Some thoughts on the possibility or well-definedness of banning specific (indecent?) contents on the net (or elsewhere): 1) All contents (files) can be seen as natural numbers. (Use your favourite encoding function.) 2) 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. 3) Every natural number n can be perceived as the encryption of every other one m (including itself) by some function enc. n = enc(m). (Proof by cardinality) Examples: Trivial enc: "If the number is n, return m." Not so trivial enc: "Take m as a one time pad to encrypt n." 4) As a consequence, every natural number can be perceived as the encryption of an Indecent Number, hence should be banned, shouldn't it? 5) The decimal representation of any irrational number (e.g. pi, e) contains the decimal representation of every natural number somewhere. (Proof by diagonalization.) Hence the algorithm for creating this decimal representation should be banned, too, shoudn't it? 6) Finally I hope this shows what great an achievement to legislation and jurisdiction such banning might become, once established. This creates a universal crime (or vice?), everybody is guilty of automatically without the tedious procedure of seeking evidence. (maybe those not knowing about numbers at all be exempt?) Virtually Yours, Rudi Raith (raith@feilmeier.de)
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.
The decimal representation of any irrational number (e.g. pi, e) contains the decimal representation of every natural number somewhere. (Proof by diagonalization.) What you say here isn't quite true. The number with decimal rep 0.10100100000010000000000000000000000001.... where the number of zero's is going 1!, 2!, 3!, 4!, ... is transcendatal, and hence irrational, but clearly doesn't contain
the decimal representation of every natural number. i'm sure the above fact is believed about e, pi & other such ``important transcendentals'' - i can't recall if there is a proof or how it goes. diagonalization is used to prove that there are uncountably many irrationals. if you want to argue the ludicrosity of trying to ban certain numbers, just consider the function f(n) = n + 1. Iterating this function yields all natural numbers, so the increment operation should clearly be banned. I'm not sure how much programming you can do without increment. - robbie -- ---------------------------------------------------------------------- robbie gates | it's not a religion, it's just a technique. apprentice algebraist | it's just a way of making you speak. pgp key available | - "destination", the church.
participants (3)
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Robbie Gates -
Rudi Raith -
Vladimir Z. Nuri