Re: patenting colimits?

[Vaughan Pratt <pratt@cs.stanford.edu>]

On 5/25/2009 6:35 AM, Ronnie Brown wrote:
> Larry Lambe passed on the following url to me for comment and I
> thought it would be of interest to others on the category theory
> list, with more expertise than I. I have not had time to study it,
> but on the face of it,  it seems like patenting mathematics, and to
> be deplored intensely.  Am I wrong?
>
>
> http://www.freepatentsonline.com/6964037.html

I skimmed the patent briefly just now, dated 2005.  I was amused to see
Dusko Pavlovic's name on it, I hadn't realized Dusko had become an
inventor (congrats, Dusko).

My first impression was that it's patenting the application of a
category theory technique to the composition of hierarchically organized
software specifications.  It wasn't immediately clear to me which claims
in the patent someone "skilled in the art" wouldn't have come up with
right away given the problem(s) claimed to have been overcome.  Since
simply aggregating things is an obvious technique, the role of the
morphisms in regulating the overlaps in the aggregation is obviously
key.  That of course is far too well known to be patentable itself.
What I couldn't find on a first pass was what problem was overcome by
what clever *and novel* trick.

As with any patent, its viability will depend on how original the
application is.  Any prior art applying it in this way will render it
vulnerable, but if the method is sufficiently novel it may serve its
intended purpose of temporarily (namely until 2025) barring entry of
others to whatever market turns out to have been created by this
application, unless the would-be competitor can come up with a
satisfactory alternative that does not infringe on this patent.
(Imagine a jury wrestling with the question of whether amalgamation as
used in logic and algebra infringes on a patent based on colimits.)

Mathematicians who are philosophically opposed to seeing their ideas put
to use in the business world should either stick to those parts of
mathematics least likely to be of practical use or prepare for the shock
of seeing their ideas used for the benefit of the non-mathematical
public in ways that enrich primarily the "last-mile" people bringing
those ideas to the public.

In the first two decades of the internet, some academics took the
attitude that no one should derive commercial benefit from the internet,
and protested strenuously whenever anyone appeared to be trying to do
so.  That dam burst around 1995, and the purists were run over in the
resulting stampede.

There is no point trying to stand in the way of a similar stampede for
commercial applications of category theory.  Either colimits will turn
out not to be a particularly effective way of assembling software
specifications, in which case the patent will have been a waste of
money, or they will turn out to be of use, in which case the purists
will (hopefully) be run over as they were for the internet.

More importantly from the perspective of mathematics, the latter outcome
will motivate the funding agencies to take category theory more
seriously and steer more support in its direction so it can grow faster
and be even more useful.  This would make category theory a secondary
beneficiary behind the primary "last-mile" beneficiaries, giving it a
more engineering flavour that brings it closer to the standing of
academic electrical engineering and computer science, whose status is
that of secondary beneficiaries of practical applications behind such
primary beneficiaries as Oracle and HP.  This connection with
practicality has not impeded theoretical computer science, which has
done quite well in the reflected glory of usefulness to the public at large.

The biggest risk to which this patent subjects category theory is that
if it fails to benefit its assignee, Kestrel, for want of interest in
its methods, then that outcome might be used in arguments against
raising the funding level for category theory research.  Funding might
then stay at the low level appropriate for truly pure mathematics, pure
in Hardy's sense of having no practical application, just enough to
support the most talented contributors to the subject while encouraging
the rest to apply their enthusiasm for mathematics to areas of greater
public benefit.

Mathematicians wanting to prevent business people from applying
mathematical results to practical problems via the usual protocols of
the business world (e.g. patents) for fear it will somehow impede or
impurify mathematics are like parents wanting to prevent doctors from
disease-proofing their kids via the usual protocols of the medical world
(e.g. vaccination) for fear it will somehow cause autism or turn their
kids into needle-using junkies.  The arguments that there are better
protocols than patents or vaccination are not widely accepted today in
the respective professional communities currently using them, though of
course that sort of thing can change with the advent of new insights and
better methods.

Vaughan Pratt


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