Frank and Jon,
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. 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. 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. Nick Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University <mailto:[email protected]> [email protected] <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/ From: Friam <[email protected]> On Behalf Of Frank Wimberly Sent: Saturday, June 20, 2020 10:56 AM To: The Friday Morning Applied Complexity Coffee Group <[email protected]> Subject: Re: [FRIAM] Thanks again Marcus Excellent, as Glen would say. My explanation for Nick assumes applied mathematicians. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Sat, Jun 20, 2020, 10:45 AM Jon Zingale <[email protected] <mailto:[email protected]> > wrote: The isomorphism *isn't*, in some sense, enough. For instance, the rationals can be philosophically different than the integers. Sure we can identify them via diagonal argument, but when we want a field we don't reach for the integers. I claim that something similar is happening here and that the point of the article is missed when we jump to the isomorphism. Gisin would have just talked about the rationals if he meant the rationals, instead, he invokes Chaitin and computability on purpose. The truncation simplification obfuscates the deeper point. He is making an ontological claim about the universe and one that theoreticians of quantum theory may appreciate but applied mathematicians will not. The subjectivity of an observer is forced on us by classical logic. Here he constructs a physics over a completely different topos and what follows is not needing to make the observer interpretation. This point is significant enough to think about as being *more* than just truncation, it establishes what can be meant by randomness and the possibility that determinacy may be an illusion, even in macroscopic physics. -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam <http://bit.ly/virtualfriam> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
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