On 09 May 2017, at 00:58, Russell Standish wrote:
On Mon, May 08, 2017 at 12:42:01PM +0200, Bruno Marchal wrote:
I don't think they need to halt. They need only to go through our
local state. A priori, the halting computations might have a null
measure among all computations, so that the global "physical"
measure might be determined only by the Non Halting computations.
Just a technical detail out of the scope of your argument, to be
sure, but it might have technical consequences when we do the math
though.
But the halting computations does not have zero measure in the space
of all computations. (I'm assuming you mean zero measure when you say
"null measure"). The probability of a machine halting is the Chaitin
Omega number, provably between 0 and 1.
That might be interesting, but I am not sure it works for the first
person points of view, which actually pertains also on the oracles
(simulated by the infinities of big natural numbers, in the first
person perspectives). If we take them into account, the modal logics
remains invariant for this addition, but the experiences explode in a
continuum (due to the (random) oracles, notably), and in that case
halting computations, which are only enumerable, get a measure zero
(with most reasonable 3p measure known here). This is complicated, and
it needs the quantified G* to be translated in arithmetic and to keep
intact our means to distinguish quanta and qualia, so, let us keep
this in the open problems. I certainly would have liked using Chaitin
theorem, but it is not the most urgent (so to speak). This is related,
in recursion theory, to the two dualities creative/productive, versus
simple/immune. Maybe (I speculate here) the simple/immune "duality" is
needed for finding the hamiltonian (like the creative/^productive is
used, through G, for the physical statistical measure).
Bruno
I don't think this changes your first two sentences, though :).
Cheers
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Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow [email protected]
Economics, Kingston University http://www.hpcoders.com.au
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