Ozbib,people talk about spirituality in a religious sense,yet fail to see it in a mathematical or scientific sense.Notions of approaching zero in calculus to determine volume and acceleration,infinity,and now in physics,black holes,parrallel universes, etc are non ordinary realities.These things are revealing an entire new reality that the traditional religions have failed to deliver.

I do not believe in the traditional concept of a singular divine being,but I do believe in a greater consciousness afforded to us by the disciplines of science, maths and the humanities.That does not mean however that we will have a consciousness beyond this life or that there is a singular awareness guiding it.

Thanks for the references.

Dear David,

I was not referring to Plato’s philosophy as such (as far as I can see, both he and Aristotle had far reaching philosophical insights) only to the understanding of mathematics - referred to as “Platonism” (remember, I used quotation marks), sometimes called “realism” - an attitude that many working mathematicians share, namely, that (pure) mathematics is a description of an ideal structure that exists independently of humanity. The alternative is “formalism” that sees mathematics more or less just as a game with symbols that humans invent. Of course, both approaches acknowledge the seminal role of applications, in describing physical reality - c.f. Eugene Wigner’s “unreasonable effectiveness of mathematics.

I indeed think BOTH approaches have their point - namely that mathematics is about BOTH discoveries AND inventions - although for my world-view purposes I like to emphasize the discovery side. The metaphor about the edifice and vine was just an attempt to illustrate/explain this seeming discovery/invention dichotomy.

I am not sure I understand the relevance of Atkins and Heaviside to this. Heaviside, like Dirac, belongs to pioneers in applied mathematics, working intuitively. They needed Laurent Schwarz to turn their intuition into “kosher” (pure) mathematics, a task that is still waiting for somebody e.g. in the case of Feynman integrals.

Thank you for the information about Heaviside. I was not aware of his mental disorder, however he would not be the only mathematical genius thus affected (c.f. John F. Nash of “The Beautiful Mind” or recently Grigori Y. Perelman).

bushbred:

"Certainly the greatest weakness of our OLO or OLO's is the lack of an Adjudicator or the inability to either find one, or design one.

Reckon that is what our OLO smart arses should be thinking about rather than tearing mental strips of each other, as well as off Prominent Thinkers of history".

I don't know what you mean. So far as I'm concerned, I've debated an interesting topic using the proper form and manners. It may have gotten a little off topic but it was otherwise productive and worthwhile, I think. At no time have I been "tearing mental strips off" anyone. So what qualifies me, and my antagonist presumably, as a "smart arse"? I for one am here to learn and adjust my views accordingly. I try to make thoughtful contributions on important issues. I challenge peoples thinking, which in some cases is seized, and I don't pull punches as a rule. I expect the same treatment myself.
A sure way to get rid of me would be to get your adjudicator, that would save any of us the effort of independent thought. We could just mouth our prejudices then have the adjudicator overrule with hers.
We certainly need someone to keep an eye on the tone and language (though Graham, could you please change the designation from the puritanical "profanity" to "expletive"!)
I look to OLO for rigorous debate, as well as more light-hearted discussions and a spot of satire, but I have no desire to be glib.
I'll leave that to others.

I'll say again, Squeers, that tearing strips of each other, is no way of looking for answers regarding what is the matter with today's world.

Reckon the lack of female participants shows how OLO has sadly become male territory.

Dear David f

Exactly. Frank Herbert showed our plastic religions for what they are and defines them at the same time. His basic theme that religion, ceremony, dogma et al are BS. I agree. But because our concept of 'God' in all the BS forms that we have invented do not exist that does not mean that there is not something beyond our comprehension. All we can say is that if there is then we cannot comprehend it.

Dear George,

Perelman not accepting the Fields prize does not indicate mental disorder to me. It may be simply good sense in that he felt accepting the prize would move his life in a direction he didn't want it to go. I know of no other reason to ascribe any mental disorder to him.

I see Plato's theory of forms as an unpleasant expression of conservatism. Everything has degenerated from original perfection. There is no hope. Everybody hates me. Guess I'll go eat worms.

I included Atkins because the castle metaphor you cited made me think of his metaphor.

I included Grassman because mathematics is not only invention/discovery. It is also getting your work accepted and known so other people can build on it. Like Mendel in genetics and Wegener in tectonics Grassman's vector calculus was not immediately accepted. Heaviside and Gibbs encouraged its use. I brought in Heaviside's eccentricities because I thought them interesting.

Squeers: ... his [Marx's] critique of capitalism remains compelling.

Dear Squeers,

Marx's critique predicted the disappearance of the middle class as most of it would sink into the lower class. He predicted a greater concentration of business in great monopolies. There is a plethora of small business and an increasing middle class in the capitalist countries. Bernstein noted this in 1899 and was attacked by orthodox Marxists for noticing that Marx was wrong.

Marxism is tyranny appealing to authoritarian peasant countries such as czarist Russia while fascism is tyranny appealing to authoritarian capitalist countries such as Germany and Italy. Wrong-headed Marx predicted that the capitalist countries would be first to adopt communism.

It was no accident that both tyrannies adopted the policy of mass murder of those they dehumanised. The class struggle has the same dynamic as the race or national struggle.

Dear bushbred,

I agree that it is sad OLO is primarily male territory. I think that’s a reflection of Australian society. In Norway boys and girls from an early age are encouraged to interact, and the sexual roles are not as sharply defined.