Thursday, 8 March 2018

The Möbius Strip and Bessler’s Wheel.

I recently posted a little piece about my search for potential clues to Besser’s wheel, among ancient symbols, in particular the yin yang symbol.  Another of my favourites, not so old but intriguing nevertheless, is the sign for infinity in mathematics, the lemniscate. It has the appearance of a sideways figure eight, and although there are variations they are all similar.


This was introduced by John Wallis in 1655, and although he did not explain his choice of this symbol, it has been conjectured to be a variant form of a Roman numeral for 1,000 (originally CIƆ, also), which was sometimes used to mean "many", or of the Greek letter (omega), the last letter in the Greek alphabet, can also mean, infinity.






Lastly and most fascinating of all is the Möbius strap or band.  A simple device to make; take a long rectangle of paper or just a longish strip,nd join one end to the other, but put a half twist in before connecting two ends. I don’t want to bore you with all the quirks attached to this remarkably simple design but you can find plenty of information on the internet.

The interesting point for me is the apparent similarities to be found between the infinity symbol and the Möbius band. Admittedly the lemniscate doeasn't usually have a half twist in the path of the strip but I have seen some drawn like that and I wondered of the artist got confused or was it just an additional twist!

This brings me to the Toys page MT138.139.140 and 141.

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Note the lower pair of figures labelled 'D'.  are shown in spiral or twisted design whereas the upper pair labelled  'C', are in straight stripes.  I've always wondered if that is meant to convey that the lower pair have a half twist in their relative positions somewhat like the infinity symbol of even the Möbius band?

I did try to manipulate my drawing of the figures 'D' to demonstrate what I meant but it ended up just confusing, so if anyone wants to try their hand at it I'll gladly post their pic here if its better than mine! So the right half of the ‘D’ figures needs turning up side down and flipped horizontally to complete the spiral move. To me the spiral is suggesting a upside down move as well as a horizontal flip.

This is not necessarily the right explanation but it needs some kind of examination and it has the typical look of a Bessler clue.

I believe I have discussed some of this many many years ago but I can't remember where or when, so apologies if we have been here before, but I definitely didn't associate the Möbius strip and the infinity symbol together along with the figures 'D' in the Toys page at that earlier time.

There may be some way of introducing Möbius-like mechanical configurations into Bessler's wheel?

JC

27 comments:

  1. What you require for the blog is a good header image John. That would increase the visual quality of the blog dramatically.

    ReplyDelete
    Replies
    1. Working on it yellow. :-)

      JC

      Delete
    2. Wonderful! You may want to try Canva. It has wonderful templates for blog banners.

      Delete
    3. Like this: https://www.canva.com/templates/web-banners/MACFUdU7R0c-classic-industrial-blog-title/
      This one looks like the cover of your book; https://www.canva.com/templates/web-banners/MAA_AUb5xbk-exhibition/?query=blog%20header

      https://www.canva.com/templates/web-banners/MABAWI2yhxs-art-museums-to-visit-europe/?query=blog%20header

      There are dozens of other templates. I think they are also free.

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  2. John,
    I remember speculating about the infinity sign the last time you mentioned it.
    I suggested that the mechanism could be a cylinder, weighted on one side with a spiral groove in it, and a ball running back and forth in the slot.
    Now I'm thinking, it might be the reverse, the ball rolling downward may turn the cylinder, thus lifting the weight.

    ReplyDelete
  3. the twisted figures 'clue' simply points to springs .... ?
    Jon

    ReplyDelete
  4. Now, I've been looking at the toys page, and decided to take it at face value.
    If A & B are a chain, seen from two different perspectives, and C&D are weights like a sledge hammer standing on the ends of their handles, also similar in appearance to the spinning top.
    The mechanism could work like this.
    Each spoke of the wheel consists of two parallel planks, fixed to the outer edges of the hub and the rim, this leaves a gap between the boards where the mechanism fits.
    The mechanism is two, on end hammerlike weights, with their pivots at the non-weight end, positioned one above the other. At the 12 O'clock position, the top weight will be prevented from falling to the left by a stop, and the bottom weight will be prevented from falling to the right, also by a stop.
    The chain is wound between them, like a reversed "S" (Z).
    At just after 12 O'clock, the outer weight falls to the right, pulling most of the chain up, making it top heavy.
    At 6 O'clock, the inner weight falls back, moving the weight of the chain towards the hub.
    Where the lazy tongs come in, maybe, instead of the weights acting on a chain, they push on the tong's crossbars.

    ReplyDelete
  5. I really don't believe there is a code, but there are definitely clues here and there...

    You may find interesting that in both Merseburg and Kassel wheel figures, the component with number 8 (which looks like the infinity symbol) is "the pendulum"...

    ReplyDelete
  6. I too strongly feel that there is no code...and, yes...clues can be found in many places...also, these clues are quite adequate...it is just enough to keep one on the right track...

    ReplyDelete
    Replies
    1. You raise an interesting point, yellow, when is a clue a code, and a code a clue? I tend to call these various pieces of information, codes, but there are also other pieces of information which are best described as clues. The difference for me lies in the fact that the clues are fairly obviously clues, written in text, whereas the pieces of code may or may not appear obvious and are disguised so that their meaning is not clear and they can be both textual and graphic.

      JC

      Delete
    2. Bessler Wheel can be easily solved that is if we can only think of it within the confines of simplicity... Bessler was a genuine man and there shouldn't be any doubt about it...he left some valuable clues and also the descriptions by witnesses too are very valuable...its all about how the lever-weight system is designed and arranged...the total number of this mechanism is crucial for the wheel to self start...it is also important to keep in mind that there is only one design which can make the wheel to rotate and till this design is incorporated success can be evading...

      Delete
    3. I agree with you that the lever-weight system is the unique feature that make PM possible, but I think that uniqueness design lies within the prime mover. Any of his OB wheel designs like MT9 will self start. What is needed is the prime mover to shift the weights to the OB position.

      Delete
    4. The lever-weight system itself is the prime mover...such is the design...

      Delete
  7. You know the answer lies in the way you look at things truly you have to think in a different way Bessler said it lateral thinking and intuition.
    Funny thing I did a search on the internet and the term lateral thinking was attributed in 1967 to a man called dr. Edward de Bono I wonder if he ever read Bessler's work!!! I guess everyone steals from everyone else.

    ReplyDelete
  8. Wow ... love the new color theme ...

    ReplyDelete
    Replies
    1. Thanks anon. I may play with it a bit more.

      JC

      Delete
    2. I would use a white template John. It would help figures blend to the blog. Since the subject has historical significance and you are an author may be you should use a serif font. I dig the header BTW.

      Delete
    3. Boo hoo. I don't like the white page. It looks old school, cold, and unsophisticated. Jazz it up.

      Delete
    4. Grey, really, how about the off white (cream) color in the background swirls???

      Delete
  9. I think the Mobius Strip, the Yin and Yang (Taichi symbol), and the Infinity symbol, when drawn similarly, are indicative of the weight movement within the Bessler Wheel - not the entire symbol, but half of the symbol, resembling something like an S shape.

    ReplyDelete
    Replies
    1. If you look at MT26, the 'C' weights at the end of the 'D' rods move along an arc (from rim to axle) producing something of a Yin and Yang (S) shape.

      Delete
  10. John, can you share more of the wisdom from the clues?

    ReplyDelete
  11. John,

    Have not been around since your 'new look' appeared here. I must say it really is swell!

    Since 'the number' of the year seems to be "5", what if Bessler emphasized it here-and there so as to mislead searchers away from the one actual?

    Further, has any 5 combination of whatevers yet resulted in any anomalous results, that might be encouraging as to correctness of choice?

    Just another "naughty puppy" thought.

    Yet another year of life churns it's way to conclusion . . .

    James

    ReplyDelete
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