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:
Objects, by being lifted through the third dimension, could be made to appear in or disappear from the two-dimensional world at will.
An object completely surrounded by a line could be lifted out of the enclosed space through the third dimension.
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.
A right-handed object could be turned over through the third dimension and made to re-appear as a left-handed object.
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. ***