Hi Liz

 My $.0001.

On Mon, Dec 16, 2013 at 8:23 PM, LizR <lizj...@gmail.com> wrote:

> On 17 December 2013 14:03, meekerdb <meeke...@verizon.net> wrote:
>>  On 12/16/2013 4:41 PM, LizR wrote:
>>  On 17 December 2013 13:07, meekerdb <meeke...@verizon.net> 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. 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"?

> (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?

>> 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.


Kindest Regards,

Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099



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