[Haskell-cafe] Category Theory woes

[Nick Rudnick]

Richard O'Keefe wrote:
>
> On Feb 19, 2010, at 2:48 PM, Nick Rudnick wrote:
>> Please tell me the aspect you feel uneasy with, and please give me 
>> your opinion, whether (in case of accepting this) you would rather 
>> choose to consider Human as referrer and Int as referee of the 
>> opposite -- for I think this is a deep question.
> I've read enough philosophy to be wary of treating "reference"
> as a simple concept.  And linguistically, "referees" are people
> you find telling rugby players "naughty naughty".  Don't you
> mean "referrer" and "referent"?
> Yes, thanks. I am not a native English speaker, and in my mother tongue, 
> a referent is somebody who refers, so I missed the guess... Such 
> statements are exactly what I was looking for... So, as a reference is 
> directed, it is possible to distinguish
>
> referrer ::= the one which does refer to s.th.
>
> referent ::= one which is referred to by s.th.
>
> Of course a basic point about language is that the association
> between sounds and meanings is (for the most part) arbitrary.
I would rather like to say it is not strictly determined, as an 
evolutionary tendence towards, say ergonomy, cannot be overlooked, can it?

> Why should the terminology of mathematics be any different?
;-) Realizing an evolutionary tendence towards ergonony, is my subject...
> Why is a "small dark floating cloud, indicating rain", called
> a "water-dog"?  Water, yes, but dog?  Why are the brackets at
> each end of a fire-place called "fire-dogs"?  Why are unusually
> attractive women called "foxes" (the females of that species
> being "vixens", and both sexes smelly)?  
:-)) The shape of the genitals, which might come into associative 
imagination of the hopeful observer?? (The same with cats, bears, etc.) 
[... desperately afraid of getting kicked out of this mailing list ;-))]

Thanks for this beautiful example and, honestly, again I ask again 
whether we may regard this as «just noise»: In contrary, aren't such 
usages not paradigmatical examples of memes, which as products of 
memetic evolution, should be studied for their motivational value?

Let me guess: Our cerebral language system is highly coupled with our 
intentional system, so that it helps learning to have motivating 
«animation» enclosed... Isn't this in use in contemporary learning 
environments...?

The problem I see is that common maths claims an exception in claiming 
that, in it's domain, namings are no more than noise -- possible 
motivated by an extreme rejection of anything between «strictly formally 
determined» and «noise». This standpoint again does not realize the 
developments in foundations of mathematics of at least the century ago 
-- put roughly, this comes close to Hilbert's programme...

To my mind, any of the breakthroughs of the last decades -- like 
incompleteness, strange attractors, algorithmic information theory, 
CCCs, and not the least computing science itself with metaprogramming, 
soft computing, its linear types/modes and monads (!) -- have to do with 
constructs which emancipate such claims of ex ante predetermination. 
Isn't category theory pretty much a part of all this?

> What's the logic in
> doggedness being a term of praise but bitchiness of opprobrium?
Sexism...??

> We can hope for mathematical terms to be used consistently,
> but asking for them to be transparent is probably too much to
> hope for.  (We can and should use intention-revealing names
> in a program, but doing it across the totality of all programs
> is something never achieved and probably never achievable.)
We have jokers: Evolutionary media, like markdown or even stylesheet may 
allow us to switch and translate in a moment, and many more useful 
gimmicks... Online collaboration platforms...

And we can stay pragmatical: If we can reach a (broad, to my 
estimate...) public, which originally would have to say «the book has 
really left me dumbfounded» (so the originator of this thread) and offer 
them an entertaining intuitive way -- why not even in a 
self-configurable way? -- category theory could be introduced to 
contemporary culture.

Personally, I can't accept statements like (in another posting) «You 
need a lot of training in abstraction to learn very abstract concepts. 
Joe Sixpack's common sense isn't prepared for that.»

Instead, I think that there is good evidence to believe that there are 
lots of isomorphisms to be found between every day's life and 
terminology and concepts category theory -- *not* to be confused with 
its *applications to maths*...

And, to close in your figurative style:

Which woman gets hurt by a change of clothes?

Cheers,

Nick