Saying that “everything is math” is not an explanation of what math is, in the sense of lawful processes in mathematicians’ heads, and more generally in decision-making.
It seems fairly obvious that a mathematician’s head is doing a physics computation, which is logically correlated with an abstract neural-network computation (representing its mind), which is logically correlated with whatever part of math that the mathematician is considering. “Everything is math” doesn’t tell us the exact nature of those logical correlations, but neither does it hurt our attempt to find out, as far as I can tell.
Also, I don’t understand what you mean by “staying at the level of natural phenomena” nor how that helps to “sidestepping the confusion”.
It seems fairly obvious that a mathematician’s head is doing a physics computation, which is logically correlated with an abstract neural-network computation (representing its mind), which is logically correlated with whatever part of math that the mathematician is considering.
My point is that you don’t need to make that last step, saying that process in the head is related to some abstract math. Instead, take two processes in two heads, and relate them directly, through the physics stuff.
To make an analogy, when you see two similar plants, it’s confusing to talk about them being instances of the same platonic plant. Instead, by saying that they are similar, you mean that you formed certain representations of them in your own mind, and the representations considerably match: it’s a concrete operation that is performed by one who recognizes the connection.
With math, relating processes (or formulas) through denotational semantics has a danger of losing track of the procedure that relates them, which can in some cases be unfeasible, and limitations on which may be important. Some things you can’t even pinpoint to the semantics: are these two programs equal, in the sense of producing the same results for the same inputs? That is, what are those mathematical objects that correspond to each of them? You’ll never know, and thus the question is effectively meaningless.
Interaction between specific details of implementation is part of decision-making as well as of the decisions themselves. Introducing abstract representation that abstracts away the details in unspecified fashion and gets communicated through the ether may confuse the situation.
Ok, that’s much clearer, and while I don’t know if I agree with you completely, there’s nothing you said that I object to.
I think confusion arose in the first place because you interpreted “platonic computation” to mean the denotational semantics of a computation, whereas Eliezer (and others) were using it to refer to the “abstract neural-network computation” as opposed to the “physics computation” involving wavefunctions and such, or the “physical world” with physical particles/wavefunctions (whatever that means).
It seems fairly obvious that a mathematician’s head is doing a physics computation, which is logically correlated with an abstract neural-network computation (representing its mind), which is logically correlated with whatever part of math that the mathematician is considering. “Everything is math” doesn’t tell us the exact nature of those logical correlations, but neither does it hurt our attempt to find out, as far as I can tell.
Also, I don’t understand what you mean by “staying at the level of natural phenomena” nor how that helps to “sidestepping the confusion”.
My point is that you don’t need to make that last step, saying that process in the head is related to some abstract math. Instead, take two processes in two heads, and relate them directly, through the physics stuff.
To make an analogy, when you see two similar plants, it’s confusing to talk about them being instances of the same platonic plant. Instead, by saying that they are similar, you mean that you formed certain representations of them in your own mind, and the representations considerably match: it’s a concrete operation that is performed by one who recognizes the connection.
With math, relating processes (or formulas) through denotational semantics has a danger of losing track of the procedure that relates them, which can in some cases be unfeasible, and limitations on which may be important. Some things you can’t even pinpoint to the semantics: are these two programs equal, in the sense of producing the same results for the same inputs? That is, what are those mathematical objects that correspond to each of them? You’ll never know, and thus the question is effectively meaningless.
Interaction between specific details of implementation is part of decision-making as well as of the decisions themselves. Introducing abstract representation that abstracts away the details in unspecified fashion and gets communicated through the ether may confuse the situation.
Ok, that’s much clearer, and while I don’t know if I agree with you completely, there’s nothing you said that I object to.
I think confusion arose in the first place because you interpreted “platonic computation” to mean the denotational semantics of a computation, whereas Eliezer (and others) were using it to refer to the “abstract neural-network computation” as opposed to the “physics computation” involving wavefunctions and such, or the “physical world” with physical particles/wavefunctions (whatever that means).