Hi Doug, It is not just a side note ... an interesting one, indeed, and raises couple of curious questions: 1. Which applications need negative time usage in Maxwell equations and what simulations/analysis methods are used? 2. What is the status of current research into finding magnetic monopoles and which groups/individuals are doing it? I don't much worry about somebody rewriting Maxwell equations and embracing infamy (why ?) ... that will be a while, if at all, I guess. Thanks, Sainath -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Doug McKean Sent: Monday, December 03, 2001 10:42 AM To: Signal Integrity Group Subject: [SI-LIST] Re: Square wave harmonics Just a side note ... There's several "problems" with modelling by way of Fourier or using Maxwell's equations. But in our reality, for our purposes, they work just fine. One, in Fourier Analysis, the use of negative frequency to mathematically balance out a bilateral frequency assumption for an integral has some conceptual problems. Another, in Maxwell, the equations are just as happy to use negative time in the time variable as positive time which makes for some obvious causality problems. The two mentioned above resulted from a prevailing scientific analysis/philosphy which at the time presumed the universe to be totally deterministic. I.e., all one needed to know was just the state of the universe at the present moment and then one could predict anything of it in the future or analyze anything in the past. Or so they thought. And again, with Maxwell, a couple of the equations require the assumption of magnetic dipoles as a basis. Current research into finding a magnetic monopole will require ALL of Maxwell to be rewritten. Thus the reason why there's real concern in their existance. The person finding magnetic monopoles and subsequently rewriting Maxwell's equations will put that person down in infamy. Quantum mechanics, chaos theory and the various offshoots from them have since challenged that deterministic model. And it will be interesting to see how that all works out. - Doug McKean ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu