[FRIAM] Can empirical discoveries be mathematical?

Mon Sep 13 18:17:09 EDT 2021

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 <thompnickson2 at 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
>
> ThompNickSon2 at gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> *From:* Friam <friam-bounces at redfish.com> *On Behalf Of *Roger Frye
> *Sent:* Tuesday, September 7, 2021 9:28 AM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam at 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 <wimberly3 at 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.charles at 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.mackichan at 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, thompnickson2 at 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?
>
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