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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>On Behalf Of </span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>Kelly Anderson<br><b>Subject:</b> Re: [ExI] dicovery of irrational numbers<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><div><div><p class=MsoNormal>On Wed, Dec 18, 2013 at 11:34 AM, John Clark <<a href="mailto:johnkclark@gmail.com" target="_blank">johnkclark@gmail.com</a>> wrote:<o:p></o:p></p><div><div><p class=MsoNormal>On Wed, Dec 18, 2013 at 12:58 PM, spike <<a href="mailto:spike66@att.net" target="_blank">spike66@att.net</a>> wrote:<o:p></o:p></p></div><div><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='color:#1F497D'>>></span>> I am open to suggestion for how to present irrationals in a more friendly way, especially since I have more bad news for that lad: most numbers are irrational. <o:p></o:p></p></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div></div><div><p class=MsoNormal><span style='color:#1F497D'>>></span>It's even worst than that, at least with PI (and e) there is a infinite series that produces it so you can find a decimal that is as close to PI as you like, but most irrationals, nearly all in fact, are not like that, no infinite series or anything else can produce them, they're not computable, so you can't even get good approximations. We can't even point at most numbers. <span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Oy, good point. My son is reacting much like scientists do when we keep finding out there isn’t really a simple consistent underlying principle, or if so, we still don’t know it.<o:p></o:p></span></p></div></div></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span style='color:#1F497D'>>…</span>Have you introduced him to the concept of significant digits?<span style='color:#1F497D'>...<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>Yes.<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>>…</span> That should assuage his little engineer even if his little mathematician is stomping about inside his head<span style='color:#1F497D'>…<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>Ja, that part is OK, but math is clean and precise. Even I agree that irrationals are ugly things. I love them anyway; all numbers are my friends. But pi is ugly. It has inner beauty with that way cool series expansion. Actually it has a number of expansions, but my favorite is pi= 4/1-4/3+4/5-4/7… oh so cool is this.<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>>…</span>If that doesn't help, you can introduce Chaos<span style='color:#1F497D'>…<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>I put him off on that one. He has a physics comic book which mentions Schroedinger’s Cat. Being an animal lover, he wanted to know what that was all about. I deflected into the Uncertainty Principle for now.<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>>…</span> Then he can throw out the notion of Newton's "Clockwork Universe" altogether and have only one upset instead of two. He won't like it when he finds out about chaos later, so you might as well tell him about this now as well...<span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>That’s been my philosophy: kids can take bad news better than we grownups can.<o:p></o:p></span></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span style='color:#1F497D'>>…</span>I'll leave it up to you as to when to introduce the truth of Santa Claus. :-)<span style='color:#1F497D'> –</span>Kelly<span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I anticipated that one, never introduced the concept. Living where we do, there isn’t much said about Santa Claus. Most of my son’s friends are Buddhist from China or Vietnam, a few Hindu, one Muslim, plenty of agnostics and atheists. I just dropped him off at the home of the Muslim family for a play date. They have a Christmas tree. Oy.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>spike <o:p></o:p></span></p></div><div><p class=MsoNormal><o:p> </o:p></p></div></div></div></div></div></body></html>