Do not read this blog post if you do not want your mind-blown outside the bounds of four-dimensional space-time. Kind of like what happens when the characters in The Great God Pan look upon the face of the supernatural unveiled. Or when the powder of Ibn Ghazi hits the spot in The Dunwich Horror. This happened to me as a side-effect of undertaking my Abramelin operation this year (i.e. my mind being blown, not literally having an experience with the child of Yog Sothoth), so now I’m inflicting this upon the rest of humanity. Muah ha ha! Ia Shub Niggurath!
But I digress. We normally think of space-time as having four dimensions: height, width, depth, and time. But ask yourself this:
How big is a Thought?
How wide is a dream?
How deep is a Memory?
Thoughts, dreams and memories all exist, hence they must exist within spacetime, yet they can’t be measured in terms of the conventional four dimensions. Hence they are Dimension-less, no?
It occurred to me, whilst I was in some altered state of consciousness or other, that if a thing exists yet cannot be measured in terms height, width, depth or time, then the fact of its existence must constitute a separate Dimension in addition to the preceding four. Hence, we are actually living in five-dimensional space-time, to wit:
- Existence (Karl Popper’s Third World, that of the Objective contents of Thoughts).
Now, this is where things get complicated. Consider the following diagram:
Despite the lurid nature of the introductory paragraph, this is not meant to induce major SAN loss. Instead it’s essentially a colour-coded diagram.
Complex numbers are those which consist of a Real and Imaginary part, the latter being a multiple of i, the imaginary square root of -1. Such numbers cannot be represented on a number-line, but they can be represented on a graph – an “Argand Diagram” – where two number lines become the two axes.
However: what if one wanted to display the effects of a Function which involves Complex Numbers? If one were using only Real numbers, this would be easy – just plot a graph. However, this can’t be done with Complex Numbers, as the set of Complex Numbers on which the Function is already performed is already a graph – that is to say, a two-dimensional diagram. Hence the only way to plot a function with Complex Numbers is to somehow come up with a four dimensional diagram – two dimensions for the original Complex Number, and a further two to represent the results of the Function when applied to that number.
It is not literally possible to represent Four Dimensions in just two. Hence, some way must be found to approximate the results – one such way might be by “Domain Colouring,” producing a diagram like that above. In computing terms, every possible colour has an RGB value, or 24-bits. Hence a Complex Number may be represented by assigning 12 of those bits to the Real part, and 12 to the Imaginary part. The colour of the diagram thus becomes the two extra axes needed to complete the Four-Dimensional representation. We have in effect simulated the representation of four dimensions in two dimensions, by adding extra layers of Meaning to the two-dimensional plane.
What however would happen if one were to analyse the above picture from a Magical perspective? One might break it down as follows:
|The Complex Plane||No extra layers of Meaning||The Two Dimensional Object|
|The colour of each point on the plane, which has been calculated mathematically.||Two extra layers of Meaning||(representation of) the Four Dimensional Object|
|Subjective perception that Red is associated with Mars, Orange with the Sun, Yellow with Mercury, etc etc etc||Even more extra layers of Meaning||(representation of) a Five- or more- Dimensional object, i.e. a Hyperdimensional Object.|
Again, consider the following photograph:
This might be analysed thus:
|The two dimensional plane – i.e. your computer or phone screen||No extra layers of Meaning||The Two Dimensional Object|
|The particular gradation of light and shade to serve precisely defined purpose – i.e. to depict a person.||In this instance, one extra layer of meaning||(representation of) the Three Dimensional Object|
|Objective facts associated with this photograph, i.e. that it depicts Aleister Crowley||Extra layer or layers of Meaning||(representation of) the Four or more Dimensional Object|
|Subjective thoughts that one adds thereto, e.g. ones feelings about Crowley, his life and / or teachings, Thelema, etc||Even more layers of Meaning||(representation of) a Hyperdimensional Object with potentially unlimited number of dimensions (? 93?)|
Or again, this Tarot card, from the BOTA deck:
Without going into as much detail as previously, one may say that this can be analysed in terms of:
- The two-dimensional plane;
- The objective fact that it depicts a specific Tarot card;
- The layer of meaning BOTA teaches in the Introduction to Tarot course;
- The layer of meaning BOTA teaches in the Tarot Fundamentals course;
- The layer of meaning BOTA teaches in the Developing Supersensory Powers course;
- The layer of meaning etc etc etc you get the idea.
In other words – “Meaning” is our way of depicting Higher Dimensions within the confines of conventional Space-Time. Meaning is not those Higher Dimensions themselves, but a convenient representation thereof. Consequently, it is possible if not to conceive of Hyperspace, then to conceive of approximations thereof, hence:
- Layers of Objective Meaning which one overlays the preceding five; and
- Layers of Subjective Meaning which one overlays any or all of the preceding;
The final two being virtual categories allowing for a potentially infinite number of actual dimensions. Conversely when, in Occultism, one studies a Symbol and one perceives that it has many layers to it (as all good symbols do), one may conceive of the Symbol as an object existing in Hyperspace, either metaphorically or even literally.
I was going to answer a question on Quora.com, “What do I do if I just threw my tarot cards on the ground out of anger?” A number of respondents answered along the lines of “Get rid of them, for they come from Satan!” Some more respondents answered “Get rid of them, they are a load of rubbish anyway.” A number just responded, “Just pick them up and clean them up, they’re just cards.”
“But,” I thought to myself, “they’re not just cards.” The simple answer to such a question would go like this:
Assume for one moment it is your unconscious mind which does the divination, and the tarot cards are just tools it employs for the purpose. Your Unconscious Mind will remember the day you treated its tools with disrespect, and will respond by showing you a similar lack of concern, by not providing you with an accurate tarot divination again.
However, a hyperspatial analysis might go like this: they are cards with pictures on them; pictures which have multiple layers of meaning both objective and subjective – and moreover, the connections which one builds with them in ones mind become reified as the psychic keys which unlock the intuition which in turn provides the real answer to the divination. A Tarot Card is thus a perfect example of a Hyperdimensional magical object – nay, a Hyperdimensional Entity – of which the Card laying on the ground where it has been carelessly thrown is but a five dimensional cross-section: which is a long way of saying that a Tarot card is far too important to ever be treated lightly.
I rather think that many of the concepts across which one comes in the Western Mystery Tradition, which at first sight are unexplainable to the rational mind, suddenly become explainable when one starts thinking in terms of the geometry of higher dimensions. For example: the Qabalistic Tree of Life. We all know that it has Ten Sephiroth and Twenty-Two paths, but some theories also say there are four Qabalistic Worlds, and moreover, each Sephirah has a Tree within it. Is there one Tree, four Trees, or forty? Are there Ten Sephiroth or four-hundred? Are (e.g.) Kether of Atziluth, Kether of Briah, Kether of Yetzirah, and Kether of Malkuth the same, different, related to one another, separated or conjoined and if so how? Is each one within the succeeding one like Russian dolls, and how can one conceive of any of them if they are or they are not?
One could try to resolve the incongruities by assuming that curious position of the meditative mind in which all dualities are resolved and the critical intellectual faculty is by-passed… if one wanted to limit oneself to thinking in three-dimensions. Alternatively, one could regard the Tree of Life as a Hyperspatial Object – that each Sephiroth is not a Sphere but a Hypersphere – in which case one can perfectly reasonably say that there is only one Tree of Life, one set of Sephiroth and Netivoth, and that a particular part – e.g. Malkuth of Malkuth of Assiah – is but a cross-section of the Hyper-Object (in this example, the Malkuth Hypersphere) that happens to be visible to us at one particular moment.
Ironically, though, Higher Dimensional Geometry also forces us to re-evaluate what we think we know about esotericism. For example: many of the theories which are candidates for a “theory of everything” in Physics posit the existence of multiple dimensions. If one were therefore to look at this from a Magical perspective, one would have to say that if the Universe is inherently Hyperspatial, then the Creator of the Universe must be a Hyperdimensional Deity. Hence, when we try to represent this Hyper-God using lower-dimensional symbols, we must accept the inevitability of failing to capture a fully accurate picture. The Sepher Yetzirah, for example, suggests that the Twenty Two letters of the Hebrew Alphabet can be arranged to form the Cube of Space. But what if the cosmos were more accurately represented not by a Cube but by a Tesseract? Or a Hypercube of five or more dimensions? If the former, then the Hebrew Alphabet would have to have forty-nine extra letters. Hey! Perhaps that means the language spoken by God and His angels in Heaven is infinitely more complex than anything of which us lower-dimensional creatures can conceive? I have not calculated how many letters would be required to make a hypercube of any higher order, primarily for my own convenience, but also because I feel that without knowing just how many dimensions in total are involved, it would be idle speculation.