Results and Explanation of Probability Analysis

Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 2:07 pm

Aquiman asked that I get this started by posting the charts and basic info. He will chime in soon with his thoughts. He is still doing analysis on this, and looking at other codes. Remember, he started this as someone who thought that the Kite - Wilks work on the codes was likely wrong, and he thought a probability analysis would prove that. So, I think, as someone who is cautious and careful by nature, and likes hard evidence, he is still processing what this means, applying it to different codes and has not yet formed a final conclusion.

Even so the numbers in this first stage report are quite impressive, and totally refute one of the central beliefs of the critics, that "virtually any" letter string can produce the 18 letter name of Theodore J Kaczynski.

Aquiman has a masters degree in Applied Physics, and works at one of the top ten research universites in America, where among other things he does failure analysis using computers and probabilty/statistical models.

AQUIMAN:

Over the last several weeks, I attempted to perform a comprehensive analysis of AK's (et al) cipher theories. It turned out to be a very difficult task and I now hate math. What follows will, no doubt, be quite a boring read for most; however, I believe it may shed some light on how useful probability analysis can (or cannot) be in regards to proving or disproving theories. For those without a math background, I hope I've explained things well enough to understand probability analysis in general. For the math geeks (like myself), I hope I don't bore you... but at least you will be able to correct any mistakes I may have made along the way. Comments, criticisms, and suggestions are welcome. Be gentle.

*********

First, I want to discuss some basic probability and then delve into why this was not the typical probability exercise. Let’s take the name “Theodore J. Kazcynski.” For each of the 18 letters in his name, we have a bag filled with all 26 letters of the alphabet. If you reach into the first bag, the odds of pulling out the “T” are one in 26. Reaching into the second bag, the probability is again 1/26 that the “H” will be chosen. The overall probability that a “T” and an “H” will be chosen from the first and second bags respectively is 1/26 x 1/26 = 1/676. Someone choosing one letter from each bag, hoping to spell out the entire 18 letter name should expect that the odds are very thin; (1/26)^18 to be precise.

Let’s make the odds a little better. You can now choose one letter from each bag, but you don’t have tp choose the letters in “name order.” You can then rearrange them any way you like to try and spell the name. The number of possible arrangements of 18 different letters would be 18! (i.e., 18x17x16…x2x1). All the letter in THIS name, however, are not unique; there are two E’s, two O’s, and two K’s. Therefore, the number of unique arrangements is given by 18!/(2!x2!x2!). The overall probability then of choosing 18 letters (each from a different bag) and obtaining any one of those arrangements is (1/26)^18 x 18!/(2!x2!x2!).

This is where things begin to get tricky. AK, Kite, et al have proposed that you can use a Caesar shift (of -9, -6, -3, +3, +6, or +9) on each letter, essentially giving you six additional letters from each bag; not just any letters, but those within the constraints of the allowed shifts. The difficulty now lies in determining the number of permutations of 18 sets of seven letters, several of which may be duplicated between sets.

The total number of arrangements when choosing one of seven letters from each of the 18 sets is given by 7^18; however, they are not all unique. Many arrangements are duplicates, not just because of the three pairs of duplicate letters in the name, but also because of the Caesar shifts. Take the letters “H” and “E” for example. With Caesar shifts, they form the following sets: {Q, N, K, H, E, B, Y} and {N, K, H, E, B, Y, V}. There are six duplicates just within those two sets. Eighteen sets will share many more.

A “closed-form” mathematical solution to this problem is not readily apparent (and likely does not exist). Therefore, a brute-force computer program was developed to determine the number of unique arrangements and corresponding probability of obtaining at least one of those arrangements. For 18 letters with Caesar shifts, the number of possible arrangements borders on infinity. To obtain a “true” probability for the proposed solution of 18 letters, it would literally take years to run all the permutations, even if I had the computing power; my computer could only handle nine letters with Caesar shifts. The results of the analysis of two nine letter sets are shown below.


Probability Analysis For Obtaining THEODOREJ and KACZYNSKI in a Random 9 Letter Section of Code.jpg
Probability Analysis For Obtaining THEODOREJ and KACZYNSKI in a Random 9 Letter Section of Code.jpg (91.71 KiB) Viewed 7193 times


Probability Analysis THEODOREJ Part One.jpg
Probability Analysis THEODOREJ Part One.jpg (34.48 KiB) Viewed 7184 times


Probability Analysis THEODOREJ Part Two.jpg
Probability Analysis THEODOREJ Part Two.jpg (26.13 KiB) Viewed 7222 times
Last edited by akwilks on Tue May 10, 2011 3:28 pm, edited 1 time in total.
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Re: Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 2:12 pm

Probability Analysis KACZYNSKI Part One.jpg
Probability Analysis KACZYNSKI Part One.jpg (34.3 KiB) Viewed 7214 times


Probability Analysis KACZYNSKI Part Two.jpg
Probability Analysis KACZYNSKI Part Two.jpg (26.12 KiB) Viewed 7198 times


I could only give an estimate as to what the outcome might be for the full 18 letter set, based on the trends of two subsets of nine letters. I can theorize that the general trend would continue downward (as I extend a trend line past nine letters), falling to maybe 1% or so. I'm sure it would bounce around a bit on the way as seen in the two corresponding graphs, but likely be small in the end. Now, if the final 18 were something like ODEHTJROENKZAIKSCY, where THEODORE and KAZCYNSKI were in separate nine letter groupings, then I'm allowed to multiply the two probabilities together to get 0.176%. Otherwise, I can only hazard a guess at this time. I would not theorize that the probability is going to rise substantially (if it rose at all) from nine to 18 letters anyway. So <5% is a pretty good bet.

For the sake of argument, let’s say the probability is 1%. What does this really mean? Well, it means that out of a near infinite number of unique arrangements, 1% of them can form the name “Theodore J. Kazcynski.” This will be in the neighborhood of 3x10^23 possibilities (a rough guess), infinity in and of itself. So while I can pat myself on the back for a valiant effort to “prove” something, I’m not sure I was able to prove anything one way or another; there are just too many variables, too many possibilities. The one true result of this analysis is that you cannot obtain any name out of any set of code when using Caesar shifts and anagramming.

I do applaud AK’s efforts, unsurpassed dedication, and pursuit of the truth. There are many other reasons why TJK should not be dismissed as a suspect; however, I’m not sure the results here do much to support the cipher theory. AK has additional suggestions, which I will look at as time permits. They are good suggestions that may be able to substantially narrow down the possibilities as to whether or not TJK authored these ciphers. I encourage AK and others to uncover all possibilities so we can get that much closer to the truth. I’m keeping an open mind and will help if I’m able. If I have not explained these results well enough, please ask and I’ll do my best to clear things up.
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Re: Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 2:20 pm

Aquiman -

Thanks again for taking the time to do this work. I think it is an important step in the right direction, perhaps to be followed up by more steps from you, me or someone else who takes the ball and moves it further.

The code work by Zander Kite and myself, often assisted by Doug Oswell and others, was dismissed by most of the posters at ZodiacKillerFacts. The primary reason was the majority of critics said that the Caesar Code method produced so many letters, and thus names, that the discovery of the 18 letter TJK name was totally insignificant. Many posters told me that ANY 18 letters string when Caesar shifted would likely produce the TJK name, thus a "100%" probability"; others said the odds of the TJK name appearing by chance in any 18 letter string were "65% or better", "more the 50%" or "about 50%". And thus, the appearance of the name was not significant. I said that the work of Kite and myself showed that it was not very likely to occur, and that the odds of the TJK name appearing by chance were probably 10% or less, and indeed possibly as low as 5% or less.

Well, we now have for the first time the results of an independent computer study done by a qualified professional who was skeptical of the work, and it shows that the odds are about 3% for "THEODOREJ" to appear, 5% for "KACZYNSKI" to appear and perhaps 1% or less for both to appear. In my opinion, based on what the critics said before and what Kite and I said before, their predictions and my predictions, this is total vindication for me and proof that I was right, and it won't make any difference at all. The people who didn't believe in the code work, the majority will still not believe in it. Doesn't matter if it is 5%, 1% or 1/10 of 1%!

For those 25 to 30 persons who do think my code work was likely correct, now you know you weren't wrong, and hopefully this work by Aqui will encourage us to keep digging - not just on the code, but on the handwriting, the MO, the timeline, the psychology and everything else! And I will keep making FOIA requests and appeals.

The FBI Code Unit, Cal DOJ and SFPD will eventually see these results when they are final, and if they make a difference to them, perhaps there is hope.

But as you see even Aqui thinks that multiplicty of possible letter combinations and possible names means (in his opinion, I strongly disagree) that even a very low probability result like 3% carries little water. As I said before, using the Caesar Code method, Zodiac didn't just hide his needle of a name in haystack - he hid it in a stack of needles. He didn't want to get caught - yet he wanted his name and legacy in the codes. He accomplished both. Zodiac wins again.

For the people that are interested, and for Aqui to consider, here are how I apply his results to the codes, and what I think they mean.

***************

Probability Analysis For Obtaining THEODOREJ and KACZYNSKI in a Random 9 Letter Section of Code.jpg
Probability Analysis For Obtaining THEODOREJ and KACZYNSKI in a Random 9 Letter Section of Code.jpg (91.71 KiB) Viewed 7171 times


***************

TO SOLVE THE ZODIAC "MY NAME IS..." CODE:

I use the same basic Caesar Code shift system with the 0-3-6-9 shift values as in the Map Code and 18 unsolved.

A 13 symbol code is way too short to devise a solvable entirely new code key, so it is highly likely Zodiac mostly used the existing Harden Key. To start the first stage translation of symbols that we saw in the first code, I use all Harden Key, with the exception of "E" I solve as a "C" - because we already have two "E" 's, and in Harden a backwards "E" does translate as a "C". I cannot create the cross circle Zodiac symbol on my computer so it is represented here as a "+".

But what about symbols that did not appear in the first code, thus no Harden translation is available? Here I solve the anchor symbol (Aries) (represented below by a "^") as an "O", based on the fact that a very similar symbol, just with a short line on top, was solved as an "O" by the Harden's, and I solved the same symbol without the short line on top as an "O" in the Mt. Diablo Map Code, which appears to have been correct. I solve the three circled "8" ' s, symbols for Taurus, (represented below by "8" 's) as a "T", primarily by conventional ETA frequency analysis, as "T" is the second most used letter in the English language and we already have two "E" 's.

So we have 8 symbols translated by Harden Code, 2 symbols based on Harden Key and 3 solved by new analysis.



Code : A E N + 8 K 8 M 8 ^ N A M

Trans: W C E D T S T H T O E W H

Chart:

F L N M C B C Q C X N F Q
C I K J . Z Y Z N Z U K C N
Z F H G W V W K W R H Z K

W C E D T S T H T O E W H

T Z B A Q P Q E Q L B T E
Q W Y X N M N B N I Y Q B
N T V U K J K Y K F V N Y


6 6 6 3 9 0 6 0 0 0 0 9 9
C I K A K S Z H T O E N Y


Once again we have "666", as well as "0000" and "99".

Solution:

T H E O K A C Z Y N S K I
0 0 0 0 . 9 3 6 6 9 9 0 6 6


When the name is put together, we see that "THEO" is produced by shift values of "0000", which seems to be intended, and highly unlikely that it would arise by chance. We do have THEO continuous, with anagramming but no actual Caesar shift needed. And KACZ continuous.

Based on the work of Aqui, I think we can say that there is a 0.069 chance, or 6.9% chance, of getting THEO. And 0.075 chance, or 7.5% chance of getting KACZ. To get BOTH, with THEO and KACZ continuous, the chances are 0.069 x 0.075 = 0.005, or "0.5%" or "One Half Of One Percent".

Aqui - and others - does that seem to be about right?

If so, what might that mean? Wouldn't a chance result of only 0.5% be by definition significant, as it implies a 99.5% chance that the name WAS INTENTIONALLY PLACED? Do I make an error? Or is just that the multiplicity of possible names from a Caesar Code renders ANY result meaningless to many persons?


***************

ZODIAC 340 Code

I would also be very much interested to see what Aqui and others think about my proposed 340 solution. I don't know if you can subject that to a probability and/or computer analysis. There are three stages to it. There is the actual proposed first stage solution - HERCEAN B I GIVE THEM HELL TOO THEO SEE A NAME THOSE FOOLSHALL SEE; then the words that appear vertically, backwards and diagonally like GAME, LIST, BOMBS, DUEL, LEASH, BARS; then the Caesar Code 0-3-6-9 application, just like in the Unsolved 18, that produces KACZYNSKI between THEO and SEE A NAME.

There are no cheats in this solution. Every one symbol translates to one letter. When you solve the first four lines, a lot of the rest of the code is filled in. And by the time you solve line eight, most of the rest of the code is filled in. The code solution provides clear English langauge words and phrases, and key Zodiac concepts and themes.

FOR THE PURPOSES OF THIS PROBABILITY ANALYSIS ONLY, I WOULD ASK AQUI AND OTHERS TO ACCEPT (JUST FOR THE MOMENT) THAT THE PROPOSED FIRST STAGE SOLUTION IS CORRECT, OR AT LEAST POSSIBLY CORRECT.


Zodiac 340 Code Solution 1986 Graysmith.jpg
Zodiac 340 Code Solution 1986 Graysmith.jpg (55.89 KiB) Viewed 7166 times



Don and Bettye Harden, using their thoughts and analysis of what Zodiac would likely say, correctly guessed the opening line of the Zodiac 408 Code as "I like killing". That provided the key to solving the rest of the 408 code. And so it is the case here as well with the 340. The opening line provides the key to solving the code.

Here the opening line, perhaps inspired by Jack the Ripper's "MR. LUSK FROM HELL" opening on a letter, says:

HERB CAEN I GIVE THEM HELL TOO.

Zodiac does some word scrambles and anagrams to increase difficulty, sometimes creating alternate or hidden meanings. This opening line literally reads, perhaps alluding to the task of solving this code, that it is HERCEAN BIG. A task worthy of HERCULES, a difficult job, is called HERCULEAN, and here we have a shortened version HERCEAN, followed by BIG. And Zodiac suspect and then SF Bay area resident Theodore Kaczynski used HERCULES as an alias when he was a young man - he signed a letter as HERCULES.


As you decode the 340 and translate that first line as HERC EANB (HERB CAEN) I GIVE THE HELL TOO, on the 4th line the words SEE A NAME start to appear, and on the amazing 8th line appears THESE FOOLSHALL SEE.

What is it that we "shall see"? Right before SEE A NAME on the 4th line, on the 3rd line we see SLEU(TH) THEO. THEO is Greek for God. Is Zodiac proclaiming himself God, or mocking God? Or is THEO a clue to his name? Perhaps a clue to the name THEODORE Kaczynski, who like the Zodiac wrote taunting letters to police, demanded his words appear on the front page of the newspaper, designed bombs and threatened mass transit, was a serial killer and lived in the SF Bay area in the time frame.

Then there are the many word finds in this code solution.

The most incredible of all, IMO, is the stunning and connected DUEL LIST BOMBS THEO SEE A NAME, plus going backwards from the "B" in BOMBS an anagram for BLAST. Zodiac talked about a "little LIST" and he talked about "BOMBS" AND "BLAST", and here we have LIST going into BOMBS with a BLAST. With THEO, then SEE A NAME.

I will go on record, absolutely NO WAY that all happens by chance, that was intended by the maker of the 340 Code, and that is Zodiac. This is his message.

The we have I GIVE THEM HELL TOO, THEO, then SEE A NAME, then THESE FOOLSHALL SEE. All relevant messages, coherent, no anagrams, consistent themes of seeing hidden things.


Zodiac 340 First Stage Solution Marked.jpg
Zodiac 340 First Stage Solution Marked.jpg (95.34 KiB) Viewed 7164 times


THE KEY SEQUENCE:

A close up on a series of amazing word finds in the 340 solution.

L....S....E....*....I....L....U.....E....H....S....T.....H....E....O....L....H....S
S....E....E....A....N..A...M....E....B....W....E.....O....L....L....R....K....E
S....E....I....L.....L....L....F....M....I.....A.....P.....I....L....L....S....G....A
E....M....R....N....P....A....O....D....E...M....A....G....P....C....E....T....T
O....A....L....S....T....B....N....E....U...*.....S.....H....B....L....L....E....I
..................S
............I
......L


So we have "LIST" leading to the "T" in "A L S T B", a probable anagram for "BLAST" (a word Zodiac used, something like 'when I have my BLAST'), with the "B" then forming a diagonal "BOMBS". Which leads us to "THEO", then "SEE A NAME". We also have a vertical SEAT, a place a student can be confined to, thus a type of restraint. Following SEAT is TIES. We also have a perfect backwards "GAME".

The words BLAST, BOMBS, LIST and GAME are absolutely key words that Zodiac used repeatedly.

It is impossible that they would all appear by chance??? They serve as validation that this is indeed the correct solution.

Robert Graysmith then tried to force a solution out of some parts of the solution that were not as clear, because he did not realize that some those parts require a seperate second stage analysis using a Caesar Code method with letter shifts of 0, 3, 6 and 9.


----------------------------------------------------------------------------
What follows below is very likely the correct solution to the mystery of the 9 letters around the THEO...SEE A NAME section of the decode, and it follows code principles and is mathematically consistent, and produces a stunning result:

R U D N Q B C Q N X U Q B
O R A K N Y Z N K U R N Y
L O X H K V W K H R O K V

I L U E H S T H E O L H S

F I R B E P Q E B L I E P
C F O Y B M N B Y I F B M
Z C L V Y J K Y V F C Y J

The number sequence to solve it is:

9 9 6 6 6 6 - 0 0 0 0 -3 3 0 0 0 0 0 - 0 0 0 0
Z C AK N Y T H E O I K S S E E A N A M E

For the name, that breaks down as 99 6666 0000 33 0. That is clearly NOT random.

That is a number sequence of patterned repeats. Two digits repeat (99), then four digits repeat (6666), then four digits repeat (0000), then two digits repeat (33). Then it finishes off with the last letter of the name (0), and the SEEA is a four digits repeat (0000), and it finishes with yet another four digits repeat for NAME (0000). Amazing!

The letters involve only a very mild anagram application to get the name:

Z - CAK - NY - THEO - IKS



"KAC" appears exactly and perfectly backwards with values of:
-669

"ZYN" has the "YN" part backwards with the "Z" put into place with values of:
-966

"SKI" appears exactly and perfectly backwards with values of:
-033

"THEO" appears as is, normal forward left to right read, with values of:
-0000

First Stage Solution - As Given:

9 9 - 6 6 6 6 - 0 0 0 0 - 3 3 - 0 - 0 0 0 0 - 0 0 0 0
Z C - AK N Y - T H E O - I K -S - S E E A - N A M E


Final Solution - Letters Arranged To Spell Last Name:

0 0 0 0 - 6 6 9 9 6 6 0 3 3 - 0 0 0 0 - 0 0 0 0
T H E O - K A C Z Y N S K I - S E E A - N A M E


***** ***** ***** *****

AQUI - AND OTHERS - IN TERMS OF THE PROBABILITY STUDY RESULTS:

My question is, is it fair and reasonable to use the TBZ/Aqui Report numbers as follows?

Chance of THEO appearing is 0.069 or 6.9%

Chance of KACZYN appearing is 0.074 or 7.4%

Chance of both appearing in a continuous sequence of code, as they do here, is approx 0.005 or 0.5% or "One half of one percent".

Is that fair and accurate?

And isn't that quite an amazing result? In particular, when considered with the 1% or less chance of getting the name in the Unsolved 18? And the appearance of the same name or variants of it in the Map Code and My Name Is Code?


Thanks to all who are interested, and special thanks to Aqui (even if I haven't YET convinced him that his results are quite amazing!)
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Re: Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 2:51 pm

Thanks to Sean for the questions/criticisms, and of course for TBZ/Aqui for undertaking this project.

There were and are two main objections to the Kite - Wilks code work -

1. You can get other names using the method

and, it is related,

2. The appearance of the name THEODORE J KACZYNSKI is likely just random chance


In fact many told me that given the Caesar method, they thought it 90 to 100% likely the TJK name would come up in ANY 18 letter string; others said it was "probably" the case it would come up in any string, or "more then likely" that it would.

So, if those who dismissed the code work in its entirety because they thought the odds were 50% or better, what is their reaction now that the final results show the odds to be 3% or less for THEODOREJ and 5% for KACZYNSKI? And even 1% or less for both? So far the reaction is "Doesn't matter."

If the analysis shows only a 5% chance of random occurence, can we say that it also shows a 95% likelihood that the name was placed? I think so, but I honestly don't know for sure.

If there is a 95% likelihood the name "Theodore J Kaczynski" was placed in the unsolved 18 from the first Zodiac Code, does the prove that Kaczynski was the Zodiac? No, not automatically and not by itself.

First, you have to consider all the other evidence pointing to TK as a suspect (he lived in the area, he did become a serial killer, he knew about codes and bomb designs, similar handwriting, similar in many ways to the sketches) plus any evidence in mitigation pointing towards TK not being Zodiac.

Then you have to ask, "If the TJK name was placed, what are reasonable explanations"?

My thoughts:

1. The name occurs by random chance.

It seems the final outcome of the analysis by TBZ/Aqui, it that there is a 5% or less chance of this. If the chance is 20% or greater, that will be one thing - another thing if it is around 10% - and another thing if it is 3% or less. But, based on the preliminary numbers, it is appearing very unlikley the name would appear by chance. It seems the final numbers will be around 1% of both 9 digit names by a random chance. I find that very impressive - I now know some agree, and some disagree. And then although TBZ/Aqui may not have the desire or time to carry the analysis this far, you would also need to ask why "THEODORE J KACZYNSKI" or "THEO KACZYNSKI" appears in all the other Zodiac Codes, and what the odds of that happening by chance are.

2. Someone, the real Zodiac Killer, placed the name in the codes.

Kaczynski was a math professor at Berkeley. Could someone - maybe a disgruntled student, a rival professor, a reader of his journal articles - have placed his name in the codes? I suppose it is possible. But it seems highly unlikely. Ted mostly kept to himself. He made very few friends, none really, and at the same time, no known enemies. I can't think of any reason why someone would put his name into the codes. It just doesn't hold water.

3. "Zodiac" was a team of two or more persons - Ted did the code work and put his name into them, but someone else was the actual killer.

There have been some group theories in the Z case. But the bulk of the evidence supports the notion that Zodiac is one man. That one man wrote the letters, wrote the car door message, did the codes and did the killings.

4. Ted Kaczynski was the Zodiac, and as the Zodiac told us, his "name" and "identity" were in the codes, and if the codes were cracked we would "have" him.

Given that Ted Kaczynski generally matches the Zodiac description, lived in the SF Bay area at the time, had expertise in codes and bombs, and DID become a serial killer who wrote letters to newspapers extorting his words onto the front page, this is clearly the simplest, most logical, most direct and IMO most likely answer...IF we can conclude that there is a very high likelihood (95% or better) that the name was placed.

*****

You CAN indeed get other names out of the 18 unsolved, using a Caesar Code matrix based on +9, +6, +3, 0, -3, -6, -9 shifts. That is a weakness. I admit that.

For example:

By Zsearcher : GARETH SEWELL PENN ZK

My Take: A decent effort. But this doesn't work. The "ZK" is just thrown in, it doesn't make any sense.

So we have a 16 letter name. As such, it has to be disregarded, because the two extra letters when Caesar shifted give you 14 letters to pick from - it invalidates (pretty much completely IMO, maybe TBZ/Aqui can clarify) the production of a name of 16 letters. Zodiac gives us 18 letters at the end, and it has to be an 18 letter name for the probability analysis to hold up. In fact, I think Penn mostly went by the style of "GARETH PENN" or "GARETH S PENN", which are 10 and 11 letter names. Ted did sign his papers "Theodore J Kaczynski", and in a code he devised as a young man, told the person he hid "the 18 letters of his name" in the musical composition on the last letter of each line.

By Glurk: Here are a few more names that will fit, using just the last 17 (or 18):

"EBE......" Solutions:

BY ANGEL KRISTOPHEN
KENNY JOSH FREDERICK
CHRISTOPHER B NEWIK
BUNKEY JUG WILBERTH
WILBERT SHULY CHEVY
CHRISTOPHER Q HYNN NJ
BY JOHN ELY KRISTOPHE
WILBERTH KENN MARCE
NESTON W CHRISTOPHE

My Take: Also a good effort. My response would be, most of these don't sound like real names. I doubt there is a "BUNKEY JUG WILBERTH" in the 1969 San Fran phone book. Maybe the Alabama phone book (Sorry JON!!!) If there was a KENNY JOSH FREDERICK in the 1969 SF phone book, then I would question, "Is he a white male between the ages of 25 and 40 in 1969? Did he look somewhat like the sketch? Does he have expertise in code making and bomb design? Is there any evidence he was or became a serial killer? Etc. Etc."

In other words, the production of ANY name in the code - TJK, GP, anyone - is ONE element of evidence to be considered.

There are also all the unique elements attached to the TJK name as it appears in the code, most or all of which we don't find with any other name that can be produced in the code - the EE, OO, KK are matched by double letters in the EBE string, the internal math, the patterns, etc., etc. I have gone over all these repeatedly so I will spare you all! Anyone who hasn't seen this analysis it is here:

viewtopic.php?f=14&t=86&st=0&sk=t&sd=a



C...N...Q...R...V...R...X...Q...Y...N...A...C...C...N...N...K...N...R
Z...K...N...O...S...O...U...N...V...K...X....Z...Z...K...K...H...K...O
W..H...K.. L...P....L...R...K...S....H...U...W..W..H...H...E...H...L
T...E...H...I...M...I....O...H....P....E...R...T...T...E...E...B....E...I
Q...B...E...F...J...F....L...E....M....B...O...Q...Q..B...B...Y....B...F
N...Y...B...C...G..C....I....B...J....Y....L...N...N...Y...Y...V....Y...C
K...V...Y...Z...D...Z...F...Y...G....V....I....K...K...V...V...S...V...Z


0...3...3...6....9...6...3....3...6...6.....9...9...6....6...9...9...6....0

***************

Also, remember you can't get Arthur Leigh Allen, or Richard Gaikowski, or any name with more than one "A", from the Unsolved 18 Caesar matrix. In fact, most of the names glurk came up with were rather silly and contrived, and most not likely real names. So, it is true you can get some other names, but its not like you can get most of the names in the SF phone book.

Then, you have the question of why the TJK name alone, of all the suspect names, ALSO appears in the My Name Is, Map Code and Zodiac 340.

Aquiman stated:

I need to be clear/honest about something... It's true, the percentages ARE a lot less than I expected. However, I've subsequently spoken with two separate analysts at work, who have stated that I should not put much weight on those numbers given the near-infinite number of solutions. I believe that the largest meaning they hold, is that the assumption that "you can obtain that name from any set of letters" is incorrect. I don't think it was fair for people to state that assumption as if it were fact... it's not. AK, I still believe it's possible we can narrow things down a bit with your suggestions, results of which would ultimately hold more meaning/weight than we can assign to these numbers. I apologize for initially "misinterpreting" the significance of these results, but I'm muddling through this as well. It was not my intent to mislead, but simply to obtain a probability. I don't intend on letting this die. It's a "work in progress." As I stated previously, I would appreciate anyone with an opinion to weigh in on this. New sets of eyes and ideas can only help.

Linda stated:

Big Z/Aquiman - you have done an amazing job of putting this work together. I wish I could completely comprehend the art of de-coding and analyzing pieces as you and others are very able to do. Although I realize that the probabilities are still not 100%, it does help to narrow down the possibility that TK's name is encompassed in the Z codes, and narrowing in on the high possibility that, added to the inumerable pieces of circumstantial evidence against him, TK may, in fact, truly be the infamous Zodiac Killer.

Thanks again for all your hard work (and AK, too)!
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Re: Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 2:56 pm

I do appreciate any comments and criticisms, and will deal with more of them tomorrow, after some study and thought.

But two I need to respond to now.

First, if I offer you a bet of $10 to win $100 with 97% odds, based on 97 red balls in a bag of 100 balls, blindfold you and if you pick a red, you win. Do you take the bet? I think you do. Lets say you like those odds and take the bet. Now I say, wait, I will offer you a bet of $10 to win $100 with 97% odds, based on 970 red balls in a bag of 1,000. Do you still take the bet? I think you do, as the odds of 97% winning are the same.

I think the same is true here Aqui. I think your initial feeling that the 97% odds of the name being placed as significant was correct. Your colleagues warning that the large number changes things doesn't make any sense to me, mathematically speaking. We have the universe we were given, be it 100 possible names or 1,000. Odds of chance happening of 3% are small with either number set. The odds of 3% are the same regardless, just as the the chance of winning by getting a red ball is the same whether it is 97 out of 100, 970 out of 1000, or 9700 out of 10,000. Right?

And most importantly, second:

Sean said:

"It's manufactured stuff. please also go back and look at the other code efforts here. The impression given is that we can use this 0,3,6,9 pattern to produce kazcynski several times...ergo, there's really something here...there's absolutely not. It's all cart before the horse stuff...why? because it's set up to extract that name.
There are no rules, they come later....symbols are being changed all over the place, not because it was the most logical thing to do but because without changing "correctly" you don't get kazcynski, which is the object of the exercise."

AK: Well, that is simply NOT TRUE. What you are saying is that I have cherry picked letters, come up with bogus translations of dubious invention, in an effort to get the name Kaczynski. A serious charge. Lets see if its true.

UNSOLVED 18 FROM THE ZODIAC 408 CODE

All 18 letters come from the FBI certified correct Harden Key. So 0% cherry picking, yet we get the name THEODORE J KACZYNSKI.

ZODIAC 340 CODE

The solution used is NOT MINE. Out of the 340 translations, I did 0 (ZERO). The origins of the solution I use come from Robert Graysmith, but significantly modified and improved by several members of the old ZodiacKiller Board such as Kite, Claston, Ed, Obiwan (and maybe even Sean, I can't remember). The name "THEO" appears as is, correct spelling, no anagrams, no Caesar shifts, in the 1979 FBI file version from Graysmith (or someone who had a very similar solution). 17 years before anyone ever heard of Theodore Kaczynski! And probably done by Graysmith, who thought Allen was the Zodiac. So who cherry picked the name THEO? Who cherry picked the words SEE A NAME right before THEO? Who cherry picked the 9 letters that appear around THEO, that Caesar shift to KACZYNSKI, including appearances of CAK and IKS? Not me, I was playing with my GI Joe and watching Scooby Doo cartoons.

ZODIAC PHILLIPS 66 MT DIABLO MAP CODE

The fact is when I started work on this code I did NOT think Kaczynski was the Zodiac. I thought Kaczynski was a political terrorist, and thus very unlikely to have been gunning down teens in lovers lanes. He was on my suspect list, as were Allen (#1), Gaikowski, Kane, Davis and Marshall.

Out of the 32 symbols, 28 are translated by the Harden Key. 4 symbols never appeared before, so I translate those. Two of those symbols were "C", which I translated as "C". One I translated based on Harden, and one I admit to mainly using number pattern and word solving to translate. I translated that one as an "X", with the objective (I admit) of using it for a Caesar shifted "D" and seeing if it would fit into the existing number pattern and as a word solve as by using pure HARDEN KEY for 28 of the symbols I had ZO_IAC IN. Word solves are a legitimate code solving method.

So, in the Map Code, I did not have TJK (or anyone) in mind as a suspect, I had all the major suspect names down, as well as looking for all names, SF street names, California cities, and 28 of the 32 are solved by Harden Key, 2 as is, 1 based on Harden and 1 as a number/word solve. So at most I can be accused of "cherry picking" 1 out of the 32 letters, and that letter was an "X" used as a 6 Caesar shift to give me a "D" for "ZODIAC". I already had a backwards "J", which by Harden Key translates as an "X" ("thrilling eXperience" in the 408) Caesar shifted for a "D" in "THEODORE" and had "ZO_IAC". Hmm, whats missing?

ZODIAC MY NAME IS CODE

This one does present the most oppurtunity for cherry picking, as out of the 13 symbols 4 don't appear in the 408, thus there is no Harden Key available. And I do admit that by the time I started serious work on this code, I had done the Map Code and found the TJK name there, and had developed a major interest in TJK as a suspect. Thus, while I don't recall intentionally trying to solve to get the TJK name, I can rightly be regarded as at least being suspect for an unintentional bias, and certainly I did not forget that his name starts with a "T".


So I could be guilty of intentional/unintentional cherry picking. Except I really don't think I was. To solve the THREE circled "8" 's as a "T" was totally legitimate and justifiable, having two "E" 's and going to the next most common letter "T". Also, you called these circled "8" 's a Taurus symbol. I never thought of that/didn't know that, but if they are symbols of Taurus, that is another legit reason to consider solving them as a "T"! Aside from the ETA frequency analysis. And I don't think anyone can argue much with my decison to solve the anchor symbol (Aries) as an "O", based on the fact that a very similar symbol, just with a short line on top, was solved as an "O" by the Harden's. What letter other than "O" would anyone suggest is better?

CONCLUSION

I totally reject the notion of cherry picking, and the facts back me up. My proposed code solutions may be right or wrong, but they can stand or fall on their own merits, there was no cherry picking, forces or fabrications.

UNSOLVED: 18 OF 18 FROM ZODIAC

340: 0 OF 340 DONE BY ME, ABOUT 300 DONE BY ROBERT GRAYSMITH IN 1979 WAY BEFORE TJK WAS ARRESTED, ABOUT 40 DONE BY SEVERAL RESEARCHERS ON THE OLD ZODIACKILLER BOARD IN THE YEAR 2000

MAP CODE: 28 OF 32 FROM ZODIAC FIRST CODE HARDEN KEY, 2 OTHERS AS IS FROM ZODIAC, 1 SOLVED BASED ON HARDEN, 1 SOLVED TOTALLY BY ME

MY NAME IS: 8 DIRECT FROM ZODIAC FIRST CODE HARDEN KEY, 2 SIMILAR TO HARDEN KEY, 3 NEW SYMBOLS SOLVED BY ME - THE CIRCLED 8 TAURUS SYMBOLS SOLVED AS A "T"
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Re: Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 3:05 pm

I put out this question:

Here is a little Zodiac 340 Code problem I have run into.

I would love to get the input from as many people as possible. Even if you know nothing about codes, you can participate. Some knowledge of the Zodiac case is helpful. At this point I am trying to "word solve", which is when you have part or most of a code done, but need to translate a symbol to a letter, and will often decide in large part on the basis of "If I solve this symbol as this letter, does it create a word, either naturally or with anagram use, and is it likely a word the code maker (in this case, Zodiac) would use?"

I am trying to solve for the symbol "+". I know from other outside factors it is very, very likely to be either an "M" or an "L". Given those parameters, with the following sections of code complete, would you solve the "+" as an "M" or an "L", and why? Or is there a very strong case to be made to solve as another letter?

D U E +

+ E O

B L + E I

S H A + L

Answer from Morf:

Seems like an L to me,

D U E + ......DUEL

+ E O.......LEO

B L + E I ......BELLI (misspelled)

S H A + L.......SHALL

They seem to fit naturally,without jamming them in. Since I am not strong with codes, I have no idea if I am right.

My response:


Thanks Morf, Linda, Sandy and thebigZ!

That was my take as well, that "L" (Old ZK Board solution from year 2000, which slightly modified the 1986 Graysmith version from the book "Zodiac") seems to fit very strongly, and "M" not at all (Robert Graysmith from 1979 FBI file).

It is important for something I am working on, so I wanted a second opinion, and to see if it would be a consensus. It is, and mostly from people who have little to no interest in my POI or any preset ideas about the code, so that is cool.

A critic made the accustaion that the entire 3rd line of my proposed 340 solution was in fact a cherry picked concoction done by Zander Kite in 2000 - four years after Theodore Kaczynski was arrested. I said no, that is false. I said almost every single letter of the key part of line three, the "THEO" and most if not all of the 9 letters surrounding it before "SEE A NAME", were in fact either in the 1979 FBI file or the eventual refined version done by Graysmith in his 1986 book "Zodiac", which was published 10 years BEFORE Kaczynski was arrested.

Well, lets go to the source and find out who was right.

Here is the FBI file, go to page 102 for the start of the discussion. Of course the FBI rightly dismissed the final version of the Graysmith solution, as parst of it seem very forced and feel wrong.

But the raw translation, before Graysmith tries to force it, was largely correct and done by generally accepted code principles.


http://foia.fbi.gov/zodiac/zodiac5.pdf

You can see it does indeed say "THEO" right before "SEE A NAME" - almost two decades before Theodore Kaczynski was known to the public.


THEO SEE A NAME Code Solution From 1979 FBI File.jpg
THEO SEE A NAME Code Solution From 1979 FBI File.jpg (64.47 KiB) Viewed 7139 times



***** ***** *****

Now lets look at the claim of the critic. Here is the 1979 FBI file version:

I L U E H E T H E O M H S

And now here is the old ZK Board solution from 2000, which is a modified version of the 1986 Graysmith solution:

I L U E H S T H E O L H S

What can we say based on this?

1. We can see that "THEO" does indeed appear in the 1979 version.

2. We can see that of the 9 letters surrounding "THEO", 7 of the 9 are identical between the 1979 and 2000 versions. The only differences are in the E/S and the M/L.

3. In the 1986 book by Robert Graysmith "Zodiac", he offers the translation on this third line as "SLEUTH SHOLD". While we don't have access to his raw translation from 1986, it appears that Graysmith by then HAD changed his "E" to an "S" - to get "SLEUTH", and his "M" to an "L" to get "SHOLD" (meaning "should"). Thus it seems almost certain that by 1986 - 10 years before the arrest of TJK - Graysmith had the identical translation as seen in the 2000 Old ZK Board solution.

4. In the case of the E/S question, it doesn't really matter anyway, as the "S" gives you a Caesar shifted "Y" on the +6 line, while an "E" gives you a Caesar shifted "Y" on the -6 line.

5. In the case of the M/L question, it does matter. With the "L" you can get an "I", which completes the Caesar translation of the whole line as "THEO KACZYNSKI". With an "M", you cannot get an "I", and thus the whole things crashes and fails for lack of the last letter needed, an "I". But we have seen that Graysmith almost certainly had by 1986 translated it as an "L", to get "SHOLD", and not as an "M". And in any event, when we look at the symbol in other places in the 340, we see that an "M" gives us the nonsensical "DUEM", "MEO", "BLMEI" and "SHAML", while the "L" translation gives us "DUEL", "LEO", BLLEI (possible anagram for BELLI or BELL) and "SHALL". A group of 4 researchers, 3 of whom have little to no interest in TJK as a suspect, agreed that in and of itself, seperate from any other considerations, the translation of "L" makes much more sense in the context of this proposed solution by Graysmith and fits very well, while the "M" seems not to fit at all. (Thanks to Morf, Linda, Sandy, thebigZ!)

Thus, the accusation of the critic is proven INCORRECT.

The third line of the Zodiac 340 Code, seen below, has all 13 letters translated in 1986.

When applied to a Caesar Code shift matrix of 0-3-6-9 shifts, you get the incredible result of THEO KACZYNSKI.


ZODIAC 340 Code

I would also be very much interested to see what Aqui and others think about my proposed 340 solution. I don't know if you can subject that to a probability and/or computer analysis. There are three stages to it. There is the actual proposed first stage solution - HERCEAN B I GIVE THEM HELL TOO THEO SEE A NAME THOSE FOOLSHALL SEE; then the words that appear vertically, backwards and diagonally like GAME, LIST, BOMBS, DUEL, LEASH, BARS; then the Caesar Code 0-3-6-9 application, just like in the Unsolved 18, that produces KACZYNSKI between THEO and SEE A NAME. It also transforms "ASK DLA" into "ASK GOD".

There are no cheats in this solution. Every one symbol translates to one letter. When you solve the first four lines, a lot of the rest of the code is filled in. And by the time you solve line eight, most of the rest of the code is filled in. The code solution provides clear English langauge words and phrases, and key Zodiac concepts and themes.

See: viewtopic.php?f=14&t=36&start=150


----------------------------------------------------------------------------
What follows below is very likely the correct solution to the mystery of the 9 letters around the THEO...SEE A NAME section of the decode, and it follows code principles and is mathematically consistent, and produces a stunning result:

R U D N Q B C Q N X U Q B
O R A K N Y Z N K U R N Y
L O X H K V W K H R O K V

I L U E H S T H E O L H S

F I R B E P Q E B L I E P
C F O Y B M N B Y I F B M
Z C L V Y J K Y V F C Y J

The number sequence to solve it is:

9 9 6 6 6 6 - 0 0 0 0 -3 3 0 0 0 0 0 - 0 0 0 0
Z C AK N Y T H E O I K S S E E A N A M E

For the name, that breaks down as 99 6666 0000 33 0. That is clearly NOT random.
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Re: Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 3:14 pm

He is still doing some numbers crunching, but I am hoping that very soon TBZ/Aquiman will give his thoughts here at unazod. Until then, here is an interesting little exchange we had at http://www.zodiackillersite.forummotion.com.

thebigZ/Aquiman:

Ok… So I posted the results, some “friendly” discussion has ensued as to their significance, I’ve checked and re-checked, pondered, etc. Some members (here and elsewhere) have PM’d me with some opinions and questions. Some have suggested that there “must be a mistake somewhere.” There may very well be; however, at this time, I think I’m going to stick by the numbers I came up with. I believe the real issue is what the results mean, rather than what they are. My interpretation is as follows:

1) The average likelihood of obtaining an 18 letter name/sequence (using AK’s Caesar shift and anagramming techniques) is roughly five percent. That is for ANY 18 letter sequence that can be obtained from this methodology. Depending on the amount of “overlap” of sets (i.e., sets formed by Caesar shifted letters), that likelihood will vary from anywhere between approximately one to ten percent. I believe what I have been able to successfully demonstrate (at least to myself) is that this likelihood is not nearly as high as once thought. Some had suggested it could be upwards of 95%; it is not.

2) You cannot obtain any name you want out of an 18 character sequence. It is impossible to determine the number of names that can be obtained, though it is likely that there are many possibilities.

3) If a name is obtained (even with its accompanying five percent likelihood), it would be faulty logic to assume that it was intentionally placed there. I think this is the “point of departure” between TJK code proponents and skeptics. I’ll give an example to demonstrate why I believe we cannot jump to any conclusions. Without getting into the detailed math, I’ll just state some poker hand probabilities. Here is the link if you want to check them out for yourself.

There are 2,598,960 possible 5-card poker hands. There are 5,148 ways of being dealt a flush (all five cards of the same suit). This number includes straight and royal flushes. So the probability that I am dealt any flush is 5,148/2,598,960 = 0.2%. Just because I am dealt a flush does not imply that the deck was stacked. Nor does it mean my flush is special (unless there’s money involved), because the probability of obtaining one set of five specific cards is exactly the same as obtaining any other. For example, I have as much of a chance being dealt a royal heart flush as I do of being dealt the 2 of clubs, 3 and 6 of spades, jack of diamonds, and ace of hearts. The fact is I cannot prove that the deck is stacked based on one hand alone. If I am dealt a flush in several hands in a row, however, I might suspect there is something going on. Therefore, we need to determine if the phenomenon of extracting a specific name from different sets of code is repeatable.

By “repeatable,” I’m suggesting that the same name can be extracted using the same methodology. I’m skeptical that this has been adequately shown. Even though AK et al have pulled TJK from different ciphers, it would be more convincing if identical sets of Caesar shifts were involved, otherwise I feel like I’m “looking” through the deck for another flush. Additionally, while I consider the 18 character decipherment from the 408 a distinct possibility, the 32 character decipherment leaves something to be desired… not because it’s impossible (it obviously IS possible), but because it ignores Zodiac’s instructions to consider “radians and # inches along the radians.” Regarding AK’s solution… could TJK have implied that Zodiac was a ticking time bomb buried inside the mathematician? Did we have to catch him (dig up the bomb) before he struck again (exploded)? Sure, I guess so. But it’s a bit of a stretch IMO.

Clearly, the extraction of a name from so many possibilities would not hold up in the eyes of LE… unless it was exactly repeatable. There are various ways to obtain the same name, though I really haven’t looked at it that closely. I certainly don’t believe the results of the analysis hurt the case for TJK; I just don’t believe they are very earth-shattering as they stand. There are many other reasons, which AK has repeatedly outlined, why TJK is a viable Z suspect. In general, however, I believe more work needs to be done to convince the skeptics and LE of the code solutions. AK has suggested there are "patterns" to the Caesar shift numbers. This is something else that needs to be examined a little more closely. It's on my list.

AK Wilks:

TBZ/Aquiman - As usual you make some excellent points. And as always you proceed in a cautious manner and demand proof and more studies, which is good. At this time, we may differ in just how significant your findings and the code work are - perhaps there will be a lot less difference in a month or so.

Funny that the critics insist "There must be a mistake in the numbers!" But they can't tell you where the mistake in your numbers or methods are! Thats weak. If there was a mistake, they would find it. They haven't, because I don't think there are any.

1. Yes. The critics said "any" letter string could produce the TJK name. Others told me in it would be 50% or more, 66% or more, 90% to 100%. Instead, we are looking at most at 5 to 10%, and for both more like 1%. I do take that as confirmation of one of the central aspects of why I argued the code results were significant.

2. Yes I agree. You cannot get "any name" out of the unsolved 18 or "any" other 18. You can get other names, but it is not the case that any 18 letter string will get you any 18 letter name, as argued by the critics.

3. Good analogy, and you give me some points to consider. Take the poker analogy - it is one thing if a dealer deals himself a straight flush. Ok, he got lucky...maybe. But then you ask him to produce a NEW deck of cards, and he does. And proceeds to deal himself a straight flush again. NOW you get suspicuous! You ask him to produce a new deck, he does, and deals himself an aces and kings full house. At that point, I think you leave the table, because you know something is up!

So, it is one thing to get the TJK 18 letter name in the unsolved 18, maybe with odds of 1 or 2%. OK, fine. Luck, coincidence, whatever. But then to get THEO KACZYNSKI from the 3rd line of the Graysmith solution to the Zodiac 340 Code from 1986? Where THEO appears as is, no anagrams, no shifts? And the last name appears as Z CAK NY ISK? And THEN to have the same 13 letter THEO KACZYNSKI appear in the Zodiac My Name Is Code, using for a 1st stage solution 8 translations from the Zodiac 408 Harden Key, 2 based on Harden Key and the 3 new Taurus symbols logically solved as a "T"? Then throw in the Map Code with the 18 letter TJK name...I think my proposed code solutions will stand or fall based on the appearance of the name in ALL the unsolved codes. That is where we get beyond odds and into the reality of PLACEMENT. If there is a 2 to 5% chance of the name appearing in any one code, what are the odds it appears in 4 seperate codes? Aren't we talking like 1 in 500 odds at that point, maybe even closer to 1 in 1,000?

I admit there are problems with the Map Code as I solved it. Your analysis reveals that getting an 18 letter name out of 18 letters is much, much more impressive odds wise then getting an 18 letter name out of 32 letters. Also, while I stand behind the TJK name and the numerical palindrome clue sequence on the map that produces it, I have never been as strong on the other 14 letters. In fact, I think "ZODIAC IN DOCTOR THEODORE J KACZYNSKI" may well be wrong. It may say "ZODIAC LINCOLN MT HEODORE J KACZYNSKI".

You are right to note Z says he is giving us a bomb location. Keep in mind, however, that Zodiac did make a threat against a bus then told the SF Chronicle it was a joke AND that Ted Kaczynski (as "FC" aka the Unabomber) threatened to blow up a jet out of LAX then later wrote the SF Chronicle and said it was a "prank". So I think the "map code to the hidden bomb" could be another trick.

And if it does say "LINCOLN MT", well, at that time Ted actually HAD buried guns, ammo, food and probably bombs there! Indeed a few months before Zodiac sent the Map Code (which I say had his name and location) he had left a letter at his parents home which they were worried was a suicide note. And Ted had wrote that he had hidden caches of guns, ammo, food and "weapons" (maybe bombs?) in anticipation of a fight with the police in which he "feverently hoped I will not be taken alive". Was the Map Code his way of "suicide by cop"? Giving them his name and general location, soon to be location? Did he later change his mind, as when he wrote 'might as well make some effort to avoid detection...I won't give up my life that easily', and perhaps send the message saying the map code was about "radians" as a way to throw off police efforts to solve it?

As for the method being "exactly repeatable" through all the codes, that is an interesting criticism. A fair one. Maybe Kite has some ideas on that. I need to think about that more, but I would say the method is the same. A Caesar Code shift with 0-3-6-9 values. I never propose any method besides a Caesar shift, and I never propose any numbers besides 0-3-6-9. Also, all the codes rely most heavily on the 6 and 9 lines. The Map Code sequence matches a number that Zodiac creates on the map by placing the "9" on his crosshair between two "66" symbols. There are patterns in all the codes, most dealing with internal math, such as in the unsolved 18 all the shift numbers for THEODOREJ adding up to "33", which appears in that name, the numbers for "KACZYNSKI" adding up to "66", which appears in THAT name. There are differences in all the code solutions, they are not the same exact numbers. But the method is the same, many of the numbers similar and many of the patterns and math similar in concept.

Thanks again for your careful work and analysis TBZ/Aquiman! I look forward to seeing you post your work at unazod and zkf, and to seeing more of your study of other aspects of these codes.

***** ***** *****
Some critics of my code work complain about the anagram aspect.

But look at this.

This is the "CIF..." sequence created by using the Harden Key, the code key made by Zodiac, to solve 28 of the 32 symbols, in the order given by Zodiac in the Mt. Dibalo Phillips 66 Code letter. Look at the very "hot" sequence it naturally creates, which I have circled in red:


Zodiac Phillips 66 Mt Diablo Map Code YTHDRZIKZJOKO Sequence.jpg
Zodiac Phillips 66 Mt Diablo Map Code YTHDRZIKZJOKO Sequence.jpg (68.79 KiB) Viewed 7125 times


Y T H D R Z I K Z J O K O

Right there we have all these letters:

T H _ O D O R _ J K _ _ Z Y _ _ K I

12 of the 18 letters in Theodore J Kaczynski + an extra Z!!!

A continuous sequence which gives 12 of the 18 letters in the name. Plus, we see THDR. Which is THEODORE without the "E, O" vowels.
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Re: Results and Explanation of Probability Analysis

Postby akwilks on Tue May 10, 2011 6:06 pm

The solved portion of the first Zodiac Code had the last 18 characters which are unsolved.

The last 18 letters are:

E..B..E..O..R..I..E..T..E..M..E..T..H..H..P..I..T..I

This is actually 9 seperate letters, the rest are repeats:

E..B..e..O..R..I..e..T..e..M..e..t..H..h..P..i..t..i

The 9 seperate letters are:

E B O R I T M H P

For reasons which will be clear soon, I am going to take these 9 seperate letters that appear in the unsolved 18 and re-arrange their order:

E R I T P H M B O

Why did Zodiac select these 9 letters? He told us the code held his name...but then said we would not "give us" his name. Names usually go at the end of letters. Did he hide his name in these 9 letters, and do we have to "find it", as he would not "give" it to us? He also said if the code was cracked we would "have" him, and that the code contains his "identity".

What is significant about these 9 letters?

Let us create a Caesar Code Matrix with 0, 3, 6 and 9 for shift values. A "+" at the bottom indicates the letter string goes FORWARD in the alphabet, a "-" indicates it goes BACKWARDS in the alphabet.


* A * * Y * * K *
K X C Z V N S H I
H U F WS K P E L
E R I T P H M B O
* * L * M * J * *
* * O * J * G * *
* * * * * * D * *
+ + -+ + + + + -


That is a Caesar Matrix for the 9 letters we have in the unsolved 18. What do you see? Do you see what Kite saw, who discovered this? Do you see what I see?

Do you see the last name of a Zodiac suspect, a known serial killer, bomb designer and code expert who lived in the SF Bay area during 1967 to 1969? Do you also see his first name?

Look again - I will color the last name of this suspect:


* A * * Y * * K *
K X C Z V N S H I
H U F WS K P E L
E R I T P H M B O
* * L * M * J * *
* * O * J * G * *
* * * * * * D * *
+ + - + + + + + -


Now you can clearly see the last name. And how it appears in a PATTERN.

6..9..6..6..9..6..6..9..6 (To be precise it is +6 +9 -6, +6 +9 +6, +6 +9 -6).

Can we calculate the odds that the name occurs from random chance? And in that pattern?

But also consider this - the 9 letters used in the unsolved last 18 from the first Zodiac Code don't just produce the name KACZYNSKI in a patterned way, they also produce the name THEODOREJ as well. In fact, 5 of the 9 letters used in the last unsolved 18 are in the name THEODOREJ, and the rest are produced by Caesar shift.


* A * * Y * * K *
K X C Z V N S H I
H U F WS K P E L
E R I T P H M B O
* * L * M * J * *
* * O * J * G * *
* * * * * * D * *
+ + - + + + + +-



Looking at the 9 letters used by Zodiac in the final unsolved 18 in the Zodiac 408 Code, it does appear (to me) that the numbers in the Aquiman Report would apply, so that the odds of getting BOTH a "THEODOREJ" and also a "KACZYNSKI" from the same continuous 9 letter sequence would be "0.176%" or "just less than 2/10 of 1%". Amazing!
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Re: Results and Explanation of Probability Analysis

Postby KITE on Tue May 10, 2011 9:05 pm

Okay, if we are going to talk probability here and chance and odds and so forth---what about this? We have the name Theodore J Kaczynski and the name of an unknown serial killer: The Zodiac. What is the probability in the following. THE ZODIAC is nine of the 18 letters: THEODORE J KACZYNSKI. THE ZODIAC matches up with the beginning and end of the name: THE---------ZYNSKI. THE and then ZYNSKI, a six letter close-out that like ZODIAC is six letters and begins with a Z. Then, (THE ZYNSKI) anagrams out, with only a switch of 2 letters to (THE Z IN SKY), an interesting word game as it could relate to The Zodiac. But, most compellingly, in my opinion, is what happens when you minus TEN from every letter in the name Theodore J Kaczynski. Take a Look:
T......H.....E.....O.....D.....O.....R.....E.....J.....K.....A.....C.....Z.....Y.....N.....S.....K.....I.....
.J......X.....U.....E.....T.....E.....H.....U.....Z.....A.....Q.....S.....P.....O....D.....I.....A......Y....

Notice, right after the Z in Kaczynski, below, you have ODIA. That's an extremely exceptional coincidence, in my opinion. And the totality of it all is downright eerie, if you ask me. Take a look at this, where I mark with a (Y) if the letter is capable of minusing TEN without going thru the alphabet, an N otherwise.

Y....N....N.....Y.....N.....Y.....Y.....N.....N.....Y.....N.....N.....Y.....Y.....Y.....Y....Y....N

The most is TWO, except the series of FIVE that begins with the Z. Another coincidence! In fact, let's see what this looks like if not allowed to go thru the alphabet:
T.....H.....E.....O.....D.....O......R.....E.....J.....K.....A.....C.....Z.....Y.....N.....S.....K.....I.....
J...................E............E......H.................A...................P.....O....D......I.....A...........

What are the odds that the four letter after the Z in Kaczynski minus ten to ODIA? Perhaps the word TENS as seen here: (T)heodor(E)jkaczy(NS)ki. Perhaps it is part of the possible puzzle?
KITE
 
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Re: Results and Explanation of Probability Analysis

Postby KITE on Wed May 11, 2011 8:26 pm

For the purpose of probability, take a look at these five, though there are other quality possible cryptics. ONE: The unknown 18: THEODOREJKACZYNSKI=TEHIMIOHPERTTEEBEI=033696336699669960. Stressing that the (3) double letters all equal the same letter. The patterned number string. A low percentage of names can qualify, yet another letter-writing serial murderer's name can. TWO: The 340 cipher: ZCAKNY THEO IKS from ILUEHS THEO LHS 996666 330. The no-meaning backward C symbol marks the 13 that close out Line 3. The next words in the straight text are: SEE A NAME. BOMBS runs up diagonally to THEO. (PTEK LEASH) are nearby in Column 5, read vertically. Kaczynski uses (KEPT ON A LEASH) in his writings to lecture society. THREE: THE ZODIAC are nine letters in the 18 THEODORE J KACZYNSKI. Compare the beginning and end of the 18 with The Zodiac: THE ZODIAC, THE ZYNSKI. Using a Caesar shift of (-20,-10,0,+10,+20), you have THE ZYNSKI=THE ZODIAC (0,0,0,0,-10,-10,-10,-10,+20). And then consider the word game of THE Z IN SKY(anagram of THE ZYNSKI),to THE ZODIAC. FOUR: The Unabomber identifying number 553254394. The suggestion that the number represent letters. For example the three 5's are actually 5,15,25 or EOY. So-- 5,15,3,2,25,4,13,9,14. What goes a long way to perhaps confirming this form of cryptic is that (5,15)=20 (3,2,25)=30 (4,13,9,14)=40. The first 2=20 Next 3=30 and last 4=40. The resulting letters are EOCBYDMIN. EOCBYDMIN=KIZKYASCN 6,6,3,9,0,3,6,6,0. Notice O=I, C=Z D=A. Those letters anagram to ZODIAC. FIVE: Enoch W. Fischer ENOCHWFISCHER can be (0,3,6,9) Caesar shifted to THEO KACZYNSKI. The name CAESAR may perhaps have influenced Zodiac and/or Kaczynski to use the method as perhaps a promotion of ancient cultures. And also, the number 0,3,6,9 when attaching the number for letter for those numbers when read backwards (9,6,3,0)= (I FC Z)?
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