Comments on: Weyl on good and evil http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/ Dedicated to the mathematical arts. Thu, 20 Nov 2008 13:04:16 +0000 http://wordpress.org/?v=2.5.1 By: octracker http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-498 octracker Thu, 09 Mar 2006 07:31:09 +0000 http://www.arsmathematica.net/?p=243#comment-498 I have met the devil and his name is Nicolas Bourbaki. I have met the devil and his name is Nicolas Bourbaki.

]]> By: KorayC http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-489 KorayC Tue, 07 Mar 2006 23:24:36 +0000 http://www.arsmathematica.net/?p=243#comment-489 <blockquote> You can develop incredible insight into how those symbols behave, but you’re not doing geometry. </blockquote> But isn't that what's precisely nice about mathematics that I don't have to develop the intuition to do geometry, physics, etc. ? Intuition is certainly good to have and I wish I had it for all kinds of subjects, but there's no methodical way to develop it.

You can develop incredible insight into how those symbols behave, but you’re not doing geometry.

But isn’t that what’s precisely nice about mathematics that I don’t have to develop the intuition to do geometry, physics, etc. ? Intuition is certainly good to have and I wish I had it for all kinds of subjects, but there’s no methodical way to develop it.

]]> By: PeterMcB http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-487 PeterMcB Sun, 05 Mar 2006 15:36:33 +0000 http://www.arsmathematica.net/?p=243#comment-487 You are correct, Sigfpe, that algebra allows geometry to be done by people without geometric intuition. But what is the nature of this intuition? I doubt anyone had or has any *inherent* intuition for non-Euclidean geometry, since our entire every-day experience as children is Euclidean. Physicists only started to think that the Universe may be better modeled with a non-Euclidean geometry after such geometries had been developed by those clever algebraists, Gauss, Bolyai and Riemann. Some other clever people --eg, Frege -- simply could not accept that non-Euclidean geometry was more than abstract nonsense, unconnected to anything in the real world. You are correct, Sigfpe, that algebra allows geometry to be done by people without geometric intuition. But what is the nature of this intuition? I doubt anyone had or has any *inherent* intuition for non-Euclidean geometry, since our entire every-day experience as children is Euclidean. Physicists only started to think that the Universe may be better modeled with a non-Euclidean geometry after such geometries had been developed by those clever algebraists, Gauss, Bolyai and Riemann. Some other clever people –eg, Frege — simply could not accept that non-Euclidean geometry was more than abstract nonsense, unconnected to anything in the real world.

]]> By: michael http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-486 michael Sun, 05 Mar 2006 02:14:27 +0000 http://www.arsmathematica.net/?p=243#comment-486 make that "one" make that “one”

]]> By: michael http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-485 michael Sun, 05 Mar 2006 02:13:55 +0000 http://www.arsmathematica.net/?p=243#comment-485 I for onw revel in my devilishness I for onw revel in my devilishness

]]> By: sigfpe http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-484 sigfpe Sun, 05 Mar 2006 00:33:35 +0000 http://www.arsmathematica.net/?p=243#comment-484 Instead of learning to solve the problem algebra allows you instead to manipulate symbols. The Devil's minion, Descartes, allowed people with no geometrical insight to start proving theorems about geometry. You can develop incredible insight into how those symbols behave, but you're not doing geometry. Even worse, people can be so far removed that they even fail to realise that they are doing geometry. Instead of learning to solve the problem algebra allows you instead to manipulate symbols. The Devil’s minion, Descartes, allowed people with no geometrical insight to start proving theorems about geometry. You can develop incredible insight into how those symbols behave, but you’re not doing geometry. Even worse, people can be so far removed that they even fail to realise that they are doing geometry.

]]> By: Walt http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-483 Walt Fri, 03 Mar 2006 21:28:24 +0000 http://www.arsmathematica.net/?p=243#comment-483 Ford: I wondered the same thing about algebra being the devil, which probably demonstrates that we're both irretrievably damned. Ford: I wondered the same thing about algebra being the devil, which probably demonstrates that we’re both irretrievably damned.

]]> By: chrisb http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-482 chrisb Fri, 03 Mar 2006 16:54:28 +0000 http://www.arsmathematica.net/?p=243#comment-482 Reminds me of Atiyah's comments regarding the "Faustian Offer" in "Mathematics in the 20th Century" (Bull. of the London Math. Soc. 34 (2002) 1-15) (or see duch.mimuw.edu.pl/~sjack/atiyah.ps). Reminds me of Atiyah’s comments regarding the “Faustian Offer” in “Mathematics in the 20th Century” (Bull. of the London Math. Soc. 34 (2002) 1-15) (or see duch.mimuw.edu.pl/~sjack/atiyah.ps).

]]> By: ford http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-481 ford Fri, 03 Mar 2006 08:58:24 +0000 http://www.arsmathematica.net/?p=243#comment-481 How is topology/category theory winning? Why is Abstract Algebra cast as "the devil"? How is topology/category theory winning?

Why is Abstract Algebra cast as “the devil”?

]]> By: michael http://www.arsmathematica.net/archives/2006/03/02/weyl-on-good-and-evil/#comment-480 michael Fri, 03 Mar 2006 06:50:18 +0000 http://www.arsmathematica.net/?p=243#comment-480 You forgot the second sentence. "And the devil is winning." You forgot the second sentence. “And the devil is winning.”

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