Re: additions

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

bob coecke proposed to add quantum computing to andre joyal's list of
important directions of categorical research, but andre rejected it. i
cannot overstate my respect for andre's work and judgement. but this left
me pondering.

like andre, i must confess that i am quite ignorant about quantum
computing. (unlike andre, i am also ignorant about many other categorical
topics on his list.)  but we probably all know the following.

most results in quantum computing are theorems about hilbert spaces.
quantum computing is a *tensor calculus*. but it is a tensor calculus of a
special kind: it attempts to describe a wildly unintuitive world. even the
greatest contributors, like von neumann and feynman, deplored the gap
between the quantum world, imposed on us in the lab, and the intuitions
imposed on us in everyday life. now category theory often helps where the
common intuitions fail. many of its applications demonstrate this. so
quantum computation might be an opportunity for an effective application
of *geometry of tensor calculus*.

is it really wise to reject an attempt to develop this, as objectionable
as it might be in any details? physicists like string diagrams, category
theorists like string diagrams. most communities would actively reach
out...

is it just my impression, or are category theorists a little more
sceptical about the value of applications than most mathematical
communities? they seem to seek a recognition that categories are useful
across mathematics, but then hesitate to recognize the depth and value of
the applications in the other areas. --- can it be that we suffer from a
superiority complex of some sort?

the questions raised in the *well kept secret* thread were:

1) why are the achievements of category theory not recognized publicly?
2) what have we done to deserve the opprobium?
3) how can we convince the sceptics?

please allow me to add one more:

4) how can the achievements of category theory be used to expand its
future developments and applications, and not to constrain them?

with best wishes,
-- dusko



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