Zodiackiller.com Message Board: Theories: "THE RADIAN THEORY" IS IT CONSIDERED VALID?

I HAVE A QUESTION CONCERNING THE "RADIAN THEORY"
PUT FORTH BY GARETH PENN. IS THIS GENERALLY THOUGHT TO BE A VALID THEORY. I'M NEW TO THE CASE SO IT MIGHT BE A STUPID QUESTION. IT JUST SEEMS TO BE FAR FETCHED TO ME

It is far fatched, and as far as I am concerned, has absolutely no basis in fact and exists only in Penn's mind. I have shown that theory to be completely untenable and bankrupt, as the regular readers/posters of this board can attest to. Actually, it was fairly easy to do so, and Penn even attempted a weak rebuttal last month, but strangely enough, we haven't heard from him since then. Gee, I wonder why...?

Hello:
I was watching a show on TLC about the zodiac killer and there were two clues that I find interesting. One is the symbol and he said that he is collecting slaves for the afterlife. Well I was just reading a book that tells about this very thing it is an old book.

I'm wondering if the occult connections to this case have been explored thoroughly enough. Several aspects of the story lead me to wonder this, such as:
1)the fact that the cross-in-circle logo is an occult symbol, representing the four cardinal directions, the four seasons, and Hippocrates' four humors.
2)Satanic cults place great emphasis on the cardinal directions when performing their rituals. The map Zodiac sent to police featured a cross marked on top of Mt. Diablo--spanish for "devil mountain." He seemed very concerned with the locations of the murder scenes in relation to specific angles emanating from Mt. Diablo, which suggests to me that he may have been trying to perform a ritual of some kind.
3)Satanic cults and secret societies (especially those that fall under the Freemasonic umbrella) are highly concerned with the underlying mathematics of nature and human events. Initiates are ranked according to a system of degrees, such as those used in measuring angles (hence the killer's fascination with radians.)
4)The killer's suggestion that he was collecting slaves for the afterlife hints at some involvement with or interest in Satanism and/or the occult.
I'll be the first to admit that I am no expert on either this case or the occult. I don't practice witchcraft, nor am I a police detective. But it does strike me as odd that the occult angles of this case seem not to have been pursued in any great depth. I am hoping someone out there can either elaborate on or refute my theories.

Well, duh....
Had I checked the rest of the message board, I might have noticed the numerous occult references contained therein. Oh, well...hopefully I added something to the discussion.
I was just considering Penn's radian theory...my first thought was, how could Zodiac have been an Ivy-league professor, when he couldn't spell worth a darn? Don't you have to have some writing ability to gain entry into an Ivy League school, and especially to become a professor?
But then, I began to wonder if Zodiac's frequent misspellings were a deliberate ruse, designed to mask his true intelligence...I noticed that in a few cases, he spelled the same word in different ways...such inconsistency seems odd.

The radian theory is totally bankrupt, as I have demonstrated time and again here on this board. In the first place, Penn claims the radian, using Mt. Diablo as the vertex, passes through Presidio Heights and Blue Rock Springs. Nothing can be further from the truth. Since Z gave us a map to use in conjunction with his code to find a "buried bomb," we should be using HIS map and not anyone else's.

When we look at his map (found elsewhere on this site) BRS is not even on it! Penn saw the map (he admitted as much in Times 17), yet he conveniently and conspicuously failed to mentioned this critical fact. I suspect the reason is because then his theory wouldn't work, and he'd have nothing on which to base his book and make $$$ from it.

Using known landmarks, it was easy to calculate the angle between BRS and PH on Z's Phillips 66 map section, and the closest I could measure is 58.5 degrees. Since a radian is the angle subtended by an arc of equal length to its radius (about 57.3 degrees), the "radian" is too big. Thus, the theory doesn't wash. Penn ignored this and continued to write his book anyway.

In any case, Penn gives no reason as to why one leg of the radian should pass through BRS, because it was on LHR that Z began to "collect slaves for his afterlife," and PH is where it ended, thus those two points should plot the "radian," not BRS and PH. I suspect the real reason he chose BRS and not LHR is because LHR is one degree further east as measured from Mt. Diablo, therefore, the "radian" would have been 59.5 degrees. It was easier for him to fudge 1.2 degrees rather than 2.2 degrees, and I suspect he assumed that no one would bother to check his facts (too bad he didn't know about me, otherwise he would have thought twice before foisting his "theory" on an unsuspecting public).

What it boils down to is, don't waste your time on Penn or his theory. All he has managed to do is further confuse the case and accuse an innocent man of serial murder. And the sad part is, he is so arrogant that he doesn't even see it.

I thought that the radians may just be a counting system zodiac was using to signify his victims. Not the actual placement but just the number of victims. Six radians completes a full circle. Maybe that is why he stopped killing he had completed a full circle.

Ed wrote:
"Using known landmarks, it was easy to calculate the angle between BRS
and PH on Z's Phillips 66 map section, and the closest I could measure
is 58.5 degrees. Since a radian is the angle subtended by an arc of
equal length to its radius (about 57.3 degrees), the "radian" is too
big. Thus, the theory doesn't wash."

First off, I trust your intellect and it sounds like you've measured the radian pretty accurately -- I've used a felt pen (like Z), which gave me a little more wiggle-room and puts me closer to the true radian value. Regardless, I still think that even if the angle were 2 degrees off either way, the radian hint in the July 1970 postscript would still be significant. A small variance like that could be caused by the curvature of the earth, for one thing, or the lack of victims in the exact spot, for another. In any case, my feeling is that angle BRS-Mt.D-PH is close enough, for the simple reason that Z mentioned a radian, by name, in conjunction with the map.

When considering the possibility that Z was referring to this radian when he mentioned them in his postscript, remember that Z doesn't have to be an Ivy Leaguer to know the term. It's fairly obscure, but it isn't knowledge exclusive to one east coast academic. A carpenter, surveyor, or engineer, or even someone who apprenticed under one, could have known what a radian is. Accepting one part of Penn's hypothesis doesn't necessitate swallowing the whole thing -- as I've learned.

--Jake
http://members.aol.com/Jakewark/index.html
"This is the Zodiac Speaking..."

Question: On the November 9th message, page 6, there is a modified crossed-circle that has several x's on it. Do those in fact point to the murder sites when placed on Diablo?

I've never checked, I'd need an acetate sheet, felt-tipped pen and a map before I do the "Penn thing."

Jake... the reasons I have a problem with the whole radian "theory" are:

1) It is not a radian;

2) Z never said anything about using murder sites to plot a radian;

3) Z said that by using his map and code, which had to do with radians (plural) and the number of inches (plural) along the radians (plural), you could find a buried bomb;

4) Since Z started "collecting slaves for his afterlife" at LHR, one would think that the radian, if it existed, would plot the beginning and end of his crime spree (it obviously plots the end, so why not the beginning?), so therefore it is not logical to have BRS as one point instead of LHR;

5) BRS, one of the three critical points used to plot the radian, is not even on the map section Z provided for us to locate his bomb!

Mention of the term "radians" twice in one letter does not dictate (to me anyway) that we must draw an angle that approximates one radian using BRS, Mt. D and PH to do so, and ignore the rest of Z's clues about what the map, code and hint were really about. I still think that, just like Z said, the code, when deciphered, will yield measurements in radians and inches to be used on his map to pinpoint the spot he claimed he buried a bomb. Anything else is putting words in his mouth (or ink in his felt-tipped Penn).

Besides, if we start plotting radians, we must somehow fit inches in there; we cannot use one part of his clue and ignore the rest (why did Penn focus on radians and not inches in the first place?). Since Z used the term "radians" in the plural but Penn thought that it must actually be singular, then Z's use of the term "inches" in the plural therefore means that it is singular also. Thus, we have one radian and one inch. We have the radian (sort of), but where do we start measuring the inch from? Since Penn arbitrarily chose BRS (as far as I can tell, for no other reason except that it sort of fit), maybe we should start measuring the inch from another point. Hey, how about Lake B? Since BRS isn't on Z's map but Penn used it anyway, maybe we should get another map, plot the Lake B attack site, and measure one inch from there to see what that points at. Maybe it's Hunter's Running Deer Ranch... or is it Carl's ranch?

The point is, the entire theory is ridiculous, since it makes use of only one single word while completely ignoring everything else Z wrote in conjunction with it, and is even shakier when we realize that Penn apparently fabricated the story about how he went to the Napa Library, looked at a few books, and discovered Z's true identity.

I'll need a lot more to convince me that the radian truly exists. What Penn plotted is close, but so what? His approach was totally nonsensical and illogical, and it flies in the face of the facts.

Just throwing in my own ignorant blurb here: Maybe his referance to the burried bomb was actually refering to one of the Naval Weapon Stations... Maybe he worked there as well ... we are all just guessing! J

Zodiac's hint stated "radians and # inches along the radians." This implies that the radian is being used as a measure of arc, not angle.

The Unabomber-Zodiac Connection

Oh, man, I'm in trouble now -- defending a theory I only partially adhere to myself. Here we go...

Ed wrote:
"1) It is not a radian;"

Even with the most sharpest pencil and most accurate protractor, it would still be impossible to draw a true radian angle, since the measurement itself is based on the transcendental number pi, which as we all know never ends. So in that respect, even the physicists at MIT couldn't draw a true radian in a lab, never mind execute one in physical space over something like 700 squre miles.

More to your point, though, there has to be a variance, and I think that one of 1.2 (or even 2.2) degrees is not so great a differential that we should throw out the idea that something is going on here.

"2) Z never said anything about using murder sites to plot a radian;"

He never said anything about Lake Berryessa, either, but we're all agreed that someone was killed there.

"3) Z said that by using his map and code, which had to do with radians
(plural) and the number of inches (plural) along the radians (plural),
you could find a buried bomb;"

True, but we know that it had something to do with Mt. Diablo. It is not, to my mind, a huge logical jump to suppose that maybe a radian (singular, admittedly) might be placed on the point that Z pinpointed for us.

No bomb was ever found, nor was any other explanation for Z's reference to radians and the number of inches along them. However, Z's use of the term, in conjunction with the map, the annotation of Mt Diablo, and the intellectual ability that a reference to magnetic north implies, suggests to me that he had something in mind, and that we should pay attention to what we do find here.

"4) Since Z started "collecting slaves for his afterlife" at LHR, one
would think that the radian, if it existed, would plot the beginning and
end of his crime spree (it obviously plots the end, so why not the
beginning?), so therefore it is not logical to have BRS as one point
instead of LHR;"

This is totally true, and as Tom has pointed out, the Berryessa attack came before the SF attack, further screwing up the logical order of things. What can I say? You're right.

"5) BRS, one of the three critical points used to plot the radian, is not
even on the map section Z provided for us to locate his bomb!"

Yes, but it still exists there in space! The magnetic north pole isn't on Z's map either, but because he refers to it, we know that the "0" arrow of his crossed-circle is still supposed to point there.

"Mention of the term "radians" twice in one letter does not dictate (to
me anyway) that we must draw an angle that approximates one radian using
BRS, Mt. D and PH to do so, and ignore the rest of Z's clues about what
the map, code and hint were really about. I still think that, just like
Z said, the code, when deciphered, will yield measurements in radians
and inches to be used on his map to pinpoint the spot he claimed he
buried a bomb. Anything else is putting words in his mouth (or ink in
his felt-tipped Penn)."

Well, we're doing the best we can, working with inomplete knowledge of the killer's agenda. Z's threats to plant a bomb were all bluffs, however, and it's possible, if not probable, that there is no bomb anywhere. Since no bomb was found, does this mean that the map, code, and subsequent postscript are worthless and should be thrown out? What Penn found -- and buried beneath a mountain of extraneous half-truth -- is the most likely explanation for those three artifacts that has yet been proposed.

"Besides, if we start plotting radians, we must somehow fit inches in
there; we cannot use one part of his clue and ignore the rest (why did
Penn focus on radians and not inches in the first place?)."

The code having never been solved (unless you count Penn's solution, which I don't), I think you'd have to start with radians, since they're what's supposed to be measured. If you want to measure a desk, for instance, you don't start measuring space and then fit the desk into it, you go to the desk with a ruler and measure it. You need to find the object before you can count how many inches it takes up.

In the case of the radian, which is invisible, you would need a landmark. Luckily, Z provided us with one when he drew his stylized crossed-circle on Mt. Diablo. Since the only clues we have are a radian (which has an apex) and a landmark, it only makes sense to put the one over the other.

Having done this, the logical step is to rotate the radian until something happens. If we lay it facing due north, the western leg crosses the intersection of the nearest lines of latitude and longitude, which might be interesting to someone who knows about maps. This is the intersection of 38 N Lat and 122 W Long -- Mike O's birthday and alleged favorite number aside, this doesn't mean much. Rotating the angle further west, though, does produce something -- a leg running through Presidio Heights and a leg running through Vallejo very close to both murder sites.

To ignore this mathematically demonstrable fact is, to me, not just illogical but counterintuitive. To be sure, Penn was wrong about an awful lot. So was Graysmith, though, and his book is still a valuable reference tool. For that matter, Teddy Roosevelt was reduced to anti-Irish hatemongering late in his career, but his work to save the Adirondacks was noble and just. For my money, the radian is a valuable clue -- not to any suspect, but to what kind of mind Z posessed.

--Jake
http://members.aol.com/Jakewark/index.html
"This is the Zodiac Speaking...

"No bomb was ever found, nor was any other explanation for Z's reference to radians and the number of inches along them. However, Z's use of the term, in conjunction with the map, the annotation of Mt Diablo, and the intellectual ability that a reference to magnetic north implies, suggests to me that he had something in mind, and that we should pay attention to what we do find here. "

I keep reading about this "intellectual ability" connected with magnetic north, a connection I didn't realize existed! All this means is that Z could have been a member of a Boy Scout troop that taught wildnerness survival (map reading being the specific section), taken a course on map reading, or just simply bothered to read the instructions that came with his nifty new compass and secret decoder ring. (My compass came with a book that told how to find true north and even tell time with the compass.) The ONLY thing magnetic north proves is that Z had the ability to read.

RADIANS is just about the same - trig in high school, or just plain abuse of the word like so many do.

If you consider the bomb to have been fake and the stated reason for the map and cipher to also be misleading, why would you then insist that there be any real meaning whatsoever in these artifacts, especially one so esoteric and pointless as perfect radians intersecting kill sites? The police already knew where the sites were, and the Radian Theory offers no new sites, so why would Z have bothered?

It is far more logical to consider that Penn's theory is "the work of an ingenius and fertile imagination" than to consider that Z was some super-human mathematical genius. Z's first kill sites were sloppy and poorly planned, his first cipher was extremely sloppy and riddled with errors, and we know he made unsubstantiated claims and provided "untruths" on demand. Hardly the work and careful planning of a genius.

I agree with Glen I see no signs of a genius mentality. I see a sick person sending letters to newspapers for attention. These letters are so filled with lies, I wonder if we should trust any claim made by the Zodiac. Maybe there is no deeper meaning to them then that.

Glen wrote:
"I keep reading about this "intellectual ability" connected with magnetic
north, a connection I didn't realize existed!"

There's only one poster here who suggests that Z was a genius, and it isn't me. If you'd read my first post in this thread, you might have come across this sentence: "A carpenter, surveyor, or engineer, or even someone who apprenticed under one, could have known what a radian is." My point is not that Z was a genius (again, I've pointed out that a genius wouldn't leave so many prints behind), but that he was comfortable with maps and the graphic expression of abstract concepts -- to wit, a radian executed by murders at planned locations.

"....RADIANS is just about the same - trig in high school, or just plain
abuse of the word like so many do."

If the word had been used without any other indication of the author's familiarity with it, I would be inclined to agree, but the fact is that we have the word, the location, and a recognizable approximation of one. What more do you want?

"If you consider the bomb to have been fake and the stated reason for the
map and cipher to also be misleading, why would you then insist that
there be any real meaning whatsoever in these artifacts, especially one
so esoteric and pointless as perfect radians intersecting kill sites?"

Again, because meaning has been divined! Just look at it! Esotericity and pointlessness are irrelevant; we are talking about a madman. I'm not trying to answer why he did it, I'm just pointing out that he did.

"The police already knew where the sites were, and the Radian Theory
offers no new sites, so why would Z have bothered?"

Well hell, why would he bother writing letters at all?

My guess is that Z wanted to prove that he knew something that most people didn't, which was the value of a radian. Yes, a lot of people know it, no argument here, but the fact is that most people don't -- take a survey if you want. Certainly, no investigating agency did.

"It is far more logical to consider that Penn's theory is "the work of an
ingenius and fertile imagination" than to consider that Z was some
super-human mathematical genius."

Put words in someone else's mouth -- I'm not here to defend Penn's ouvre. Some of it makes sense, most of it is subjective and overcomplicated. I think too many people are caught up with proving the entire thing right or wrong, but you won't catch me making that mistake.

--Jake
http://members.aol.com/Jakewark/index.html
"This is the Zodiac Speaking..."

Do any of you remember the fire on MT. Diablo? That fire was done by someone who thought it would be a more interesting fire if it was a done in a perfect circle around the mt. I don't know how someone could direct a fire, unless it was done with a string of small bombs,strung together over a long period of time. That mt. is big ,it would take along time to do it, and go unnoticed. (Just a thought)

Jake, my post wasn't directly pointed at you, but toward some of the statements that are generally associated with the Radian theory. I hold no animosity toward those who believe in the Radian theory to some extent, but I must always point out that the theory is not in keeping with the facts. I might also point out that Penn's book strikes a real cord of anger inside me, and it will come out every time I discuss anything involved with the man.

Sorry if we disagree, but a house has to be built on a good foundation, and Penn built his on quicksand. These following comments are not directed at you, but are simply meant to make others think twice before buying even a portion of something that has no basis in fact, no matter how fascinating it is in concept.

Stating something like "the intellectual ability that a reference to magnetic north implies" demonstrates a direct influence from Penn's work. It's akin to Penn saying that less than 1 percent of the population knew what a radian was. That means less than 1 percent of us ever took required math subjects in school? There is no above average implied intellect involved with knowing something like magnetic north or what a radian is, even if it can be proven that Z in fact used radians.

As far as a pole for how many of us know the exact definition of a radian, I agree. Most would know enough to say that it is related to an arc of a circle, but just about everybody interested enough does know how to use a dictionary, which requires no mathematical skill or knowledge whatsoever!

"If the word had been used without any other indication of the author's familiarity with it, I would be inclined to agree, but the fact is that we have the word, the location, and a recognizable approximation of one. What more do you want?"

What you have is a map with a symbol drawn on Mt. Diablo with a notation that 0 is to be set to magnetic north. Where is the approximation of a radian on this map? The symbol is not marked with degrees, instead it's marked clockwise with 3, 6, 9 and 0, such as the hands on a watch. Hardly an engineer's representation of a radian, but the numeric notations have much wider implications if one considers alternate uses of the word "radian".

You also have the statement that the map and cipher are to be used to determine the location of a bomb, nothing else. There is NO approximation of a radian on this map, and there is NO reason to believe that Z drew a point on Mt. Diablo to reveal already known kill sites. Even if we ignore all the other physical evidence, it's just not in keeping with Z's massive ego to reveal something that is already known or fails to give him further credit.

So why would I have any reason at all to believe Penn's Radian theory has any basis in fact?

"Again, because meaning has been divined! Just look at it!"

"Divined" is the operative word here. Yes, we all saw Penn on TV sitting in front of his neat little computer screen with arcs and radians drawn through kill sites. We also heard the statement that these calculations come up with measurements that EXACTLY equal a radian, so why hasn't anybody else been able to duplicate Penn's work EXACTLY? Because it HAS been intuitively DIVINED, and therefore does not reside in our plane of physical existence.

Fact, Jake. In order for Penn to have come up with this theory in the first place, he had to have ignored all other physical evidence presented him in order to "look beyond" the known facts and see radians through kill sites. In Penn's world, these "new facts" don't exist approximately as they do in our realm, but PRECISELY and EXACTLY as he sees them from his plane of existence.

Combine the obvious about the Radian theory and add it to the rest of Penn's research. Given the rest of Penn's "FACTS" and the inexcusable and possibly even criminal accusations he leveled toward a totally innocent bystander based on leads he followed because of his "Radian theory", it is safe to say that it is a FACT that Penn is an incompetent and unqualified researcher who should be disregarded - even shunned - by all other qualified researchers.

To sum up - Penn ignored all physical evidence and instead came up with something that ignored all the known facts.

Penn supported his impressions by stating them as precise fact, when the truth is that they are at best approximations of an aberrant idea that was arrived at by DIVINE intervention.

Penn used these impressions to build a case against a totally innocent human being, accusing this person of being a multiple murder, or worse.

Don't anyone think I'll let up on this line for even a second. I personally consider Penn's work to be a work of criminal magnitude. It demonstrates total disregard for established patterns of scientific research, it demonstrates a total irresponsibility toward duties to public information, it demonstrates a criminal disregard for individual privacy, and it demonstrates a criminal disregard for the laws of the United States as established by our Constitution.

One thing I find troubling about this post is that it seems as if we are supposed to "pretend" that Zodiac did not mention "radians". Clearly, he mentioned it, and even more clearly... he didn't just pull this out of his you know what. No matter how wacky, it's obvious he has something in mind here. The only question is what. I haven't heard anyone else come up with any explanations on it. I can't imagine why Z would mention Mt. Diablo if it wasn't involved with this either. Whether anyone agree's with Penns theories, you will not be able to ignore Z's reference to these. He went to some trouble to write them out, send the map, mention the magnetic variance, etc. Penn's coming up with a suspect etc., is another topic in and of itself. It doesn't negate "radians" in any way. In otherwords, Penn does not equal radians! Yes, I myself got a big kick out of Penn's "binary morse code" bit. But I have to agree with Jake, 1.2 degree's is not a lot.

Quite right, 1.2 or 2.2 degrees is not a lot, but one would think that if Z had really intended to constuct a radian in the Bay Area (which is nowhere indicated in any of his literature), he would have taken a little more care to make the angle closer to 57.3 degrees. If it was measurable on his map as 57.5 degrees, I would tend to agree that perhaps that is what he intended, were it not for the rest of the clues that go along with the term "radians." To wit:

As I have said over and over, Z said that "The map coupled with this code will tell you where the bomb is buried." He included a map AND a code to use. One month later, he included a hint: "P.S. The Mt. Diablo code concerns inches & # radians along the inches."

Now, at no time did Z say to use murder sites to plot out a radian. Nor did he indicate anywhere that only ONE radian was to be used! Quite the contrary, when we read what he actually wrote, decipher the code, and use what he provided (the map), surely the result would be directions to start at Mt. D, measure a certain number of radians in a clockwise direction from the center of Z's "magnetic indicator" on Mt. D (presumably from zero), and then measure out a certain number of inches from the center to discover the place the "bomb" was buried. Whether there was a bomb or not is completely irrelevant.

Thus, after reading the text as it was obviously meant to be read, that is the only solution I can come up with. How Penn read this and completely ignored everything else but grabbed hold of the term "radians" like a pitbull, I will not understand, because that is not what Z meant. His own written words say so.

Considering the code was only 32 characters long, using radians rather than degrees to convey circular measure is logical. There are 2 pi radians in a circle (approximately 6.3), and so, for the sake of argument, if the bomb was located on a line drawn from the just before the 6 on the "magnetic indicator," it would make more sense for Z to have encoded "three radians" rather than encode "one hundred and seventy one point nine degrees." Twelve characters versus thirty-nine. Or, for that matter, "one hundred and seventy degrees" (27 characters) or "one hundred and seventy two degrees" (30 characters). That makes the code much more difficult to decipher.

In the end, while yes, I do agree that the sites as plotted do coincidentally come close to one radian, when we take into consideration Z's own written word, so what? He didn't say to do that or that he meant to do that, he wrote something completely different that happened to also use the term "radians."

Just for geometric exactness, one or two degrees can be can be a tremendous amount of distance between two rays depending on their distance from the vertex.
Bruce D.

"Now, at no time did Z say to use murder sites to plot out a radian. Nor did he indicate anywhere that only ONE radian was to be used! "

True on both points. I have to agree, it appears that he if referencing the bomb location and not a murder site. Perhaps the murder site being so darn close to one radian is purely coincidence. It's close enough to make one wonder though. Keep in mind, if Z were to try and have one of the murder sites fall exactly on one radian, it wouldn't be that easy to do. He still had to get the victim into a secluded spot as well as have it fall on the radian. If this was his intent then 1.2 or 2.2 degrees would fall into the "fudge factor" I would think. This also applies to the bomb by the way. If a radian is 57.3 degrees and one leg of the angle is magnetic north, then there would only be 6 direct lines radiating from Mt. Diablo that the bomb could be placed. How likely is it that he would be able to put it exactly on one of these legs? Not very. Therefore, one of the variables must be an offset from magnetic north, no?

Glen wrote:
"I might also point out that Penn's book strikes a real cord of anger inside me, and it will come out every time I discuss anything involved with the man....I personally consider Penn's work to be a work of criminal magnitude."

Wow! Well, I recognize that you have strong feelings about this, and they don't particularly conflict with my own, so I'll try to be as specific as I can about what I believe and why.

"Stating something like "the intellectual ability that a reference to magnetic north implies" demonstrates a direct influence from Penn's work. It's akin to Penn saying that less than 1 percent of the population knew what a radian was. That means less than 1 percent of us ever took required math subjects in school? There is no above average implied intellect involved with knowing something like magnetic north or what a radian is, even if it can be proven that Z in fact used radians."

I can speak from experience when I say that only one person of about one hundred that I have introduced the radian theory to was previously cognizant of the term. Maybe they learned it in school and forgot it, maybe they all failed math -- believe it or not, most people aren't on-line codebreakers -- but I had to explain it over and over again. Further, every single newspaper account I've read of Penn's exploits (the operative word) misuses the word. Every single one! Wouldn't you assume that a reporter for a big city paper would have taken required math subjects in school?

"What you have is a map with a symbol drawn on Mt. Diablo with a notation that 0 is to be set to magnetic north. Where is the approximation of a radian on this map?"

I was referring to angle formed by Mt. Diablo and the murder sites. I didn't mean to imply that it was drawn by Z on the map he sent.

"You also have the statement that the map and cipher are to be used to determine the location of a bomb, nothing else. There is NO approximation of a radian on this map, and there is NO reason to believe that Z drew a point on Mt. Diablo to reveal already known kill sites."

I suppose the only way I can answer this is to say that I'm not willing to accept that much coincidence. I find that there is a reason to believe this, because Z himself used the word -- admittedly in a different context -- and I can draw one on a map connecting the murder sites with the apex on Z's own landmark.

Every time the radian is brought up, Penn's entire corpus is dragged into the conversation. I'll state again for the record that I'm not here to defend it or endorse it. I think, though, that it would be foolish to throw the baby out with the bathwater on this one.

--Jake
http://members.aol.com/Jakewark/index.html
"This is the Zodiac Speaking..."

Kevin wrote: "Perhaps the murder site being so darn close to one radian is purely coincidence."

It is close to one radian, that I will concede (nor have I ever denied it, btw), but considering my arguments above, I think that's all it is: coincidence, and nothing more.

"If a radian is 57.3 degrees and one leg of the angle is magnetic north, then there would only be 6 direct lines radiating from Mt. Diablo that the bomb could be placed. How likely is it that he would be able to put it exactly on one of these legs? Not very."

Interesting that you mentioned 57.3 degrees, but in the very same sentence said there would only be six radians radiating from Mt. D. Who said anything about only whole radians being used? What if the angle was 4.5 radians, or perhaps encoded as "four and a half radians?" Therefore, the "bomb" could be located anywhere on the map, and not just on six radial lines. The point is, I think that, when deciphered, the code will indicate a radian measure between zero and six radians, possibly with fractions. Once the angle is determined, then all one has to do is measure out the specified number of inches to find the location Z claimed a bomb was buried.

Just to clear up something posted by "Scott" on 8/25: six radians do not comprise a full circle, a full circle consists of (2 x pi) radians, or about 6.283.

Am I the only one here that thinks somehow his map and reference was possibly refering to Concord Naval Weapons Station? Can someone tell me why this idea couldn't fit into play here? Theres nothing to back up this thought-but I keep going back to it! Thanks , J

Zodiac's Phillips 66 map and code could mean anything, which was probably his intent.

"I can speak from experience when I say that only one person of about one hundred that I have introduced the radian theory to was previously cognizant of the term. Maybe they learned it in school and forgot it, maybe they all failed math -- believe it or not, most people aren't on-line codebreakers -- but I had to explain it over and over again. Further, every single newspaper account I've read of Penn's exploits (the operative word) misuses the word. Every single one! Wouldn't you assume that a reporter for a big city paper would have taken required math subjects in school?"

Thanks Jake, for reminding me that I tend to travel in offbeat circles. On the other hand, that's what drew me here, wasn't it? :-)

Your observation is a lesser percentage than my observation, but let's examine your statement. If they don't know what a radian is, what do they THINK it is? If the newspapers misuse the term, how do they misuse it? This was precisely my point in a previous discussion on the old board.

My observation about how the term is misused came from reading things mathematical and seeing time and again that even mathematicians sometimes refer to a "radius" as a "radian". In the art world, I've often seen a beam of painted light radiating from a central point referred to as a "radian". Hence my argument that for all we know at this juncture, (and by your own calculation), Zodiac was like 99 percent of the people and misused the term in his own writing. That's far better odds than Z being the 1 percent who actually used the word correctly.

The evidence suggests this as well. A Zodiac symbol numbered in its four quadrants with 3,6,9 and 0, like a watch face. A "radian" on a watch would be a hand position if the word were misused. (An hour-hand position such as 8:34 corresponds to a specific and easily calculated angle, a good and simple way of encoding information.)

We read that the intended purpose of the map and the cipher is to demonstrate the location of a bomb, but we can easily dismiss this piece of information as "misdirection".

The next piece of evidence is the map itself. If one leg of the radian is at magnetic north, there is only one other leg, which leaves the only meaningful (and missing) measurement to be the inches along that leg. If this is the case, it's quite possible that the true meaning of the word "radian" was not overlooked by police, rather abandoned because this single leg without another measurement is of little value.

Gareth Penn has no use for "inches along radians" because it is also misdirection? Let him tell us in his own words how he arrived at the precise "radian", looking for mention of magnetic north:

"I bought a sheet of clear acetate and a marking pen. Using a protractor and straight-edge, I drew an angle of between 57 and 58 degrees on the acetate and then laid the acetate over a map of the Bay Area. I placed the apex of the angle on Mount Diablo, then rotated the angle until one leg passed through the scene of the murder at Blue Rock Springs. Then I felt as if a ton of bricks had fallen on me.

The other leg of the angle went straight through Presidio Heights in San Francisco where the Zodiac had murdered the cabbie. It was the most shocking experience of my entire life. Instantly, I knew exactly what kind of person he was. He had chosen a cab driver as his last victim in the Bay Area because he needed a victim in a particular place at a particular time, and a cab driver is the most transportable kind of victim possible ...."

If one leg of the radian does not line up to magnetic north, then why did Zodiac use "magnetic north" in the first place? If "magnetic north" has no bearing on the radian, then it stands to reason that Mt. Diablo has no bearing on the radian either, since "magnetic north" and Mt. Diablo are physically connected in the instruction map.

Magnetic north has no meaning to Gareth Penn, because all he needs is Mt. Diablo to establish his theory.

Without connection to magnetic north or Mt. Diablo, we could measure radians just about anywhere, and guess what, Penn did just that. He wasn't satisfied with Mt. Diablo. He had to use kill sites and other unexplained points as apexes for further lines and radians to carry his theory forward, always cloaking them in long-winded esoteric reasoning. Where do you think he got the big Z for Zorro drawn all across the San Francisco Bay area? I can tell you quite frankly where he got it from, but I'd have to mention a body part the board censors probably wouldn't let me print.

Magnetic north meant nothing to Penn, and although he started at Mt. Diablo, that was his only stop at that location before he moved on to new planets. Inches along radians meant nothing to Penn because he broke the lines and caused intersections wherever it suited his theory. Bomb? What bomb? It never entered Penn's mind that the subject was a bomb!

Penn thought - and still thinks, that the Zodiac was a mathematical genius, always talking to him through the lines and numbers Penn created in his own sick mind. What Zodiac wrote was for the uninformed public, but Penn and only Penn knew the true Zodiac. As Penn says himself:

"He was far from being a demented moron. If anything, he was a genius. He was coldly calculating and incredibly evil."

Penn may have found his Moriarty in an innocent mathematics professor and will hound him to his death, but in our world there still exists the burden of proof and the sound duplication of effort by scientific experiment. These are the only things that finally make any theory valid. Penn is above all this, however. What did he write you, Jake?

"...It would seem that the jury is still out on the question of whether there is intelligent life on this planet."

Not wanting to live with us Morons, that's probably why Gareth Penn is out travelling the galaxy as much as he does! And this is a person who considers the Zodiac a Genius? Oddly enough, Gareth Penn's personal identification with a sick perverted murderer is the only thing that makes perfect sense out of all Penn has said.

I'd much rather concentrate on the facts and solve the cipher from that angle, if for nothing else, to demonstrate to Mr. Gareth Penn the wickedness and foolishness of his endeavours. I pity a man who has wasted so much time and so much useful intellect and energy listening to voices and hounding innocent people.

I told you I get a little hostile when I'm on the subject of Gareth Penn, so please excuse me if I've offended anyone - with the possible exception of Gareth Penn.

i also mentioned the 2pi radians thing on friday, but it was deleted. i wonder why.

anybody know?

Glen, I think we'll have to agree to disagree on this one. You and Ed both raise excruciatingly well-made points, and all I can say is that I see some kind of link between Z's use of the term, the annotation of Mt. Diablo, and the angle formed by that landmark and the Vallejo/SF sites. I can't vouch for Penn's methods, and I certainly can't explain why Z wrote what he did, but to my mind, there is a correlation. Anyway, I've frankly had enough of GP right now, and arguing for one of his points isn't exactly on my to-do list.

--Jake
http://members.aol.com/Jakewark/index.html
"This is the Zodiac Speaking..."

Jake, I understand the need for closure on this issue, as the subject of Gareth Penn brings out the worst in me. Every time I read something actually published as fact when fact is totally disregarded - and in Penn's case, to see him draw such harmful conclusions from falsehood that cause irreparable harm to an individual, well, I can't say how much that drives me to anger. So let me end this conversation with a direct for Gareth Penn:

Penn puts himself forward as a theorist with statements such as:

"The scientific test of a theory is whether or not it is able to predict the outcome of data which the theorist has never seen before."

"The true test of a scientific theory is its ability to predict phenomena hitherto unseen by the theorist."

These statements and self-claims put Penn above the average researcher and investigator, making Penn a simple theorist, devoid of the responsibilities associated with hard-line research. He's too good to stoop to the level of actually having to face his theories or the people he's hurt by placing his theories into a publication for monetary gain. In short, he's a d...less f...head who's too cowardly to defend his "theories" in the light of day or courtroom. He enjoys all the money his "theories" bring in, and also enjoys not having to defend them in any arena that involves his peers or plaintiffs.

I'll make a prediction here, in true Gareth Penn style, and even bet money on it, in true Gareth Penn style. Gareth Penn will never take me to court, no matter how badly I speak of him, because he knows that in any slander suit, the burden of proof is on him, and he can't win. In a slander suit he'd be facing a jury of six of his peers, who when analyzing his evidence and hearing my true and logical explanation of Penn's work, will readily rule that anything I have said or will say about Gareth Penn is far less despicable than Gareth Penn himself.

Gareth, consider this an open challenge to defend your book and future writings, or I'll be all over you and your publisher if you publish any further nonsense. Gareth, you're my public enemy number one, so give me one chance to take your sorry hide and theories to court. With your knowledge all you've done is wasted your career chasing shadows of who you once were. There is no greater sentence for an intelligent man than to have his years whiled away in useless and meaningless pursuits. You have my pity, but never my respect.

Hey Tom, how about making all posts to the board require a name. If you have something to say you should at least have the guts to sign your name to it.

Michael

Oh boy, now I know I don't belong here in the Trig. class. With that in mind...

Sandy; the use of diesel or kerosene or most flammable oil based accelerates would work if one were attempting to burn a circle.

As a speculation alone: What if this guy like Diablo in translation and just threw gobbeldy-goop in the letters to raise the dust? Z claimed he would blow up a bus of kids, said his name was in the next letter and on and on. Z is one fellow I would not buy a car from. I don't hold fast to the letters much because I doubt the man's honesty. I trust the Stine shirt clippings, but outside of that and his ammunition summaries, I see reason to believe that the writings served no purpose outside of terror, manipulation and as an eventual alibi in his alleged satanic, or cultism beliefs.

Auckum's razor? I can't recall the spelling, but I think it may apply. Basically it is: the most simple explanation given the sum total of know facts is the most likely explanation scientifically. Now I will return to the evidence boards and not bother the really smart folks in this mathematics board again.

That'll be Occam's Razor, Chrissy...

Back in the day, I think it was spelled "Ockham."

Yes, that is the razor and does it not apply here? I learned of the rule in Astronomy 101, but I know investigators who seem to follow the precept. Not being wise in math, I seem to find the side-roads with these concepts a bit hard to swallow considering the initiator of this concept was a questionable source:Zodiac.

I would like to propose a possibility that the radian theory is not bankrupt. It is in fact in my opinion completely misplaced. So I have a job for you mathmaticians out there involved in this puzzle.

I am an astrologer and I have done a very signifigant work up into this entire case from many different and profoundly impressive occult views focusing on astrology.

The problem with your radian theory as I see it is that no one has any clue what numbers to plug in in order to play with the formula. So here is a theory no one else has even addressed to my knoweldge.

For one the cipher code contains heiroglyphs interspersed into it which are glyphs for "planetary aspects" as someone else has already pointed out. But no one took it any farther then that. Furthurmore there are exactly 12 of those glyphs in the cipher aside from the text. They consist of:

colored in circle: New Moon phase: = conujunction of Sun and moon at a zero degree radian

non colored circle: Full moon phase= sun moon opposision at 180 degree radian

Triangle: Trine aspect between two planets = 120 degree radian

square: Square aspect between two planets= 90 degree radain

Upside down V with a horizontal line over the top: This is an "inconjunction" (not a semisquare as someone else suggested...) and that radian angle is at 150 degrees just short of an opposistion.

Now then. If I were deciphering this code, firstly I'd try to stay on theme: "This is the zodiac speaking" and that means astrology. I would play with those mathmatical coordinates and I would try to glean something else from the rest of this cipher text which may indicate a series of planetary placements in space which may be indicative of a horoscope of some kind. Also latitude and longitude and time of day according to a 24 hour military clock. I would focus on radian sections also which consist of 12 sections of 30 degrees of space. Each sign of the zodiac takes up 30 degrees of space and has rulership over each of the 12 houses in the horoscope diagram.

Mt. Diablo is possibly an allegory for the zodiacal sign of Capricorn the Mtn Goat. This sign is ruled by the planet Saturn which also sometimes has Satanic associations. Furthurmore, if the Z killer has suggested that MT. Diablo is the apex of whatever radian is in question.....note the coincidental astrological fact that Capricorn rules over the Midheaven which is located at the apex of the Prime meridian in the horoscope. The Zenith of the circle. I have reason to believe that possibly what we have here is astrological coordinates and not geographical coordinates.

Also you will notice that some of the aspect glyphs are colored in on the cipher text. The neww moon was obvious. The others took me a little while to ponder. I decided that possibly what we are dealing with is a definition between an applying or waxing aspect and a seperating or waning aspect. The new moon is colored in. It is waxing in its approach in the cycle. So a colored in triangle would be a 120 radian aspect in its "approach" possibly , so would the colored in square. This is useful as it may give you some idea of which quadrant or which side of the hemisphere these radians refer to in their motion around the circle. Have fun. Let me know if you find anything. Personally I would extract those 12 glyphs and seperate them from the text and see if the text comes up with anything else to substantiate planetary references or coordinates in sidereal space, signs of the zodiac or whatever. I would seriously focus this math on astronomical data. I am not entirely sure about the colored in glyph theory, but its the best guess I've got at the moment.

Dragon: Merriam-Webster online defines a radian thus:

A unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc equal in length to the radius.

In other words, there are 2pi (about 6.28) radians in a circle, and each radian is approximately 57.296 degrees of arc. While I find what you have proposed fascinating, and I know next to nothing of astrology, your use of the term "radian" is misplaced, unless it has an entirely different astrological meaning not found in the dictionary.

Your use of terms such as "180 degree radian" I take to mean "180 degree angle," or perhaps "180 degree radial line," neither of which actually refer to radians.

Now, there is the possibility that Z used the term "radians" incorrectly, and did mean something along the lines of what you proposed.

Hello Dragon! The ciphers have been proven to contain actual messages but I didn't even realize it until now that the astrolgical symbols they are coded with actually tell us when he kills!

I've said it once and I'll say it a thousand times that I am not an astrologer but I do know enough to see that something was going on here with it.

Someone else had said that Z killed during new and full moon phases. Most of the times the sun and moon were in cardinal signs so these are the squares and oppositions. Trine would be like water, air, earth and fire signs and I don't know what that would apply to. You say also conjunction with the sun and moon, meaning they would be in the same sign (like 12/20 sun-moon but I have to double check)? All my symbol meanings I obtained from books. You mentioned inconjunction. What exactly does that mean? Just outside of a true conjunction?

I've been waiting for someone who knew what they were talking about to come along! I've said it before too, to think of the radian theory in terms of astrology.....Also, what do you think about the "Z squiggle" on the bottom of the Bates had to die letter? I say it's an Aries symbol on top of an angle symbol. If we could just link the astrology theory with the radian theory I think we would accomplish something. I also wonder if Zodiac applied his chart to what was going on on the days he killed.

Hello Hurly....

I'm not sure what Z squiggle your talking about, I'd have to go and look but if its the one I'm thinking of, I"m not exactly sure. I thought it was a character from the theban alphabet but it doesn't exactly match any of those letters. But its really close.

An inconjunction is a 150 degree aspect. Its one of the minor aspects.

Thanks for the info Dragon. Yes, the "Z squiggle" I'm referring to is what was signed on the bottom of the Bates had to die letter. I don't know the theban alphabet but something else to research!

Hurly....how are your cipher skills? Are you knowledgeable about that?

Also the conjunction I was refering to was an example of one of the symbols in the cipher. The colored in circle which is a glyph for the new moon. And a new moon astronomicly is a sun moon conjunction (so basicly a zero degree radian) a conjunction is any two or more planets right next to each other.

The "inconjunct" is also called a "quincunx". Thats the 150 degree aspect.

hm, cipher skills....I'm lucky I can spell my own name! But I'd love to know what you're getting at.

I've heard the word "quincunx". So a new moon being a sun moon conjunction would mean the sun and moon are occupying the same sign?

Hurley, yes that is correct. Do have an email address?

You can e-mail by clicking on my name.

I think the "radians and the inches along the radians" must mean something to Zodiac (although sometimes he did give out completely false clues).

What do radians mean? I think we give Z too much credit in analysing mathematically as has been done by Penn and others. If you follow the Ressler and Hazelwood style of profiling these serial killers want us to think they are brilliant, they want to view themselves as brillinat of course. They are usually low intelligence* and unable to socialize by having normal relationships with women. Probably did live in his mom's basement. (Now child molesters on the other hand can often have hi IQ and jobs like teachers, priests and psychologists etc..


We need to look at "radians and the inches along.." the way Z may have looked at it or wanted us to look at it.

What if we try putting a zodiac wheel superimposed on the map Z used with Mt Diablo as the center. I think the angles are about as much as the avg person think as being radian-like.

Heres an example of a zodiac wheel see this link http://malephika.formmailer.net/zwheel.html

I saw some mention of a wheel on the board before briefly.... there were of course murders in other directions from Mt Diablo that could link up with the vectors drawn from Mt Diablo, too.

Im at a loss for getting a 66 gas station size map like Z used (?)Id like to measure the "inches along the radian" or the vector.
*footnote-I know how can Z have a low or average IQ but be so smart to have never been caught?Serial killers are cunning like animals as they seek their prey but it doesn't mean this Z guy was some sort of genius. He's just a messed up sicko thats all.

Law123, you wrote:

I think we give Z too much credit in analysing mathematically as has been done by Penn and others.

You are correct there, I don't think Z had any intention of doing things the way Penn imagined (with an emphasis on "imagined"). However, that doesn't mean that Z didn't know what a "radian" was. I think he did, and that it was meant to be used the way he said to use it, as I've explained in previous posts.

I think most of us, here on the board and in the general public, are incorrectly biased to regard most or all serial killers as evil genuises. That's because most of the fiction about this type of crime portrays them as such. I'm not condemning the books and movies (Red Dragon is great and Bone Collector isn't bad, as 2 examples). But the truth is that most killers are not genuises, just because most people aren't genuises. As defined by IQ testing only about 2-3% of individuals meet the criteria for genuis, and that's an arbitrary cutoff set statistically.
Most of the clues and signature indications left by killers are not for our benefit, but theirs. Only in rare cases, when a main component of the signature is to demonstrate superiority and confound the police do we see this type of deliberate leaving of clues. Zodicc, of course, is a prototypical example of this type, along with his desire to terrify the entire polulation. This still does not mean that Zodiac was a genius, I doubt that. I suspect he was not stupid, either, but probably average or slightly above, intelligence. Before we doubt that such a person could commit such a list of crimes, remember that, again by definition, MOST people are average intelligence and they manage with their lives and with numerous hobbies and activities.

Mike: most killers are morons with IQ's probably not much better than Forrest Gump's; if they had any degree of intelligence, they wouldn't get caught. Average is considered to be 90-110, with genius at 150+. I've always thought of Z has being in the 120-130 range, but, even then, not smart or imaginative enough to construct a radian. At the very least, it is an artifact coincidental to the crimes (it does, after all, approximate one radian at roughly 58.5°), but I've never believed it was mapped out with purpose.