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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>No. I never managed upside down. Wait a minute! Is upside down an exception to the rule? Oh, no, it isn\u2019t. It reverses front to back. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Barry, this is all coming from something I thought I heard EricS say about trying to get out of logic what only empirical observation will provide. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>N<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>Nick Thompson<o:p></o:p></p><p class=MsoNormal><a href="mailto:ThompNickSon2@gmail.com"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal><a href="https://wordpress.clarku.edu/nthompson/"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><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>Barry MacKichan<br><b>Sent:</b> Friday, September 3, 2021 3:51 PM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br><b>Subject:</b> Re: [FRIAM] Can empirical discoveries be mathematical?<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p><span style='font-family:"Arial",sans-serif'>Well, your discovery was certainly empirical.<o:p></o:p></span></p><p><span style='font-family:"Arial",sans-serif'>The explanation is mathematical, having to do what you can do with an oriented surface. BTW, did you take a picture when you put it on upside down? I can visualize a couple of ways you could have done that, but if you weren\u2019t doing hand stands the pictures are not pretty.<o:p></o:p></span></p><p><span style='font-family:"Arial",sans-serif'>\u2014Barry<o:p></o:p></span></p><p><span style='font-family:"Arial",sans-serif'>On 3 Sep 2021, at 11:23, <a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a> wrote:<o:p></o:p></span></p></div><blockquote style='border:none;border-left:solid #777777 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:0in;margin-right:0in;margin-bottom:3.75pt'><div id=AA42256F-ED4E-452E-88AA-ABFE70D6FA6C><div><p style='margin:0in'><span style='color:#777777'>Colleagues,<o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'> <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'>Years ago, my daughter, who knows I hate to shop, bought me a bunch of plain T-shirts. The label\u2019s on the shirts were printed, rather than attached, and so have faded. Each morning, this leaves me with the problem of decerning which is the front and which the back of the shirt, and even, which the inside and which the out-. After years of fussing with these shirts I decerned a pattern. Up/down, inside-in/inside-out, left/right, front/back, crossed arms/uncrossed arms, you can\u2019t do one transformation without doing at least one other. <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'> <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'>Is this an empirical discovery or a mathematical one? <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'> <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'>I guess it boils down to whether \u201cfront/back\u201d entails in its meaning another transformation. Should we call empirical discoveries \u201cdiscoveries\u201d and mathematical discoveries \u201crevelations\u201d?<o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'> <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'>Nick <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'> <o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'>Nick Thompson<o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'><a href="mailto:ThompNickSon2@gmail.com">ThompNickSon2@gmail.com</a><o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'><a href="https://wordpress.clarku.edu/nthompson/">https://wordpress.clarku.edu/nthompson/</a><o:p></o:p></span></p><p style='margin:0in'><span style='color:#777777'> <o:p></o:p></span></p></div></div></blockquote><div><blockquote style='border:none;border-left:solid #777777 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:0in;margin-right:0in;margin-bottom:3.75pt'><p><span style='font-family:"Arial",sans-serif;color:#777777'>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam<br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com"><span style='color:#777777'>http://redfish.com/mailman/listinfo/friam_redfish.com</span></a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/"><span style='color:#777777'>http://friam-comic.blogspot.com/</span></a><br>archives: <a href="http://friam.471366.n2.nabble.com/"><span style='color:#777777'>http://friam.471366.n2.nabble.com/</span></a><o:p></o:p></span></p></blockquote></div></div></div></body></html>