# Infinitesimal roadmap (was Re: Numbers, Machine and Father Ted)

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Le 21-oct.-06, à 02:12, David Nyman a écrit :```
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> Yes, of course, Brent - hence my comments later on in my post. But in
> fact, comp implies that the normal physics model can't 'fit all the
> data', if we include (as we must) the 1-person pov itself in 'the
> data'. And my point is also that a model which is, in this respect
> particularly, so counter to 'normal science' is especially provocative
> and deserves much attention.  Well, it gets it on this list but
> unfortunately much of the debate goes round in circles because the
> concepts are hard to grapple with, let alone master sufficiently to
> rebut (short of IMHO sterile debates about 'reification'). Hence we
> don't get very far... hence (please) THE ROADMAP. But I wouldn't want
> Bruno to feel I was harrassing him...

Not at all. Actually, you just make higher the probability that I write
that [censored] english version of my thesis.

Let me give you an infinitesimal roadmap:

1) UDA

UDA shows that if we are digital machine then we cannot distinguish any
reality from purely arithmetical one, and that we have to justify the
"physical laws" by some measure on some relations between numbers. It
fits a recurring intuition in this list: we have to define "observer
moments" and we have to find a measure on them (absolute for some,
relative for others, ...)
UDA uses the comp hypothesis: YD + CT + AR    (Yes doctor + Church
Thesis + Arithmetical Realism)

2) AUDA

Mmmmh.... Let me put it in this way. AUDA is the same as UDA except
that it uses the a-comp hypothesis. a-comp is just CT + AR. "a" is for
"arithmetical". No need to implicate yourself personally with complex
personal questions like "should I say yes to the doctor and what
happens after self-duplication ...".
The trick is simple if not naive. Instead of interviewing you or humans
like in the UDA, I interview "directly" the machine. Not all machines
are interesting here, but thanks to AR, or classical AR, I can limit
the interview on a "platonist" (here it means a theorem prover
accepting the P v ~P principle) self-referentially correct sufficiently
chatty (proving) universal machine.

Things to understand for AUDA:
1) The absoluteness of the notion of computability (this is equivalent
with the understanding that CT is not trivial at all: CT entails that
absoluteness. Such absoluteness are rare events in mathematics and
logics).
2) The  irreducible relativeness of the notion of provability (this is
incompleteness, and it follows also from CT, through very few
diagonalizations).
3) The provability logics. G, G* and their intensional (modal) variants.

David, what is your relation with computers? Do you know one or two
programming languages? Do you know classical propositional logic?
formally, informally? I can really start from zero, if only (obviously)
that is what I have to do with the universal machine in the interview!
Nevertheless, according to your background I can accelerate here and
there at least in the roadmap.

I appreciate your interest, don't hesitate to harass me more. I feel I
little bit guilty for the list which does not always appreciate the
importance of putting all the cards on the table at some point, but
then it has to be a little more technical. Perhaps it could be an
opportunity also to take the train ...

Bruno

http://iridia.ulb.ac.be/~marchal/

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