Do all games of chess exist in some form?
There Are More Games of Chess Possible Than Atoms In The Universehttps://curiosity.com/topics/there-are-more-games-of-chess-possible-than-atoms-in-the-universe-curiosity/
In the 1950s, mathematician Claude Shannon wrote a paper about how one could program a computer to play chess. In it, he made a quick calculation to determine how many different games of chess were possible, and came up with the number 10^120. This is a very, very large number — the number of atoms in the observable universe, by comparison, is only estimated to be around 10^80.
Do all those games exist in some form.
Obviously they exist as potentials, but there must be an exact number, and exact sets of moves.
General discussion of where information exists.
Where do all the digits of pi in base 10 exist?
Comments (25)
all chess piece locations and moves are what's possible in the concept of chess.
In the sense that each game can be perfectly described they exist.
In the Information Universe the answer is that the variations of the games do exist.
All information is available it is only our ability to detect or use it that limits us. So infinity does not exist. The universe is self contained therefore all answers to all queries are within it. That mean that the variations are in fact finite.
Time: the great and mighty ruler of our existence is the defining factor by which we are able to detect and use information.
Off topic: Shannon miscalculates. The average sensible game might last 80 moves, but the average legal game averages about 5000 moves, so the number is more like 10^400.
The number of atoms in the visible universe is far different from the number of atoms in the universe, and the huge chess number is less than the latter. I hate such comparisons to that or 'grains of sand' and such.
On topic:The game of tic-tac-toe seems to have human countably many games, and this doesn't change the subject being discussed. The size of the number is irrelevant.
@kill jepetto:
The moves are possibilities yes, but not random. They're totally determined and the number of legal chess games or positions is quite defined and some exact finite number. Kippo points this out.
Quoting Kippo
The rules do not allow repeat configurations (beyond 2), so such games would not be legal games. There is also a max length game, so the count is finite in that direction as well.
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So do these games 'exist'? I suppose that depends on how one defines what it means to exist, and what things qualify as existing by that definition. I'm a relativist, so thing 1 exists to thing 2. Thus I might say that all of them exist as abstractions to humans (I can distinguish two different games from each other, or tell if two games are the same one), but they don't exist as abstractions to a rock since rocks seem not to make those abstract distinctions. That answer is consistent with my definitions, but there seems to be no correct definitions.
The rules allow it to happen, but a player can claim a draw if it does happen... see the threefold repetition rule.
But my definition was incomplete. Revised defintion of a complete game of chess...including draws of two types and resignations
A complete game of chess is an ordered sequence of board configurations that ends in either stalemate or checkmate or a forced draw or an agreed draw or a resignation, with the next configuration in the forward direction being rules-of-play compatible with its predecessor. There are a finite number of them if you disallow repeat configurations.
What about if a game has only existed as part of an AI playing against itself?
According to the OP, we're talking about possible chess games (some huge number), not actually played ones (as per Marchesk's constructivist definition). Both ways, the list seems finite.
The number of possible games is infinite if the 50 move rule is allowed to be bypassed (not noticed). The repeated-position stipulation can be ignored, allowing positions to be repeated up to 50 times.\
Your definition seems to be the constructivist one then: Played games where there are players involved. In that case, the list is very definitely finite since only so many games are played in all history. Far less than 10^120. In possible games, any game can be aborted by resignation or something at any point, so it is really a count of valid chess states since it is legal to do so in any state.
I was going to ask you about games played on alien planets that don't necessarily exist in our observable universe, but the AI question is a good start to that.
If you discount them, then existence is anthropocentric, which seems distasteful. So I'm glad you include them.
Isn't that essentially what humans do? How might the human ones count then if that's all the AI is doing?
My thinking is that we interpret the AI as playing itself in chess because we've set it up to train itself in a way that leads to self-improved chess play. But is that the same thing as actually playing chess?
Since we invented the game to play amongst ourselves, it's safe to say that humans play chess.
A chess game existing would be a game being played.
A chess move existing would be a move that is being made or has just been performed. A move that give the opponent a consequence.
If it was three moves ago, it only exists as a historic move.
It no longer exists.
When you say "exist in some form" you make the question very broad.
One might than wonder if a computer vs human play on a computer and the computer calculates various moves, but do not end up making them, do they exist in some form?
Yes, but do all of them exist?
Do the sum of all calculated possible moves in all chessgames being played right now end up being all possible chess combinations?
When we imagine such a thing we will also have to imagine quite bad moves, because right at this very moment children are also playing chess and chess moves in books and movies as they too exist in some form.
How many games of chess are being played right now and how many possible moves and situations do these players calculate?
Will it be all possible chess combinations?
When someone ask if something exist, and we answer a bit later we might be wrong, because there is a time constraint. If you ask how many elephants exists and you get an answer one year later that around 5000 elephants exists, The answer will be referring to what is known with a high probability at the very moment but you were referring to probably the days around when you asked your question.
During that year perhaps around 500 elephants was killed and died. So if someone answers your question if something is existing year later their answer might be wrong.
In order for someone to answer if all possible combinations exist in some form, and say yes, they need to know that the total amount of all imagined possible moves at any single time will be all possible moves and not less.
That would be exist in some form, but in order for a chessmove to be defined as existing the move has to be performed, so they do not exist in the usual sense of what we mean with existence when we use the word existing refering to a move in a game and existing right now.
It comes down to semantics.
They all exist in some form, as a possibility, which is just as a concept. But that form is kind of uninteresting as everything that is possible can exist as a concept.
It is more interesting to ponder the question of existing or might exist in such a way that it will end up creating consequences for someone at the moment you receive the answer.
No. The only ones that exist in some form are the ones that people are currently playing, currently thinking about, or the past ones that are recorded in some manner where the record is still extant.
It must be possible to calculate all of the possible moves, though, since there would be a finite (but ridiculously huge) number of them.
It depends how you define "game". If you include actual date, time, place and players then a game must always exist by definition. I think my definition would be better, and then if you add your data it would be a "game session". Then "sessions" would always exist, but not all "games" would belong to a session.
But if the computer already calculated it to 10^80, it would have reached that end and therefore these exist, as they have been tested out? Or can they only exist if humans do the calculation?
Calcuating how many different possible games can be isn't the same thing as there being those games. You calculate how many different possible game there can be by mutiplying n number of possible opening moves by m number of possible second moves, etc.
I'm a nominalist a la believing that there are no real abstracts.
Misread the OP, thought the computer calculated it by playing the moves. But, let's say that it does just this. Wouldn't that count as the games being played and therefore exist? So if they program a computer to play a new game that is always in a slight variance of the last game, but can never be the same game, it would eventually have played all games possible, i.e all games exist.
What if say there is a mathematical problem, that doesn't have a proof, like the Fermat maths thing years ago....he was said to have written a simple proof for that problem, but that the proof was lost.
If there is a proof to some mathematical situation, but it hasn't been discovered, does it exist?
Say there is an amazing proof for the Pythagoras' right angle triangle thing, but it hasn't been discovered(I know there are many proofs).....if it is discovered tomorrow, did it always exist? Did it exist today?
No mathematical objects, equations, arguments, proofs, etc. exist unless they're made explicit. That means that a number like 5,628,901,782,332,415,515 doesn't exist until someone expresses it, and it only exists insofar as someone is expressing it, thinking it, or it's recorded in some still-extant form (for example written on a piece of paper and the paper hasn't burned up or whatever). Again, I don't buy that there are any real abstracts. Numbers only exist as concrete particulars.
The question doesn't have meaning, because the word "exist" isn't metaphysically or ontologically-defined.
...at least not when it's used unqualified and absolute, without specifying a context in which you speak of something being (...and, even then, I'd avoid the word "exist", and word it another way).
Michael Ossipoff
9 Sa
how about this definition of 'exist'; locatable.
Does the truck, I saw this morning going along the main road exist?
Is it locatable?
Under that definition it probably does exist. I could maybe track it down if I had access to the ANPR network.
Under that definition, is any game of chess possible not locatable?
how about this deinition of 'exist': Locatable.
does Edinburgh exist....is it locatable?
Is any game of chess not locatable...?