Re: patenting colimits?

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

hi.

On Mon, 25 May 2009, Toby Bartels wrote:
> Ronnie Brown wrote:
[snip]
>> it seems like patenting mathematics, and to be deplored
>> intensely.
>> [...]
> I trust that it was published in one of the cited journal articles.
>
> As (at least) one of the listed inventors is a reader of the list,
> we might hear the other side; I'd be interested.

yes, i stand guilty as accused: we patented colimits. but just the
*hereditary* ones. so if you compute 1+1, you don't owe me anything. but
if you compute 1+(1+0), then expect a letter from my lawyers, the same
ones representing MPAA, RIAA and elsevier.

but those 1s that you are computing with must be software specifications,
ie in the form "spec 1 endspec", or something like that...

in fact i prolly shouldn't be joking about this. patent laws are a deadly
serious symptom.

speaking of diseases, do you know that about 30% of human genome is
patented? most of the potential cancer and parkinson disease genes are
owned by a couple of companies. that means that if i want to test whether
i have some cancer-related gene, i have to go to a lab that has the
monopoly on testing that gene (since they rarely license to others). they
will charge me a monopoly price, and if i want to test 5 genes, i may have
to write to 5 different labs. if i want a second opinion about the test,
whoever gives it to me may be sued. and there is no second test.

the motivation for this statute is that it provides incentives for
research.

in contrast with the genes, mathematics cannot be patented, nor
copyrighted, even according to the current crazy laws. officially and
explicitly not. if you say in a patent application that you have this
extremely original result, which never occurred to anyone else, and you
would like to patent it --- they will reject it. the same with copyright:
if you try to copyright a theorem, it will not work: anyone can cite your
theorem without paying you.

*but* if you write a book, and present pythagora's theorem in it, you will
not only be able to copyright it, but it will actually be almost
impossible for you to distribute your book without copyright it, and
without selling the copyright to a publisher. so anyone who wants to use
your version of pythagoras' theorem has to ask your publisher's
permission.

patents are crazier than copyright --- but maybe not that much crazier.
you cannot patent mathematics, but you can patent "method and apparatus"
for a particular application of pythagoras' theorem. (they always call it
"method and apparatus".) you cannot patent modular exponentiation, nor the
conjecture that inverting it (ie computing the discrete logarithms) is
computationally unfeasible. but you can patent a method and apparatus to
share a public key by exchanging and multiplying two modular exponents.
the essence of your originality argument will rely upon the novel use of
the conjecture that the discrete logarithms are hard to compute, on which
the security of your system is based.

what i just described is the *diffie-hellman* patent of public key
cryptography. it may sound crazy to pure mathematicians, but there is very
little doubt that the diffie-hellman invention changed the world of
cryptography, networks, the web. our banks would work differently without
diffie-hellman. (ironically, it turned out that some british civil
servants working at GCHQ discovered the diffie-hellman discovery 9 years
before diffie and hellman, see http://jya.com/nsam-160.htm but the UK
governement classified it all, and even paid royalties for the
diffie-hellman patent.)

our colimits patent was, of course, not of comparable importance, although
the underlying math was perhaps slightly less obvious. i'll only comment
about it because toby asked. many people in software specification
community (starting with goguen and burstall) thought that colimits were a
good tool for composing sofware specifications. the objects of the
category where you are computing the colimits are theories in some formal
language, and the morphisms are the interpretations that map axioms to
theorems. many people studied that approach, and a couple of tools really
used it. but when you really start building software with such a tool, you
find that the method hampers software reuse and evolution: a colimit
composes your components by cooking them up into a big unreadable
specification. so you find yourself saving the diagram of your colimit all
the time, and trying to relate the content of the colimit spec with its
nodes. (which ironically repeats the first lesson about the colimits: the
colimit is not just the tip of the cocone, but the whole thing.)

anyway, instead of computing the colimits of specs and then building new
diagrams of the resulting unreadable specs to compute even more unreadable
(and unmodifiable!) specs as colimits, we wanted to build a category where
the objects would be diagrams of diagrams of diagrams... of specs, and the
morphisms would be such that each diagram (of diagrams...) would be a
colimit of itself, when externalized. that is what the requirement of a
non-destructive colimit operation amounts to.

what is patented is not that category, but the method to implement and use
it to build and maintain software specs. we did some of implementing and
using, and some of it was fun, but definitely not the shortest way to
building the kind of software that needed to be built.

i don't think that we published anything about this construction. the
patent description was written by the lawyer (a very bright woman, i think
with an MIT PhD, who now runs the world for google). some other things
that we didn't publish were perhaps closer to a mathematical result. but
the purpose of it all was to build software, not to publish mathematical
results.

we just patented it so that all those geneticists have to pay us some day,
or give us some free genetic testing in exchange for hereditary diagrams
;)

-- dusko



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