Bessler’s Favourite Number

This is just an idea that has been hanging around in the back of my mind, for ever, it seems.  Everyone is well aware of Bessler’s apparent obsession with the number 5 (and mine!).  There are numerous pointers indicating to its importance in Bessler’s mind.  I won’t repeat the many indicators but….what if it has nothing to do with the number of mechanisms inside the wheel?

Recent comments on this blog brought to my mind this question and a possible connection with the frequency of the number five.  The Fibonacci numbers are well known and their relationship to the golden ratio.

We know that Bessler was familiar with the golden ratio and the Fibonacci numbers because he demonstrates it with MT137.  See my blogs dated 25th October last year and 7th September 2024.

And https://johncollinsnews.blogspot.com/2025/10/a-brief-reminder-about-besslers.html

https://johncollinsnews.blogspot.com/2024/09/johann-besslers-aka-orffyreus-maschinen.html

He knew the maths, 360/1.618 = 222.5 or  360-222.5=137.5 Curiously 1/137.5 = 00727272727 etc. and 5x72=360, the basic numbers of the pentagram again. 

He needed to fill the gap between MT136 and the first number in the Toys page, 138.  He did this with MT137, which seems to be an of odd inclusion considering the MT was a collection of machinery drawings.  MT137 has no  apparent mechanical properties usable in a Bessler wheel. It does, however show it’s connection with the golden ratio. 

He demonstrated his requirement to achieve certain totals by using a collection of related numbers to get the final total to some significant number.  He used this technique in all the drawings in GB and DT.  

So the Toys page had the four numbers pencilled on the bottom left corner of the page, 138,139,140 and 141.  

There are 141 bible references in Chapter 55 of his Apologia Poetica, and 55 four line stanzas. We know that this number 55 is constantly shown  as well as 5.  In the Fibonacci serine’s of numbers 5 and 55 are present,  why would he push the importance of a those two numbers?  Perhaps he was actually pushing the golden ratio.

141 has only two factors, 3 and 47.  MT47 has three number 47s.  Euclid’s instruction 47 shows how to construct a pentagram. He also describes construction of a  line representing the golden ration, although he doesn’t give it that name.

The Toys page numbers total 558. The 55 seems a popular number for Bessler, but what of the 8?  Well the three numbers in 558 total 18 and that is the basic number in the pentagram, all the angles are multiples of 18. 

The number connected with then Golden ratio is 1.618, but 0.618 is its conjugate and is close to SoS’s Bessler’s favourite number 0.777…

I wondered if the actual measurement ratio which was thought to be 0.777 might actually be 0.618?

I don’t know because I never knew how SoS found the 0.777.  However given Bessler apparent obsession with the number 5 and 55, and the pentagon, I don’t think it’s too much of a stretch to connect the golden ratio with SoS’s favourite Bessler number 0.777.

JC