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<div style="font-family:sans-serif"><div style="white-space:normal"><p dir="auto">Well, your discovery was certainly empirical.</p>
<p dir="auto">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’t doing hand stands the pictures are not pretty.</p>
<p dir="auto">—Barry</p>
<p dir="auto">On 3 Sep 2021, at 11:23, thompnickson2@gmail.com wrote:</p>
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<blockquote style="border-left:2px solid #777; color:#777; margin:0 0 5px; padding-left:5px"><div id="AA42256F-ED4E-452E-88AA-ABFE70D6FA6C"><div lang="EN-US" link="#0563C1" vlink="#954F72" style="word-wrap:break-word"><div style="page:WordSection1"><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'>Colleagues,</p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'> </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'>Years ago, my daughter, who knows I hate to shop, bought me a bunch of plain T-shirts. The label’s 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’t do one transformation without doing at least one other. </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'> </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'>Is this an empirical discovery or a mathematical one? </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'> </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'>I guess it boils down to whether “front/back” entails in its meaning another transformation. Should we call empirical discoveries “discoveries” and mathematical discoveries “revelations”?</p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'> </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'>Nick </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'> </p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'>Nick Thompson</p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'><a href="mailto:ThompNickSon2@gmail.com">ThompNickSon2@gmail.com</a></p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'><a href="https://wordpress.clarku.edu/nthompson/">https://wordpress.clarku.edu/nthompson/</a></p><p style='font-family:"Calibri", sans-serif; font-size:11pt; margin:0'> </p></div></div></div></blockquote>
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