Forbidden Numbers

* There are forbidden things
* Things can be represented with numbers

Therefore there are forbidden numbers.

Oh, they are big. 3, 12, 45... are definitively authorized numbers.
Forbidden numbers can have millions of digits.
Lets take an example.
Suppose it is illegal to like ice cream.

Now consider the following (awful) script.
f="I love ice cream";
(echo -n "ibase=16;"; echo -n "$f"|hexdump -C|cut -c 11-58|sed "s/ //g"\
|tr abcdef ABCDEF|while read i ; do echo -n "$i"; done; echo )|bc

(the question "wtf is that ?" is left as an exercise for the reader)

This number "codes" the illegal string 'I love ice cream'.
If you imagine that the magnetic states of each bit on a hard drive are
0 or 1, the string *is* physically the number computed above.
Hey, so wouldn't this one be a forbidden number ?

Now, the funny side.

Something like
dd if=/dev/random of=rnd.tar.bz2 bs=1024k count=16
creates a file with a pseudo-random content.
So it could be a forbidden one.

by Little Neo, 2004

Addendum (2007) :
Other kinds of numbers may pretend to the honorific title of forbidden numbers : keys of security systems. In the context of the protection of author's rights set up by the audiovisual industry, CSS (Content Scrambling System, to encrypt DVDs) keys, or the HD-DVD processing key are illegal numbers ; in the US their divulgation violates the DMCA (Digital Millenium Copyright Act). A few years ago, Phil Carmody discovered an illegal prime number coding a particular executable on a specific architecture. The banking world uses asymetric schemes for electronic transactions, and the associated private keys are, finally, only numbers ; whose abstract character doesn't take out their value !