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Home / Learning Center / MODELS / Flatland and Higher Dimensionality

Maps, Models and Metaphors for the Messianic Age

Flatland and Higher Dimensionality

 
Joel David Bakst ©1990,2002 All rights reserved
 
            A recurring theme in the literature of the Kabbalah and the most pivotal event in Torah Cosmology is the event of the Garden of Eden: Adam and Eve, the Serpent, the eating of the fruit of the Tree of Knowledge of Good and Evil and the resulting "fall". Yet, from early on this short account - and for that matter, the entire written Torah - has been the source of much confusion, even among scholars and spiritual seekers. 
            To some the events described in the Torah are not to be taken literally. Rather, if they have any meaning beyond that of mythology then they must be of an allegorical nature, containing subtle truths intended for the initiated. Numerous works of philosophy, occult theosophy, modern day gurus and wizened teachers proclaim the "real" transpersonal truth of scripture. From this perspective an attempt to understand scripture literally is just "not getting it". 
            On the other hand, there are those who interpret the narrative only in a literal sense. They picture Adam and Eve more or less as a present day man and woman, the serpent as some kind of bi-pedal reptilian creature and the Tree of Knowledge as a large vegetative growth. The literal word is the literal truth. The wealth of art works, particularly during the middle ages and up until this day, attests to this gross personification. To attempt to understand the verses otherwise is considered to be a blasphemous insult to God and truth [1].
            In Torah cosmology, however, both views are true. Furthermore, both are necessary. Yes, thereareprofound and eternal meanings in the text far beyond its simple narrative account. This is the level of the Torah exploration known as the sod/esoteric dimension. And yes, the text is also true to the literal narrative that is known as the p'shat/literal dimension. This is the intention of the sage-mystics of the Talmud who teach us that, "Ain mikra yotzae meday p'shuto" - A scriptural verse [despite its hidden truth] can never disregard its plain meaning [2]. Yet, even if we accept this principle how do we relate to this hermaphrodite Adam as a real human being existing within chronological time and at the same time also as a transcendent entity and archetypal consciousness? Better yet, just how did the kabbalists picture Adam and his reality?
            The sage-mystic Rabbi Moshe Chayyim Luzzatto (RAMCHAL) commenting in early 18th century Italy wrote concerning the two trees in the garden - the Tree of Knowledge and the Tree of Life:
            "Certainly no verse can disregard its plain meaning and the Trees were trees and the fruit was fruit and the act of eating was eating. However, the fruit was so ethereal and the act of eating was so ethereal that our [mundane] thoughts cannot picture it as they are capable only of picturing things of a corporeal nature” [3].
            The answer is that the rabbis, knowing full well the limitations of their own minds, did not picture anything! Now, not only our dilemma remains unresolved, but it has even been further compounded. How can something be literally true, have existed in time and space and yet, not be of a concrete reality? How does the Torah expect us to relate to the description of the events of Gan Eden? How do we relate to that which we cannot conceptualize?
            From the perspective of Torah cosmology our dilemma comes about due to our lack of familiarity with the concept of dimensionally - both higher and lower. In the Kabbalah this is known as Torat haO'lamot--the teachings regarding worlds or dimensions. The entire Kabbalah is based on this system and years of study and meditation are required to grasp its depth and complexities. There is, however, a powerful, yet deceptively simple model that is now available. With a little application we can begin to "see" that which we cannot perceive. 
            A little over a hundred years ago a small book was written by the mathematician and Shakespearean scholar, Edwin A. Abbot called Flatland - a Romance of Many Dimensions that has since achieved a popularity that has never diminished. Although there are numerous works concerning the subject to this day Flatland is probably the best introduction into the manner of perceiving higher and lower dimensionally.
            In this satirical story we are made to understand the way in which the inhabitants of Pointland (zero dimensions), Lineland (one dimension), and Flatland (two dimensions) are satisfied with their universes. They are not only incapable of understanding the limitations of their view but are enraged by any attempt to enforce them to transcend those limitations.
            We might well imagine that we, from our superior viewpoint of three dimensions, faced with no fewer than three stages of transcendence - from point to line, from line to plane, from plane to solid - would be ready to understand the concept of step-by-step increase and decrease of dimensional space without number. Certainly, we could accept and understand a universe of four spatial dimensions.
            Not so! Abbot shows how an inhabitant of Spaceland (our own familiar three-dimensional Universe), after explaining in detail the two-dimensional limitations of Flatland, and forcing an inhabitant of that plane to accept the additional dimension, himself falls into a rage when asked to contemplate a fourth dimension.
            A synopsis of the story has been well depicted by Marilyn Ferguson in The Aquarian Conspiracy:
            In the durable Victorian fantasy, Flatland, the characters are assorted geometric shapes living in an exclusively two-dimensional world. As the story opens, the narrator, a middle-aged Square, has a disturbing dream in which he visits a one-dimensional realm, Lineland, whose inhabitants can move only from point to point. With mounting frustration he attempts to explain himself -- that he is a Line of Lines, from a domain where you can move not only from point to point but also from side to side. The angry Linelanders are about to attack him when he awakens.
            Later that same day he attempts to help his grandson, a little Hexagon, with his studies. The grandson suggests the possibility of a Third Dimension -- a realm with up and down as well as side to side. The Square proclaims this notion foolish and unimaginable.
            That very night the Square has an extraordinary, life-changing encounter: a visit from an inhabitant of Spaceland, the realm of Three Dimensions.
            At first the Square is merely puzzled by his visitor, a peculiar circle who seems to change in size, even disappear. The visitor explains that he is a Sphere. He only seems to change size and disappear because he was moving toward the Square in space [our three dimensional reality] and descending at the same time [thus, as the 3-D ball passes through the 2-D surface all that can be perceived is an increasing and decreasing line at the commonly shared points of intersection. Furthermore, since the Flatlanders have no height from which to glimpse an aerial view of the Space intruder they cannot see its circular shape just as if we were to bend down and look at a round coin eye to eye at its surface level - it would appear only as a straight line. Only after a Flatlander would circumscribe the intruder and felt his lack of edges would it be known that this strange new "Flatlander" was indeed a circle]. 
            Realizing that argument alone will not convince the Square of the Third Dimension, the exasperated Sphere creates for him an experience of depth. the Square is badly shaken:
            There was a dizzy, sickening sensation of sight that was not like seeing: I saw a Line that was no Line; Space that was not Space. I was myself and not myself. When I could find voice, I shrieked aloud in agony, "Either this is madness or it is Hell."
            "It is neither", calmly replied the voice of the Sphere. "It is knowledge; it is three dimensions. Open your eyes once again and try to look steadily."
            Having had an insight into another dimension, the Square becomes an Evangelist, attempting to convince his fellow Flatlanders that Space is more than just a wild notion of mathematicians. Because of his insistence he is finally imprisoned, for the public good. Every year thereafter the high priest of Flatland, the Chief Circle, checks with him to see if he has regained his senses, but the stubborn Square continues to insist that there is a third dimension. He cannot forget it, he cannot explain it.
            The story goes on and on with each page being an amusing exercise in training the mind to develop something akin to a whole new set of muscles. To one trained at a young age for a reverence for the esoteric and later initiated into the subtleties of Torah cosmology ascending and descending through varying dimensionality has always been axiomatic.
            In conclusion I quote from Rabbi Shlomo Eliyashuv, the great early 20th century Lithuanian kabbalist from the esoteric school of the Gaon of Vilna. Armed now with powerful tool of the Flatland metaphor we can peer into a drop of the Or HaGanuz - the Hidden Light - of the Gan - where we descended from and where we are ascending.
             "Remember and do not forget the elevated stature and original level of all reality as well as the stature and transcendent level of Adam HaRishon before the Fall. The act of eating was then of a totally different nature and thus all of these matters are elevated and transcendent from our conceptualization. This is especially true regarding the Tree of Knowledge in the Garden of Eden. Even in the present Soul World [also known as the "Garden of Eden" where departed souls reside until the total transubstantiation of all reality takes place in the 7th millennium] which contains only spirit [and no relative corporeal bodies] there is absolutely no physical eating at all - all the more so was this true according to the exalted and elevated stature of Adam HaRishon and his original level of existence. Now, even though all these events that are recorded in the Torah are as they are written and are in exact accordance with their literal meaning, they are, however, totally beyond are ability to grasp their substance. This is due to the fact that at that period all realities in their entirety utterly and absolutely transcended our present existence to a degree that is inexpressibly awesome. Yet, there has been a devolutionary collapse of all these matters in exact ration from the time of the Fall until now in a completely isomorphic fashion. The regression has been from each subtle plane of existence to its corresponding grosser plane, which in turn devolved into its corresponding grosser mirror image almost ad infinitum. The digression goes from soul to body to garment and to garment within garment like a stamp that leaves its imprint only to become in turn another stamp itself and to leave its imprint and so forth. Thus, all the layers are exact duplicates of each other each being true according to its particular essence. Thus, the final and most exterior manifestation [of the events as written in the Torah] is literally true. This is sufficient [for the one who understands]".
 
Notes:
[1] See,e.g., Rambam in Hilchot Melachim where Islam and Christianity are examples of these two extreme views.
[2] Shabbat 63a, Yavamot 24a, Pesikta Zutra VaYaetzay 29b and 49d
[3] Da'at Tevunot, page 114 (siman 126).

 

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