I’ve just been discussing Zodiac’s spelling errors and in the course of that conversation, the topic of Radian’s came up and it got me thinking and asking myself a few questions, questions that I don’t have the answers too.
First of all, before I go any further, I must add a Disclaimer at this point and point out that, When it comes to Mathmatics overall, that obviously includes angle’s and degree’s etc, I am pathetically usless. Maths to me is another language that I don’t speak, nor do I wish to learn (lol). So, here’s the questions i found myself thinking.
According to a claim made by a Mathematician, the word ‘Radian’ was not a word that was in the active vocabulary of 99% of U.S Citzens back in the late 60’s, and so Zodiac seems to be in the 1% of the population that did know of this word. Based on the fact that only 1% of the population knew of this word and what it means, I think it’s safe to draw a few assumptions based on this fact.
This first assumption is, A Radian Angle itself, 57.3 Degrees, is an angle that would only be know, and used, by a very very small number of people for a very very small number of reasons. They are likely to do the same type of jobs, which would require this very unusual angle to be used. I don’t see how even being a mathmatics teacher at University would need to know this Angle, if only 1% of the population are aware of the Angle, then it’s not being taught to student’s as part of their Maths Degree.
It seem’s to me, and I accept that I may be way off the mark and totally wrong with this, that a Radian would only be used by very specific type of person/persons, in very specific type of situations. So, the questions are…
What type of Job might you do, or hobby you may have, that would expose you to the Radian?
Does Zodiac know of this 57.3 Degree angle because he does a job that would require him to be aware of it, a job that most of the 1% that are aware of Radian’s do?
I think Zodiac is doing one of two things by making reference to A Radian. He is either giving a huge clue to his identity by letting it be known that he is in that 1%, and that significantly narrows down the likely type of person he is, and the type of employment he has. Or, he has simply discovered this Angle by mistake/fluke, realized how obsecure it is, and decided to throw this in the letter to again confuse police by making them ask "How can this man know of A Radian angle that is only used in very advanced matamatics, who also seems to be able to construct Homophonic Substitution Cipher’s when he feel’s like it, and yet seem’s unable to spell the word ‘Victim’? Always spelling it ‘Victom’.
What are people’s views? Did Zodiac know of Radian’s because he needed to, if so, we can assume he was familiar with advanced math’s. Or, was he simply trying to make an impression and inflate his ego by referencing a Radian after he read about it in a book?
"So it’s sorta social. Demented and sad, but social, right?" Judd Nelson.
I find that odd most in the 60’s wouldnt know what a radian was. Heck, we were sending people to the moon! I think that is a false statement (I know not made by you Chappie!)….as all that is basic math. Even then.
Here’s the clip from the docmentary series ‘Case Reopened’ from which I quoted the ‘Radian is not in the active vocabulary of 99% of the U.S population. Foreward the clip to 6.00 minutes, and the Radian issue starts there.
"So it’s sorta social. Demented and sad, but social, right?" Judd Nelson.
I still believe it’s more likely he meant Radius, a line from the centre of a circle to it’s perimeter..in keeping with the 0.3.6.9 diagram on the map. The plural being Radii. Perhaps he thought the plural of Radius was Radians.
I still believe it’s more likely he meant Radius, a line from the centre of a circle to it’s perimeter..in keeping with the 0.3.6.9 diagram on the map. The plural being Radii. Perhaps he thought the plural of Radius was Radians.
Wouldn’t be surprised. Plus it gives a reason as to why the markers on the logo are all on the right hand side, it would work with the map and the centre placement over Mt Diablo even more so, I think when set to Mag North.
I’m sure someone somewhere has presented as to why it makes for it to be radians but I don’t know I’m afraid. Too much maths make MEGO.
I still believe it’s more likely he meant Radius, a line from the centre of a circle to it’s perimeter..in keeping with the 0.3.6.9 diagram on the map. The plural being Radii. Perhaps he thought the plural of Radius was Radians.
Well Radius could have been what he meant, but according to Gareth Penn, also confirmed by Michael Butterfield in the video, the scenes of Zodiac’s attacks at Blue Rock Springs and Paul Stine’s murder in Presidio Heights, when they are connected to Mt. Diablo on a map, form one Radian Angle of 57.3 Degrees.
If this is an unarguable fact (And I don’t know that it is as I don’t own a map of S.F and even if I did, wouldn’t have a clue how to test the Radian Theory due to my alergy to all things mathematical lol), then this would seem to suggest that Zodiac meant exactly what he said, A Radian.
"So it’s sorta social. Demented and sad, but social, right?" Judd Nelson.
I believe M. Butterfield has run a mile from that since, even to the point of apologising.
In any event (at least as far as I am concerned) you have to look at the history. Z sends his Mt Diablo code coupled with a map. On that map he draws his symbol over mt Diablo but this time marks it 0,3,6,9. He comes back later (see Trav’s image above) and draws a circle and as you can see, it is marked at 30 degrees and or the hours of a clock. Again, in the little list letter he gives the clue Radians and inches along the radians.
Even at face value it’s hard to imagine he’s speaking about anything other than a point along some radius. However this is all in connection with the bomb code. If we believe he meant a Radian measure we have to believe it was in relation to finding the bomb. If we believe Radian we have to believe that he marked these circles incorrectly.
Penn comes along and decides to use the word Radian is highly significant and takes it out of this context (where to find the bomb) and sets about trying to prove that Z used this measure 57.3 degrees to align his murders and/or claim there was something to it, especially as LHR and SF roughly approximates that angle. It sounded good at one point or rather worth a look,as Penn backed it up with the idea of Z being able to place a victim (Stine) to achieve this.
For me there is just way too much to be taken on faith, it gets more complicated when we consider the Radian has more to do with an arc measurement and others have futher complicated it, by using different maps to back up their claims. LB isn’t even on the Phillips Map.
The only thing that has ever been shown, is that the measurement between SF and LHR is close to 57.3 or 60 degrees. Even if it was intended and this is taken to be a true Radian, I’ve never seen anything to take it beyond that.
I have never been a big fan of these type of theories, the murders forming a certain angle, or pattern, or the connection to Water due to LAKE Berryessa, LAKE Herman Rd, Blue Rock Springs, and the fire hydran at Washingon & Cherry.
I mean it could be that the place names are all associated with water because there is a significant hidden meaning, or it could be due to the murders being commited in The BAY area?
And I have always struggled to see why Zodiac would commit murders in places where he could later send a map and show that the two site’s he attacked at form a certain Angle. The reaction for me to that would be, Ooooook, so that forms a rectangle……What’s your point? Lol. It’s totally pointless to point out an angle formed in a certain place on a map, just for the sake of pointing it out itslef. Without giving a reason why that may be significant, the angle is usless.
And anyway, as I said elsewhere on this site, Zodiac was not a thorough planning serial killer, that is the misconception that many seem to have of him. BTK is a prime example of a planning, thinking, attention to detail killer. It’s quite obvious, to me anyway, that Zodiac was your classic opportunistic killer. He can’t plan to attack a couple at Blue Rock Springs Park on July 4 around midnight because theres no way of knowing if there will be anyone there. Zodiac’s Victim’s chouse the exact location of the crimes, not Zodiac. Same with the litle island at Berryessa, oppoprunity. And if the man reported by several witnesses at Berryessa that day was Zodiac, then that again suggests he was hanging around, waiting and searching for the right opportunity to present itself. The break in this pattern comes with Paul Stine, Zodiac is probably fed up of having to search for victims for hours on end with no guarntee of success, and with the events of Berryessa still fresh in his mind from two weeks previous, Zodiac probably decided that this time he would control who the victim would be (his occupation anyway), carry out his homicidal urges at a time that he decided, and at a location of his choice. This time Zodiac wanted, and got, total control of his victim, even directing him to the location of his own demise. That’s why Paul Stine was targeted, because he was a taxi driver. As I said in the other post also, I find it so ironic that Zodiac seems to have changed his MO from couples in secluded lanes, to a lone male taxi driver because he wanted more control in geting a victim to a place he wanted, straight away without having to loiter around the area for ages first, and this very act of taking control and seemingly planning this murder knowing exaclty where he’s going, who the victim is, and how he will escape, this very act of planning this crime with fine detail, was the one and only crime he comitted where, after all the planning and having crotrol himself, he commits the crime, exits the taxi, walks down Cherry St, onto Jackson St and straight into, what should have been, the arms of the arresting officer that was coming up the hill straight towards him. If Fouke or Zelms had only got out just to do a quick pat down search of the man on the sidewalk outside 3712 Jackson St, they’d have found his pistol no doubt, along with Paul stine’s blood soaked shirt, Car Keys to his cab and his wallet with his ID. Caught there and then with these possessions Zodiac can appeal to Mel Beli all he wants, even he couldn’t defend you against that evidence and Zodiac would have had one foot on Jackson Street, the other in The Gas Chamber.
"So it’s sorta social. Demented and sad, but social, right?" Judd Nelson.
I wouldn’t be a great supporter of the killing in certain places to create some sort of cartographic symbolism. Makes for good TV sometimes though.
Zodiac’s a bit more of problem though than just saying he didn’t kill in specific places for any reason. Why is it a problem? because of his communications. If he hadn’t written or phoned we would just have the crime scenes and patterns and the evidence that pertains to those. From that, I’m surmising that, even if you did subscribe to the idea of location ‘meaning’ something you could plot them on a map and see if it’s a boat or a duck or a pentagram or nothing but either way decide if they appear random or not.
Zodiac complicated this seemingly simple process with communications. Specifically vague, unidentified marks and apparent symbolism in the communications and also probably unbreakable ciphers giving clues to the location of something. He introduces things that we have to decipher to not only find out where they are (the map and bomb location) but also what they are (the symbol on the bus bomb letter with the 5 points marked).
I think they were random and opportunistic but that doesn’t mean that he didn’t then weave the information into his puzzles. Technically he kinda did if you think about it – the car door. The information was presented there right along with by knife, which depending on what you believe, later became part of the back of the halloween card. Now that’s ok but what about the ones that don’t make sense because we don’t know what they are or represent; unlike the car door which literally spells it out for us. Well we have to figure those out. Why? well anything that we can crack or decipher will give us some new information, even if it’s completely useless it still completes the picture that little bit more.
So whilst Zodiac most likely didn’t choose his victims based on location or reason we kinda have to check that he didn’t subsequently use the information for some other purpose. If he hadn’t written we wouldn’t have this problem. The way, unfortunately, to do that or at least approach it would be to assume that there might be a signifigance to all aspects of the murders, including dates and locations just in case there was later but just not at the time of, or before, the actual crimes.
Stoopid Zodiac, stoopid busy work.
Yes I think Zodiac knew about radians, circles and points of convergence because he studied mathematics and geometry, as did the chap who wrote this paper.
http://homepages.rpi.edu/~bulloj/tjk/tjk2.html
"Let D denote the unit disk |z| < 1, C its boundary, and let f(z) be any function that is defined in D and takes its values in some metric space S. Then a boundary function for f is a function t on C such that for every x ( C there exists an arc v at x with
lim f(z) = t(x).
z -> x
z ( v "
MODERATOR
I’ve just been discussing Zodiac’s spelling errors and in the course of that conversation, the topic of Radians came up and it got me thinking and asking myself a few questions, questions that I don’t have the answers to.
First of all, before I go any further, I must add a Disclaimer at this point and point out that, When it comes to Mathematics overall, that obviously includes angle’s and degree’s etc, I am pathetically useless. Maths to me is another language that I don’t speak, nor do I wish to learn (lol). So, here’s the questions i found myself thinking.
According to a claim made by a Mathematician, the word ‘Radian’ was not a word that was in the active vocabulary of 99% of U.S Citzens back in the late 60’s, and so Zodiac seems to be in the 1% of the population that did know of this word. Based on the fact that only 1% of the population knew of this word and what it means, I think it’s safe to draw a few assumptions based on this fact.
Ok, just stop right here. You said "according to a claim made by a mathematician." You know who you are referring to here, right? Gareth Penn. You might want to look him up, he is not exactly what any of us associated with the Zodiac case would call an unbiased mathematician. And to then go from a claim made by him to say "I think it’s safe to draw a few assumptions based on this fact." Well, quite a bit of a HUGE leap there. Gareth Penn has made quite a few claims. I don’t think I’d call any of them a fact.
This first assumption is, A Radian Angle itself, 57.3 Degrees, is an angle that would only be know, and used, by a very very small number of people for a very very small number of reasons. They are likely to do the same type of jobs, which would require this very unusual angle to be used. I don’t see how even being a mathematics teacher at University would need to know this Angle, if only 1% of the population are aware of the Angle, then it’s not being taught to student’s as part of their Maths Degree.
A radian works out to be slightly less than 57.3 degrees in fact, but is more used in calculus and higher maths to write equations more in a more elegant fashion than using degrees. The wikipedia article is pretty good:
http://en.wikipedia.org/wiki/Radian
It seems to me, and I accept that I may be way off the mark and totally wrong with this, that a Radian would only be used by very specific type of person/persons, in very specific type of situations. So, the questions are…
What type of Job might you do, or hobby you may have, that would expose you to the Radian? Does Zodiac know of this 57.3 Degree angle because he does a job that would require him to be aware of it, a job that most of the 1% that are aware of Radian’s do?
Again, you are taking a bold claim by Gareth Penn and asserting it as fact. How did it become a fact? Radians are widely used in many fields involving math such as engineering, electronics, ecology, economy, and etc.
I think Zodiac is doing one of two things by making reference to A Radian. He is either giving a huge clue to his identity by letting it be known that he is in that 1%, and that significantly narrows down the likely type of person he is, and the type of employment he has. Or, he has simply discovered this Angle by mistake/fluke, realized how obscure it is, and decided to throw this in the letter to again confuse police by making them ask "How can this man know of A Radian angle that is only used in very advanced mathematics, who also seems to be able to construct Homophonic Substitution Cipher’s when he feel’s like it, and yet seems unable to spell the word ‘Victim’? Always spelling it ‘Victom’.
What are people’s views? Did Zodiac know of Radians because he needed to, if so, we can assume he was familiar with advanced math’s. Or, was he simply trying to make an impression and inflate his ego by referencing a Radian after he read about it in a book?
With all that said, my view is the latter. Zodiac himself probably wouldn’t know a radian from a radial tire if it fell from the sky and landed on his head. He was trying to impress.
-glurk
——————————–
I don’t believe in monsters.
Zodiac knew what he was doing.
Degrees can be changed into Radians and vice versa.
"How to Change Degrees to Radians – For Dummies" – http://www.dummies.com/how-to/content/h … dians.html
"Radians are very useful when doing computations involving other numbers, because radians are the same type of number. Degrees are of a different type or category."
This is why I think the code was NUMBERS….not letters.
**
Here is another and this one has a calculator at the bottom: http://betterexplained.com/articles/int … d-radians/
“Radians make math easier!” the experts say, without a simple reason why (discussions involving Taylor series are not simple). Today we’ll uncover what radians really are, and the intuitive reason they make math easier.
On a side note – degrees and clocks can pinpoint locations. THAT is what Zodiac was trying to do…tell us where his "bomb" was "buried"…(or maybe just a note saying FU)
Watch this clip" "Basic 8th grade math": (click on it)
I see a lot of potential problems with what you are suggesting Tahoe but I’m a little unclear on what your exact proposals are for the code itself. That is whether you are suggesting a conversion of Radians to degrees or degrees to Radians and how that would apply to the code.
Regarding your main suggestion, that the code is Numbers not letters, is there not an obvious flaw? You would have 10 numbers (0 through 9) and perhaps a decimal point. 11 characters in all. However the code has only three repeats from 32, leaving 29 different symbols. This would mean that many of the symbols have multiple values. Ok, Zodiac did that in the 408 at least, but with a 32 symbol code and individual numbers throwing the location/solution off, it would be absolutely impossible to solve from the get go. With letters you could at least guess what a word might be from surrounding values, but with numbers you couldn’t even begin with one, not to mind guess the next one without listing all in sequence.
Now, that’s not to suggest that there could not be some numbers in the code.
Radian measure is used in mathematics like trigonometry and calculus because it makes complex calculations much easier than using standard degree measurement. If your using the calculus derivative formulas for sine and cosine they are much simpler to do if your using radians and a total nightmare if your using degree measurement.
I don’t think it means much that the Zodiac used the word radian in one of his messages. Maybe he was trying to appear a lot smarter than he actually was. Especially from a guy who misspelled basic vocabulary words in his many messages.