[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.
>> 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
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
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