[Haskell-cafe] Category Theory woes

Nick Rudnick joerg.rudnick at t-online.de
Thu Feb 18 18:05:18 EST 2010

Hans Aberg wrote:
> 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.
>> 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 
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,


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