Maschinen Tractate 137, and Some Important Numbers?

The subject of this blog might seem a bit unusual but perhaps it might spark some new ideas?

Some of you may be aware of the work I've published on www.theorffyreuscode.com  Three of the pages refer to the dodecagram on MT 137, which precedes the 'Toys' page, MT 138. 139. 140 and 141. I wrote that Johann David Heinichen, 1683-1729, a German musician, introduced the concept known as the ‘circles of fifths’ in 1711 (he called it Quintenzirkel). I suggested that MT 137 being similar to his quintenzirkel was designed to point to the circle of fifths, thus being another pointer to the number 5.

That has all been discussed before, here. This time my interest was directed to the MT number itself, written clearly on the bottom of the page - 137. I know Bessler was fascinated by the history and the relationship between numbers and letters and their hidden meanings and of course all the popular codes of the era, and it seemed to me that he had included the number quite deliberately, even if it was somewhat roughly executed. We know he had to add the Toys page in a hurry due to a possible impending arrest, and replaced the existing pages which gave the secret of the wheel. My guess is that he also added the MT 137 at the same time. As it had no mechanical resonance I think it was a deliberate inclusion along with in the Toys page.

MT 137, is the only illustration in the MT which doesn’t appear to show any mechanisms. One reason for this was, as I suggested above, to provide a hint towards the circle of fifths, but as Bessler usually included two or even three pieces of information in each of his clues I felt there could be something additional, that was invisible to me. A Google search of the number 137 for anything connected to his work produced the following information, but I’m still not sure if it’s relevant. Hopefully you will find it interesting, and in particular my final piece. Most of what follows is way over my head, but I include it because of the perceived importance of this number, both now and historically.

So, in the world of physics, it has been suggested that the number 137 could lie at the heart of a grand unified theory, relating theories of electromagnetism, quantum mechanics and gravity.

There is something called the ‘fine structure constant’, a physical constant with no dimension is approximately 1/137, and it’s reciprocal was said to be the integer 137, although later work suggested it was closer to 137.036.

Richard Feynman wrote the following about the number 137.

‘It has been a mystery ever since it was discovered more than fifty years ago, and Pauli famously quipped, “When I die my first question to the Devil will be: What is the meaning of the fine structure constant?” Unfortunately Pauli died without accomplishing his goal in the Red Cross Hospital of Zurich in Room 137—and he was aware of that synchronistic irony before he died. Theoretical physicists put this number up on their wall and worry about it. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed his pencil.’

In the Hebrew Kabbalah, the word has a Gematria value of 137, symbolically, this word indicates the threshold between the physical dimension and the utterly spiritual dimension. In other words, at the boundary line of the physical world, the number 137 emerges. The wisdom of Kabbalah is to find correspondences between the mundane and spiritual levels of reality.

Here are some quotes from some web sites.

“In his Nobel lecture delivered in Stockholm on 13 December 1946, Pauli expressed his goal was to establish a theory “which will determine the value of the fine-structure constant and will thus explain the atomistic structure of electricity, which is such an essential quality of all atomic sources of electric fields actually occurring in nature."

Cosmologist Robert L. Oldershaw argues that “137 is the relationship of the strength of the unit electromagnetic interaction compared with the strength of the unit gravitational interaction. That sounds pretty fundamental to me.”’

‘In the Bohr atomic model, the innermost electron of a hypothetical atom with atomic number 137 would be orbiting just below the speed of light, and the next heaviest element would be impossible because its electron would have to exceed c. Atoms close to the theoretical limit of 137 are unstable and not found in the universe’.

https://www.secretsinplainsight.com/why

The following is skimmed and abbreviated from my forthcoming book, which will be published later this year.

I was intrigued by the possibility that the number 137 was recognised to have special properties in Bessler’s time. There are websites devoted to such things as the properties of the three main pyramids which allude to the number 137, plus the Kabbalah, numerology, Freemasons, etc.

But I discovered that Bessler was hinting at the relationship between 137 and the golden angle or the golden mean, well known to the ancient Egyptians and the Greeks who called it phi, after the Greek sculptor Phideas. Phi, the golden ratio, is equal to 1.618, plus an unending succession of numbers. Plato discussed the subject at length in his Timaeus and of course there are the Leonardo Fibonacci series of numbers, and the laws of nature also dependant on the gold mean!

In geometry, the golden angle is the smaller of the two angles created by dividing the circumference of a circle according to the golden ratio, thus creating two arcs so that the ratio of the length of the smaller arc to the length of the larger is the same as the ration of the larger arc to the full circumference of the circle.

This provides two radii with angles of two particular degrees. The golden angle is 137.508. I suspect that using the number 137 for his dodecagram seemed like a good idea to the inventor, but he couldn’t name it MT 137.5, that would be too obvious. Bessler used the golden ratio routinely in his drawings and it was more commonly integrated in works of art than it is today. A search for the subject on the BW forum throws up many links.

Why did he add this page? Much of the work I have done on finding and interpreting his coded work was useful, but not a first sight and it was hard to explain when out of context. 

Bessler’s clues, if solved in isolation, get the confirmation of their validity from solving other related clues. This clue of the number MT 137 is an example of this. I have found, subsequent to the investigation of this clue, confirmatory examples of at least two precisely executed angles of 137.5 within his drawings. The connections I pointed out in my orffyreuscode.com web site also a showed a heptagram within the dodecagram, which, as well as the pentagram, includes numerous examples of the golden mean or ratio.

But there is a further mystery - or am I becoming even more paranoid than before?

The Toys page is numbered at the bottom as 138, 139, 140, and 141, but why? The page is labelled with A, B, C, D and E, and these five letters were obviously on the page before he added his four handwritten numbers. So four page numbers for five labelled itemss? It has been suggested that the Toys page replaces four pages which were burnt or buried, but why did he need to remind himself by numbering the page in this way?  He could just dig up the ink blocks he buried when he needed them. Maybe he decide to add MT 137 at the last minute so he could use the number 137 with the do-decagram and add a pointer to the golden angle, there rather than on the Toys page? But if he then added the other four numbers to the Toys page why not end with 142 to cover the five items on the page, instead of number 141? Perhaps he needed to end with 141 and he had already used 137. He had a record of including more numbers than necessary to reach a significant total.

141 is the product of two prime numbers 3 and 47. Coincidentally (maybe) there are 141 bible references in chapter 55, within the 55 verses of his Apologia Poetica.  The number 47 brings to mind Eulclid's 47th proposition but which can exhibit the properties of the golden ratio with some additional extras.  It describes the 345 right triangle with its accompanying squares. That particular figure was adopted by the Freemasons a while ago, so perhaps he is demonstrating his knowledge of the craft. Apparently the Euclid’s 47th proposition is discussed in the Freemason 33rd degree, and a Masonic publication, Anderson’s “constitutions”, was published in 1723, it mentions that “ the greater Pythagoras provided the author of the 47th proposition of Euclid’s first book“

In 1723 Bessler was well established at Kassel, a centre of Freemasonry, and I’m sure he was familiar with the “Constitutions”.  The history and use of the 345 right angle is described in detail and a number of its additional features described which I was unaware of.  One of the angles produced in the additional features is 108 degrees which looks uninteresting but 360 divided by 108 equals 3.3333, the 33rd degree? 108 is the largest angle in the pentagram, all the angles in pentagram are multiples of 18, the smallest angle in the pentagram 18, 36, 54, 72, 90 and 108, so I’m sure that there is a golden ratio in there. The Kepler triangle also exhibits the golden ratio.

I prefer to think that although Bessler was using the language of Alchemy he was actually disguising mechanical processes. It makes more sense than him going off at a tangent and talking about things of a magical nature.

All comments welcome.

JC

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

Johann Bessler’s (aka Orffyreus’) Maschinen Tractate.l

The publication mentioned in the title of this post, Maschinen Tractate, was never published by Bessler but was found in his possessions after his death. I have producedca digital copy and a printed version available from the side panel of this post. It includes an English translation of Bessler’s handwritten notes, which were difficult to read, but still useful.

Bessler’s Maschinen Tractate (MT) consisted of 141 illustrations designed to lead one to the discovery of Bessler’s Perpetual Motion machine. Originally intended to provide material for his planned school for apprentices, it unfortunately lacks the final illustration depicting the solution. I called the final page, ‘The Toys Page’, because it includes a brief reference to ‘children’s games’. This final page has the numbers 138, 139, 140 and 141 added to the bottom left of the picture. The page immediately before the toys page was numbered MT137, which was the logical number for the preceding page.

There is a possible explanation for the inclusion of those numbers. Firstly 141 is only divisible by 3 and 47. Euclid’s 47th proposition shows how to construct a pentagram and I’ve shown that most his construction method can be seen in his two pictures of his Merseberg and Weissenstein wheel. 

But interestingly adding together all four numbers written at the foot of the ‘Toys’ page produces a total of 558, and 55 we know is one of Bessler’s most favourite numbers, but the 8 is not so easily explained. However adding these three numbers brings the total to 18, the key number in the pentagram. So here we have a typical Bessler move designed to make us think and seek an explanation - suggesting the pentagram again.

As I have pointed out previously MT137 contains the musical ‘circle of fifths’ diagram, a guide for musicians. It takes the form of a dodecagram, a twelve pointed star. See adjacent picture of MT137.

Some of you may be aware of the work I've published on www.theorffyreuscode.com .Three of the pages refer to the dodecagram on MT 137. I wrote that Johann David Heinichen, 1683-1729, a German musician, introduced the concept known as the ‘circles of fifths’ in 1711 (he called it Quintenzirkel). I suggested that MT 137 being similar to his quintenzirkel was designed to point to the circle of fifths, thus being another pointer to the number five.

I was drawn to this illustration, MT137 because it looked like a random addition but I knew that nothing in Bessler’s books was devoid of purpose. We know that Bessler was fascinated by the history and the relationship between numbers and letters and their hidden meanings and of course all the popular codes of the era, and it seemed to me that he had included the number quite deliberately, even if it was somewhat roughly executed. I believe that he added the Toys page later in life and replaced some of the existing pages which gave the secret of the wheel. My guess is that he also added the MT 137 at the same time.

MT 137, is the only illustration in the MT which doesn’t appear to show any mechanisms. One reason for this was, as I suggested above, to provide a hint towards the circle of fifths, but as Bessler usually included two or even three pieces of information in each of his clues I felt there could be something additional, that was invisible to me. 

I was intrigued by the possibility that the number 137 was recognised to have special properties in Bessler’s time. There are websites devoted to such things as the properties of the three main pyramids which allude to the number 137, plus the Kabbalah, numerology, Freemasons, etc. I’m inserting an interesting link about the number 137, the GOD particle.

“Leon Max Lederman is an American experimental physicist who received the Nobel Prize for Physics in 1988. In his book, “The God Particle”, he writes:

“One hundred thirty-seven is the inverse of something called the fine-structure constant.”

https://www.ancient-origins.net/ancient-places-africa/hidden-message-khafre-s-pyramid-what-were-builders-trying-tell-us-008646#google_vignette

But I discovered that Bessler was hinting at the relationship between 137 and the golden angle or the golden mean, well known to the ancient Egyptians and the Greeks who called it phi, after the Greek sculptor Phideas. Phi, the golden ratio, is equal to 1.618, plus an unending succession of numbers. Plato discussed the subject at length in his Timaeus and of course there are the Leonardo Fibonacci series of numbers, and the laws of nature also dependant on the gold mean!

In geometry, the golden angle is the smaller of the two angles created by dividing the circumference of a circle according to the golden ratio, thus creating two arcs so that the ratio of the length of the smaller arc to the length of the larger is the same as the ration of the larger arc to the full circumference of the circle.

I must thank Trevor, a long time correspondent for pointing out the error in the above illustration.  360/1.618 is of course 222.5 and not 225.5.  I originally posted the illustration back in 2020, but nobody noticed then, me included. 😃

This provides two radii with angles of two particular degrees. The golden angle is 137.508. I suspect that using the number 137 for his dodecagram seemed like a good idea to the inventor, but he couldn’t name it MT 137.5, that would be too obvious. Bessler used the golden ratio routinely in his drawings and it was more commonly integrated in works of art than it is today. 

If you use two radii to divide a circle according to the golden ratio it yields sectors of approximately 137° (1.618, the golden ratio) and 222°, hence it being the numbered 137. 

To be accurate 360/1.618 = 222.5 and 360-222.5=137.5 Curiously 1/137.5 = 00727272727 etc. and 5x72=360, the basic numbers of the pentagram again.

But it is also interesting that 137.5/55 = 2.5 exactly because in his musical circle of fifths Heinichen explained that the circle of fifths gets its name from the fact that you travel across the circle from one point to another 5/12th away, or 2.5 segments away, in order to find circle of fifths. This is a way of organising pitches as a sequence of perfect fifths. 

In the above illustration the circle with its 137.5 degree angle also mimics a clock at five o’clock, which is a good pointer to the circle of fifths. But in truth with the hands showing five o’clock the angle would be 150 degrees (5x30) not 137.5. To show the angle as 137.5 with the hour hand at five, the minute hand is in fact closer to the number one on the clock, or 12.5 degrees nearer, 

Check out my web site at www.theorffyreuscode.com

JC

Bessler's Septagram/ Heptagram

When I described my findings on the MT 137 figure on my website at http://www.theorffyreuscode.com/html/mt_137_a.html
I showed how it represented the musical circle of fifths publicised by Johann David Heinichen, 1683-1729, a famous German musician who lived and worked in Weissenfels at the same time as Bessler.  See the first two figures below.  MT 137 on left, modern version of Heinichen's circle of fifths to the right

In part two of the same page of the website at
http://www.theorffyreuscode.com/html/mt_137_part_two.html, I showed how Bessler had included a hidden septagram or heptagram, which is a seven-pointed star drawn with seven straight strokes, and sometimes drawn inside a circle.  Deleting the black lines on the original MT 137, or circle of fifths illustration, as in the middle figure below, and redrawing them to skim the edge of the inner black circle produces a heptagram, as shown in the third figure below.   This geometric figure has numerous associations with occult and religious symbolism, but lack of space prevents those discussions here at this moment.

What I had not appreciated was just how difficult it is to draw a circle with seven equal divisions, and that means that the inclusion of the heptagram in MT 137 cannot be considered as a coincidence, but is deliberate.  A circle divided into seven equal segments has seven interior angles of 51.428571 degrees.  This makes it impossible to get an accurate measured angle and there is no system available using ruler and compass, although you can get an approximation by dividing the circumference by seven and walking a set of compaases around it, or simply dividing the circle into seven angles of 51.5 degrees. I drew a heptagram and tried inscribing a circle within it to match the inner circle in MT 137, it is not at all easy!

The two figures lend themselves to a simple code - draw the connecting lines from one point numbered 1 and then follow the logical progression clockwise or anticlockwise and you get, for instance in the septagram,
1 to 4
4 to 7
7 to 3
3 to 6
6 to 2
2 to 5
5 to 1 .  The same applies to the dodecagram using the numbers 1 to 12.

Curiously the sides of the Great Pyramid is said to have a slope angle which is close to one-seventh of a circle, i.e. 51.4°, so I guess a reasonable approximation could be 51.5 degrees.

The number 51.42857 contains six repeating digits of 1/7, and is the best-known cyclic number in base 10. If it is multiplied by 2, 3, 4, 5, or 6, the answer will be a cyclic permutation of itself, and will correspond to the repeating digits of 2/7, 3/7, 4/7, 5/7, or 6/7 respectively.

1 × 142,857 = 142,857
2 × 142,857 = 285,714
3 × 142,857 = 428,571
4 × 142,857 = 571,428
5 × 142,857 = 714,285
6 × 142,857 = 857,142
7 × 142,857 = 999,999

The last one, 7 times, is a surprise..  (found at http://en.wikipedia.org/wiki/142857_(number)  )

So another mystery beckons - why did Bessler include a heptagram in MT 137?  5 or 7 mechanisms?

JC

10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’

Addition to www.theorffyreuscode.com

Following some serendipitous studies I found what I believe is an interesting piece of information regarding MT 137 - but only for those who relish the code-breaking requirements of Bessler's  tortuous coded constructions.  It doesn't shed any more light upon the meaning of MT 137, but for me it confirms what I have always thought - that the drawing is only intended to be another secret pointer to the number 5.

I have added yet another page to the http://www.theorffyreuscode.com/ web site and an extra button MT 137 C!  I have slightly altered MT 137 A, and MT 137 B although I doubt anyone will notice the difference.  I'm not posting anything on BW forum because I don't think anyone is particularly interested.  That's not sour grapes, its just the way it is.  I don't think that repetitive revelations that yet another piece of code appears to suggest the number 5 will light anyone's fire, not even mine, but I do have an interest in all things Bessler and I am constantly intrigued to find new layers of meaning within his writing/drawing.

The only thing I would say is that after all these discoveries relating to the number 5, I must admit that I am perplexed at the ubiquity of it and concerned that something so apparently important to Bessler should be ignored simply because there is so much of it.

JC

The TOYS Page, 137, 141 and 47 and the Freemasons.

Many here will be aware that the ‘Toys’ page in Johann Bessler’s Maschinen Tractate was numbered MT 138,  139, 140 and 141.  I suggested that the drawings he destroyed or buried were replaced by this curious page of what appear to be toys, but perhaps there was another reason.

 The previous page was numbered MT137, which was the logical number for the preceding page.  As I pointed out previously MT137 contains the musical ‘circle of fifths’, plus if you use two radii to divide a circle according to the golden ratio it yields sectors of approximately 137° (1.618, the golden ratio) and 222°, hence the number 137. 

So 360/1.618 = 222.5 .  360-222.5=137.5 Curiously 1/137.5 = 00727272727 etc.  5x72=360.

The pentagram is of course constructed with numerous examples of the golden ratio.

I should add there is a huge amount of discussion in scientific circles about the mystery of the number 137. https://en.m.wikipedia.org/wiki/137_(number)

The final number on the Toys page is 141, is an interesting choice.  The number of Bible references in Bessler’s Declaration of Faith also number 141. Only 3 and 47 are divisors of  141. This brings to mind Euclid’s 47th problem. MT47 has a curious feature, the number 47 is repeated upside down within the drawing.

Bessler seems to be underlining the importance of the number 47. It could suggest the requirement for a 3:4:5 right angle in his wheel?

Other reasons occur to me which could explain Bessler’s inclusion of these numbers but it would be too much speculation at this point.

I’m aware of suggestions that Bessler was involved with FreeMasonry and so I offer the following information gleaned from 

https://bricksmasons.com/blogs/masonic-education/the-47th-problem-of-euclid

“The 47th Problem of Euclid or 47th Proposition of Euclid is also known as the Pythagorean Theorem. It is represented by three squares.

The symbol of the 47th problem of Euclid looks mysterious to the uninitiated, and a lot of them often ponder on what this Masonic symbol means.

Some Masonic historians describe the 47th Problem of Euclid as something that connotes a love of the sciences and the arts. But that definition leaves a lot unsaid. In this article, we’ll shed more light on the 47th Problem of Euclid. Our explanation will include the Masonic Square along with Pythagoras’s Theory.

Euclid 

Euclid is known as the Father of Geometry. He lived several years after Pythagoras, and he continued the work of Pythagoras. Euclid focused mainly on the 3:4:5 ratio puzzle. Some sources have it that he had to make a sacrifice of 100 cattle or oxen before he could solve the puzzle. Some other sources have it that the Egyptians had long solved the puzzle before he did.

The Pythagoras Theorem 

The Pythagoras theorem states that in a right-angled triangle, the sum of the squares on the two sides is equal to the square of the hypotenuse. So, for a right-angled triangle with lengths of sides in the ratio 3:4:5, ‘5’ represents the hypotenuse or the longest side.

3: 4: 5

32: 42: 52

9: 16: 25

9 + 16 = 25

The first four numbers are 1, 2, 3 and 4. Let us write down the squares of these numbers.

      12:22:32:42   

      1: 4: 9: 16  

When you subtract each square from the next one, you get 3, 5, 7.

4-1 = 3            

9-4 = 5 

16-9 = 7

The ratio 3: 5: 7 is very important. The ratio represents the steps in Freemasonry. They are the steps are the exact number of brothers that form the number of Master Masons needed to open a lodge.

3 Master Mason

5 Fellow Craft

7 Entered Apprentice

3: 5: 7 represents the steps in the Winding Stair that leads to the Middle Chamber.

The 47th Problem of Euclid is necessary for constructing a foundation that is architecturally correct as established by the use of the square. This is important to Operative Masons as well as Speculative Masons.

The 47th Problem of Euclid is a mathematical ratio that allows a Master Mason to square his square when it is out of square.  

In the old days, old wooden carpenter squares had one longer leg because they were created using the 3: 4: 5 ratio from the 47th problem of Euclid. But carpenters of today use squares that have equal legs.

If you have four sticks and a piece of string, you can work out the 47th Problem of Euclid on your own. You will be able to create a perfect square with these. The string should be about 40 inches in length, and the four sticks must be strong enough to stick into soft soil. You will also need a black marker to mark the rope.”

I remain unconvinced of Bessler’s membership of the Masons, but he seems to have had some knowledge or interest in them.

JC

Johann Bessler's Graphic Clues

Despite including several drawings illustrating his wheel (although external views only) in his publications, Grundlicher Berchicht, Apologia Poetica and Das Triuphirende, most people have seized upon his unpublished work which I have called his Maschinen Tractate (MT) (although there is no such title contained within its pages) to try to find answers to the Perpetual Motion (PM) machine. The MT contains 141 illustrations prepared for printing and some of the pages have handwritten comments attached to them.  But there is a note on the first page which warns the reader that he, Bessler, has destroyed or hidden any that show the workings of his wheel.  He does stress that careful study of the remaining drawings could lead someone with a perceptive intelligence to find the solution.

Many people have taken this to mean that a careful study of every page is necessary to find the answers, but in my opinion, Bessler would not have included serious information in all 141 drawings or even some of them, which were completed over a considerable length of time.  But also he would have had no idea that an arrest charge was imminent and therefore he would have had no time to add numerous drawings done painstakingly on wooden blocks for printing.  I'm sure his original intention was to conclude the MT with an explanation of how his wheel worked, but due to the possibility of imminent arrest he removed those particular pages and replaced them with an illustration on paper. The page which I called "the Toys" page is numbered 138, 139, 140 and 141.  This is the only page with more than one page number, therefore I think it is only necessary to study that single page.  The fact that it includes four page numbers suggests that it replaces those original four pages, the ones showing how his wheel worked.

It is true that there are hints at othe hidden information within the preceeding 137 pages and perhaps he did insert pointers to additonal information but it is my belief that these little clues pointed to the some small features within his concept, not intended to convey the complete picture.  If we assume that his MT was designed to be a tool for teaching his apprentices at his planned school then these small inclusions might have been there to raise points of discussion within his anticipated classroom.

So the 'Toys' page may well hold some important information that while not providing the full picture, might prompt us in the right direction.  One other picture, MT 137, appears to be prepared for printing might have been added as additional clue.  You can read my hypothesis about this page on my web site at www.theorffyreuscode.com :-
 http://www.theorffyreuscode.com./html/mt_137_a.html 
Check out pages '2' and '3' too for the full picture.

Note the drawings below include the original MT137 and below it,  how to construct MT 137 taken from the web site linked above, and if you have read the above link you will know that I have always worked on the assumption that there were five mechanisms.  There are several supporting clues which also point to the same number.

In the 'Toys' drawing below I have divided the drawing into five sections.  I used the figure marked 'A' to guide me and included one of five pairs of depictions; one straight vertical and one pair of verticals in each division.  In the 'Toys' drawing there are five letters, A, B, C, D  and E - note that, five letters.  An apparently hastily added sketch of  a spinning top is labelled '5', not 'F' to follow 'E'.  and he calls it '5', not '6'.  Weird?  Or is he trying to tell us something?

Splitting the drawings into five parts reveals some information.  In each division in 'A', you can see, drawn vertically, two uprights surmounted by a single one.. They bear a striking resemblance to the figures labelled 'C' and 'D', which are shown horizontally.  But why two 'C' and 'D's?  I think only one hammer is needed in 'C' plus the parallel rods.  The same in 'D' but the hammer used is rotated around the other way to point outwards or to the left.

The item marked 'E' is the storks-bill, lazy tongs, scissor jacks or whatever you prefer to call them.  Item '5' is a spinning top, just in case no one makes the connection that this is all about a rotating device.  I won't explain item 'B' as it would require too much extra explanation here, but obviously it has a connection with item 'A'. But I will show its meaning later this year, when I've checked a couple of things out first.

Lastly the text is hard to read at item '5' but has been variously translated :-

" 5. Children's game in which there is something extraordinary for anyone who knows how to apply them in a different way."

  Mike, my translator had several goes at it and came to the conclusion that his version was right, but who knows?

JC

Orffyreus' use of Hebrew letters

I was leafing through Bessler's "Der rechtgläubige Orffyreer", http://books.google.co.uk/books and noticed that page 13 has some curious hand-drawn black markings on it which I recognised as, possibly, items from the Hebrew alphabet, which Bessler mentioned in his Apologia Poetica, he learned during his stay in Prague.

A glance at the picture below tells the story.  Bessler has inked in the Hebrew letters between the two parts of the decorative pattern at the head of the page. Below is a piece I copied from the page and in it I have included two examples found on the internet which clearly match what Bessler has written.  He has reproduced the Tetragrammaton, which is what the Jews call the word for their God - Yahwey.

The Tetragrammaton, from Greek  meaning a word having four letters, refers to the name of the God of Israel YHWH used in the Hebrew Bible. Different spellings of the tetragrammaton occur in Jewish magical papyri found in Egypt. One of these forms is the heptagram, These four letters are usually transliterated from Hebrew as IHVH in Latin, JHWH in German, French and Dutch, and JHVH/YHWH in English. This has been variously rendered as "Yahweh" or as "Jehovah", based on the Latin form of the term, while the Hebrew text does not clearly indicate the omitted vowels. It translates most basically as "I am that I am" or "I will be that which I now am".

The Latin pronunciation of the letter I/J as a consonant sound was, the 'y' sound of the English word 'you'. This changed in descendent languages into various stronger consonants, including at one point in French the 'j' sound of the word 'juice', and this was the sound the letter came to be used for in English. Thus the English pronunciation of the older form Jehovah has this 'j' sound, following the English pronunciation of its Latin spelling. In order to preserve the Latin and approximate Hebrew pronunciation of Jahweh, however, the English spelling was changed to Yahweh.

The septagram/heptagram is important in Western Kabbalah, where it symbolizes the sphere of Netzach, the seven planets, the seven alchemical metals, and the seven days of the week.

  [My thanks to Wikipedia for the above information.]

I assume Bessler wished to include the Jewish version of Christianity in his unified Christain religion and he did use the word JEHOVA frequently throughout this document.  This does lend credibility to Bessler's claim that he learned some Hebrew during his stay in Prague.   With reference to the above quote from Wikipeida I should also mention the presence of the heptagram in MT 137 as explained on my web site at www.theorffyreuscode.com - see the four MT 137 links there.

JC

Johann Bessler and a Few Coincidences?

There seem to be some related features within Bessler’s documents which may be coincidental, or not - so I have tried to draw conclusions from them by assuming that they are deliberate.  I’m sure some will disagree but I think it worth pointing them out, just in case they were intended to catch our eye for some reason.

It’s sometimes easy to see things as coincidences rather than intentional occurrences.  For instance I like the fact that Bessler stresses the importance of the number 5, and 55.  My birthday is on the 5th day of month 2, obviously a coincidence, how could it be otherwise?  I was born in 1945, Bessler died in 1745 just another coincidence.  There is one more example which I’ll mention later. 

The document I have always referred to as the “Toys” page is numbered MT 138, 139, 140 and 141.  This is logical as it follows MT 137. There are actually five drawings on the page lettered A B C D and E plus what appears to be a late addition of a hand drawn figure with the number 5 adjacent. So we appear to have four pages, apparently with five drawings labelled with letters plus one more number 5.

At first sight I believed the intention was to show that this page was intended to replace four others, destroyed or buried, after his arrest.  But this assumes that either he was charged but not imprisoned otherwise he might not have had time to prepare for searches or confiscation of his documents, so the charges he was accused of made him hurry to take precautions against such actions against him.  This is possible, but why would he need to remind himself of four pages buried or destroyed?

The total of 141 is interesting.  It seems as though he wanted to get to that number and not beyond, but numbering the ‘Toys’ page 138 would seem to have been good enough.  141 is not a prime number and it’s only factors are 3 times 47.  If we turn to MT 47 we discover that inserted within  the drawing which is numbered 47, another number 47, twice in fact because one is the mirror image of the other so there are three number 47s present on the page. Is this a pointer to the number 141 or the reverse or is it just a coincidence?

Bessler’s ‘Declaration of Faith’ which appears in his “Apologia Poetica” chapter 55, contains numerous Bible references, 141 to be precise.  So if we assume the same link as before, what is the relevance of the number 47?  The first thing which occurred to me was Euclid’s 47th proposition. Was Bessler drawing attention to it for some reason.

“In any right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse.” It’s also a 3, 4, 5 triangle, see below.  I’m sure I needn’t go into any detail about this, but the figure also relates to the Freemasons symbol as you can see further below. Maybe this was the connection he sought to hint at.

There other pointers to the Freemasons and I guess it’s up to people if they think the above is relevant.  But most likely, in my opinion it points to Pythagoras who is believed to be the originator of much of Euclid’s Propositions, and thus to geometry, which ties in with Bessler’s second portrait in his Das Triumphirende book (DT)

One other coincidence for now, which I wrote about in 2019.  I wrote “I have a copy of a document, a panegyric addressed to Karl annually, but it has something unique.  As many will know, Bessler was very fond of chronograms, which is a phrase or inscription in which letters such as M, D, C, X, L, I, W and V can be read as Roman numerals giving a date. He provides dozens and dozens of them in some of his documents and curious as they are, they don’t appear to hold any coded information.

This particular one includes the year.........2019! He also wrote them for 1519, 1619, 1719, 1819 and 1919.  But why 2019 and why did he stop,there? It could have been the year his solution was discovered - what a coincidence that would have been.  If it had, everyone would have believed that Bessler had somehow predicted the future, but it didn’t happen, and if it had, it would still be just a coincidence.

In my experience I find that Bessler added more clues, hints and implications as and when they occurred to him, consequently one often comes across new and exciting ‘coincidences’ seemingly added almost as an afterthought.

Of course the following is just  a happy coincidence, my new house which I hope to move into before the end of this month is numbered 47.  No!  I wouldn’t buy a house because I liked its number!  And I’m not into the Freemasonry.

JC

A confusion of clues.

I've had some requests asking for more clues and it's not easy to point to the clues without giving too much away too soon!  I say this because I still would like to try and make my own prototype first.  However I think that unless you know the principle which drives the wheel, the clues may not be any use anyway.

  

Obviously the most useful clue would be one which would lead to an understanding of this principle, but again, I really don't want to share that yet.  On the other hand there may be people out there who do know the principle but have not yet worked out how to incorporate it within the wheel, so they might indeed find my clues useful.

It has always been clear to me that if Bessler wished to preserve and subsequently reveal his design for the benefit of post-humous recognition, or to prove he thought of the solution first, it would have to be contained within some drawings, as well as in text.  It seems to me to be almost impossible to describe the function of a machine in text alone. Sure, you can give some good clues but a picture is worth a thousand words.  So the drawings hold the best clues, but which are they?  In my opinion he would have set down those clues as soon as possible, which means the drawings in Grundlicher Bericht, Das Triumphirende and Apologia Poetica contain the original graphic clues.  I agree there are clues in Maschinen Tractate but they are not as useful as some others, apart from the 'toys' page.

As far as I know, the drawing at the end of the Apologia Poetica is only of use in telling us that there are five mechanisms in the ideal machine - and the same can be said for the MT 137, but I may be wrong about that - or my interpretation of what the fives mean may be wrong or inadequate.  I should also remind everyone that it might simply point to chapter 55 of his Apologia Poetica which obviously contains a wealth of undeciphered hidden text.

For me the portraits only hold information which points to a pentagram.  As before, I assume this refers to the number five again. I'm not convinced that Bessler would or could have included any clues which would show how his machine worked, within the portraits, however I am well aware that at least one other person has found what they regard as useful information there, so I must await the revelation of that information before I can arrive at an informed opinion.

I think it was John Worton who commented that Bessler hid in plain sight the secret of his machine in his woodcut images available for all to see for three hundred years. What better place to hide such information than within a drawing which is open to public scrutiny and has been for 300 years?

And finally I must echo Doug's words, 'some of us have been looking at simulations way too much..'

JC

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Divide the toys page into five parts.

I feel that the clues I have published may be too subtle for some to accept. This puzzles me, but of course I've had many years to study them and get inside Bessler's mind.  Obviously some people think I may be fooling myself but I have good reasons for thinking the clues are deliberate and real.  I never intended to give anything away when I published the clues and therefore by themselves they may seem unimportant, but I hope to explain why they are helpful in discovering the solution to Bessler's wheel.  I won't publish any more as I shall be away for a two weeks and will have to close the comments facility until my return.  I am taking a small computer with me and if I can find a wifi hotspot somewhere then I'll try to write something.  So, in the mean time....

3 days to go - 7th clue.  The items in the Toys page in MT, numbered 138, 139, 140 and 141, are labelled A, B, C, D and E (1, 2, 3, 4, 5).  There is an additional hand-drawn item, a spinning top, which includes in the notes attached to it the number 5 (five again!). You can rather neatly divide the drawing labelled 'A' horizontally into five equal divisions.  You can run the horizontal lines across to the left and find that they match well with item 'B' and further across to the stork's bill/lazy tongs.

It has always seemed clear to me that the items labelled 'A' and 'B' are the same things - and with the five divisions in place, show they are also five repeated versions of items 'C' and 'D'.  'A' is shown with the five mechanical arrangements labelled 'C' and 'D' in an open position, and 'B' is the same but closed.

But item labelled 'E' is also similar - you should think of it as 'C' and 'D' linked together.

In other words, as I said in another post, the drawings are not what they appear to be, at first sight.

One more thing.  I could never understand why Johann Bessler added four numbers to the bottom of the page and I assumed that it was to show which pages he had omitted.  In fact this doesn't make sense because this is the last page and followed on from 137, which would have been the last page before he added the toys page. But four numbers doesn't relate to the five (or six) drawings he labelled, but here's an idea - 138, 139, 140 and 141 totals 558.

JC

The Mystery of the 684 X's in Apologia Poetica

Occasionally I've commented on Bessler's graphic codes, but have generally said little about the non-graphic ones.  But as the subject of the infamous x's scattered throughout Apologia Poetica, came up recently on Besslerwheel forum, I thought I'd update people on my own efforts to extract meaning from them.  I know this is not as interesting as discussing possble mechanical arrangements but there are many people who are still bent on deciphering what Bessler's secret message said.

The mysterious inclusion of 684 x’s scattered in an apparently random fashion at the ends of many of the 7000 plus lines of poetry which compose the Apologia Poetica, has been the subject of some debate.  In fact these x’s are actually abbreviations for the phrase et cetera, and one might think that that is a satisfactory explanation for their presence, but 684 seems an excessive use of the Latin expression and their numbers are reduced to a normal amount, less than ten, in his subsequent book, Das Triumphirende.  The presence of 28 &c's in addition to the et ceteras used, would seem to make the necessity of using the Latin abbreviation redundant, anyway.

The presence of so many et ceteras and the various hints at the existence of a hidden message within the Apologia Poetica lead one inevitably to question the large number of these abbreviations.  In some cases there are as many as seven consecutive lines each ending in the Latin expression.

There are 397 et ceteras in part one of Apologia Poetica, and 287 in part two, totalling 684.  I have omitted the  &c's and the many NB’s and NB’s because I am uncertain about their relevance to a secret message.  But just for the record there are 9 + 19 = 28  &c’s, and 20 + 176 = 196 NB’s. Anyway in preparation for devising his code, Bessler must have written his text and then looked for a way to hide it within his existing work.  I assumed that he then circled or underlined the letters or words he sought for his text and then used some method to identify the line containing that letter or word.  I suggest that he marked this line by placing the et cetera sign at the end of it. There is no mileage, in my opinion, in trying to read something in the positioniong of these abbreviations, either from the front or the back of the page; their positioning is too similar to each other for any one to detect any subtle differences.

The next step was to leave some means of guiding us to the correct letter or word on that line. I tried various ways of identifying a letter or word, but came to the conclusion that a letter was too time consuming and as he had a plethora of suitable words to pick from, why make his job more difficult if he could use full words and still hide them.  If one assumes an average of five letters per word then from a total of 684 ‘et ceteras’, he had about 137 words to complete his secret message, whereas if each et cetera indicated a whole word he would have potentially 684!  I suspect the answer lies somewhere between those two figures.

The method he used to hide his words had to be very strong.  This becomes even more obvious when you consider such passages as this one on page 27 of the Apologia Poetica, which has no fewer than six consecutive lines with the et cetera 'X' at the end.

If each lines contained a word from his text in the order in which it naturally ocurred, it would not take long to find the identifier and hence the whole coded message could be read. And that is not the only page containing six or more consecutive lines with  et ceteras at their ends.  An additional clue may be found in the presence of double et ceteras which appear in part two of Apologia Poetica. Here are a couple below:-

Note the second one is positioned just after two blanks.  The missing word is ‘Schelmen’ meaning ‘rogue’ or ‘rascall’.  For further information on the use of the blanks visit my web site at www.theorffyreuscode.com

I then wondered if the meaning and even the position of the et ceteras themselves were irrelevant.  Maybe the secret lay in the number of them per page.  If there was just one et cetera on a page, maybe that meant 'line one' held the missing word.  As a check I looked at the title page which has one et cetera on it and assumed ‘one’ et cetera meant line ‘one’.  The first word is ORFFYREI  which looks promising, but then it all goes wrong again.  In the subsequent page with et ceteras on it, nothing else supports this idea.  I tried various alternatives such as counting lines from the top on odd pages and from the bottom on even ones, but no dice.

But consider this, if each page which has one or more et ceteras on it, is meant to hide one complete word, there are potentially 226 words.  That is the number of pages which have et ceteras on them.  I feel that this way lies the solution.  It is too tempting to be drawn into considering the line with the et cetera on it rather than just counting how may X's there are and using that number to find the word.

One more thing might be worth taking into account.  The whole book is written in rhyming couplets except for part of Chapter 55, which I have discussed at www.orffyreus.net - maybe there is some way to assign the number of et ceteras to a couplet?

Good luck to those who are persuing this line of enquiry, and I know there are several, from my email correspondence.

JC

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