On 27 Oct 2014, at 12:04, Russell Standish wrote:
On Mon, Oct 27, 2014 at 11:20:59PM +1300, LizR wrote:
On 25 October 2014 12:19, Russell Standish <[email protected]>
wrote:
So you know for certainty that the arrival times of electrons in a
Geiger counter from a beta decay source is computable. How?
This point was originally about real numbers (wasn't it?)
You (Russell) said that Bruno has shown that real numbers must be
part of
the phenomenal world if comp is true, but not ontological (because
comp
assumes only integer arithmetic and that only with certain
operations).
I'm not sure if I follow this, but my guess is that comp says that
some
phenomena we experience can generate an arbitrary string of random
digits -
as many digits as we care to measure. Or something like that...? I
guess
that has to be the case if there is first person indeterminacy. Or
have I
got this completely wrong?
No, you're right on the money. Real numbers are basically just
infinite sequences of random integers, most of which are uncomputable.
Which is what FPI is.
Yes. In the case of iterated self-duplication. That leads to randomness.
Now the FPI on the sigma_1 arithmetic, or on the UD, which contains
much more than simple iterated self-duplication, (it contains all
rational approximations of all Heisenberg matrices evolution or
waves, ..., and much more), should be physics, notably the physics of
what is below our substitution level. Comp predicts/explains why it
looks like there are "parallel universes/computations" below our
substitution level. Comp predicts also (I think) a continuous
background, if only due to the presence of those "stupid" iterated
duplications of oneself in arithmetic.
Bruno
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Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
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