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Tree of Life
As pointed out in #4 of Sacred geometry/Tree of Life, the tetractys at the heart of Pythagoras' teachings is conceptually equivalent to the Tree of Life. This tells us that holistic systems, such as the very space-time continuum itself, are 10-fold in nature. This is precisely what superstring theory predicts! Nine dimensions of space accompany the dimension of time. The 10 yods of the tetractys symbolize the 10 dimensions of space-time. The three white yods at its corners symbolize the three large-scale dimensions of the everyday world, or, rather, the very universe itself. The six black hexagonal yods at the corners of a hexagon denote the six curled-up, or "compactified," dimensions predicted by superstring theory but not yet detected by experimental, high-energy physics. The square-shaped hexagonal yod at the centre of the tetractys denotes the dimension of time. Because of the one-to-one correspondence between the ten Sephiroth of the Tree of Life and the ten yods of the tetractys (see here), there is no alternative, more natural way of interpreting the yods in terms of the 10 dimensions of superstring space-time. For example, it is counter-intuitive to suppose that the three uppermost yods in the tetractys denote large-scale dimensions because this would put on the same footing one of the members of the Supernal Triad symbolized by the yod at the top corner of the tetractys and two of the Sephiroth of Construction denoted by the two black hexagonal yods in its second row, whilst the two other corners symbolizing the remaining two members of the Supernal Triad would then denote compactified dimensions. Implausibly, this would mean that that two types of yods denote the three large-scale dimensions. Instead, the two basic classes of yods — corners of tetractyses and hexagonal yods — denote two types of dimensions, one large-scale, the other compactified. The central hexagonal yod that symbolizes the dimension of time corresponds, appropriately, to Malkuth, the temporal universe. The explanation of the great scientific mystery of why six dimensions remained curled-up as space-time expanded after the Big Bang (or before it in a hypothesized inflation era) has all to do with the basic, Kabbalistic distinction between the subjective Supernal Triad, which exist outside all realities, both physical and superphysical, and the seven objective Sephiroth of Construction, which manifest in these realities. Superstring space-time is a whole because it expresses a Sephirah (namely, Malkuth), a Divine Quality that is whole in itself, and so it must conform to the Pythagorean symbol of such spiritual wholeness, namely, the tetractys. That is why superstring space-time has to be 10-dimensional. That is why the emergence in the earliest era of the universe of three large-scale dimensions of space and six microscopic dimensions is no mystery — at least from Kabbalistic and Pythagorean perspectives. Rather, this 3:7 division of the 10 dimensions of superstring space-time is plain, incontestable evidence that the physical universe — the lowest level of the spiritual cosmos — conforms to the 10-fold nature of God as symbolized by both the Tree of Life and the tetractys. This is because the space-time continuum is Malkuth of the Cosmic Tree of Life. It is the final stage of realization of the 10-fold Divine Life.
According to M-theory, the as yet unformulated "theory of everything" that unifies supergravity theories with superstring theory, space-time has 11 dimensions. This is still consistent with the above interpretation provided that the central hexagonal yod is now interpreted as the tenth dimension of space, which is either a circle (SO(32) heterotic superstrings) or a 1-dimensional gap between the two parallel space-time sheets to which E8×E8′ heterotic superstrings of ordinary matter (E8′-singlet states) and shadow matter (E8-singlet states) are confined. This means that both 10-dimensional, superstring space-time and the 10-dimensional space of the grand, unified M-theory conform to the Pythagorean tetractys representation of holistic systems.
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