is that of a flexure or
curve. There is a valid element in the notion of the curvature of
space but not enough of truth wholly to validate the notion. Since
the very reality of space is a matter which can be determined only
by the conformance of the consciousness with it in such a manner
as to render the conception of it entirely unintelligible to the
intellect except in so far as it may be able to identify itself with
the space-process, there is much room for the serious questioning of
the mathematic conclusion upon the grounds of its fragmentariness if
not entirely upon the basis of its invalidity. Wherefore it may be
seen that any search for either the center or the extreme outer limits
which proceeds in a manner conformable to the external indications of
the intellectual order is vain, indeed. Although it is undoubtedly
true that the attainment of a central or frontier position in space
does not involve any lineal progression whatsoever, the same being
attainable, not by progression nor by overcoming distances, but by a
subtle adjustment, yea, a sort of attachment of the consciousness to
the order of becoming which binds the appearance of space, wherever
one may be, it is nevertheless difficult and painful for the intellect
to grasp the totality of this truth at one sweep. Indeed, it is not
possible for it, alone and unaided by the intuition, to grasp it at
all. Hence, the mathematician who depends entirely upon the deliveries
of the intellect which conform, in their passage from the conceptual to
the written or spoken word, to all the rigors of mathetic requirements,
fails utterly in perceiving the magnitude of this conception and all
its connotations; he fails because his prejudices and the woof and warp
of his intellectual habits prevent his assuming a sympathetic attitude
toward it and thereby precluding at the start any calm consideration
of it. And not only is this true of the mathematician but of all those
whose endeavors are confined to the plane of purely sensuous and
logical data. It would, therefore, appear that our entire attitude
towards things spatial must be changed before we can even begin to
perceive the reality which is really the object of all researches in
this domain. But, on the surface, there is after all little difference
between the ultimate facts involved in these two totally different
conceptions. Mathematically speaking, all progression eastward would
terminate at the west, and _vice versa_; and the same would be true
regardless of the point from which progression might originate. Always
the terminus would be the opposite of the starting point. Then, too,
it might be said that if we sought the space-center we should arrive
at the circumference. The difficulty with this view is that there is
a very remote, though important, connection between it and the truth
of the matter. But the partiality of this view, and the absence of
either experience or intuition to intimate a more reasonable view,
serve effectively to buttress it as a hypothesis acceptable to many.
Thus it is ever more difficult to supplant a near-truth than it is to
gain credence for the whole truth. On the other hand, according to the
view which we maintain here, it is quite true that the seeking of the
kosmic space-center will reveal the circumference; that the search for
the nadir will uncover the zenith; the east effloresces as the west,
and a northward journey will wind up at the south, etc., but in quite a
different manner from that which the mathematician has in mind when he
postulates the curvature of space. Our view involves no space curvature
nor any other spatial distortion. _It deals with space as reality, as
a dynamic process, a flux which, like the sea, is continually casting
itself upon the shores of chaos and falling back upon itself only to
be recast against the rock-bound coast of its chaotic limits._ Now,
that which falls back upon itself and rolls in a recurrent movement
upon its own surface is _life_ which, in its recession is the natural
and kosmic limitations of itself, generates matter in all its varied
expressions. Space, in its extensity, cannot transcend life; for it is
the path which life makes in its _out-coming_, its manifestation. Of
the chaotic fringe which circumscribes the manifested universe it is
absurd to say that it is vital or psychological in any sense of these
terms. For notwithstanding the fact that out of its very substance are
engendered life, intellectuality, spatiality and materiality, it is
nevertheless none of these in its primary essence. It is Chaos-Kosmos;
because from its content the kosmos is evolved, and it still remains;
it is chaos-spatiality; chaos-materiality; chaos-intellectuality;
chaos-geometricity; because these are engendered by the movement of
life in chaos while at the same time there remains a residuum of the
chaogenetic substance which constitutes the limitations of all these
subsequent processes. In this sense, the chaogenetic fringe becomes
the limits of the manifested universe so that it would appear that all
those major processes outlined above are finite manifestations of the
eternal chaos. But none of those possibilities of motion which are
found in these major movements of the kosmos can be logically said to
exist in chaos. It is the embodiment of everything that is the opposite
of those qualities which may be found in them, that is, in materiality,
vitality, spatiality, intellectuality and geometricity.
Apropos to this phase of the discussion let us examine briefly one
of its most significant implications, both mathematical and kosmic,
which arises out of the fact that space is an engendered product of
life that is bound by the fringe of chaos which sustains and limits
it. The chaotic fringe plus manifesting kosmos constitute the absolute
magnitude of the kosmos. The manifestation factor is complemented by
the chaos factor and together the two define the _full_ universe.
Kosmogony is the universal movement of all kosmic elements or factors
in diminishing the chaotic complement and reducing it to kosmic order
or geometrism. It is undoubtedly impossible to determine mathematically
the exact volume of either complement or the ratio of the one to the
other; yet it is conceivable that the chaotic fringe is greater in
extent than the ordered portion of the kosmic uni-circle or universe.
It is even conceivable that the difference, upon the basis of the
meaning of the Pythagorean Tetragrammaton and the view outlined in the
Chapter on the "Mystery of Space," is as seven to three wherefrom the
conclusion might be drawn that the universe has yet seven complete
stages more or less of evolution before the close of the Great Cycle of
Manifestation when the fringe of chaos shall have been totally used up
in the work of creation. But for those who may experience impatience at
the infinitude of the process when viewed in this light the terms may
be reversed and the difference may be conceived as the ratio of three
to seven wherefrom the conclusion would follow that the kosmogonic
process is seven-tenths complete, as it will not vary the seeming
infinitude either way it may be determined. The notion, despite its
speculative character, offers an explanation of otherwise inexplicable
conditions, and, on account of its profound connotations, may even
be found to be productive of the highest good in its equilibrating
influence upon our mode of thinking.
In any event, there does appear to be a subtle relation subsisting
between true numbers and kosmogony. Number is a phase of the kosmogonic
movement, a measurer of the intellect and the establisher of the
geometrism of space, answering tentatively to the numericity of pure
being. In fact, being actually expresses number and number itself is an
evolution and not a thing posited once for all as a pure, invariable
form in the universe. It is, like the kosmos, in a state of becoming
and there may yet appear to our cognitive powers a whole series of new
numbers pure in itself and altogether conformable to the conditions
reigning at the time.
The symbology of the circle, in all times recognized as the true symbol
of the kosmos in eternity, of eternity itself, of the archetypal, of
space, duration and Ultimate Perfection, is replete with profound
significations. But it should be understood that the circle is a
symbol of the _perfected universe_ and not the universe in a state
of evolution. It symbolizes perfection, completion and the ultimate
union of the manifesting with the archetypal which results in the
crowning deed of Perfection. The circle is, therefore, not a symbol
of the universe as it now stands; it does not represent a snapshot
view of the kosmos but the universe as a _full_. It cannot be a _full_
until it has attained the _ne plus ultra_ of completion; for a kosmic
full is that state to be attained by the manifested kosmos upon the
termination of all the fundamental processes now in operation. But it
is this state that the circle really represents, and by virtue of which
it possesses its intrinsic qualities and also in virtue of which the
intellect recognizes these qualities. The properties of understanding
and recognizance in the intellect are veritably fixed by the _status
quo_ of the universe during every stage. That is, the focus of the
intellect, like the focus of a chromatic lens, is adjusted by the fiat
of the nature and eternal fitness of things to correspond exactly with
every state through which the kosmos itself passes. This is one of the
obvious implications of the phanerobiogenic behavior of the kosmos
and is necessarily resident in the notion of the genesis of space and
intellectuality as consubstantial and coördinate factors.
_Wherefore the more cogent is the reason for the belief that the
inherent qualities of the kosmogonic fundamentals; as, vitality,
materiality, spatiality, intellectuality and geometricity, are true
variants, and that their variability is proportional to the progress of
these major movements toward the ultimate satisfaction of the original
creative impulse._ May it not be, therefore, that the indeterminate
character of the ratio of the diameter to the circumference
(3.1415926...), is due to causes far more profound than the crudity of
our micrometers or the mere supposed fact of the circle's peculiarity?
May it not also be true that the _pi proportion_ shall become a whole
number, and in its integration, keep apace with the perfecting process
of the kosmos, diminishing, by retrogression to one or increasing, by
progression, to ten which, after all, is essentially unity, being the
perfect numeral? It is not without the utmost assurance that these
queries will be categorically questioned by the orthodox, creed-loyal,
strictly intellectual type that we sketch these implications, but it is
felt to be an urgent duty to remind all such that the most effective
barrier to realization in the field of philosophy is an intolerant
attitude towards all lines of thought which suggest the impermanence
of conditions as we find them in the kosmos at the present time. The
fact is that our lives are so distressingly short that we have neither
time nor opportunity to watch the changing moods of the kosmos nor
discern the gradual reduction of mere appearance to the firm basis of
reality, and accordingly, the intellect tenaciously clings to those
notions which it derives from the instant-exposure which the lens of
intellectual conceivability allots to it. Once the view is taken it
is immediately invested with everlastingness. This everlastingness is
then imputed to the kosmos in that particular pose, attitude or state.
Always the intellect beholds in that passing view, snatched from the
fleeting panorama of eternal duration, a picture of itself which it
mistakes for the reality of the not-self.
The inclination of the axis of the earth toward the plane of its orbit
is approximately twenty-three and one-half degrees. No well-informed
astronomer, however, doubts now the fact that this ecliptic angle
is being gradually lessened; because, as a result of centuries of
observation, it has been found to be decreasing at the rate of about
46.3 seconds per century. Yet no intellect is able to perceive in
any given lifetime the actual decrement of this angle. It is only by
careful measurements after centuries of waiting that a difference can
be discovered at all. Thus it may even be so with the ratio of the
diameter to the circumference of a circle, the only difference being
that it has not yet been determined whether there is a _decrement_ or
an _increase_ in the size of the ratio.
The _pi_ proportion is, then, a register or measurer of the slow,
measured approach of the manifesting kosmos to the standard of ultimate
perfection. Therefore, and in view of these considerations, we may not
hesitate to confirm our belief in the validity of the notion that it
actually and literally expresses the key to the evolutionary status
of kosmogony. The mathematical determination which limits it as an
unchangeable, inelastic quantity is, consequently, only partially true
and leads to the inclusion of this quantity under the category of
mathematical near-truths, for such it appears to be in spite of its
rigorous establishment.
The formal topography into which the intellect spreads when seeking the
ideal and the abstract is not a condition which is derivable from the
real essence of life or matter, but, on the other hand, is a product
of the intellect itself partaking of its nature rather than of the
nature of reality. There is, therefore, a very important distinction to
be made between all deliveries of the intellect and the realism both
of the objects and conditions to which the intellectual deliveries
pertain. One of the most marked peculiarities of the human intellect is
the fact that it always unavoidably stamps its own nature and features
upon every datum which passes through it to the consciousness. The
utmost importance attaches to this phenomenon, for the reason that
it points to the necessity of carefully scrutinizing intellectual
deliveries and the making of allowances for those ever-present
characteristics which the intellect superimposes upon its data. Perhaps
the inherent colorific quality which it imposes upon our knowledge
would be better understood if a similitude were indulged at this
juncture. The intellect may be likened to a color-bearing instrument
which, when it has once handled an object, leaves forever its own color
transfused into every cell and fiber of the object so that when the
same object is presented to the consciousness for purposes of cognition
it bears always the same peculiar marks and colorations which the
intellect, in its manipulation of it, places thereon. In this respect
the intellect may also be said to be like a potter who has but one mold
and that of a peculiar formation. Hence, whatever wares it presents to
the consciousness will invariably be found to be molded in conformity
with that particular mold. If it were possible to view reality or the
essential nature of things the difficulty which now the intellect
lays in the path of direct and uncolored cognition would be obviated;
for then there no longer would be any necessity of viewing things as
they are colored or molded by the intellect. The intuition, being a
process of pure consciousness, will, when it has arisen to a position
where it may dominate the intellect as the intellect now dominates
it, so modify this tendency which we see so ineradicably bound up in
the very nature of the intellect that the apparently insurmountable
difficulties which it has interposed between mere perception and a
direct cognitive operation will be quite completely overcome. Thus, in
the above, is discovered another obstacle which posits itself between
the notion of space as reality and the intellectual determination of
it which the mathematician examines and to which his consciousness
is necessarily limited. Furthermore, it may be perceived also how
easily the mind may be deluded into thinking that the intellectual
notion which it entertains of space is necessarily correct, when
obversely, it is simply examining a concept which has been remade by
the intellect into a form which is not at all unlike its own peculiar
nature, and therefore, as much short of reality as the intellect
itself is. Similarly, if the mathematical mind succeed in catching a
glimpse of the reality of space in the form of an intimation, which,
in itself though fragmentary, is nevertheless true, its consciousness
is finally deprived of the true validity thereof simply because of the
behavior of the intellect in its manipulation of it. The importance
of these intellectual difficulties cannot be over-estimated for they
furnish the grounds for the ineptitude of intellectual determinations
made in a sphere of motility to which the intellect is a stranger.
And this fact will appear more evident when it is perceived that
quite the entire content of human knowledge has been thoroughly
vitiated by them. So that only in those very rare moments which (in a
highly sensitive mentality) enable the intuition to gain a momentary
ascendancy over the intellect is it possible for the Thinker to catch
hold of realism itself, and project the truth of what he sees into the
lower, intellectual consciousness. But so small is that portion of our
knowledge which owes its origin to the intuition that when compared
with the totality of that which we seem to understand it is well-nigh
negligible. And then, when it is considered that at present there is
no way of conceptualizing adequately the intuitograph so as to make it
propagable the insignificance of this form of knowledge is even more
notable. It can now be seen in how large a measure the notion of the
curvature of space is merely an intellectual translation of a true
intuition into the terms of the intellect which, in the very nature
of the case, can only approximate the truth because of its colorific
habits.
A similar declaration may be made of that other datum of
metageometrical knowledge which postulates the ultimate convergence
of parallel lines. In fact, what has been said as to the perisophical
nature of the notion of space-curvature will apply with equal force
to the idea of parallel convergence since the latter is a derivative
of the former. But there is yet another consideration, apart from the
colorific influence of the intellect, which, although it partakes of
the nature of this quality, is nevertheless a near-truth of quite
a different order. This may be better understood by referring to
the _graph_ showing the inverse ratio of objective space to the
consciousness.[28] Let us suppose that the _graph_ may also represent
the Thinker's outlook into the world of spatiality. It then appears
that, because of that movement of consciousness in its pursuit of
life which, as it expands, makes the objective world to appear to be
diminished in proportion to the extent of its expansion, it is quite
natural, under such circumstances, that parallel lines drawn anywhere
in the limits of the objective world should seem to come to a point in
the ultimate extension of themselves. While this _graph_ is not meant
to depict such a view, it may be found nevertheless, to be a true
delineation of the topography of that state of mind into which the
metageometrician brings himself when he visualizes space as _curved_;
for there is no doubt but that a state of intellectual ecstasy, such
as that in which the mind of the metageometrician must be functioning
in order to perceive space in that form, is quite different from the
normal and, therefore, in need of a different topographical survey.
But, if we grant that in the creational aspects of space there is
conceivable an ever-present tendency to convolution, or a rolling back
upon itself, it is imaginable that parallel lines inscribed either upon
its surface or in its texture need not necessarily meet but maintain
their parallelism regardless of the complexity of the convolutions. The
convergence of parallel lines is much like a tangent in the outgrowth
of the idea from the notion of space-curvature. The more a tangential
line is extended the farther away from the circumference it becomes
and consequently less in agreement therewith. The more subsidiary
propositions or corollaries are multiplied the more remote from the
truth the determinations become and especially is this true of the
hypothesis of space curvature.
[28] Figure 20.
In the notion of the manifoldness of space, by virtue of which it is
conceived as existing in a series of superimposable and generable
manifolds of varying degrees of complexity, are discernible traces
of that intuitional intimation which underlies the assertion that
because of the necessary phenomenalization of reality for the purpose
of manifestation to the intellect it appears to exist in a series of
separate degrees, each one more refined and subtle than the preceding
one and requiring a more highly developed species of consciousness for
its comprehension. In other words, that intuitional glimpse of the
essential character of reality, as viewed by the human consciousness,
which impinged upon the minds of RIEMANN and BELTRAMI leading them
to postulate as a corollary proposition to space-curvature, its
manifoldness, is nothing more nor less than the intuition that the
universum of spatiality cannot otherwise present itself to the
intellect, owing to its peculiar adaptation to the sensuous, except by
a series of continuous degrees which are perceptible only in proportion
as the understanding is magnified to conform with it. After all,
however, it is not improbable that the very objectivism of the universe
in manifestation subsists in just the manner in which this intuitive
glimpse implies and that the wisdom and utilitariness of the kosmogonic
process which engendered spatiality are clearly demonstrated in that
arrangement of the contents of the kosmos which presents the grossest
elements of phenomena first to the intellect in its most impotent
state while reserving the less crass for that time when the Thinker
shall have evolved a cognitive organ adaptable to its presentations.
Those metageometricians who cling to the idea of the manifoldness of
space, based as we have shown upon the pseudo-interpretation of a
rather vague hint arising out of an unquestionably true intuition, have
allowed themselves to fall into the unconscious error of magnifying
the importance of the mere insinuation as to the space-nature to such
an extent as wholly to obscure in their own minds and in the minds of
those who think after them whatever of the true vision that may have
been grasped by them. Furthermore, it is indubitably true that that
same peculiarity of arrangement by which impalpable and invisible
forces really subtend gross matter producing that subtle schematism in
virtue of which the visible is subjoined to the invisible, the sensuous
to the non-sensuous, spirit to matter, etc., also characterizes the
appearance of spatiality to the human understanding. While there is a
superficial semblance of separate and discrete manifolds into which
space may be divided there are, in reality, no such sharp lines of
demarkation between the subtle and the gross, between the visible
and the invisible or between spirit and matter, each of these being
capable of reduction, by insensible degrees, into the other regardless
as to whether the reductional process originates on the side of the
most refined or on that of the grossest. Accordingly, there are no
reasonable grounds upon which the notion of a space-manifold may be
justified except as a metageometrical near-truth.
In addition to the foregoing, there are yet other very fundamental
considerations which would seem to debar the totality of analytical
conclusions as to the nature of space from any claim to ultimate
reliability and trustworthiness. These are _first_: the fact that
analyses are absolutely incapable of dealing with life; that being
the direct product of a sort of mechanical consistency which marks
the intellectual operations it has adaptability only for dealing
with fragments or disconnected parts, and that without any reference
whatsoever to the current of life or the flow of reality which has
produced the parts. This fact is clearly shown in that attitude of the
understanding which inevitably leads it to the declaration that a line
is an infinite series of points, a plane an infinite series of lines,
and a cube, an infinite series of planes, and so on, indefinitely.
To do this, to look upon all phenomena as a series of parts similar
to each other and piled, one upon the other, or juxtaposed in the
manner which they are discovered in the sensible world, is the natural
tendency of the intellect and this tendency finds its most facile
expression in analytics. Inadaptability of this sort is especially
observable in all problems of arithmetical analysis in which the vital
element is a factor. When these analyses are carried to their logical
conclusion, as has been shown in the chapter on "The Fourth Dimension,"
invariably they end in an evident absurdity. But it is at their very
conclusion where the life-element is encountered, where reality is
approached, that they break down. The failure of analysis, then, to
encompass life, to fit into its requirements and to satisfy its natural
outcome seems clearly to establish the basis of the perisophical
nature of the entirety of analytical claims, especially that species
of analysis which seeks the remoter fields of the conceptual for its
determinations. _Second_: the close connection which has been seen to
subsist between space and life as joint products of the same movement
makes it obvious that the same ultimate rule of interpretation must be
applied to both in order to insure correct and dependable judgments
regarding them. How different would be the intellectual attitude
towards space if it were considered in the same light as vitality,
provided one really understood anything about vitality! Moreover, as
it appears certain that the path of the intellect does not run in
the same direction as the path which life makes, but in an inverse
direction, it is clear that the judgments of the former, as to the
action and essence of the latter, must necessarily be ultimately
unreliable. It can readily be seen, however, that should the intellect
be focused so as to follow the path of life, to attach itself to the
very stream of life, it would have necessarily to neglect materiality.
And such an adjustment would, of course, obviate the need of a
material life at all for humanity. In fact, a physical life with an
intellect would be impossible under such conditions. It is well to
recognize the suitability of the present schematism and not to become
unwisely restive because of it; but it is also fitting that we should
discriminate between that which is possible for the intellect chained
to materiality and that which is impossible for it, in such a state,
when foraying in a territory foreign to its nature, and beyond its
powers to master.
The predominating tendency in the intellect to account for the
universe of life, mind and matter upon a strictly mechanical basis
is undoubtedly due to the constitution of the intellect which does
not admit of its direct consideration of the vital essence of things.
We are bound ineluctably to the surface of things. All our knowledge
is therefore superficial. We are even bound to the surface of ideas,
and cannot penetrate to the interior of these realities. Our art
is the reproductions of superfices; our philosophies are the husks
of eternalities; our religions, the habiliments of relations, and
while it cannot be doubted that this arrangement is pre-eminently
the best possible one for the present stage of man's evolution, it
is nevertheless worth while to note that it is this very restricted
activity of the intellect which shuts out from man's consciousness
those very elements about which he is most concerned when he goes into
the field of philosophy in search of a solution to his unanswerable
queries. But some progress most surely is made when the mind is
enabled to see its plight and recognize what are the difficulties and
limitations that lie in its path of ultimate attainment.
It is believed that the mechanistic, or true, character of the
intellect reached its zenith in the mind of LAGRANGE when he succeeded
in reducing the entirety of physics to certain mechanical laws and
formulæ which he embodied in his "_Mecanique Analytique_" This work
is undoubtedly the capstone of intellectual endeavors and stands
as a monument which marks the culmination of the present stage of
intellectual development. In thus placing the _Mecanique_ at the apex
of intellectual endeavors it is not thereby meant to be implied that
the intellect shall not make more progress nor that other formulæ,
equally as marvelous as those which LAGRANGE discovered, may be
devised, nor that other laws, heretofore undreamed of, may be found;
but what is maintained is the fact that while there will be growth and
development these will run along other channels, perhaps in the realm
of the intuitable, and not any longer, especially so notably as now,
in an opposite direction against the current of life and reality; and
further, that there will be a gradual turning away from mechanics to
biogenetics, from diversity to unity, from the purely intellectual
to the intuitional, and withal a final getting rid of the bonds of
illusion, of that thralldom of mechanics, whereupon will slowly arise
the obsolescence of all those disparities which may now be recognized
in our knowledge and in the applications of the intellect to the data
of the objective world.
Because the intellect is unsuited to deal with reality, and because of
its peculiar adaptation for diversity, for multiplicity, due to its
mechanistic _modus vivendi_, there has grown up a voluminous catalogue
of systems of philosophy. These embody such a multitudinous array of
beliefs, ideas, conceptions, theories and conjectures and constitute
a movement in human thought which oscillates between the empiricist
on the one hand and the transcendentalist on the other; between the
idealist and the realist, leaning sometimes towards the Platonic,
the Cartesian and the Kantian and at other times towards SPINOZA,
ARISTOTLE, SPENCER and SOCRATES, always terminating by multiplying the
number of diverse beliefs rather than unifying them that the conclusion
is unavoidable that so marked a lack of unanimity is indicative of
a profound mental prestriction. It was, therefore, inevitable that
mathematics should fall under the same spell and brook no let nor
hindrance until it had succeeded in devising several diverse systems
of geometry which it has done for the mere joy of doing something, of
following its instinctive aptitudes. There is no other basis for the
heterogeneity of our philosophies, our mathematics, indeed our beliefs
than this mechanical, and hence, radically illusionary character of the
intellect in consequence of which we have had to be satisfied with mere
glimpses, hints, intimations and faint glimmerings of reality, of life,
and of those kosmic movements which, if we had the ability to trace
them from their source outward, would lead us unerringly to a truer and
deeper knowledge of those things that under the present schematism must
remain for us a closed book.
The criterion of truth for us, constituted as we are and wedged
in between the stream of life and its shore of materiality, must
be that which relates our knowledge both to the stream and to the
shore. It must be so that all predicates which purport to approach
it shall exhibit a dual reference--one that relates to materiality
and another that relates to vitality, and yet a third that shall
combine these two relations into one. All assertions, therefore, which
pertain exclusively to either of these elements--to materiality or to
life--are necessarily partial, fragmentary and perisophical in nature.
Mathematics, because it relates to matter and the mechanical forces set
up by matter acting against matter cannot be said to agree with such
a criterion; art, because it relates to snapshots or static views of
matter is even more remote in its agreement; philosophy, as it has been
known in the past and is known to-day, because it seeks to deal with
a vitality fashioned after the image of materiality has failed when
posited alongside of this criterion; and thus, the intellectual toil of
millions of years has been in vain in so far as it has not succeeded
even in raising a corner of the cover which hides reality from our view.
A near-truth is any variation from this standard, this norm or
criterion. It may be either logical, cognitive, scientific or even
metaphysical. To define: a logical truth is a predicate based upon
and involving the coherency and consistency of thoughts themselves; a
cognitive truth is the conformity of knowledge with so much of reality
as is known; scientific truth is the conformity of thoughts to things
and conditions. All of these are obviously near-truths. Then, too, a
near-truth may be defined as an assertion based upon the criterion of
truth but falling within the category of cognitive truths owing to
insufficiency of data or vision. Such indeed are those metageometrical
predicates--_n_-dimensionality, space-flexure, space-manifoldness and
all other assertions based upon these in general and specifically. Any
recognition of truth must clearly embrace both the vital and material
aspects of its subject in order to be adequately inclusive, that is, it
should include the causative, the sustentative, the relational and the
developmental factors. These four factors are considered necessary and
sufficient to determine the conformity of any view to the criterion of
truth for when we are cognizant of the cause of a subject, understand
the sustentative factors which keep it in existence, are conversant
with its relations to other subjects and can follow its developmental
variations until we come to its final status, why then, our knowledge
is both sufficient and ultimate so far as that subject is concerned.
Is it asking too much of mathematics or of philosophy or any system of
thought that it conform to these standards or to this criterion before
we shall accept it as final? Or shall we be satisfied with less than
this? Let us hope not.
In the foregoing presentation stress has been placed upon the
fragmentary, and therefore, illusionary character of the intellect in
order to arrive at an understanding of the difficulties under which
real knowledge has to be acquired and to indicate the inanity of all
attempts to resolve the riddle of space by means of mathematics though
regarded as the most typical exemplification of the mechanistic nature
of the intellect. And further, to show that, on account of the radical
incongruity which estranges life, the producer of spatiality, from the
intellect which returns again to scrutinize the passage of life in
its outward expressions, no hope of ever gaining the true viewpoint
by means of the intellect need be entertained. But in doing so, it is
deemed fitting that a note of warning should be sounded against any
abortive attempts that may be made to obscure or distort the results of
such a close discrimination lest the true import of the examination be
lost for, if we emphasize the vanity of the intellect in the pursuit of
that which it is by nature unsuited to attain we also equally stress
the wise utilitarianism which limits it to the performance of the
tasks assigned while at the same time reserving for the function of
more highly evolved powers, and indeed, for the intuition itself, the
solution of the riddle of spatiality. And if we declare the futility
of the mathematical method in all endeavors aimed at unveiling the
mysteries of life and mind, and of that movement which has its roots
set in eternal duration from which it proceeds in an endless continuity
of purpose and promise, we do also recognize that in the science of
mathematics the intellect shall, as in no other method of cognition,
most fully fulfill the kosmic intent of its existence; and moreover, in
the pursuit thereof it shall push the frontiers of its possibilities
outward until it can be said almost to be able to make disposition of
life itself--at least to that point where, when the intuition shall
have come into its own, the passage from the mechanics of matter to the
dynamics of life, shall be comparatively easy and natural.