Editor's Note: This is the latest in a series of articles by Gareth on the Zodiac murders. The "Calculus" article referred to is "The Calculus of Evil," Mensa Bulletin, July/August 1985.
[quoteright]On 20 April 1970, the Zodiac murderer sent the San Francisco Chronicle a two-page letter in which the author continued a series of threats to attack a bus. The second page of that letter, consisting of a diagram of the infernal device which the author proposed to use in his bus attack, is published here for the first time. It was suppressed by the police in 1970 and has languished in their filing cabinets for the last sixteen years.
I acquired a copy of the San Francisco PD photograph of the document in March 1982, by which time I had become accustomed to finding a certain well-defined vocabulary in the Zodiac literature, expressed by numbers in a dazzling variety of means, often in the form of what might be called "invisible geometry." The Bus Bomb Diagram proved to be a rich source of this new art form.
The first thing that struck my eye was the lopsidedness of the crossed-circle signature at the foot of the page. The cross in most Zodiac documents is about as square as freehand drawing can make it. Here, it is distinctly and uncharacteristically cattywampus. Something else that stood out was the pair of tag-ends where the author began and ended his circle. I noticed that the equals sign in he expression "=10" points straight at this ragged joint. Measuring the linear dimension between the center of the circle, marked by the cross, and the point where the tag-ends cross, I found that they are exactly 10mm apart. The police had always read this as a claim of ten murder victims, but as with most such supposed claims, the author does not actually say that. Depending on how one interprets the word "victim," the Zodiac had eight victims (persons attacked), or six (dead). There is an objective phenomenon to which the statement "=10" relates, by virtue of propinquity, and which is also factually correct, i.e. that the radius of this circle is 10mm. Far from being a vainglorious boast, this statement is a key to reading the diagram.
The next thing that struck my eye was that the back of the figure inscribed in the object labeled "Timer" appeared to line up with the (near-) vertical stroke of the cross. A straightedge confirmed this observation. The same instrument demonstrated that an extension of the horizontal stroke of the cross passes directly through the center of the zero in the phrase "SFPD = 0." So far, I had three circular objects joined center-to-center by invisible lines.
There were two other circular objects in the diagram, namely the suns in the top and side views of the bus bomb. I noticed that near the top-view sun, the Zodiac had written the H of the word "light'' with a peculiar up-tick, making the letter resemble an Arabic numeral 2. In the side-view sun, the U was written so as to resemble a backwards Arabic 2. They formed a pair of bookends. I drew lines connecting the center of the "Timer" with the points of the Arabic 2's. I found the centers of the suns by bisecting these lines within the circles, as I did with the zero of "SFPD = 0." The result is shown here as Figure 1. The two lines joining the center of the "Timer" to the centers of the suns were indicated by letters written so as to resemble the Arabic 2. Each of these two lines is exactly 95mm in length. 95 is binary 1 011 111 (my redivision), Morse TWO. The angle which they form subtends an arc of 38 degrees.
The angle formed by top-view sun, "Timer," and crossed circle is 130 degrees. "Timer," crossed circle, and zero form a 70-degree angle. 70 is the double of 35, a familiar item of vocabulary. For those who are not familiar with base-two arithmetic, it should be pointed out that multiplication or division by powers of two does not alter the basic "spelling" of binary numbers; it merely moves the decimal point around. 35 is binary 100011; 70 is 1000110. I read the zero-suffix as a two- multiplier that performs the same semantic function as the Roman II does in English. Elizabeth II, for instance, is the emulator or successor of Elizabeth I. "35 x 2" is the emulator or successor of his original, "35."
The dimensions of the figure formed by these five circles produce a familiar Zodiac formulation: the sum of 95, 95, 144, and 74+mm (the last line is somewhere between 74 and 75 mm) is 408+mm, or 130pimm. The angular and dimensional measurements of this figure, in other words, reproduce most of the vocabulary items demonstrated in the July 1969 cryptogram, the 340-character cipher, and the Exorcist Letter. The only omission is one hundred.
The logic of the diagram seemed, on the basis of the five-circle figure, to consist of joining together like figures by invisible lines, center to center. The next obvious class of like figures was the photoelectric "switches," of which there are four. I found their centers by drawing diagonals in them, then joined them with my straightedge.
The resulting figure is an irregular four-sided polygon with rather interesting properties (Figure 2). Each of the two shorter lines is a multiple of nine (45mm = 5x9; 36mm = 4x9), and their sum is the square of nine, 81 (45 + 36). Each of the longer sides is exactly double its opposite (90mm = 45 x 2; 72mm = 36 x 2). The angle formed by the two shorter lines is 140 degrees, which I simply redivide in base-two notation as 100011 00, 35 followed by the Morse letter I. I construe this statement as a typical Zodiac sentence, consisting of a subject (I) and a predicate (35), saying in English, "I (am) 35." As I pointed out in "Calculus," a similar redivision of the word BUS results in the expression 10000010 00, 130 followed by I, or "I (am) 130." Zodiac sentences use ME (Morse 110) prepositively but I (Morse 00) postpositively because prepositive use of I would involve leading zeros.
Geometric analysis of the diagram had eliminated the circles and the "swiches" as classes of like objects. All that remained was a pair of buses, a car and car battery, and the singular object, "String of Bombs." By constructing diagonals in "String of Bombs," I found that the geometric center of the figure was the cross of the F in "of." I used that point to relate to the two buses and to the car and car battery, which, while not like objects, at least have the word "car" in common. I found the centers of all these figures by drawing diagonals in them, then connected them with my straightedge to the F of "String of Bombs" as shown in Figures 3 and 4.
The figure Car-Car Battery-F forms a 117-degree angle. I pointed out in "Calculus" that the third crossed-circle sign in the 340-character cipher marks character #117. That number happens to denote the longitude of Riverside, California, where the Zodiac got his first victim into his power by disconnecting her battery while she was away from her car, then offering her a lift home when she found that it would not start. Note the coy postscript, "I hope you have fun trying to figgure (sic) out who I killed." As the above observations suggest, the unknown crime to which Z refers is the murder of Cheri Jo Bates in Riverside in October 1966. Authorship of that crime was not attributed to the Zodiac until seven months after receipt of the Bus Bomb Diagram.
In "Calculus," I said that the starting-point for my interest in the Zodiac murders was the discovery that the widely-separated sites of two Zodiac murders formed a radian angle with respect to the peak of Mount Diablo. I did not point out that the peak of that mountain is marked by a US Geological Survey benchmark, Vertical Angle Benchmark (VABM)
3849. VABM 3849 is the most important geodetic landmark in the San Francisco Bay Area; it is the zero-point for the USGS's township numbering scheme. It is also the apex of the radian angle which the Zodiac suggested in his letter of 28 June 1970 would be found on Mount Diablo.
On 28 November 1981, a Harvard graduate student named Joan Webster returned to Boston from a Thanksgiving visit with her parents in New Jersey. The last time that anyone admits to seeing her alive was when she was standing at the baggage carousel in the Eastern Airlines terminal at Logan Airport in Boston. Some time after that, she vanished from the face of the earth. So did her tote bag, which has never been found.
But Joan Webster's purse, containing her ID, was found next to the southbound lanes of Highway 107, out in a desolate marshy area between Boston and Lynn. Her suitcase turned up in a luggage locker at the Greyhound bus terminal in downtown Boston. No one has supplied a logical explanation for the dispersal of her effects all over the map of Massachusetts; nor has anyone explained why her (presumed) murderer would dispose of her body and tote bag so effectively that four years' searching has failed to turn them up, but leave the purse and suitcase — in two widely-separated locations — where they were certain to be found. The murderer's behavior was anomalous, or so it seemed.
The seeming anomalies in the behavior of Joan Webster's abductor and murderer appear to be resolved by geometric analysis, just as the Zodiac's anomalous-seeming behavior in murdering the San Francisco cabby was cleared up by the discovery that Z had done so in order to construct a gigantic geometric design (the radian) on the map of the Bay Area.
Use of a USGS topographic map of Boston shows that the baggage-claim area of the Eastern Airlines terminal at Logan Airport, the Greyhound terminal on Copley Square in Boston, and the Highway 107 site are joined by a gigantic 38-degree angle. The USGS notes four benchmarks in central Boston. One of them, BM9, is right at the Greyhound bus terminal; it forms the apex of the 38-degree angle.
I think that what I am suggesting is obvious. The Bus Bomb Diagram alludes, in a sly mathematical fashion, to an unknown Zodiac crime committed in the past (Riverside: car battery and 117-degree angle) and to an unknown Zodiac crime which is still, at the time of composition, eleven years in the offing (Boston: bus and 38-degree angle). The consistent use of angular structures having a benchmark at the apex characterizes the Zodiac in his Bay Area phase (radian on VABM 3849) and the abduction and murder of Joan Webster (38-degree angle on BM 9). A similar angular artifact having a benchmark at its apex, clearly alluding to the Riverside murder, is available; but it cannot be discussed here for legal reasons.
The degree of cold-blooded calculation involved in this scheme is chilling enough. What is even more horrifying, however, is the idea
that if the Bus Bomb Diagram and other Zodiac documents had been published sixteen years ago, the murder of Joan Webster might well have been averted.
I would like it to be known that I have copyrighted not only my solution to the Bus Bomb Diagram, but also the diagram itself. It is now my literary property. I have done this not so much for selfish as for tactical reasons. I am now in the position of being able to challenge the author of this work of art to step forward to dispute my claim.
© 1985 Gareth Penn
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