Thurston: On Proof and progress
Locked
Thurston: On Proof and progress
 
|
Dear Friammers,
We have decided to carry on from our seminar on Emergence to one on Mathematical Thinking. Although we don't meet for a month, I found myself reading the first assignment, Thurston's On Proof and Progress in Mathematics. Now Thurston loves mathematics and is apparently good at it, but he is firm in arguing that the process of proof is not as the normative account would have it. Given our local debates about the ideal of formalism and given my suspicion that many computer programmers suffer from math envy (the way experimental psychologists suffer from physics envy), I was astonished by the following paragraphs.
Astonished, and yet, instantly convinced that it was true. Note that Thurston is proud of how mathematicians do their work; no criticism here.
You would almost think that computer programming was the Queen of the Sciences.
Nick
I wonder what you all think about it.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://www.cusf.org [City University of Santa Fe]
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Thurston: On Proof and progress
|
|
Quite flattering to us programmers. (Here's the actual article.) My experience, though, is that programming is easier. (I was a mediocre math major as an undergraduate and then found computer science, something I could actually do.) A similar argument might conclude that driving from New York to Los Angeles is even harder than programming because of all the details one must get right to arrive in the right place with crashing into anything. But that doesn't mean it's either difficult or formally correct.
-- Russ Abbott _____________________________________________ Professor, Computer Science California State University, Los Angeles Cell phone: 310-621-3805 o Check out my blog at http://russabbott.blogspot.com/ On Mon, Dec 14, 2009 at 9:43 PM, Nicholas Thompson <[hidden email]> wrote:
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
|
|
Programming is much easier because much of it is a process of trial and error. You can generate any old crap (many programmers do) and gradually refine it by successively throwing it at: a) a compiler, b) a set of unit tests (written by yourself) c) a set of system tests d) a set of acceptance tests. The ultimate determinant of "correctness" is whether the customer agrees to pay you for your deliverables. This is not necessarily related to "correctness" or "fit for purpose". I don't believe at all that the bar for acceptable mathematical proof is lower than that for programming. It couldn't be! Regards, Saul
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Thurston: On Proof and progress
|
|
In reply to this post by Nick Thompson
Careful, here, everybody.
I don't want to be party to a misrepresentation of Thurston's point. It is not that maths is easier that computer programming or that computer programmers are more rigorous than mathematicians. It is that the heart of mathematical proof is not in its rigor. Rigor often comes AFTER the proof is, to all intents and purposes, agreed to.
Russ has kindly provided a link to the original article; don't take the word of a former english major. Have a look at it.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://www.cusf.org [City University of Santa Fe]
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Thurston: On Proof and progress
|
|
In reply to this post by Nick Thompson
By these criterion, Psychology is the King of the
Sciences. Nick knows
full well, but many Friammers would be surprised how much effort psychologists
put into projects that are 'not even close' to formally
correct! Eric On Tue, Dec 15, 2009 12:43 AM, "Nicholas Thompson" <[hidden email]> wrote: Eric Charles Professional Student and Assistant Professor of Psychology Penn State University Altoona, PA 16601 ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Thurston: On Proof and progress
|
|
In reply to this post by scaganoff
Saul Caganoff wrote:
> Programming is much easier because much of it is a process of trial > and error. You can generate any old crap (many programmers do) and > gradually refine it by successively throwing it at: > > a) a compiler Yes, some of the rigor is now automated. That's progress. Programming is about writing and inventing things. That's a messy business, at least if it is done well. Marcus ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Thurston: On Proof and progress
|
|
In reply to this post by Nick Thompson
Thus spake Nicholas Thompson circa 12/14/2009 09:43 PM:
> I wonder what you all think about it. It seems clear to me ... digression: for those that don't know, whenever someone says "it seems clear to me", they are about to say something fragile and weak that can be shattered with the slightest tap of a tiny hammer and implicitly _requesting_ someone to knock that chip off their shoulder ... they're exposing their soft underbelly in the hopes of egging you on ... ;-) Just FYI... Anyway, it seems clear to me that computers (and hence computer programming) are part of the banal evolution of life, wherein each organism makes every effort to externalize costs and internalize profit. This amounts to "extended physiology". Computers are externalized lobes of our brains. The point is to shed the costly, low margins parts of the effort out into the environment but preserve the efficient, high margins parts for ourselves. By this reasoning, OF COURSE programming takes much more investment for much less return. The point is to do the menial work to externalize that part of our physiology so that the more deeply meaningful part of the work can be done more efficiently inside our skin. It's analogous to outsourcing those jobs we've mastered to developing countries. We already know how to run a call center; so why not outsource it to India or China? Let's save our own resources for something with a higher return on investment! The Hilbert programme (and Babbage's difference engine, etc.) is all about reducing as much math to formalism as possible ... making it automatic, machinery... EXTERNALIZING that part of our brains so we can concentrate on the interesting stuff. That's what computers are. And, it's no different than any other effort to extend our physiology. All our engineering efforts, from building sky scrapers, flying to the moon, roads, paper clips, etc. They're all tools. They're all ways to shed the costly, low ROI stuff so that we can concentrate on what's important. -- glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Thurston: On Proof and progress
|
Administrator
|
In reply to this post by Nick Thompson
I believe Thurston is referring to the formal syntax of the computer languages he is using: there is no ambiguity .. even to the point of having syntax rules, generally in BNF (Backus–Naur Form). And at the time of his writing the article, he was likely using Algol, a rather advanced and sophisticated language, and one with the first interesting representations of data structures .. called Records in Algol as I recall.
Thus in some ways computer programs can be validated, in that their syntax is rigorous. And naturally the compiler enforces these rules. Theorems do not have quite that concreteness, although being exposed to a wide community is sorta a similar scheme of rigor. -- Owen On Dec 14, 2009, at 10:43 PM, Nicholas Thompson wrote:
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
«
Return to Friam
|
1 view|%1 views
| Free forum by Nabble | Edit this page |