what is math?
Locked
 
|
This essay seems like a literate summary of discussions that Friam's chaotic orbits have visited from time to time.
May you dream that you are awake. -- rec -- - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/ |
|
|
Reuben Hersh, who came to.Friam a couple of times and us well-known to some of us, wrote a book with the title "What is Mathematics, Really" which presents one point of view. I believe the Platonic position appeals to me the most. All right triangles have the Pythagorean property regardless. F --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Tue, Mar 2, 2021, 7:50 AM Roger Critchlow <[hidden email]> wrote:
- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/ |
|
|
In reply to this post by Roger Critchlow-2
Roger, This is great! I love the Darwin quote: He is supposed to have concluded that “a mathematician is a blind man in a dark room looking for a black cat which isn’t there.” It sounds apochrophal to me, but I will take it. n Nick Thompson https://wordpress.clarku.edu/nthompson/ From: Friam <[hidden email]> On Behalf Of Roger Critchlow This essay seems like a literate summary of discussions that Friam's chaotic orbits have visited from time to time. May you dream that you are awake. -- rec -- - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/ |
|
In reply to this post by Roger Critchlow-2
Thanks, Roger. I appreciate the aphorisms that attempt to
place mathematics in the context of a larger human project: - The largest coherent artifact that’s been built by civilization. - The longest continuous human thought. but then also, by contrast: - A proto-text whose existence is only postulated. Also along humanitarian lines, there is the view presented in Imre Lakatos' "Proofs and Refutations"[∴]. There, the process of doing mathematics provides grounds for a human discourse that spans generations, the medium as well as the common object allowing minds separated in time and space to meet. The literature of mathematics then, as portrayed by Lakatos, manifests as a side-effect of intimacies expressed between humans over these strange grounds. [∴] https://en.wikipedia.org/wiki/Proofs_and_Refutations -- Sent from: 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/ |
|
|
This post was updated on .
Or how about, "The easiest problems humanity has to solve"?
-- Sent from: 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/ |
|
|
In reply to this post by Roger Critchlow-2
REC - I particularly appreciated the second paragraph riff on "what is mathematics". Out of the dozen(s) of statements, I couldn't find any I patently disagreed with, though some felt more meaningful/relevant than others. Even more perhaps, I appreciate your characterization of our
perigrinations as chaotic orbits. - SAS On 3/2/21 7:50 AM, Roger Critchlow
wrote:
- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/ |
|
|
In reply to this post by Roger Critchlow-2
Nice article. Steven Strogatz would say it is "the joy of x" - the name of one of his books and his podcast (recommendable by the way) https://www.quantamagazine.org/tag/the-joy-of-x -J. -------- Original message -------- From: Roger Critchlow <[hidden email]> Date: 3/2/21 15:51 (GMT+01:00) To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> Subject: [FRIAM] what is math? This essay seems like a literate summary of discussions that Friam's chaotic orbits have visited from time to time.
May you dream that you are awake. -- rec -- - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/ |
|
|
In reply to this post by Roger Critchlow-2
So all of FRIAM after my post went to the spam folder. It struck me that computer programs are ideal artefacts which have empirical existence. That is, sort of like math in that they're all airy-fairy, but then sort of like rocks, too. If I take a piece of gneiss and break it into pieces, I can send the pieces to all my fellow geologists and we all can perform experiments on our individual pieces and come to a Peircian conclusion about the nature of the rock. I can do that with a computer program, too, but I just make copies and send them to my fellow nerds, and we can all perform experiments on our individual copies and come to a Peircian conclusion about the nature of the program. So math proofs and scientific papers were an earlier form of this, but they don't have an empirical existence, or none that's any help. We can come to a Peircian conclusion about the weight and number of pages and density of type in the manuscript, but we cannot make it run. You either understand or you don't, and if you understand, you either agree or you don't. But the only real existence of the proof or paper is the subjective experience of reading the document, which quickly discourages almost everybody. That's a much different experience than gamers trading riffs to try out at tricky points in a game, or climate modelers figuring out how to squeeze another digit of signal out of the noise. There are still issues of technical competence, but there is an object of study rather than a subject of study, and when people share an object of study, they can independently confirm and extend observations, which can be shared, and so on. Seems like a kind of multiplier. And, of course, some computer programs are just highly refined crap, like gmail's spam filter. -- rec -- On Tue, Mar 2, 2021 at 4:21 PM Jochen Fromm <[hidden email]> wrote:
- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/ |
|
All things are highly refined crap! ... including all computer programs.
The (not-so-interesting) problem with what you lay out is that some computer programs (e.g. https://isabelle.in.tum.de/dist/library/HOL/HOL-ex/Sqrt.html) are proofs and vice versa. The interesting part is where the disjunction is nonempty. It would be cool to have a list of non-programmable proofs ... or non-provable programs. The interesting part of what you lay out is that programs make the requirements on their language more in-your-face than in proofs. It would be cool to know how many programs survive language changes ... a bit like how (I imagine in my ignorance) category theory helps us talk about proofs that survive language changes. It's tempting to say "None. No computer programs survive language changes." But that's not entirely true. The exercise with the fast inverse square root hack, where GCC optimizes, in part, by choosing particular ASM routines but TCC does not, shows a language change where the extensional effect is similar but not the same (TCC compiled one takes longer to execute than the GCC compiled one). Typical use of "programming language" says they're the same because both TCC and GCC compile them just fine (and GCC with different -Ox flags as well). But, really, they're different languages because they have a different *product*. Encapsulation is an ideal, a myth. On 3/3/21 1:40 PM, Roger Critchlow wrote: > So all of FRIAM after my post went to the spam folder. > > It struck me that computer programs are ideal artefacts which have empirical existence. That is, sort of like math in that they're all airy-fairy, but then sort of like rocks, too. > > If I take a piece of gneiss and break it into pieces, I can send the pieces to all my fellow geologists and we all can perform experiments on our individual pieces and come to a Peircian conclusion about the nature of the rock. I can do that with a computer program, too, but I just make copies and send them to my fellow nerds, and we can all perform experiments on our individual copies and come to a Peircian conclusion about the nature of the program. > > So math proofs and scientific papers were an earlier form of this, but they don't have an empirical existence, or none that's any help. We can come to a Peircian conclusion about the weight and number of pages and density of type in the manuscript, but we cannot make it run. You either understand or you don't, and if you understand, you either agree or you don't. But the only real existence of the proof or paper is the subjective experience of reading the document, which quickly discourages almost everybody. > > That's a much different experience than gamers trading riffs to try out at tricky points in a game, or climate modelers figuring out how to squeeze another digit of signal out of the noise. There are still issues of technical competence, but there is an object of study rather than a subject of study, and when people share an object of study, they can independently confirm and extend observations, which can be shared, and so on. Seems like a kind of multiplier. > > And, of course, some computer programs are just highly refined crap, like gmail's spam filter. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
|
«
Return to Friam
|
1 view|%1 views
| Free forum by Nabble | Edit this page |