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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal>So, Frank. Think of the coast of England/Scotland. It is infinitely indented. Anytime we draw a map of it, we enclose every point on that coast line and an area that is not within that coastline. So, wrap England in plastic film and pull the film as tight as we can. We have a shroud. Is there a mathematical name for that? OK, now, let the plastic be infinitely flexible, and let us suck all the air out of the space between the shroud and the coastline. What do we have now? Is there a mathematical name for that? <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Let me give them both names. Let me call one a shroud and the other a super shrink wrap. I can imagine some mathematician, just for the hell of it, spending a life time working out what the area is between the shroud and the super shrink wrap. And then, having worked all that out, claiming, as do you, that none of these entities, shroud, ssw, or area between, exist in nature. They are mathematical objects, only. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Which is why Hywel used to say what he used to say about mathematics. Am I write about any of this? <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Nick <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Nicholas Thompson<o:p></o:p></p><p class=MsoNormal>Emeritus Professor of Ethology and Psychology<o:p></o:p></p><p class=MsoNormal>Clark University<o:p></o:p></p><p class=MsoNormal><a href="mailto:ThompNickSon2@gmail.com">ThompNickSon2@gmail.com</a><o:p></o:p></p><p class=MsoNormal><a href="https://wordpress.clarku.edu/nthompson/">https://wordpress.clarku.edu/nthompson/</a><o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Friam <friam-bounces@redfish.com> <b>On Behalf Of </b>Frank Wimberly<br><b>Sent:</b> Friday, June 5, 2020 8:07 PM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br><b>Subject:</b> [FRIAM] Manifold Clarification<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>I said that no physical object is a manifold. This may be a better answer to Nick's question. The envelope of a cloud, if it could be defined, might be a manifold depending on cusps etc. Those might be handled by combining manifolds of different dimensions. This would not be a realizable project in my opinion.<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt'>Frank<o:p></o:p></p><div><p class=MsoNormal>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM<o:p></o:p></p></div></div></div></div></body></html>