Structure and reversibility - what about irreversibility?

[SteveA]

Assume for a second that we want to map out some landscape and discover the surroundings.

Any information we gain about the terrain needs to be unifiable if we're to see it as a whole. This fundamentally requires that some origin exist and everything can be tied together relative to that point (in the case of physical experiences this would be an observer).

Any motion away from such an origin needs to be able to return, otherwise the results of that are not known and we could see this similar to operations that are reversible.

In information theory, we can collect information from an environment and perform various transformations upon it (which in many ways is the same as adding information to it in the context of a memory of what operations have been preformed on it), but if we remove some of that information, it isn't recoverable and that's an irreversible operation.

If we assume all structures in time determine rigid cause and effect relationship across time, then these need to all arise from reversible operations in time, otherwise the manner of getting to a moment is not determined by the past and has no such "provable" bidirectional cause and effect structure.

This reversibility is observed in physical laws and has been (in a sense, ironically) seen as a conundrum in physics as it doesn't correlate with the perceived directionality of time inherent in conscious perceptions.

Quantum mechanics could be showing us the existence of unidirectional and effectively creative and non-deterministic (at least from our perspective) events in time.

Let's generalize upon what reversibility and irreversibility are:

If we have some set of states (such as a list of potential decisions we can make) and we correlate these with some subsequent state (such as a result of an action), then if there is a way to return to the initial state we can integrate that subsequent state as a potentially valid result we can provably reach (for example, if we drop an apple, and it falls on the ground and we can return to a state in which we can, once again drop the apple, then we can assume we can continue to drop apples and prove they fall and repeat the "experiment" any number of times to build confidence in the result).

On the other hand, if we have a transition to a state that we cannot return to, then this transition only occurs in one direction and the information regarding those pathways isn't seen as a determinable structure to that initial state - it's a figurative leap of faith.

With regard to a "Theory of Everything" for science, this would appear to place it in the context of potentially all operations for which information is conserved and a return to an origin(al state) can be constructed, though additionally in the context of science as a social institution we could potentially need to restrict this further to the set of processes that can both return to an origin as well as those processes that can be used to bidirectionally communicate information regarding those, between multiple observers, with some measure of statistical confidence (and as usual, when we try to integrate multiple perspectives things become uncertain).

[ggullet]

in order to have reversibilty existence of the first action would have to be completely erased in order to assure non contamination of the second action, and so on. in which case there would be no way to make comparisons and build confidence. therefore choice is an illusion

[SteveA]

in order to have reversibilty existence of the first action would have to be completely erased in order to assure non contamination of the second action, and so on. in which case there would be no way to make comparisons and build confidence. therefore choice is an illusion

If we use logic, then yes, choice would seem to have to be an illusion, but there could exist things for which no logic can be applied.

In my post above, it would still seem required that logic (or a persistent structure) still apply beyond such an event horizon if the motion occured via. some motion/change derived from a preexisting logic/structure as it would appear a paradox to be able to reach some state based upon a motion determined by some form only to reach a state that was not determined by that form of motion ... the motion should have never occured in that case.

As an analogy, if we were in space and used the positions of stars to guide by, any motions that were determined by them would appear to have to remain within the same space as them, or similarly we could not count to a next number and arrive at something that wasn't a number.

The manner in which a change of state occurs, determines the space in which the change/motion occurs and this would seem true of logic or form in general and I'd assume, for example, that even something that appeared to be an event horizon, though potentially solely a motion in one direction (much like time) would have to at least retain/inherit some structure of a space beyond it, if it was attached in properties to some specific position or form in the previous space, because if it didn't, how could a motion determined by one form of space/logic leads to a state that was not determined by that motion? It seems as though if that was the case, it would be equivalent to a wall instead.

And again, regarding choice, I tend to agree with you that there is no (longer) free will, at least not in terms of how things unfold over time from some timeless perspective, which we don't have access to, beyond the simple that fact we are what we are.

But there are multiple ways of looking at this and recognize that cause and effect apply both ways. We could say that the universe has been going along on its merry way for billions of year to reach this point in which we were predetermined to have this conversation, but it goes both ways, we could also say that because we (wanted) to have this conversation, the universe was predetermined billions of years ago to get us here in order that it become possible.

Also, though such a predetermination can exist, without knowledge of what it is, there is nothing specific that it must be and we're free to discover in any manner we want what it is as no actions would violate that predetermination.

My assumption is that whatever determines what that timeless aspect of oneself is, is also the source of such predetermination ... so basically it's the same predetermination as the fact that, whereever you go, there you are and it could have been that everything was predetermined to do what it wanted to do and we're currently in the process of learning/discovering what that is.

Another interesting consideration is that, given an unlimited number of possible "initial" states, there similarly exists the equivalent of an unlimited quantity of finite choices possible (for example, if we said that each digit of pi was a decision of 1 of 10 options, then there would be the equivalent of an infinite number of decisions that could be made over time), so though it could be predetermined, there would appear to be a lot of decisions left to be made (ok, "discovering" what those decisions were).

In itself, free will isn't of value ... the intent of making a decision is to have things to be determined to be according to that decision. If things were not predetermined by a choice, but were left to something else to make a whimsical decision, then there would not truly be a choice, and also, if someone was presented with various options regarding some condition, what would the ideal choice be? It would appear that there's no reason to select anything other than the best (unless some exploration is desired, in which case that would still become the "best" decision - to select something that was non-optimal in some respect in order to experience it in comparison).

One insight I had a while back was that ultimately it would appear better to be tied to everything I love than have the freedom to be somewhere else that I wouldn't want to be ... given the choice, where else would you want to be? (If there's something else, I'm not clever enough to figure it out and that's a "fate" I'm willing to accept )

[Lloyd Gillespie]

Another interesting consideration is that, given an unlimited number of possible "initial" states, there similarly exists the equivalent of an unlimited quantity of finite choices possible (for example, if we said that each digit of pi was a decision of 1 of 10 options, then there would be the equivalent of an infinite number of decisions that could be made over time), so though it could be predetermined, there would appear to be a lot of decisions left to be made (ok, "discovering" what those decisions were).

So Steve, what you're saying is that mathematics is incomplete logic__as it's possible to divide every single digit into its infinite bits...

So, in reality mathematics is nothing but theology, until I make the Free-Will Choice to offer the Ultimate Formula__X/X = 1 + IEE...

I think that's funny__All Individual Digits Have Infinite Divisional Attributes/Functions/Products/Sums...

I always knew, there was a way to create a fully functioning Infinity Math...

1 = ∞ n 1

[SteveA]

So Steve, what you're saying is that mathematics is incomplete logic__as it's possible to divide every single digit into its infinite bits...

If we consider irrational numbers to be a part of mathematics, then yes. Someone could write any arbitrary string of bits and interpret these to be a recursive computation over time with, yet again, any arbitrary point of divergence and it can always be a deterministic growth yet still retain an unbounded future potential ... a quantity in the process of being constructed.

For example, there are an infinite number of possible ways to iterate a convergence toward Pi. All the divergences can be "infinitesimal", which simply means that any finite measurement can be made to appear to agree with a construction of Pi, yet at any point there can be a divergence in the next digit ... and then we're simply computing some other irrational number.

I didn't make those rules. That's what the conventional mathematical definitions use. They added "free will" to shrink and compress the information.

What's the next decimal digit of 3.14159?

Or which is the "correct" formula for Pi?

Also, could a representation of Pi in two relatively prime bases ever create identical fractional quantities? (No, unless they're all zero, and that's why rational numbers aren't the "unified field" either).

http://mathworld.wolfram.com/PiFormulas.html

There is no correct formula for Pi in the (misnoemered) "real" number system.

Not only do these different representations use different intermediate forms of "space" in their construction, but we could prove that the quantities constructed could not even be equal to each other. It's only a ratio of quantities that approaches an identical (yet arbitrarily selected) limit, which is connected to NONE of them!

If we used this logic with natural numbers, that identity is equated with having a manner of representation that doesn't allow points to be placed between two quantities, then we could prove all natural numbers are equal to each other because there is no natural number between 2 and 3, hence, using the "logic" of (un)"real" numbers, we could declare that 2 and 3 are equal to each other (in the limit).

Well of course, 3 would also be equal to 4 and then 5 etc. and we have an informational black hole (and yes, that's how mathematical singularities occur).

I'm simply stating how logic works with respect to information - if mathematics is not logical, then no, I don't do mathematics.

So, in reality mathematics is nothing but theology, until I make the Free-Will Choice to offer the Ultimate Formula__X/X = 1 + IEE...

Yes, until you change your mind.

How many revisions has mathematics gone through over the last couple millenia? Irrational numbers have always been the thorn. The resolution is that an irrational number is not a number at all but a recursive algorithm of unbounded complexity that generates infinite sets.

If we really wanted to be more precise regarding something like the concept of Pi, it's a two dimensional array of paired quantities (ratios of n/m).

One dimension is the specific form of construction of Pi and the other is the iteration number (the component of time, or how far into the computation the currently accepted approximation is). These are really all rolled up into a single dimension of time, so we have a process that both constructs new approximations for Pi as well having that process "delve" into each of these.

And that's basically the history of mathematics in a nutshell. Creating new languages, writing a few stories in each of them and seeing how the cultures of each interact. Picking a few favorites and continuing on.

I think that's funny__All Individual Digits Have Infinite Divisional Attributes/Functions/Products/Sums...

I hadn't considered that possibility, but yes, you might have (accidently? ... oops, almost forgot I don't believe in accidents ) hit on something. The information context of a digit is determined by the space in which it exists - a growing space gives a growing information context to each digit. The sum is greater than it's parts (in many cases this gain is logarithmic and has chaotic/spectral features).

Yes, consider how individual digits would be required to be placed in a space. A manner to localize these would be needed. The dimensions and properties of the space would need to increase as new digits were added and this could even alter the context of past events/digits.

Thanks for the idea.

I always knew, there was a way to create a fully functioning Infinity Math...

Pure creativity. Then again, there might be some maximal possible form of growth. If there is some some finite set of operations that could encapsulate all such forms, then, yes, we'd basically be able to simply count through an infinite evolution of mathematical systems. (Not that this would necessarily be the same as evolution here and these events could be reordered in their respective timelines).

Within a limited context, it could be possible to do this (the problem is whether or not that "limited context" actually equates with all contexts).

1 = ∞ n 1

I remembered seeing some correlations with your ideas here and a self observation.

Imagine the universe was at some state in time representable by a quantity, n.

In order to have "n" make a relative observation of an equivalent of "n", we'd have to use "n" as our metric, which would mean constructing n*n, in order to observe (n*n)/n=n, but if it's all connected, then a construction of n*n would be appended to n and the total quantity encapsulating the observation would be (n+n*n) or n(n+1) and the observation of this (virtual) structure, relative to the new state of n*n would be n(n+1)/(n*n)=1+1/n and that closely matches your form.

If n is "infinite", then we have 3 quantities involved (n, n*n, and the total n*n+n) and could make comparisons in 2 different directions along each "axis"/dimension in reciprocal forms and different characteristics in each of these directions.