Generic motion in N dimensions will imply pairwise rotational motion between any two dimensions.

Humans perceive three dimensions. This is reflected in the rotational degrees of freedom of the limbs and torso. Bioenergy (qi) circulates in three circles; around the legs, around the arms and around the spine (up the front of the torso and down the back). The arms have the capability of circulating energy in an orthogonal direction to the leg energy circulation, this implies that humans can manipulate three dimensions of motion.

It can be seen that simpler animals are restricted in operating in certain pairwise combinations of motion simulatensously. The idea is that higher states of consiousness such as humans vs animals is reflected in the dimensionality (number of dimensions) of the motions that are available for manipulation. Animals must support their torso with both sets of limbs, and are thereby restricted to the i,j and i,k motions, whereas humans have i,j; j,k; and i,k (where i,j,k are orthogonal dimensions of motion ).

Given N dimensions, the next state of evolution in consciousness would involve the fourth dimension, which can have pairwise combination with any other motions.

There are other possible motions beyond pairwise combinations. These are the n-fold rotations which can be though of as simultaneous combination of pairwise rotations. The basic 3d example could be thought of as i -> j and i -> k simultaneously. This requires a minimum of two displacements in the i dimension. In general, an n-fold rotation is defined as simultaneous mixing among n dimensions. There are N choose 2 (https://en.wikipedia.org/wiki/Binomial_coefficient) combinations of pairwise mixings, and in general N choose M combinations of M-fold rotational motion. There are M! (https://en.wikipedia.org/wiki/Factorial) ways of permuting the M dimensions involved in the rotation, and all permutations are played out in equal proprotion due to the N-dimensional nature of time (being a recirprocal of space). Sequence of rotational mixing (spin direction) corresponds to the mixing of the temporal coordinates, i, j, k. The phase of the rotation would then correspond to the spacial sequence. "Phase" and "Direction" are concepts that are reflections of the mind which collapses time into 1 dimension, or by the fourier transform (https://en.wikipedia.org/wiki/Fourier_transform) collapse space into 1 dimension.

## N Dimensional Motion

### Re: N Dimensional Motion

Based on observation, a "quantized increase" in dimension tends to follow a power series, not a linear progression. A 1D system expands to 2D, then to 4D, then to 8D (2

^{0}, 2

^{1}, 2

^{2}, 2

^{3}...), the same way geometry increases. Evolution should follow the progression of 2

^{n}→ 2

^{n+1}, dimensionally.

I would consider phase and direction to be more of the minds "interpretation" of the limited, sensory data (sensation and intuition) being presented to it. Larson points out that only ONE scalar dimension can be fully expressed in a coordinate system (where our senses operate), so to compensate for motion in other dimensions the mind would have to invent other concepts to account for the abnormal behavior. Nehru's example of ferromagnetism comes to mind... a piece of loadstone behaves differently than other rocks of similar composition because a third, scalar dimension is acting upon it. If we directly interpret sensory data of a loadstone, it should not do what it does--be magnetic. So we invent a "magnetic" concept to explain this effect of an unseen dimension.blaine wrote: ↑Sun Apr 29, 2018 6:47 pm"Phase" and "Direction" are concepts that are reflections of the mind which collapses time into 1 dimension, or by the fourier transform (https://en.wikipedia.org/wiki/Fourier_transform) collapse space into 1 dimension.

Every dogma has its day...