QsDyn-6
From the measure of distance in the quasic grid from the Surreal (Conway) view we can plot where certain levels of discrete games will emerge if we find an evolution at certain nodes to so plot the preternatural state of the abstract space into some direction...this is the greater rule beyond where in a quasic n-dimensional chessgame that in general may not distinguish the wins or draws with certainty we observe at least a duality as to what are systems and subsystems of the binary powers in unity. This post on fb contains some of the thoughts on this.
So, the good news is that this rule has its place in the totality of concrete and abstract considerations - a sort of logic as issues of degrees of freedom, and that with a little tweaking our existing notations can be useful in describing the general state of things. Are you asking me for further discussion? The logical space, concrete or abstract at some level we see in the chaos of small changes in QM influencing great changes at some state will approach unity... this unity is like a conceptual lens where this rule may be expressed in different abstract dimensions without contradiction... and what we see thru it is after all the results and interpretations of what we actually see in the slit experiments regardless of if we or the apparatus chooses to observe the underlying primitive space so as to apply such a "mysterious" rule. On a calculator a^n + b^n approaches 1 does it not? In a sense you are saying fundamental things, information theory like, which tends to agree with my simple statement that more than just the algebra is involved here but more like the arithmetic. Under the surface of truly balanced equations, at the in-variance of our zones of horizons information can be said to be equal between dimension, say 2D into 3D mapping. But if in the quantum sense we allow a still deeper grounding as a matter of widest uncertainty thus widest degrees of freedom we need more to explain general possibilities of theory. There is nothing "mysterious" about higher dimensions (Euclidean at least) but it seems to me that our minds are such a lens, perhaps partial also in its directions as to what is formal necessity, that observes and computes these things regardless if space is absolute, empty, or distance as remote measure, or that in effect or real such a Born like juxtaposition of mirrors we say some dimensions or values can be useful in the description a concrete rather than just methods of simplification of formulas otherwise very cumbersome or if expanded almost impossible to reduce over all of time.
[ This posted in comment to Neil Bates on the Born Rule that for some reason does not seem to show up there. But it does relate to what I call Quasic Dynamics 6 posting notes pending inspired by Jaya's clay model as both concrete and abstract as was the case in predicting the near future models in my candle making designs- In general designs are two years delayed before someone thinks of them and the most improbable design is thought of and bought by someone- yet the general principles can be taken and expanded on by someone. For me I took hints from structures of things like branching in nature of the flora around me for a starting point. It seems the great problem in a start up or proposal of ideas is that in principle one has to compete with oneself for access of forces in the market place if our ideas make a difference and are not indirectly shared.]
As far as this limitation over the abstract directions and divisions in the representations where our sentience can be described as such a lens or useful physical device, The King is more limited in moves unlike the Queen or knight save in looping reflections in abstract x y z 3D directions so in 3D the board where the piece is he particle and the board the field the total cells regardless of boundary is reduced by 1/4 th an so on...
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And the stars also... How deeply am I seeing? 37 and 73
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