Posted by
Steve Smith on
Apr 27, 2009; 1:00am
URL: http://friam.383.s1.nabble.com/The-Unreasonable-Effectiveness-of-Mathematics-in-the-Natural-Sciences-tp2714601p2721252.html
Owen Densmore wrote:
On Apr 26, 2009, at 10:16 AM, Steve Smith wrote:
Well said/observed David, I too am a
Lakoff/Johnson/Nunez fan in this matter.
While I am quite enamored of mathematics and it's fortuitous
application to all sorts of phenomenology, Physics being somehow the
most "pure" in an ideological sense, I've always been suspicious of the
conclusion that "the Universe *is* Mathematics".
OK: Show how it is not, then.
Tricky, tricky!
... that always turns out well, trying to prove a negative! ;)
I'll raise your conceptual Jui Jitsu and raise you a bit of
conceptual Aikido.
< extra-Large work-gloves-encrusted-with-manure coming off now! >
My claim is *not* that the Universe is *not* Mathematics, but rather
that I am suspicious of any such claim. I *do* think there is a
strong relation, but I don't think it is an *identity*.
This discussion also begs the age-old
question of whether we are "inventing" or "discovering" mathematics.
No it doesn't. We are discovering it.
I contend that Mathematics is a (special) subset of Language and I do
not know what it would mean (philosophically) to claim that we are
*discovering* Language. That said, I think the closest one could
come to claiming that we *discover* Mathematics would be one of two (or
both) arguments: 1) Given that we have have developed a subset of
Mathematics (and therefore Language) known as Mathematical Logic, it
is to say that we *discover* elaborations and extens based in it; 2)
We *invent* Mathematics (Mathematical Language) to describe the
phenomenological patterns which we *discover*.
I agree that the "Effectiveness of Mathematics" is fabulously
amazing... but I'd ascribe an anthropic explanation of this before I
would *insist* that this means that *the Universe IS Mathematics*.
Science has a long history of ignoring phenomenology that it doesn't
(yet) have the mathematics to describe. Think of the
pre-nonlinear-science era (roughly pre-1980) and the consequent
*explosion* that came with
the development (application and elaboration really) of nonlinear
mathematics. We suddenly *discovered* all kinds of things which we
had been observing for millenia, but for which we had no concise
language for thinking. Similarly with Newton/Leibniz Infinitesimal
Calculus.
And in the contrapositive: What of Mathematics which has no connection
to any known phenomonology? When it appears that we are *inventing*
or *discovering* patterns in the language of mathematics, are we
discovering patterns about the physical world? Does this mean that we
simply haven't looked long enough, or under
enough rugs? Can we depend on any new mathematics we might "invent"
actually to be a new understanding about the (physical) universe
itself? I'm sure there are plenty of positive examples of this, and
naturally any negative examples are just waiting for a positive one to
negate them.
It *does not* surprise me that the preponderance of the Mathematics we
have developed is *highly useful* for understanding or explaining the
elaborate collection of phenomenology we have recorded in human
history. Mathematics *is* the language we use to describe such
phenomenology (precisely and unambiguously).
That said, you may also remember that I am a big fan of the likes of
David Bohm and his
Holographic
Theories of the Universe and Ed Fredking and his
Digital
Information Mechanics, which have a vaguely similar odor to "The
Universe IS Mathematics".
On the other hand, I have to admit to arguing with myself (and
Lakoff/Johnson/Nunez) here to some degree... I think they would insist
that *all* Mathematics (and Thinking?) is Embodied and therefore must
ground out (somewhere) in some experience
We are slowly becoming wise.
I'd be hard pressed to claim Wisdom(human_race) is a monotonic
increasing function. And I have to question whether more understanding
of phenomenology is equal to wisdom. It is not clear to me that after
Hari Seldon develops Psychohistory, that we will be significantly more
wise about what it means to be human. We might be able to predict
human behaviour at various levels to varying degrees of granularity and
accuracy, but *as always*, is prediction equal to understanding?
We are uncovering the Structure of Everything.
If you are a strict materialist, then I agree that this is a
consequence of your argument... if you are not, then I think it is
likely that you will have to agree that one can make formal
mathematical statements that do not relate in any way to the physical
world? That there might be wisdom and beauty which cannot be described
mathematically?
Methinks Godel is on my side on this one.
We are peaking under the Rug.
Whilst sweeping more things under it? <grin>
God is one smart dude.
Expect some backlash from the Athiests and the Feminists (and
Polytheists and Animists, and ...)! <grin>
I just read Dave West's "rebuttal" and while I am more generous in
quantity to the value/utility/applicability of Mathematics to
Phenomenology and more generally, it's relation to Epistimology, I
agree with his intuitive assessment that there is plenty human
knowledge and experience left that Mathematics *doesn't* provide any
traction against.
Oddly, those with *more* Math than I (BS Mathematics/Physics + 30 years
of random graduate courses/studies) would simply claim that my
Mathematics is wanting, while those with *less* would join me in
noticing that those with *too much* Mathematics have a tendency to
ignore/dismiss/negate anything they cannot describe Mathematically (a
tautological argument at best). An Astrophysicist colleague calls the
latter type of Mathematicians (many of them good friends of his)
"MathHoles"... I won't tell you what *they* call *him*.
- Steve
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