Re: Mathematical Model of GLUTs and Lookups

From: Lee Corbin (
Date: Thu Apr 17 2008 - 21:56:34 MDT

I had written

> > I don't think that the domain of the [your] function is [should be] S,
> > however. The domain of the function G is the GLUT itself; G takes
> > entries of the GLUT to other entries.

and Stuart writes

> Still some confusions (I see G as a function on S - it takes one state
> of the system, and gives you another (subsequent) state, so is a
> function)! But the main ideas are there.

Perhaps we resolve this by noting that the first GLUT (involving no
hashing) has entries that *are* polynomials, or which *are* states
of a computer or brain, or which *are* generations of the Life Board?
Maybe we are saying the same thing? It's probably a minor point,
but I like math, and precision feels good :-)

> Let me paraphrase the argument I've been circling around:
> A GLUT may be hash equivalent to consciousness; but if there exists a
> set-up that is not too complicated, where the rules of consciousness
> are not too complicated (compared with a full GLUT), then we should
> take this set up as really "telling us something about consciousness"
> rather than the GLUT, which tells us little.

I take you to mean the following. We really have a large variety
of GLUTs and it would be well to distinguish them. They are,
respectively, the ones which contain addresses (of course),
and addresses such that the contents at a particular address is

case 1: a polynomial (or simple text encoding of one)
case 2: a generation of Conway's Life
case 3: a state of a Turing machine, or other regular computer
case 4: a living thinking human brain state

Don't you think we need to subscript the term "GLUT", e.g.,
GLUTp, GLUTcl, GLUTtm, GLUTh (h for human), GLUTa
(a for alien).

> In this way, modern methods are telling us more about these objects
> than classical methods, just as some compact theory of consciousness
> tells us more than a GLUT.

It certainly has that potential, and my intuition says we can get there,
if we have not already.

> This is especially true if you consider "partial truths": a partial truth
> on a GLUT is just some sort of sub-GLUT, a partial truth of a
> theory of consciousness can be considerably simpler (even relative
> to the theory of consciousness).

Very interesting. Sort of parallel to partial function. Might examples be

(A) suppose that the huge GLUTh or GLUTa passes not only
      a Turing Test, but convinced several people, each given
      three hours, that it is conscious as well as intelligent.
(B) a subset of (A) consisting of the first hour for each interrogator
      (with the GLUT becoming suddenly silent afterwards)
(C) a subset of (A) but with gaps, so that (I believe) the GLUT
      just ignores many questions, though somehow seems aware
      in many cases that it had failed to answer, or aware that
      in its opinion the interrogator had been off-line

If these don't work, then I'm not following your last paragraph.

> Do you want me to go over the polynomial example again,
> dealing with your comments? I will, if you think that knowing
> the specifics will be useful!

Thanks for the offer. I'm tempted, but I'll take a rain-check if
that's all right. Your patience is exemplary!
> PS: What is this "end of time" you were mentioning? :-)

Julian Barbour wrote, as you probably know, a book with that
title, and there are other theories which attempt to reduce time
to something else (e.g. configuration space or mathematical
structures in Platonia). I still want to avoid having to believe
in those, for several reasons, most notably because it *could*
(in my eyes, at least) reduce moral decisions to gibberish.


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