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Questions I would ask God about the game of Go

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Re: Questions I would ask God about the game of Go

#91

Post by tromp »

tzs wrote: post #83

I once tried to write a math/CS nerd's description of the rules of Go. There's an XHTML file of the results at https://pastebin.com/Cn7tbv98 if anyone is curious. Below is a text version: Here is an attempt to describe the rules of Go precisely. This is actually for a generalization of Go that I call MANGO, which stands for MAth Nerd Go Equipment To play Mango, you need the following: • A countable set, I. • A set, C…

I tried the same with the Logical Rules of Go [1] which translate easily into Haskell.

[1] https://tromp.github.io/go.html

Re: Questions I would ask God about the game of Go

#92

Post by CydeWeys »

samatman wrote: post #89
samatman wrote: post #84

Earlier quoted context omitted.

I discovered a game in the Go family. It's played on a grid of overlapping circles, without counting the origin as an intersection. Every intersection has exactly four liberties, so it adds an optional move of a stone after each placement. Liberties are counted after both the placement and the move, so a player can't occupy a point with no liberties and then slide to capture. Anecdotally, it's enjoyable. Thing is, I…

I meant to say, any given alien race. If there are enough intelligent aliens than it's just a numbers game. But would it be more than half? I doubt this. Sure would be fun to find out.

Yeah, that's the thing, there's likely to be lots of different alien species, so it is indeed a numbers game. I wouldn't want to try giving the odds of each alien species discovering Go, but so long as those odds are non-zero, which seems quite likely, the total number of Go inventions across the universe is likely to be quite large.

This naturally introduces the idea of a "universality constant" for any given game, i.e. what percentage of species will have invented that exact game. For obvious reasons this figure is likely to be much higher for, say, Go, Connect-N, or Hex, than for something like Chess.

Re: Questions I would ask God about the game of Go

#93

Post by CydeWeys »

coldtea wrote: post #86
CydeWeys wrote: post #79

Earlier quoted context omitted.

I know we're firmly into joke territory at this point, but anyway, if that were true, then line pieces would fall faster when oriented vertically than horizontally. Clearly the real answer is that Tetris is played in a weightless vacuum, and that pieces are shot at a constant speed from somewhere offscreen.

> Clearly the real answer is that Tetris is played in a weightless vacuum, and that pieces are shot at a constant speed from somewhere offscreen. Obviously not, since the speed increases as the game progresses (of course the planet could have increased its mass in the meantime).

The speed the pieces are fired at is constant within each round, and then increases between rounds.

Obviously the tetrominoes are being fired by a variable speed railgun and the current is being increased with each round.

Re: Questions I would ask God about the game of Go

#94

Post by CydeWeys »

jefftk wrote: post #90
CydeWeys wrote: post #85

Earlier quoted context omitted.

This is awesome! Any idea where Chess would stack up? I'm assuming it'd be greater than Checkers in that list, but how much greater? And would Nim be simpler than Gomoku (Connect-N)?

If you or someone else would like to have a go at writing one I'd be happy to review and add it! https://github.com/jeffkaufman/game-complexity

Nice.

I wonder, would it make sense to encode the idea of a square and hex grid with pieces of two different colors as a library of sorts, such that this basic grid implementation doesn't count against each game individually? The boards are very widely reused, generic, mathematical concepts. This would give something like Go or Connect-N a fairer shot of competing against something like a Nim, which only needs a single integer accumulator to represent its game state.

Re: Questions I would ask God about the game of Go

#95

Post by mcbuilder »

daseiner1 wrote: post #76
mcbuilder wrote: post #23

Would not Alpha Go Zero and related algorithms give us a good insight into the question about what openings alien's might play? Isn't it really tackling the game from first (or zeroth if you will) principles, just simulated games without the historical baggage coming from human study. It has also considerably changed our own knowledge of the opening.

Are you implying alien societies wouldn’t (don’t?!) have their own historical baggage?

No, but I didn't make it clear in my question that I was assuming that the aliens would devise a similar Alpha Zero algorithm to that we have. The concepts of self play, reinforcement learning, and MCTS are obviously more universal than the exact year komi was introduced. I was more asking if using an "optimal" algorithm would reduce historical baggage in both aliens and humans, and lead to a similar convergence in terms of good go openings. However, even our choice of algorithms may be based result of historical events, and can we really conclude we've ever really found the optimum.

Re: Questions I would ask God about the game of Go

#96

Post by jefftk »

CydeWeys wrote: post #94
jefftk wrote: post #90

Earlier quoted context omitted.

If you or someone else would like to have a go at writing one I'd be happy to review and add it! https://github.com/jeffkaufman/game-complexity

Nice. I wonder, would it make sense to encode the idea of a square and hex grid with pieces of two different colors as a library of sorts, such that this basic grid implementation doesn't count against each game individually? The boards are very widely reused, generic, mathematical concepts. This would give something like Go or Connect-N a fairer shot of competing against something like a Nim, which only needs a sing…

The compressed Go program gets only 2.3% smaller post-gzip (13 bytes) if you remove the definition of the board: b=[[' ']*19 for x in range(19)]

Most of the complexity is in what changes players are allowed to make to the board.

Re: Questions I would ask God about the game of Go

#98

Post by zeebeecee »

CydeWeys wrote: post #46
grawprog wrote: post #45

Earlier quoted context omitted.

>If Shogi, Checkers, or Stratego weren't human games I wouldn't be surprised to learn them from aliens. Why do all theories about aliens start with the implication that they're similar enough that they developed the way we did, they think like we do, have similar senses, brain structure and locomotion. Any aliens that have evolved to any kind of level of intelligence would have done so under the conditions specific t…

Why are people so quick to assume that every single other alien species would be completely unfathomable to us? We all share the same physics, chemistry, and mathematics of our common universe. For example, there's only three dimensions, and there's only three regular polygons that can tessellate a grid. Unless you're going to posit that there's no alien species whatsoever that will even come up with the concept of a…

Even assuming that the concept of "game" would exist elsewhere seems like a ridiculous assumption. All of the things you are saying, even "purely mathematical" are just reflections of the way humans sense the world. Any alien species you are imagining here is just a reflection of mankind.

Anyway, since probably won't know anytime soon, and perhaps never, this kind of speculation is a bit useless. But if we ever found an alien species, it seems unlikely we would be able communicate with them any more than we can communicate with a piece of rock.

Re: Questions I would ask God about the game of Go

#99

Post by CydeWeys »

zeebeecee wrote: post #98
CydeWeys wrote: post #46

Earlier quoted context omitted.

Why are people so quick to assume that every single other alien species would be completely unfathomable to us? We all share the same physics, chemistry, and mathematics of our common universe. For example, there's only three dimensions, and there's only three regular polygons that can tessellate a grid. Unless you're going to posit that there's no alien species whatsoever that will even come up with the concept of a…

Even assuming that the concept of "game" would exist elsewhere seems like a ridiculous assumption. All of the things you are saying, even "purely mathematical" are just reflections of the way humans sense the world. Any alien species you are imagining here is just a reflection of mankind. Anyway, since probably won't know anytime soon, and perhaps never, this kind of speculation is a bit useless. But if we ever found…

I'm not saying that every alien species would have the same concept of a game, but you really think it's "ridiculous" that any other alien species might have a similar concept of a game? Adversarial games are not even that far removed from the normal competition that is part of natural selection that yields intelligence in the first place.

You're making a lot of assumptions about things that you claim are impossible or would never happen, without explaining how you're coming to those assumptions. And the "communicate with a piece of rock" bit is just flat-out bad argumentation, as rocks aren't intelligent and thus cannot communicate by definition.

Re: Questions I would ask God about the game of Go

#100

Post by darkkindness »

dkarras wrote: post #35
CydeWeys wrote: post #6

> Is go played anywhere else in the universe, and was it discovered by chance there? > What openings do aliens play? I love these questions about if anyone else in the universe is playing Go. My gut response would be yes -- it's a simple enough game (regular game grid of any size roughly 5x5 on up, one type of piece, two players take turns alternating placing pieces, and any that are surrounded are removed). I suspec…

It's a weird thought I admit but as a computer game, I believe "Tetris" could have been independently "discovered". Board size - gravity rules - scoring etc. are arbitrary but there is some fundamental elegance about all possible tetrominos creating a game that is that fun. At the very least non tetris (so no creating and destroying lines) but a game with all possible tetrominos probably would exist.

After tetrominos, purely mathematical games with pentomino tiling at its core are definitely discovered games. It's doable but not always simple to build a given shape of size 5n with n pentominos. Ever seen the "fill an n by m rectangle with pentominoes" problem?

As an aside, my favorite variant of this is from an old game Puzzle Pirates: https://www.youtube.com/watch?v=XRQIHyC__kc

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