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Kasparov OpEd On His Latest Match
molrak writes "Garry Kasparov has written his thoughts and observations on the difference between his recent battle with Deep Junior as opposed to his battle against Deep Blue, including some of the fundamental differences between the two programs. If you missed out on the event, you can catch up with it at the site of the event's sponsor, including both 2d and 3d viewing options. (Note, viewing options require both site registration with x3dworld and proprietary Microsoft software.)"
Kasparov seems to think that making a powerful chess machine would constitute creating a machine with the power to "think." I hardly believe that to be correct, and moreover .. with enough proccessing power, a computer could map out chess moves far further into the future than kasparov could ever hope to.
.. where does one go after they realise that chess is only a little game?
I guess the real question has more to do with
Not only was the lastest match a tie, Kasparov actually made a stupid (for him) mistake in one of the earlier games which he might've won. The human element, it'll getcha every time. If Kasparov could always play at his best like Deep Junior can, then he could quite likely have beaten it this time around, too. Still, Deep Junior was an impressive, sexy bitch, as Kasparov says in this article. If _Kasparov_ is impressed, you should be, too!
For instance, there are more lines for 1. e4 than any other and some of those lines, if played right, can go 40 moves and more. At that point the opening overlaps the middle and the only way to be win by suprise (read creativity) is to find a new line. But in creating the new line - which can amount to one different move throughout the sequence that creates new possibilities, or lines - you are, as a byproduct, creating a new opening.
So I want to offer this - The game of Chess is where humans will always have the advantage. But machines can help us by figuring out which lines are well thought out and which ones have flaws. The counter to that is that we are the only ones that can think out the lines in the first place!
"From of old, there are not lacking things that have attained Oneness." - Lao Tzu
Is this game fun? Probably not. :) But that doesn't take away from the fact that an intelligent human could look at a source printout and figure out if it halted or not, but no general algorithm can be deduced that would do so. Thus, for a computer to win at this game, it would actually have to show intelligence, and not raw computational skill.
I was with you right up to the end. However it is most certainly not shown that a human can solve the halting problem. It is proven that (in the general case) no algorithm can say whether a program halts. The only way a human can prove whether an algorithm halts is by using mathematical formalisms that are also limited.
What people can often do is make an "intelligent" guess about whether a program halts. In fact computers can do this too: you can provide a machine with a set of heuristics (rules of thumb) that it can use to estimate the likelihood that a program will halt. That program could do better than random, just as a human could. But that is not the same as proving the program does or does not halt.
I have never seen any evidence to suggest that humans can solve the halting problem for the class of unsolvable programs.
Nevertheless you are right that there are unsolvable games. In fact there are an infinite number of them.
Sailing over the event horizon
Maybe I'm misreading what you said, but that sounds like Fischer was the arrogant one, and Kasparov was just being polite.
It's hard to be religious when certain people are never incinerated by bolts of lightning.
But that doesn't take away from the fact that an intelligent human could look at a source printout and figure out if it halted or not, but no general algorithm can be deduced that would do so.
Complete, utter, and unmitigated bullshit.
If it can't be solved algorithmically, humans can't solve it either. Even if a human came up with the right solution, in the general case, you would never be able to prove it!
Simple example: I write a program which "solves" chess. In other words, it loops through every possible game configuration and determines whether, say, white can always force a win. If so, it halts. Otherwise, it just drops into an infinite loop. Now, naturally, this game would take longer than the universe's lifespan to run, but that's not the point. The point is that determining whether or not this program halts is equivalent to solving the problem in the first place! To know whether or not it halts, you have to know whether or not white can always force a win. The halting problem is equally unsolvable for both man and machine. We both use algorithms, even if we don't understand our own algorithms. The fact that we do use algorithms means that we're just as subject to the rules of what is and is not computable.
Put in other terms, a computer simulating a human brain would be able to solve the exact same problems as a human, and in the same ways. If a human can solve a problem (and prove it, not just make an intelligent guess), then it's by definition computable. The only counter to that is to assume that it is impossible to build a computer that simulates a human brain, but you're on shaky ground making such a claim.
ZFS: because love is never having to say fsck