8 ms·

I like how Ken Jennings dealt with the 'Go complexity' analogy: "Go is famously a more complex game than chess, with its larger board, longer games, and many m

I like how Ken Jennings dealt with the 'Go complexity' analogy: "Go is famously a more complex game than chess, with its larger board, longer games, and many more pieces. Google’s DeepMind artificial intelligence team likes to say that there are more possible Go boards than atoms in the known universe, but that vastly understates the computational problem. There are about 10^170 board positions in Go, and only 10^80 atoms in the universe. That means that if there were as many parallel universes as there are atoms in our universe (!), then the total number of atoms in all those universes combined would be close to the possibilities on a single Go board." http://www.slate.com/articles/technology/technology/2016/03/google_s_alphago_defeated_go_champion_lee_sedol_ken_jennings_explains_what.html http://www.slate.com/articles/technology/technology/2016/03/...

IsaacL 10y ago
Go is very complex, and the fact that DeepMind could tackle this complexity is a huge technical achievement. No minimax-based AI could have tackled such a large state space. However, other problems have even larger state spaces. Imagine writing an AI which read project Euler problem descriptions (in English) and output working code (in some given programming language). Keep outputs limited to 100-line scripts, max 80 characters per line. There's roughly 100 usable characters in ASCII, so the possible space of 100-line programs is roughly: (10^2)^(80 * 100) = 10^16000. You could simplify this by having the AI work with predefined tokens rather than individual characters, but it's still a vast amount of combinations. Then consider 1000-line or 10000-line programs, and you see how high a mountain AI still has to climb. Humans are able to "compress" this state space via conceptual reasoning, which is much more complex than the "pattern recognition" many deep learning researchers are chasing. (See "Introduction to Objectivist Epistemology" for more on how humans think in concepts - I'm planning to write more at some point on how this book shows where the practical limits of AI lie).
Retric 10y ago
Don't conflate the "Observable Universe" with the actual Universe. We flat out don't know how big the actual Universe is. So, it could be 10^80, 10^800, or even A(10, 80)* Atoms. *https://en.wikipedia.org/wiki/Ackermann_function https://en.wikipedia.org/wiki/Ackermann_function
- dsfuoi 10y ago
  It could be infinite.
  - levemi 10y ago
    If that is the case was the universe once finite and then went infinite during the early (big bang) expansion? I don't understand how something could have expanded if it was always infinite in size. I'm not even sure the concept of expansion even makes sense. What is infinite + 1? It's just infinite. It seems more like the expansion is a distribution of internal things.
    - stouset 10y ago
      Take the set of positive integers (0, 1, 2…). Double them, so you have (0, 2, 4…). You had an infinite list of numbers, all "compact" (no room for more positive integers inbetween them), and with a simple mathematical transform, you've given yourself space for a second equally-sized infinity of integers to fit neatly inside of them.
    - DonaldFisk 10y ago
      You can see back as far as the Big Bang, approximately 14 billion years ago, so all matter in the visible Universe is within 14 billion light years of the Earth. However, the space the Universe occupies is only really finite if it's positively curved. If it's flat or negatively curved, the space it occupies is infinite, and if its density is constant, it must contain an infinite amount of matter even though we only see part of it. The Big Bang is a singularity - a point with infinite density. It's hard to get your head around intuitively, but it all makes sense mathematically. (The maths is pretty hard, and rarely covered at undergraduate level.) The simplest model in rough agreement with observations is called the Einstein-de Sitter Model, and it's flat with a zero cosmological constant. See http://www.britannica.com/science/cosmology-astronomy/Relativistic-cosmologies#ref1069808 http://www.britannica.com/science/cosmology-astronomy/Relati... More general models are covered here: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Solutions https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...
tossaway1 10y ago
> the total number of atoms in all those universes combined would be close Close?? Wouldn't it still be roughly 10 billion times smaller...?
- vidarh 10y ago
  When you're dealing with numbers on the order of 10^80 to 10^170, I think you're entitled to calling that "close".
  - Nevermark 10y ago
    The ratio is 10^90 which is not small. The subtractive difference rounds to 10^170. In either case, I think its fair to say that 10^170 is unimaginably larger than 10^80. But if differences become so large we cannot imagine the differences, then we could imagine there are no differences at all, so ... psychologically/subjectively there would be no difference?
    - bmm6o 10y ago
      The comparison in question is between 10^170 and 10^160 (= 10^80 * 10^80). So "just" a factor of 10^10.
sametmax 10y ago
Comparing combinations with numbers of items is unfair. In Go, the number of items is the number of pieces, and it's very small. In the universe, the number of combinations of positions of all the atoms is, well, wonderful.
- deepnet 10y ago
  Compared with a googol our Universe has negligible atoms , 10^100 - 10^80 = ~10^100 Compared with a googolplex (10^(10^100)) the entire Evrettian metaverse is negligible as (10^(10^100) - 10^80^2 * (average quarks in atom) * leptons(10^200) * dark multiplier(10^2) = ~1 googolplex Has anyone ever used a googolplex for anything ? [For ~ read approximately]
  - tromp 10y ago
    Matthieu Walraet "used" a googolplex as a lower bound on the number of possible Go games, in http://matthieuw.github.io/go-games-number/GoGamesNumber.pdf http://matthieuw.github.io/go-games-number/GoGamesNumber.pdf Does that count:-?
    - deepnet 10y ago
      That is a staggering amount of possible Go games, no wonder tree search failed to improve without the Convnet pruning. Makes me wonder if Deepmind could learn Go without first learning from the big dataset of expert games to train the convnet to prune the tree. Which implies that Deepmind couldn't learn to play Go without first being taught by us (the expert games). So AlphaGo learnt Go from us. It took a human brain to crack the problem of Go and the AI learned from our solutions it did not discover them itself - still a very great breakthrough. Would Lee Sedol have won if he could use MCTS to assist his evaluation ? ( Arguably the MCTS is a non-AI component of deepmind & does not learn ). MCTS = Monte Carlo Tree Search, where repeated random playouts evaluate moves by randomly sampling the tree of following (googolplex) possible moves.
      - tromp 10y ago
randommodnar 10y ago
While this comparison highlights that yes, there are very many possible Go games, it's really apples to oranges. The real comparison would be the number of pieces on a Go board (19x19 = 361) compared to the number of atoms in the universe. And then to compare the number of possible board positions in Go, with the number of possible atom positions in the universe, and in this case I think the universe wins.....
- dack 10y ago
  especially considering all go boards exist _within_ the universe!

IsaacL 10y ago

Go is very complex, and the fact that DeepMind could tackle this complexity is a huge technical achievement. No minimax-based AI could have tackled such a large state space. However, other problems have even larger state spaces. Imagine writing an AI which read project Euler problem descriptions (in English) and output working code (in some given programming language). Keep outputs limited to 100-line scripts, max 80 characters per line. There's roughly 100 usable characters in ASCII, so the possible space of 100-line programs is roughly: (10^2)^(80 * 100) = 10^16000. You could simplify this by having the AI work with predefined tokens rather than individual characters, but it's still a vast amount of combinations. Then consider 1000-line or 10000-line programs, and you see how high a mountain AI still has to climb. Humans are able to "compress" this state space via conceptual reasoning, which is much more complex than the "pattern recognition" many deep learning researchers are chasing. (See "Introduction to Objectivist Epistemology" for more on how humans think in concepts - I'm planning to write more at some point on how this book shows where the practical limits of AI lie).

Retric 10y ago

Don't conflate the "Observable Universe" with the actual Universe. We flat out don't know how big the actual Universe is. So, it could be 10^80, 10^800, or even A(10, 80)* Atoms. *https://en.wikipedia.org/wiki/Ackermann_function https://en.wikipedia.org/wiki/Ackermann_function

dsfuoi 10y ago
It could be infinite.
- levemi 10y ago
  If that is the case was the universe once finite and then went infinite during the early (big bang) expansion? I don't understand how something could have expanded if it was always infinite in size. I'm not even sure the concept of expansion even makes sense. What is infinite + 1? It's just infinite. It seems more like the expansion is a distribution of internal things.
  - stouset 10y ago
    Take the set of positive integers (0, 1, 2…). Double them, so you have (0, 2, 4…). You had an infinite list of numbers, all "compact" (no room for more positive integers inbetween them), and with a simple mathematical transform, you've given yourself space for a second equally-sized infinity of integers to fit neatly inside of them.
  - DonaldFisk 10y ago
    You can see back as far as the Big Bang, approximately 14 billion years ago, so all matter in the visible Universe is within 14 billion light years of the Earth. However, the space the Universe occupies is only really finite if it's positively curved. If it's flat or negatively curved, the space it occupies is infinite, and if its density is constant, it must contain an infinite amount of matter even though we only see part of it. The Big Bang is a singularity - a point with infinite density. It's hard to get your head around intuitively, but it all makes sense mathematically. (The maths is pretty hard, and rarely covered at undergraduate level.) The simplest model in rough agreement with observations is called the Einstein-de Sitter Model, and it's flat with a zero cosmological constant. See http://www.britannica.com/science/cosmology-astronomy/Relativistic-cosmologies#ref1069808 http://www.britannica.com/science/cosmology-astronomy/Relati... More general models are covered here: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Solutions https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...

tossaway1 10y ago

> the total number of atoms in all those universes combined would be close Close?? Wouldn't it still be roughly 10 billion times smaller...?

vidarh 10y ago
When you're dealing with numbers on the order of 10^80 to 10^170, I think you're entitled to calling that "close".
- Nevermark 10y ago
  The ratio is 10^90 which is not small. The subtractive difference rounds to 10^170. In either case, I think its fair to say that 10^170 is unimaginably larger than 10^80. But if differences become so large we cannot imagine the differences, then we could imagine there are no differences at all, so ... psychologically/subjectively there would be no difference?
  - bmm6o 10y ago
    The comparison in question is between 10^170 and 10^160 (= 10^80 * 10^80). So "just" a factor of 10^10.

sametmax 10y ago

Comparing combinations with numbers of items is unfair. In Go, the number of items is the number of pieces, and it's very small. In the universe, the number of combinations of positions of all the atoms is, well, wonderful.

deepnet 10y ago
Compared with a googol our Universe has negligible atoms , 10^100 - 10^80 = ~10^100 Compared with a googolplex (10^(10^100)) the entire Evrettian metaverse is negligible as (10^(10^100) - 10^80^2 * (average quarks in atom) * leptons(10^200) * dark multiplier(10^2) = ~1 googolplex Has anyone ever used a googolplex for anything ? [For ~ read approximately]
- tromp 10y ago
  Matthieu Walraet "used" a googolplex as a lower bound on the number of possible Go games, in http://matthieuw.github.io/go-games-number/GoGamesNumber.pdf http://matthieuw.github.io/go-games-number/GoGamesNumber.pdf Does that count:-?
  - deepnet 10y ago
    That is a staggering amount of possible Go games, no wonder tree search failed to improve without the Convnet pruning. Makes me wonder if Deepmind could learn Go without first learning from the big dataset of expert games to train the convnet to prune the tree. Which implies that Deepmind couldn't learn to play Go without first being taught by us (the expert games). So AlphaGo learnt Go from us. It took a human brain to crack the problem of Go and the AI learned from our solutions it did not discover them itself - still a very great breakthrough. Would Lee Sedol have won if he could use MCTS to assist his evaluation ? ( Arguably the MCTS is a non-AI component of deepmind & does not learn ). MCTS = Monte Carlo Tree Search, where repeated random playouts evaluate moves by randomly sampling the tree of following (googolplex) possible moves.
    - tromp 10y ago

randommodnar 10y ago

While this comparison highlights that yes, there are very many possible Go games, it's really apples to oranges. The real comparison would be the number of pieces on a Go board (19x19 = 361) compared to the number of atoms in the universe. And then to compare the number of possible board positions in Go, with the number of possible atom positions in the universe, and in this case I think the universe wins.....

dack 10y ago
especially considering all go boards exist _within_ the universe!