Posted by
Steve Smith on
Apr 28, 2009; 9:07pm
URL: http://friam.383.s1.nabble.com/The-Unreasonable-Effectiveness-of-Mathematics-in-the-Natural-Sciences-tp2714601p2736936.html
I fear the below continues to be argumentative on my part. I can't
seem to quite discover or render the kernel of my point here.
Apologies to all for my lack of clarity, it is probably from trying to
hold materialist,
- Steve
Russ Abbott wrote:
Awhile ago on this thread I said that mathematics is
effective because there are regularities in nature. No one commented on
that.
I think we all share this as a working understanding of how mathematics
and nature relate to each other. I believe we developed mathematics
precisely for that purpose. One could say our mathematics evolved,
others could say we "discovered" it. Even the more obscure branches of
pure/abstract Math seems to have second-order relations... even if it
doesn't describe patterns in the world, it describes patterns in
mathematics itself (abstract algebra, group/set/catagory theory, etc.)
There have been many comments discussing whether what goes
on in our minds matters, but very little about what goes on outside our
minds.
My position (and I will look for some references to back it up) is that
I don't believe we can *know* that anything exists outside of our mind,
that the physical universe, that physical reality is anything more than
an hallucination or a projection of the mind. Naturally even this
description is problematic as it begs the question (some more) of "what
is mind?" and "who am I chattering on with here, if nothing outside my
mind exists, anyway?"
It's amusing to poke fun at the way some people think,
but I'm not sure it gets us anywhere.
If you are referring to my references to folk knowledge, quite the
contrary. I hold folk knowledge in high esteem and practice it as a
matter of course, possibly more directly than most folks on this list.
It is how I cook, build, grow, heat my house, etc. all by colloquial
understandings of the phenomenology of normal everyday things (foods,
fire, materials, plants, etc.)
My curious mind constantly checks these things against the scientific
abstractions I know of, and am amused at how well they work and then
amused even more when they don't work so well. I don't imagine for a
second that the abstractions are *wrong*, but rather that my
observations or application of them is more likely flawed. For
example, when the tree I might be cutting falls a different direction
than I intended (and predicted), I don't imagine that gravity hiccuped
or even that the "wood sprites" niggled it just to frustrate me. When
the cake I'm baking falls, it is the result of "opening the door when I
shouldn't", not the kitchen sprites, but not precisely "pressure waves
induced by the ...." either. On the other hand, an animist
understanding would probably work generally as well. In all cases, I
hold (at least) a dual state of understanding... a colloquial one (the
sun rises, passes through the zenith, then sets every day) and a more
scientific one (the earth rotates, exposing the sun at different angles
through the day) with no problems. I could maybe even pack in a deist,
animist or anthropomorphic understanding on top of that (Ur the Sun
God, or blazing chariots, etc.) if it suited me. And I wouldn't *have
to* be confused about which type of understanding I was using, though I
certainly could be.
Are there regularities in nature? If so, then why is it surprising that
mathematics is useful for describing them?
It would appear that if there is a physical universe distinct from our
minds, then there are many regularities and that this thing we call
mathematics (which we developed, evolved, or discovered) is
specifically useful for describing it.
If there is no such thing, and the physical universe is a projection or
hallucination of our mind, then it is even *less* surprising that our
minds have a language specifically attuned to describing it (i.e.
Mathematics).
The limits to the former are interesting (hidden variables, dark
matter/energy, unified this-n-that theories) and even moreso in the
latter (e.g. godel's incompleteness theorem) perhaps.
On the other hand, one might claim that even asking that
question is imposing our (perhaps foolish) mental model of what we mean
by regularities on nature. But taking that stance suggests that we
can't get out of our minds at all and there is no point in having this
discussion.
I concede that this discussion is only interesting to the extent that
we accept a separate physical universe as a working model. We don't
have to believe in it in any "absolute" sense, but if it is not our
working model, the discussion is generally moot (or masturbatory?).
So which side are you on
All of them. It depends.
it useful to share with each other what goes on in our
(separate) minds?
If such things (separate minds) exist, then yes, it is useful (or at
least highly compelling, else why this list, why this discussion?).
Is it possible that what goes on in our minds can be
mapped onto what goes on in nature?
Back to the fundamental question. If the Universe IS Mathematics, then
somehow we are saying the inverse... "what goes on in nature" is mapped
implicitly onto our minds (or somesuch). If the Mathematics is
*merely* a good language for describing what we observe in nature, then
we are doing precisely what you say "mapping what goes on in our minds
- Mathematics - onto what we observe in nature".
I think the above is the kernel of the question/conversation here...
and it does not preclude the question of whether we "invent" or
"discover" Mathematics. Though I've come to prefer "evolve" where the
fitness function is (almost) precisely "how well does it
predict/describe/explain Nature?"
I don't suppose many of us would ask "Isn't it amazing how well a
beaver is adapted to living in a stream in forested woodlands?"
Intelligent Designers have a simple answer to this, and Evolutionists
have a completely different but in it's own way even more parsimonious
and compelling answer. But neither (I don't think) would want to
suggest that "Woodland Streams *are* Beaverness", though I think there
is something like an animist understanding that would say that, and to
the extent that woodland streams *are* co-evolved with Beavers, such
might hold yet-more truth than the first two ("God made it so!"
"Darwin already explained all that!").
So, maybe a different kind of answer would be "Humans and their
Mathematical/Logical understanding of the Physical World have
co-evolved".
Or is there no point in attempting to exchange thoughts
since they are all just internal foolishness? Evolution suggests that
it is not all just internal foolishness. If it were we wouldn't have
evolved to have these thoughts. One could argue that that thought
itself is just as much internal foolishness as any other. But then why
bother to write it down and send it to this list?
This sounds like internal foolishness and I can't imagine why anyone
would bother to write it down and send it to the list. <grin>
Seriously. I clearly believe it is important to make the distinction
between a (non)provable, absolute truth (The Universe IS Mathematics)
and a practical, working model that Mathematics is very useful for
describing the Physical Universe. Science is about measurement, about
hypothesis generation and testing, and about repeatability. It is
grounded in the idea of a separate, independent-of-mind physical
Universe. I don't think this understanding, however, precludes the
possibility that what *appears* to our minds as an independent,
separately realized, physical Universe, is "merely" a projection of the
mind (whatever that is).
I've probably only managed to continue to muddy the water here.
Probably from holding too many disparate types of understanding
(materialist/existentialist/animist/deist) in my head at one time. Me
and the Red Queen. Perhaps if I only run faster and think more
impossible things before breakfast!
- Steve
-- Russ
On Tue, Apr 28, 2009 at 11:16 AM, Steve
Smith
<[hidden email]> wrote:
Very well said, methinks.
An approach needn't even lose it's utility to poke fun at it, it merely
has to lose "Universal Utility". I believe many folk remedies,
crafts, knowledge fall into that category. They become "vestigal"
knowledge for entire generations until circumstances drift far enough
(or abruptly enough) that they become the only or best (known) answer
to a given problem (again).
Come the revolution, we'll all be chewing willow bark and slippery elm
to relieve what ails us, and laughing at our forefathers who thought
all medicine had to be manufactured and shipped in a bottle. In the
meantime, such remedies seem somewhere between "quaint" and "absurd".
glen e. p. ropella wroteth circa early c21:
Thus spake Steve Smith circa 04/26/2009 06:06 PM:
Nicholas Thompson wrote:
Why should nature give a fig for the tricks we play with our words?
The Anthropic Principle might have a play in this.
I think this is the fundamental reason for the unreasonableness. Math,
like any other language, helps us be goal-oriented. And anything that
helps us be goal-oriented will _seem_ true to us, regardless of whether
it is true or not.
This is the situation for just about any method: burning witches,
hunting Communists, making marijuana illegal, worshiping mythical
beings, meditating surrounded by crystals and incense, voodoo dolls,
murdering people in foreign lands, torturing enemy combatants, etc. If
it focuses our attention and allows us to maintain focus on some
objective, then, as a tool, it _is_ useful and will _seem_ true.
When it ceases to be useful, we will be surprised, sit back, and wonder
why we were so enamored with it before... and many of us will even poke
fun of and deride those people who still find it useful.
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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at
http://www.friam.org