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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>Colleagues,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Is this an empirical discovery or a mathematical one? <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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”?<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>Nick Thompson<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></div></body></html>