<html><head></head><body><div style="font-family: Verdana;font-size: 12.0px;"><div>
<div>
<div name="quote" style="margin:10px 5px 5px 10px; padding: 10px 0 10px 10px; border-left:2px solid #C3D9E5; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;">
<div name="quoted-content">
<div style="background-color: white;">
<div style="direction: ltr;font-family: Tahoma;color: rgb(0,0,0);font-size: 10.0pt;">
<p class="MsoNormal">John Williamson wrote:</p>
<p class="MsoNormal"><span style="font-size: 10pt; line-height: 1.6em;">"Thank you for your thoughtful reply. I agree wholeheartedly that maths is doing more to obscure �C rather than illuminate �C the basic processes of nature. </span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span>A case in point is this obsession with the “fourier transform”. Why? This is mere maths .<span> </span>Maths appropriate for the simple harmonic oscillator �C but not much more. It is a red herring.<span> </span>Actually it not nearly as sophisticated as a red herring. Proof: listen to synthesizer music that involves only fourier components…"</span></p>
<p class="MsoNormal">******************************************************************************************************************************</p>
<p class="MsoNormal">Dear John:</p>
<p class="MsoNormal"><span style="font-size: 10pt; line-height: 1.6em;">FYI: The "obsession" with the mere mathy Fourier X-form is actually a bit of logical argumentation regarding what is and what is not ontological. The Fourier x-form pertains to continious sitations, including the harmonic oscillaotr in a certin sense. But, as you must know, the solutions to the wave equation with the HO potential are Hermite polynomials x exp(wt). That is, they have pattern of oscillations across the span of the HO range which as a whole 'breath' or oscillate in time as a unit, up an down (in and out, really), as it were, not back and forth.</span></p>
<p class="MsoNormal">Now, as an experimentalist, certanily you must have observed that ALL observed HO's in every lab oscillate back and forth! Thus, the so-called QM soltuions (actually the Fourier-Hilbert eigenvectors) do not correspond to any thing in the lab-world. Empirically, they cannot be identified with onta. They are a fiction. A useful one when used properly to compute the series or x-form of an expression for the motion of a HO which is realizable in fact.</p>
<p class="MsoNormal">Note: "photons" are sometimes identified with single HO Fourier components, which is underhanded argument that they, along with waves, do not exist. </p>
<p class="MsoNormal">As to synthesizers: insofar as the Fourier cannot be identified with onta, or in other words, with a signal actually generated by mortals by means of their mechanical-electrical contraptions, they alone are not what is in fact involved. What is hppening in a synthesizer (or any signal generator) is that a real signal for which the very low components dominate in an approximation, are excited so that they appear to be single Fourier components when not looking too close! </p>
<p class="MsoNormal"><span style="font-size: 10pt; line-height: 1.6em;">Apropos classical E&M, the problem is less etherial: pure plane waves cannot be generated from point-charge sources in 3-d space, as there are no infinite planes of charge. Acustically its the same deal: strick an key on a piano, a pure note is not the result. To get such requires stricking the string EXACTLY in the middle with in infinitesimally sharp hammer (without slicing the string)---ignoring the nonlinearitites of the string even. </span></p>
<p class="MsoNormal">And (more revealingly) you have ignored the oxymoronic fact that much of modern Physics dwells on E&M fields for which there is NO source! If the "lab" is arbitter of truth, then ...</p>
<p class="MsoNormal">Further, "maths" is fundamentally symbolic logic for the which the "rules" of self-consistency have been codified. It helps anayize relationships between a set of primative entites IF first these enetities are characterized hypotheically and their basic interrelationships are given. The issues being discussed in this exchange virtually always have to do with the specification and characterization of primative elements. If theorizing is done on the basis of vague characterization of the such primative elements, the results, both the math and the accompanying stroy (interpretation) quickly get so complex that inconsistencies become nearly impossible to detect. This is being done repeatedly with the notion of "field" when the term is used differently from is origional meaning (evident quickly when the source is not considered). A "field theory" without sources is techno-mythology, a new kind of religion. </p>
<p class="MsoNormal">ciao, Al</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
</div>
</div>
</div>
</div>
</div>
</div>
<style type="text/css"><!--p.MsoNormal, li.MsoNormal, div.MsoNormal {
margin: 0.0cm;
font-size: 12.0pt;
font-family: Cambria;
}
*.MsoChpDefault {
font-family: Cambria;
}
div.WordSection1 {
page: WordSection1;
}
BODY {
}
BODY {
}
BODY {
}
BODY {
}
BODY {
}
--></style></div></body></html>