Clarification: P66 may be the key, not the plotting surface

When I first posted my Z32 candidate, I assumed that SIX INCHES had to be measured physically on the Phillips 66 map itself.

After seeing Shaq’s direct plotting, I realised two things: the supplied P66 section is much smaller than I had assumed — about 8″ × 6¾” (20.3 × 17.1 cm) — and my SIX/SIX construction does not physically land at Neary when six literal inches are measured on that sheet.

I initially thought this was a serious problem with the plaintext.

I now think the problem may instead be the assumption that P66 has to be the final plotting surface.

Zodiac wrote:

“The map coupled with this code will tell you where the bomb is set.”

He did not say that the destination had to be physically plotted on that particular sheet.

My current interpretation is therefore:

P66 supplies the system. Z32 supplies the values.

P66 gives us:

• Mount Diablo as the origin
• the 0–3–6–9 dial
• “0 is to be set to Mag. N.”
• approximately 1 inch = 6.4 miles

Within my restricted plaintext grammar,

AT [direction] [distance] INCHES FROM MOUNT DIABLO [destination]

the Z32 repeat structure selects SIX / SIX before any geography is examined.

Among the four values actually printed on the dial — ZERO, THREE, SIX and NINE — SIX is the only three-letter direction that fits the remaining space, while the repeated-symbol constraints also select SIX as the distance word.

This gives:

AT SIX SIX INCHES FROM MOUNT DIABLO ??T

So SIX/SIX is not being chosen because Neary happens to lie there. The values come first.

The first SIX selects position 6 on the dial.

If:

0 = Magnetic North

then:

6 = Magnetic South

or, mathematically, half a revolution / π radians.

I now think this should be understood as a real-world magnetic reference, established by a magnetic compass in the original 1970 method, rather than by treating the graphical north of the P66 road map as precision geometry.

This distinction matters. If the road map itself is slightly misaligned and we use its graphical north as exact True North, that error is carried into the resulting bearing.

A compass does not depend on the road graphics. It establishes the real-world magnetic direction independently.

The second SIX gives:

SIX INCHES

If the destination were being plotted directly on P66, no conversion would be necessary. We could simply measure six physical inches.

But if P66 is instead the decoding key, then we need a map-independent geographic distance:

6 × 6.4 ≈ 38.4 miles

So the combined instruction becomes:

FROM MOUNT DIABLO
MAGNETIC SOUTH
APPROXIMATELY 38.4 MILES

That vector can then be transferred to a more suitable map using that map’s own scale.

The second map does not need to have the same scale as P66. That is exactly why the conversion from inches to miles matters.

The workflow therefore becomes:

P66 + Z32 → geographic vector → second map → location

rather than:

Z32 → ruler/protractor directly on P66 → location

Only after fixing that vector do I check the geography.

Neary Quarry is approximately 38.4 miles from Mount Diablo and lies very close to the corresponding magnetic-south direction.

That is why the remaining:

??T → PIT

is interesting to me.

The important order is:

Z32 structure → SIX/SIX

then:

P66 → Magnetic South / 38.4 miles

and only then:

geography → Neary Quarry

So the main correction to my earlier posts is simple:

I no longer think SIX INCHES should be physically plotted on P66.

I originally assumed P66 had to perform two jobs: decode the instruction and serve as the final plotting map.

I now think it may only need to perform the first.

P66 may be the key that converts Z32 into a real-world direction and distance.

I am not claiming this proves the plaintext. The largest remaining plaintext assumption is still FROM MOUNT DIABLO, because the map itself already supplies Mount Diablo, and PIT is not completely cipher-forced.

But the proposed mechanism is now quite simple:

P66 is the key.
Z32 selects SIX/SIX.
The magnetic reference gives the direction.
The printed scale gives the distance.
A second map gives the location.

Posted by: @northkey

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Clarification: P66 may be the key, not the plotting surface

When I first posted my Z32 candidate, I assumed that SIX INCHES had to be measured physically on the Phillips 66 map itself.

After seeing Shaq’s direct plotting, I realised two things: the supplied P66 section is much smaller than I had assumed — about 8″ × 6¾” (20.3 × 17.1 cm) — and my SIX/SIX construction does not physically land at Neary when six literal inches are measured on that sheet.

I initially thought this was a serious problem with the plaintext.

I now think the problem may instead be the assumption that P66 has to be the final plotting surface.

Zodiac wrote:

“The map coupled with this code will tell you where the bomb is set.”

He did not say that the destination had to be physically plotted on that particular sheet.

Neither did he say:

“The map coupled with this code followed by a calculation and then another map will tell you where the bomb is set.”

The range is in inches. There is nowhere else, other than on this precise map, that LE could have plotted a distance in “inches.”

Why must the Phillips 66 map be the final plotting surface?

My interpretation does not use it that way. The map supplies the orientation and scale required by the code. SIX INCHES on a map whose printed scale is approximately 6.4 miles per inch defines a real-world distance of approximately 38.4 miles.

Once that distance and the bearing have been derived, they describe a geographic vector from Mount Diablo. Transferring that vector to a map of suitable scale does not change the distance derived from the Phillips 66 map.

So I agree that measuring six physical inches directly on the Phillips 66 sheet does not reach my proposed endpoint. Where we differ is the assumption that Zodiac required the Phillips 66 sheet itself to be the final plotting surface.

Firstly, the Phillips map is not 6.4 miles to the inch, as has been clearly shown. Secondly, the instruction to use “the map” and “this code” is a complete instruction and doesn’t require anything further to enable it to be carried out, hence adding something further is contraindicated and arbitrary. Thirdly, the interpretation you propose would have produced a distance in miles, not inches. And to be complete, we cannot lay off inches on any other map if we have not been told which map and what its scale and, in any case, we would simply have been given that map instead.

The direct and unambiguous statement of method and the method you propose generate different locations. Which of these two methods do you suppose LE would have been expected to have pursued on having received a physical map along with a decoded distance in inches, and on what basis do you consider them to have been in error in doing so?

Thanks. I think there are three separate issues here.

Firstly, I agree that it has more recently been shown that the Phillips 66 map’s actual geographic scale does not correspond precisely to the 6.4 miles per inch printed on the map. But that does not change the information available to Zodiac or to a recipient of the map in 1970.

My interpretation uses the scale as it was printed on the map Zodiac supplied. Whether that printed scale was geographically accurate is a separate question. A modern demonstration that the map itself was inaccurate cannot retrospectively alter the scale that a solver in 1970 was given and would have had to work with.

Secondly, I don’t think this requires adding anything to the instruction. The map and the code are sufficient to perform the operation I am proposing.

The code supplies the number of inches, while the supplied map provides the scale needed to convert that map distance into an approximate real-world distance. Once that conversion has been made, the result is a geographic distance, not a measurement tied to a particular sheet of paper.

Using a more detailed map afterwards would therefore not add another element to the code or require Zodiac to specify another map. It would simply be the practical means of plotting and examining the resulting location in greater detail. This is particularly relevant when the object being sought was supposedly buried, while the supplied Phillips 66 map is essentially a road map and contains very little local terrain detail.

Thirdly, my interpretation does produce a distance in inches first, exactly as Zodiac stated.

The sequence is:

SIX → 6 inches

Only when those 6 inches are coupled with the scale printed on the supplied map do they become an approximate real-world distance:

6 inches × 6.4 miles per inch = approximately 38.4 miles.

So the cipher is not producing approximately 38.4 miles instead of inches. It produces the number of inches first; the supplied map then converts that map measurement into the corresponding approximate real-world distance.

Once that distance has been established as approximately 38.4 miles, it can be transferred to a more detailed map covering the same area. The scale of that second map changes only how approximately 38.4 miles is represented on paper; it does not change the geographic distance itself. A more detailed map can then be used to examine the actual terrain and features around the resulting location.

In that sense, both parts of Zodiac’s instruction are being used: the code supplies the inches, and the supplied map gives those inches geographic meaning.

As to your final question about what LE would have been expected to do, I don’t think I need to argue that LE was “in error” if they attempted to lay the decoded inches directly onto the Phillips 66 map. That is certainly a reasonable interpretation of the instruction.

What I am proposing is an alternative interpretation of how the map and code work together: the Phillips 66 map establishes the geographic vector, and a more detailed map can then be used to examine where that vector actually terminates on the ground. Given that the stated objective was to locate something supposedly buried, I don’t think moving from a road map to detailed mapping after establishing the approximate real-world distance is an arbitrary additional decoding step.

The two interpretations produce different locations, so ultimately that difference is something that can be tested geographically rather than resolved simply by assuming at the outset which interpretation Zodiac intended.

Posted by: @northkey

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Firstly, … My interpretation uses the scale as it was printed on the map Zodiac supplied. 

For which we would have expected:

“The [scale on the] map coupled with this code will tell you where the bomb is set.”

Posted by: @northkey

Secondly, I don’t think this requires adding anything to the instruction. The map and the code are sufficient to perform the operation I am proposing.

It requires 1.) an initial additional conversion step, from inches to a real-world distance in miles, followed by 2.) a second conversion from miles back to the inches of some other map, when we have a perfectly serviceable map on which we can immediately lay an inch ruler right here in our hand. Rather, “real-world” distance demands:

“The Mt. Diablo Code concerns Radians + # [miles] along the radians”

Posted by: @northkey

The two interpretations produce different locations, so ultimately that difference is something that can be tested geographically rather than resolved simply by assuming at the outset which interpretation Zodiac intended.

One of these “interpretations” follows the directions as given, the other supplements these directions with steps that are not indicated, limits the use of “the Map” to just “the scale on the Map” and challenges reason as to why we would be using inches and not miles at all. They are not equally reasonable and we should not be looking for “intent” any deeper than what we are immediately and unambiguously given.

In 1970, having a paper map and laying a ruler over it is precisely the action we (and The Zodiac) would expect to have been triggered in the evidence room upon solution of the cipher.

Posted by: @northkey

↑

Firstly, I agree that it has more recently been shown that the Phillips 66 map’s actual geographic scale does not correspond precisely to the 6.4 miles per inch printed on the map. But that does not change the information available to Zodiac or to a recipient of the map in 1970.

In 1970 The Zodiac would have been fully aware that what he was sending was part of a “gas station road map” and that distances deduced from it would be poorly matched to real-world distances. 

I’ll try to address both of your posts together here.

In 1970, the natural reaction to receiving a paper map and a result expressed in inches would indeed have been to put a ruler on that map and measure directly from Mount Diablo. That is PRECISELY what I think Zodiac expected them to do. I don’t disagree with you on that point at all.

Where we differ is in assuming that the most immediate operation must therefore also be the complete one. That literal approach has not produced a generally accepted solution to Z32 in more than half a century, so I don’t think its apparent obviousness is, by itself, a strong reason to exclude another operation.

Nor does my interpretation reduce “the Map” simply to its scale. Mount Diablo provides the geographic origin, the 0–3–6–9 diagram provides the directional framework with 0 set to magnetic north, and the printed scale converts the decoded six inches into approximately 38.4 miles.

You ask why Zodiac would use inches rather than miles. In my interpretation, that is precisely the point: if he gave the distance directly in miles, the map scale would have no function. Giving it in inches forces the decoded value to interact with the map.

So I agree completely about what someone in the evidence room in 1970 would most naturally have done first. I just don’t think that establishes that it was the final operation Zodiac intended.

As to your second post, I think you have stated the relevant point rather well yourself:

“In 1970 The Zodiac would have been fully aware that what he was sending was part of a ‘gas station road map’ and that distances deduced from it would be poorly matched to real-world distances.”

I agree.

And that is precisely why I question whether Zodiac intended a ruler measurement on that gas-station map to provide the final real-world location.

Posted by: @northkey

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As to your second post, I think you have stated the relevant point rather well yourself:

“In 1970 The Zodiac would have been fully aware that what he was sending was part of a ‘gas station road map’ and that distances deduced from it would be poorly matched to real-world distances.”

I agree.

And that is precisely why I question whether Zodiac intended a ruler measurement on that gas-station map to provide the final real-world location.

More that any of your other points, I think that this is the one that gets us to the very heart of where modern-day solution approaches go astray in not fully transporting the solver back to 1970. We are so attuned to dropping some precise coordinate or zip code into Google Maps and have it give us a location so precise that we can zoom in to Street View and check out the very face of our never-seen-before destination that we forget the world wasn’t always like this.

I am not old enough to have been navigating around the country in 1970, but I was doing exactly this in the late 80s and 90s. We drove by maps that, at best, might be able to get you to roughly the intended side of the destination town or city, but not to the door of your cabin or hotel. For that, you would be relying on nearby landmarks or even, most of the time, resigning yourself to asking a local when you get there for final directions.

Turning to Z32, today we naturally expect that somehow The Zodiac had given us such precise directions that we only had to arrive there and take out a shovel. We become, understandably at first, dissatisfied with the Phillips 66 and then start to look for some method of conversion that will again get us to GMaps precision.

The problem posed, though, is merely to determine “where the bomb is set.” “It is dug into a sloping hillside adjacent to the municipal office of a certain gas company on Willow Street in Pittsburg right by the street lamp” is one possible answer to our question “where is the bomb set?” But then, so is “East of the I80 in central Vallejo” also a valid answer, as is “somewhere in Concord.”

So, I would rather turn your point here right around on its head and ask why, having been given only a crappy gas station map, are we allowing our modern-day street view expectations to have us searching for somewhere more precise than merely “somewhere kind of around here?”

According to a 1970s mindset, both the Phillips and an inch ruler are totally up to what we would expect from the era.

Posted by: @northkey

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You ask why Zodiac would use inches rather than miles. In my interpretation, that is precisely the point: if he gave the distance directly in miles, the map scale would have no function. Giving it in inches forces the decoded value to interact with the map.

To what end? If we’re to be working with real-world distances just encode the distance in miles, forget the map altogether and then send a postscript later reading:

“The code concerns radians from Mag. N + # miles along the Radians from the Devil’s Mountain.”

I think your broader point about putting ourselves back into a 1970 mindset is a good one, and I agree that we should not expect modern GPS-level precision from a Phillips 66 road map.

There is, however, one additional 1970s tool that I think needs to be included in the picture: a compass.

The Phillips map and an inch ruler can give us distance at the map’s stated scale, but the map itself cannot give us the magnetic direction Zodiac explicitly asks us to establish when he says that “0 is to be set to Mag. N.” For that, the solver needs a compass to establish magnetic north.

So I think I would slightly modify your last sentence rather than disagree with it: according to a 1970s mindset, a Phillips road map, a compass and an inch ruler are entirely consistent with the tools we would expect someone to use.

And, interestingly, those are precisely the three things needed for the operation I am proposing: the compass establishes magnetic north, the Zodiac diagram establishes the direction from Mount Diablo, and the ruler together with the Phillips scale establishes the distance.

But couldn’t the same question be asked of the cipher itself?

Why didn’t Zodiac simply provide the entire instruction in plaintext?

He chose to provide a map, a cipher, and instructions involving radians and magnetic north.

My interpretation is that these elements were intended to work together. The inches are converted through the map scale into miles, allowing the resulting distance and direction to be transferred to a more detailed map.

That doesn’t establish that my interpretation is correct, but I don’t think the fact that Zodiac could have expressed the distance more directly is, by itself, an objection to it.

A compass has a clear use in navigation, but we’re not navigating here, we’re merely pin-pointing a rough location on a map. Nobody is suggesting we actually have to proceed from Mount Diablo to our destination.

I personally have little doubt that the introduction of the magnetic north shift was simply for the reason that when he proceeded to divide out the 12 map-north radials on the Phillips 66 he noticed that his destination lay just to one side of right in between two radials and realised that a shift through the magnetic declination of the time would get him right on one of them and greatly simplify things. It seems likely that part units might be required for the “inches” but the Z32 is too short to have fractions in the bearing as well.

Posted by: @northkey

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He chose to provide a map, a cipher, and instructions involving radians and magnetic north.

My interpretation is that these elements were intended to work together.

1. Solve the cipher;
2. Draw out a line from Mount Diablo on the map according to the given bearing, having added 17°;
3. Measure out the “# inches” along the line just constructed.

What do you see as missing here? What is not “working together?”

Posted by: @shaqmeister

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1. Solve the cipher;
2. Draw out a line from Mount Diablo on the map according to the given bearing, having added 17°;
3. Measure out the “# inches” along the line just constructed.

To wind it back, then, to the required initial considerations as regards interpretation of what we are being asked to do I must return to the fundamental question: Why would anyone think that it is not simply and obviously this? What is wrong with it being this? Why are you even looking for something else?

It will be the answers to this question that will betray the cognitive bias inherent in the modern GPS mapping era.