On 20 May 2014 16:12, meekerdb <[email protected]> wrote:
> On 5/19/2014 7:13 PM, LizR wrote:
>
> On 19 May 2014 13:13, meekerdb <[email protected]> wrote:
>
>> On 5/18/2014 5:40 PM, LizR wrote:
>>
>> On 17 May 2014 10:06, John Mikes <[email protected]> wrote:
>>
>>> Dear Liz, thanks for your care to reflect upon my text and I apologize
>>> for my LATE REPLY.
>>> You ask about my opinion on Tegmark's "math-realism" - well, if it were
>>> REALISM
>>> indeed, he would not have had to classify it 'mathemaitcal'. I consider
>>> it a fine sub chapter to ideas about *realism* what we MAY NOT KNOW at
>>> our present level.
>>> Smart Einstein etc. may have invented 'analogue' relativity etc., it
>>> does not exclude all those other ways Nature may apply beyond our present
>>> knowledge.
>>> Our ongoing 'scientific thinking' - IS - inherently mathematical, so
>>> wherever you look you find it in the books.
>>>
>>
>> I assume the implication of what you're saying here is that the reason
>> physics appears mathematical is because that's the way we think. I suspect
>> most physicists would say the opposite - that we think that way because
>> that's how nature works (or at least that's how it appears to work so far).
>> If one is going to take the position that maths is a human invention, then
>> one has the hard problem of explaining why maths is so "unreasonably
>> effective" in physics while no other system of thought comes close.
>>
>>
>> Not at all. A lot of math was invented to describe theories of
>> physics. If you have some idea of how the world is, e.g. it consists of
>> persistent identifiable objects, or all matter pulls on other matter; And
>> you want to work out the consequences of the idea and make it precise with
>> no inconsistencies - you've invented some math (unless you can apply some
>> that's already invented - see Norm Levitt's quip).
>>
>
> If you want to call discovering that charges and so on obey the inverse
> square law "inventing some maths", fine. But it sure looks to me like it
> was discovered.
>
>
> Which? That it's possible to have force law of the form F=k/r^a? Or that
> the value a=2 produces nice elliptical orbits as observered?
>
Both. It all works mathematically, even when only it approximates to
reality.
All of which implies that maths is something that is discovered, and
indeed could be discovered independently in different cultures, times,
places - and on different planets or in different universes.
> I think it only implies that some parts of math are "discovered" like
> counting (which was discovered by evolution) and when people invented
> language and logically inference and concepts like "successor" and "..."
> they "discovered" there was a lot more math they could infer.
>
Like Maxwell's equations, say? We discovered, and continue to discover,
that the world obeys mathematical rules.
Unless you 'discover' within the human mind.
>
Well, yes, just like you will "discover" any concept within a mind, by
definition. (Or I guess within textbooks, in a codified form). The evidence
seems fairly strong that you will discover the same mathematical concepts
within ANY mind which looks into the subject, and has sufficient ingenuity
to work out the answers to various questions, because mathematical truths
appear to be universal (e.g. Pythagoras' theorem didn't only work for the
Ancient Greeks, 17 will always be prime, the square root of 2 will always
be irrational, etc). Only minds can appreciate these facts, just as only
minds can discover the law of universal gravitation.
Which is a strange thing to say since it turned out there was no such
> thing as the law of universal gravitation; it was just an approximation to
> another theory, general relativity, which we're pretty sure is wrong but we
> just haven't been able to invent a better one. So how is a non-existent
> law "discovered"?
>
This one was discovered as an approximation.
Notice how that parses; what is "one"? It's a theory that was *invented*...and
> turned out to be only an approximation.
>
The theory is invented, the maths is discovered. Maths kicks back.
Otherwise those prizes and fields medals and whatnot would fall like
dominoes.
Would you like to bet that the true theory *won't *be describable by
maths?
You're missing my point. Every theory (and we never know whether they're
> true) in the future will be describable by maths because it's what we
> require of a scientific description: precision, logical coherence. Just go
> back and read your own emails to John Ross.
>
> I may well be missing your point, but it *looks* like you're saying that
we are inventing mathematical explanations because that's "what we require
of a scientific description". IMHO that isn't the case, because when we use
"what we require of an explanation", we end up with religion. When we use
something that can be tested, experimentally falsified and so on -- i.e.
when we look for the sort of explanation *the world* requires -- we end up
with science, and so far it appears, for whatever reason, to operate on
mathematical principles. The universe exhibits symmetry, regularity and a
host of other features that it could easily not have exhibited, and which
are all amenable to mathematical description. I'm not making any radical
Brunoesque (or Tegmarkesque) claims about it, I'm just repeating what
hundreds of scientists have observed, and as far as I can see with good
justification, the (fairly trivial) observation that scientific theories
are couched in the language of mathematics because that is what works.
Nothing else appears to work, and the only sensible explanation I can see
for that is that it is how the universe operates.
Anyway, I expect you will explain the point I am missing.
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