(no subject)
Jun. 7th, 2013 09:31 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
davvAnd something I've been thinking about now and then:
What is a computer? Well, a computer is something that takes an input (a program), another input (the initial state) and produces an output. A physical computer thus is given matter arranged in a certain way, and rearranges it to produce the output; and the kind of computers we know has matter arranged in the form of charges in a circuit (memory).
But the problem with this is that it doesn't seem obvious how to discern whether or not a given collection of matter is a computer or not. The universe acts upon every collection of matter according to the rules of physics, so these collections of matter change configuration. It seems in principle possible to look at any collection of matter and say that this is a computer, where the inputs (programs and parameters) are given by certain states, and the output is given by those states after, say, a million years. A solar system could be a "computer" where the inputs are the initial positions of the planets at time zero, and the outputs are the positions of the planets a billion years later.
One might try to rescue that definition by saying that a true computer has greatest possible variety in its outputs. That is to say, that if you alter the inputs, the outputs will vary maximally. This would correspond to the intuition that a computer is as powerful as possible: there's no other device that can calculate more than it can, given enough time.
But that, again, has problems. Because we've not defined the representations the inputs take, we could consider a system that takes as an "input" a computer (or something we know is a computer, like the box under my desk right now), operates on it, and puts ink on a sheet of paper to represent the output. But the whole system is not the computer. The computer is the box under the desk. So it'd seem that, according to this definition, a computer is a minimal system that is as powerful as possible (so that any nested computer has the outer shells removed). But does that mean that ordinary computers with redundant inputs are also no longer computers? That doesn't seem right either.
And why is this significant? Well, the computational idea of the universe considers the universe to be like a computer. But what a computer is can't be defined without intent (i.e. "I know this is a computer because that's what I intended it to be when I made it"), then that statement is vague or tautologous according to the definition given.
There's also another problem that suggests a tautology. Say, for the sake of the argument, that we're in a dualist universe. There's some kind of magical interface that connects consciousness to the real world, and consciousness is also hypercomputational (with respect to a Turing machine). Then that doesn't alter the definition of a computer above, as "being maximally powerful with regards to the variety of input-output transforms". All it means is that a computer, so defined, must include a consciousness to be a computer. Given that gotcha, nothing changes. The "computational" account of the universe still holds: the universe can do everything a computer can. Every computer simply has to be sufficiently diverse to call upon every transformation that could be physically realized - otherwise it's not a computer. In that particular universe, every maximally powerful computer would have to include the magical interface.
So it would seem that for computationalism to make any sense, the definition of computers would have to be something else. But I can't quite see what it would be, that would not either be too vague or too specific.
(It might be as simple as: "a computer is something that is as powerful, with respect to the input-output transformations it can eventually create, as the thing we built in the 1950s and that we subsequently called a computer". If that's the definition, then a claim of a computational universe has at least some specificity. The claim would be to the effect of: "there's no part of the universe that can rearrange matter to produce more unpredictability than can a computer, as defined by the capabilities of a certain 1940s-1950s machine, given enough time". And whatever one may say about that claim, at least it's not tautologous.)
What is a computer? Well, a computer is something that takes an input (a program), another input (the initial state) and produces an output. A physical computer thus is given matter arranged in a certain way, and rearranges it to produce the output; and the kind of computers we know has matter arranged in the form of charges in a circuit (memory).
But the problem with this is that it doesn't seem obvious how to discern whether or not a given collection of matter is a computer or not. The universe acts upon every collection of matter according to the rules of physics, so these collections of matter change configuration. It seems in principle possible to look at any collection of matter and say that this is a computer, where the inputs (programs and parameters) are given by certain states, and the output is given by those states after, say, a million years. A solar system could be a "computer" where the inputs are the initial positions of the planets at time zero, and the outputs are the positions of the planets a billion years later.
One might try to rescue that definition by saying that a true computer has greatest possible variety in its outputs. That is to say, that if you alter the inputs, the outputs will vary maximally. This would correspond to the intuition that a computer is as powerful as possible: there's no other device that can calculate more than it can, given enough time.
But that, again, has problems. Because we've not defined the representations the inputs take, we could consider a system that takes as an "input" a computer (or something we know is a computer, like the box under my desk right now), operates on it, and puts ink on a sheet of paper to represent the output. But the whole system is not the computer. The computer is the box under the desk. So it'd seem that, according to this definition, a computer is a minimal system that is as powerful as possible (so that any nested computer has the outer shells removed). But does that mean that ordinary computers with redundant inputs are also no longer computers? That doesn't seem right either.
And why is this significant? Well, the computational idea of the universe considers the universe to be like a computer. But what a computer is can't be defined without intent (i.e. "I know this is a computer because that's what I intended it to be when I made it"), then that statement is vague or tautologous according to the definition given.
There's also another problem that suggests a tautology. Say, for the sake of the argument, that we're in a dualist universe. There's some kind of magical interface that connects consciousness to the real world, and consciousness is also hypercomputational (with respect to a Turing machine). Then that doesn't alter the definition of a computer above, as "being maximally powerful with regards to the variety of input-output transforms". All it means is that a computer, so defined, must include a consciousness to be a computer. Given that gotcha, nothing changes. The "computational" account of the universe still holds: the universe can do everything a computer can. Every computer simply has to be sufficiently diverse to call upon every transformation that could be physically realized - otherwise it's not a computer. In that particular universe, every maximally powerful computer would have to include the magical interface.
So it would seem that for computationalism to make any sense, the definition of computers would have to be something else. But I can't quite see what it would be, that would not either be too vague or too specific.
(It might be as simple as: "a computer is something that is as powerful, with respect to the input-output transformations it can eventually create, as the thing we built in the 1950s and that we subsequently called a computer". If that's the definition, then a claim of a computational universe has at least some specificity. The claim would be to the effect of: "there's no part of the universe that can rearrange matter to produce more unpredictability than can a computer, as defined by the capabilities of a certain 1940s-1950s machine, given enough time". And whatever one may say about that claim, at least it's not tautologous.)
no subject
Date: 2013-06-24 11:07 am (UTC)The usefulness of the Church-Turing thesis does not come from anything special about Turing machines or recursive functions, but from the peculiar result that all machines of a sufficient power end up being equivalent in power. To get your definition more in line with that set of machines, I think you would have to add some notion of finitude: for instance, that a computer executes finitely many steps, each of which has finite precision.
no subject
Date: 2013-06-25 01:39 pm (UTC)Thus, concrete computationalism may have content in two ways. First, it could be seen either as a claim that the universe or that the mind is no more powerful than a Turing machine.
Second, it could be seen as a way of considering the universe. The computational point of view would put the evolution of stuff before the stuff itself. Computers being general would thus the whole point: the "point of view" is of the transitions embodied in the particular arrangements of matter, not of the matter itself.
I think the second way of looking at it is less common than the first, though. (It could be interesting to make a "transformation-centric philosophy" for some critters!)
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Good point about the real hypercomputer. In hindsight, I can kinda see it, because programs are in some respects mathematical functions. (If you take away the side effects, even more so!)
no subject
Date: 2013-06-30 07:31 am (UTC)