It doesn't take much observing to realize that rotations of an object in 3D are not commutative.
--- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Fri, Sep 3, 2021, 12:41 PM Russ Abbott <russ.abb...@gmail.com> wrote: > I would guess that most mathematical discoveries are first encountered > empirically. Then the mathematician who encounters it attempts to prove the > observed phenomenon mathematically. Your bachelor example illustrates. Once > you discovered the apparent phenomenon that all unmarried men are > bachelors -- and as you also noticed that all bachelors are unmarried -- > you proved that the two collections are identical by determining that > that's how bachelor is defined, a mathematical relationship. Will you be > writing up and submitting this result to a mathematics journal -- rather > than, for example, to a journal of sociology? > > -- Russ Abbott > Professor Emeritus, Computer Science > California State University, Los Angeles > > > On Fri, Sep 3, 2021 at 11:09 AM Pieter Steenekamp < > piet...@randcontrols.co.za> wrote: > >> Eric, >> >> Nick's question and the parsing of discoveries into two types intrigue >> me. I'm an engineer, so maybe I have a deep seeded philosophy of science >> envy? >> >> Pieter >> >> On Fri, 3 Sept 2021 at 19:58, Eric Charles < >> eric.phillip.char...@gmail.com> wrote: >> >>> Why are we parsing discoveries into those two types? >>> >>> I think traditionally, "mathematical" would have been synonymous with >>> "rigorous deduction groin a minimal number of axioms", but I doubt that >>> approach is clear cut anymore. >>> >>> Given that you claim to have sussed out your insight via systematic >>> *empirical* observation, and you claim it regarding a particular class >>> of *empirical* objects... I'd go with "empirical"... if I had to choose >>> one for you... but I'm also not sure why we would play this game to begin >>> with. >>> >>> Unless you confessed to me that it was insecurities tied to a deep >>> seeded physics envy... in which case I'd at least understand why you >>> asked. >>> >>> On Fri, Sep 3, 2021, 1:25 PM <thompnicks...@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 >>>> >>>> thompnicks...@gmail.com >>>> >>>> https://wordpress.clarku.edu/nthompson/ >>>> >>>> >>>> >>>> *From:* Friam <friam-boun...@redfish.com> *On Behalf Of *Pieter >>>> Steenekamp >>>> *Sent:* Friday, September 3, 2021 12:48 PM >>>> *To:* The Friday Morning Applied Complexity Coffee Group < >>>> friam@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, <thompnicks...@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 >>>> >>>> thompnicks...@gmail.com >>>> >>>> https://wordpress.clarku.edu/nthompson/ >>>> >>>> >>>> >>>> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . >>>> 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/ >> > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > 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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