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</o:shapelayout></xml><![endif]--></head><body bgcolor=white 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><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'> extropy-chat [mailto:extropy-chat-bounces@lists.extropy.org] <b>On Behalf Of </b>Anders Sandberg<br></span><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:#1F497D'>…</span></b><o:p></o:p></p></div></div><div><div><p><span style='color:#1F497D'>>>…</span><span style='color:#1F497D'>Hmmm, that is a bit close to improper procedure. A bit too religioney for my taste. {8^D However, in the particular case of Fermi’s Paradox, I am flat desperate.</span><o:p></o:p></p></div><p class=MsoNormal><br><span style='color:#1F497D'>>…</span>As one of our locals once said, "pluralitas non est ponenda sine necessitate" - do not add extra stuff to your theory unless you need it. But the *kind* of stuff can be strange: extra dimensions are not stranger than other kinds of matter or negative numbers. But simpler, less extravagant stuff is of course always preferable<span style='color:#1F497D'>….</span>Anders Sandberg<o:p></o:p></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'>Ja. I wasn’t there when it happened, but visualize what it was like when Heron and later Bombelli introduced the notion of imaginary numbers. Plenty of the grumpy old professors must have dismissed the whole idea as silliness, just some kind of useless game. It was probably a lot like postulating an additional dimension.<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'>Well look at it now: how in the heeeeellll could we do without that concept today? Controls engineering would fumble around trying an alternative way to predict regions of instability without a complex plane; we might still be struggling to explain why singularities happen and where. We wouldn’t have Euler’s equation. We would be back to elementary school explanations (still being used today) that the square root of a negative number is undefined. (Why do they do that still? Now in Algebra 2 they will need to tell the students that something they have always been taught is wrong, not just incomplete, it is wrooooong.)<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'>When I hear additional dimensions being proposed, I just compare the notion to complex numbers: if it explains something or correctly predicts something, bring em on. Just because I can’t visualize them does not mean they aren’t there. Just because they are imaginary doesn’t mean they are not real. (Well, if you must get all literal on me… Oy, imaginary: terrible terminology, bad idea. Shoulda been called vertical numbers or intangible numbers rather than that misleading term imaginary. Instead of real, imaginary and complex, we should have called them horizontal, vertical and diagonal numbers respectively, or tangible, intangible and outangible numbers respectively. Or perhaps trangible, rather than that awful term complex?)<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><p class=MsoNormal><o:p> </o:p></p></div><p class=MsoNormal><o:p> </o:p></p></div></body></html>