[FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

Group theory.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Fri, Sep 3, 2021, 11:25 AM <thompnickson2 at gmail.com> wrote:

> By discovery, I mean only happening on a regularity that was unexpected.
>
>
>
> I guess I didn’t need all the razzle-dazzle about the t-shirts.  Let’s say
> that I, being totally naïve of logic, announced to friam that I had made a
> survey of all my never-married male friends and each and every one claimed
> to be a bachelor.  I offered to you-all, as an insight, that all unmarried
> men are bachelors.   I think I have made that “discovery” empirically; you
> might have arrived at the same insight logically.  Perhaps the empirical vs
> mathematical thing is methodological.  Of course, I now realize that
> inorder to arrive at my empirical conclusion, I had to invoke the logical
> form, induction: this man is un-married, this man is a batchelor, all
> batchelors are unmarried.  You might have arrived at the same conclusion
> deductively (i.e., mathematically).
>
>
>
> Nick Thompson
>
> ThompNickSon2 at gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
> *From:* Friam <friam-bounces at redfish.com> *On Behalf Of *Pieter Steenekamp
> *Sent:* Friday, September 3, 2021 12:48 PM
> *To:* The Friday Morning Applied Complexity Coffee Group <
> friam at redfish.com>
> *Subject:* Re: [FRIAM] Can empirical discoveries be mathematical?
>
>
>
> Nick,
>
> I quote from https://www.britannica.com/science/scientific-theory
>
> "In attempting to explain objects and events, the scientist employs (1)
> careful observation or experiments, (2) reports of regularities, and (3)
> systematic explanatory schemes (theories). The statements of regularities,
> if accurate, may be taken as empirical laws expressing continuing
> relationships among the objects or characteristics observed."
>
> Based on this, I reckon, because you have reported the regularities, you
> have discovered an empirical scientific law. Congratulations!
>
> Next is to systematically explain it, then you have a scientific theory!
>
> Maybe I did not answer your question? You asked if this is an empirical
> discovery or a mathematical one.
>
>
> IMO you have done only the first part, the empirical discovery. This could
> now be taken further and if you can prove it using formal mathematics, then
> only can you claim you have made a mathematical discovery. So, it is (not
> yet) a mathematical discovery. Sorry to blow your bubble.
>
> P
>
>
>
> On Fri, 3 Sept 2021 at 17:24, <thompnickson2 at gmail.com> wrote:
>
> Colleagues,
>
>
>
> Years ago, my daughter, who knows I hate to shop, bought me a bunch of
> plain T-shirts.  The label’s on the shirts were printed, rather than
> attached, and so have faded.  Each morning, this leaves me with the problem
> of decerning which is the front and which the back of the shirt, and even,
> which the inside and which the out-.  After years of fussing with these
> shirts I decerned a pattern.  Up/down, inside-in/inside-out, left/right,
> front/back, crossed arms/uncrossed arms, you can’t do one transformation
> without doing at least one other.
>
>
>
> Is this an empirical discovery or a mathematical one?
>
>
>
> I guess it boils down to whether “front/back” entails in its meaning
> another transformation.   Should we call empirical discoveries
> “discoveries” and mathematical discoveries “revelations”?
>
>
>
> Nick
>
>
>
> Nick Thompson
>
> ThompNickSon2 at gmail.com
>
> https://wordpress.clarku.edu/nthompson/
>
>
>
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