Re: FINAL QUESTION: your natlangs. Sorry this is the last of the survey...

Tommie Powell wrote:

> In 1962, some mathematician at NSA "proved" that a "zero-entropy" language
> would be theoretically possible.  In other words, if you had such a
> language, then, no matter how you jumbled up a sentence's symbols, the
> result would be some other sentence that made sense.
Actually, the proof's trivial.  Here's a sketch:

1) Start with a generator that generates all possible English-oid
random strings (those using only a-z and space with terminal
period, question mark, or exclamation mark) in increasing order of
length.  You may want to chop off this process when you get beyond
sentences that take 100 years to say.

2) Apply a filter to this that passes all and only those outputs
that are actually sensible English sentences.  This assumes that
there really is an effective procedure for detecting sense in an
English sentence, AFAIK an unresolved question but one which intuitively
seems reasonable.

3) Assign each of these a sequentially increasing integer.

The result is zero-entropy, at least at the sentence level: there are
a countable infinity of grammatical and sensible English sentences,
and scrambling the digits of an integer will always give another
integer.

Once you want to make discourse, however, there will be at least some
return of entropy:  "Passengers will please refrain from using
restrooms while the train is in the station" is not really likely
to be followed by "Darling, I love you!"  However, that degree
of entropy is probably insufficient for cryptanalysis.

> There's no such thing as an unbreakable code [...].
Well, there is one-time encryption, which depends on destroying the
*usable* entropy by mixing in 1 bit of truly random 1key for every bit
of message.

--
John Cowan      http://www.ccil.org/~cowan              cowan@ccil.org
        You tollerday donsk?  N.  You tolkatiff scowegian?  Nn.
        You spigotty anglease?  Nnn.  You phonio saxo?  Nnnn.
                Clear all so!  'Tis a Jute.... (Finnegans Wake 16.5)