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 ocies; 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 ultimateto 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 atumnar 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 andhis 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
E
IOGR
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l-Postulate, by
d, by A
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ol. VI, pp
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h Dim
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y H. P.
h Dim
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108-109; 144-145; 181-214; 25
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, P. 404
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Romances, C
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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
ion and the
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 curlized, 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 excrescenceslt 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 theantithesis 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 bs 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 pprocesses
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