No Subject

["Vladimir Z. Nuri" <vznuri@netcom.com>]

>I suppose that there is a predicate indecent_p(n), which is true if n
>represents something indecent, false otherwise. (Some implementation
>of such a predicate could be a police officer arresting you upon
>presentation of the number to him, yielding true. :-) ) Such numbers
>may be called "Indecent Numbers", their "posession", "transfer",
>etc. be banned.

interesting idea. but I suspect you could prove there is no such 
function indecent_p(n) by other ideas you present in your article,
namely diagonalization and the use of encryption schemes.

rough sketch: it would be easy to create an "encryption" or
encoding scheme that maps 'n' for which indecent_p(n) is 
true onto 'm' for which indecent_p(m)
is false, and vice versa, for sufficiently complex indecent_p(n)
("insufficiently complex" versions of the function would be e.g.
versions that are true or false for only a finite number of cases,
or other situations).

hence you get a contradiction.

this all is under the heading of "steganography" of course. it seems
to me some interesting basic theorems in steganography such as the
above are waiting to be explored, in the way that Shannon explored
some of the very basic information theory areas without really giving
a lot of practical results.

in fact what annoys me about people is that they talk about various
functions as if they can even exist, when it is transparently obvious they
cannot; another common example here:

- "detect_encryption(n)" where n is a message. endlessly assumed in
various messages here on the list of people who fear a police state.

- "detect_randomness(n)" where n is a sequence. presumably used
by a police state to outlaw random strings. (similar to above)

this ties in with another point I like to make in this line of thinking:
Shakespeare once said, "there is nothing good or evil, but thinking makes
it so". I would say, "there are no tyrannical laws, but thinking makes
it so". it seems to me a lot of people here do the hard intellectual labor
of trying to figure out/anticipate how a police state could exist in the 
20th century of cyberspace. be careful what you think about, because
thinking can make it so.