<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">I think you are referring to structure of multiplication of complex numbers. <div class="">Any complex number </div><div class="">z = R exp(i Theta) </div><div class="">(R a real number non-negative) and multiplying two complex numbers corresponds to </div><div class="">adding the angles and multiplying the radii.</div><div class=""><br class=""></div><div class="">Note that we have Euler’s formula</div><div class=""><br class=""></div><div class=""> exp(i Theta) = cos(Theta) + i sin(Theta).</div><div class=""><br class=""></div><div class="">So exp(i Theta)exp(i Phi) = [cos(Theta) + i sin(Theta)][cos(Phi) + i sin(Phi)]</div><div class=""><br class=""></div><div class=""> = [cos(Theta)cos(Phi) - sin(Theta)sin(Phi)] +i[sin(Theta)cos(Phi) + cos(Theta)(sin(Phi)]</div><div class=""> </div><div class=""> = cos(Theta + Phi) + i sin(Theta + Phi).</div><div class=""><div><br class=""></div><div><div class="">The fact that Lambek can write down a set of vectors in 4-space whose sums correspond to the particle interactions is not trivial.</div><div class=""><br class=""></div><div class="">The quaternions encode rotations of vectors in 3 and 4 space. There may be a rotational interpretation or extension of Lambek that uses these </div><div class="">quaternion properties. I think Lambek expected something of this sort, but did not find it. </div><div class="">Otherwise, he would have written about it. </div><div class="">One can look for it.</div><div class=""><br class=""></div><div class=""><br class=""></div><blockquote type="cite" class=""><div class="">On Jan 30, 2025, at 11:49 AM, Walter Johnston <<a href="mailto:williampatonmalcolm@gmail.com" class="">williampatonmalcolm@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="auto" class="">Dear Luke,<div dir="auto" class="">That sounds like a BRILLIANT observation to perhaps point to a vehicle for progress.</div><div dir="auto" class="">Bless </div></div><br class=""><div class="gmail_quote"><div dir="ltr" class="">On Thu, 30 Jan 2025, 17:27 Luke Kenneth Casson Leighton <<a href="mailto:lkcl@lkcl.net" class="">lkcl@lkcl.net</a> wrote:<br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br class=""><br class="">On Sunday, January 26, 2025, Luke Kenneth Casson Leighton <<a href="mailto:lkcl@lkcl.net" target="_blank" rel="noreferrer" class="">lkcl@lkcl.net</a>> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br class=""><br class="">On Sunday, January 26, 2025, Louis Kauffman <<a href="mailto:loukau@gmail.com" target="_blank" rel="noreferrer" class="">loukau@gmail.com</a>> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word;line-break:after-white-space" class="">Dear Folks,</div></blockquote><div class=""><br class=""></div><div class="">that said: as you discovered, Lou: Braiding itself I believe has merit in that once placed into a loop (as Sundance does - creating in his theory a Mobius strip) it can represent both phase and position of contributing components, and as you progress down the strip, the interaction between components is clearly and naturaly shown in 2D (on paper) which makes understanding easy.</div></blockquote><div class=""><br class=""></div><div class="">hilarious.</div><div class=""><br class=""></div><div class="">I just did some investigation into addition of unit vectors. it turns out that if the vectors being added are equal length, their addition is *directly equivalent* to the addition of their angles relative to a given common fixed axis [trigonometric quadrant shenanigans notwithstanding]</div><div class=""><br class=""></div><div class="">it's going to be something to do with trigonometric identities</div><div class=""><br class=""></div><div class=""><table style="color:rgb(68,68,68);font-family:sans-serif;font-size:16px" class=""><tbody class=""><tr class=""><td align="right" style="padding-right:1em" class="">Sine</td><td class=""><span style="color:rgb(136,136,136)" class=""></span><span id="m_5920863208546019020MathJax-Element-43-Frame" role="textbox" aria-readonly="true" style="display:inline;line-height:normal;word-spacing:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px" class=""><span id="m_5920863208546019020MathJax-Span-864" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:18.641em" class=""><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:15.266em;height:0px;font-size:19.52px" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-865" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-869" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">sin</span><span id="m_5920863208546019020MathJax-Span-870" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-871" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">(</span></span><span id="m_5920863208546019020MathJax-Span-872" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-873" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">±</span><span id="m_5920863208546019020MathJax-Span-874" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">α</span><span id="m_5920863208546019020MathJax-Span-875" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">)</span></span></span><span id="m_5920863208546019020MathJax-Span-876" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">=</span><span id="m_5920863208546019020MathJax-Span-877" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">sin</span><span id="m_5920863208546019020MathJax-Span-878" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-879" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-880" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">cos</span><span id="m_5920863208546019020MathJax-Span-881" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-882" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">α</span><span id="m_5920863208546019020MathJax-Span-883" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">±</span><span id="m_5920863208546019020MathJax-Span-884" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">cos</span><span id="m_5920863208546019020MathJax-Span-885" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-886" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-887" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">sin</span><span id="m_5920863208546019020MathJax-Span-888" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-889" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">α</span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.766em" class=""></span></span></span><span style="display:inline-block;border-width:0px 0px 0px 0em;border-top-style:initial;border-right-style:initial;border-bottom-style:initial;border-left-style:solid;border-color:initial;padding:0px;margin:0px;vertical-align:-0.368em;line-height:normal;overflow:hidden;width:0px;height:1.345em" class=""></span></span></span></td></tr><tr class=""><td align="right" style="padding-right:1em" class="">Cosine</td><td class=""><span style="color:rgb(136,136,136)" class=""></span><span id="m_5920863208546019020MathJax-Element-44-Frame" role="textbox" aria-readonly="true" style="display:inline;line-height:normal;word-spacing:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px" class=""><span id="m_5920863208546019020MathJax-Span-890" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:18.766em" class=""><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:15.369em;height:0px;font-size:19.52px" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-891" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-895" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">cos</span><span id="m_5920863208546019020MathJax-Span-896" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-897" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">(</span></span><span id="m_5920863208546019020MathJax-Span-898" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-899" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">±</span><span id="m_5920863208546019020MathJax-Span-900" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">α</span><span id="m_5920863208546019020MathJax-Span-901" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">)</span></span></span><span id="m_5920863208546019020MathJax-Span-902" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">=</span><span id="m_5920863208546019020MathJax-Span-903" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">cos</span><span id="m_5920863208546019020MathJax-Span-904" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-905" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-906" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">cos</span><span id="m_5920863208546019020MathJax-Span-907" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-908" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">α</span><span id="m_5920863208546019020MathJax-Span-909" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">∓</span><span id="m_5920863208546019020MathJax-Span-910" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">sin</span><span id="m_5920863208546019020MathJax-Span-911" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-912" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-913" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">sin </span></span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.766em" class=""></span><span style="font-size:16px" class="">α</span></span></span><span style="display:inline-block;border-width:0px 0px 0px 0em;border-top-style:initial;border-right-style:initial;border-bottom-style:initial;border-left-style:solid;border-color:initial;padding:0px;margin:0px;vertical-align:-0.368em;line-height:normal;overflow:hidden;width:0px;height:1.345em" class=""></span></span></span></td></tr></tbody></table><table style="color:rgb(68,68,68);font-family:sans-serif;font-size:16px" class=""><tbody class=""><tr class=""><td align="right" style="padding-right:1em" class=""></td><td class=""><span id="m_5920863208546019020MathJax-Element-16-Frame" role="textbox" aria-readonly="true" style="display:inline;line-height:normal;word-spacing:normal;white-space:nowrap;float:none;direction:ltr;border:0px;padding:0px;margin:0px" class=""><span id="m_5920863208546019020MathJax-Span-223" style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:9.703em" class=""><span 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style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-224" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-227" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:1.766em;height:0px" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-228" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">cos</span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.766em" class=""></span></span><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-229" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-size:13.8006px;font-family:MathJax_Main" class="">2</span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.254em" class=""></span></span></span></span><span id="m_5920863208546019020MathJax-Span-230" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-231" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-232" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">+</span><span id="m_5920863208546019020MathJax-Span-233" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:1.663em;height:0px" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-234" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">sin</span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.766em" class=""></span></span><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-235" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-size:13.8006px;font-family:MathJax_Main" class="">2</span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.254em" class=""></span></span></span></span><span id="m_5920863208546019020MathJax-Span-236" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-237" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-238" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">=</span><span id="m_5920863208546019020MathJax-Span-239" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">1</span><span id="m_5920863208546019020MathJax-Span-240" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-size:16.0064px" class=""> </span></span></span></span></span></span></span></td></tr></tbody></table><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-224" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-232" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">+</span><span id="m_5920863208546019020MathJax-Span-233" style="display:inline;border:0px;padding:0px 0px 0px 0.222em;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:1.663em;height:0px" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-234" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">sin</span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.766em" class=""></span></span><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span id="m_5920863208546019020MathJax-Span-235" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-size:13.8006px;font-family:MathJax_Main" class="">2</span><span style="display:inline-block;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;width:0px;height:2.254em" class=""></span></span></span></span><span id="m_5920863208546019020MathJax-Span-236" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""></span><span id="m_5920863208546019020MathJax-Span-237" style="display:inline;border:0px;padding:0px 0px 0px 0.167em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Math;font-style:italic" class="">θ</span><span id="m_5920863208546019020MathJax-Span-238" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">=</span><span id="m_5920863208546019020MathJax-Span-239" style="display:inline;border:0px;padding:0px 0px 0px 0.278em;margin:0px;vertical-align:0px;line-height:normal;font-family:MathJax_Main" class="">1</span><span id="m_5920863208546019020MathJax-Span-240" style="display:inline;border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal" class=""><span style="border:0px;padding:0px;margin:0px;vertical-align:0px;line-height:normal;font-size:16.0064px" class=""> </span></span></span></span></span></span></span></td></tr></tbody></table></div><div class="">and pythogorean identity sin2(a) + cos2(a)=1 and x^2 + y^2 = 1</div><div class=""><br class=""></div><div class="">combining when angles are restricted to clock positions, to give a near-embarrasing direct equivalence between unit vector addition and unit *angle* addition.</div><div class=""><br class=""></div><div class="">this mathematic elegance is responsible for dividing the Helon and Preon Model Community from the Standard Model Community for over 50 years!</div><div class=""><br class=""></div><div class="">reason: where Preons thought they were summing and subtracting particles of 1/3 charge, actually by a massive coincidence they were summing and subtracting *angles*!</div><div class=""><br class=""></div><div class="">aka *phases*!</div><div class=""><br class=""></div><div class="">face-palm moment :)</div><div class=""><br class=""></div><div class="">l.</div><div class=""><br class=""></div><div class="">p.s. this is why Lambek's Model looks like it does Vector arithmetic...</div><div class=""><br class=""></div><br class=""><br class="">-- <br class=""><div dir="ltr" class="">---<br class="">geometry: without it life is pointless<div class="">the fibonacci series: easy as 1 1 2 3</div></div><br class="">
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