Math Mutation 60: Drop That Number Or We'll Shoot!
Would it surprise you to learn that there are certain situations
in which writing down a mathematical theorem, or even a particular
number, can be a violation of the law? This odd situation results
from the interactions between copyrights, trade secrets, and American
law in the modern world. Under the U.S. Digital Millenium Copyright
Act, or DMCA, originally passed in 1998, virtually any attempt to
circumvent protection of copywrighted works, including figuring out
any encryption methods, is against the law. Many researchers were
unhappy about this, as research into encryption is a vital and active
area of modern mathematics, and under some interpretations, much of it
could be considered illegal. Probably the most famous specific
controversy that came up related to this law was the publication of
the DeCSS encryption algorithm, which was used to encode video DVD
files.
David Tourtesky, professor of computer science at Carnegie Mellon,
made a strong case that the DeCSS algorithm belongs to the realm of
mathematics and of free speech, and should not in itself be considered
an illegal device. To support his case, he came up with a really
silly gallery of different ways of expressing the DeCSS algorithm.
Here are a few:
The most basic example is the original computer program that
directly decodes DVDs, obviously the most legally shaky case.
Next there is a computer program written in what is known as a
"functional language". A functional language is essentially a
computer program that doubles as the statement of a mathematical
theorem. Can it really still be illegal?
Then, taking it a step further, the gallery contains a pure
mathematical theorem proving that DVDs can be decoded. The decryption
algorithm is described within the proof, without providing actual
computer code to do so. Can it really still be illegal?
Moving off in an artistic direction, the gallery also contains a
haiku poem which states the essential properties of the algorithm, in
carefully structures syllables as prescribed by ancient Japanese
artistic techniques. Along similar lines, there is a dramatic audio
reading of the algorithm, including musical and square-dance variants.
Can you be arrested for dancing to the tune of an illegal theorem?
Then there is an artificially constructed DNA sequence that encodes
the algorithm. With recent technological developments, maybe we could
actually build an illegal bacterium!
Another example is the board from a game of "minesweeper", in which
the patterns of mines describe the DeCSS algorithm. I guess as long
as you get blown up before uncovering all the mines, you won't violate
the law.
And what I find the funniest is an encoding of the algorithm as a
single prime number. This should not be a surprise to those of you
who listened to podcast 25, where we discussed how Godel proved his
famous theroem by converting arbitrary statements into numbers. But
could this be the first case in history of a particular number being
illegal? Can you go to jail for numerical possession?
You can look at the link in the show notes to see the full
gallery. It's pretty fun to come up with lists like this, but I do
think Touretzky was glossing over a serious issue. I'm not a lawyer,
but if you take his arguments to an extreme, it seems to me like you
have to throw away all concepts of copywright, trademark, and patent.
I think we do owe a lot of our modern technology to the fact that
people can come up with ideas and expect they will get some kind of
legal protection; are we really ready to toss all that out in order to
regain full mathematical consistency?
In the end, Touretzky didn't convince the judge, and the DMCA
remained in effect. So maybe we do have to accept a world in which
every once in a while, math really can be illegal. But don't worry--
if I end up in jail, I promise to find a way to keep this podcast
going.
And this has been your math mutation for today.
References:
DMCA at Wikipedia
IEEE Spectrum article on
the DMCA
David
Touretzky's gallery of DeCSS descramblers