This paper explores the possibility that the square root of minus one (a complex number in mathematical terms) is the correct symbol for absolute Consciousness.
Definition: C.C.C. (Certain Consciousness Changes) refers to a change of consciousness brought on by either a meditative state (e.g. a Buddhist "trance"), or by taking a psychedelic substance (see Masters and Houston's "Varieties of Psychedelic Experience").
People have the ability to alter their space-time frameworks by certain consciousness changes (C.C.C.), where their subjective sense of time speeds up, while their "psychic" sense of space increases (distance "collapses"). In other words, a subject might think that five hours had gone by, while actually only two hours had elapsed; also he might have experienced vivid sense impressions of objects, which made them seem closer to him psychicly (cosmic consciousness).
These results are fairly well known, yet little work has been done in attempting to relate them to the laws of physics, especially to the law of special relativity, which shows that the laws of physics remain invariant under different space-time reference systems that are moving at different velocities with respect to each other. According to the special theory of relativity, the time and length scales of one coordinate system moving at velocity v with respect to another will appear to be changed by a factor of the square root of (1 - v*v /c*c) [throughout this paper "*" is used as the multiplication symbol] where c is the speed of light. This factor, using physical velocities, is never greater than 1.
Attempting to interrelate consciousness to a
physical framework, let us generalize the coordinate systems to
be two people, one of whom, in comparison to the other, is
undergoing Certain Consciousness Changes. Call him CCC and call
the other person the observer. CCC's sense of time will speed
up while his sense of distance (radial with him as the
center) will make objects seem psychicly closer
to him. This means for CCC that the square root of (1 - v*v /
c*c) is greater than 1, and the only way this
can occur is if he is moving at a velocity of v' = i times v,
where i = the square root of minus one, so that v'*v' = iv*iv =
-(v*v). This does not make any sense physically, for the two
people, who may be sitting next to each other, are obviously not
physically moving with respect to each other, so it must mean
that CCC has his coordinate system moving with respect to the
observer's at a velocity v' into an imaginary direction in space
- he is truly 'spaced out'! The person in C.C.C watching a clock
will think the time it ticks off is slow. To the
observer, who finds out from CCC that their time seems to be
moving slowly, it is explained by the relativistic equation:
Time(CCC's) = Time(Observer's) * gamma, where gamma = 1 divided
by the square root of (1 - v*v / c*c), where v is some fraction
(or multiple!) of
(i * c). In a similar way, as his consciousness "expands", CCC's sense of a distance between an object and himself will be that it has lessened - the observer will explain it as an expansion of CCC's "measuring rod" according to the relativistic formula: Length(CCC's) = Length(Observer's) divided by gamma
(1/(1 - v*v / c*c)), where again v is some portion or multiple of (i * c).
The argument that someone in C.C.C. achieves a velocity into an "imaginary" dimension is supported by laws for the general wave equations of light and sound where the solution is of the form L (amplitude) = exp(iw(t - x/v)) which by Euler's theorem can be put into the form L = cos w(t - x/v) + i times sine w(t - x/v). In some treatments of physics, the complex sine term is considered physically meaningless and only the cosine term is "real". Perhaps, however, the subject in C.C.C. "perceives" the sine term as well as the cosine term, giving him more sense impressions per unit of objective time than is normal. By perceiving the sine term, his subjective time is speeded up and the distance from the object is "shortened" as his awareness of it increases. Thus we have a complementary description of what happens to someone's space-time framework during C.C.C. - an explanation that dovetails in with the argument in the opening section. We now see that the subject in C.C.C. achieves a mental velocity into the i-dimension, which allows him to pick up, bump into, and perceive the imaginary (in a mathematical sense) components of waves (stimuli).
Also, the time-dependent classical and Schroedinger wave equations use the square-root of minus one ( i ), while the time-independent equation for standing waves does not. In my view, time and consciousness are closely bound, so this is another indication that consciousness is represented by i.
Not only does the person in C.C.C. perceive more, but also the quality of what he perceives is greatly different. Most people in strong C.C.C. undergo a mystical experience where they become 'one' with the universe. Thus there is a correlation of complex i-space with a super-consciousness. Since all matter in modern physics is considered to have a complex ( i ) component, this consciousness can be said to pervade the universe. It is actually this consciousness that the person in C.C.C. 'merges' with in complex space, altering his space-time matrix.
The square root of -1 is a better representation of consciousness than infinity because the square root of -1 has an unsolvable quality while infinity can be visualized as a lot of something.
Reality is based on paradox (life is full of twists and turns). Therefore i (the square root of -1) is an apt representation since i to the third power = -i, and i to the fifth power = i.
The square root of minus one is the geometric
mean between opposites:
+1 / i = i / -1; and plus / i = i / minus; and Yang / i = i / Yin. Another way of putting it is that i exemplifies nonduality.
The square root of -1 is necessary as a factor of unity. The infinite roots of unity (one) are of the form (cos A + i times sine A) [de Moivre's Theorem]. Cos A, for example, could represent the physical part of the universe while i times sine A could be the mental part.
"To see a World in a Grain of Sand, And a Heaven in a Wild Flower, Hold Infinity in the palm of your hand, And Eternity in an Hour." - William Blake in "Auguries of Innocence"
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