Scaling for Equivalent SPACE:
Scaling for Equivalent TIME:
We are able to discern π and Φ as discrete magnitudes in projection to (3D) equivalent space (+ clock time). Ultimately, this IS the apparent spatial separation that provides for the concept of dimension along with the perceived 'flow of time'.
This is *not* the case with ϕ and Π, as being representative of projections of motion in (3D) coordinate time (+ clock space), we cannot see locations in time; however, we can see how motion in time effects motion in space as an equivalence -- we call these "forces".
Here that equivalence is to reduce the motion in time to a net effect in that we are only able to observe the ratio of these two magnitudes in proportion -- two imaginary magnitudes become real as one:
I want to call this an apparent-equivalent equivalent apparent space -- as adding a leading 'apparent-equivalent' pejorative flips the whole thing (in 3D) from time to space in our mind -- and suspect this is the '2' that forms the base of the scalar-to-coordinate dimensional expansion series, analogous to how e is used as "½" of the projective equivalence where eπi + 1 = 0.Equivalent Apparent Time
Quantum e = ϕ/Π = (±i)/(±i/2) = 2 = 1+1
There's a very good reason the '±' are contained within as here these are polarities for the formation of poles. When we mix these we get scalar combinations '++', '+-', '-+', and '--' as conjugate products of two roots.
Recall that as '++' and '--' are separate "directions" they cannot be discerned in coordinate space i.e. they are different but in the same manner, and as there is no direction change ('+' → '-' or '-' → '+'), and order of operations matters; this set of four polarities (2 of 2D poles as '±') are reduced to a set of 3 as (1) no change, (2) change in aspect one as scalar time followed by change in aspect two as scalar space, (3) and change in aspect one as scalar space followed by change in aspect two as scalar time.
Here they are: 21 = 2, 22 = 4, and 23 = 8 as equivalent scalar "directions" (UoM) for motions in 1, 2, or 3 scalar dimensions: The Affine (1 scalar dimension below the "speed of light"), The Metric (2 scalar dimensions below the "speed of light"), and The Euclidean (3 scalar dimensions below the "speed of light").
We recall 20 = 1 is reserved for the Projective stratum (4 "points" at infinity).
Cheat sheet a.k.a. Definitions:
An 'apparently-equivalent equivalently-apparent' perspective forms a boundary perspective. Apparently-equivalent IS the inverse-conjugate of equivalently-apparent hence this IS a unit boundary -- a 3D pole. In this case a perceived "local" unit boundary as it is totally apparent. This forms the boundary space as a 3D "bubble" for containing a quad (2x2) projected set of 3D holographic perspectives as two pairs of coordinate systems, each with their own inverse-conjugate clock. Welcome to the The Desert of The Real.FIRST Equivalent Reciprocal is Apparent means apparent Inverse of the aspects of space and time -- simple 1x1D inversion i.e. flip it!: e.g. One (1) apparent pole inverts to form 2 apparent polarities.
SECOND Equivalent Reciprocal is Equivalent means Conjugate (which must be treated differently as aspects of space and time as conjugation implies discrete geometry) -- 1x2D invert: e.g. Two (2) apparently-2D polarities inversely conjugate to form four (4) as an apparent three (3).
THIRD Equivalent Reciprocal is Apparent-equivalent means Inverse-conjugate and is a 2D mixing of a pair of 2-dimensional rotational relationships (in space-time and/or time-space) -- 2x2D invert and hold invariant one "point" to allow for geometric casting to (3D) coordinate system plus a clock: e.g. Two (2) sets of three (3) of equivalently-apparently-3D conjugates inversely combine to form four (4) sets of four (4) as apparently-equivalent equivalently-apparent perspectives.
Note: Operations are applied in order of "inside-out" with respect to the operations/dimensions as/of primary operator. For example: a big, green apple is primary operator 'apple' where 'green' is first operand (discernment), and 'big' is second operand, etc. as net temporal displacements would be so ordered in equivalent space
We recall, there is only UNITY. Everything is reducible to One.
Inverse (i.e. apparent-equivalent) Quantum e is then 1/2 (also real) or what we call the 'Half-life' of radioactive decay:
This is a double-equivalence... an equivalent equivalent scalar magnitude. There are three labels applied to time. Why is this not a triple equivalence? The answer is to do with our non-observance of true Space and Time, we observe equivalent space and equivalent time, the first derivative of Space and Time only; and because these are but abstractions to our mind they are but aspects of space and time. As such, these polarities as root magnitudes are always apparent. This is implied as applied to the Affine down to the Euclidean.Apparent-Equivalent Equivalent Apparent Time:
"Think3D" Inverse Quantum e = 1/2 = 1/(1+1)
The so-called half-life is how we experience an apparent-equivalent linear-step time evolution of an exponential growth series in time (increasing squares as OUTWARD motion from UNITY) as equivalent space in apparent time i.e. 3D coordinate space + CLOCK TIME (Whew! Thinking in 3D can be challenging!)
This is a temporal atomic supernova -- explosion in time ↔ implosion in space -- the net magnitude of which plays out in (3D) coordinate space as 'half-life' to our perspective as this motion in time must be scaled to an equivalent clock in all 3 scalar dimensions to allow for 3D inversion (reciprocation) in preparation for an equivalent apparent projection to be made by differentiation with respect to CLOCK TIME, a unit boundary (i.e. light or the "speed of light"), or CLOCK SPACE, the same unit boundary inversely expressed.
We can see how we had to cast across two apparent (polarity-based) boundaries... that's a double-cast and yep, we HAD to translation to the Metric to convert to an equivalence (an 'equivalent-equivalence') on the other side of the perceived "local" unit boundary.
Another possible link:
Placing Φ and π in proportion and rooting (transforms equivalence space → equivalent equivalent space)*: e.g. Φ/π = √(1/4) = 1/2
* object-oriented programmers will recognize this as a pointer to a pointer for passing complex data structures or routine entry points as arguments to other routines. The Universe appears to use a 3-tuple pair of binary flip-flops as pointers to pointers to pointers for determining "location" in either projective (3D coordinate) space or projective (3D coordinate) time. The final bit selects Parity as "direction".