Thursday, 13 May 2021

Johann Bessler’s Hidden Codes - Golden Ratio (phi) and MT 137

This blog is based on a draft version I wrote a couple of years ago and I’ve added a few illustrations to help my explanations.  It’s more of an update on work I’ve done but not all of it has been shared before.  I hope it’s of interest.

The presence of a pentagram in some of Bessler’s drawings is well established and it is generally recognised that it is at least an indication of Bessler’s intention to point out at every opportunity his fascination with the number five.  See above for an example of the pentagram in a Bessler illustration.  His frequent use of alphanumeric and the Hebrew atbash and albam codes also reflect this apparent obsession.

The angles in the pentagram are exclusively multiples of the number 18; thus the numbers are 18, 36, 54, 72, 90 and 108 - plus the number 5.  With the the benefit of his various codes, Bessler could manipulate the number 5 as an ‘E’, the fifth letter of the alphabet, or as an atbash cipher, the letter ‘R’, which in turn becomes the number 18.  The letter ‘R’ being the 18th letter of the alphabet chimes nicely with the smallest pentagram number.  This applies to all the pentagram numbers Bessler used.



The Golden Ratio in Merseburg Wheel - 24 squares and 24 rectangles, 24 numbers.

The golden ratio is embedded within the construction of the pentagram and it is also present in all of Bessler’s publications, but one particular place where it seems to be absent is Bessler’s Maschinen Tractate, in particular MT 137.  The illustration is a dodecagram, with no clues as to its role in the MT - it almost looks like an afterthought, with no discernible mechanical design or purpose.

MT 137

My initial speculation which, I still firmly believe is correct, is that MT 137 illustrates something which is used by musicians today. Johann David Heinichen, 1683-1729, a German musician, introduced the concept known as the ‘circles of fifths’ in 1711 (he called it Quintenzirkel). He was born, raised and got married in Weissenfels, the same place which Bessler moved to after Draschwitz, and close to Obergreisslau. Despite his interest in music, Heinichen practiced law in Weissenfels until 1709. However, he maintained his interest in music and was at the samne time composing operas. In 1710, he published the first edition of his major treatise on the theory of music (Thoroughbass). This contained his theory of circle of fifths.

A Modern version Heinichen’s circle of fifths.

Bessler lived in Weissenfels in 1714 and had a history of building organs. In 1717 Heinichen became a colleague of Johann Sebastian Bach at the court of Prince Leopold of Anhalt-Cöthen, then went on to be Kapellmeister to the Elector of Saxony. In 1721, Heinichen married in Weissenfels. In between these events his success attracted the attention of Duke Moritz Wilhelm who appointed him to be court composer at Zeitz. As many who have read my biography about Bessler will know, Moritz Wilhelm’s court was home to many learned men who persuaded the great Leibniz to investigate Bessler’s claims. There is a lot hof correspondence about Bessler between those members of the Court at Zeitz.

So it seems highly likely although not proven, that MT 137 represents Heinrich’s ‘circle of fifths’. This fits in with Bessler’s obsession with the number 5. The ‘Circle of Fifths’ is an easy way to find out which key a song is in. It tells you how many sharps or flats are in a given key. It is called the ‘Circle of Fifths’ because as you go clockwise, you go up a fifth. Even though I don’t claim to know much about musical theory I understand that you start on, say middle C, then count round the edge of the circle five places which brings you to F. This same technique is applied for any note.

However there is more to MT 137 than meets the eye.  Recently I discovered the reason for MT 137’s inclusion in MT and also why it was placed where it was. First, remember that Bessler had studied clocks and was able to repair them, also I have posted information here previously, about the presence of a hidden clock in two of  Bessler’s drawings.  Next note that MT 137 is a dodecagram, in other words it has twelve points on the circumference not unlike a clock.

So far then we have a clock, a circle of fifths and a possibly missing phi, or golden ratio.  No where have I found any reference to phi being an integral part of the dodecagram and yet… MT 137 is a circle of 360 degrees.  The number for Phi is about 1.618.  If we divide 360 by 1.618 we get 137.5 degrees and 222.5 degrees.  If you look at a clock face and you have the hour hand at twelve o’clock and the minute hand at five o’clock, the angle between them is 137.5 degrees, and the larger angle is 222.5 degrees. 

Examples below of when the angle between the hands is 137.5 and 12.25. There are, in total 44  golden moments, that is, times when the angle between the hands of the clock equals the golden angle 137.5.



I believe that Bessler named and placed MT 137 in this way hoping that someone would make the connection between the circle, phi and the pentagrams.  The number 137, the dodecagram and the golden ratio are too well represented and the connections too obvious once you see them, to be due to chance.


360 divided by 1.618 = 222.5 and 360 - 222.5 = 137.5

I include one more illustration showing the twelve to five line in Bessler’s MT 137 as it would be used in the circle of fifths.  C to F in Heinrich’s version of his circle of fifths.




To recap, MT 137 may represent the musical circle of fifths. 

It is labelled 137 to point to the potential inclusion of the calculation of the 360 degrees of a circle divided by 1.618 which means MT 137 also includes the golden ratio.

In the dodecagram the circle of fifths matches at least one of the golden moments and maybe more than one with twelve o’clock to five o’clock line.

NB. I should point out that in the illustration of the clock showing the time as twelve twenty-five, to demonstrate the two golden angles, the hour hand at twelve would in reality be nearly half way to the next hour  i.e., closer to the one o’clock point in order to fulfil the angle of 137.5.  This point should be remembered in all calculations.  The other pictures are showing the hand positions more accurately. My bad illustration!

PS - I forgot to say that the 24 numbers used in the Merseburg wheel drawing above, plus the 24 squares plus the 24 rectangles adds up to 72 which is the fifth of pentagram, 72 x 5 = 360.

JC

I thought this aphorism most appropriate to our cause.

Most of the important things in the world have been accomplished by people who have kept on trying when there seemed to be no hope at all.”                                                

Dale Carnegie



26 comments:

  1. I haven't paid much attention to MT137 in the past, but will give it another look soon. I can't do it now, but will see if I can find any numerological clues in it in a day or so. However, I'm not too optimistic that I'll find much because there's not much to it other than what JC has already pointed out. But I've learned that often the Bessler drawings that one thinks aren't very important can actually turn out to be some of the most important ones!

    Sayer of Sooths

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  2. Questa é stata una mia interpretazione di tempo fa che alcuni di voi avrà già visto https://www.youtube.com/watch?v=n7cd-WADsN0

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    1. PG wrote, “ This was my interpretation from some time ago that some of you will have already seen https://www.youtube.com/watch?v=n7cd-WADsN0 “

      Have seen that interpretation somewhere, not sure if it was yours. I also tried something similar myself, a few years ago. Interesting, but I think it will fail. But thank you.

      JC

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  3. The blue horizontal and vertical lines you added to the Merseburg Wheel drawing line up almost perfectly with objects such as the wheel columns. He sure was accurate in his measurements and carvings when creating the block for this drawing (or was it created freehand?). Regardless of how the drawing was created, one thing is certain, the drawing is square, that is, the objects within the drawing are not stretched or distorted.

    That said, I find it interesting that the angled rope that runs from the window down to the pulley, that some refer to as the hypotenuse of a 3-4-5 triangle, is not even close in angle to the hypotenuse of a 3-4-5 triangle. There is no way you can use the excuse that the drawing is stretched or deformed when everything else lines up with the grid lines, and the line itself is straight. It's time to look for a new explanation on the significance or purpose of the angled rope.

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    1. The angled rope forms a chord behind the wheel to point to the pentagram shown at the top of the page.

      JC

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    2. There's really no significance to the angle of the "angled rope" in the Merseburg wheel drawing other than the angle it had near the floor was one that would allow the compound pendulum's lower weight to swing from side to side without hitting the rope.

      But, I don't think Bessler ever attached the two pendulums to the axle when he was doing one of his impressive brick hoist demonstrations. Such a demonstration requires the wheel to be rotating at its maximum speed before a loop at the end of the rope is suddenly attached to that little metal piece (#34) on the axle. Both pendulums had to be removed because they were intended to reduce the wheel's speed to save on wear and tear to its internal mechanisms and they prevented the wheel from reaching the maximum speed and momentum needed for the hoisting.

      Bessler Curious

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  4. Hello, John. Just a little (musical) note. To be exact, one must count seven degrees to find the fifth. From C, count seven semi-tones and you have G, its fifth. From C, counting five degrees leads you to the fourth F.

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    1. Hi Michel, I wrote what learned from the Heinrich’s history. Perhaps I counted in the wrong direction?

      JC

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  5. Part 1 of 2:

    I finally got a chance to take a closer look at MT137 as I said I would and did find some interesting numerological information in it.

    JC's analysis suggests that MT137 was based on Heinichen's Circle of Fifths and that seems like a definite possibility to me. However, the drawing could also be a Kabbalistic talisman symbol known as the "4th Pentacle of Mercury". It was considered a very powerful talisman that would allow one to understand all of the mysteries of the universe and uncover all of its secrets. It could also be used to summon and command certain spirits. Apparently it was once popular among scientists, scholars, and secret society types. I'm a believer in the power of things like lucky charms and talismans so maybe wearing one of these could help someone in their quest for pm today. Here's what it looks like when made into a modern necklace pendant that you can wear:

    https://i.ebayimg.com/images/g/C18AAOSwFwNd77y3/s-l300.jpg

    But, the drawing's real importance may simply be that it's the 137th drawing in MT assuming that was supposed to be its actual ordinal number in the work if Bessler had ever published it. As I've mentioned in the past, 13 is a number associated with God in the Bible who dwells in the 7th and top level of Heaven. In numerology both numbers are considered to be lucky. This is also the ONLY drawing in MT that combines both of these numbers and that caught my attention of course.

    MT137 appears just before the four that contained the secret details of his wheels would have appeared if Bessler had not removed and destroyed them. So maybe MT137 was intended to tell readers of MT that, if they could understand its hidden meanings, then what they were soon to see revealed was, as far as Bessler was concerned, a very lucky design given to him by God? As a representation of the Fourth Pentacle of Mercury, however, MT137 could have been intended to tell the secret society types of Bessler's day that he had found the secret of his pm wheels using the power of that magical talisman. I suspect that in Bessler's personal version of Christianity he combined numerology and symbolism from the Bible, mystical literature, and the various secret societies springing up in his area of Europe at the time. That would probably have gotten him quickly branded as a heretic by many of his local clergymen.

    The twelve points in the drawing could also represent the twelve apostles going out into all parts of the world to spread the gospel message with the circle in the center, symbolic of perfection, representing their divine leader Jesus who, just before his ascension, commanded them to take his message to the entire world. Then again, maybe the circle in the center represents one of Bessler's 12 foot diameter wheels and the points indicate his desire that the news of it would eventually spread all over the world?

    Sayer of Sooths

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    1. Part 2 of 2:

      The 12 points in MT 137 could also suggest the hours on a clock dial and can symbolize a clock or the passage of time. Maybe this drawing was Bessler's way of saying that the students of MT had spent enough time studying how different machines based on different principles could fail to give pm and it was now time for them to see what actually worked which was his successful design? Maybe the drawing was unfinished for some reason? With ambiguous figures like this many interpretations of their actual purposes are possible.

      One can numerologically manipulate the digits in 137 and get some interesting clues from them. 1 + 7 = 8 and this suggests eight levers with attached weights inside of the drum. If we add the first two digits we get 1 + 3 = 4 and if we multiply the last two digits we get 3 x 7 = 21. Adding this sum and product gives us 4 + 21 = 25 which is the alphanumerical value of the letter "Y" and, imo, again tells us Bessler was using levers with that letter's unusual shape to them. If we add all of the digits in 137 together we get 1 + 3 + 7 = 11. The 11th letter of the alphabet is "K" and this could refer to the wheel Bessler built in the city of Kassal whose name begins with the letter "K".

      There are twelve points made from twelve lines in the drawing. Multiplying those numbers gives us 12 x 12 = 144. This is another number that shows up in the Bible. It was also the diameter of both the Merseburg and Kassal wheels in inches. If we multiply the first two digits in 144 by the last digit we get 14 x 4 = 56. By adding the digits in 56 we get 5 + 6 = 11 and again this is the alphanumeric value of the letter "K" and could refer to the Kassal wheel. If we then divide 56 inches by the radius of either the Merseburg or Kassal wheels, which was 72 inches, we get 56 inches / 72 inches = 0.7777777777... which is an INFINITE series of lucky 7's! Stumbling across this made me feel like I'd hit a jackpot on some casino's slot machine! Again, I have to consider this too much of a coincidence to be one.

      This suggests to me that 56 inches measured from the center of the axle out toward the drum's rim is an important distance inside of Bessler's big 12 foot diameter wheels. Maybe it's the distance where the levers were attached to the drum with pivots? IIRC someone who was a witness at the official examination of the Merseburg wheel said he saw Bessler struggling with a lever inside of the drum that was near its outer rim. If a lever's pivot in the drum was only 72 inches - 56 inches = 16 inches from the drum's rim, then that is very close to it. This also suggests that the length of one of the three "Y" arms in a lever, probably the one with a weight attached to it, would have been less than 16 inches. Also, the sum of the digits in 16 is 1 + 6 = 7 so there's that lucky number again!

      I wish I could give a more precise analysis of MT137, but that requires more numbers and there aren't many associated with this odd drawing. Hopefully some will find what little I was able to extract from it to be of interest along with my various interpretations of possible meanings for it. It's really too bad Bessler did not leave a note for this drawing which also suggests to me that it was unfinished for some reason.

      Sayer of Sooths

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    2. Thank you SoS. You have obviously put a lot of research and effort into your comments and I respect that. For me numerology is an unproven belief in the effects of numbers on events but I don’t dismiss it out of hand, I just don’t know. I always note something of interest in your comments and in this case it’s the pentacle of Mercury. My first thought was that pentacle implied something relating to the number five, but apparently not so. There are considerable versions of its etymology and it comes down to personal opinion. Pentacol can mean talisman or it can refer to a pendant hung around the neck, or indeed to the number five. Fascinating.

      JC

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    3. SoS wrote "Stumbling across this made me feel like I'd hit a jackpot on some casino's slot machine!"

      You certainly did! SoS, you have a rare talent for zeroing in on clues like this.

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    4. If anyone wants to wear his 4th Pentacle of Mercury as a finger ring instead of on a neck chain I found this seller who makes it into finger rings. He has it in .925 solid silver, gold or rhodium plated, and even solid 18kt gold which is the most expensive. These rings are handmade and shipped from Prague in the Czech Republic. It was in Prague that Bessler made his first attempts to build perpetual motion machines while consulting with a Jesuit priest and a rabbi there. Fawk Bessler could have gotten this magic talisman from that rabbi and was wearing it while he slaved away chasing after perpetual motion!

      https://www.etsy.com/listing/801787969/witchcraft-fourth-pentacle-of-mercury?ga_order=most_relevant&ga_search_type=all&ga_view_type=gallery&ga_search_query=4th+pentacle+mercury+ring&ref=sr_gallery-1-9&organic_search_click=1&frs=1

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    6. Here's some more information about that fourth pentacle of mercury design.

      In the centre is the name of God or "El". The Hebrew letters between and inside of the points of the dodecagram make the sentence "Supreme One, fix thou the volatile and let there be unto the void restriction". The area around the design is called a vesicle and contains the Latin sentence "Sapinetia et virtus in domo eius et Scentia omnium rerum manet apud e um in Seculum Seculi" which translates into the English "Wisdom and virtue are in his house and the knowledge of all things remaineth with him forever".

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    7. Before anyone puts down the use of good luck charms and magical talismans, keep in mind that there are millions of religious types out there right now wearing crosses and various kinds of medals with images of saints on them. They are all really magical talismans intended to bring the wearer good luck or protection from evil. Some think if they die while wearing one then their soul will automatically go right up to heaven! I know people that carry lucky charms with them like mummified rabbit feet and different kinds of coins. Do they actually work? Who knows? But they do give their wearers some peace of mind and who can't use that in these stressful times we live in?

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    8. Good comment anon 14.41.

      JC

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    9. Looks like John prefers to hang his good luck charms on the wall rather than wear them!

      https://assets.vice.com/content-images/contentimage/163769/John-Collins--workshop--3-.jpg

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    10. For inspiration rather than good luck, anon 06.00. But I’ll take good luck too.!

      JC

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    11. Yes I’ve deleted all comments inspired by Ken’s ridiculous book. I am mighty suspicious that there are so many comments apparently supporting his imaginary clues and I suspect the author of most of them is Ken.

      I don’t know why you can’t have your own blog instead of abusing my blog.

      JC

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  6. John, many of the comments you deleted were based on the .7777777 magic ratio and had nothing to do with Ken. Since we are finding this length relationship in Bessler's drawings it is a valid topic worthy of discussion and research.

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    1. Ken's findings in the DT portrait, whether actual clues or not, led to the wheel design he put forward. I believe it is a piece of work worthy of discussion in order to find it legitimate or not, especially now that the .77777 magic ratio has been found in the wheel.

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    2. I understand your point anon, 18.52, and I’d love to explain why I dismiss it so easily but I don’t want to publish any of my work yet. I can tell you that the ‘.7777’ discovery is no such thing. The actual siting of the pivots is well established and I will explain due course, how and why I know this for a fact.

      JC

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    3. Well this is the "John Collins Blog" and not the "John Collins Forum", so you are entitled to delete posts you do not agree with. You might want to consider turning off commenting altogether. I myself don't want to continue posting only to find those posts and related replies gone some day.

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    4. That new Bessler lucky ratio clue seems to have really got John shook up. Maybe because he didn't discover it first? He's deleted dozens of comments here to hide the fact that others were finding that same ratio (0.777) in several of Bessler's drawings which only proves it is a real and very important clue. They probably won't be leaving any more comments here as a result of him censoring their efforts the way he did and who could blame them? That's just what we need around here since this blog has been sliding steadily downhill ever since it hit a peak of 122 comments in a single week for that last March 6th blog.

      John may not like that new clue, but it must be a very important one for Bessler to have used it in several of his drawings and that's what really counts. If any wheel design John ever comes up with again does not use that special ratio then that means it cannot be the same as Bessler's design and probably won't work. The thought of that is probably shaking him up even more!

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    5. Good bye guys, it’s been fun, but you’re really doing my head in.

      JC

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