[s-c-h]

pi, e, √2 are thought to be normal [0], which would make them Disjunctive sequences [1]. This means that every finite string appears as a substring in them, including for example all Shakespeare works, and the ADN of every person [2].

In particular they contain this illegal prime number, and the gzipped and non-gzipped versions of this program in every programming language possible.

Does that mean that they may become illegal someday if they are proven to be normal?

[0] https://en.wikipedia.org/wiki/Normal_number

[1] https://en.wikipedia.org/wiki/Disjunctive_sequence

[2] http://sprott.physics.wisc.edu/pickover/pimatrix.html

(edited to add links)

[dTal]

Nah.

What does it mean to "contain" information?

These discussions often use an implicit definition "if you enumerate an infinite series of digits according to some rule, you will eventually generate any arbitrary string". But that'll never fly legally. Under this definition, the boring old system of counting up from 0 also "contains" every number, and in fact is a much more efficient system for doing so. Pickover's pi-based mysticism loses its magic a bit!

On the other hand, the practical, everyday sense is "meaningful information can be extracted, with an input of information very much smaller". Hard drive images "contain" files, requiring only a few dozen bytes to specify which one. Encrypted files likewise generally only require a few dozen bits to recover. This is much more legally relevant, as it allows the possessor of the "container" to act on its contents.

Pi does not qualify, as the index to any meaningful information in its digits will be far larger than the information itself. Writing "pi" on the back of my hand will not help me cheat on my Shakespeare exam. It's merely a highly inefficient coding scheme.

https://qntm.org/number

[wz1000]

> πfs is a revolutionary new file system that, instead of wasting space storing your data on your hard drive, stores your data in π!

https://github.com/philipl/pifs

[s-c-h]

Thanks for the reference. Even the github issues are fun to read. In particular this one is relevant here: PiFS installs large volumes of objectionable content and copyright violations (https://github.com/philipl/pifs/issues/2)

[Fargren]

You can easily iterate over all binary strings to generate your illegal number too. That way you don't need to rely on the normality of transcendental numbers. If you concatenate all base numbers in base 2, you even get a number that's normal to base 2. There's no proof that it's normal to most other bases, though.

[dilyevsky]

Not to mention there's a full archive of all tentacle porn ever produced in there.