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).

(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.)

>
> 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" ?

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