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FQXi FORUM
CATEGORY: Ultimate Reality
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TOPIC: Does Math Evolve?
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 | | image: fdecomite |
Here’s what I’m wondering: At Plank Density or greater, distinctions such as “here” and “there” have no operational meaning. When the universe was at this density, were simple arithmetical operations true?
If we say yes, we are agreeing that a binary operation, such as addition, has meaning *when it has no referent*. This would be a foundational assertion of the first order. At Plank density there is no “this (object)” plus “that (object),” even in principle; nor is there a “before” or “after,” which are at least implied by the two sides of an equivalence.
If we say the operation is still true, it seems there are only two interpretations. One is that mathematics is supra-natural, existing outside spacetime; though, despite its philosophical popularity, it’s hard to see what this could actually mean.
The other option is that math evolves, so that certain statements become true as they become operationally possible. Or do they become true as they become computationally possible . . .?
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There are three fundamental and interrelated relationships of reference for perspective. The three fundamental relationships of reference for perspective are the relationship of the dimensions of Cartesian coordinates with the dimensions of polar coordinates, the relationship of finite with the infinite, and the relationship of 'still' with motion (or constant motion with accelerated motion). Each of these three fundamental relationships are not, in-and-of themselves, a 'given' (that is, not an independent and necessary foundation of physics), but rather, the result of the ‘overlapping’, or exchange, of the designated parameters of the other two. And so, it is the relationships of fundamental references that define tiered perspective (that is, a perspective co-existing within an ‘Other’ overriding perspective) and perspective exchange (that is, consideration, or ‘thought’) as the foundation for all perception (physical observations and symbolic considerations). That is, there is no 'point' of origin, but instead, a relationship determines existence and experience through tiered interrelated combinations of fundamental references into perception ternaries. In other words, various tiers, or ternary combinations, of the constituent references of the three fundamental relationships represent all perspectives and perspective exchanges. The three fundamental relationships are not completely independent of each other, but rather, are interrelated and overlapping (like interacting ‘whirlpools’), in one or two of the three constituent references comprising the involved respective perception ternaries. So, every ‘object’, number, and experience, every physical and mathematical observation and consideration, is represented by overlapping ternary combinations of the constituent references within the three fundamental relationships of reference. And the relationship of tiered combinations forms the perception ternary—the perceived, the perceiver, and the reference of measurement. The model/metaphor is a self-proving totality that is entirely perspective-based, and the necessitated foundation for existence that results from the tiered-ternary relationships of fundamental references, providing its own inter-exchanging context and its own reciprocating cause.
This presents a physics/mathematics continuum, or overlapping exchange, that is based upon the binary relationship of ‘within’ and ‘without’, representing the one-or-two-of-three of the constituent references in a perception ternary. That is, the overlapping of one, or the overlapping of two of the constituent references in the various constituent tiers, or ternary combinations, determines the relationship as ‘without’ or ‘within’, respectively. Thus, in physics (or ‘without’—reference paired with perceived in perception ternary), the three fundamental relationships of reference form, by perspective, the three fundamental overlapping and interrelated concepts of distance, time/speed, and mass/acceleration; and in mathematics (or ‘within’—the symbolic pairs the reference with the perceiver in the perception ternary), the three fundamental relationships of reference form, by perspective, the three overlapping and interrelated fundamental ‘constants’ which divide, or provide the exchange for, the three fundamental concepts of physics—namely, epsilon, pi, and phi (the golden ratio). That is, epsilon represents mathematically the divide, or reference of exchange, between distance and speed, pi represents mathematically the divide, or reference of exchange, between linear distance and rotational distance, and phi represents mathematically the divide, or reference of exchange, between linear distance and area (dimensional shift). Further, every ‘physical’ observation is symbolic in one-of-three of the perception ternary; and conversely, every ‘mathematical’ consideration is physical (more truly, of other tiered consideration) in one-of-three of its analogous perception ternary. So, mathematics, whether as numerical values, operations, or their corresponding geometry, is the result of tiered co-perception (or, tiered perspective and perspective exchange), just as with physics, with overlapping and exchanging references ‘within’ and ‘without’, so that each completes the other.
In this way, all values can therefore be defined completely only through the multiple and interrelated contexts (references) of tiered perspectives, thereby representing a ‘number’ (or perception ternary) not as an exact, or ‘given’, absolute, but rather in relation to another perception ternary which is separated by one-or-two of their constituent fundamental references—for instance, relating, as a perceived proportion, a fundamental concept like that of time or dimensions to distance. So, ‘value’ and ‘path’ (or, act of calculation) ‘trade places’ (exchange) and are defined in the same way that ‘observer’ and ‘object’ do in their physical correlation. That is, the ‘constants’ (constant only by co-perspective), pi, phi, and epsilon, as well as the exchanges between them, represented by the polar and Cartesian forms of complex numbers (‘i’), frame the foundation for the mathematical correlate of perspective and perspective exchange. And, as with the three fundamental concepts of physics, these values are overlapping and interrelated.
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Very interesting, of course one can define a "perspective" space, relative to observation?..and thus: space is continuous if matter is absent, and discrete if matter is present. The appearence of matter are the "bits" of non continuous space!
Introduce matter to space and Time appears into the equation, a "bit" of matter creates a "length" of time?
Now mathematically one can relate certain number partitions with parity of ODD + EVEN in congrugences:
10 > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 >0
EVEN-ODD-EVEN-ODD... down to an EVEN zero, and of coure any even number can be partitioned, or halved!...
add two odd numbers you get an even number result, add two even numbers together and you still get an even result?..now add odd + even numbers, you get odd result!
In measure terms it can be related to space being "even" added with matter "odd" and the rusulting spacetime comes out at '3'..related to of course 3-D!
At the planck scale there must be partitioning of space dimensions, and the appearence of little string "bits" are a virtual quantity, born out of trying to continue a path of matter within a constrained path of continuous space, a "zero" patch of space without matter can be sliced in "two", and you end up with a (string) quantity that is increasing, at least in energy terms, of into theorized "extra-dimensional arena's" ?..by the way the matter "time", componant is obviously planck "odd" or 1, and cannot be halved, or broken down any further than three "bits" or fractional quarks.
Down at the string scale, there is a doubling of string energy, as you calculate the energies exponentially gat greater, "strings" shoulkd really be thought of links in a chain, break one and another two takes it place, not in another dimensions, but literally in a certain scale, or to be correct density!
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