Thursday, 15 February 2018

The Number FIve and Phi and Bessler’s Wheel.

Over the last few years I have posted many pieces of encoded material along with my interpretation of what they mean, but none have been of help in finding the design inside Bessler's wheel.  Not posting anything that might be of help was, I admit, a deliberate move on my part for two reasons; firstly, to try to interest others in looking, finding and interpreting other pieces of code, but secondly to retain for my own benefit anything which I believed would help me to find the actual solution.  What follows is a little bit of information which could lead to discovering some of the requirements of the wheel. There will be more to follow.

Because of the presence of the pentagram in many of Bessler’s drawings and his apparent obsession with the number five and 55, it’s been a bit of an obsession of mine too, to try and find some information  concerning these apparent clues, that would be helpful.

The number five is intrinsically related to Phi and the Fibonacci series. Phi represents the Golden Ratio, 1.618 and in the Greek alphabet looks like this, ⏀.

It has been suggested that the ‘0’ part of the Phi symbol represents ‘nothing’, and the short vertical line is the number ‘1’, or unity. Therefore adding one to nothing leads to the Fibonacci series; 0, 1, 1, 2, 3, 5, 8, 13, towards infinity and Phi, or the golden ratio 1.618, an integral part of the pentagram.

You can start the Fibonacci series from 0 or 1, and starting from 1 the 5th letter is 5, and the 10th letter is 55 and outside of the Fibonacci series the numbers 1 to 10 total of 55. Bessler uses these numbers in different ways in several of his drawings.  The square root of 5 = 2.236 although there are at least 10 billion digits after, according to Wikipedia, despite  that, a close approximation can be achieved by 161/72 which gives 2.23611. Curious how 72 shows up there, being as it is a fifth part of the pentagram.

Nearly every angle inside Bessler's wheel is based on the angle of 18 degrees, the smallest angle used in the pentagram.  Others include 36, 54, 72, 90 and 108, all multiples of 18, except one which is 30 degrees.  All the angles including some covering angular movement not normally required for a pentagram are also derived from the angle of 18 degrees.

Although Bessler stressed the need for five mechanisms it is clear that he also considered using the odd numbers 7 and 9. This gave him the alternative to fit more of them into the wheels without compromising the effectiveness of the wheel. To fit more mechanisms inside his wheel would require them to operate further out from the wheel’s centre, and make them smaller. But given the huge size of the Kassel wheel, that might have been an option he chose to make. Despite it being almost the same diameter as the Merseberg wheel it only turned at half the speed which might be because it contained more smaller mechanisms, with reduced length of movement in those parts which were designed to move.

Having 7 or 9 mechanisms might help support the idea that the witness, Fisher von Elach, did hear the sound of ‘about’ eight weights landing on the side towards which the wheel turned.  In Bessler’s Maschinen Tractate document you can see that some drawings are numbered in an individual way, and have a special characteristic which the others don't have and you can read more about it on my web page at
http://www.theorffyreuscode.com/html/mt_numbers___letters.html
Those numbers above 50 which contain the number 2 show the 2 as a Z rather than a 2, but only if they are odd numbers.  So in the numbers 52, 72, and 92, the 2 is appears as a Z, but all the remaining numbers use a curved number 2.  Notice that number variants start after number 50, this supports the notion that a minimum of five mechanisms are necessary.

I can't prove any of this until I have working model, but I firmly believe that the single number 5 denotes five mechanisms, and the 55 denotes two weights in each mechanism.  So in the above image the odd numbers mean you can use 5, 7 or 9 mechanisms, and the Z-like 2s can be read as 2 - or two horizontal Roman numerals, V, representing 5, something Bessler does in numerous other examples.  He also uses the letter W to convey two 'V's or 5s.

There are other implications in the above text which I have not touched upon which may help others to make progress in discovering some of Bessler's construction details.

JC

1. If we look at how Bessler behaved and what Karl said, a 5,7 or 9 mechanisms sound too complex. It must be much simpler.

1. All mechanisms inside the wheel are similar...and, each mechanism is very simple to build...just a lever weight combination...they just perform in unison...their main task is to I'm balance the wheel...they function in an amazing way...even eight mechanisms together appear very simple...one just has to look at a mechanism and note how it is housed in the arrangement to grab the much protected secret...it is a wonder still to realize that no one has yet found out the secret despite it's extreme simplicity... Bessler wasn't really worried about someone soon coming up with his design...but he feared leaking the wheel secret...

2. If the mechanisms are the same may be you are right Suresh, but I think John is saying 5 different mechanisms.

2. And of course, ZZ together makes the Jolly Blacksmith pantograph toy.

3. You keep saying " Bessler stressed that 5 mechanisms were used ", as if it is factual. Can you show us one advantage of using 5 mechanisms through 360 deg. vs. 4 or 6?
Thanks, Justsomeone

1. Yes, when I post my defensive publication.

JC

4. Hi John Collins!!
Why put the 'secret' to the wheel in code, when there is so much information, written in, (thanks to you), plain English? Plus the pictures of MT-. If you forgive me for asking.
Sam Peppiatt

1. There’s it enough prose to deduce every detail Sam.

JC

2. there is enough or there isn't enough???

3. Sorry, fat finger typing! There is not enough information in the prose to work out what is needed, unless you have deciphered chapter 55 of Apologia Poetica?

JC

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1. You’ve got me there Stephen, I don’t understand the questions? ðŸ¤”

8. Grasshopper's hind legs resembles stork's bill..

9. The ratio Ï† is related to the geometrical construction of the pentagon or decagon.
For instance, when you draw a decagon inside a circle, the ratio between the radius of the circle and the side of the decagon is the ratio Ï† = (1+√5)/2 = 1.6180339 ...
. radius = side × 1,618
By the way, the symbol Ï† (phi) was chosen because it sounds like the first syllable of "Fibonacci".
The series beginning with 0 and 1 is only one of the infinite set of Fibonnacci sequences.
Examples:
2, 5, 7, 12, 19, 31 ... is a Fibonacci series
3, 4, 7, 11, 18, 29 ... is another one, etc.
Generalization: {a, b, a + b, a + 2b, 2a + 3b, 3a + 5b ...}, with a and b any natural numbers.

1. Thank you Michel, I didn’t know about the other Finonacci series.

JC

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1. You're right, this ratio was known long before Fibonacci.
It was known to the Greeks as the

.                    . “dividing a line in the extreme and mean ratio”
See, for instance, Euclides, "Elements", VI, 30.
https://mathcs.clarku.edu/~djoyce/elements/bookVI/propVI30.html

and to Renaissance artists as the “Divine Proportion”.
It was also called the "Golden Section".

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1. Thanks Stephen, I think?

JC

2. Actually thanks indeed, I did not know that about the storksbill seed, fascinating. Good find Stephen.

JC

13. I read that as a child, Fibonacci travelled around North Africa with his father, where he learned about Arabic mathematics, and what are generally referred to as the Fibonacci numbers and the method for their formation were originally published by Virahanka between A.D. 600 and 800. Gopala prior to A.D. 1135,and Hemacandra c. A.D. 1150, all prior to L. Fibonacci c. A.D. 1202.

JC

14. John, are you talking about same 5 mechanisms placed inside the wheel? or these 5 mechanisms are all different?

1. Hi yellow, from my above post,
“the single number 5 denotes five mechanisms, and the 55 denotes two weights in each mechanism”.

JC

2. OK. I see. there is one mechanism that is duplicated 5 times.
Odd number of mechanisms may have merit. Check electronic ring oscillators. They require odd number of stages. The stages are also identical. Since, the wheel is basically a mechanical oscillator, your design may have a connection to the ring oscillator.

15. If we look at all the historical failed devices we can easily make out that the internal mechanisms are all designed same...there must not be any doubt about it...the principle is same in all cases...one sure way to achieve quick success is cone to a concensco...we still cannot afford to hold differences here...but first we need to shatter a few myths...that Bessler wheel is a PM...that gravity cannot be directly used...that Bessler was a fraud...that the wheel mechanism is too complex...that there are more than one way to design BW...that secret codes left by Bessler needs cracking...that this is against physics' laws...that movement can be achieved with less than eight internal mechanisms...etc., etc.,...

16. Weights act in pairs...this does not necessarily mean double weights in each mechanism...like a see-saw in a childrens park weight acts against the weight in the opposite mechanism on the ascending side... IMHO course...

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17. You could be right but what I feel is that weights act in pairs means is like a see-saw pair but an innovation in the mechanism ensures that one side always remains heavy...

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26. Children mean weights and columns levers...

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28. Stephen... offspring and spokes...how do they relate to Bessler Wheel?...

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31. Ok...thanks...but I want to know why we can't relate children to weights and columns to levers?...

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