On 24 Jun 2016, at 21:47, John Clark wrote:
On Fri, Jun 24, 2016 at 12:04 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
> Read the definition in the literature, it does not involve
physical assumption.
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 just meant that if you consult the literature, 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.
Here you make a "knock on the table argument", but that the ancient
already knew that this is invalid.
>> in fact nothing is Turing emulable, not even
arithmetic, UNLESS the Turing Machine in question is physical.
> The sigma_1 part of arithmetic is Turing emulable,
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. Some, like Turing, will indeed participate in
the physical implementation. Babbage discovered it, and get the main
consequences, I think, when realizing that his description language
was as much powerfull than its machine, which is the HaHa of Church's
thesis.
>> If there was only one thing in the physical world
mathematicians wouldn't have the slightest intuition about what
numbers mean, they'd just be playing with squiggles. Of course if
there was only one thing in the physical world mathematicians
couldn't even exist, but never mind.
> You confuse
No I don't confuse.
> the mathematics developed by the humans, which are very
plausibly inspired by the observation of nature, and the reality of
some mathematical facts.
You admit that to a mathematician who had no experience with
anything physical a equation would just mean a sequence of squiggles
that had a "=" squiggle somewhere in it, and that's all it would
mean. That's it.
A local truth does not make a global truth false. The numbers, as
studied today, by mathematicians, does not use physical assumption.
They use arithmetical, or set theoretical assumptions.
But 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.
It is an an infinity of dream, John, albeit some can be quite
persistent one, and apparently sharable.
And it is not math which is the fundamental science, it is more a
science of the universal person, the one defined by G and G* and its
important intensional variants, in relation with consistency, and truth.
Stephen Hawking once asked:
"What is it that breathes fire into the equations and makes a
universe for them to describe? The usual approach of science of
constructing a mathematical model cannot answer the questions of why
there should be a universe for the model to describe. Why does the
universe go to all the bother of existing?"
Hawking is saying a mathematical model can't explain why the
physical exists,
I guess he means theory. I agree with him. You need at least a theory
of the mind and belief, to have at the least a believer in something.
But this arithmetic provides amply.
but I think a physical model (like a brain) can explain why
mathematics exists.
Also, here, I am afraid we abstract away from the fact that just
defining the brain activity involves implicit assumption in numbers
and something turing universal.
Higher levels can not be expected to explain the existence of
more fundamental levels, but more fundamental levels can explain
higher levels, and physics is more fundamental than mathematics.
If you were not stuck in step 3, you would plausibly understood that
if we assume Church-Thesis, and "yes doctor", things are no more that
simple, and the theoretical computationalist has the task to derive
physics from the universal machine mind. But just the genuine
intensional restriction on this domain gives basically what we ere
searching: an intuitionistic logic for the first person, a quantum
logic for the better/observer, and hopefully some day some "Gleason
theorem" providing the unique (quantum) measure.
It is more rich than physics in the sense that it gives the quantum
logic and the qualia logic, which resemble, yet are different.
Note that eventually the quanta themselves are sort of qualia, which
makes Everett MWI saving us from solipsism, we do share rich and
probably very deep (arithmetical) dreams.
Bruno
John K Clark
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