Subject: Re: Pulsor Space-Time Synopsis - d:\pulsor\pulsor02.htm Date: Tue, 12 May 1998 20:07:59 -0500 From: vead@uconect.net To: vead@uconect.net This is the dejanews "emailable" version. ------------------------------------------------------------------------------ This message was forwarded to you from Deja News by vead@uconect.net. Deja News, the discussion network, offers free web-based access to more than 50,000 high-quality discussion forums. Come and visit us on the web at http://www.dejanews.com/=zzz_maf/ ------------------------------------------------------------------------------ (beginning of original message) Subject: Re: Pulsor Space-Time Synopsis From: Vead@q.continuum.net (D. Manchester) Date: 1996/02/19 Newsgroups: sci.fractals In article , rosully@aww.com says... > >> Hi. I notice that (like me) many in this newsgroup are involved in >> fractal computations. Forgive me if this posting is misdirected, but >> on the chance this is a place for a weird perspective on the >> Mandelbrot set, I have advanced some ideas about it in the last part. >> Please contribute any thoughts regarding the strange attractor >> discussion. Thanks, Dave M. > >Dave, > > I can only comment of some of your meta-mathematical points. :-) > >> 4. A Reason for Chaos >> >> About 400 years ago Leonard Euler interrelated our five most >> important mathematical constants in his famous equation >> >> (i*pi) >> e = -1. > > FTR, to display the five constants that should be > > (i*pi) > e + 1 = 0. > > >> Normally we take this as just a convenient way to interpret our >> number system. >> >> But what if there is more to it than that? Why is this the way it >> is? I think that Euler's equation says something quite profound about >> number theory, and the limits of mathematical epistemology. >> >> I contend that these 5 constants (e, pi, 1, 0, -1, and i) behave as >> strange attractors in defining any possible mathematical system. > > Of course, there are many mathematical systems that do not require >any of these constants: permutation groups, non-cartesian geometry, >logic, topology, etc. On the other hand, these constants do play a >central role in analytic mathematics: calculus, complex analysis, >Hilbert Space, etc. The origin of some of these constants does favor a >view of epistemological necessity but not all. Let's review the reason >for existence of these constants: > > 0 -- the additive identity (fixed point for addition) > 1 -- the multiplicative identity (fixed point for multiplication) > e -- fixed point of the differential operator > pi -- the Euclidean ratio of circumference to diameter > i -- orthogonal vector to (1,0) > > The first three seem to have a deeper root in mathematical >epistemology than the other two. Although you can name them anything, >0, 1, and e originate because of their role as fixed points. Pi plays a >similar role for the most simple figure in plane geometry but it value >can differ depending of the geometry selected. For example, the value >of Pi in taxi-cab geometry is 4. Finally, i seems quite pedestrian. >There are any number of vectors orthogonal to (0,1); i is but one. > >Rick > __ __ __ __ __ __ >---------------------__/\_\/\_\/\_\/\_\/\_\/\_\__----------------------- >Altofirma WebWords /\_\/_/\/_/\/_/\/_/\/_/\/_/\_\ Richard P. O'Sullivan >http://www.aww.com/ \/_/\_\/\_\/\_\/\_\/\_\/\_\/_/ rosully@aww.com >--------------------- \/_/\/_/\/_/\/_/\/_/\/_/ ----------------------- > >Cookie De Jour >-------------- >'Any sufficiently advanced bureaucracy is indistinguishable from >molasses.' - Unknown Richard, here's an update on my thinking since Your reply, (which, btw, I very much enjoyed : ) )... ...And the Beat Goes On... By Vead@q.continuum.net (C) 1996 David C. Manchester Dear Chris, Lauren, and Glenn, This is just a quick note to bring You up to date with the current development of my thinking with regard to the Pulsor paradigm. It is starting to seem to me that... Plank's Constant is the result of a Fractally - Broken Symmetry in which Euler's constants (i, 0, 1, pi, and e) together and separately behave as Strange attractors, and manifesting themselves collectively and deter- ministically across temporal and spatial discontinuity through the Mandlebro set, on the one hand, through Shannon's Entropy on another, wrt Consciousness and Observation in the outmost Pulsor area, and wrt IMAGE of EVENT within the inmost portion, where all time, space channels of extension and all mass/energy quantum events contents flow inward toward, in the manner of a kind of temporal and representational "black hole". This represents indeterminacy in our current measurement systems as well as the granularity of our current representational systems. Evaluate the Euler identity and constants from the viewpoints of Lyapunov exponents and ask, where is Plank's constant in this? Plank's constant denotes a fractally determined threshold on continuity itself, and is of a granular, discrete value in the outmost shell of the Pulsor. Plank's constant bears a kind of Lyapunov relationship to the fractally broken symmetry evidenced in Euler's identity, and in the Mandlebrot Set. In other words, Why should GOD play dice, when a (self-similar nonperiodic sensitively-dependent on initial conditions) Fractal is Sure Thing? And it provides an error-correcting ON-MESSAGE function whose evidence we see in the Mandlebrot set. The Mandlebrot Set is a kind of snapshot of this dynamic. So is Euler's equation, only for the epistemologically determinate aspects of the Number system,i.e. from opposite ends of their relationship to Plank's constant. >From that same starting point of indeterminacy at the center of the pulsor arise not just Plank & Mandlebrot, but Shannon and Lyapunov as well. The work of each converge in Pulsor modeling. This Strange symmetry is germane to understanding how to imagine a model that includes both current QED/QCD, and the very collapse of representability and the the ability to expostulate about coodinate systems themselves "on the inside" region of a Pulsor. How can You intelligently talk about it in terms of no xyzt orthogonal plane? The center of the Pulsor is the discontiuity at 0, and at the granular boundaries of all representable systems; and for that matter, it is probably provably the same as any discontinuity in any imaginable phase-space. --dcm Er...excuse me. that should have been "Why should GOD play dice, when (Plank-Lyapunov Broken Symmetry) offers a sure thing?" A "sure thing" in terms of consistency of IMAGE and MESSAGE in the inner and outer portions of a pulsor. Perhaps it should be called a chronon, since it is the field of both Time and Gravity whose threshold is the collapse of a probability function, Shroedinger's for transactions involving consciousness. ...............Pulsors and chronons and squares. Oh, My! *) -------Dave :) ========================================================================= "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."- Amendment I to the Constitution of the United States. D.Manchester Vead@q.continuum.net ========================================================================== (end of original message) ------------------------------------------------------------------------------ You can view the original message at http://www.dejanews.com/=zzz_maf/getdoc.xp?AN=140066502 or search http://www.dejanews.com/=zzz_maf/ for related messages. We hope to see you soon at Deja News, the discussion network.