Pivots and repeating reversible trigrams

[smithy Profile]

Trav, it IS a hoot! And I want to see "how the batwing explains why the taxi was parked the way it was" desperately.
See, I don't know why you'd choose 45 degree slants for connecting your characters, or what it shows, if I'm honest. It must show something. It does show there's a lot of characters in the 340 and you can join them up a lot but I wouldn't know what on earth to do with that information at all. I've never seen anyone else present that info though, so all I can do is say "Respect!" And go have another think.
Does it show this is the best way to connect them up and it doesn't work and the stats aren't as good as if you do it another way? Ahhhh... well..... lol

To me the gapped n-grams may reveal more about the internal structure as a whole (such as ciphertext orientation), rather than specifics about words that fit. This is because there are still too many possibilities on word boundaries within the repeated gapped n-grams to make a conclusion.

I'm with you, had considered that. Also, I suppose a repeat A_B_C could be a transposed ABC__.

I don't know what this means either, yes they are words/no they aren't/maybe....
Also, if there is transposition, and that transposition is ordered, logical and alters the original text in a single direction (?) or multiple ordered directions (?) then it's a useable fact huh? Or is it?
It doesn't help me with the internal structure, I'm trying to say, since I can't make the jump from this to any kind of ciphertext orientation.

"Repeated sequences (any direction)" does that, but only for n-grams where n is greater than 2. This is easy to change, though.

Let me know when you're done jaw-jakin' with AK and get to this.

Made me laugh.

Bear in mind I also have no idea what I'm doing except documenting simple patterns. It could all be a load of 'gnupung' for all I know.

It's all good. The cipher-wits haven't solved it yet, maybe it's up to us half-wits.

It's all really good and who are the cipher-wits anyway?!
IMHO anything that throws up new questions and new ways to look at the 340 is great, awesome, interesting, entertaining and, umm, great.

Jazzerman, my head just exploded. It made a small squelching noise.

[Jazzerman Profile]

Jazzerman, my head just exploded. It made a small squelching noise.

LOL ...It's never the exploding heads that bother me, but the squelching sound they make afterward.

I figure we always need to keep in mind that these type of patterns seem to naturally show up in cryptography, as Doranchak himself has noted before. I don't like to jump to conclusions, but I'm going to go out on a limb here and say that pivots and symmetry (a topic I brought up) are not going to lead anywhere. However, I've been proven wrong before, and in the case of the 340 I'd love to be proven wrong again.

[traveller1st Profile]

Trav, it IS a hoot! And I want to see "how the batwing explains why the taxi was parked the way it was" desperately.
See, I don't know why you'd choose 45 degree slants for connecting your characters, or what it shows, if I'm honest. It must show something.

The batwing made me do it. Seriously lol. With the way it was aligned the 1gap repeats lined up under it's 'feet' and that's how I first noticed them. Hey at the very least it maybe shows another commonality to the previous solvable cipher. I don't know if it must mean anything. As Jazzerman pointed out from his own look at these things it might just prove - it's a cipher of sorts. Which is a good solid start ha ha.

If you are wondering why the batwing even got near the 340 it's because I was looking at the halloween card and it struck me that the 3 signatures at the bottom may not have been signatures but symbols. The batwing on the envelope above the Z, the batwing on the card beside the Z and the crosshair. I just wondered if he trying to draw our attention to those 2 symbols and they do appear together on the 340 right at the bottom centre but not in the right order. They are the crosshair and then the Z reading from left to right. I decided to have a look at it and brought the batwing along for company

Unless I accidentally learn stuff from everyone here that thinks more logically about these things and with better knowledge then all of my posts regarding this subject matter will be, and always has been, in the vein of "does this mean anything?" - "No" - "Ok then" as opposed to "Look what I found".

Just above the crosshair in the bottom centre I see the word - BOYO - that's got to be important, do the math

[doranchak Profile Website]

OK, math can be kind of cool sometimes. Let's look at this again:



The question is: Given this cipher text, how often would we expect such patterns to occur naturally (by chance)?

Let's look at the symbol "B". It occurs 12 times in the 340-symbol cipher text. So, for any given position of the cipher text, there is a 12/340 = 3.5% chance for the symbol B to appear.

Now let's consider the diagonal repeat patterns. For any given pair of positions, the chance for B to appear in both positions of the pair is: 12/340 * 12/340 = 0.12%.

Now let's ask a more general question: For a given pair of positions, what are the odds for ANY symbol to appear in both positions of the pair? The calculation is: (Sum of (fi*fi))/(340*340), where fi is the # of occurrences of the i'th symbol. Here is the resulting arithmetic for all symbols: (5^2 + 2^2 + 2^2 + 7^2 + 5^2 + 6^2 + 24^2 + 5^2 + 6^2 + 3^2 + 3^2 + 9^2 + 2^2 + 6^2 + 7^2 + 3^2 + 3^2 + 4^2 + 4^2 + 2^2 + 3^2 + 6^2 + 4^2 + 1^2 + 2^2 + 12^2 + 5^2 + 4^2 + 3^2 + 10^2 + 6^2 + 4^2 + 4^2 + 7^2 + 6^2 + 7^2 + 5^2 + 10^2 + 3^2 + 8^2 + 4^2 + 5^2 + 5^2 + 6^2 + 6^2 + 2^2 + 4^2 + 4^2 + 6^2 + 3^2 + 3^2 + 10^2 + 5^2 + 4^2 + 2^2 + 5^2 + 7^2 + 11^2 + 2^2 + 4^2 + 5^2 + 9^2 + 10^2) / (340^2) = 2.228%

So, now we need to consider how many different pairs of positions to test. In the 340 cipher, there are 270 different diagonal pairs (with a one-symbol gap) in the "/" direction, and 270 in the "\" direction, for a total of 540 pairs. The explanation for 270 is:

A diagonal pair can only be formed for 18 of 20 rows.
A diagonal pair can only be formed for 15 of 17 columns.
15 * 18 = 270 possible pairs.

Therefore, the expected number of matching pairs should be: 540*0.02228 = 12.03 pairs. Trav identifies 13 pairs in his image. Pretty close, eh?

(someone should double check my math. if it's correct, then perhaps i can promote myself up from quarter-wit to half-wit.)

[entropy Profile]

This thread needs a "like" button for those of us from the facebook generation. I don't totally understand this newfangled cipherbabble but I like it, like it, yes I do.

[Wrench Profile]

(someone should double check my math. if it's correct, then perhaps i can promote myself up from quarter-wit to half-wit.)

I checked what I could, after all you've done for me, and got same results.

Now let's ask a more general question: For a given pair of positions, what are the odds for ANY symbol to appear in both positions of the pair? The calculation is: (Sum of (fi*fi))/(340*340), where fi is the # of occurrences of the i'th symbol. Here is the resulting arithmetic for all symbols: (5^2 + 2^2 + 2^2 + 7^2 + 5^2 + 6^2 + 24^2 + 5^2 + 6^2 + 3^2 + 3^2 + 9^2 + 2^2 + 6^2 + 7^2 + 3^2 + 3^2 + 4^2 + 4^2 + 2^2 + 3^2 + 6^2 + 4^2 + 1^2 + 2^2 + 12^2 + 5^2 + 4^2 + 3^2 + 10^2 + 6^2 + 4^2 + 4^2 + 7^2 + 6^2 + 7^2 + 5^2 + 10^2 + 3^2 + 8^2 + 4^2 + 5^2 + 5^2 + 6^2 + 6^2 + 2^2 + 4^2 + 4^2 + 6^2 + 3^2 + 3^2 + 10^2 + 5^2 + 4^2 + 2^2 + 5^2 + 7^2 + 11^2 + 2^2 + 4^2 + 5^2 + 9^2 + 10^2) / (340^2) = 2.228%

But this is going to require at least a 3/4 wit. Smithy?

Travs patterns are interesting. I spent at least a year looking at the 340 before I saw the pivots, and even then someone had to tell me. Maybe there are still patterns to find that will reveal something.

[smithy Profile]

But this is going to require at least a 3/4 wit. Smithy?

Ha ha! Flatterer! You're wrong by a number of 1/4's I think, but I can't calculate how many.
I'm happy to comfirm that D's talking about pairing 63 symbols, which seems pretty close - I counted them too.

[traveller1st Profile]

Maths is cool. Good work guys. I just wish the 1/64 of my brain that's reserved for it wasn't broken. I know you're all waiting for me to ask this so I can be graded on the witometer but what's it mean? lol.

I've got as far as understanding that statistically they are probably supposed to be there and not unusual - is that right? If that is the case can that tell us anything about it as a cipher as opposed to a bunch of symbols of a certain number?

Excuse the naive questions but the glue has gone to my head from trying to make the batwing into a pair of clip on sunglasses.

[doranchak Profile Website]

I interpret the results to mean that the diagonal patterns are not statistically significant, because they arise so easily from chance. If we randomly shuffled the cipher text, those diagonal patterns would probably appear often enough to suggest that no significance can be placed on their appearance.

I did a similar computation for the 408. There are 660 possible pairs (2 directions * 22 rows * 15 columns) that we can test for matching symbols. So, the expected number of matches is estimated by: 660 * (5^2 + 10^2 + 11^2 + 4^2 + 8^2 + 8^2 + 6^2 + 8^2 + 8^2 + 3^2 + 8^2 + 14^2 + 7^2 + 6^2 + 8^2 + 12^2 + 6^2 + 9^2 + 6^2 + 7^2 + 8^2 + 11^2 + 6^2 + 5^2 + 8^2 + 8^2 + 6^2 + 7^2 + 11^2 + 5^2 + 12^2 + 6^2 + 7^2 + 10^2 + 9^2 + 9^2 + 9^2 + 10^2 + 8^2 + 5^2 + 6^2 + 8^2 + 6^2 + 6^2 + 10^2 + 3^2 + 1^2 + 9^2 + 5^2 + 6^2 + 16^2 + 7^2 + 7^2 + 4^2) / (408^2) = 14 pairs.

The 408 actually has 19 pairs, so the estimate is off a bit. Still, the end result is that we expect a healthy dose of chance occurrences of these kinds of patterns.

[traveller1st Profile]

Ok gotcha now. Thanks for explaining.

I had more stuff basically extrapolating out from those. I had put a post together when I just got the feeling that it was going to be more of the same. I had started to look at vertical matches with gaps and then gaps but with a pivot point. Whilst they were interesting patterns I couldn't help but feel they were just that, patterns. Turns out it might not be a complete waste though.

I decided to go back and start from scratch with the pivots themselves. I was wondering where they led. By that I mean what else was on the same axis as them so I mapped it. Now I don't know if this is because I'm still working in diagonals but it kinda looks like a lot of stuff is on the same axis as them. By a lot of stuff I mean matching symbols with gaps 1-8 on the diagonals, matching symbols with a non matching pivot point and a gap of 2 x 4 rotations and matching symbols with gaps 1-4 on the vertical.

I'm aware that the mapped out axis cover quite a bit of the cipher but the overall clustering appears to follow that 'X' shape. It may just be a map of how the pivots affect diagonal symmetry within the cipher? Nooooooo idea what it means, if anything.

pivots-axis.jpg [ 222.24 KiB | Viewed 248 times ]