Why is it that we talk about caring and preference, pleasure and pain,
and "proper behavior", when it comes to trying to figure out the basic
nature of reality? (I've noticed that a lot of the thought experiments
on this list feature pleasure or pain decision making.) For me this is
a rhetorical question, because I believe that personhood is at the very
core of reality. However, the point of my post is that this is one of
those assumptions that we tend to take for granted without thinking
about why we can assume it, and what its implications are. Or we just
insert it into our thought experiments thinking that we aren't really
assuming it as basic to everything but just making the argument more
tangible. However, I would discourage this since there are those of us
like me who take personhood to be at the core, and so this makes the
thought experiment loaded to begin with. On the other hand, can we
have a theory of everything without making that assumption? If so,
what would that look like? What would the comparison between math and
physical reality look like without it? (Perhaps something like the
Riemann hypothesis TOE would fall into that category.) Can Wei Dai's
approach below be done without it?
Tom
-----Original Message-----
From: Wei Dai <weidai.domain.name.hidden>
To: everything-list.domain.name.hidden
Sent: Wed, 29 Mar 2006 11:58:31 -0800
Subject: proper behavior for a mathematical substructure
Is there a difference between physical existence and mathematical
existence?
I suggest thinking about this problem from a different angle.
Consider a mathematical substructure as a rational decision maker. It
seems
to me that making a decision ideally would consist of the following
steps:
1. Identify the mathematical structure that corresponds to "me" (i.e.,
my
current observer-moment)
2. Identify the mathematical structures that contain me as
substructures.
3. Decide which of those I care about.
4. For each option I have, and each mathematical structure (containing
me)
that I care about, deduce the consequences on that structure of me
taking
that option.
5. Find the set of consequences that I prefer overall, and take the
option
that corresponds to it.
Of course each of these steps may be dauntingly difficult, maybe even
impossible for natural human beings, but does anyone disagree that this
is
the ideal of rationality that an AI, or perhaps a computationally
augmented
human being, should strive for?
How would a difference between physical existence and mathematical
existence, if there is one, affect this ideal of decision making? It's
a
rhetorical question because I don't think that it would. One possible
answer
may be that a rational decision maker in step 3 would decide to only
care
about those structures that have physical existence. But among the
structures that contain him as substructures, how would he know which
ones
have physical existence, and which one only have mathematical
existence? And
even if he could somehow find out, I don't see any reason why he must
not
care about those structures that only have mathematical existence.
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Received on Thu Mar 30 2006 - 19:50:26 PST