The Mystery of Space

New Percept

ers of Perception and the Possibility of Attainment-The Influence and Place of the Pituitary Body and the Pineal Gland in the Evolution of Additional Faculties-Th

ntal conditions. But no sooner than agreement has been attained under one set of conditions new conditions arise and require a new setting, new adaptative movements. Thus there is a continuous proceeding from stage to stage, going from the grossest to the subtlest and most refined, always the form is being pushed onward and upward by life. But adaptation is not undergone for the benefit of the form, but more truly for the informing principle. It is the progression of the life-element which constitutes the adaptation of form to form and to their peculiar environs. The form is a tool or instrument of life which it discards the moment it fails to respond to its requirements. Thus forms are constantly being assumed and as constantly being relinquished. But no effort of life is lost regardless as to whether the action is performed in o

cies; the third great undulation in the current of life effects the endowment of the world-plasm with those tendencies that are to build around themselves forms appropriate to their fulfillment. This ensoulment of the world-plasm with tendencies and the consequent segmentation of it into separate forms by these tendencies constitute the primary stag

radistinction to the relative unpliability of matter, and due also to the fact that life is kinetic and matter, being a mere deposit of life, is static. Life is mobility while matter is immobility and thus in possessing a greater range of freedom is, of course, correspondingly superior; but in this adaptation of itself to the labyrinthine cavities and multiformed interstices in matter it exhibits but a seeming serfdom which is really not a serfdom but a mastery. It is as if a man had taken lumber, hardware and stone and built a house wherein he might dwell-life has merely used matter, molded and fashioned it so as to make for itself a medium, a dwelling-place wher

y of life's operations will have upon humanity or the form which it ensouls as the human organism. For it is impossible that humanity shall escape either the general or the specific results of the exalting power which life exerts over materiality and its appurtenances. It is, of course, impossible here to go into the various implications of this general forward movement of the universum of mate

scope of motility is achieved by humanity there is always found a set of kosmic conditions which answers thereto. The cardinal principles of the doctrine of evolution are not, therefore, adverse to the conclusion that the organs of sense-perception-hearing, touch, sight, taste and smell-have not been endowed upon the human race or attained by it at one time; but rather that each answering to a newly acquired need and opening a wider scope of motility for the intellect has been evolved separately and in due order. It would also seem that the quality of consciousness, as it has been manifested in the various stages of life through which it has passed, and especially the mineral, vegetal and lower animal, has not always been of the same degree of efficiency. Nor has it enjoyed the same kind of freedom which it now enjoys in the highly evolved genus homo. It is equally apparent that matter itself has not always been in possession of the same qualities and characteristics which it now exhibits; but that it, too, has gone through various stages of evolution bringing forward into each new stage the transmuted results of each preceding one as a basis for further evolution and expansion. The innumerabl

ossible co?rdination and co?peration. Accordingly, notwithstanding the fact that materiality must possess in potentiality all the qualities which it will at any time reveal, it is nevertheless necessary that these qualities shall come forth gradually and in due order. Similarly, humanity has come into possession of its various faculties of mind, and powers of physiological functions, by insensible degrees, the higher always being held in abeyance until the lower is fully developed. Those faculties which are to bestow added powers, additional freedom and a greater scope of motility are the ones which appear later than those which are truly primitive in character. These facts have been amply demonstrated by the science of embryology wherein it is shown t

re at work to-day processes which in the future shall culminate in the evolution of newer, higher and more complicately organized species of plants, animals and minerals. Every year brings fresh evidences that crystallize the conviction that the earth has been the scene for the appearance of many strange orders of animal life. Fossiliferous strata are

hich we have only to witness the marvelous strides already made in the discovery of radio-active substances, the Roentgen, Becquerel, Leonard and other kinds of rays. It Is quite confidently believed that these forward movements in every branch of intellectual pursuit, these combined efforts of the intellect, in peering into the occult side of material things, are in response to the evolutionary needs of the Thinker, and in addition, are the evidences, and shall in time be the cause, of the development of an additional set of faculties. Function, or the performance of acts, determines faculty or the power of action and ultimate

to be wondered at that the voice of the prophet is heard and respected throughout the earth; for, indeed the mathematician is a spokesman who, as a rule, is unmoved by sudden outbursts of passion and ecstatic frenzies of emotions but calmly and dispassionately verifies his conclusions, tests them for consistency and having found them to satisfy the most rigorous mathetic requirements hesitates not to propound them. For this cause humanity respects the mathematician, and when he speaks listens to his voice. It is well, too, that this is so; f

point where it encounters life it fails, it becomes confused and its dictatorship becomes a mockery, its decrees remain unexecuted and futile. In taking this view we have certainly no desire to offend the mathematician or to detract from the glory of his monarchistic rulership over the intellectual progress of the r

btedly the time will come when it, too, shall reward the Thinker's labors with that which shall be more precious than the crown of gold which the intellect has won. Then, the intellect, grown old and decrepit with years of reigning shall become dim and crystal-shaped and finally pass into automatism or reflexive movements where without the urge of volitional impulses it will perform with exactness, precision and utter

ater which we drink and in the air which we breathe; and if our ears could detect the microphonic vibrations which register in the delicate apparatus of some microphones the dead, vacuum-stillness of nature's great silences would appear as a babel of voices by the seaside. The sense of touch, responding to the same range of vibrations as the micrometer, would reveal actually the interstices between particles of the densest elements; and gold, silver, platinum and mercury would seem but honeycombs of matter. But, to the forward-looking there is no element of absurdity in the expectation that all these senses shall, one day, be able to dispense with the artificial aid of physical apparatus and perform, with even greater precision and faithfulness, the task which t

eir fetters. Sir Oliver Lodge, in his book, the Survival of Man,[29] says: "Man's outlook upon the universe is entering upon a new phase. Simultaneously with the beginning of a revolutionary increase in his powers of physical locomotion-which will soon be extended to a third dimension and no longer limited to a solid or liquid surface-his power of

clusions which Sir Oliver Lodge expresses in the above, and thus to satisfy his own mind that the process by whic

cont

n places, and like excavators engaged in boring a tunnel from opposite ends amid the roar of water and other n

le that these acuter senses, these new faculties are now existing in the human race in a rudimentary stage and are designed to become the universal possession of all. That this is to be the almost immediate outcome of the perpetual exalting power which life exercises not alone over materiality but over human organs and faculties as well, seems to be the one big, outstanding implication of the evolutionary process. The presence of such functions as the ability to sense the invisible and the inaudible, to answer to vibrations far subtler than anything in the scope of our external sense-organs, certainly indicates the existence of rudimentary faculties which make these functions possible. Back of these vague, indefinite functions, back of every supernormal or abnormal manifestation of man's mentality and back of all that class of phenomena which take their rise out of supersensuous areas must lie, in ever increasing potency, faculties and organs, however rudimentary, which are the source of these manifestations. Life, that ineluctable agent of creation, which is incessantly pushing outward the confines of the intellect's scope of motility, never wearying, never tiring nor sleeping, has long ago, in the dim and distant past of man's evolution, laid the foundations; and in fact, with one stroke of its creative hand, has molded the organs which are to become the active media of these new faculties. And now, these incipient demonstrations, these infantile struggles which we see now and again outputting from them, are but the specializing processes through which, in their later development, these organs are proceeding. These are the outward signs which should tell us that life is breaking up these organs into special parts, assigning to each a certain division of labor and making of each a perfect co?rdinate of all the others. It is, by these very dispread exhibitions, cutting up, special

drigemina. It is otherwise known as the "conarium" the "pinus" or "epiphysis." Situated at the base of the brain, it is held in position by a fold of the pia mater while its base is connected with the cerebrum by two pedicles. It contains amylaceous and gritty, calcareous particles constituting the brain sand. There are, however, marked structural resemblances between the pineal gland and the pituitary body and their formation is perhaps the most interesting feature of the development of the thalamencephalon or mid-brain. The hypophysis cerebri or pituitary body is a small, ovoid, pale, reddish mass varying in weight from five to ten grains and situated at the basal extremity of the brain in a depression of the cranium known as the sella turcica, a configuration very much like a Turkish saddle in shape. It is a composite, ductless gland and consists of two divisions, an anterior and a posterior, connected by an intermedial portion-all of which are at

umnar epithelium and contains numerous racemose glands for the secretion of mucous or pituita. It is also vascular and the veins which ramify it have a plexiform or net-work like arrangement. It divides into two membranes-a respiratory, which is concerned in breathing, and an olfactory region. The respiratory re

and even speedy death. Hypertrophy of the gland is directly associated with certain diseases, such as giantism and acromegaly. The latter is a disease which causes a general enlargement of the bones of the head, feet and hands, usually occurring between the ages of twenty and forty years, and most frequently in females. The fact that these diseases are so closely associated with a hypertrophic condition of the pituitary gland has led to the conclusion that perhaps the giants or Cyclops of ancient times were cases of giantism or acromegaly. This view, while interesting from t

ich while it may also be verified will not be found so easy of verification as the above-mentioned physiological facts, and not by the same means; yet they are nevertheless deserving of a place here. It is th

nd more pronounced. The pituitary body is the energizer of the pineal gland and, as its pulsating arc rises more and more until it contacts the pineal gland, it awakens and arouses it into a renewed activity in much the same manner as current electricity excites nervous tissue. When the pineal gland is thus aroused clairvoyant perception is said to become possible. These are facts which cannot be proved by the materialistic man of science nor can they be demonstrated to the layman who has to depend alone upon sense-deliveries for his knowledge. This is true for the reason that, in the first place, it is n

cope nor microphone; in sheer vanity is he adjured to look within-into the interior of life, of mind and the things which he handles with his instruments-for the answers to his queries, for the path which leads into the wake of life and consciousness. Because his utter loyalty and devotion to the modus vivendi of the intellect will not permit this; but, after all, it is not wholly wise to allure him away unbetimes from his search after truth through superficialities nor to inveigle him into giving up his tenacious prosecution of the physically determinable. We would not have it so; for, perchance, he, too, one fine day, in the quiet of his laboratory shall come upon the data which may substantiate i

ed in the mid-brain, safely secluded from all external interference, they are naturally limited to stimuli which come from within, or it may be said, they are responsive to excitations that are more spiritual than those which come through the external sense-organs. If, as has been said they control the internal processes of metabolism (anabolism and katabolism), oxygenation, nutrition, and other important internal movements, none of which can be said to be under the control of the intellect, is it not, therefore, justly assumed that their response is directed towards stimuli which arise interiorly or upon a plane higher than the intellectual? It is a matter of scientific knowledge that those persons gifted with clairvoyance, and commonly known as "sensitives" are far more responsive to nervous excitation than those who are not so gifted. This would seem to imply that, on account of the superactivity of these two organs, t

gans, it must be apparent that these manifestations are apprehended by a perceptual mechanism which is entirely independent of external sense presentations but which is an interior and subtler form of psychic activity. Sounds which are heard by so-called "sensitives" and objects which are perceived by e

ys Paul Carus,[32] "and describe all the characteristics of four-dimensional space, so long as we remain in the realm of abstract thought and do not venture to make use of our motility and execute our plans in an actualized construction of motion; but as soon as we make an a priori construction of the scope of our motility, we find out the incompatibility of the whole scheme." Thus mathematicians are forced to relinquish all hopes of transforming the world of life into a sort of four-space dwelling place where everything is done according to the laws of mathematics. But whether they shall accept it or not there is a wider, truer and more rational view which recognizes all metageometrical investigations, as well as all kindred phenomena, as universal evidences indeed, as the very causes which, in the future humanity, will actually awaken and cause to be accelerated in their development these little inner sense-organs, the pineal gland and the pituitary body, whose perfect development promises to provide for the Thinker's consciousness an avenue of expression such as humanity has possessed never before. And too, it is not without full knowledge of the fact that it has been customary, among certain scientists or perhaps all of them, to regard these bodies, at least the pineal gland, as vestigal organs belonging to the past of human evolution, that we make these assertions. Yet, as man proceeds in the perfection of mechanical science, in the development of instruments of precision that aid his external senses, responds more and more to the subtle vibrations teeming everywhere in the atmosphere about him, and comes, in the course of time, naturally to possess a more sensitively keyed nervous mechanism, a finer body and higher spiritual aspirations, there will be a corresponding widening of his scope of vision and

his appliances, perceiving the innermost realities of things and processes? What if it were possible for him, with these added powers, to see and examine without the aid of the magnifying lens the electron, the atom and the molecule? What if the cell, the bacterium, and other invisible forms of life would then deliver up their secrets to his knowing mind? What if he could sense with his own inner vision, the ul

will man rise higher, driven on by the current of life with the mass of materiality, to a point of complete spiritualization

e forms of labor which are so exacting as to leave him no time for the development of his higher powers into the hands of machinery. He will not be free until he has done this well-nigh completely. This is the task of the intellect

nd will use the language of the intuition-direct and instantaneous cognition. Philosophy will be regenerated, re-created. Speculation will give way to truth and there shall be but one philosophy and that shall be the knowledge of the real. Mathematics, the royal insignia of the intellectual life, because it can deal only with immobilities, with segments and parts and has no aptitude for the continuous flow, will yield its kingdom to a higher form of kinetics which will serve the intuitive faculty as mathematics now serve the intellect. S

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F., On Space of

ence, Vol. VIII (1

N

es held in, until lower

on kept i

the inaudible and

no room fo

t, invigorating

s, realizin

sis inevitably e

cs, math

egaly

tic, of the in

, of life on

s physical and chemi

ical world pushed over

ceptible to the

lity of

matical l

n, purpos

made by an o

m bestowed by hig

zones of

etative, intell

an, of the T

ing, life

ion, life

Egyptian

f psychog

different, from

antities and

of the rules

, of scientifi

f space-ge

geomet

nd to the laws of

to popularize the

between two processe

able of dealin

fold, the

anufacture of the

onformity of the n

echanical origin of

cal nature

pace, a curi

urth dimensio

of consci

e senses to

nsciousness

idean geo

of the de

man's per

ssalage of

dynamic, spa

erialistic, of

life against

es of mater

ori,

owledg

ness, 1

he principle

he common mensurat

ical evid

imed

totl

he contents of t

criterion

er conscio

ew faculties in

mathetic con

ns, categ

ed upon, disadv

ent, 224

end of evolutio

nsciousness to the o

iculty of, by the in

e-conscio

need of a mo

things s

tes that transcend

pulsat

the intellec

opened to inner per

culty of awareness

body and the p

, general res

eterminant of

the existence of

rees

symbol of a mo

ress i

s sphere o

tze

o the Thinker's

om determined b

ndless laby

os, in a s

order

, infinit

rel ra

ation of conscio

hekot

interiori

mericity

co-extensive w

discar

ugenio, 1-2

the mani

e pseudosp

of matter by

eometry as i

new realitie

he min

assage from me

o, from mec

urth dimension

and the el

s, 2-3, 46,

of a hype

he physi

sciousnes

dards

endencies of the Think

te of the i

formal, of g

sensible wor

n four-dimensi

tageometr

n spa

sentation of the

3-4, 5

as a performan

lony, 2

as an aposteriori

, pykno

ometric, the

conclusions, p

iod of involu

ny, 23

ion of chaos

boratory

eny, define

s egg-pl

tion o

nt of li

res o

eometri

llectua

eriali

tialit

osmos, 215

ph symbolizing

niverse, fixed by

changes in the,

nsional, of t

r, fall into zone

uclidean s

etween the real

tive, and the our

d, of creativ

ance of process

he symbol

sed, our inte

udienc

voyan

nt percep

ing, of metag

hristoph,

ford

or systematizing

stantaneous,

ies of di

ethod o

intuitive,

e for systema

quality, dim

onsciousne

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um, th

y and evoluti

te range

of, derived from s

as a sh

ace, gradual

n and awa

d upon prior

he, of the m

bolic, dependenc

and the Th

tograms

pendent upon sen

the percep

elated to the

d mathema

ization, t

ependent upon evo

hetic, complex d

nto shape by th

ween intellect and t

between concepts

aced out between re

ality of

d kosmos, graph

ter of the sen

ake of

time

larity

riori

of, and ju

a sca

to ultimate

nant of dim

life

able qua

, to the order

, and dim

rees

the validity o

ution

ion of,

ended

us of

nd the planes o

ntary vi

, in the gen

tation

r, and

anes o

ory of

ion of, with

itiona

entire range of

s of,

Elysian fi

primitive

of, 18

hics o

e sensuous to th

truths from d

orld as inst

ation of notions

ed inw

on of the s

l, of man

es, the sc

mathematical,

ncy, kos

yperspatial

erion of g

nsistenc

etrician cur

lized, cannot be o

the mea

traffick

intellectuality and

f the psychi

mathetic, the

of paralle

ions, du

as spatial de

pace, 94, 9

ms of,

ee, 1

f ideas and

quadrige

orbits of pa

signific

pregnated sc

he, of the i

try as consistency

ruth,

kes,

ccession of

tion of

strate

enerati

energy spent in elabora

s component in the f

the doctrine of, for

lement in the

measur

and metageome

bert,

te,

win

Great K

illy

rth dimension

e intel

rical ratio to the circ

ul, of kosmi

, apotheos

trary determ

ificatio

of reali

basic ide

reality and phanta

s of li

arte

ut in material

er to dispose of

l, the necessity of, inher

ors of con

eriod of mental

he intuitive fac

ics of

io of, to the cir

ween concept a

atical and perce

eal and the actu

al, among

agining the four

ating an in

e acquisition of r

ace, the log

metageometr

tinct stage in p

of space me

analys

embert,

on of a tart

itrary cont

mblage of

rectio

exte

the surface o

spac

definition

gitimate an

d by consci

xplain spiri

on of the

directio

of all tr

le to actu

n-Euclidean

of a plane

f material ma

a prio

existence of

ty, and the

on the will of th

nception of, purel

fficulties w

ceptual

e, the f

no basis in cons

pon one a

f segmenting spa

n as dim

with the sensib

rical, as excrescences

lt of methodic r

e edict of,

ess, the fr

he intellect by t

ties, beset

nceptual and perceptual

of the fragmentative

sfinite q

e of, won by t

se of evol

ned, 6; 128,

ciousn

non, 2

meanin

sis, 208

in the evolut

n and s

erna

arance, spac

he intellect,

nebulous yo

new,

oresces a

the

percep

overei

s dependen

atment

sych

y of self-con

fine

red to chop

h-place of

nloh

of the non-Euclid

tal develo

evolution

non-Euclidean

and blind

on ether as four

direct co

ment of

of the worl

ce, and the phenom

formation of th

of consciou

artificial an

sis, t

cribed by hyperspat

ental, as wor

fourth dimensional

ast in a n

46, 70

parallel-p

ying elem

cal, exemplifies int

ty of frag

continuous

norms of r

elemen

cement o

l, forward mo

vicissitud

f, gover

, result

chronous with evolu

aracteristics o

time requi

on of the f

f matter int

w perceptive e

higher plane,

ative testimony of,

and conce

patial, system

pace as an u

y, degraded int

matical, and the fo

Roentgen

-mas

nscious deter

e criterion o

facets of

ts to re

s symboli

modele

dual deriva

ous with evolution of ma

ended

by the hyperd

n must win h

evidenced by f

ary nature

source

the intell

issible cha

ned by fu

ly exte

han the in

self-conscio

uitiv

ion in highe

s, the awake

ed by the in

ion in highe

ry conditio

utcropping

stify the objective exis

the parallel-postula

ssessed by k

atheti

hne

nboundedness

, Camille,

property of

space a

nse objects and ideal

ference between memory i

onsciousne

intell

e creation of

ative en

eato

c ener

vehicle o

nition

ver the path of

not exist i

dealty

erse not a

od of mental d

Euclidean g

different alcoh

ality, justifi

curiosity of

Riem

ivertise

ss does not a

ce of, de

t of matt

, glibly pro

e, 8

nizens

main o

tudy

logies to po

, analogical rea

scendental

ude of the i

rrent as a co

ability

Newcom

of the intelle

view of the

ion, tende

k to cell-d

m, a n

by absence

ematic

ntal

ing for th

usness in ge

eedom of t

degree

le, for the

haogeneti

orderlin

thekos

chau

universe

etermines

latent faculties

and histo

stinctive, of t

, totality o

f reali

reness as

Frederick, 8-

or of the non-Euc

of Rhode

, as propert

space, Key

ce by l

the, of the

ypertetrah

f space, 2

h, its nebul

form

nsible w

eedom of consc

trici

based upon a negation of

e poss

, engender

ished by

trism, establi

tent

ometrism of

ed by the in

the basis

anti-Euc

y of magnitude

ficial

wo-fo

kdown

period of the no

e system

s Element

bulwark

ry Geomet

al geom

the divine g

le syste

essence

, at variance with the

pon a misco

by qualitative

ative peri

ublished tr

tive peri

inal issu

and develop

lidation

key

n-Euclidean ge

arization

kart's tre

consisten

elements

ceptual know

non-Lege

d commensurabl

corresponden

, continui

tism

f the reality

ion of the

formation, di

to a new dom

een manifestation and

of, mastered

B., note, 49,

, Max,

oltz,

he concrete, the

, C. H

ourth dime

mind, three great

, the, of r

, J.,

son

exalting power

ndaries of, an

eration o

as a prophecy of

space

t to the in

re of arriving at a recogn

assage thit

figurative mou

ovement

powerful so

lized cons

e of new fa

es fatu

llusi

higher consc

s an evolutiona

ed with re

tion o

borative testimony

baffling to ma

a sign of ment

f, a fairy

of, the non

s hiding pl

l difficulti

x pillar

as the toys of

rahedron

of the pitui

lume, t

, a superf

e, utility

admissibil

ty of the non-E

manni

on of, B

he logical difficultie

examination

real, kosmic ch

al value o

ords as sym

ranche

ism of

ymbolis

f consciousness

objects of

things-in-th

i and hyper

of plane-rota

tesser

ity of, recoi

the fourth dime

emises of, the

lane-rotation, the

symbolism of, n

action of the origi

ty of reality to

fe estranged by

al as sp

lectual determinati

eted in the terms

s of unity, n

as a pr

ecomin

allels through

a capital i

oncept

te dread

ativity

f abstract

non-Euclidean

Grang

intell

bulum,

ns of perc

e, realities

of the geome

osure and i

lect likened to a

ement of the pas

ess, the sensib

, form a

ractional part

s domination of

ion with the s

opograp

atiali

eposits o

ut by life in m

m of Sensat

tant-expo

itive facu

ze of div

-bearing ins

earchli

fashioner of ph

of the con

erpretative

tism of,

seize l

y a diadem

by the int

d for matt

the grooves

e as a monu

ield of vi

for starts and

e tendency to

termined by m

r individu

ceaselessness

f, its influence

nstituti

and mode

ocus

lusion

nary charac

nsibility of r

tive functi

gments

oods

ating tenden

fic tendenc

f, against dis

deal with re

ality and

ity, consub

extensive with spatial

source

r makes hi

and automat

nker as a

ligence and the deg

osmic, of the

here of our, as c

, the gr

ity of b

andards of, vary as co

s of mater

and brothe

unalizat

dle of spat

ssor of the i

served by ma

by the int

abeyance

tion of the

nt of a spatial

ympathetic atti

of the devel

l consciou

ity of, over t

nd the lead

Thin

bile and f

eptualizat

mility

ture o

ms, as con

ntacting the egopsychic con

er-conce

ulty of tran

vaunted, of the l

s, psycho

geometrical, and the

antithesis of e

involut

matte

ovement

stages o

reation

of a hydro

priori, Ka

aculty a pr

s of aff

replica of co

be predicated upon fra

e intel

ening of e

ore at variance with t

thesis

ments long d

ower of math

multi-dimensional

-dimensio

sense-deliveries

ce of the fourt

5, 181,

aculty of t

ea of sp

on the hyperspac

ature of t

as an intu

kos,

chaos

Chaos-Theos-

ology

sis, no

ty, fring

ound coa

ficance

c conscio

riod

of nature, the four

ackson, and freed

ude of metageo

imensiona

imensionality

ability of hy

lix, 12,

, all, re

certitude of th

ric o

cal nature

lm of, laid bare b

atical, apriority

non-Euclidean, s

iculties of

m of life and to the s

degrees ex

ere o

atizatio

sciousness as a

cation

the latent geo

cope

eter,

ciousness, graph

s of the cont

ate of be

itude

ds of

the consist

Cosm

n the tuitional and the in

labors, signi

, Joseph

-3, 32

he parallel-p

rt, J

theory of pa

the pass

ndre

tz' di

rd ra

matic, permiss

ophus,

nsformation

incapable of de

ciousness

ted in pykno

ourth dim

ude of mathem

wer to c

t of crea

ative a

pressi

of material

gencies in pr

as engenderi

f, and the i

y a radical i

r of, and human

on of its

of, 2

an instrum

ibable si

ive actio

has no aptit

ive, val

fe of the T

ollowed by i

ixed by consci

facts of, a

admits of endle

ment of ch

sage

hrough spat

to manip

nt moveme

ty of eg

s in the cur

ueness

nd conscious

olutionary res

ream, t

d, and the four

ness as a s

ars and

here of, consc

enerating

aight, a

inciple runs back t

cularity of, in

ki, 55, 6

r Oliver,

s archi

ional for

ta o

ws in the grooves

wer of, over

allowabili

he game

olism of

he limits o

ng of

of bein

iousnes

tive,

e, 2

enz

, Mart

geometry, a

ous, of hyp

c consciou

e, N., 222

and non-mani

nite, though

red by the

, 61-

al manifoldnesses, as

ntional cons

intuiti

, as a nea

ng, 8

s in the fourt

a, 213, 2

and involutio

ogic as

ini, of l

life over

ensible wo

as a deposit

tial with spat

g spatial

teristic

ed by kosm

derment

ative with sp

stices

lect

ity, sho

d into spir

ns and the d

ions of consc

nomenal w

rophet

ed by hum

ds of ma

inant of the quality

riterion of

intent of the

ymbolo

lidea

it encounte

titude for

yielded to k

judicative powe

rthodox

d conception

e intellect in

nition

origin of four

ds o

ous doma

bmissive to laws o

emblems of kos

d of,

nd, syncretiz

of life a

posit of

ycombs

morphosed b

s wedded

of, in four

of, and fa

planes

ion of, as end

cted upon by tot

f, with s

ersum

remonials of

, as property

hyperspaces, th

ce determined by

ms of s

ce, n-dimension

Analytique

he passage from, to th

tics, the pa

from, to bioge

octrine of, due

red in the om

s god

n, determinativ

ative peri

tive peri

er mysteries o

out-feelings

nciple of

adaptation of p

raph,

intellectual co

and his envir

stigations and the n

cians and hy

otation about

curved s

rth dimen

the mysteries

e direction of

mma of

sense-d

n the atti

al obliqui

thought

dealized cons

, as a stepp

fine

, the fat

fabric

s of matter

monopyk

stage of spa

eserves of, usurped b

um of kosmic cons

of the

he ample explicatio

c consciou

f, to the evolution

om from con

ms of physical

new fr

cle of li

ed to ma

m of, and

ntial with

of the k

of, and conc

he duo

t attained simu

uence of hypers

s progeni

pochs of the hi

the limitat

y of, with

quintopyknon as th

e, and the hy

y, life

our-dimensional

se of evolu

man, the gul

on, the,

, defined, 1

ties, mat

the kos

eny, 13

the creati

the scop

rward, in kn

as an evolu

nce of Kan

fe in c

uality of space, ju

ion of hypo

uition as prom

er, of creativ

ow-lying pl

ife and

and the four-sp

revelation of, foresh

eactio

s copes of consciousn

dinate

y, as a phase o

of intellec

of concept

le with percep

ification

hat the intellect

tes conce

mperceptib

Eddin,

mbols, ide

esentative,

um-stillne

consciousness r

ruth,

from criterio

n partial k

urvature

manifold

osity

a bulwark of

body,

ogra

e Thinker's sc

cal communi

Simon,

ur-dimensional

fourth di

and the meaning

as they act

emma

g of the

s obtain

as antithesis of

nifestat

ncement of human

, cut off from

e assigned by t

ness as a,

found by sy

atural ge

inant, of com

ple presentations to

phase of kosm

infinitesimal

ty of be

and idea

into the fourt

ification of cons

ptual, of metage

ism, math

and the sc

syche

f kosmic cons

d factor of

fine

presented by

pitulates phy

difference between,

discovered by th

fiat o

otality

lines

d by function to

by life into sp

volutio

of mathe

new adjus

f the Thinker,

iritualization

, a hie

te and the surfa

non-Euclidea

ed by Eu

Lobach

- Mann

to demonstr

lements of

ri's pro

, converg

, through a g

at infi

ory o

echanics to bi

anics to dy

space to four

tic contri

pace,

ife, sinuosi

e intellect, r

maton of

n the Thinker, t

in of, and the s

organs

d by conc

, and th

aomorphoge

minativ

hekot

nature of ana

phism,

f mathetic licen

cularity

in the four

ty, line of demark

world

-ideal,

world age, ev

plain, on the basis of t

by the int

y interpreta

hod of appre

amply explained by sc

he inverse of

the criterion

eration

and zones of

he unilluminated pool of sense-c

and onto

nted in o

diment of all po

as space-act

the princip

of the b

n, significa

n space-cur

rgized by the pit

he, 3

vestigal

ening, general r

ody and the

n organ,

M. Sajou

ertroph

cation

he, 3

enerating e

into the fourth

ears to be di

about a,

planes of

e as a succes

mic, striv

ychi

ferentiat

to,

ivine geome

ow conscio

as geomet

idea

us, of the i

space

iverse a

cair

y of parallels th

rating el

tion o

of points,

n concrete and

as property o

of the fourth

-Euclidean g

n the world of

pace, the m

ems, the multi

attained at one an

aya,

mic quie

atical, not justified

, ensouli

vention of, and the la

h dimension as a t

ved, of arriving at

lution a con

as a dyn

clu

kosmic, and

ward terminates

tion about a

ntuitographs, di

metric, subjuncti

and the shape

Beltrami's c

ature o

f consciou

nsmut

sis, alche

smic

the printing

is, mind's

wn phase

ding fact

eny, de

y, 45,

athematical, and

n-Euclid

kosmic pri

of space-g

osis

volution

morphotic p

processes

nsion as comm

raic, cannot repr

ciousness as a

dim, 1

mensiona

knosis,

inciple as basis o

opykn

is and the a

g of, 17

inciple as basis

ity to evol

lenden

-Tama

Yoga

when unsanctioned

as a mys

er as a par

its degree

e Thin

lif

ess as touch

tion inverse to the

eneity

nary natu

ite gam

d the states of

f, bewilders

thematical

and the sens

main of ma

gical qual

thread

ensional sc

bstractioniz

sible to the

st, of th

ve way to g

symbolis

ent to beings on

n convention

rsensu

ife and consc

he cognition o

ension of

rent

ed as l

ow o

g stream

of presentin

contact

scrutable q

cured

-space glibly

ead o

ersum

supersen

fe and consciou

consciousness a

fest and the

images upo

lopment of the

of all kn

and rea

hanges

exhibited to t

oods by the i

ousness as basis

suous, compared wit

ovement in the

sychic, of e

the unexpl

nal impre

iality and the

. B., 18, 19,

imited sp

urvature

rminative

ite spa

four-s

manifo

or of the m

ases of ge

en ray

about a l

a plane,

llustrate

corpuscu

, vague functions

volution of f

Girolamo,

M., on the pit

suitability of t

Ferdinand Ka

-Euclidean g

bsolute o

and real

ger empi

al attitu

of the, opposed to

c impressio

mpregnated, o

py, and e

of, for spatial u

the g

copla

immensity o

e unive

kosm

nscious

spac

aking fa

minatio

nsisten

urcica,

dean geome

sts on the i

rned by the met

one, justified

lism of

the sphere of,

nswer of, to

, as domain of

mpressions, as

isms of the

he principle

knon, t

s kosmic materia

tic, the,

2

nes of ma

knon, t

ined as kosmic sen

as emotional

to a sense pr

wgrap

nature's

agent and pr

n the pathway

ates

f intellectual

edict of d

ensional ent

quartopykn

conscious

alized cons

namic pro

-mother

mblage of s

ecomi

of another

ence of the

urved

c appearan

born of kat

d product of

lution,

e extensi

able quan

nite con

tional co

ic order

e of non-manif

h of li

eudosp

r roomin

m of co?r

nded exte

of, the consc

basis of non-Eucl

y distinct from

iptic

derment

ial natu

lends itself to

our

nalized s

ations

dimensi

Carus

of, efforts at maki

lity of, b

is of,

rely formal con

nd the Creati

oldness

the coeval

ry of,

answered to b

of non-manif

, the character

pure f

sage

h for, must be

oncilable with the

of, and the non-Euc

and tridimen

of devis

gical natu

ounded with

on the cur

unity

with mat

, as chemism and

nter, th

nsciousn

irect pr

th the individual

as an arbitrary

ear-tr

ure o

eed fo

, in terms of th

the constru

esis, 20,

abet o

letion

rm o

as a ba

sm of, 20

nifold,

and reality, Eucl

tems

archeological

owledg

Thinker,

ment of,

aries

alizatio

rocess,

yperspace as a ste

omnipsych

and the int

l with material

rom non-spa

ative with ma

mity of, wi

, and the i

se of

's outloo

of nas

, Herbe

oza,

the pheno

im of, regarding the f

ateriality tran

iple of

ds of

ation of th

mental o

the end of e

of, in the non-Euc

rie, F

pyknosi

opyknoti

M., on space as

onsciousness; one una

determined by

alized four-d

angul

less than two

s, as intuit

al, as the in

nd automatism of

ceptual,

odim, t

borg,

chic, and t

symbols of

sm of l

aphical imp

alitie

e-delive

e-genesi

ting planes of c

tical knowle

of faculties and pro

on of mind a

d the norm o

school of

hic impre

ponent in the four

evolution, th

us, 56

effect upon con

ellect as sci

ed to flower as fa

gmentate, the i

represented b

strate

e, 2

lements

co?rdinat

ntellect, incapabl

mmaton,

dron, t

cephalon

les

f knowle

and the impossibility

e dual nat

alue

selves, the id

of the fourth

pure intellig

er of the in

al to the e

moved from the s

rce of the

concep

h to the kosmic

arger l

tment of t

ense-impre

ealis

spac

ment of r

tude of the degrees

riers of cons

therhood

rees of r

ulation of

ture of

eurogra

ew facu

ceptive f

tuitary

s the spiri

ousness and

ence upon

tacting the exter

the universe of

ematism of cogni

e of awar

etween, and the in

ionary nee

hing yearn

e must be sought i

act, elevating

ged abstract, b

spect of cons

d of time

unte

ioning, li

of the in

consciousn

tion between idea

n mental cons

he realm of, and

e as a lim

finit

reali

se of evolu

angular sum

, 22, 129,

nsion,

lity and prim

e space-

of percept

f the pheno

fficienc

n, the,

is, 17, 2

ared with

ion of,

ets o

ds of

s not illum

d the intuitive

Thule,

e, as a finit

ree, in the cur

, and metageometri

rcle,

of all kno

s of real

of all exi

end of a

fourth dime

ers as fraction

and spac

realizat

based upon the formal cha

a glorifie

a ful

plen

ven planes o

, fixed by con

and condit

pure f

ted, and the

chanical origin of,

in the

of appea

and consci

m of rea

spac

e as a sy

s which shuts

he, 129,

sciousn

fine

ent of m

of a new f

llness of

athematical c

he intellect to the

, vitiating in

the ide

agmentary ev

ellectua

5,

space into many

as the, of ma

f life, f

mind a

of kosmic e

the in

hte

, John

nn, no

mbols of ide

the chil

t of conscious

f, and geo

ifying the fourth dimensi

ions of, identified w

nd hyperspace e

e, as a c

in of a pe

nesis

sm, kathe

ental ess

Raja

earth, the

claims of the s

Affinit

er, th

TNO

cience Monthly, vo

lletin, Vol. III, 1893-4, p. 79, G. B. Ha

. 37, Trans. by J. P. Ma

th dimension is dwelt upon at length. The view which he expressed in this article, of course, served greatly to popularize the conception among the learned men of the

. 14-17; 36, 37 (1873); also M

ser, Adrian Professor of Math

formerly of the University of Texas, whose labors in connection with the popular exposition of the non-Euclidean g

point on the line BA

Euclidean Geo

ature, Vol.

l. XVI, 1896, Mathem

st, Vol. XIX,

ical Review, V

ations of Mathe

dations of Mat

e, Vol. VII, p.

tions of Mathema

cal Review, Vol. V,

l. XVI, 1896, Mathem

n, Simply Explained, edit

Dimension, p. 7

242, edited b

ce, Vol. VII, 1

See F

II, also Philosophical Revie

to involution. It is the end of evolution, but also the beginning of involu

asm; A Theory of Her

Figur

e pp. 3

known, p. 4

osmo-Conception, p

ons of Mathem

riber'

ed except in obvious cases of typographical errors. Inconsistencies

ry of Space) betwen the table of conten