Saturday, 7 November 2015

Some of Bessler's Wheel numbering clues described.

This is a brief account of the odd numbering used by Bessler in labeling his two wheels, the Weissenstein one from Grundlicher Bericht and the second one the Merseberg wheel from Das Triumphans. For simplicity I shall refer to them as the W wheel and the M wheel.

By the way, click once on either illustration to get a large version to see the numbering more easily.





It becomes quite clear that some of the items are ‘over-numbered’.  By that I mean that Bessler seems to have labelled the parts with a particular number more often than one might think was necessary. For example the main pillar supporting the wheel is numbered 4, four times.  The slimmer pillars are numbered 12, and two of them to the left are numbered twice each, yet the other two are only numbered once each. Some numbers appear more often than others and not just because they are attached to more similar pieces. After number 18 the rest of the numbers are lone examples. I speculated that this was done to achieve a certain total, and having identified each part once with its number, he then sought to add to the total by labelling the same parts more than once. Obviously the higher numbers would make the jumps toward his desired total too big so he started at the lower end of the range and gradually added numbers until he had achieved his desired end.  Why he did this was unclear to me at the time.

In the W wheel there are two number 18’s yet one has been omitted in the M wheel – error or deliberate anomaly? In the W wheel the number 5 is barely visible in the box at the bottom of the sideways-on wheel, yet it has clearly been omitted in the M wheel.  In the W wheel some of the weights at the ends of the pendulums are numbered 11, there are eight of them, yet in the M wheel one of them has been omitted.  Finally in the W wheel there are two number 24’s attached to the padlocks, yet in the M wheel one of them has been reversed to become 42.  How can we explain all these anomalies?

The omission of 5 and 18 in the W wheel is explained by the fact that 5 is the most important number to Bessler because of its importance to the pentagram, and 18 degrees is the basic angle of the pentagram.  Changing the number 24 to 42 can be explained by the omission of 18, because 42 - 24 = 18.  Bessler ensured we got this information by altering the second drawing.  First he removed the 5 and an 11 (5 x 11=55).  Then he assumed that we would compare the two drawings and realize that the second one not only omitted these two numbers, but also when totalled the numbers add up to 633, whereas in the M wheel the total is 649.  But of course 633 from 649 equalled 16 (5 + 11).

In the first drawing the numbers, composed from 59 numbers, add up to 649, which is, interestingly, equal to 59 x 11 (both prime numbers).  In the second drawing the numbers add up to 633, which is 16 short of the 649.  In the second drawing the numbers 5 and one of the 11s has been omitted, which is why the second drawing does not match the 649 of the first drawing.  In both drawings the picture cuts off the left hand end of the drawing and in the process cuts off one of the number 11 weights.  If, in the first drawing, this is added to the 649 of the first drawing it produces the number 660, and because we then have 60 numbers, 660 divided by 60 equals 11, but more interestingly, 660 divided by 12 equals 55!  The same applies to the second drawing but you have to add the extra eleven to make 660.

JC

 10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.

15 comments:

  1. I think you messed up a bit here, John. Both of your illustrations above are of the Merseberg wheel shown in Grundlicher Bericht. You mention the Weissenstein Wheel, but there is no illustration of it.

    You wrote: " Finally in the W wheel there are two number 24’s attached to the padlocks, yet in the M wheel one of them has been reversed to become 42. How can we explain all these anomalies?" Again, this matter of the numbers 24 and 42 only applies to the illustrations of the Merseberg wheel in GB and DT and you did not provide the Merseberg wheel from DT which shows the number 42.

    I, too, have noticed the reversal of the number 24 in the side view of the Merseberg wheel to become a 42 as shown in the end on view of that wheel in DT. The reason is simple. Imagine you wrote the number 24 on a card and then rotated the card through an angle of 180 degrees. The digits would, of course, be upside down, but if you righted the individual digits without again rotating the card, they would read as 42. Bessler is telling us that the end on view of the Merseberg wheel as shown in DT is derived from the side view of it after the axle and drum have rotated clockwise through 180 degrees. This is confirmed by the position of the long pendulum arm attached to the end of the axle around which the rope is wrapped. We see that he is saying that for each half oscillation a wheel's pendulum, the axle and drum rotate through 180 degrees or a half of a rotation. Thus, a full oscillation of each of the pendulums (consisting of two swings from side to side) takes place during one rotation of the axle. I think he just added this embellishment so that he could help the viewer understand why the pendulum arms attached to the end of the axle with the rope wrapped around it were in different positions.

    PS Hope your planned move is going smoothly. Personally, I hate moving...very stressful.

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    1. Sorry Ken and thanks for pointing out my error. The reason I was refraining from posting on the blog, was to try to avoid simple mistakes! Oops again!

      The move has been held up since the buyer backed out! So it's back on the market again and viewers traipsing through the house again. Looks as though we'll be here 'til after Christmas now.

      JC

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    2. I like your explanation for the reversed number 24. I have my own which is different to yours, but I suppose there are as many different explanations as there are people trying to explain it.

      JC

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  2. Yes, but any of those four as added numeralogically renders all six's.

    Add all those together and one has 24; reduce these the same way and we
    are back to our 6 which is a pair of 3's ("as above, so below"), which IS KEY . . .

    "For which the lock's hole does lustily beckon, like a scullery maid's 'n gone without wreckin!"

    And just as does IT'S SHAPE too, for one drawings-worth???

    All throughout drawings of physical things, 3's, 6's and 12's do predominate. (Does not the Apologia Wheel scream-out it's own members' number? As in three or six?)

    Fives seem to not factor-in really, nor will they serve physically to render-out force-wise four-times original lift impetus? Bessler does require this after all, so as to BE HIS OWN configuration?

    (Sorry John, with all due respect.)

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    1. No need for apologies James, always pleased to get a response, negative or positive. I hope to surprise all of you one day with my own interpretation of Bessler clues.

      I would like find a local amateur, but expert, animator to make an animation of my design and have sent an email to my local paper seeking such. I have already received an excellent offer from a respected member of the BWF, but I need someone local so that we can easily cooperate on the project.

      JC

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    2. Animations are nice, but, remember that they are not simulations. An animation does not have to obey the laws of physics while an accurate simulation must. As soon as you finally publish your design, whether as a static image or animation, I will try to make an accurate simulation. If you have something real, I will know it and, shortly thereafter, so will you and everyone else!

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    3. Yes simulations not animations. That extra glass of wine's to blame!

      I appreciate your offer, Ken, but for me the simulation is to test a theory, but I don't need to test my theory, I need to explain how it works hence the need for an animation, which can still be designed to follow the laws of physics.

      Animations can offer a much clearer explanation and be far more realistic than a simululation. Most services I have looked at recently offer a combination of both simulation and animation and that is what I need.

      JC

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    4. I see your point Ken; with animations you can make things seem to work but with simulations they will not work if they contradict mechanical physics.

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    5. Precisely. One can, literally, put anything on a monitor screen and make it move any way he wants. He may think it would work like that if built, but, most likely, it will not. Only when one has an accurate simulation can he be reasonably sure it will work when a physical model is made...and, even, then there is no absolute guarantee. Ultimately, it is really the physical build that counts and, unfortunately, working on them can be an arduous and time consuming process. Simulations help one avoid working on designs that are dead ends and allow one to focus his limited resources of energy and time (not to mention money!) on the ones that show the most promise. For these reasons, I always encourage the new pm chasers out there to get a simple to use simulation program like "Working Model 2D" and practice with it. In a few hours one will then find that he can make about 90% of whatever he dreams up for a possible imbalanced wheel design and see if it has some potential. When I started with this program I was amazed at how wrong I was about the way I thought assemblages of parts would work. That can be a sobering experience. There was another user, a guy named "Jim_Mich" on another site who published a quick startup guide for using WM2D and anyone wanting to use it might want to check that out.

      Update. I've passed model # 1400 and finally settled on a particular design that I am convinced is "it". Again, it was that "ink blot" in the second DT portrait that led me to it. I should know in a few days if I've found it or not. At this point, I remain optimistic. But, I've been "optimistic" before only to be yet again disappointed. Failure after failure while pm chasing is certainly a draining experience. But, I think it also has a positive aspect. In order to continue one's research, his cerebral neurons have to sort of bounce back from being drained of their various neurochemicals. That continuous process of draining and replenishment of the various biochemicals in the neurons I believe actually exercises the cerebral circuitry and, over time, strengthens them. Perhaps this constant "exercise" can help one ward off the various forms of dementia that can beset the average aging person. I often think that, even if one fails to find a working pm design, that bitter disappointment might be compensated for by being able to reach the age of, say, 100 with a strong mind that is free of such things as cognitive impairment, memory loss, mood instability, and personality change. A rather equitable trade when one thinks about it.

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    6. K.B., call me dumb if you like but, where is this "ink blot" to be found on "the second DT portrait" ?

      And . . . seen any neat B&W Sci-Fi flicks recently (or anything else)?

      - James -

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    7. That "ink blot"? Look at the goniometer in the second portrait. That's that big thing with the two pointed arms that are held together by a screw. This gadget is used to measure angles. Note that if you drop a vertical line from Bessler's right eye downward, it precisely intersects the screw that holds the arms of the goniometer together. That's his way of telling the reverse engineer that he needs to study everything that the sweep of the goniometer arms includes very carefully. There are several items that are indicated. First, there is one part of the drafting square that the lower goniometer arm rests on, then there is the carpenter's plumb bob that the 14 inch ruler is carefully balanced on, and, finally, there is a weird piece of paper that has been cut so that it is a sector of a circle. Every line on that piece of paper contains a clue to how the various coordinating ropes in Bessler's secret imbalanced pm wheel were arranged. To the casual observer, it appears to mean nothing. However, to the person who will eventually solve the mystery, every line's significance must be fully understood. I have managed to decode the significance of all of the lines except for one. It is the top most straight line that slants downward slightly as it extends from the left to the right. Note that at its right end it intersects one of the curved lines that runs around the curving perimeter of the piece of paper. Now, here's the problem. When one magnifies that spot where the intersection takes place, he notices that there is a weird triangular shaped "ink blot" near the intersection point. That blot, imo, was not accidental, but rather put there on purpose to tell the reverse engineer that he must not connect one end of the main coordinating rope to where he thinks its supposed to be, but, rather, to another nearby spot. I think I've isolated where that nearby spot is and I'm now testing models that use the rope there.

      I need to emphasize here that every single item in the portraits has some symbolic meaning with regards to the actual design Bessler used. Some items, of course, provide more information than others. Likewise, the words below the portraits contain alphanumeric codes that also provide information about where to attach the ropes, what angles some of the ascending side levers must have when the entire mechanism has been "adjusted", and what spring constants and weight masses must be used. He must have spent an enormous amount of time designing the portraits and they are so cleverly conceived that no one has managed to extract the secret they contain in about three centuries now. I fully intend to be the first! And, if I am successful, everyone out there in pm chasing land will know about it shortly thereafter.

      Speaking of sci-fi flicks, I did see one really great B & W one a few days ago. It was called "The Vampire" which was made in 1957 and I highly recommend it. It involves a small town doctor who is called in to help a sick medical researcher who is experimenting with extracts made from vampire bat blood. The medical researcher dies, but entrusts a vial of pills made from the extract to the doctor. He accidentally takes some when he mixes them up with his migraine pills. Well, you can guess the rest of it...absolutely "classic" '50's horror!

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    8. Superb! - Excellent! - Outstanding!

      You can always be counted upon for analyses and information, when and where requested pertinently, K.B.

      It is way more than I ever could have expected, that you have now provided.

      You ARE a gentleman and a scholar and, without any doubt whatsoever, you tread lightly that Dextral Path headed toward Goodness.

      Regarding the flick "The Vampire," if it is to be found on YouTube, then I will be seeing it this morning. It sounds positively horrible and horrifying, which is just what I need while considering all of your information as newly imparted.

      Many thanks for going to all the trouble.

      - James -

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