By the Numbers, or To the Letter Message Board: Theories: By the Numbers, or To the Letter

By Peter H (Peter_H) ( - on Friday, October 19, 2001 - 01:30 pm:

Dear Ray, Bookworm and anyone seriously trying to put their theories in perspective:

Please consider this:

There are exactly twelve tones in the western musical scale. In fact those twelve tones cover all the notes of all the keys in western music. Virtually every piece of music written in any key you have ever heard is composed of nothing more than combinations of those tweleve tones. Every melody consists of sequences of those tones used one at a time. All of the music of western civilization, from Beethoven's 9th to Beck's Bolero is made up of nothing more than these twelve building blocks.

There are ten numerals in the western mathematic lexicon. Every number and every mathematical formula and concept ever imagined can be expressed by combinations of these ten symbols, with a couple of dots and squiggles to connect them.

There are 26 letters in the English alphabet. Every English word ever written, and any composition of those words, from "See spot run" to "ontogeny recapitulates phylogeny" was composed of lines of those 26 symbols, with a few interstitial dots and squiggles. Every thought ever conceived can be expressed as such a combination.

Among any reasonably large set of material, say the works of Shakespeare or the Zodiac Killer, composed of the 36 alphanumeric symbols alone -- not to mention the augmetation of astrological symbols and other symbological systems, there are bound to be thousands of possible routes of interconnection between and among purely mechanical sequencing, random occurrance, syntax and meaning. Finding things like the reversal of a three unit sequence here and its recurrence there is absolutely nothing more than the inevitable but random result of an almost infinitely flexible set of symbols.

Thoreau explored this principle in a much narrower literary sense in "Walden", and demonstrated that even on the relatively abstract level of etymology and syntax, he could fnd a connection between just about any two phenomena in the universe.

A reasonably developed English vocabulary consists of about 20,000 words. The Oxford English Dictionary contains about ten times that number. Imagine the possibilities.

Pseudo-statistical and pseudo-alphanumericological exploration is bound -- I would say statistically certain -- to turn up hundreds and thousands of apparently meaningful connections. They actually mean nothing. They are a function of absolutely nothing more than the variety of combinations and constructions possible given a relatively few basic elements, like the twelve tones of the musical scale.

If you don't believe me, try the game of "Seven Degrees of Kevin Bacon". In that game, one player names a movie star, and the attempt is made to connect that star with Kevin Bacon through all the other costars the first one worked with in some movie, until you get a connection with someone in a movie with Kevin Bacon. No more than seven degrees of removal (costar of costar of costar of costar of costar costar of costar of Bacon) are allowed. The astounding thing is how rarely the connection needs more than two or three degrees, leading all involved to remark that Kevin Bacon must be the most prolific and wide ranging actor of all time. Wrong. You get a similar result if you call the game "Seven Degrees of Harry Dean Stanton, or Denholme Elliot or Scott Paulin or you name it". Its just another case of the variety of combinations resulting from a very few variables: hundreds of movies and hundreds of stars all connect directly to none other than Kevin Bacon. Right. Its "full of sound and fury, signifying nothing".

By Bookworm (Bookworm) ( - on Friday, October 19, 2001 - 07:17 pm:

Peter, I agree, that's why they don't usually prosecute on circumstancial evidence alone.

I keep an open mind even on my own sleuthing(that I could sometimes/always be wrong.)

It's easy to stray off from physical evidence (best proof,) to what this person was reading, watching on TV, and then when that doesn't help to start guessing about what we probably will never know.

But communicating and exchanging ideas on this message board can only help, especially in cold cases.

By William Baker (Bill_Baker) ( - on Friday, October 19, 2001 - 07:54 pm:

Bookworm, sorry to disagree with the first of your premises, but contrary to popular misconceptions, circumstantial evidence is the most common evidence upon which prosecutions are initiated. To my knowledge, evidence is of three types: circumstantial, direct and documentary. Direct evidence deals basically with eyewitness testimony. And we all are aware how unreliable eyewitness testimony can be. All physical evidence, including DNA, fingerprint comparisons, etc., are circumstantial evidence. And documentary evidence speaks for itself.

I don't disagree entirely with the point you made, but I wanted to clarify the legal status of circumstantial evidence in criminal prosecutions.

By Ed N (Ed_N) ( - on Friday, October 19, 2001 - 10:52 pm:

Peter: I agree entirely. You put it quite eloquently.

By Ray N (Ray_N) ( - on Saturday, October 20, 2001 - 01:26 pm:

Peter -

Thank you for taking the time and effort to start this thread. I think it's great to hear your views on this subject, especially since you disagree with me so strongly. I'll tell you though, what you've said here is, as in your other posts, probably true from the standpoint of pure logic, or in other words, as Spock sees the Universe.

I think it may be possible that you are getting so hung up on what you perceive to be a pointless exercise on my part that you miss the bulk of what I am trying to say with it (my forest and trees reference). I have never claimed that I came up with irrefutable numbers that can have but one conclusion. I merely offered them as food for thought.

I would like to make a couple of points here and I would like you to consider them, as I considered your thinking, in a new light. Try for a moment to let go of that in you which cannot accept that which cannot be taken apart, studied, concluded, verified, labeled, and organized.

I will use the very good examples you have chosen, if you don't mind. First off, let's look at your statement that "there are bound to be thousands of possible routes of interconnection between and among purely mechanical sequencing, random occurance, syntax and meaning. Finding things like the reversal of a three unit sequence here and its recurrence there is absolutely nothing more than the inevitable but random result of an almost infinitely flexible set of symbols."

Peter, nothing could be truer. BUT, let's look at a real world example of the unavoidable fact that there must logically be something wrong with this argument, even if we don't know what it is that's wrong. I'm sure you know this, but for the benefit of anyone who doesn't, let me briefly recap how Ted Kaczynski was identified as the Unabomber. U stated that he would stop sending mail bombs if the New York Times (I think it was) would print his 30,000 word manifesto. Thinking that this might give investigators something to latch onto, Postal Inspectors insisted that this demand be met even though FBI investigators were loathe to comply. Well, as it turns out, Ted's brother noticed some word groupings that seemed familiar to him. According to your statement quoted here, any such similarities in a 30,000 word manifesto would be the "inevitable but random result of an almost infinitely flexible set of symbols." Moreover, in furtherance to your claim, the phrases in question were not all that remarkable. "No big deal". "...sooner rather than later". "They want to have their cake and eat it, too." I think probably everybody has said these things at one time or another. The end result of the brother's observations was, however, that a long, complicated, and expensive investigation, based on making logical conclusions about whatever evidence was available, which had for all intents and purposes gotten nowhere, was in one swift stroke circumvented by his tip which led directly to Ted. For this to be dismissed as pure random mechanical sequencing is absurd. There obviously was some meaning there, because the first and only person who came forward with information closed the case. From your standpoint, it was not logical for the brother to form the suspicions he did. For me, the fact that he did is simply beyond chance.

Which brings me to your use of the term "apparently meaningful" with which you describe connections which are in the end meaningless. I think it is of utmost importance to realize that "apparently meaningful" must not be taken as a synonymn for "meaningless". For as many apparently meaningful connections as there may be at least some of them are going to turn out to be truly meaningful in the end, even though most of them won't. So, what is needed is a method of deciding which apparently meaningful connections deserve a second look before discarding them as meaningless. For one to take the position that all such apparently meaningful connections have an equal chance of being meaningless, as you apparently do, means you would have to be saying that Ted Kaczynski was busted by pure, dumb luck of the draw - a 1 in 250,000,000 jackpot.

From another perspective, if we took all the notes of all the songs which have ever been written and threw them in a big, jumbled pile, we couldn't possibly hope to reach in and pull out, say...500 or 1000 notes which just happened to be a famous Concerto. If, on the other hand, say we were nontheless stupidly searching for such a Concerto and we pulled out some notes that sounded almost organized like the ones we were looking for. Would we say, "Nah, throw them aside, we couldn't possibly have gotten that lucky." Or, would we at least take a closer look at them before casting them out?

What we have to do is take some reasonable steps to thin out this pile in which we are searching to a manageable size. No sure-fire way exists to do it with accuracy. All we can do is make speculative efforts. But should that prevent us from trying? The worst that can happen is that we fail, which is the same thing that would occur if we just said, "God, look at that pile of notes. We're not even going to try." My method was merely such a speculative effort.

As far as the Six Degrees of Separation example. You are quite right, one could reach the wrong conclusion about Kevin Bacon. And one could play the game with any other star and reach endless flawed conclusions. But this game doesn't attempt to make correct conclusions, it merely shows that there are millions of truly meaningless connections out there, mixed in with the meaningful ones. Did you offer this example because you think I don't realize there are many possible connections and not all of them have meaning?

I think the Unabomber example in particular points out that there are some facets of how the brain forms relationships and establishes links that, although not fully understood, can produce amazing results. This is what makes it the best computer there ever was. Remember, for all his logic, knowledge, and intellect Spock was often at a loss to explain how humans could far surpass his abilities in some areas. He admired us as we admired him.

Live Long and Prosper, pH.


BTW, anyone who wants to can look at the Unabomber Manifesto to see these phrases in the context in which they were used.

By Ray N (Ray_N) ( - on Saturday, October 20, 2001 - 01:40 pm:

Sorry. Here is the Unabomber Manifesto.

By Douglas Oswell (Dowland) ( - on Saturday, October 20, 2001 - 10:15 pm:

Ray, the textual analysis of the Unabomber Manifesto was rendered after David Kaczynski came forward with his suspicions. Those suspicions were based on the similarity in thematic content between the Manifesto and his brother's anti-technology philosophy, and were originally noted by David's wife, not David himself. The later textual analysis compared such phrases as Kaczynski's "eat your cake and have it too," which is a rarely-used form of "have your cake and eat it too," as well as a variety of others that were virtually (not exclusively) unique to Kaczynski.

By Ray N (Ray_N) ( - on Saturday, October 20, 2001 - 11:47 pm:

I see. Well, I guess I shouldn't put so much faith in the accuracy of what is shown on TV then! Still, those virtually unique phrases were there all along, even if the connections weren't made until later. Connections exist not only where you find them, but places where you don't as well.

By Douglas Oswell (Dowland) ( - on Sunday, October 21, 2001 - 07:20 am:

Ray, I wasn't trying to contend with your point of view, but simply correcting what appeared to have been a misconception. Just to show you how confusing the whole thing was, David Kaczynski later filed an affidavit in which he claimed that the FBI had misinterpreted his original statements and that he had actually ruled out Ted in his own mind as a possible Unabom suspect.

By Peter H (Peter_H) ( - on Monday, October 22, 2001 - 08:33 am:


Thanks for all the care and attention to your response to my ramblings. And thanks as well to other responders.

A few points: First, as to "that which cannot be taken apart, studied, concluded, verified, labeled, and organized." To me, this describes a realm or set of phenomena other than fact. And what else are we here to deal with? The use of numbers in looking at something like the identity of an unknown killer is only meaningful, not to mention useful, if it helps "take[] apart, study[], conclude[], verif[y], label[], and organize[]." That is clearly what you were trying to do with your discussion of the mathematics of ALA's vist to Riverside. And it's what numbers are for.

Second, a point Douglas made but did not provide the analytical basis for, is that U was nailed on a very specific suspicion triggered by an objective comparison of virtually unique phrasing, phrasing that was self evidently idiosyncratic without resort to any mathematical or statistical refinement or manipulation. It was one man's suspicion of a very specific individual, which turned out to be correct. Even if your version of events were correct, however, it is fundamentally different from what you are trying to do with ALA and what Bookworm is trying to do with the Z culture as a whole. With respect to your efforts, the Manifesto profile described a possible educational background by comparing the Manifesto to a large body of literature outside of and objectively unconnected with U or any specific suspect. My thesis is not, as you put it that "ANY such similarities in a 30,000 word manifesto WOULD be the 'inevitable but random result of an almost infinitely flexible set of symbols.' " (my emphasis) My point is that ANY such similarities COULD be random, and neither your nor Bookworms approach provides any means of distinguishing between the meaningful ones and the random. Comparison with concepts in an external universe of literature provides that means. This is also different from your approach, in that it does not begin with the null hypothesis of a particular suspect, but arrives at a suspect based on the objective comparison. ted only became a suspect when his mother noticed the similarities. ALA did not become a CJB suspect because he was in Riverside that weekend, but because Z was suspected and he was already a Z suspect. The TK process begins with no assumptions or other controllng characteristics, such as "is also a likely suspect in another crime of such and such a character". It differs from Bookworm's approach in that it does not attempt to draw connections within a known body of literature, but between two separate bodies of literature. It also relied on identifying connections between inherently -- and intuitively -- related concepts, that occur virtually unconsciously, such as expressions of philosophical concepts, not on cryptic clues that would have to be consciously contrived and deliberately hidden in order to carry the meaning attributed to them. "Manteca" is a prime example of this.

Finally, on poor Kevin Bacon. The point here is not that STARS are connected (you even know who Scott Paulin is?) but that a connection can be contrived between just about any two things, and the intuitive unlikelihood of the connection is absolutely no indication or means of determining whether the connection really has any meaning. This was directed more at Bookworm's observations than yours. The correlary for your approach, however, is that once it is acknowledged that ALA's presence in Riverside raises the liklihood that to some degree that he did CJB, there is nothing short of a rigorous, disciplined statistical analysis that can add anything to the weight of that evidence, and such an analysis is impossible. That was the point I was trying to smoke out with my plea for an applied statistician to jump in any time. For example, when DNA evidence is presented, it must always be qualified with the statistical evidence of how the DNA narrows the search. Since DNA is not unique, the expert presenting it typically says something like "This match has a 1 in 100 milion probability of occuring randomly". But it does so on the basis of known data, such as the occurrance of similar DNA strings in a given sample. this is meaningful because it connects a selected data point (the suspect) with a set of randomly occurring data points (all DNA). This is a relatively simple statistic, one that can be tested and verified. The probabilities of any group or individual being in Riverside on a particular weekend simply do not lend themselves to anything like that analysis for many reasons. One important reason is that it deals with a self selecting sample. People choose to go to Riverside, innocent visitors and coed killers alike: unlike DNA, they don't just go thee at random. Second, the sample selects itself for more reasons than can possibly be accounted for "mathematically". To put any probabilities on the phenomenon is meaningless simply because it involves dozens of variables, each of which dilutes statistical confidence.

By Jake (Jake) ( - on Monday, October 22, 2001 - 05:48 pm:

Catch me, I'm swooning...


By Ray N (Ray_N) ( - on Tuesday, October 23, 2001 - 12:24 am:


With regard to the reference to labeling and organizing which I made, you are correct I was alluding to a realm other than fact. I did that because I wanted you to realize that pure facts aren't everything and look at the Unabomber example from a perspective other than that which we have been discussing, i.e. scientific analysis. I wanted to point out that when David Kaczynski (or whomever it was) noticed similarities in the Manifesto, whether thematic or grammar specific, he was making connections in some part of his brain not at all without any mathematical manipulation or reduction, based upon his experience with a specific individual. The point I was trying to make in using this example was that connections to almost anyone known to anyone who knew Ted probably could have been made in a document so large as the Manifesto. Yet, the connection was made to the correct person. (It was a misstatement on my part to use the words "ANY...WOULD". I understood your meaning to be "ANY...COULD".) I refer to this as the "TLAR" capability of the brain. ("That Looks About Right"). An example of this is when an outfielder makes a running catch. He uses information from his senses to arrive at just the right spot at just the right time to intercept the ball. This is processed by the brain electronically, but not numerically. In other words, he's not running Newton's equations in his head, he just gets the sense that he needs to speed up or slow down or turn left or right. It is this property of the brain which I call into evidence that there was nothing random about the parts of the Manifesto which sent up flags in whomever's mind. This could never be figured out by a statistical analysis, and yet such an analysis of sorts took place with a nearly impossible result, which kind of beats up a bit on the old scientific method.

It's absolutely true that my approach provides no means of distinguishing between the meaningful connections and the random ones. That must be accomplished by the verification of any suspected meaningful connections by the use of other corroborating or exculpatory evidence. If none exists, no verification is possible! I'm quite sure I never proposed that statistics could accomplish this. That would be like saying we could start with a null hypothesis for everyone, and take into account all factored possibilities arriving at the conclusion that the culprit is one of 10 people or even John Q. Bagadonitz of Blue Earth, MN. What you don't seem to be getting is that's not what I tried to accomplish. What I tried to do was to reduce the google of possible connections. If the vast majority of these are truly random, then the vast majority shouldn't point to our subject, right? This is why we have to know who our subject is, and not start with the null hypothesis for him. Rather, we pick out as many connections as we can that seem to point to him, and discard the rest. We of course now know that anything we picked out is highly supsect of being random, and must be thoroughly verified by other evidence. The good news is that we don't have that many things to check anymore. If we picked right, we might make the case. If we picked wrong, which we may well have, then we fail. So what? Don't even try?

So of course my example of one of these possible connections was Allen's presence at Riverside. The statistical method didn't get me there, it was the other way around. First came the speculative premise, and all the numbers did was to verify in my own mind that his random appearance there was unlikely. I already knew that it was, I just wanted to satisfy myself with something tangible. You seem to keep insisting it is my intent to jail someone with this approach. Far from it, I only want to acknowledge possibilities and take investigative steps to prove or disprove them as the existing evidence allows.

For instance, it's like you say with DNA evidence in court. Most people think if you just hold up two autorads together and they overlap, you've got the right guy. Not true, all the autorads say is that this guy's markers match that sample. It only becomes incriminating when it is shown that the DNA fragment in question is one in which there are known polymorphisms, which is a fancy word for variations, across the human race(s). It can then be shown that there are this many base pairs in the fragment and that there is a corresponding such and such chance of this particular sequence occuring at random in any one individual. But like you say, this requires lots of knowns which then proceed towards an unknown. With DNA, you have all the knowns you need and can be extremely confident statistically. So confident, in fact, that you can execute a person on the basis of a set of equations! This is untrue in the case of my analysis, because the actions of persons are not truly random but rather are the result of circumstances, intentions, decisions, etc. As you say it, it is a "self-selecting sample". While true that this would reduce the confidence I would have in my numbers, you have to acknowledge that there is no physical event in the universe that is truly random. So the degree or "purity" of the randomness directly effects the "purity" of the results. I have continously said that I know the numbers I came up with can't be perfect, because the information I started out with couldn't be perfect. (Probably why nobody took the pro statistician bait, for there is no way TO know all that must be known here for an exhaustive analysis. Either that or nobody here is a pro stats person!) But can't I account for these known imperfections by intentionally using ranges which consistently favor the subject in question? Can't I compensate by being satisfied with odds like 1 in 200 or 1 in 500 rather than the 1 in millions that I would need in court? Remember, all I am trying to do is satisfy myself of this guy's viability for purposes of obtaining samples and running tests!

In other words, I had a hunch - the realm other than fact - and I'm trying to see whether it has any basis for existence in the physical world - that which can be verified, etc, etc...

Of course, I could have skipped the exercise entirely and just dismissed him as a suspect because of his wrists, fingerprints, and handwriting, but then I wouldn't have gotten the opportunity to break in my new keyboard, would I?


By Peter H (Peter_H) ( - on Tuesday, October 23, 2001 - 02:35 pm:


Sorry, but pure facts ARE everything:

It comes down to this. ALA was in Riverside. That makes it more rather than less likely that he did CJB. To paraphrase Mae West, numbers have nothin to do with it. It can't be quantified, and "mathematics" add nothing to the meaning of the fact that ALA was there.

And no, I don't insist on proof beyond a reasonable doubt, nor am I trying to convict anyone. I am just trying to weigh the facts and examine which facts make it more or less likely that anyone in particular might be Z. Does his being in Riverside make it more Likely that he was Z? Absolutely not. Based on the opinions on this board, it's probably no better than 50/50 that Z did CJB. So ALA's presence in Riverside adds nothing to ALA as a Z suspect, absent a hech of a lot stronger connection between CJB and Z.

I am not trying to say that your method fails because you have not proved that ALA is Z , or anything like that. I am saying that it fails because beyond noting that ALA was in Riverside, no amount of mathematical speculation shows it any more or less likely that he did CJB, and certainly not that he was Z.

By Ray N (Ray_N) ( - on Wednesday, October 24, 2001 - 01:27 am:

Well, then I'm taking MY FOOTBALL and I'm going straight home!

By Peter H (Peter_H) ( - on Wednesday, October 24, 2001 - 08:17 am:

Hey, Ray:

No one is saying you can't play. In fact, we need you on the team. It's just that we have kicked your football around so much, the seams are busted and it won't hold hold air.

By Ray N (Ray_N) ( - on Wednesday, October 24, 2001 - 12:51 pm:

Thanks. Actually, I was kidding. I'll just make one more post on this thread, and then I'm done. I agree with the board that 50/50 is probably a good guess as far as ALA for CJB. I just want to flatly state I was not trying to prove with math that he killed her or that he was Z, I was only trying to show the board how it might look that way. I acknowledge that numbers can be misleading if not presented correctly. The biggest mistake I made was probably the first statement in my first post when I claimed ALA was the "best suspect" because of my analysis. I should have said, at most, "a viable suspect".

Thanks everybody for your feedback.


By Zander Kite (Zk) ( - on Wednesday, May 22, 2002 - 09:52 pm:

Qoutes from this thread: "Finding things like the reversal of a three unit sequence here.. and there.".....also: "They want to have their cake and eat it too." That saying was reversed by Kaczynski. When you reverse Ted's name you have: IKSNYZ CAKE RODO EHT. Coincidence? Consider the quote "You shake a pretty mean cake, Batman." And Zodiac mails birthday letters or otherwise one year anniversaries marking some of his crimes. As tempting as these things seem, I assure you they are only coincidence, thus agreeing with the premise of this thread. - Zander "doesn't know a dammed thing about computers, can barely turn one on" Kite.

By Peter H (Peter_H) ( - on Thursday, May 23, 2002 - 07:16 am:


Glad to see you got it. Wish it were contagious, caise it sure doesn't seem to spread very fast.