<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 wrote the following for Reuben Hersh’s memorial. The story is from when Reuben, Vera and I were in the same carpool to UNM.<div class=""><br class=""></div><div class=""><div class=""><font color="#0432ff" class="">During one of our commutes, Reuben and I were sharing the back seat and Reuben brought up the subject of quaternions. For the mathematician quaternions, which are the extension of simple complex numbers from two to three dimensions, have a long and interesting history. Their discovery took a long time even though some of the best mathematicians worked the problem. Nevertheless, they are both simple and elegant. Reuben, of course, loved them for both the history and the mathematics and was going to talk about them in his upcoming class. I mentioned that quaternions are used extensively in computer graphics (any student who takes a class in computer graphics knows about them), animation (for designing camera paths), aerospace (for head mounted displays) and by NASA (in rocket control systems). Reuben was amazed. His response was “Someone actually uses them!?” When we got to Albuquerque, Reuben, still in a state of amazement, dragged me to his class, put me in front, and his introduction was “this guy is going to tell you how people actually use quaternions.” He then sat in the back, thoroughly enjoying my impromptu lecture. </font></div><div class=""><font color="#0432ff" class=""><br class=""></font></div><div class=""><span style="caret-color: rgb(4, 50, 255);" class="">Ed</span></div><div class=""><br class=""></div><div class="">
<span class="Apple-style-span" style="border-collapse: separate; font-variant-ligatures: normal; font-variant-east-asian: normal; font-variant-position: normal; line-height: normal; border-spacing: 0px; -webkit-text-decorations-in-effect: none;"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div class="">_______________________</div><div class=""><br class="Apple-interchange-newline">Ed Angel<br class=""><br class=""></div><div class="">Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)<br class="">Professor Emeritus of Computer Science, University of New Mexico<br class=""><br class="">1017 Sierra Pinon</div><div class="">Santa Fe, NM 87501<br class="">505-984-0136 (home)<span class="Apple-tab-span" style="white-space: pre; "> </span> <span class="Apple-tab-span" style="white-space: pre; "> </span><a href="mailto:angel@cs.unm.edu" class="">angel@cs.unm.edu</a></div><div class="">505-453-4944 (cell) <span class="Apple-tab-span" style="white-space: pre; "> </span><span class="Apple-tab-span" style="white-space: pre; "> </span><a href="http://www.cs.unm.edu/~angel" class="">http://www.cs.unm.edu/~angel</a><br class=""></div></span></span>
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<div><br class=""><blockquote type="cite" class=""><div class="">On Sep 7, 2020, at 2:17 PM, Tom Johnson <<a href="mailto:tom@jtjohnson.com" class="">tom@jtjohnson.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.<br class=""><br class=""><a href="https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/?fbclid=IwAR32bY8dnkg_hCYImiFlJgJL3g_r1CR9Eos4V_YEPcb7bvYJWlTe-8-83fY" class="">https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/?fbclid=IwAR32bY8dnkg_hCYImiFlJgJL3g_r1CR9Eos4V_YEPcb7bvYJWlTe-8-83fY</a> <br class=""><br class="">TJ<br class=""><div class=""><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><br class="">============================================<br class="">Tom Johnson - <a href="mailto:tom@jtjohnson.com" target="_blank" class="">tom@jtjohnson.com</a><br class="">Institute for Analytic Journalism -- Santa Fe, NM USA<br class="">505.577.6482(c) 505.473.9646(h)<br class=""><a href="http://nmfog.org/" target="_blank" class=""><b class=""><font color="#0b5394" class="">NM Foundation for Open Government</font></b></a><br class=""><b class=""><font color="#0000ff" class="">Check out <a href="https://www.facebook.com/pages/Its-The-Peoples-Data/1599854626919671" target="_blank" class="">It's The People's Data</a></font></b> </div><div class="">============================================</div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
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