A completely different example of mathematical metaphor is representation theory. The formula 3*3 + 4*4 = 5*5 can be represented as a right triangle with the sides touching the right angle having lengths of 3 and 4, and the hypotenuse having length 5. I like to think of one representation being a metaphor for the other.
On Mon, Sep 13, 2021 at 11:52 AM <thompnicks...@gmail.com> wrote: > Roger, > > > > If I weren’t immured with my income tax, I would engage you on this. I > believe that metaphor -- aka “abduction”? – is the root of all evil *and* > the root of all good. And then I wonder about the connection to the naming > fallacy. The naming fallacy I take to be the idea that if two things have > the same name, they have the same properties. This assertion is absurd as > a statement of fact but often useful as a source of hypotheses. So, on > this view, we humans take Adam’s Task very seriously. We stumble around > the world naming every new experience that confronts us and then > frantically try to work out how much we can trust the implications of that > name. “My love is … a … rose! How long are her thorns?” > > > > Ugh! I now see that I have gone all anthropocentric, here. What IS the > relation between perception (cognition, what-have-you) and naming. The > Whorf hypothesis would have it that all perception is run though a > dictionary, but I understand that the Whorf hypothesis is not wearing well, > these days, and, more important, animals perceive quite well without > dictionaries. Classical conditioning (a la Pavlov) produces abductions. > (This bell MEANS foodpowder) Would a dog think, “This bell is … a > ….foodpowder!” Probably not. It might think “Oh Goody Food Powder!” So > whatever the naming thing contributes, it is layered on to something else, > something more fundamental. (Two bird hunters are walking through the > underbrush, guns ready when, the leader calls out “Duck.”; his companion, > stops, raises his gun, and scans the sky, only to be struck full in the > face by a bent hickory sapling.] > > > > These are the things I might have written to you about were I not doing my > income tax. > > > > Nick > > > > Nick Thompson > > thompnicks...@gmail.com > > https://wordpress.clarku.edu/nthompson/ > > > > *From:* Friam <friam-boun...@redfish.com> *On Behalf Of *Roger Frye > *Sent:* Tuesday, September 7, 2021 9:28 AM > *To:* The Friday Morning Applied Complexity Coffee Group < > friam@redfish.com> > *Subject:* Re: [FRIAM] Can empirical discoveries be mathematical? > > > > Reuben had an article in Issue 65 of Eureka Magazine titled 'Solving > Problems by "Cheating": Operational Calculi, Function Theory, and > Differential Equations'. The article is a compilation of tricks that he ran > across during his career that seemed to apply in a general way to solving > problems. The theme is that you doodle with methods that you have no right > to assume would work in this particular case, and if you get something > worthwhile, then go back and prove it. > > > > Towards the end of his life he became more interested in the metaphors > that are at the basis of mathematical thinking, the bodily actions that > have been abstracted into mathematical concepts. Yuri I. Manin also spoke > of Mathematics as Metaphor is a slightly different way in his essays. > > > > -Roger > > > > > > On Mon, Sep 6, 2021 at 8:34 PM Frank Wimberly <wimber...@gmail.com> wrote: > > Our late friend Reuben Hersh was interested in these questions. > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > > > On Mon, Sep 6, 2021, 7:58 PM Eric Charles <eric.phillip.char...@gmail.com> > wrote: > > As I said a few days ago: I think traditionally, "mathematical" would > have been synonymous with "rigorous deduction from a minimal number of > axioms", but I doubt that approach is clear cut anymore. > > > > I am pretty confident that modern mathematics is WAY more open-field than > that. The Stanford Encyclopedia of Philosophy seems to agree with that > intuition, though I think it is an even broader topic than implied by just > this entry: Non-Deductive Methods in Mathematics (Stanford Encyclopedia > of Philosophy) > <https://plato.stanford.edu/entries/mathematics-nondeductive/> > > > > > > > > > On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan < > barry.mackic...@mackichan.com> wrote: > > Briefly, and in my opinion, mathematics can only make claims like ‘if A is > true then B is true’. To say B is true, you must also say A is true. > Eventually you have to go back to the beginning of the deductive chain, and > the truth of the initial statement is inductive, not deductive or > mathematics. You can predict the time and place of an eclipse, and this > prediction is based on mathematics and a mathematical model of reality — > Newton’s laws in this case. But the truth of this prediction is inductive > since the initial positions and velocities for the calculation are > inductive, as is the applicability of Newton’s laws to reality, and even > the ‘fact’ that mathematics can describe the universe is inductive. > > And Einstein showed that the applicability of Newton’s laws was in fact > wrong and offered a new model — which we inductively accept as true, if > only provisionally. > > Mathematics cannot prove any statement about the real world. Any such > statement will depend at some point on an inductive truth or a definition. > > —Barry > > > > On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote: > > Ok, is mathematics (logic, etc.) a way of arriving at true propositions > distinct from observation or are mathematical truths different from > empirical truths? > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ >
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