Re: The Mathematics of Crankery

[reeds@xxxxxxxxxxxxxxxx (Jim Reeds)]

What Dennis is asking is very close to the idea of  the
"unicity distance" in Claude Shannon's 1949 paper
"Communication Theory of Secrecy Systems", refered to by
Friedman in his "Shakespearean Ciphers Examined", page 22.
Wish I had time to expound futher.  It's discussed in
elementary information theory textbooks and in crypto books
written by people with an information theory bent.  There
are a few papers on the subject in "Cryptologia", and one
by Martin Hellman in the IEEE IT journal in about 1978.
I am very fond of the treatement in a little MIT press paperback
by Gordon Raisbeck, published in the early 1960s.

On Sep 18, 22:35, Dennis wrote:

> Subject: The Mathematics of Crankery
> 	Here's something I've long wondered about.  We know
> that if you have a decipherment system with enough
> knobs to twiddle and/or an unknown text that is short
> enough, you can read anything into anything.  Typically
> such bogus systems are exposed as bogus by reduction to
> absurdity.  Thus Friedmann used the Shakespearean
> ciphers to read that he, William Friedmann, had written
> Shakespeare's plays himself.  The detractors of the
> "Bible Code" used that system to read prophecies of
> assassinations of world leaders into "Moby Dick".
> 
> 	I wonder if there is some rigorous mathematical system
> to disprove such systems.  I think that the statistical
> concept of "degrees of freedom" is involved, but I'm
> not a good enough mathematician to carry it further.  
> 
> 	Some systems are loose enough to read things into a
> text of any size, no matter how large.  Edo Nyland's
> system may be an example of this.  
> 
> 	Some systems read isolated snippets of intelligible
> text in a large text.  The Bible Code is an example of
> this.  
> 
> 	Other systems only work on short unknown texts.  The
> Phaistos Disk is a very short text; therefore many
> systems can read intelligible text into it, and many of
> these systems would fail on a longer sample of Phaistos
> Disk text.  
> 
> 	So.  Could we find the degrees of freedom in a
> decipherment scheme, the degrees of freedom in the
> ciphertext, and prove whether the two taken together
> constitute a valid or a bogus decipherment system?
> 
> Dennis
>-- End of excerpt from Dennis



-- 
Jim Reeds, AT&T Labs - Research
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