[Haskell-cafe] Category Theory woes

Hans Aberg haberg at math.su.se
Thu Feb 18 17:22:08 EST 2010

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.

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.

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.


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