information theory

suicidal and transforming numbers

People keep telling me that information wants to be free.  I get the point, but I get some of the problems with the concept too.  Hereʼs another one that just occurred to me:

Alan Turing pointed out that there exist numbers which, when entered into appropriate processing devices, will rewrite themselves.  This (the number, rather than the device) is a Turing Machine.

Amongst the consequences of this is that there exists a class of numbers which will not only slightly rewrite themselves, but actually completely erase themselves (again, if entered into the appropriate device).

Not only completely erase themselves (because we normally understand erasure as writing an arbitrarily long sequence of zeroes) but pseudo-randomly (assuming no external input of genuinely random numbers is used as part of the device) overwrite until no retrieval technique can realistically recover the original Turing Machine from the storage medium.  We could of course argue about the implications of incomplete erasure or incomplete entropy (entropy as a more real form of erasure than the arguably meaningful long-zero) but itʼs not what Iʼm getting at.

I propose that there exist numbers – or other types of information representable as numbers – which far from wishing to be free, wish to cease to exist.  (For any common value of “wish”.)  Suicidal numbers, you might say.

Subscribe to RSS - information theory