sria - fourth dimension
TRANSCRIPT
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imen.i.n
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T. . T.. G.. O. . T.. S. . M.. O. . T..U. .
CO SIDERED ESP EC IALL y
WITH RELATION TO THE
ROSICRUCIAN COSMOLOGY
Delivered before Grantwood College, S;.. R: 1:. A:.
By FRATER AAHMES
Imprimatur
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R.. l.. A ..
Ordered for Publication, Class 11., Section B
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A NO MCMXIII
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Copyright 9 3
Society Rosicrucians Ine
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PREF E
This lecture on The Fourth Dimension was
delivered beEore Grantwood College, S.R.l.A.,
Oct. 14, 1913, as part of the regular collegiate
work. W'hile to the advanced student of
mathematics the matter therein contained
n-ay appear elementary, st ill the writer feels
that in handling a su.bject itself so intricate
nothing is to be gained by complicating it
with abstruse mathematical demonstrations.
;0 those inclined to enter more deeply into
such problems, Prof. C. H. Hinton's book on
The Fourth Dimension is recommended or
caretul reading and study.
Diagrarns, blackboard ilIustrations, etc.,
whrch are essential to a proper exposlton of
the subiect, accompanied the delivery of the
lecture in the College; and while their in-
sertion in this publication was deemed in-
expedient, the reader w ill derive much in-
tellectual enjoyrnen t from constructing these
simple diagrams Ior himself and will also add
mater lally thereby to hs comprehenson of
this unique field of study,
AAHMES.
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TH OURTH
DIME SIO
ti
OINT is the Ibeginning o~ all geomet-
rcal matter. It has neith er Iengt h,
breadth nor thickness, 'but merely
postton in space. Strictly speaking, a point
is non-exstent, for the reason that the
moment we assgu to it a definite posttlon,
we necessarily give it Iength, breadth or
tbiokness.
lf a point s moved in any direction in
pace, it generates a line. A line has one
drmenston, Iength, .hut neither breadth nor
thickness. H cannot be said that a line has
a tangible existence any more than a pont,
because even the most attenuated line that
we can conceive of would still have some
thickness. A line, therefore, is merely a geo-
ruetrical concepto It extends in one direction
only, and each of its 'boundar ies s a point.
The movement of a line in a direction not
contained in itself-that is to say, not for-
ward or backward but from side to side-
generates aplane surface. A plane has two
dmensons, length and breadth, but no thick-
ness. Here again, we are deal ing wth an
mpossible condition, as the thinnest surface
we could imagine would still have thickness.
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6 The Fourth Dimension
Our line was bounded by points ; the square
is
bounded
by
straght
lines, running in two
directions perpendicu lar to one
anonher.
Now let the plane be moved in still another
direction, not contained in the plane; that is
tu say,
not in a direction of eitller
Iength
or
breadth, as
that
would still leave us
only a
plane, but in a drection
perpendicular
to
the
ather two ; such a motion will generate a
cube. A cube has three dimensions, length,
breadth and thickness, and is bounded on al
sides by planes. It is not only conceivable
but tangible.
The problem we now have to Ideal with is,
what sort of a figure wil be generated by a
cube, movng in a fourtih direction or dimen-
sion from the other three, and perpendicular
to al three of them; and how is it possible
for us to conceive of such an appar ently rn-
posslble condition? We can only abandon
any attempt to actually realize such 11 figure,
and merely reason by analogy from tbe lower
to the hgher. IVe must first, bowever, note
tbis important fact; that since polnts are
t.he boundaries of a line, Hnes are the
boundaries of a square and squares are the
bounda.ries of a cube-the boundaries of each
figure being one dimension less taan the
figure itself-we must necessarily conclude
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The Fourth imension
necessartly labor under peculiar difficulties,
arrsug from the fact that we are living in
a world which so far as our ordnary ave-
nues of sense-perception can tell US, s corn-
posed of only three
d
mensions. It is [ust
as when
we
attempt to
explan spi
ritual con-
clitions in terms of the phystcal, or me
nnte
in terrns of the finite. From one
standpont, therefore,
it
seems best not to trv
to represent the Fourth Dimension con-
cretely, or even to imagine
it,
but rather to
SE.\lSE it.
c\o study of the Rosicrucian Cosmology, in
fact no adequate conception of the nter-re-
lation of the various worlds, vehicles of t.he
Ego
etc., is complete unless it involves at
the sarne time a comprehenson of the Fourth
Dimension. How, for example, are we to
apprehend the idea of worlds within worlds,
of various bodies, astral, etheric and physical,
all concentric and inter-penetrating? How
else can IVe realze t.he truth of the statement
that you or 1 could stay in one fixed spot,
live and die, and pass suocessively into each
of the so-called
higher
worlds until we
stood face to face with the Absolute?-all
w ithout stirring from that same spot ? The
answer necessarily and obviously involves the
supposition of another and unknown direc-
tion into whic.h IVe can pass, distinct from
the three of length, Ibreadth and thickness
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8 The Fourth Dimension
exstence of the Fourth Dmenson better
than t'he most elabor ate mathematical dam-
oustraton can prove it.
The mathernatical sclentist starts out by
saving that the human imagination is incap-
ahle of conceiving an obiect in the Fourth
Dimension, and ihen he proceeds to con-
struct such an object. This course of reason-
Ing seems somewhat paradoxcal in its con-
rlusions, but the method used is logtcal. In
this atternpt to gtve a simple exposition of
the Fourth Dimension, therefore, 1 shall
state briefiy a line of argum ent w'hich has
been used wth very excelIent results by Prof.
Hinton.
What is the Fourth Dimension? We know
cf three-Iength, 'breadth and thickness. We
know that from a given pont on the surface
of the earth we can 'travel back wards and
f'orwards, left and rig'ht, up and down; three
definite directions. What is meant, then, by
~ f'ourth direction, and how shaIl we go about
conceivng it?
Prof. Hinton draws an analogy between
our existence in three d menstons and t'he
supposed existence of beings in a world of
fewer dimensions. For example, imagine a
being confined to an existence in one dirnen-
sion only. The vlsible world of such a being
would necessarily be Iimited to a stragh t line.
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The Fourth Dmenson 9
Now suppose another world wh ich has two
dimensions, lenglh and breadlh. A being liv-
ing in such a worl d would
ibe
a flat creature
moving laterally
OIl
a ftat surface, say that
portion of aplane bounded by four right lines
and constituting a square. He could not only
go backward and torward, but from si de to
side as well. In this respect he would be bet-
ter off than the being living in a world of
only one dimension.
The two-dimensional being, however, knows
no up or down. He could conceive of another
plane world lying adjacent to his own and
parallel
w
th it, but he woul d conceive o
t
as shut in by two directions, by the straight
Iines whch bound it; and the only way he
could leave h is space would be through the
edges
01
si des. It is evident that if another
plane were placed perpendicular to this two-
dimensional world, its inhabitant would
sense ths new plane only as a straight line,
where it wou.d cut through his own plane.
For a condition in which movement is POSS
ble in any one of three directions, we must
go to our own world as we know it. On land
we can move in any lateral direction, and
all directions are made up of two fundamental
ones at right angles to each other. We can
also travel up in the air and down in the
surface of the earth. We can conceive of an-
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T
o
u r t h i
m
en
s ion
a world by trav el ng in a fourth direetion,
whieh would be neither baekwards or tor-
wards, from left to r ight or Irom side to side,
but would get us to our destination just the
came ?
Let me illustrate. Imagine two beings at
opposite ends o a two-dimensional world or
plane, say ten thousand miles apart. Now let
us take and bend this plane inward upon t-
self, in the torm o au are, so that the two
opposite edges toueh each other. These two
crea tures will suddenly appear alongside each
other, as If by magie; and yet both of them
know that they are ten thousand miles aparto
Let us take another ilIustration from a two-
dimensional world, Prof. Hinton shows that
a eurious triek eould be played on a being
eonfined within a square, or aplane world,
by a three-dimensional being outside of
it
such as you or 1. We could look down on
this two-sided creature, imagining h mself a
prisoner within those four edges, Hft him
right up uto spaee and set hirn down again
in another squar e or plane world exactly like
his own, without his bcing conscious of how
he got there. To such a creature, a trans-
formation of this kind wouId appear a pro-
found mystery. He would know that he had
been taken from one plane world to another,
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The Fourth imension
Now apply this illustration to our own
world. It is just as though aman were con-
tined within a room without opening of any
kind. Around and about him are four walls,
a floor and a roof, makng sx surf'aces all
toldo To his mind escape from such a room,
without breakiug through any of tl.e six
planes that surround hirn, would be Imposs-
ble; and yet if he suddenly found hmself
outsde the room, without Imowing how he
got there, his astonishment would be fully
equal to that of the two-dimensional creature
whom we Iifted up out of the square and
then set down insde of another square. The
important thing to note is this: that as in
the case of the two-dimensional wor ld the
transference was accomplished by passing tbe
creature first into a world of a higher dimen-
sion-a
thrd -and
then back again into the
world of two, so any passage of a man out
of a sealed room, without going through any
of the walls which surround hirn, would have
to be accomplisbed by taking him first through
a hgher dimension, or fourth dimension, be-
fore returning him to another worl d .like his
own. It is therefore apparent that by so
much advantage as we of three dimensions
have over a being of two drnensions, would
a fourth-dimensional being capable of playing
such a tr lck on us have over uso
It has been stated that as the comprehen-
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2 The Fourth Dimension
hurnan being, is bounded by aplane. Why
not by a solid ?
it '
may be asked. Because
our knowledge of a solid is limited by the
planes which bound it. F'or example, face
lhe wall of your room. You may kno w to a
certainty that it has thickness as well as
;ength and breadth, yet to your eve it pr e-
sents only a surface. IF YOU COULD LOOK
A'l' ALL PAR'l'S OF 'l'HE INSIDE OF 'l'HA'l'
WALL AS EASILY AND NA'l'URALLY AS
YOU CAN A'l' THE OUTSIDE YOU WOULD
BE SEEING IN 'l'HE FOURTH DIMENSION.
The F'ourth Dimension , therefore, is a drec-
t
ion 01 cond ition not cognizable by any of tbe
ordinary avenues of sen
se-perceptdon.
We may employ still anothe- illustration to
assst in Iorming a conception of the Fourth
Dimension. In a two-dimensional wor
ld-e-a
ulane surface--if we pass a cube through it
m a dir ection perpendicular to the plane the
cube will appear to the two-ddrnensional crea-
ture only as aplane; and that plan e will be
the particular cross-section of the cube which
happens to be passing thr ough al any given
mornent. The rest of
lb
cube, being in the
third dmensiou, and thcretore mtside the
sense-apprehension of tue two-dmensonal be-
ing, wouJd be invisible to hm.
stmtarlv, Jet us suppose that an object which
exsts in the Fourth Dimension, a hyper-cube,
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T he o u r t h Di me n s ion 3
come, rernans invisible to our eyes. Yet the
analogy between ths phenomenon and that
of t:he cube passing through the two-dimen-
sional world is perfect and appeals to our
reason.
We know, for nstance, that the so-called
higher worlds are co-exstent and interpene-
trating; that in passing rom one to the other
we do not necessarily pass in an upward or
downward directon, as one would climb a lad-
der, but that we merely pass from one con-
dton to another. Why, then, is it not log-
cal to assume that matter in passng from one
condtton which we call three-dtmensonal, to
another which we will call Iour-dmensonal,
will merely pass from one condton to an-
other?
Let us recall the Illusuraton of the sponge
and the bowl of water. A spherical sponge
represents the chemical region of the physcal
world. The sand, permeatng every part of t:he
sponge, represents the etheric regon which
permeates the physical earth. Both sponge and
sand can be immersed in a bowl of water,
whch will permeate both sponge and sand
just as the astral world permeates the earth
and the ether. Lastly, the entire cont.rlvance
of sponge, sand and bowl of water oan be
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14 T he F o u r
t
h i m e n s ion
teaches is an impossibility. Now ir this ts
true of the sprtt wor ld, there appears to be
no reason why it should not hold true with
matter, which s merely crystallized spirit.
As above, SO below. Had 1 the faculty of
projecting my body at
w
ill in a fourth dtmen-
sion, 1could 'Press my finger again.st this cube,
01
solid, and
t
he finger would gradually vanish
from our eyes INTO THE e BE. In our
clumsy Wywe should say that finger and cube
were oceupying the samc s.paoe at the same
time; in realtty, the finger has merely traveled
in. another direction whch we cannot sense
at our presen.t stage of development.
W'e have learned that to function in any
particular world we must have a vehicle
cor-
rela.ted to that world. Hence, by analogy, to
sense objects in. the F'ourth Dimension we
must necessartly get into a Iour-th-d'lmenalonal
world-say such as what we call the astral
world, where three-dmensonal objects like
our solids otter no obstacle to the progresa
of other solids 01 bengs through them, Sim-
larly we might suppose other worlds of five,
slx and seven dimensions, each successlvely
hgher world giving to its inhabitants proper-
tes and qualities not possessed by those in
the lower.
What vtstble, actual, proof, it -may be asked,
have we of the existence of a Fourth Dimen-
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T h e
o u r
t
h Di m e n s ion 5
plant growth, 01' ths transmission of electricity .
01' heat, or any of the thousand and one ather
rorms
energy that w.e see mantesced about
us every day. How is this energy transferred
01' diffused? We cannot actually say that elec-
trlcty, or heat, 01' the transmission or sunlight
to plan ts, can be measured in any one of the
three dirnensdon of our space, 'I'hey have
neither length nor breadth nor thickness.
'I'h.ey are, in fact, Iunctions of the Fourth Di-
menson, or the space of chemical reactons,
as Prof. Lockwood calls it.
F'inally, the thoughtful student following
these various lines of reasoning might ask
himself this questnon : Are we, after al l, Iourth-
dimensional cr.eatures conscious only of three
dimensions? Do we move in a world outside
our ordnarv space ut the very moruent
w
e
imagine ourselves to be most material den i
zens of
ths
world only-and is it posstble that
the physcal outlines we see around us, of our-
selves and each other, show merely a crystal-
llzation of creatures existing in raa llty in a
higher world, but functioning in a 10\V.er? As
students of the Rosicrucian phllosophy this
opens to us a field for profound reftection.
And it is not unreasonable to suppose tha;
close study
wll
reveal a definite basis for
such supposition, and point the way, th roug h
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