proper behavior for a mathematical substructure
Wei Dai
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.
Brent Meeker
> 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.
This seems to assume a dualism in which you are both a mathematical structure
and at also stand outside the structure caring and making decisions.
Brent Meeker
John M
Wei and Brent:
considering Wei's Q#1 and 2 the thought occurred to me
(being almost a virgin in thinking in mathematical
constructs) that this looks as an even harder problem
than Chalmers's famous neurological "hard problem".
For me, at least.
With the Q#3 I would ask "who is I?" Mathematically of
course. Otherwise we don't know. That would require a
mix of 1st and 3rd person notions which is confusing.
Same with Q#4.
A dilemma of a subset like: validity of a legal
position" is easier, because it is only 3rd person
related (except for an inclusion of "my opinion" into
it.
So I can't wait for a solution to Brent's addition:
"how to formulate such meanings in math constructs?"
Especially in self reference to the formulator "I".
Physical existence (for me) is no more plausible than
a mathematical existence: both are figments of the
mind upon (maybe poorly perceived) impacts we can use
only as interpreted for ourselves.
John M
Wei Dai
> This seems to assume a dualism in which you are both a mathematical
> structure
> and at also stand outside the structure caring and making decisions.
What makes you say "stand outside the structure"? I'd say instead that I am
a mathematical structure that cares and makes decision. (Assume that I am an
ideal decision maker, instead of the actual me.) Perhaps you say that
because while making a decision, I don't seem to be treating myself as a
mathematical structure. It might seem that if I did, I can just logically
deduce my own decisions instead of going through those steps.
I'd answer this by arguing that it is impossible for me to logically deduce
my own decisions, therefore the only way for me to know what my decisions
are is to actually make the decisions. To see this, suppose a method exists
to predict one's own decisions. But then we can construct an AI that uses
this method on itself and then do the opposite of what the method predicts.
marc....@gmail.com
mathematics. However physical properties by themselves aren't
mathematical properties. Which properties do we call 'physical'?
There appear to be three main classes of properties that we interpret
as 'physical': *spatial* properties, *topological* (or containment)
properties, and *functional* properties.
Perhaps one should say that physical properties are 'partial'
mathematics. Let me try to clarify what I mean by analogy - take the
prime factorization of a non-prime number. The primes are in some
sense 'components' (or building blocks) of the non-primes. By analogy
with this, one could say that physical properties are *metaphysical
components* of mathematical entities. Physical properties by
themselves are not mathematical properties, but in combination with
other (non-physical) metaphysical entities, you build mathematical
entities. Or another analogy might be that physical properties are in
some sense 'the metaphysical square root' of mathematics.
1Z
John M wrote:
> With the Q#3 I would ask "who is I?" Mathematically of> course. Otherwise we don't know.
Really ?
daddy...@aol.com
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
Bruno Marchal
Le 29-mars-06, à 21:58, Wei Dai a écrit :
>
> 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)
You can't. It is just absolutely impossible in term of first person OM
(implicitly the OM notion of Bostrom), and you can, but only by guess
and chance, for some third person description of the OM. But in that
case ....
> 2. Identify the mathematical structures that contain me as
> substructures.
... There will be an unameable infinity of such mathematical
structures. I think P. Jones got that right.
To apply your trick we need to get the physial laws from comp first
(but then i'm OK).
> 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?
OK then, but with the proviso above (and apparently you are aware of
the difficulties).
>
> How would a difference between physical existence and mathematical
> existence, if there is one, affect this ideal of decision making?
By affecting the very structure of the physical laws. Of course that
will not change the way you prepare coffee (nor will the choice between
Loop Theory and String theory affects such things).
> 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 with the comp hyp, what would that mean?
> 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.
Because with comp, even if matter exists, it is devoid of any
explanation power. Like the Napoleon's God is unnecessary in a
Laplacian Universe. If you accept comp, what do you mean by Physical?
It seems the UDA shows such a notion is untenable as primitive notion.
The physical is really what emerges from the interference of many
"mathematical histories" The "many" is due to person's inability to
make distinction of the finer grained histories; finer relatively to
its substitution level.
Bruno