On The Nature Of Infinity

[Fred Henderson]

<snip

The universe can be both infinite AND expanding. <snip>

That can only mean that infinity is really just the outer limits of measureability. Which must mean that we can measure past the outer edge of the ever expanding universe, for if we couldn't, we wouldn't know that it was infinite. Make sense?

By the way, did you know that I have proven that someone existed before God? It's so pbvious. For if people tell me that God exists because you can't get something from nothing, then I tell them that someone must have created God.

[Brad Thomson]

...someone must have created God.

Perhaps, but what created THAT someone, or where did THAT someone or something come from, ad inifinitum? Either we suppose an infinite regress, which does not explain existence in the first place, or we suppose the appearance of existence from nothing, with no cause, with no explanation. So, either way existence cannot be explained- there is no explanation, no reason, no before, no purpose except the purpose it chooses to give itself after the fact.

[Fred Henderson]

Perhaps, but what created THAT someone, or where did THAT someone or something come from, ad inifinitum? Either we suppose an infinite regress, which does not explain existence in the first place, or we suppose the appearance of existence from nothing, with no cause, with no explanation. So, either way existence cannot be explained- there is no explanation, no reason, no before, no purpose except the purpose it chooses to give itself after the fact.

I would call this a kind of backwards, or double-ended, infinity, not only does time never end, it never begins as well. Which means there is no time except the present.

:)

[Brad Thomson]

I would call this a kind of backwards, or double-ended, infinity, not only does time never end, it never begins as well. Which means there is no time except the present.

:)

Agreed, this is the next step in the logic. Time is always now/beginning/ending. So, existence is not miraculous once, it is perpetually miraculous, one now/miracle after another after another. Not only does Time/Substance come from and return to nothing, it keeps doing so time after time after time.

[Pargat Perrer]

Agreed, this is the next step in the logic. Time is always now/beginning/ending. So, existence is not miraculous once, it is perpetually miraculous, one now/miracle after another after another. Not only does Time/Substance come from and return to nothing, it keeps doing so time after time after time.

Imagine you are standing on an Earth-sized sphere in which the entire surface is homogeneous, unchanging. You can only see down at your feet, that you are standing on this surface. Beyond your feet, you can only see total blackness. You are facing some direction which you cannot change, i.e. you cannot turn your feet in some other direction. You are compelled by some force to take a step forward. You look down and you are standing on the same surface, Nothing seems to have changed You step again ... and again ... and again ... onward into infinity, you cannot stop stepping forward. Nothing ever changes in terms of what you can see of the surface. However, perhaps things change in the square foot or so of the environment above the surface.

You are compelled to keep moving forward, step by step at a constant rate, and whatever is in your square-foot visible environment above the surface moves with you. You can remember "past times" when perhaps something different appeared in the square-foot volume above your feet. Maybe a solar system appeared, and then a planet, and then life on the planet, etc etc. Maybe a time comes when you can see an entire Universe within your square foot of volume. , and the Universe moves with you, and with each step it changes.

Could not time be this sphere? It would seem in your mind to never begin and never end. The ticking of time is your footsteps, always in the same direction, and you cannot "jump" ahead, you can only step at a constant, never-ending rate. If you occupy a square foot that you once occupied before, there is no way of knowing it.

[Brad Thomson]

The theory that Time is circular is held by some. One argument, based upon the supposition of the existence of matter, suggests that because the amount of matter is finite, and because it operates according to the immutable laws of the interaction of matter, eventually the same material configuration will return since there is a finite number of possible combinations, and when this happens the same laws will be in effect and thus the same sequence of events will ensue repeatedly, unto eternity. But in this case, Time, or the events in time, are not actually circular, it is rather a spiral of events in an ever moving forward time. Of course, I do not believe this theory, though Nietzsche argues for it in The Will to Power. This is his "eternal recurrence", which I do not accept. If Time is Substance is Mind, then such a thing is impossible, because even if every mind thought the same thoughts at the same time as had happened at some point in the past, there would still be the memory of having done so manifesting itself sooner or later, preventing a spiral repetition even if thought wanted to repeat. We can think the same thoughts as we did yesterday, but when we do so we know it, so in a sense they are not the same thoughts, or they are the same thoughts in terms of quality, but they are knowingly numerically distinct.

[Fred Henderson]

What time is it?

[Pargat Perrer]

The theory that Time is circular is held by some. One argument, based upon the supposition of the existence of matter, suggests that because the amount of matter is finite, and because it operates according to the immutable laws of the interaction of matter, eventually the same material configuration will return since there is a finite number of possible combinations, and when this happens the same laws will be in effect and thus the same sequence of events will ensue repeatedly, unto eternity. But in this case, Time, or the events in time, are not actually circular, it is rather a spiral of events in an ever moving forward time. Of course, I do not believe this theory, though Nietzsche argues for it in The Will to Power. This is his "eternal recurrence", which I do not accept. If Time is Substance is Mind, then such a thing is impossible, because even if every mind thought the same thoughts at the same time as had happened at some point in the past, there would still be the memory of having done so manifesting itself sooner or later, preventing a spiral repetition even if thought wanted to repeat. We can think the same thoughts as we did yesterday, but when we do so we know it, so in a sense they are not the same thoughts, or they are the same thoughts in terms of quality, but they are knowingly numerically distinct.

I was not suggesting that there is a repetition in either states of matter or the events that ensue from such states of matter. I was suggesting that time may be imagined as a 3D sphere. When a point on the sphere is "arrived at" once again in a particular spacetime universe, it doesn't require that the states of matter in that universe are identical to what they were the last time that point was arrived at. They could be completely different on each such traversal of that point.

It could even be imagined that the sphere of time is very small, and points on its "surface" are being arrived at very rapidly. The dimensions of the sphere could even be subatomically small. Perhaps the diameter of the sphere has some bearing on the speed of light in that particular universe.

The point is that we humans cannot observe the sphere of time, and so first of all, we do not have any idea that we are repeatedly traversing the sphere again and again. But secondly, and this is the MAIN point, it means that time could have no beginning.

As I think you have stated Brad, time could be the only thing that is real. If we imagine it as this 3D sphere that can never be observed, in part or in whole (but can be measured in a particular spacetime universe moving on its surface), everything that exists (which might be an infinite set of spacetime universes that appear, move, and disappear like sunspots on the surface of the sun) does so on time's spherical surface and moves in one direction only, at a constant rate determined for a particular universe by the speed of light for that universe. How long has this been going on? Infinitely perhaps, since this sphere of time has always existed. (EDIT: the sphere of time is itself outside of time, because time is really the surface of the sphere, therefore time itself can be imagined as non-changing.)

And I am proposing that what COULD make each spacetime universe appear in a "Big Bang" on the surface of time is an infinitesimal change in the speed of light, which will keep increasing forever to create an infinity of future spacetime universes.

As to the "why" of such a totality .... only the Supra-Natural, as Bob calls it, could possibly know.

I have jokingly imagined that this Supra-Natural could merely be a sports and entertainment fan, and just wants to watch more games and movies. Our Earth may be in its most desired form right now, to go forward about 5 billion Earth years until the Sun turns into a red dwarf and vaporizes Earth. So God has about 5 billion years' worth of NHL, NFL, MLB, NBA, golf, curling, tennis etc etc, and of Hollywood and Bollywood movies to look forward to from us .... who are only 1 of an infinity of such sources.

[Frank Dixon]

Max Euwe (1901-1981, World Champion 1935-37, GM from 1950) did his PhD thesis in Mathematics at the University of Amsterdam in 1924, with infinity applications to the question of whether a chess game must end. His thesis supervisor was the legendary Dutch mathematician L.E.J. Brouwer. I ordered a copy from the university, and still have it; I can understand most of it, although it is in Dutch language.

[Brad Thomson]

Alan Tomalty has calculated the longest possible chess game given the rule that the game ends on a threefold repetition where the same player is to move and the pieces all have the same potential, and the 50-move rule wherein there must be either a capture or a pawn move by 50 moves or the game is a draw. I think he came up with somewhere between 500,000 and 600,000 moves but my memory may be failing me as it often does nowadays, and it may have been 5,000,000 to 6,000,000. Basically, Alan reasoned that you make 50 knight moves without repeating, then make one pawn move and do the same thing again, and again and so on and eventually a capture and on and on and on with 50 moves in between each pawn move or capture until such time as no mating material remains. Why Alan wanted to perform this stunt, or feat, he did not say. :)

[Frank Dixon]

Thanks so much to Brad for posting about Alan Tomalty's efforts in this realm! This could be of importance in some research I have been doing!

[Pargat Perrer]

Posted by Brad Thomson:
Alan Tomalty has calculated the longest possible chess game given the rule that the game ends on a threefold repetition where the same player is to move and the pieces all have the same potential, and the 50-move rule wherein there must be either a capture or a pawn move by 50 moves or the game is a draw. I think he came up with somewhere between 500,000 and 600,000 moves but my memory may be failing me as it often does nowadays, and it may have been 5,000,000 to 6,000,000. Basically, Alan reasoned that you make 50 knight moves without repeating, then make one pawn move and do the same thing again, and again and so on and eventually a capture and on and on and on with 50 moves in between each pawn move or capture until such time as no mating material remains. Why Alan wanted to perform this stunt, or feat, he did not say. :)

Thanks so much to Brad for posting about Alan Tomalty's efforts in this realm! This could be of importance in some research I have been doing!

Frank, are you doing research on the longest game possible in chess? or something else?

Chess is a game with some rules designed specifically to prevent a game from going on forever.

Hostage Chess, invented by John Leslie, on the other hand has no such restrictions. Since captured pieces can be reinstated on the board, including Pawns, a Hostage Chess game could potentially go on for an infinite number of moves. AFAIK, Hostage Chess has no 50-move rule, and also if both players have lost many pieces at some point, one player cannot prevent the opponent from bringing back captured pieces onto the board.

Therefore Hostage Chess presents a unique possibility: all legal chess positions (which one highly researched estimate* is approximately [4.82 +- 0.03] * 10^44) minus the ones in which either King is checkmated may occur in a single game of Hostage Chess, given enough time of course.

* see https://github.com/tromp/ChessPositionRanking

[Fred Henderson]

Here's something else that just occurred to me...

It is generally accepted that the universe is ever expanding, It follows obviously that the universe is not infinite, for if it were, there would be no space left for it to expand into. Either that, or the very nature (concept?) of infinity is blown out of the water. So there must be something else out there besides the universe, and that is the space that the universe is filling up. Ergo, the ... entity that I have previously proven created God, must have also created all that empty space.


Brings to mind "Horton Hears a Who"

[Pargat Perrer]

Here's something else that just occurred to me...

It is generally accepted that the universe is ever expanding, It follows obviously that the universe is not infinite, for if it were, there would be no space left for it to expand into. Either that, or the very nature (concept?) of infinity is blown out of the water. So there must be something else out there besides the universe, and that is the space that the universe is filling up. Ergo, the ... entity that I have previously proven created God, must have also created all that empty space.


Brings to mind "Horton Hears a Who"

The expansion of the universe is going on in all directions at once, which means the universe is filling up with spacetime just as a balloon expands in all directions as you blow it up.

So the universe is filling up with spacetime ... which means spacetime DOES NOT EXIST outside the universe. It is impossible for our brains to imagine, but there is absolutely NOTHING the universe is "expanding into".

Supposedly, before the Big Bang, absolutely nothing existed. Not space, not time. Zilch.

EDIT: it just occured to me, the theory of the metaverse, that there are multiple parallel universes ... it might be possible that our universe by expanding is causing some other universe(s) to contract. If true, there is some sort of "boundary" between universes.