From: Mark Steven Heyman (markheyman@infoproconsulting.com)
Date: Wed Jan 05 2005 - 17:00:36 GMT
Hi Ian,
I think you're responding to me, not Paul... Anyway, just for
clarification for any math buffs out there...
On 5 Jan 2005 at 11:49, Ian Glendinning wrote:
Hmmm Paul,
We may have to agree to differ, (but I'm no mathematician)
I don't see the Euler identity stated or proven on that page, merely
lots of example integrals that use variants of it,
msh says:
Well, Euler is proved elsewhere. The Schroedinger page shows that
Euler is necessary to even begin to describe quantum behavior, thus
my original point that Quantum Mechanics relies on Euler. BTW, this
idea is hardly MINE in any sense. I believe it's pretty well accepted
that Schroedinger opened the door to QM, and his equations don't work
without Euler.
ian:
Whether the Euler identity underlies Schroedinger and Quantum Physics
in any direct significant way, or merely indirectly through its
integrals being a useful was to represent wave equations which do
underly them is a moot point...
msh says:
Maybe moot, but mysterious and interesting, is my point.
ian:
but hey ... that wasn't really the point was it (whatever the actual
maths) the point as you say was ...
"Isn't it wonderful / amazing / awesome (spooky even) that such
maths underlies so much reality" Which we seem to agree on.
msh says:
I think this was Paul, but yep, I agree.
ian:
What we don't seem to agree on are the "significance" of the
"underlyingness" itself, and "explanations of why".
For me the maths works, is useful, consistent, repeatable,
predictable, etc is enough reason to believe, enough explanation.
Others seem to have some "cosmic purpose" in mind for an answer.
msh says:
I don't see and never have proposed any "cosmic purpose." Quite the
opposite, in fact: I think we make our own purposes. As for Euler,
I'm just a guy from Jersey kicking around some equations; I'll leave
the deep theoretical thinking to the deep theoretical thinkers.
Best,
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." > Hi Ian, and all, > > No. The identity, as proved by Euler, is e ^ (i * pi) = -1, > although his famous and quite remarkable formula is often written as > e ^ (i * pi) + 1 = 0. > > What I said was that various forms of this equation show up in a > wide variety of mathematical formulae describing all sorts of > motion, including waves, pendulums, and planets, sometimes as part > of an integral. The connection to Quantum Mechanics is through > Schroedinger's wave equation, which you can see discussed here: > > http://scienceworld.wolfram.com/physics/SchroedingerEquation.html > > If you look at the 35 or so lines on this page, you'll find > formulations of Euler all over the place. > > What's spooky to me and others is that an equation arrived at > through pure number theory should prove so useful in solving so many > previously intractable equations with direct applications in the > real world. > > But, as I've already said, I'm not suggesting this means God loves > math or something. I'm not sure what it means, if anything. This > apparent symmetry between math and physical reality may just be a > result of the fact that we our imaginative selves are an inseparable > part of the phenomena we are trying to describe, an idea that I > think will appeal to Paul and DMB. I just don't know... but I find > it interesting. > > I'm waiting to hear back from my math genius friend; he may very > well agree with you and tell me I'm all wet. > > Best, > > 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." > > > On 4 Jan 2005 at 20:29, Ian Glendinning wrote: > > Err, Mark > (and Platt who seemed to like your explanation ...) > (and Rich who choked on his tea ...) :-) > > I'm with Rich, you can't really believe that simplistic explanation > of numerical relationships underlying quantum physics, end of story, > can you. > > Factually - I believe the identity (equation) you are referring to > is more like ... The intergral of e to the i pi, from zero to two > pi, equals minus one > > (Not just e to the i pi equals minus one) > (e to the i pi itself cannot itself equal anything meaningful can it > ? The integral is a geometric construct - a metaphor - in the > complex plane, if I recall correctly) (Which interestingly I blogged > about the beauty of myself - some years ago - it first hit me > between the eyes around 30 years ago - spooky coincidence.) > > Even when (if) we can agree we've expressed the identity right - I'm > surprised to find it behind quantum mechanics - wave motion maybe, > but .. And finally, whilst I support the concept that physics > underlies everything (by axiomatic definition) quantum physics is > not (necessarily) the final word on the matter. > > Most interesting for me is that Platt sees some explanation of "why > imaginary numbers underly empirical reality" Huh ? Predictably I > still see no "reason why" even if your explanation were true, just > an explanation of a relationship which "happens to be" (if it > happened to be true) > > Ian > > ----- Original Message ----- > From: "Mark Steven Heyman" <markheyman@infoproconsulting.com> > To: <moq_discuss@moq.org> > Sent: Tuesday, January 04, 2005 2:27 AM > Subject: RE: MD "Is there anything out there?" > > > > 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 > > > > > > 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 > 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 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
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