Hi Ronald,
On 19 Dec 2008, at 14:31, ronaldheld wrote:
>
> Bruno:
> I may have missed something in the last two days.
> I still do not understand. You say this starts with the real world,
> which to me is the physical universe/Multiverse, but it actually
> starts with arithmetic.
Your remark is a bit "out of the reasoning", and as such is a bit
unclear to me. The reasoning start from the mechanist hypothesis,
which I take as the willingness to accept an artificial digital brain,
with all the usual local sense of the world. It is a quasi-operational
definition. Strictly speaking this does not presuppose your
immateriality, still less the immateriality of the physical universe,
this will appear in the conclusion of the reasoning.
I suggest that you follow the KIM thread and that you interrupt when
anything seems unclear to you. Meanwhile I sketch (only) basic
explanation below.
> How is there any mathematics with nothing to
> conceive of it?
I am afraid that, Like Einstein and some other physicists, you have a
"conventionalist" view of mathematics. This explain probably why
Einstein never commented on the work of Gödel (despite their
friendship in Princeton). The work of "modern" logician is just NOT
understandable by any "mathematical-conventionalist". I could argue
that many results by logicians, including the incompleteness
phenomenon, sign the end of the very possibility of conventionalism.
So, to answer your question, now we have very good reason to believe
that mathematics has something to conceive of it: a mathematical
reality.
The clearer way to see this is probably the discovery that the realm
of the natural numbers, conceived together with their additive and
multiplicative structure, escapes the power of any (axiomatizable)
theory. There is just no complete theory of everything capable of just
enumerating the truth about numbers. The reality of numbers escape our
theoretical power, and provably so if we add the hypothesis that we
are machines (or even super-machines or super...super-machines: the
result is quite general).
So mathematics has a proper field of study that we can aptly call the
mathematical reality. Now we know that such a reality is an infinite
reservoir of surprises. Even the apparently less rich arithmetic is
such an infinite reservoir.
> What are the computations running on, where did the
> program come from and still what is it running on. It should still
> take a net amount of enegry to run computations.
If we abstract from the fact that in practice we have to write program
and data, and read the results, it can be shown that computation per
se does not need energy. There exist purely reversible universal
computer. They compute without dissipating any energy. For example
they never erase information, because it has been shown that this
necessarily dissipate heath.
But of course this is a physicalist answer, and has nothing to do with
the fact that, if we assume comp, eventually energy itself is an
emergent phenomenon, and that energy, as time and space will emerge
from the mind, and the mind itself emerges from the computations.
So, where does those computations come from? The computations are
encoded, in many different ways, in the additive and multiplicative
relations which exists among the natural numbers. So if you agree that
a truth like "34 is an even number" or "17 is a prime number" is an
atemporal truth not depending on anything contingent, the I could show
to you that all the propositions having the shape of "the machine with
number X stop on input Y after 3456655409812228 steps" are true or
false and this independently of us in the same sense as above. Those
truth are atemporal, even "aphysical", yet, machine will develop many
growing set of "beliefs" about time, space and actuality (and
discourses about things like that), albeit such development itself is
atemporal and aspatial if I can say.
Hope this helps, if not, just follow the slow explanation to Kim.
Those explanations are slow because I am willing to work on any
infinitesimal details, so please feel free to ask anything. Well, to
be sure, the explanations are also slow because Kim and me appreciate
to digress, also, but that's part of the fun.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Sun Dec 21 2008 - 09:40:25 PST