On 28 Jun 2016, at 19:30, John Clark wrote:
On Tue, Jun 28, 2016 at 11:58 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
>> A definition will tell you absolutely positively 100%
NOTHING about the underlying nature of mathematics or physics, it
will just tell you things about human mathematical notation and
language. You learn about nature from examples not from
definitions, even the writers of dictionaries know that.
> You are just delirious or what?
I'm not delirious so I must be what.
> I just meant that if you consult the literature,
The literature is physical.
Oh!
> the notion of partial computable function, or Turing
computable function, or Church lambda calculus, and the relative
computations, etc. does not involve any physical assumption.
And that is precisely why despite their misleading names partial
computable functions or Turing computable functions
or Church lambda calculus can't actually compute or
calculate one damn thing.
A universal Turing machine can compute all Turing computable
functions. And also all Lambda computable function, and actually,
accepting the Church-Turing-Kleene-Post thesis, a universal (Turing)
machine can compute all computable functions.
Of course, for non universal machine, some computable function are not
computable.
And the extensional Church-Turing thesis admits an intentional
version, so that not only all universal machine can compute all
computable functions, but they can compute them in the same manner as
each other, that is they can all emulate all digital processes.
Just inform yourself as you seem to persist in the confusion between
the mathematical notion of computation and the notion of a physical
implementation of a universal machine, which makes possible to
exploits nature to do physical computations.
In a physical computer, a register can be build physically, for
example with a sequence of flip-flop, done with physical electrical
line and the nand gate. In arithmetic, you can build a register, that
is fine a number which will encode the sequence of numbers, like using
Gödel"s exploitation of the fundamental theorem of arithmetic: the
uniqueness of the factorization of numbers into product of prime factor.
In the first case, you will get physical boxes containing the numbers
you want to encode: say 4, 5, 4, 6.
In the second case, you will get an arithmetic register coding the
sequence, for example with gn = Gödel number, that is representation
of symbol by numbers.
2^ng(ssss0)*3^ng(sssss0)*5^ng(ssss0)*7^ng(ssssss0)
Arithmetical retrieval will be easy to define, writing p-i for the ith
prime, like
R(a, i) = the number n such that p_i^n divides a, but p_i^n+1 does
not, with a > 0.
A computation is given by what universal machine does, and "being a
computation" is primitive recursive, and easily definable in arithmetic.
Once you accept Yes-doctor, it is a simple consequence of the laws of
addition and multiplication that the exact computation made physically
right now to make you conscious of reading this paragraph right now is
emulated exactly, at the (existing by hypothesis) substitution level
in infinitely many different computational histories.
The point: If you tell me that none are real except our own physical
one, well, if you tell me this in virtue of a brain doing a
computation, all the John Clark in arithmetic will tell exactly this
to my doppelgangers, pointing ostensively on their apparent, and
indeed real for them, physical reality.
If computationalism is true, there is no way for us to distinguish
*introspectively* which universal computations supports us, and below
our substitution level, we must expected a sort of infinite sum of
computations, which QM does illustrate in some way.
>> Don't tell me show me, don't give me another definition
give me an example, calculate 2+2 without using anything
physical, or if that's too hard try 1+1. Do that and I'll concede
the argument, and immediately after that I'll get on the
phone to Silicon Valley.
> Silicon valley exists thanks to those mathematicians having
discovered the universal numbers.
That is true, Silicon Valley wouldn't exist without
mathematicians like Turing, but Silicon Valley wouldn't exist
without Silicon either.
> The numbers, as studied today, by mathematicians, does not
use physical assumption.
Mathematicians are free to make or not to make any assumption they
like, but it won't change the fact that mathematicians are
physical.
Human mathematicians are physical. But if computationalism, even the
human physicalness is an indexical. The mind of the universal machine
obeys a lot of laws which do not assume primitive physicalness. The
closure of the partial recursive functions for diagonalization and
higher orders makes numberland quite explanatively close, and with a
constructive warning by the (Löbian) universal machine against all
reductionist conception of what its personhood.
>> if pure mathematics is the most fundamental science and
contains profound truths independent of the physical world why does
the mathematician need physics to give his equations meaning?
> In the big picture, it does not.
Perhaps your "big picture" is just a bit too big. If the
fundamental meaning of the word "nothing" is infinite unbounded
homogeneity in every dimension, and I can't think of a better one
that conforms with our normal use of the word, then your "big
picture" is nothing.
You seem to be negative for the purpose of being negative.
> If you were not stuck in step 3 [...]
John Clark is not stuck at step 3, Bruno Marchal is.
Bruno Marchal assumes the very thing Bruno Marchal is trying to
prove, Bruno assumes that because when looking into the past
there is always a unique meaning to the word "you" there
will be a unique meaning to that personal pronoun when
looking into the future too;
Not at all. Quite the contrary. All what is used is the talk of each
duplicated people. Once you do assume computationalism, you know that
none of them can feel the split, unless you add magic. And none can
find an algorithm given the result of pushing the button followed by
opening the doors. To see that, you can interview good sample, well
defined in elementary statistics. in UDA, both the 3p and the 1p
admits simple 3p description. Up to now you argument has not been able
to be clarified by anyone, and that is normal, it is just bad play
with words. (which betrays a bit your agenda, I guess).
but if the multiverse exists and Everett is right then there is
no way that assumption can be correct.
Read Everett short and long version: he used that assumption.
It is not a coincidence that those who have a difficulty with
computationalism, have a difficulty with Everett, and hallucinate
spooky action at a distance. Anyway. You are the one using bad
religion to invalidate a demonstration, and, well, that is not valid.
Bruno
John K Clark
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