Infinity

[Gibsense]

Is infinity unreal? We talk about infinite space or an infinite number of real numbers between 0 and 1 a sort of endless division by 2 or whatever. But I wonder how real Infinite actually is.

• Take an infinite line and join the ends. Is it a finite circle? Or is it an infinitely expanding circle?
• How about the real numbers between 0 and 1. If you integrate from 0 to 1 you get 1. Is that like joining the ends?
• And, even if the universe is closed (as opposed to an infinite flat Euclidian one) can it expand infinitely?

It seems as if there is a resolution (like joining the ends) but more profound. As if there is something more fundamental than 'joining the ends'
I cannot crack it. Anyone?

 

[promytius]

An infinite line has no ends.
I don't know what is meant by "integrating" numbers from 0 to 1.
There is infinite room in an infinite universe for infinite expansion.

 

[Gibsense]

An infinite line has no ends.

Why/how/prove?/explain/show etc

I don't know what is meant by "integrating" numbers from 0 to 1.

I mean integration - the mathematical process - algebra-type stuff. Integration shows that if you add up all the infinite bits the total = 1. But then someone who knows better may correct me. It's a long time since I was agile with mathematics

There is infinite room in an infinite universe for infinite expansion.

No there isn't.

 

[Atlan0001]

Why/how/prove?/explain/show etc

I mean integration - the mathematical process - algebra-type stuff. Integration shows that if you add up all the infinite bits the total = 1. But then someone who knows better may correct me. It's a long time since I was agile with mathematics

No there isn't.

Yes there most certainly is. There are infinities of infinites (infinitesimals) (finites) to infinity, including universes, spaces, times, an 'Infinite MULTIVERSE Universe' (the face of the infinite density of an infinite '0' (the face of the infinite '0' of an infinite density)).

The above closed up to superposition Big Background (BC) (BB) Horizon "collapsed cosmological constant (/\) Planck (Big Crunch) (Big Bang) 'Mirror Event Horizon' of the infinity of horizon universes (universe horizons) equals a Planck [unsigned] '1'.

 

[promytius]

Regarding an infinite line; no matter what one would propose as an end of an infinite line, I would simply say, no matter what one labeled as an end, there was still more to go; so much more, that you could never approach the end... because it doesn't have one.
In our infinite universe there is an infinite number of infinite lines for which infinite sentient beings have tried to find an end. An infinite number of sentient beings found no end; while an infinite number of sentient beings found the end of an infinite line.

 

[Catastrophe]

Why/how/prove?/explain/show etc

I mean integration - the mathematical process - algebra-type stuff. Integration shows that if you add up all the infinite bits the total = 1. But then someone who knows better may correct me. It's a long time since I was agile with mathematics

No there isn't.

Introduction to Integration

Integration is a way of adding slices to find the whole. ... Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start ...

www.mathsisfun.com

Cat

 

[whoknows]

"Is infinity unreal? We talk about infinite space or an infinite number of real numbers between 0 and 1 a sort of endless division by 2 or whatever. But I wonder how real Infinite actually is."

Just a layman's thought - maths allows for smoothness and infinite division, however if spacetime is quantized, for instance defined by Planck units, then wouldn't this put a finite limit on division, and hence, on possibilities? So far as I know there are no testable physical infinities found in the real world/universe.

I wondered if there might be infinite moves in chess and found this :-

"Accurate estimates[edit]

John Tromp and Peter Österlund estimated the number of legal chess positions with a 95% confidence level at (4.822±0.028)×10 to the power 44, based on an efficiently computable bijection between integers and chess positions.[5]"

(https://en.wikipedia.org/wiki/Shannon_number)
-----

A huge number, but finite, and seemingly miniscule in number compared to the permutations of Planck units, if spacetime is quantized along those lines.

 

[Catastrophe]

As a long term chess player of some reasonable standard, I should comment on the number of positions quoted in #7. If this means, as I assume, the total number of legal positions, then a very large number would never be seen in practice. For example, if only the Black King were left, one would expect that, in practice, Black would have resigned long before. These positions would be mirrored if White were so reduced. Again, there are millions of possible positions between this example and nearer equality. Of course, this still leaves a vast number of practical possibilities.

Books of Chess Openings, such as "Modern Chess Openings", can list up to (and sometimes more than) 16 to 20 moves on either side, in some openings, and such games could easily continue for another 20 to 40 moves. In my opinion, any chess player, including professionals, over, say, 20 to 40 or more years, will scarcely dent the total moves (hence positions) possible.

The reference quoted is excellent.

I wondered if there might be infinite moves in chess and found this :-

In theory, if endless repetitions were allowed, there could be limitless numbers of moves.
However, there is a rule which imposes a draw after 3 repetitions resulting in the same position.

chess draw by repetition - Google Suche

Cat

 

[whoknows]

Check,

however, if endless repetitions did not create a unique permutation, they would not qualify, and re your earlier point, though a competent player might resign in a hopeless position, that does not mean that those unique permutations could not exist, or be played out entirely by non-sentient physics, and be finite. (the quote states legal positions btw)

So it comes down to imo, as with the Universe, whether those unique permutations are finite, or not.

 

[Catastrophe]

Please check reference, which includes

The threefold repetition rule is important because it prevents games from going on forever with the same moves being made. It can also help players who are in a bad position avoid losing.

On Chess.com, a draw by repetition happens automatically after the third repetition.

Such situations normally occur only when there are few pieces left, and either few/no pawns, or if the pawn position is blocked. It is sometimes used as an offer of an agreed draw.

Cat

 

[whoknows]

I used to play chess a fair bit, and never wanted to play one game forever, so know that rule and was grateful for it, but again it comes down to whether the unique permutations are finite or not. 10 ^44 is a Very big number.

 

[Catastrophe]

As I posted, such situations (which are rare anyway) are usually by agreement.
A ;player might repeat twice to see if the opponent is open to a draw.

This situation would normally occur, as I posted, when there are few pieces/pawns left.

I have never seen an accidental repetition on a nearly full board, and, anyway, believe it to be virtually impossible. Early in the game, players develop their pieces. Who would want to draw so early? If they did repeat early, they would be "undeveloping" their pieces, and their opponent would be more likely to go for a win. Players do not normally go to chess matches to intentionally loose, or intentionally put themselves at a disadvantage.

With a nearly empty board you will have very few possible moves - more like 10 or 20 than 10^44! Anyway, the 10^44 refers to a succession of many possible moves. At any one time, a player has only a few possibilities for one move (which, of course, is all you are allowed at one time).

For example White, at the start, has 16 possible pawn moves and 4 possible knight moves.
As you will know, many of these are considered unfavourable.

Cat