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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Frank and Jon, <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I am touched by your attempts to bring me on board with respect to the “marcus” paper, but I have to confess that I don’t quite get it. Recall that the story of my life is that I never did understand my brother, the mathematician. Because he was my older brother, I may have confused adulthood with being a mathematician, and so assumed that understanding mathematics is something I would just “grow in to”. But now he is dead, and I am older than he was when he died, I think I have to give up on that assumption. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal> I guess I understand what a rational number is and that rational numbers are a subset of computable numbers. And I guess I understand that a number which is computable to the Nth digit can be uncomputable to the nth plus one. And I guess I understand that a number that is uncomputable, is PRACTICALLY SPEAKING, random. (This last step worries me because it seems to confuse our inability to establish a fact with the existence of a fact to be established. ) But what I never could get my mind around was the relation of all of this to the notion of a “real” number. And why it matters. I suspect that for you, two, that is the easiest point to understand. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thanks for your kind indulgence. I no doubt will have to leave this topic to you wizards, but perhaps I could take one more step with you before I send you on your way.<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>Nicholas Thompson<o:p></o:p></p><p class=MsoNormal>Emeritus Professor of Ethology and Psychology<o:p></o:p></p><p class=MsoNormal>Clark University<o:p></o:p></p><p class=MsoNormal><a href="mailto:ThompNickSon2@gmail.com"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal><a href="https://wordpress.clarku.edu/nthompson/"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Friam <friam-bounces@redfish.com> <b>On Behalf Of </b>Frank Wimberly<br><b>Sent:</b> Saturday, June 20, 2020 10:56 AM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br><b>Subject:</b> Re: [FRIAM] Thanks again Marcus<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal style='margin-bottom:12.0pt'>Excellent, as Glen would say. My explanation for Nick assumes applied mathematicians.<o:p></o:p></p><div><p class=MsoNormal>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Sat, Jun 20, 2020, 10:45 AM Jon Zingale <<a href="mailto:jonzingale@gmail.com">jonzingale@gmail.com</a>> wrote:<o:p></o:p></p></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>The isomorphism *isn't*, in some sense, enough. For instance, the rationals<br>can be philosophically different than the integers. Sure we can identify<br>them via diagonal argument, but when we want a field we don't reach for the<br>integers. I claim that something similar is happening here and that the<br>point of the article is missed when we jump to the isomorphism. Gisin would<br>have just talked about the rationals if he meant the rationals, instead, he<br>invokes Chaitin and computability on purpose. The truncation simplification<br>obfuscates the deeper point. He is making an ontological claim about the<br>universe and one that theoreticians of quantum theory may appreciate but<br>applied mathematicians will not. The subjectivity of an observer is forced<br>on us by classical logic. Here he constructs a physics over a completely<br>different topos and what follows is not needing to make the observer<br>interpretation. This point is significant enough to think about as being<br>*more* than just truncation, it establishes what can be meant by randomness<br>and the possibility that determinacy may be an illusion, even in macroscopic<br>physics.<br><br><br><br>--<br>Sent from: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><br><br>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></p></blockquote></div></div></body></html>