This was my write up on this forum, which was intended to provide an alternative, direct approach to the proposal which was originally worked through via candidate exhaustion limited by form assumptions and using, I recall, an Excel spreadsheet, as it was sufficient for the purpose. That original work was presented in detail, step by step, on Tom Voights forum. I don’t frequent that forum now and haven’t since Dave Oranchak picked this one up from Morph.
Correction: It was, in fact, on this forum, through the thread “Approaching the two remaining ciphers as chess problems,” that the specific work referenced was presented.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
I want to come back to something you said earlier in this thread, because I think it’s the clearest statement of where our two approaches differ:
It’s true that the radar finding something in the triangle would prove your case, but if it didn’t find anything, that wouldn’t disprove it. Zodiac may have been pointing at the triangle, without actually physically placing anything there.
I used no computer programs. If you look at my write-up, I’m pretty step-by-step about what I did. Remember, I worked backwards – I wasn’t trying to find “the” solution, just a possible solution. So I chose a location – Arthur Leigh Allen’s house – placed it on the map, calculated the appropriate distance and angle, and then checked to see if there was a way to encode that in the cypher. When you measure three and three eights inches and 10 “radians” directly, and then look to see if those numbers could be encoded, the solution is pretty obvious.
I have to confess that I don’t find the triangle to be as compelling a piece of evidence as you do. But that’s an entirely subjective opinion and I could be totally wrong.
I appreciate the honesty here, and I want to be equally direct about why I think this matters.
Your method starts with a destination and asks whether the cipher can accommodate it. Mine starts with the cipher and asks where it points. We arrived at the same plaintext, which I think says something important about the plaintext itself — but the two methods have very different evidentiary weight.
When you work backward from Allen’s house, you can’t know whether the cipher selected that location or whether you selected it and the cipher was flexible enough to permit it. With 29 unique symbols in 32 positions, Z32 is flexible enough to permit a lot of things. That flexibility is exactly the problem the cipher has posed for 55 years. The only way to cut through it is to enumerate the possibilities and let the constraints do the filtering — which is what my paper does. Of 2,044,224 candidates, 54 survive. The cipher’s own structure (the homophonic locks, the length requirement) does the work, not my choice of suspect.
The other point I want to address is your comment that you don’t find the triangle as compelling as I do. That’s a fair position to hold, and you may be right. But I’d note that your proposal offers no physical prediction at all — Allen’s house is just a house, and the coordinates don’t actually land on it when computed mathematically rather than estimated by hand on the Phillips 66. My proposal does offer a physical prediction: there is a ~100-foot equilateral triangular depression near the decoded coordinates, next to Lake Herman Road, visible in satellite imagery dating back to at least 1982, with the feature absent in 1964 imagery. It retains water. It matches the morphology of the triangle symbol in the ciphertext. It can be tested with ground-penetrating radar.
You might be right that the cipher is gibberish. But if it isn’t gibberish, then the question is whether it points to a suspect’s house (which requires rounding, tolerance, and a pre-selected target) or to a physical feature near the Zodiac’s first crime scene (which emerges from constrained computation without reference to any suspect). I think the evidence favors the latter, but I respect that you see it differently. Either way, GPR would settle it.
@coder1987 The owner of the property that your triangle sits on should be a matter of public record, and it should require only a fairly small amount of research to identify him or her. I suggest you reach out to whoever this is and ask about the triangle. They may have some knowledge of what it is and who constructed it.
I will say this – if the symbol you found had been a big Z – or, alternately, the circle-and-crosshair symbol Zodiac often used as a signature – I would find this absolutely compelling. Instead, you found a triangle – a symbol that Zodiac never directly identifies as being of any particular significance. You have some indirect arguments about why the symbol is important – and you may be right. But this seems to never have been an important symbol for him EXCEPT as a symbol that had prominent positions in one of his cyphers (arguably, maybe in 2 of his cyphers).
It’s a little like saying the letter “e” was significant to him, my evidence being that the text of his letters used it more frequently than any other letter. Maybe, but I’m skeptical. But if you told me that the letter Z was important to him because he signed some of his letters with it, I’d believe you.
I also think @shaqmeister brings up some objections that you dismiss too quickly. But I won’t rehash those.
Still, this is just an opinion, and yours may be right. Absolutely nothing conclusive in anything I’m saying. Try contacting the owner – you may learn something of interest.
BTW – I seriously doubt that ALA’s house is the location identified in the cypher. I just think that the probability of it being the location is greater than zero.
“Instead, you found a triangle – a symbol that Zodiac never directly identifies as being of any particular significance. “
In the Zodiac’s first cipher, Z408, the first ciphertext symbol he uses, of all possible symbols, is a hollow triangle.
In the Zodiac’s last cipher, Z32, the last ciphertext symbol he uses, of all possible symbols, is a hollow triangle.
He used the same symbol for his first and last encrypted symbols.
You are entitled to call that a fluke (I haven’t calculated the odds), however there is a triangle landmark on the ground by the decoded coordinates that matches this symbol.
First cipher.
Last cipher.
@coder1987 So – it’s your contention that Zodiac knew Z32 would be his last cypher and deliberately ended it with a triangle? In other words, his intent, at the time he created Z32, was for it to be his final cypher.
This feels counter-intuitive to me, and is not what I would have assumed. He seemed to like making cyphers. I know he didn’t make any after Z32, but to say he deliberately planned not to seems like a stretch. Do you have some evidence to support this?
No, that’s not my contention. I’m not claiming he knew Z32 would be his last cipher. I’m pointing out a structural fact about the ciphers we have: the first encrypted symbol he ever published (Z408, position 1) is a hollow triangle, and the last encrypted symbol in his last cipher (Z32, position 32) is a hollow triangle. Whether he planned that or not, it’s what happened. The observation stands either way.
Now, to your earlier point — that a big Z or his crosshair symbol would be more compelling than a triangle. Think about what you’re asking for. You’re saying you’d find it compelling if the Zodiac had carved his signature into the Earth next to a crime scene. The man who was never caught, who wiped down cab interiors and wore disguises, who mailed ciphers specifically so they couldn’t be read — you’re suggesting he would have signed his excavation site with his logo? The triangle is compelling precisely because it is deniable. It doesn’t say “Zodiac was here.” It says nothing — unless you solve the cipher first, follow the coordinates, and find it waiting for you. That’s how the whole puzzle was designed to work.
You also suggest I contact the landowner and ask about the triangle. That’s reasonable advice for a curious person, but it misses the point. This isn’t a curiosity — it’s a potential evidence site in an open homicide investigation. The Zodiac explicitly wrote “You have until next Fall to dig it up.” If the cipher is solved correctly, what’s at that location is not a question for a landowner over the phone. It’s a question for ground-penetrating radar operated under law enforcement authority, so that chain of custody is preserved if something is found.
You’ve said you seriously doubt Allen’s house is the location. I agree. But the alternative you’re left with is that the cipher points to the general Vallejo area and we shrug. My alternative is that it points to a specific, testable, falsifiable site with a physical anomaly that wasn’t there in 1964 and was there by 1982. One of these paths leads somewhere. The other doesn’t.
GPR is fast, cheap, and non-invasive. If nothing is there, I’m wrong and we move on. If something is there, this case changes overnight. You have not indicated that it is worth a quick check, which would be the scientific method to knowing if something is or is not buried there. It is pretty simple.
GPR is fast, cheap, and non-invasive. If nothing is there, I’m wrong and we move on. If something is there, this case changes overnight. You have not indicated that it is worth a quick check, which would be the scientific method to knowing if something is or is not buried there. It is pretty simple.
Just for the readers at home, let’s not get bamboozled away from what is the actual, non-scientific criterion for evaluating any and all solutions. Does it indicate a location that matches the diagram that what sketched in the April 1970 letter to the San Francisco Chronicle such that the mechanics of operation of a device of this kind, as detailed, would be viable? We’re not asked to search just anywhere for random buried “somethings.” Our assignment – and it couldn’t be more clearly stated – is, and has always been, to locate this. Not the device, as there almost certainly never was one, just the location. Fast, cheap, non-invasive and no cattle disturbed in the making of this trivial assessment. You don’t even have to leave the house.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
Just for the readers at home, let’s not get bamboozled away from what is the actual, non-scientific criterion for evaluating any and all solutions. Does it indicate a location that matches the diagram that what sketched in the April 1970 letter to the San Francisco Chronicle such that the mechanics of operation of a device of this kind, as detailed, would be viable? We’re not asked to search just anywhere for random buried “somethings.” Our assignment – and it couldn’t be more clearly stated – is, and has always been, to locate this. Not the device, as there almost certainly never was one, just the location. Fast, cheap, non-invasive and no cattle disturbed in the making of this trivial assessment. You don’t even have to leave the house.
Building on what has been said, I also think — and I’m convinced — that, depending on the proposed solution (whether it’s this one, another, or my own, which I invite you to take a look at), we shouldn’t expect a “bomb” or anything physical related to that context. Zodiac loved being the center of attention, and his modus operandi did not involve using dynamite to kill.
@coder1987 But you claim we know the triangle symbol is special to Zodiac because he starts his first cypher with one and ends his last cypher with one. You say “He used the same symbol for his first and last encrypted symbols.” If he isn’t aware that Z32 is going to be his “last encrypted symbol”, then I have to go back and ask again – how do we know that the triangle symbol is of special importance to him? How does finding a triangle in the area he indicates confirm we are on the right track? I just don’t see it.
Even if they wanted to, I have my doubts that the police would be able to get a warrant to obtain access to your triangle. There’s just not the evidence here that would establish probable cause. You’ll get farther just contacting the owner directly. If you know the county the property is in, you just need to find the website for the county assessor’s office. Find the location on their property maps and make a note of the map page and parcel numbers. Then look that property up in the assessor’s automated online lookup – it will give you, among other things, the street address and the name of the owner.
You’re asking the wrong question. You keep asking whether the triangle was symbolically important to the Zodiac. I don’t need to prove that. The triangle symbol appears at positions 1, 11, and 31 of Z32. Positions 1 and 31 are a homophonic lock pair — the cipher’s own internal structure forces those two positions to share the same symbol. That’s not an interpretive claim about Zodiac’s psychology. It’s a mechanical property of the ciphertext. The triangle bookends the message because the cipher’s lock structure requires it to.
Now: there is a 100-foot equilateral triangle on the ground, 254 meters from the decoded coordinates, next to Lake Herman Road. It wasn’t there in 1964. It was there by 1982. It retains water, confirming it is a depression, not a surface marking. It matches the morphology of the cipher’s triangle symbol when overlaid without rotation or skew. You have asked me repeatedly to explain why a triangle. I have. You keep re-asking the same question as though I haven’t answered it. At some point the response to “I just don’t see it” is: I’ve shown it to you. I can’t also make you look.
On the landowner — I appreciate the practical advice, but you’re solving the wrong problem. The question is not “who owns the land.” The question is “is something buried inside a triangular depression that sits at the decoded coordinates of an unsolved cipher from an open homicide case.” A phone call to a rancher does not answer that question. GPR does.
You’ve proposed a criterion: does the location match the bomb diagram from the April 1970 letter? Let’s apply it. The diagram shows a device buried underground in a hillside location. The decoded coordinates point to a hillside in unincorporated Solano County with a triangular topographic depression — confirmed by standing water in wet-season imagery — that is consistent with excavated and backfilled soil. The Zodiac wrote “You have until next Fall to dig it up.” The site is something that was dug. Your own criterion is met.
But then you say we can evaluate this without leaving the house, and that no cattle need be disturbed. With respect — you are describing a method of investigation that is designed to never produce a conclusive answer. You can debate satellite imagery forever. You cannot debate what a GPR unit finds three feet underground. That is the difference between discussion and evidence.
I’ll put it as simply as I can. Two positions are available in this thread:
Position A: The cipher probably points to the Vallejo area, but we can’t know exactly where, and there’s no way to confirm anything, so let’s keep discussing it.
Position B: The cipher points to specific coordinates where there is a testable physical anomaly. A single non-invasive scan would either confirm or eliminate it.
Position A is unfalsifiable. Position B is falsifiable. I know which one I’d rather defend.
@lendor-77 I will be taking some time to review your proposed Z32 solution later today. Will post a response in your thread, as I see @DMW and @shaqmeister haven’t done so yet.
@coder1987 But you claim we know the triangle symbol is special to Zodiac because he starts his first cypher with one and ends his last cypher with one. You say “He used the same symbol for his first and last encrypted symbols.” If he isn’t aware that Z32 is going to be his “last encrypted symbol”, then I have to go back and ask again – how do we know that the triangle symbol is of special importance to him? How does finding a triangle in the area he indicates confirm we are on the right track? I just don’t see it.
Even if they wanted to, I have my doubts that the police would be able to get a warrant to obtain access to your triangle. There’s just not the evidence here that would establish probable cause. You’ll get farther just contacting the owner directly. If you know the county the property is in, you just need to find the website for the county assessor’s office. Find the location on their property maps and make a note of the map page and parcel numbers. Then look that property up in the assessor’s automated online lookup – it will give you, among other things, the street address and the name of the owner.
Your claim that police probably couldn’t get a warrant for a GPR scan is incorrect, and it’s worth correcting because it’s discouraging action based on a misunderstanding of the law.
First, GPR may not require a warrant at all in this case. The site is an open hillside in unincorporated Solano County — not a home, not a yard, not a curtilage. Under the open fields doctrine, established by the Supreme Court in Hester v. United States (1924) and reaffirmed in Oliver v. United States (1984), the Fourth Amendment does not protect “open fields” and therefore police searches in such areas as pastures, wooded areas, open water, and vacant lots need not comply with the requirements of warrants and probable cause. The Court in Oliver went further: an individual may not legitimately demand privacy for activities conducted out of doors in fields, except in the area immediately surrounding the home.
This isn’t an edge case. Almost 96 percent of private land in the U.S. can be searched without a warrant under this doctrine. A remote hillside with cattle trails on it is about as clear-cut an “open field” as you can get.
Second, GPR is non-invasive. Its non-invasive nature minimizes disturbance to potential evidence and preserves crime scene integrity, critical for maintaining forensic chain of custody and ensuring admissibility in court. Nothing is dug. Nothing is disturbed. The operator walks the surface with equipment roughly the size of a lawn mower. Law enforcement agencies can use ground penetrating radar technology when looking for buried or hidden evidence. Forensic investigators can use GPR to find and retrieve delicate material without causing damage.
Third, even setting aside the open fields doctrine, law enforcement doesn’t need a full warrant to conduct a preliminary GPR scan. They need landowner consent — which they can simply request. If GPR detects a subsurface anomaly, that result itself becomes the basis for probable cause to obtain a warrant for excavation. This is standard forensic procedure. GPR can be pushed along the surface to help identify specific targeted areas for further investigation. It helps to remove the guesswork out of excavating locations based on limited or no evidence.
So the actual sequence is: law enforcement contacts the landowner, requests permission to walk GPR across an open hillside for ten minutes, and either finds something or doesn’t. If they find a subsurface anomaly, they now have probable cause for a warrant to excavate. If they don’t, everyone goes home. This is not a legal obstacle. It is a phone call.
Your suggestion to look up the county assessor is fine practical advice, but it solves the wrong problem. Knowing who owns the land is step one. Getting law enforcement to make the request is step two. The legal framework for both steps already exists and is well established.
Source for the open fields doctrine: Cornell Law Institute, Fourth Amendment — Open Fields Doctrine.
You’ve proposed a criterion: does the location match the bomb diagram from the April 1970 letter? Let’s apply it. The diagram shows a device buried underground in a hillside location. The decoded coordinates point to a hillside in unincorporated Solano County with a triangular topographic depression — confirmed by standing water in wet-season imagery — that is consistent with excavated and backfilled soil. The Zodiac wrote “You have until next Fall to dig it up.” The site is something that was dug. Your own criterion is met.
No. Cherry picking again. The diagram describes the mechanism which requires proximity to the bus of both A and B, and an explosion at A that has to hit the bus. But I add this point only to keep the thread honest for our future readers.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
@shaqmeister
Can you help me understand a few things about your cattle watering hole theory?
Specifically, could you explain why a rancher would excavate a water catchment in the shape of a 100-foot equilateral triangle rather than the circular or irregular basins used on every other cattle operation in Solano County? And why this particular watering hole has three straight edges of equal length meeting at three vertices with interior angles within a degree of 60°, when cattle hooves produce scalloped, irregular erosion patterns? And why it points due north? And why it appears between 1964 and 1982 on a hillside 254 meters from the coordinates decoded from an unsolved cipher that contains triangle symbols at three positions including both ends of a homophonic lock pair? And why it happens to sit next to Lake Herman Road, where the Zodiac committed his first known murder? I ask all of this with genuine curiosity, because if there is a simple agricultural explanation that accounts for all of these features simultaneously, I would love to hear it — it would save everyone a lot of trouble.
