Re: autonomous terminology: WAS: bilax monoidal functors

[Dusko Pavlovic <Dusko.Pavlovic@comlab.ox.ac.uk>]

thanks for the suggestions about the autonomous terminology. i think i got
an idea for a minimally invasive solution.

we probably shouldn't go too deep into the general questions, but colin
mclarty's cryptic comment is very interesting to me, and it seems to
strike at the heart of some matters of interest.

On May 9, 2010, at 3:41 PM, Colin McLarty wrote:

> Dusko Pavlovic Asks
>
>> is there any reason why words should be taken seriously?
>
> That just depends on whether or not you want to be understood by
> people who do not already know everything you are going to say.

there are at least two ways to interpret this.

1) "you can only say something new if you declare what your words mean.
otherwise, people will interpret them in their own way, and understand
only what they already know." --- this is what my sociology teacher would
say.

2) "you can only say something new if you contribute to the evolution of
language. otherwise, everything you say are just words that people already
know, mostly in combinations that they already tried." --- this is what my
poetry teacher would say.

i am not sure whether you meant (1) or (2), colin. maybe you tried to say
something that i don't know already :) in any case, i suspect that many
people here would tend to disagree with my poetry teacher.

but the distinction between (1) and (2) stretches beyond my high school
teachers. eg, hilbert would surely subscribe something like (1). all those
monolithic foundations and logics and set theories can be viewed as
efforts to clearly define the words that we use in math.

categories, on the other hand, were proposed as a tool for the *working*
mathematician. people cared that category theory was a dynamic language,
with its philosophical roots in *dialectics*... not that we didn't define
our terminology; but categorical work was more about capturing conceptual
flows by adjunctions, and the flows of equations by arrows, than about
carving words in stone.

nowadays, the distinction between (1) and (2) has become very concrete.
language is processed on the web, and the problem that the meaning of data
is not clearly defined or structured has became a technical problem. two
strategies were proposed:

1) semantic web: let us standardize ontologies, anotate data
syntactically, and contribute them to the global library;

2) search: follow the hyperlinks and extract the meaning of data
dynamically, by analyzing their distribution on the network. eg, if one
web site links to another web site, then it lends it some of its
reputation, and some of its meaning.

paradigm (1) has generated a lot of interesting research. people defined
very precise very carefully classified families of terms in very large
ontologies. recently, some of them were even populated by data.

paradigm (2) works. it changed every science, and made possible a couple
of new ones. if there is a question of terminology, ask google. show me
200 papers about motivic cohomology, sorted by popularity. what is motivic
cohomology? long live dialectics. things shouldn't be taken seriously only
because of a shortage of humor in the world.

all the best,
-- dusko

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]