SoverT wrote:
At the inanimate level, the maximum stable motion possible is around 256 at a single location (117 after geometric considerations).
Notice, that you mention a motion in a singular form and you also make a statement about "single location".
A single motion cannot define a location - you need a relation between at least two motions to define a non-scalar speed, from which distance and location can be eventually derived, when even more motions are related.
I'm curious what Bruce thinks about this question: What minimum quantity of motions need to be related in order to define a Euclidean point (a single location) ?
That inquiry also brings up the question: Do two units of motion always constitute two separate motions or can they constitute two linked stages of one motion?
In my opinion, it is the latter - what we call a "single motion" in RST is
a series of units of motion (each having two reciprocal aspects) with some linkage or continuity between them.
A series of ratios or any other numbers, can have many (even infinite) members but these members are all linked. They are linked by whatever rules govern the series, e.g. monotonicity or the continuity requirement.
By this logic, two motions would represent two series of ratios. The relation between these two series defines a non-scalar speed. By compounding more relations, distance and eventually points/locations can be defined.
IMO this is how separate electrons, photons, protons, etc... arise. Each one of them consists of a series of units of motion that collectively "do their own thing", e.g. deviate a certain amount from the unit speed. If there were no separate series then there would be no separate particles with different properties.
This type of thinking also leads to the conclusion that a member belonging to one series does not belong to the other series, but the relation between members belonging to different series constitutes observation between separate objects. (objects are motions, too).
The next interesting question is: What does the relation between the units of THE SAME motion constitute ? (this is the relation between the members of the series itself )
IMO to answer these questions, we should start with the simple case of relation between two units of motion a/b and c/d. Such relation is a crossratio: a/b ÷ c/d - the famous invariant in Projective Geometry which is the centerpiece of RS2.
From the Fundamental Postulates we know that a/b must have a speed of 1 (c/d also). If you want to analyze what it means for the two reciprocal aspects of motion, you may notice that unit speed is equivalent to the restriction that each aspect changes its magnitude by one, across that unit.
But, what does it mean to "change" in that context ?
IMO "change" means that the space MUST expand
or contract by 1 spatial unit and the time MUST expand
or contract by 1 temporal unit. The vectorial direction of that expansion or contraction is arbitrary or immaterial at this stage of analysis.
Notice the words "or", which I have highlighted in the passage above. For now let's skip the question whether this expansion or contraction is 1D, 2D or 3D - it does not matter for the analysis that follows.
Therefore, we can write that crossratio as:
Expansion or Contraction / Expansion or Contraction ÷ Expansion or Contraction / Expansion or Contraction.
Writing out all of the possibilities yields this list:
1) Expansion / Expansion ÷ Expansion / Expansion
2) Expansion / Expansion ÷ Expansion / Contraction
3) Expansion / Expansion ÷ Contraction / Expansion
4) Expansion / Expansion ÷ Contraction / Contraction
5) Expansion / Contraction ÷ Expansion / Expansion
6) Expansion / Contraction ÷ Expansion / Contraction
7) Expansion / Contraction ÷ Contraction / Expansion
8) Expansion / Contraction ÷ Contraction / Contraction
9) Contraction / Expansion ÷ Expansion / Expansion
10) Contraction / Expansion ÷ Expansion / Contraction
11) Contraction / Expansion ÷ Contraction / Expansion
12) Contraction / Expansion ÷ Contraction / Contraction
13) Contraction / Contraction ÷ Expansion / Expansion
14) Contraction / Contraction ÷ Expansion / Contraction
15) Contraction / Contraction ÷ Contraction / Expansion
16) Contraction / Contraction ÷ Contraction / Contraction
...however because reversing the Expansion/Contraction direction in time is tantamount to reversing the Expansion/Contraction of space (think of a movie running backwards) and the absolute spatial or temporal reference system do not exist yet, we notice that cases 1 and 16 are isomorphic/duals.
Isomorphic are also cases 4 & 14 and 6 & 11 and many others just like the states of a Boolean XOR gate.
SoverT wrote:
What I observe in that animation is TWO locations are involved, which means the maximum stable motion should be doubled or squared or something.
That's because that was the best he could do on a spatial graph. It would be impossible to depict a temporal rotation on it.