From: Mark Steven Heyman (markheyman@infoproconsulting.com)
Date: Tue Jan 04 2005 - 02:27:56 GMT
Hi Platt, Paul, all
Platt said:
My question is, how do you explain that mathematics, a creation of
human intellect, is able to so accurately model those preferences? Is
it simply a mystery, or is there rationale for the relationship
between inorganic preferences and mathematical formulas? To me it
appears to be a relationship of cosmic and human intelligence that I
know you reject. So I'm asking for your alternative explanation.
Paul:
The mathematical formulae that have been selected for explanation of
inorganic phenomena are selected and developed for that very purpose
aren't they? Don't physicists keep trying until they can predict the
results of an experiment with more and more precision i.e., with
higher quality? As I understand it, there are always many competing
formulae and theories for any given set of data. The best ones are
kept. Is it really a mystery?
msh says:
Actually, the relationship between math and the "underlying reality"
of the physical world is considerably more startling than this. I'll
try to make this as painless as possible:
All that's necessary to start counting is the ability to distinguish
one thing from another. From counting comes our notion of number,
and all the integers, which we add, subtract, multiply, divide. From
this simple arithmetic comes the concepts of zero and infinity; and
beyond zero, the negative numbers. And there are numbers between the
integers, fractions like 1/2, 2/3, the so-called rational numbers
because they can be expressed as the ratio of two integers. Between
the rational numbers lie an infinity of transcendental numbers that
cannot be expressed as a ratio of integers, for example "pi" (the
ratio of the circumference of any circle to its diameter), and "e"
the base of natural logs.
Also, every positive number has a square root, the number that when
multiplied by itself gives you your number. But when mathematicians
discovered that no number multiplied by itself gives a negative, they
defined the square root of minus one to be a totally new "imaginary"
number, and gave it the symbol "i". All of this is derived without
measuring anything in the real world, yet it was discovered that
imaginary numbers proved invaluable in helping mathematicians solve
equations that were perfectly descriptive of empirical reality.
But here's where things start getting really spooky. Out of this non
empirical realm of numbers an astounding relationship appears. The
irrational number "pi", the irrational number "e", and the imaginary
number "i", come together in one of the simplest equations ever: e
^ i (pi) = -1, that is "e to the power of i times pi = -1".
That these three numbers should be related in this way is startling
enough, but there's more. The whole of quantum physics depends upon
this simple equation. It is the basic equation of any wave motion, a
wave on water, the sound waves coming from an air raid siren, or
electromagnetic radiation. The motion of any wave can be expressed
as a concatenation of such simple equations. AND, this equation
expresses the orbits of the planets, the swing of a pendulum and the
oscillation of an atom. In fact, the way I understand it, every
motion in the cosmos can be described by an equation of this form.
Remember now, this equation was derived without empirical measurement
of any kind, so it was clearly not a matter of "tweaking" the
equation till they got it right.
Anyway, here endeth the lecture. Sorry. But this is pretty amazing
stuff, really, and it's not so hard to see why some mathematicians
might feel that God is to be found in the beauty and perfection of
mathematics. IMO, he very fact that math is NOT phenomenal in nature
is why it's a serious contender for getting a glimpse at the
"underlying reality" of the cosmos, if there is such a thing. And,
though it may be true that "there is nothing out there" you can
understand why mathematicians and scientists have a hard time with
the "reality is an illusion" syndrome.
Anyway, if anyone wants more info about all of this, or if you just
think I'm crazy and wanna check up on me, I can provide some links.
As usual, TIA for any thoughts.
Mark Steven Heyman (msh)
-- InfoPro Consulting - The Professional Information Processors Custom Software Solutions for Windows, PDAs, and the Web Since 1983 Web Site: http://www.infoproconsulting.com "The shadows that a swinging lamp will throw, We come from nowhere and to nothing go." MOQ.ORG - http://www.moq.org Mail Archives: Aug '98 - Oct '02 - http://alt.venus.co.uk/hypermail/moq_discuss/ Nov '02 Onward - http://www.venus.co.uk/hypermail/moq_discuss/summary.html MD Queries - horse@darkstar.uk.net To unsubscribe from moq_discuss follow the instructions at: http://www.moq.org/md/subscribe.html
This archive was generated by hypermail 2.1.5 : Tue Jan 04 2005 - 03:36:17 GMT