From: Ian Glendinning (ian@psybertron.org)
Date: Wed Jan 05 2005 - 13:53:43 GMT
MoQ'ers may be interested in this link from Ray Girvan
http://www.raygirvan.co.uk/apoth/2005_01_01_arc.html#110484813056572506
Ian
----- Original Message -----
From: "Ian Glendinning" <ian@psybertron.org>
To: <moq_discuss@moq.org>
Sent: Wednesday, January 05, 2005 11:49 AM
Subject: Re: MD "Is there anything out there?"
> 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,
> 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, 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.
>
> 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.
>
> Ian
>
> ----- Original Message -----
> From: "Mark Steven Heyman" <markheyman@infoproconsulting.com>
> To: <moq_discuss@moq.org>
> Sent: Wednesday, January 05, 2005 2:03 AM
> Subject: Re: MD "Is there anything out there?"
>
>
> > 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
> > >
> >
> >
> >
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