The thorny issue of illegal numbers

If a number represents information which is forbidden by law for one to possess or distribute, that number is said to be illegal. By nature it is only possible to compose law that applies to a limited subset of reality. When it comes to prosecution for trafficking in illegal numbers, the application of murky laws to the idiosyncrasies of the real world inevitably leads to paradox that can only be resolved by additional law.

The most famous example of an illegal number was developed in 2001, a case in which the binary representation of a large prime number corresponded to a compressed version of C source code which implemented the DeCSS decryption algorithm. As this algorithm can be used to circumvent a DVD’s copy protection, the number used to generate the code was therefore deemed illegal.

The problem with labelling certain numbers as illegal is that not only can one invent situations where that number has a legitimate legal use, those situations can arise quite naturally, and furthermore even become common. The creator of the DeCSS numerical encoding scheme made precise use of that fact by choosing the algorithmic number in question to also be mathematically interesting of its own accord.

Some people might argue that holding, or even encoding, this information should not subject one to any particular laws since you just have recorded a number. Many jurisdictions would contest (and even rule) that any illegal string of code, image, or other data set that is represented as a number would make that number illegal. Regardless, considering the fact that there are many websites devoted to the cataloguing of top prime numbers in various forms, there would be significant likelihood that, at least for primes, such a number would already be published.

The video above, courtesy of mathematician James Grime, describes some instances where numbers may be of questionable legality. Others have already asked the question of whether or not numbers can be trademarked, copyrighted, or even patented. In some cases, like the numbers 737 and 747 for Boeing’s jets, the answer appears to be “yes,” at least for trademarks.

Trademarks can be valuable for society as a whole because they permit both praise and fault to be properly attributed. They are not generally meant to restrict use so much as ensure proper use. Unfortunately, as an ever-expanding range of property and idea comes to be represented in digital form – which in turn can be represented both algorithmically and numerically – exposure of the innocent to legal zealotry will increase.

Fair use for numbers

In seeking some kind of fair use for numbers, it is interesting to speculate whether some form of meta-law needs to be developed to deal with the potential abundance of derivable violation. Such laws would not necessarily just be laws about laws, but rather principles which can be universally applied to different sub-fields of law without defining particulars.

For example, in cases where there is doubt about the legality of a certain number found in someone’s possession, meta-law might dictate how that doubt is to be shared between parties on either side. One simple idea might be a meta-law stating that the right to profit can not infringe on the rights of individual privacy.

While that may seem like a pretty obvious idea, the right to profit now routinely intercedes on privacy. Obviously, privacy rights would not sit at the top of the chain, in fact in a civil society they may need to take a backseat to the even more basic rights of freedom. In this case, for example, forgoing full rights to privacy by permitting random home inspections would help countless children now living under horrendous conditions of abuse or kidnap, at the price of a little inconvenience to many. While this scenario seems far afield from that of illegal numbers, balancing privacy with the nature of the offence suggests a beginning towards sensibly gauging the gravity and penalty of any number fraud.

Bearing directly on the issue of privacy, just this week over in the US the Supreme Court recently upheld the rights of Monsanto to patent seeds (genetic information, as opposed to numeric, but information nonetheless). The seed can’t always be simply recognised as illegal, but rather may need to be sequenced into a code, and sharing the code is illegal as would be growing it without an agreement with Monsanto. This decision effectively makes the farmers who use the seeds renters, rather than owners, of the seeds they plant.

If it is possible to patent naturally occurring individual human genes, like BRAC1, then patenting painstakingly engineered sets of genes is not that unreasonable. The problem is that ensuring the right to profit, in this case, will soon mean intruding on a farmer’s property to do inspections, casting judgement on the origin of seeds that may have blown in from a neighbour, and using public funds for both enforcement and prosecution.

When it is a person that bears the result of a fault-prone binary decision of guilt, unfair penalty to that person should be seen as the greater evil when compared to a lack of fair judgement given to an entity. More generally, we might further say that distribution of a small individual penalty (or reward) to a large group of people, especially in the face of doubt, should be seen as less significant than a large judgement to an individual. A related aspect to the Monsanto case is the common perversion of seeking to popularise a judgement by making a disproportionate example of the individual.

Defining the legality of numbers and data will likely continue to become increasingly important as more of our lives are subsumed by computers. Keeping the human, and the individual, at the forefront of decisions regarding fair use is critical to making proper judgements in the best interests of society going forward.