Họp Thông Thiên Học ngày 20 tháng 7 năm 2013
[7/20/2013 5:58:33 PM] *** Group call ***
[7/20/2013 6:01:06 PM] Thuan Thi Do: CHAPTER 18
THE FOURTH DIMENSION
There are many characteristics of the astral world which agree with remarkable
exactitude with a world of four dimensions, as conceived by geometry and
mathematics. So close, in fact, is this agreement, that cases are known where a
purely intellectual study of the geometry of the fourth dimension has opened up
astral sight in the student.
The classic books on the subject are those of C. H. Hinton: Scientific Romances,
Vols. I and II: A New Era of Thought: The Fourth Dimension. These are strongly
recommended by C. W. Leadbeater, who states that the study of the fourth
dimension is the best method he knows to obtain a conception of the conditions
which prevail on the astral plane, and that C. H. Hinton's exposition of the
fourth dimension is the only one which gives any kind of explanation down here
of the constantly observed facts of astral vision.
Other, and later books are several by Claude Bragdon: The Beautiful Necessity: A
Primer of Higher Space: Fourth Dimensional Vistas; etc., Tertium Organum (a most
illuminating work) by P. D. Ouspensky, and no doubt many others.
For those who have made no study of this subject we may give here the very
barest outline of some of the main features underlying the fourth dimension.
A point, which has “position but no magnitude”, has no dimensions: a line,
created by the movement of a point, has one dimension, length: a surface,
created by the movement of a line, at right angles to itself, has two
dimensions, length and breadth: a solid, created by the movement of a surface at
right angles to itself, has three dimensions, length, breadth and thickness.
[Page 164]
A tesseract is a hypothetical object, created by the movement of a solid, in a
new direction at right angles to itself, having four dimensions, length,
breadth, thickness and another, at right angles to these three, but incapable of
being represented in our world of three dimensions.
Many of the properties of a tesseract can be deduced, according to the following
table:—
The tesseract, as described by C. H. Hinton, is stated by C. W. Leadbeater to be
a reality, being quite a familiar figure on the astral plane. In Some Occult
Experiences by J. Van Manen, an attempt is made to represent a 4-dimensional
globe graphically.
There is a close and suggestive parallel between phenomena which could be
produced by means of a three-dimensional object in a hypothetical world of two
dimensions inhabited by a being conscious only of two dimensions, and many
astral phenomena as they appear to us living in the physical or
three-dimensional world. Thus:
(1)
Objects, by being lifted through the third dimension, could be made to appear in
or disappear from the two-dimensional world at will.
(2)
An object completely surrounded by a line could be lifted out of the enclosed
space through the third dimension.
(3)
By bending a two-dimensional world, represented by a sheet of paper, two distant
points could be brought together, or even made to coincide, thus destroying the
two- dimensional conception of distance.
(4)
A right-handed object could be turned over through the third dimension and made
to re-appear as a left-handed object.
(5)
By looking down, from the third dimension, on to a two-dimensional object, every
point of the [Page 165] latter could be seen at once, and free from the
distortion of perspective.
To a being limited to a conception of two dimensions, the above would appear “
miraculous”, and completely incomprehensible.
It is curious that precisely similar tricks can be and are constantly being
played upon us, as is well known to spiritualists: (1) entities and objects
appear and disappear: (2) “ apports” of articles from great distances are made:
(3) articles are removed from closed boxes: (4) space appears to be practically
annihilated; (5) an object can be reversed, i.e., a right hand turned into a
left hand: (devil) all parts of an object, e.g., of a cube, are seen
simultaneously and free from all distortion of perspective: similarly the whole
of the matter of a closed book can be seen at once.
The explanation of the welling-up of force, e.g., in Chakrams, apparently from
nowhere, is of course that it comes from the fourth dimension.
A liquid, poured on to a surface, tends to spread itself out in two dimensions,
becoming very thin in the third dimension. Similarly a gas tends to spread
itself in three dimensions, and it may be that in so doing it becomes smaller in
the fourth dimension: i.e., the density of a gas may be a measure of its
relative thickness in the fourth dimension.
It is clear that there is no need to stop at four dimensions: for all we know,
there may be infinite dimensions of space. At any rate, it seems certain that
the astral world is four-dimensional, the mental five-dimensional, and the
buddhic six-dimensional.
It should be clear that if there are, say, seven dimensions at all, there are
seven dimensions always and everywhere: i.e., there is no such thing as a third
or fourth-dimensional being. The apparent difference is due to the limited power
of perception of the entity concerned, not to any change in the objects
perceived. This idea is very well worked out in Tertium Organum by Ouspensky.
[Page 166]
Nevertheless a man may develop astral consciousness and still be unable to
perceive or appreciate the fourth dimension. In fact it is certain that the
average man does not perceive the fourth dimension at all when he enters the
astral plane. He realises it only as a certain blurring, and most men go through
their astral lives without discovering the reality of the fourth dimension in
the matter surrounding them.
Entities, such as nature-spirits, which belong to the astral plane, have by
nature the faculty of seeing the four-dimensional aspect of all objects, but
even they do not see them perfectly, since they perceive only the astral matter
in them and not the physical, just as we perceive the physical and not the
astral.
The passage of an object through another does not raise the question of the
fourth dimension, but may be brought about by disintegration — a purely
three-dimensional method.
Time is not in reality the fourth dimension at all: yet to regard the problem
from the point of view of time is some slight, help towards understanding it.
The passage of a cone through a sheet of paper would appear to an entity living
on the sheet of paper as a circle altering in size: the entity would of course
be incapable of perceiving all the stages of the circle as existing together as
parts of one cone. Similarly for us the growth of a solid object viewed from the
buddhic plane corresponds to the view of the cone as a whole, and thus throws
some light on our own delusion of past, present and future, and on the faculty
of prevision.
The transcendental view of time is very well treated in C. H. Hinton's story
Stella, which is included in Scientific Romances, Vol. II. There are also two
interesting references to this conception in The Secret Doctrine, Vol. I, page
69, and Vol. II, page 466.
It is an interesting and significant observation that geometry as we have it now
is but a fragment, an exoteric preparation for the esoteric reality. Having lost
the true sense of space, the first step towards that knowledge is the cognition
of the fourth dimension. [Page 167]
We may conceive the Monad at the beginning of its evolution to be able to move
and to see in infinite dimensions, one of these being cut off at each downward
step, until for the physical brain-consciousness only three are left. Thus by
involution into matter we are cut off from the knowledge of all but a minute
part of the worlds which surround us, and even what is left is but imperfectly
seen.
With four-dimensional sight it may be observed that the planets which are
isolated in our three-dimensions are four-dimensionally joined, these globes
being in fact t...
[7/20/2013 6:10:08 PM] Thuan Thi Do: properties of a tesseract Points Lines
Surfaces Solids
A Point has 1
A Line has 2 1
A Four-sided surface has 4 4 1
A Cube has 8 12 6 1
A Tesseract has 16 32 24 8
[7/20/2013 6:58:50 PM] *** Call ended, duration 1:00:11 ***
[7/20/2013 6:58:54 PM] *** Group call ***
[7/20/2013 7:26:21 PM] Thuan Thi Do:
http://blavatskyarchives.com/inner/innerno16.htm
[7/20/2013 8:08:03 PM] Thuan Thi Do:
http://thongthienhoc.net/sach/CacDangSieuNhan.htm
[7/20/2013 9:53:42 PM] Thuan Thi Do:
http://www.mediafire.com/download/e1goa3ak7f43uuk/AN+TIN+THONG+THIEN+HOC++-+BIEU+TUONG+HOC+HUYEN+BI-++PDF.rar
[7/20/2013 9:55:53 PM] Thuan Thi Do:
http://www.thegioivohinh.com/diendan/showthread.php?t=150110
[7/20/2013 10:03:38 PM] *** Call ended, duration 3:04:42 ***
[6:46:11 AM] *** Missed group call. ***