QuoteOriginally posted by: And2QuoteOriginally posted by: ThinkDifferentI think this 'religious' experience comes from ignorance. Just like with a real religion i.e. the less u know about the subject the more religious is your experience coming from algebraic background i do not find 1 and 2 as very striking.I'd somewhat agree about 3. Again, as a non-geometrist, I find something like Banah-Tarski paradox or classification of exotic spheres quite fascinating.I meant the "religious experience" more as a physiological phenomenon. According to Wikipedia, there are many ways to induce the experience, including praying and "Profound sexual activity" (I guess, the 1 and 2 where somewhere in between... I hope close to praying... I may be wrong). The 1 and 2, and classification of the spheres (though, the later seems to owe it to the groups) are about structure. There are only so many different structures in the universe (yes, given postulates and the rules of logic itself - but even those can be relaxed and one still ends up with (even more) limited structures). This is essentially about the existence. On another hand, the Banach-Tarski paradox is incredible when you first learn it, but mostly because it defies your intuition (which by the time you learn about the paradox formally should be beaten up quite a bit already) about physical concept of volume - and physicists where always much better at beating up one's intuition.One thing seems to be clear: we both are not probabilists The Axiom of Choice is playing tricks again. Quote...later in his career, he [Brouwer] became the most forceful proponent of the so-called intuitionist philosophy of mathematics, which not onlyforbids the use of the Axiom of Choice but also rejects the axiom that a proposition is either true or false (thereby disallowing the method ofproof by contradiction). The consequences of taking this position are dire. For instance, an intuitionist would not accept the existence of anirrational number! In fact, in his later years, Brouwer did not view the Brouwer Fixed Point Theorem as a theorem.BTW a nephew of Brouwer is on Wilmott.
Last edited by Cuchulainn
on September 18th, 2013, 10:00 pm, edited 1 time in total.