**From:** Mitchell J Porter (*mjporter@U.Arizona.EDU*)

**Date:** Wed Jul 25 2001 - 18:46:35 MDT

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John Stick said

*> Once you
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*> find a "new physics" phenomenon that is uncomputable, if you ever do,
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*> I will bet the uncomputability will be able to be manifested in a
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*> substrate employing only the old physics as well. Uncomputability is
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*> ultimately a mathematical phenomenon, not a phvsical one, and it will
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*> be independent of the details of brain chemstry or physics.
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This doesn't make any sense. An example of a noncomputable function

would be HALT[TM,IN], defined as follows: it returns "1" if the

Turing machine TM presented with the input IN will eventually halt,

and "0" otherwise. There's no end of specific cases where it's easy

to figure out the answer, but there is no Turing machine which can

compute the function's value for all possible pairs of inputs.

The computational primitives of a Turing machine are a few

operations: read, write, move right, move left. One can imagine

adding the function HALT (in some form) as a new computational

primitive. This defines a new class of abstract computers,

capable of computing a much larger universe of functions (namely,

anything that can be expressed as a composite of Turing-computable

functions and "halting functions" for Turing machines). The

members of this new class are "oracles" of the first degree.

But if OR1 is a member of this class, then it turns out that

HALT[OR1,IN] is not computable for a first-degree oracle.

So you can define a second-order oracle which has HALT[OR1,IN]

as a new computational primitive. And so on.

If there is such a thing as "noncomputable physics", it means

that, say, the equations of motion involve noncomputable

functions. There would be processes which, over time,

transformed one set of quantitative physical properties into

another set, according to some noncomputable transformation.

Example: you have two groups of binary physical systems ('bits').

They spontaneously produce another binary entity, whose state

is HALT[TM,IN], where the first group of bits encodes a

Turing machine, and the second group of bits encodes an input

to that machine.

If there was such an interaction, you could use it to make

an oracle - to compute the values of functions that are

noncomputable for Turing machines - since it implements the

necessary new computational primitive. But if the rest of

physics involves Turing-computable processes, there's not

going to be any way to combine them to duplicate the

computational powers of this hypothetical new noncomputable

process.

This thread started with Emil Gilliam saying:

*> [what if] noncomputability lies at the heart of qualia
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and quoting Eliezer (http://sysopmind.com/archive-sl4/0103/0006.html):

*> I do think there's a good possibility that qualia
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*> are noncomputable ... But I definitely deny that the noncomputability
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*> has anything whatsoever to do with either Godelization or reflection.
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Emil seems to mean Turing-noncomputability, but Eliezer seems

to mean something else, because if it means anything, Godelization

means jumping out of the system to add a new computational

primitive (HALT[]) or a new axiom (an unprovable-but-true Godel

proposition). What I think Eliezer means is that qualia might

not be computations, or might not be spontaneously generated

by computations independent of substrate. Personally I think

that's a reasonable opinion, but it is a *separate question*

from the computability-or-otherwise of physics.

If I read him correctly, Eliezer's issue is a question of

ontological categories: what sort of thing *is* a quale

(singular of qualia)? Is it an "informational property" as

Chalmers would have it, possessed by any implementation of

a particular finite-state machine? Or is it a substrate-dependent

property, like charge or mass? Whereas Emil is asking about

*dynamics*: what are the "equations of motion" of qualia?

Are they Turing-computable or not?

It is quite consistent to maintain that qualia are

substrate-dependent but "Turing-computable", meaning

that their dynamics could be simulated and predicted

by a Turing machine. If this is true then consciousness

can be simulated without actually being created. I think

this is the simplest position, on account of

(i) the very sparse evidence that human thought has a

Turing-noncomputable dynamics, and

(ii) the difficulties in maintaining that computational

states are defined by objective (user-independent) properties

of physical systems.

**Next message:**Mitchell J Porter: "re: noncomputability"**Previous message:**Damien Broderick: "Re: What if qualia"**Next in thread:**Mitchell J Porter: "re: noncomputability"**Maybe reply:**Mitchell J Porter: "re: noncomputability"**Reply:**John Stick: "Re: noncomputability"**Maybe reply:**Mitchell J Porter: "re: noncomputability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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