Continuing those thoughts...
We've been calling these Yang and Yin; let's be cognizant though that we often deal with shadows and so there are likely yang and yin
aspects of both space and time...
equivalent space being the equivalent spatial representation of motion in time (yang aspect of yin) is one such example.
We now understand
how 1/1 = Φπ
2/16 links discrete
linear (real) motion and
rotational ("imaginary") motion to a common base scalar unity
motion.
E=mc
2 being the 3D solution in regard to reciprocal motion as observed across the unit boundary as mass/gravity.
There should be then 2D and 1D solution(s) and I suspect we have more than a few (read: all) in hand already.
In fact, each are as previously provided: two sides of a single coin when referring to the projective
aspects of space and time.
Should not "squaring of the circle" provide for the discrete set of linear-to-rotational motion (speed/energy) solutions?
For instance, is there not already an inextricable link between engine
speed (rpm measured as frequency) and engine power, itself (rate of energy per time) a function of energy (torque) output with respect to time? The engine spins and this itself creates the linear motion of the car down the road. (We're literally attempting to understand the transmission component.) The car moves the desired "direction" in space being equal-and-opposite in "direction" of the engine motion.
Put otherwise: the rate of change of velocity (acceleration) is proportional to the rate of change of speed of engine rotation (energy measured as frequency) and the radius (distance) of the motion swept out (integrated over clock
space) with respect to clock time and we call this power.
F = ma → t/s
2 = t
3/s
3 × s/t
2 where 'F' and 'a' are
conjugates
As Larson described, rotating balls moving against the linear-imposed motion of the conveyor belt in which they are located. Most of the early confusion may be caused by failure to segregate 3 scalar dimensions from 3 coordinate dimensions the latter of which can only be provided for in a low-speed (1-x) gravitational system as 3D coordinate space + 1D scalar time.
Force is a 1D push/pull vector in space-time, the result of which is the apparent "force" of gravitational attraction when expressed as a maximum of 3 (scalar) dimensions of inward motion -- i.j.k = -1 -- or 3 scalar dimensions of motion in time properly situated within a unit of space that we call the Time Region (where there can be motion in time only as space is fixed at unity). We measure this as a 1D inverse speed (energy) as we cannot measure locations in coordinate time and so observe only the shadow (3D → 1D) as the motion crosses the unit boundary or more appropriately as we view said motion from the opposite side of the unit boundary.
Dual quaternions then provide for
observation of a single dimension of time distributed over a 3D coordinate space or little spherical balls of "mass" we call atoms. The solid of time.
The relation of any two said "points" or many "points" would then constitute the gravitational "attraction" as a function of mass (depth of angular recursion in time -- unbounded counter spatial
turn measured as bounded "frequency") and distance in space. This is what digs at me when I see the internals of the exchange mechanism as (st)
2.
Not motion. The actual (i.e. fully-expressed) ratios of motion have been over-simplified (reduced) to *not* motion.
The interaction of the mass field or what we call 1D gravity (as it must be, we're in 1D space, right?) is really due 3D motion (the mass as temporal motion) turned inside-out, upside-down, and backwards in 4D (3 spatial + 1 temporal scalar) wherein mass being an outward temporal rotation in time (3D energy) becomes an inward linear motion in space, due the inherent duality of PG (projective geometry): points becomes volumes (in 3D coordinate space -- Euclidean) and volumes become points; lines become planes and planes become lines (electro-magnetic in a 'nut'). Hence, unit space (TR) -- a universe of time within a single "point" in space. Point goes in quotes as there is no zero, just inverse infinity (that is to say: inverse all or nothing) being of
no dimension.
The universe tends to work by taking one (to be defined), creating an
apparent reciprocal duality, then re-combing to pro-create something new. Do this again in the reciprocal fashion and combine once over. Now repeat that overall process in the reciprocal fashion and combine once more. Repeat.
Going back to the original thought: we do see the rotational energy of the engine and the linear motion of the conveyance as conjugates in 3D coordinate space with the ensuring orthogonal vectoral displacement in space. We explore a similar phenomenon in the Intermediate (2-x) speed range with a non-dissertation on electrical
reactance.
Seems to me that all of these state equations should be shown to be naturally coupled to the entering premise and the resulting understanding as to the proper value for π should shock the [scientific/mathematical/crypto/radio, really
whole] world to the core.
For example,
P = I2R where I (speed, s/t) is +1 on the real (DC) axis and so is equivalent to c and therefore I
2 → c
2 as in E = mc
2. Here we relate power (energy per time) to resistance (mass per time) -- in essence we've taken the first derivative of everything (with respect to clock time).