[SI-LIST] Re: Square wave harmonics

  • From: "Doug McKean" <dmckean@xxxxxxxxxxxxxxx>
  • To: "Signal Integrity Group" <si-list@xxxxxxxxxxxxx>
  • Date: Mon, 3 Dec 2001 10:42:28 -0800

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 

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