Multi-Dimensional Space-Time

The Theoscientist, Bhubaneswar, India, Dec. 2002—Feb. 2003, pp. 1—10

We have been working on a synthesis of the new discoveries relevant to Larson’s Beyond Space and Time. The following is a summary report of the development in thought so far. Recapitulating: space, time and speed (motion) are quantized. There are several speed (motion) regions of the physical universe which cannot be legitimately represented in the conventional three-dimensional spatial reference frame. In all the cases where legacy theory is encountering serious difficulties, the trouble arises because of the Procrustean attempts to fit all physical processes into the limited three-dimensional spatial frame. There is a conjugate Sector of the universe, the Cosmic Sector, which can only be represented in the analogous three-dimensional temporal reference frame. Most of the mysterious astronomical phenomena that have no proper explanation in the conventional theory turn out to be the normal Cosmic Sector phenomena as they appear to us. High-energy cosmic rays, cosmic microwave background and gamma ray bursts are typical examples.

Extrapolating the commonsense view of the universe around us to the ‘far-off’ regions—the very large, the very small and the very fast—often does not lead to truth. Time and again our (human) experience has shown this to us. There are critical points, thresholds and boundaries in the universe, crossing which the phenomena change radically.

One, Two, Three… Many

In the universe of motion speed is the primary reality. Space or time individually can appear only derivatively. Starting with a POINT, having no dimension, one can generate a LINE by moving it along a direction in space. It is not possible to generate an AREA by a point. Moving the point simultaneously along two orthogonal directions in space, with speeds U and V respectively, for example, still generates a line only—not an area.

In order to generate area we have to start with the LINE as the generator. This means that the line should already be present before its movement in an orthogonal dimension takes place. Since, to start with, the line is generated by the movement of a point, availability of a finite line segment in zero time simply implies that either the speed U or the speed V has to be infinite.

But since speed is quantized infinite speed does not exist. However, since areas actually exist, the requirement of ‘the availability of a finite line segment in zero time’ can be met by another expediency—namely, the possibility of multi-dimensional time. Suppose the motion, say, speed V, which generates the line segment from the point, pertains to a time dimension t2, orthogonal to the time dimension t1 pertaining to the speed U. Then, even though it takes time t2 to generate the line segment in the Y-direction, it would be as though it took no time from the point of view of the time dimension t1. Thus, it would be possible to generate area, and in reality the total process results in cm2/sec2 rather than cm2/sec.

Further since three-dimensional space (volume) exists, this could only be generated similarly by a three-dimensional speed cm3/sec3, with three mutually orthogonal dimensions of time available. There is documentation of states of consciousness experiencing four, five and higher-dimensional space. (Reference 1: see especially the chapter on ‘Higher Consciousness’.) This implies the possibility of n-dimensional speed, sn/tn, composed of n-dimensional space in conjunction with n-dimensional time, subsisting as a substratum for lower dimensional speed (space and time). In fact, Larson does allude to this possibility. (Beyond Space and Time, p. 41)

Larson postulates that the Third Sector (the Metaphysical Sector) is outside—that is, not part of—the Material Sector (3-Space) and the Cosmic Sector (3-Time). At the same time he posits an evolution of the ‘ethical control units’ pertaining to the Metaphysical Sector. But as I pointed out (Appendix: 1, ISUS-discuss Msg. #1110), evolution implies time. If the Metaphysical Sector is outside time no change, and therefore no evolution, is possible! But, on the other hand, the possibility of higher dimensional space-time, sn/tn—of which s3/t3 is a subset—in which they exist, not only renders them independent of the latter (s3/t3 or t3/s3) but also leaves the possibility of evolution (in other dimensions of time) open.

We have discussed the question of the dimensionality of space (time) in Reference 2. We have shown there that three-dimensional space (time) could be represented by the three orthogonal rotation operators i, j, and k with the following properties:

i2 = j2 = k2 =—1;

ij =—ji = k; jk =—kj = i; ki =—ik = j.

In a closed group of operators, like [1 i j k], the result of the combination of any number of the basal elements is also a member of the same group. The result of any such combination can be known only if all the possible binary combinations of the elements are first defined in terms of the basal elements i, j and k themselves (besides, of course, the identity operator, 1). Suppose there are n basal elements (excluding the Unit operator 1) in a group. Then the number of unique binary combinations of these elements, in which no element occurs twice, is n(n-1)/2. We can readily see that a group becomes self-sufficient (finite) only if the number of binary combinations of the basal elements is equal to the number of those basal elements themselves, that is

n(n-1)/2 = n.

The only definite solution for n is 3. (Zero and infinity are other solutions.) Therefore if we regard space (time) as a group of orthogonal rotations, its dimensionality has to be three in order to make it self-sufficient dimensionally. Otherwise the number of dimensions either has to shrink to zero, or proliferate to infinity. This means that only three-dimensional space (time) is ‘self-sustaining’ once created; whereas the higher-dimensional spaces (times) have to be sustained from ‘outside’ because some binary combinations remain to be supported (defined) from outside the group structure (by the Metaphysical existence?).

In Figure 1 we show this group property diagrammatically. Let the points (vertices) represent the basic elements of a group, namely, the ‘operators’ (other than the Unit operator). A line joining two vertices represents the binary combination. The triangle is the case in point: there are just as many base elements as there are binary combinations. In the group BC the only binary combination is BC, but it cannot be defined in terms of either of the base elements, since, BC = B, for example, requires C to be Unit operator which it is not.

In the case of groups larger than 3, there occur binary combinations (shown in color) that cannot be defined within the group and therefore require external definition. It is interesting to note the Cross, the Five-pointed Star and the Seal of Solomon among these. Religious literature is replete with explanations of their symbology. The cross represents the Second Person of the Trinity, Who stands for Space and Time (not yet separated, but potential). The Five-pointed Star is the symbol of the Perfect Man. The interlaced triangles symbolize the Reflection of God in Man. There is a great Science of Ćakrās and Maņđalās, known and practiced in India since the Vēdic times, concerned with the invocation of the Powers of Consciousness through such forms. (See Appendix 2)

The Junction of the Living and the Non-living

Suppose we take logentropy (logical entropy) to be the measure of level of organization in 3-Space in the Material Sector. Then the corresponding characteristic in the Cosmic Sector that represents the level of organization in 3-Time could be called the cosmic logentropy. Now since locations in 3-Space are only randomly connected to locations in 3-Time, it is difficult to see how the logentropy level of the material structure of the cell could be maintained—against its spontaneous tendency to get disorganized, left to itself—by a spontaneous increase of the cosmic logentropy of the cosmic control unit of the cell, as Larson proposes.

To be sure, there are processes in our Material Sector where order could increase, like in phase change from gas to liquid, or to solid.

Speaking of the inversion of the S-frame to T-frame that takes place on entering the Quantum domain (the Time Region), we pointed out (Reference 3): “…in the case of the frame-inversion (corollary # 5) of two interacting particles, unless inhibited by special conditions, we end up with six apparently different dimensions, three each of the two T-frames respectively. We require 3n dimensions to represent n particles… Scientists call this multi-dimensional manifold the ‘configuration space’…”

Now we have to realize that living systems are those special cases in which these multiple dimensions are inhibited. Instead of n T-frames, we have only one T-frame. The physical result is—the multiple-frame inhibition shows up as strong correlation of these n particles.

We have seen that the space-time progression in the Time Region is inward in space (­1/1), whereas in the Space Region of the Cosmic Sector it is inward in time (1/­1). The Time Region begins at the zero inverse speed of the T-frame, and ends at -1 inverse speed of the M-frame (see Figure 4 of Reference 3). Similarly, the Space Region begins at zero speed of the S-frame and ends at -1 speed of the M-frame. At unit level, speed and inverse speed are effectively equal (­1/1 = 1/­1). Consequently, we get the complete picture by unifying the M-frame of the Space Region and the M-frame of the Time Region.

Since gravitation always acts in opposition to the space-time progression, it acts outward in the Time Region. It also turns out that since the space-time progression acts inward in time in the Space Region of the Cosmic Sector, cosmic gravitation in the Space Region acts outward, too. The final result is that the action of gravitation in the Time Region of the Material Sector, on one hand, and of cosmic gravitation in the Space Region of the Cosmic Sector on the other, are both outward. Therefore we can readily see how the linking of the cosmic control unit with the material unit (the cell) is possible, and how they can interact, since the nature of the governing force (motion) is identical in both of them.

We should conceive of the influence of the cosmic control units to be non-local, without trying to posit them at locations in the time-space region. Perhaps the expression 'motion in space' of the cosmic unit has an unwarranted pun with the expression 'motion in space' of a material unit of the time-space region, which prompts us to liken them! But these two are not the same: while the former ranges from 0 to -1, the latter from 0 to 1. 'Motion in space' only means that the relevant quantity is the speed and 'motion in time' means that the relevant quantity is the inverse speed.

From this it follows that the matter with which a cell could be built should be within the Time Region: that is, it has to be either in the solid state or in the liquid state (or a combination of them). Similarly, the cosmic matter of the control unit has to be either in the 'inverse solid' state or in the 'inverse liquid' state, since it has to be in the corresponding Space Region, for the control to be possible. Remembering that a solid has fixed boundaries in 3-Space and a liquid variable boundaries, we wonder whether in the corresponding cases of the 'inverse solid' it has fixed boundaries in 3-Time and the 'inverse liquid' variable boundaries! The implications in the case of inverse liquid would be more tantalizing.

Now, while in a crystal of ordinary matter we have repetition in space, in the corresponding case of a crystal of the ‘matter’ of the Cosmic Sector we have repetition in time. Such a structure—a temporal structure as against a spatial structure—therefore, appears to us as a cyclical process. The periodical separation of the polynucleotide strands and their replication is just the sort of job a ‘crystal’ of the ‘matter’ of the Cosmic Sector is capable of doing.

The Theory of Living Systems

Just to demonstrate how organismic biology is catching up with what Larson explained in his Beyond Space and Time (pp. 136-139), let us quote from Fritjof Capra (The Web of Life): “The central insight of the Santiago theory is the identification of cognition, the process of knowing, with the process of life. Cognition, according to Maturana and Varela, is the activity involved in the self-generation and self-perpetuation of autopoietic networks. In other words, cognition is the very process of life.

“…In this new view, cognition involves the entire process of life—including perception, emotion, and behavior—and does not necessarily require a brain and a nervous system.

“The Santiago theory of cognition, I believe, is the first scientific theory that overcomes the Cartesian division of mind and matter, and will thus have the most far-reaching implications. Mind and matter no longer appear to belong to two separate categories, but can be seen as representing two complementary aspects of the phenomenon of life—the process aspect and the structure aspect. At all levels of life, beginning with the simplest cell, mind and matter, process and structure, are inseparably connected. Mind is immanent in living matter as the process of self-organization…”

Self-organization is an important finding. We explained (Reference 4): “In the long history of biological evolution we see a gradual building up of structural complexity, and a concomitant functional proliferation. Successive levels of organization of matter form a hierarchy, in which any given level contains all lower levels as components and is itself a component of all higher levels. Succeeding levels are structurally more complex than lower ones, inasmuch as a given level combines the complexities of all lower levels and has an additional complexity of its own. We need to make two important observations at this juncture.

“Something entirely new happens at a supervening level of organization, and this event is not explainable in terms of the lower level. A tissue, for example, is more than the sum of its cells. There is thus a leap between levels—gaps or transcendences in the evolutionary process. There is no purely logical explanation of this situation; with present understanding the relation between the levels could not be predicted.

“Secondly, in this organizational picture, the myriad entities comprising nature are living entities that are both interdependent and autonomous to a degree. They are both wholes and parts of larger wholes. In its self-assertive autonomous role, each entity is intent upon its self-consummation, whereas in its role as subsidiary part, each entity is capable of transcending itself in the interest of the greater whole. There is apparently a dynamic balance to be maintained between autonomy and submission to the needs of the next higher whole in the hierarchy.

“Through sacrifice, cooperation, and self-transcendence, something new occurs at the next higher level. The latter does not represent merely an aggregate of units of the lower level. Rather, it represents a new form, whole, or unity, which is greater than the sum of its parts.

“The Ancient Wisdom points out that concomitant with the evolution of Forms—which alone is studied by the scientists—there is an evolution of LIFE and CONSCIOUSNESS, which express themselves through these evolving Forms. The more advanced the Form is, the more the potentialities of consciousness that can manifest through it. In fact, it is the impetus from the evolving LIFE that drives the evolution of the organismic forms.

“Consciousness is relatively dormant in the Mineral Kingdom. It acquires the power to respond with feelings in the Plant Kingdom. It adds a new dimension of consciousness in the case of Animal Kingdom, namely, that of thinking. Only in the Human Kingdom does it begin to flower into the dimensions of Creative Activity and into Intuition. Direct experiencing of the unity of all LIFE, Order (Ŗita) in Nature and pure Love characterizes this new dimension of consciousness when developed. We shall refer to this as the consciousness of the Ethical Man.”

Motion—Consciousness Continuum

Referring to the fundamental basis of the whole universe, Ancient teachings assert: “Its one absolute attribute, which is itself, eternal, ceaseless Motion, is called in esoteric parlance the ‘Great Breath’, which is the perpetual motion of the universe…” (Reference 5) Explaining the semantic traps that come in the way of recognizing the identity of Eternal Motion and Consciousness, we observed (Reference 6): “A potent source of error is the misunderstanding of the nature of space and the inappropriate use of the meaning of dimension. Normally, in sense perception we cognize three dimensions of space (in the sense of three mutually perpendicular directions). The higher dimensions are referred to as being further directions in space orthogonal, at right angles, to the previous three. But this description misses the point of the occult teachings regarding the nature of space.

“The difficulty is that ‘space’ is being referred to with two different meanings. For instance, the two chief attributes taken to be characteristic of space are the ‘volumeness’ and the ‘out-there-ness’. We must realize that, in this sense, space is relative to objects ‘filling’ space. And the volume of space is tenable only in the case of this relative space. We cannot associate volume with objectless space. As such, the metrical characteristic is only one aspect of space and we should not narrow down the concept of space just to physical extensiveness. Perhaps this misconception arises out of the mistranslation of the Sanskrit word Ākāśa into English.

“On the other hand, the physical, emotional, thought, intuitional aspects etc., of living are to be taken as the various dimensions of space. Viewing space in this way, we know it not merely as metrical—this is only one aspect of it—but as a space-consciousness continuum. Perceptual space is three-dimensional. The fourth or higher dimensions cannot be taken as further extensions orthogonal to these three dimensions in the perceptual sense. As remarked, they are dimensions of the consciousness-space continuum, not of the perceptual space, the whole of which is only one dimension of the former. However, there may well be correlates of these dimensions of the consciousness-space continuum in physical space such that each dimension of consciousness may involve a projection in the metric field (i.e., space in the sense of physical extension) giving rise to further directions orthogonal to the three dimensions we cognize in sense-perception. In this way, in general, we have to understand space not as mere void or ‘volumeness’—this is only its metrical aspect—but as consciousness. That is why it is referred to as Plenum by the Seers and Ŗishis.”

We have pointed out in the previous Section the existence in Nature of a graded hierarchy of levels of organization of living structures. We can now see that this implies, on the one hand, hierarchy of spatial structures—like organ, tissue, cells, organelles, compounds etc.—and, on the other hand, hierarchy of temporal structures, which appear to us as patterns of dynamic processes in the living systems.

The teachings of Ancient Wisdom (Reference 7) inform us that the field of Human evolution spans five Tattvās (or dimensions of Consciousness)—(1) the Sense-perceptual, (2) the Emotional, (3) the Mental, (4) the Intuitional and (5) the Universal or Nirvāņic. These, of course, form a graded hierarchy of Consciousnesses—Wholes within Wholes, the ‘Higher’ transcending and containing the ‘lower’—akin to autopoiesis in living structures. The dimensionality, n, of the motion (sn/tn and tn/sn) relevant to these Tattvās turns out respectively to be 3, 4, 5, 6 and 7. To be sure the teachings mention two more Tattvās, the Para-Nirvāņic and the Mahā-Para-Nirvāņic, that pertain to Super-human stages of evolution of Consciousness.

References

  1. Leadbeater C.W., The Monad and other Essays on the Higher Consciousness, the Theosophical Publishing House, Wheaton, Illinois, USA, 1997 Email: olcott@theosmail.net (USA), theosophy@netkracker.com (India)
  2. Nehru K.V.K., “Some Thoughts on Spin,” Reciprocity, XXVI (3), Winter 1997—8, pp. 15—18
  3. Nehru K.V.K., “Non-Locality in the Reciprocal System,” Reciprocity, XXVI (1), Spring 1997, pp. 7—14
  4. Nehru K.V.K., “Empowering the Self,” The Theosophist, April 2002, pp. 253—263
  5. Nehru K.V.K., “Eternal Ceaseless Motion, the New Paradigm of Science,” The Theosophist, July 2000, pp. 377—383
  6. Nehru K.V.K., “Theosophical Materialism?” The Theosophist, October 1973, pp. 20—31
  7. Pearson N., Space, Time and Self, the Theosophical Publishing House, Wheaton, Illinois, USA, 1964
  8. Perkins J.S., A Geometry of Space and Consciousness, Theosophical Pub. House, Chennai - 600020, India, 1964
  9. Shankaranarayanan S., Sri Chakra, Dipti Publications, Sri Aurobindo Ashram, Pondicherry, India, 1973

Reciprocity articles are available at: http://library.rstheory.org/

For The Theosophist, email: theosophist@eth.net

Appendix 1: Evolution and Time (ISUS-discuss Msg. #1110)

In this Message I tried to discuss some points raised in Dan’s Message #1107.

(1) Firstly, he hints that the ethical unit could itself be in evolution. Here we encounter an impasse. According to Larson the Ethical Sector is beyond space and time. On the other hand, EVOLUTION unfolds in time. We, therefore, cannot talk of any CHANGE—since change implies time—in a domain transcending time.

To be sure, there ARE transformations that do not imply time—like those in mathematics. But these cannot be talked of as evolving.

There are other possibilities, which are presently totally beyond the ken of anthropomorphic consciousness. The subjective experience of our consciousness of time is that of a one-directional ‘getting later’. However, we have documentation of the possibility of ‘higher’ states of consciousness, through YOGIC research, wherein two- and three-dimensional time is experienced. [For example, C.W. Leadbeater, THE MONAD, Theosophical Publishing House, Wheaton, Illinois. See the chapter on ‘Time’.] For such a Consciousness, the future, present and past of our consciousness can all change! Without the knowledge, and consideration, of some of these possibilities our (and Larson’s) surmises about the nature of Sector 3 Existence might be far short of the Truth.

(3) The third item I want to comment on is about the observations, mentioned by Dan, concerning the learning by the birds, of the milk-snatching technique without transmission through physical structures (like genes).

From the scientific findings of the Seers and Ŗishis we come to know that animals—and plants too—have what we may call the GROUP MIND (or what They term the GROUP SOUL), which is associated with a large collection of individual bodies (organisms) of the same species. This is the repository of the acquired traits and explains their transmission to new offspring.

You can find two slides on GROUP SOULS in the PowerPoint file “Cosmos3 (English) Show.pps”, saved in the sub-Folder “Theosophy” of the Folder “BST” in ‘Files’ section (available at: [no longer available]). You will also find in this PowerPoint file a slide entitled “The Constitution of the Human Being” (which is, of course, the ‘ethical unit’). There is also a slide on “Individualization” which depicts the process of the creation of the Human-self (that is, the INDIVIDUAL MIND) from the previously existing GROUP MIND of the domesticated animal. The original source references for any slide can be seen in the “Notes Page” view. (See the attached PowerPoint file: “Group Soul to Human Soul (Slides).pps”)

Appendix 2: Studies on Sri Chakra

Another book that should deeply reward a student of Space-Time is A Geometry of Space and Consciousness by James S. Perkins (Reference 8). Recall the equation we considered for the possible dimensionality of a group of operators (like rotation) to be finite: n(n-1)/2 = n. From this we find that the number of external definitions (outside supports required) to be

E = n(n-1)/2 - n = n(n-3)/2

a plot of which is shown in Figure 2.

E = 0 for both n = 0 and n = 3, as we already noted. In the Occult Cosmology, both 0 and 3 represent the consecutive dimensional stages of the manifestation of the Universe. Immediately after 0, which represents the ‘Unmanifest’, comes 3, the triplicity, the basis of Manifested Universe.

The Vedic and Tantric Seers studied the function of form-patterns called Yantrās, or Chakrās, in representing and invoking the Powers of Higher Consciousness. Of these, the Sri Chakra is called verily the King of Chakras, since it embodies all other Chakras in itself. We find that its dimensionality is 9 (it is also referred to as Nava Chakra, Nava meaning nine). For n = 9, E turns out to be 27. We find that Sri Chakra is a configuration of 9 triangles (totaling 27 sides). There are 5 triangles with apex downwards superimposed on 4 triangles with apex upwards (see Figure 3).

The following extracts from the book, Sri Chakra by S. Shankaranarayanan (Reference 9) should prove to be interesting:

“According to the Tantras, especially of the Śākta school, there is one Reality, a Transcendental, Absolute immutable, ineffable. It is the Supreme Effulgence, Prakāśa. It is the Supreme appearing to be inconscient, but containing in itself the seed of consciousness. When it is self-moved to manifest something of itself, there is a movement, a deliberation on itself, an Idea…

“To this deliberation, the Tantrics give the name Vimarśa. Vimarśa means reflecting, considering, pondering over. The Absolute ponders over itself, appraises itself. … If we may call Prakāśa the original Shiva, the deliberation which is latent in him, the Vimarśa, can be called the original Shakti.

“Now this deliberation, this impulse of desire, creates a stir, a throb, spanda, which vibrates as Nāda. Initially, this Nada concentrates itself into a point. This point is the bindu, the seed of sound. It contains in itself in a highly concentrated potent form the two-in-one form of Shiva-Shakti…This is known as para bindu, the Supreme Bindu containing in itself all that have to be created. When it is in a mood to manifest, it comes down lower forming the apara bindu or the Śabda-brahman. This Bindu which is again Shiva and Shakti in one swells, ucchūna. The point-circle assumes a radius. A polarisation of Shiva and Shakti takes place; there is an unfoldment and there emerge two more Bindus, the division of Shiva and Shakti, beginning the creation. The whole creation is full of the dual poise of the static Shiva and the dynamic Shakti. Thus from one para bindu three Bindus emerge for manifestation. It will be observed that in creation, everything is not fully created, completely manifest. There are many things latent, some partially evolved, some beginning to be evolved.

“A latent but potent status containing the Shiva-Shakti in one, a static status purely of Shiva and a dynamic status purely of Shakti, all these three are simultaneously found in manifestation. Thus, the three Bindus form the primary triangle, the trikôņa, the manifestation which is a product of three guņās, the triad, tripuţi, or the three fields, tripura.” (Sri Chakra, pp. 22-25)

Prakāśa → Vimarśa → Nāda → para bindu (n=0) → apara bindu (trikôņa) (n=3)

“As the whole Sri Chakra has evolved out of the Bindu and the Trikona, the aspirant should know what these two represent.

“The Bindu as we have said, is the Para Bindu, the Supreme Bindu, the Nada that has concentrated itself into a point. This is the centre of the Sri Chakra…

“From this centre emanate the various lines, triangles and circles culminating in the shape of Sri Chakra. It is very difficult to translate the word bindu into English. We may say that it means a point, a drop, zero or cipher. It is the point of contact between the Supreme Creator and his creation, the drop which swells itself into the ocean of consciousness, the zero which gives meaning and value to the myriad numbers, the cipher through which everything is deciphered. The Bindu is not a void, śūnya. …

“The Bindu can be considered as a point-circle, not yet having a radius. It can be thought of as a triangle with no area, a point where the would-be three vertices coincide. In fact, from the Para Bindu, in the stage of evolution appear the three Bindus—the miśra Bindu containing the Shiva and the Shakti, the static Shiva Bindu and the dynamic Shakti Bindu. These three Bindus, as we have explained, form the primary triangle, mūla trikôņa. This triangle represents the creation in its triple aspects…” (Sri Chakra, pp. 28—30)

Srichakra

Figures of ANU & PARAMANU from “Occult Chemistry”