340..partially solved ;)

[Quicktrader]

..but only partially. Here we got some solid statistic out of 3.2m letters..

http://tigger.uic.edu/~jleon/mcs425-s06 ... r_freq.pdf

indicating that the TT and LL combination is the most frequent one in english language. The '++' overall occurs three times in the 340 cipher, therefore - extrapolated to 10,000 - this is equal to a frequency of 88 per 10,000 letters. This is indicating that '+' is either representing the letter 'L' or the letter 'T', all this assuming a similar cipher method like the 408.

Selecting the usage of letters in the Zodiac letters (I took wikisource, copy paste, delete blanks) leads to an overall of approximately 16,602 letters Z had used. Among those, Z had used 'TT' about 61 times per 10,000 letters and 'LL' about 113 times per 10,000 letters. Both is 'similarly close' to the frequency (88 per 10,000) of '++' in the cipher. The letter 'EE' only occurs 41 times per 10,000 letters and therefore, like the other letters, might be ruled out. Even 'LL' and 'TT' should (statistically) occur only 56 times per 10,000, but in fact Z had used the '++' 88 times per 10,000, therefore 57% more often than expected.

So which one is representing the '+' symbol, the letter 'L' or the letter 'T'? We now must assume as there are two possibilities: '+' solely representing one letter or '+' being part of a sequence with more symbols representing one letter. I now make a bet: The '+' occurs about 7% in the 340 and we do know, from the 408, that in fact there have been letters being represented by single symbols as well as by sequences of symbols. So I just bet that the '+' is representing one letter without any other symbols representing it. If I loose my bet, the '+' should for sure represent the letter 'T'.

But I do bet otherwise, which is why I have a closer look on another statistic: How often does the '+' (not the '++') occur in the cipher? 24 times, which is about 7.06%. In any english text, the letter 'T' should occur about 9.25. Therefore '+' is being ruled out for two reasons: 'T' would occur quite seldom compared to a normal statistic text AND do we know that Z had used the '++' specifically more often (+57%) than any double letter combination normally would be.

But what about the letter 'L'? This should occcur about 4.14% in any english text (and is conform with the double letter frequency mentioned above). Combining this with our knowledge (!) that Z had used the double letter '++' about 57% more often than a normal english text would do (88 times vs. 56 times, based on 3,2m letters).

We do take this for granted and take the standard 'L' frequency and combine it with the fact that Z had used the '++' 57% (!) more frequently than any double letter would be expected to be used.

4.14 x 1.57 = 6.50%

Delivering us the expected frequency of the letter 'L' in Z's cipher text, this of course under the side condition that the double letter has been used 57% more often than normal.

In fact the '+' occurs 24 times in the cipher text, therefore with a frequency of 7.06%. Comparing those two figures, we end up with 7.06/6.50 = 1,09 telling me some things:

A.) Z had used a double letter combination 57% more often than expected (statistically significant)
B.) 'LL' and 'TT' are the only double letter combinations which therefore are potential candidates for '++'
C.) Considering A.) the only matching letter is 'L' because 'T' would lead to a frequency of 14.5% (9.25%x1.57) which is not suitable to the frequency of '+' (7.06%)
D.) Suitable in fact is the frequency of '+' (7.06%) compared to the frequency of 'L', still under the side condition of a more frequent double letter usage (6.50%).
E.) According to this, Z has used the letter 'L' only 1.09 times more often than a normal english text would do (9% deviation, which should absolutely be ok for a frequency of letters).
F.) All this considered under the assumption that '+' is solely representing one alphabetical letter.

So if my bet is right, '+' is representing the letter 'L'.

QT

http://scottbryce.com/cryptograms/stats.htm

[glurk]

QT-

I think that your post assigns a bit too much authority to normal distributions. Although it is a bit unpractical, Zodiac's 340 may not follow any standard allocation.
Just as an illustration, "Gadsby," a 1939 publication consisting of 50,000+ words actually omits what would normally turn up as a common sign in most writing. It isn't
too bad of a book, in fact. Also, "A Void," a short story from 1969 also has no application of it.

Both works prohibit a COMMON glyph. What is it that is missing?

A singular symbol, which is also not in this post. Until now.

E

-glurk

(Do I think that Zodiac could possibly constrain his writing, or try to mystify and blur things? Naturally!)

[Alanbenjy]

That has to be reply of the year!

[smithy]

It isn't. He can't spell "Gatsby".

[traveller1st]

He wasn't trying to.

http://en.wikipedia.org/wiki/Gadsby_(novel)

[Quicktrader]

It is in fact right that normal distributions should work occasionally, but not always. This is a vary statistic, but imo it is also obvious that '+', with 24 out of 340 letters, is a good match with the +57% showing up of 'L' as a twofold '++'. It is a crazy farrago...but as an adaption from 3,2m it is still solid and statistically significant, too.

Not using a symbol would not automatically modify any statistical data that much. Z's writing might comply - although a bit unusual - to any normal standard writing statistic, as wording will always do.

QT
(without E)

[smithy]

He wasn't trying to.
http://en.wikipedia.org/wiki/Gadsby_(novel)

Gotcha.

[traveller1st]

He wasn't trying to.
http://en.wikipedia.org/wiki/Gadsby_(novel)

Gotcha.

I bloody knew it. As soon as I'd hit send I thought....hold on a minute lol. Well it'll serve to avoid anyone else wondering.

[glurk]

Why so much confusion? Perhaps a correct web address that works might be better?

http://en.wikipedia.org/wiki/Gadsby_(novel)

Anyways, I wasn't trying to be a smart-ass. I just think that Zodiac was aware of character frequencies and had the power, competency and aptitude to construct
a message that he intended to fit into his greater aim or design. Character frequencies in short messages are just NOT the same as in extended ones!

One just cannot expect a short passage such as the Z340 to use the standard distribution that would be found in more protracted texts. I'm quite certain!

I am not sure, though (by any means) that Zodiac used this technique in the 340 cipher, but I do think he might have. It's within his capacity, I think.

I'm sorry about the appearance of the one common missing character in the wikipedia internet address above. It was mandatory!

-gurk

[Patinky]

I'll be glad when you all solve this cypher. I've developed a permanent headache from trying to understand what is being said.

Give me psychology any day.