oops, accidentally sent to just Don Dailey ---------- Forwarded message ---------- From: Nick Apperson <[EMAIL PROTECTED]> Date: Jan 13, 2007 5:11 PM Subject: Re: [computer-go] Can Go be solved???... PLEASE help! To: [EMAIL PROTECTED]
Here is a link for anybody that is interested in why I say 2 dimensions. There are ofcourse many papers on it, but this is the basic idea. Essentially says that the maximum amount of information is proportional to the 2D surface around it. Even if we live in a many-dimensional world (I happen to believe we do), the area surrounding it would still be 2 dimensional as long as these are small dimensions. Sorry to get off track I just thought someone might find it interesting. For us we are no where near the theoretical limit of computing power, but if we had enough of it we would be subject to the theoretical maximum. Essentially, if you had enough computers to reach this limit, they would collapse into a black hole. http://en.wikipedia.org/wiki/Holographic_principle - Nick P.S. Sorry I was going ape last night. On 1/13/07, Don Dailey <[EMAIL PROTECTED]> wrote:
Ok Nick, The funny thing about this, is that I was originally defending someone who after making a simple post got flooded with all the stale size of the universe and grains of sands arguments - presumably to prove he was wrong when he made a simple statement which was correct. He made the horrible mistake of saying "1 billion" years and I guess that's where he went wrong. Everyone jumped in as if he was an idiot for thinking it would only take 1 billion years. I also admit I got annoyed with those arguments about the size of the game, I felt it was pretty redundant and I don't know of anyone on this group that needed a refresher course on this - everyone knows how huge this problem is. I'm sure you understand physics much more than I do. However, I disagree about dimensionality and if I'm wrong I have a thick skin and you can explain it to me and I will believe you. One of the theoretical limitations to computing power (which was layed out in someones posts) and I have always understood to be the case, is related to space - the physical size of the universe. If a computer can exist in 3 dimensions, couldn't an infinite number of them exist with 1 more dimension? Couldn't one be constructed that is far more highly parallel that what we can construct in our 3 physical dimensions? - Don On Sat, 2007-01-13 at 03:38 -0600, Nick Apperson wrote: > I would first just like to say, there have been many times in my life > where I have known 1000 times more than someone else and I didn't feel > the need to be an ass. I'm sure you are a nice person, but please > don't treat me like I am a moron. Some assumptions you made about me > that aren't true: > > 1) you assume I didn't understand what "solvable" means in a > mathematical sense. I think in a more important way, solvable means > "is able to be solved" and frankly that question is still able to be > debated regarding go. From a mathematical standpoint, any game with a > finite set of states is solvable. > > 2) You assume that I took 1 billion years literally... Oh my, I > would venture to say that I have had a whole lot more physics than you > have my friend and I understand how people get those numbers. > > 3) You assume that I don't know that changing the board size doesn't > necessariyl change all the properties of the game. I mean how dumb do > you think I am? > > But, I am going to point out a couple problems in what you said since > you seem to be up for being an ass. > > 1) Multiple dimensions doesn't help at all. Information processing > ability as well as informataion storing ability is proportional to a > 2D surface surrounding the area that is able to be used for the > computation. This is the upper limit given with thermodynamics which > is probably the only part of physics that has laws that are well > founded. > > 2) The reason I object to infinity as a concept is not because of my > mental inferiority. In fact, infinity is a concept that comes quite > readily to me. I learned it early in my youth and when I first saw a > graph of velocity versus time (age 12 maybe) I knew that the area > under it was displacement. I had taken calc 2 as a sophmore in > highschool. The problem I have with it in regards to what you were > talking about is that it has never been proven to exist anywhere in > the actual world and there is lots of evidence that it doesn't exist. > > > > That said, I have seen you post before and I enjoy reading your posts, > but please don't flame me. Just because I am new to computer go > doesn't mean I am a moron. I might bring something new. If you all > had it figured out already, we wouldn't be having this discussion. I > have a lot to learn from you and I look forward to that. Please be > more respectful. I am sorry that this was a harsh message, but I feel > you were unfair to attack me as you did. > > Sincerely, > Nick > > On 1/12/07, Don Dailey < [EMAIL PROTECTED]> wrote: > On Fri, 2007-01-12 at 15:43 -0600, Nick Apperson wrote: > > yeah, there are upper limits placed on computation rate by > > thermodynamics. 19x19 is way beyond those as Dave pointed > out. But, > > even if you believe that technology will improve and the > most > > revolutionary change yet will come to understanding of > physics and > > that change will give us signifigantly more computational > power and > > time etc... You can always make a bigger board. If life > comes to a > > point where go could be solved for any size board, you will > no longer > > be in this world and solving things such as "is go > solvable?" will > > have no meaning. > > Yes, you can always make a bigger problem by making a bigger > go board > but > that doesn't change the theoretical properties of the game. > The game > will always be solvable. > > The game might be trivially solvable even now to a being not > confined > to our 3 physical dimensions. I hate to get philosophical > like this, > but there are theories of other dimensions that (if true) say > we live > in a multi-dimensional universe. There may be much more > here than > we can sense and that we can perhaps take advantage of. > > But it doesn't matter. When Chris said 1 billion years you > should > have instantly realized that he didn't mean this literally, > he just > meant a correct procedure exists for solving the game. > Since no > one has proved how long the universe will last, I don't think > you > can even prove that in a practical sense it's unsolvable. If > you > lack imagination you can simply say it's not solvable because > you > believe it can't be done in your lifetime - as if science and > math > cares about how long we live or even the universe. If the > universe > will die in 10 trillion years does that mean the number 20 > trillion > is an impossible number? > > The concept of infinity is important in mathematics. It's > even useful, > but I suppose that it really should be considered meaningless > since > we all die after 70 or 80 years. > > - Don > > > > _______________________________________________ > computer-go mailing list > [email protected] > http://www.computer-go.org/mailman/listinfo/computer-go/ >
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