On 17 Dec 2013, at 03:29, Stephen Paul King wrote:
Hi Liz
My $.0001.
On Mon, Dec 16, 2013 at 8:23 PM, LizR <[email protected]> wrote:
On 17 December 2013 14:03, meekerdb <[email protected]> wrote:
On 12/16/2013 4:41 PM, LizR wrote:
On 17 December 2013 13:07, meekerdb <[email protected]> wrote:
In a sense, one can be more certain about arithmetical reality
than the physical reality. An evil demon could be responsible for
our belief in atoms, and stars, and photons, etc., but it is may
be impossible for that same demon to give us the experience of
factoring 7 in to two integers besides 1 and 7.
But that's because we made up 1 and 7 and the defintion of
factoring. They're our language and that's why we have control of
them.
If it's just something we made up, where does the "unreasonable
effectiveness" come from? (Bearing in mind that most of the non-
elementary maths that has been found to apply to physics was "made
up" with no idea that it mighe turn out to have physical
applications.)
I'm not sure your premise is true. Calculus was certainly invented
to apply to physics. Turing's machine was invented with the
physical process of computation in mind. Non-euclidean geometry of
curved spaces was invented before Einstein needed it, but it was
motivated by considering coordinates on curved surfaces like the
Earth. Fourier invented his transforms to solve heat transfer
problems. Hilbert space was an extension of vector space in
countably infinite dimensions. So the 'unreasonable effectiveness'
may be an illusion based on a selection effect. I'm on the math-fun
mailing list too and I see an awful lot of math that has no
reasonable effectiveness.
Well, maybe my sources are misinformed (Max Tegmark for example). I
imagine the "selection effect" comes about because it's hard to
think of completely abstract topics, so a lot of maths problems will
originate from something in the "real world". My point was that they
weren't invented (or discovered) with the relevant physics
application in mind (with exceptions where the physics drove the
maths, like calculus).
Thing is that Tegmark, and others, seem to forget that the "space of
all possible math" is not well behaved.
tegmark is naive about math. But apparently he seems to go on comp,
which, thanks to Church thesis as a very well behaved notion of "all".
Indeed a constructive one as the UD and elementary arithmetic
illustrate quite well.
We know this from Godel's theorems. So, how does it get to have well
behaved probability densities of "reasonable effectiveness"? Are we
"just lucky" or is there some kind of mechanism that allows us to
"sniff out" nice math?
Penrose talks of mathematical intuition. Is he "not even wrong"?
Intuition comes from the third hypostase (the first person, S4Grz1,
etc.)
(The lack of application in some cases would I suppose fit with Max
Tegmark's suggestion that maths is "out there" and different parts
of it are implemented as different universes.)
What kind of "physical universes" are required for mathematical
entities that are not provable consistent in finite time N and yet
are provably inconsistent in N+1 time?
Maybe interaction is the secret. So far math is being treated as
it where an eternal timeless creature. What if it isn't? What if it
evolves too?
By definition, arithmetical truth is out of the category of time
dependent things. Dont' confuse it with human theories which can of
course evolve.
Another answer is that we're physical beings who evolved in a
physical world and that's why we think the way we do. That not only
explains why we have developed logic and mathematics to deal with
the world, but also why quantum mechanics seems so weird compared to
Newtonian mechanics (we didn't evolve to deal with electrons).
There's a very nice, stimulating and short book by William S. Cooper
"The Evolution of Reason" which takes this idea and develops it and
even projects it into the future. http://www.amazon.com/The-Evolution-Reason-Cambridge-Philosophy/dp/0521540259
Surely the maths we "made up" to deal with the "classical" world
applies to quantum mechanics, too? Or are you saying that we had to
make up a new load of maths to deal with QM, and that "quantum
maths" is incommensurate with "Relativistic maths" and "Newtonian
maths" ?
I think that they are "discovered", not made up, in a way that
reflect the explanation of "the world" that persons have. The only
thing that physicists have over laymen is that they learned some
canonical math that was discovered by others previously.
It is as if Math is a cybervirus that lives in human minds,
evolves therein and reproduces itself via language.
This asks for non-comp, and so asks for you presenting which theory
you work in.
Bruno
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Kindest Regards,
Stephen Paul King
Senior Researcher
Mobile: (864) 567-3099
[email protected]
http://www.provensecure.us/
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