On 18 Feb 2010, at 23:02, Nick Rudnick wrote:
418 bytes in my file system... how many in my brain...? Is it efficient, inevitable?
Yes, it is efficient conceptually. The idea of closed sets let to topology, and in combination with abstractions of differential geometry led to cohomology theory which needed category theory solving problems in number theory, used in a computer language called Haskell using a feature called Currying, named after a logician and mathematician, though only one person. It is SUCCESSFUL, NO MATTER... :-)
But I spoke about efficiency, in the Pareto sense (http://en.wikipedia.org/wiki/Pareto_efficiency)... Can we say that the way in which things are done now cannot be improved??
Hans, you were the most specific response to my actual intention -- could I clear up the reference thing for you?
That seems to be an economic theory version of utilitarianism - the problem is that when dealing with concepts there may be no optimizing function to agree upon. There is an Occam's razor one may try to apply in the case of axiomatic systems, but one then finds it may be more practical with one that is not minimal. Exactly. By this I justify my questioning of inviolability of the state of art of maths terminology -- an open discussion should be allowed at any time...
As for the naming problem, it is more of a linguistic problem: the names were somehow handed by tradition, and it may be difficult to change them. For example, there is a rumor that "kangaroo" means "I do not understand" in a native language; assuming this to be true, it might be difficult to change it. Completely d'accord. This is indeed a strong problem, and I fully agree if you say that, for maths, trying this is for people with fondness for speaker's corner... :-)) But for category theory, a subject (too!) many
Hans Aberg wrote: people are complaining about, blind for its beauty, a such book -- ideally in children's language and illustrations, of course with a dictionary to original terminology in the appendix! -- could be of great positive influence on category theory itself. And the deep contemplation encompassing the *collective* creation should be most rewarding in itself -- a journey without haste into the depths of the subject.
Mathematicians though stick to their own concepts and definitions individually. For example, I had conversations with one who calls monads "triads", and then one has to cope with that.
Yes. But isn't it also an enrichment by some way? All the best, Nick