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Nitpick: AFAIK, the game of life (as a mathematical concept) is in itself a turing complete automaton, you don't need to explicitly simulate a turing machine w

by pygy_ 17y ago

Nitpick: AFAIK, the game of life (as a mathematical concept) is in itself a turing complete automaton, you don't need to explicitly simulate a turing machine with it, in the same way that you don't need to implement a turing machine on top of the lambda calculus to be able to express algorithms with it. In practice, since all computers have a limited memory, they are in fact deterministic finite-state machines. So the size of the board/RAM/whatever constrains what you can do with it, but it is as true for Life as for any language or computer system. From a practical standpoint, watching a board of Life is indeed about as interresting as watching a random memory block rendered on screen while your program is running... It's sometimes entertainging, but usually boring. I'll admit I actually have Life on my iPhone :D

raganwald 17y ago
Not a nitpick at all, we are in agreement. I appreciate that in theory a GoL program is a turing complete automaton, just as in theory Apple could use one of its legal clauses to reject a GoL application from the App Store. I was trying to hint that someone in practice writing an App using a GoL as a platform running a turing machine running an app is about as unlikely as Apple actually rejecting a GoL implementation for this reason. Or in more pithy terms, "The gap between theory and practice is narrower in theory than it is in practice." p.s. Speaking of theory... One of my favourite books is "The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge," wherein the Game of Life is used to discuss complexity, self-replication, and other fascinating topics: http://www.amazon.com/gp/redirect.html?ie=UTF8&location=http%3A%2F%2Fwww.amazon.com%2FRecursive-Universe-Complexity-Scientific-Knowledge%2Fdp%2F0809252023%2Fsr%3D1-1%2Fqid%3D1163786265%3Fie%3DUTF8%26s%3Dbooks&tag=raganwald001-20 http://www.amazon.com/gp/redirect.html?ie=UTF8&location=...
- chc 17y ago
  I think you're missing the point of a reductio ad absurdum argument. Very often, it's easy to overlook the flaws in something because we have a viewpoint that makes them look smoother than they really are. Reductio ad absurdum grabs your head and jerks it to an unnatural angle where you're looking at the flaw head-on. This precise case is not likely to happen in practice, but that doesn't matter, because the value of the situation is in helping us see a problem. If you want to see an example of where this approach might have helped, look at the children convicted of making kiddie porn for taking cell phone pics of themselves. You could have brushed off reductio ad absurdum arguments by saying, "Oh, that precise situation is so unlikely," but the flaws are real just the same.

by pygy_ 17y ago

raganwald 17y ago

Not a nitpick at all, we are in agreement. I appreciate that in theory a GoL program is a turing complete automaton, just as in theory Apple could use one of its legal clauses to reject a GoL application from the App Store. I was trying to hint that someone in practice writing an App using a GoL as a platform running a turing machine running an app is about as unlikely as Apple actually rejecting a GoL implementation for this reason. Or in more pithy terms, "The gap between theory and practice is narrower in theory than it is in practice." p.s. Speaking of theory... One of my favourite books is "The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge," wherein the Game of Life is used to discuss complexity, self-replication, and other fascinating topics: http://www.amazon.com/gp/redirect.html?ie=UTF8&location=http%3A%2F%2Fwww.amazon.com%2FRecursive-Universe-Complexity-Scientific-Knowledge%2Fdp%2F0809252023%2Fsr%3D1-1%2Fqid%3D1163786265%3Fie%3DUTF8%26s%3Dbooks&tag=raganwald001-20 http://www.amazon.com/gp/redirect.html?ie=UTF8&location=...

chc 17y ago
I think you're missing the point of a reductio ad absurdum argument. Very often, it's easy to overlook the flaws in something because we have a viewpoint that makes them look smoother than they really are. Reductio ad absurdum grabs your head and jerks it to an unnatural angle where you're looking at the flaw head-on. This precise case is not likely to happen in practice, but that doesn't matter, because the value of the situation is in helping us see a problem. If you want to see an example of where this approach might have helped, look at the children convicted of making kiddie porn for taking cell phone pics of themselves. You could have brushed off reductio ad absurdum arguments by saying, "Oh, that precise situation is so unlikely," but the flaws are real just the same.