One obvious difference is that nowhere in the brick wall is a representation of tennis. Chess computers have models of chessboards, recognize legal and illegal moves, and have some judgement of how good or poor a position is for either side.
By virtue of what property do these representations have the content that you attribute to them?
I assume you can see where I’m going here—this is an old question in philosophy of computation: what is it that makes a physical computation about anything in particular.
By virtue of what property do these representations have the content that you attribute to them?
By what virtue is a chess game a chess game and not two people playing with statues? The rules by which the chess computer operates parallel the rules by which chess operates—the behavior is mirrored within it. If you gave someone a brick wall, they couldn’t analyze it to learn how to play tennis, but if you gave someone a chess program, they could deduce from it the rules of chess.
By what virtue is a chess game a chess game and not two people playing with statues? The rules by which the chess computer operates parallel the rules by which chess operates
I don’t think it’s quite that simple. If a couple of four-year-olds encounter a chess set, and start moving the pieces around on the board, they might happen to take turns and make only legal “moves” until they got bored. I don’t think they’d be playing chess. Similarly, if a couple of incompetent adults encounter a chess set and try to play chess, but because they aren’t very smart or paying very close attention, about a quarter of their moves aren’t actually legal, they’re playing chess—they’re just making mistakes in so doing.
The equivalence I’m proposing isn’t between results or actions, but the causal springs of the actions. In your example, the children making legal chess moves are only doing so by luck—the causal chains determining their moves at no point involve the rules of chess—whereas the adults playing chess badly are doing so by a causal chain which includes the rules of chess. If you changed those rules, it would not change the children’s moves, but it would change the adults’.
this is an old question in philosophy of computation: what is it that makes a physical computation about anything in particular.
And it’s one that’s overhyped, but actually not that complicated.
A computation is “about” something else if and to the extent that there exists mutual information between the computation and the something else. Old thread on the matter.
Does observing the results of a physical process tell you something about the result of the computation 2+3? Then it’s an implementation of the addition of 2 and 3. Does it consistently tell you something about addition problems in general? Then it’s an implementation of addition.
This doesn’t fall into the trap of “joke interretations” where e.g. you apply complicated, convoluted transformations to molecular motions to hammer them into a mapping to addition. The reason is that by applying such a complicated (and probably ever-expanding) interpretation, the physical process is no longer telling you something about the answer; rather, the source of the output, by means of specifying the convoluted transformation, is you, and every result originates in you, not the physical process.
A computation is “about” something else if and to the extent that there exists mutual information between the computation and the something else.
Mutual information is defined for two random variables, and random variables are mappings from a common sample space to the variables’ domains. What are the mappings for two “things”? Mutual information doesn’t just “exist”, it is given by mappings which have to be somehow specified, and which can in general be specified to yield an arbitrary result.
This doesn’t fall into the trap of “joke interrelations” where e.g. you apply complicated, convoluted transformations to molecular motions to hammer them into a mapping to addition. The reason is that by applying such a complicated (and probably ever-expanding) interpretation, the physical process is no longer telling you something about the answer; rather, the source of the output, by means of specifying the convoluted transformation, is you, and every result originates in you, not the physical process.
When you distinguish between the mappings “originating” in the interpreter versus in the “physical process itself”, you are judging the relevance of output of mutual information calculation in the same motion (“no true Scotsman”). Mutual information doesn’t compute your answer, deciding whether the mapping came from an approved source does.
Mutual information is defined for two random variables, and random variables are mappings from a common sample space to the variables’ domains. What are the mappings for two “things”? Mutual information doesn’t just “exist”, it is given by mappings which have to be somehow specified, and which can in general be specified to yield an arbitrary result.
I wasn’t as precise as I should have been. By “mutual information”, I mean “mutual information conditional on yourself”. (Normally, “yourself” is part of the background knowledge predicating any probability and not explicitly represented.) So, as per the rest of my comment, the kind of mutual information I meant is well defined here: Physical process R implements computation C if and to the extent that, given yourself, learning R tells you something about C.
Yes, this has the counterintuitive result that the existence of a computation in a process is observer-dependent (not unlike every other physical law).
When you distinguish between the mappings “originating” in the interpreter versus in the “physical process itself”, you are judging the relevance of output of mutual information calculation in the same motion (“no true Scotsman”). Mutual information doesn’t compute your answer, deciding whether the mapping came from an approved source does.
No, mutual information is still the deciding factor. As per my above remark, if the source of the computation is really you, by means your ever-more-complex, carefully-designed mapping, then
P(C|self) = P(C|self,R)
i.e., learning about the physical process R didn’t change your beliefs about C. So, conditioning on yourself, there is no mutual information between C and R.
If you are the real source of the computation, that’s one reason the equality above can hold, but not the only reason.
I wasn’t as precise as I should have been. By “mutual information”, I mean “mutual information conditional on yourself”. (Normally, “yourself” is part of the background knowledge predicating any probability and not explicitly represented.) So, as per the rest of my comment, the kind of mutual information I meant is well defined here: Physical process R implements computation C if and to the extent that, given yourself, learning R tells you something about C.
Vague and doesn’t seem relevant. What is the sample space, what are the mappings? Conditioning means restricting to a subset of the sample space, and seeing how the mappings from the probability measure defined on it redraw the probability distributions on the variables’ domains. You still need those mappings, it’s what relates different variables to each other.
Are you saying, then, that the meaning of a computation depends on what the user thinks or the programmer intends, rather than being intrinsic to the computation?
Well, it could depend on what the computation thinks.
But my point was that the brick wall doesn’t keep track of the ball.
Whether a robot tennis player keeps track of the ball or not doesn’t depend on what I think it does or how I thought I designed it. It is a fact of the matter.
One obvious difference is that nowhere in the brick wall is a representation of tennis. Chess computers have models of chessboards, recognize legal and illegal moves, and have some judgement of how good or poor a position is for either side.
By virtue of what property do these representations have the content that you attribute to them?
I assume you can see where I’m going here—this is an old question in philosophy of computation: what is it that makes a physical computation about anything in particular.
By what virtue is a chess game a chess game and not two people playing with statues? The rules by which the chess computer operates parallel the rules by which chess operates—the behavior is mirrored within it. If you gave someone a brick wall, they couldn’t analyze it to learn how to play tennis, but if you gave someone a chess program, they could deduce from it the rules of chess.
I don’t think it’s quite that simple. If a couple of four-year-olds encounter a chess set, and start moving the pieces around on the board, they might happen to take turns and make only legal “moves” until they got bored. I don’t think they’d be playing chess. Similarly, if a couple of incompetent adults encounter a chess set and try to play chess, but because they aren’t very smart or paying very close attention, about a quarter of their moves aren’t actually legal, they’re playing chess—they’re just making mistakes in so doing.
The equivalence I’m proposing isn’t between results or actions, but the causal springs of the actions. In your example, the children making legal chess moves are only doing so by luck—the causal chains determining their moves at no point involve the rules of chess—whereas the adults playing chess badly are doing so by a causal chain which includes the rules of chess. If you changed those rules, it would not change the children’s moves, but it would change the adults’.
Wow, great minds think alike. ;-)
(No, I didn’t see your reply before posting.)
And it’s one that’s overhyped, but actually not that complicated.
A computation is “about” something else if and to the extent that there exists mutual information between the computation and the something else. Old thread on the matter.
Does observing the results of a physical process tell you something about the result of the computation 2+3? Then it’s an implementation of the addition of 2 and 3. Does it consistently tell you something about addition problems in general? Then it’s an implementation of addition.
This doesn’t fall into the trap of “joke interretations” where e.g. you apply complicated, convoluted transformations to molecular motions to hammer them into a mapping to addition. The reason is that by applying such a complicated (and probably ever-expanding) interpretation, the physical process is no longer telling you something about the answer; rather, the source of the output, by means of specifying the convoluted transformation, is you, and every result originates in you, not the physical process.
Mutual information is defined for two random variables, and random variables are mappings from a common sample space to the variables’ domains. What are the mappings for two “things”? Mutual information doesn’t just “exist”, it is given by mappings which have to be somehow specified, and which can in general be specified to yield an arbitrary result.
When you distinguish between the mappings “originating” in the interpreter versus in the “physical process itself”, you are judging the relevance of output of mutual information calculation in the same motion (“no true Scotsman”). Mutual information doesn’t compute your answer, deciding whether the mapping came from an approved source does.
I wasn’t as precise as I should have been. By “mutual information”, I mean “mutual information conditional on yourself”. (Normally, “yourself” is part of the background knowledge predicating any probability and not explicitly represented.) So, as per the rest of my comment, the kind of mutual information I meant is well defined here: Physical process R implements computation C if and to the extent that, given yourself, learning R tells you something about C.
Yes, this has the counterintuitive result that the existence of a computation in a process is observer-dependent (not unlike every other physical law).
No, mutual information is still the deciding factor. As per my above remark, if the source of the computation is really you, by means your ever-more-complex, carefully-designed mapping, then
P(C|self) = P(C|self,R)
i.e., learning about the physical process R didn’t change your beliefs about C. So, conditioning on yourself, there is no mutual information between C and R.
If you are the real source of the computation, that’s one reason the equality above can hold, but not the only reason.
Vague and doesn’t seem relevant. What is the sample space, what are the mappings? Conditioning means restricting to a subset of the sample space, and seeing how the mappings from the probability measure defined on it redraw the probability distributions on the variables’ domains. You still need those mappings, it’s what relates different variables to each other.
“This is a lot easier to understand if you remember that the point of the system is to keep track of sheep.”
http://yudkowsky.net/rational/the-simple-truth
Are you saying, then, that the meaning of a computation depends on what the user thinks or the programmer intends, rather than being intrinsic to the computation?
Well, it could depend on what the computation thinks.
But my point was that the brick wall doesn’t keep track of the ball.
Whether a robot tennis player keeps track of the ball or not doesn’t depend on what I think it does or how I thought I designed it. It is a fact of the matter.
Suppose I dip the ball in paint before I start hitting it against the wall, so it leaves paintmarks there. Is the wall keeping track of the ball now?
You can’t keep track of sheep by dropping pebbles down a well.