Did Bessler simply square the circle..perhaps?!!

[Gill Simo]

'Tis very hard to openly suggest this...like most I've long since learnt the pain of making bold claims without physical proof...but I suspect, with some fear I must confess, that what follows could very likely be the long sought after Principle of/for Perpetual Motion that Bessler referred to...

And yeah, should that be so then indeed, it's stupidly simple...in a way. Somehow blindingly obvious, whilst also clearly oh so very illusive.
-------------------
Please consider the Euler's Disc...its motion.

And with this principle of motion in mind ponder please on how that motion could possibly be facilitated? ....very illusive yet entirely possible perhaps?

Like this I think?

FIG 2...a disc is viewed side on, tilting over. In turning this disc will appear perpendicular to the axle line after 90 degree of turn...it will appear to tilt over in the reverse after a further 90 degree of turn...back to perpendicular after another 90....back to its starting tilt after the final 90.

Thus, in turning, the disc will appear to swing back/forth...left/right. The disc will appear to do this, when viewed side-on anywhere around the circumference.

I'm guessing there's a correct term for this disc's motion...gyrating perhaps?
Whatever...I strongly suspect that this motion...about a fixed POINT (not AXLE) in the gravitational field perpetuates.

Here's how it might be achieved...by means of both the Sabu Tri-Lobed Disc & Bessler's engraving.

The Sabu Disc....please refer to FIG 1.

To the left we have a Sabu Disc with four correctly proportioned spheres resting on it.

Starting at the top we have a sphere resting on a petal...it is closest to your nose as you view therefore.
At the bottom we have a sphere resting in a shoe...furthest from your nose.

To the left we have a sphere that's positioned between the top/bottom spheres...it is tucked under the top sphere & over the bottom. In terms of your nose this sphere sits further back than the top sphere but not as far back as the bottom sphere...it is between the two.
The sphere to the right likewise...under the top, over the bottom...same distance from your nose as the sphere to the left.

So..if the four spheres were a solid, round, disc then this disc would, as viewed, be slanting towards you at the top, away from you at the bottom, in the vertical plane & parallel across your eyes in the horizontal.

A second Sabu Disc is placed on top....sorry but I can't possibly draw the result. I can only reference that other disc to the right in FIG 1 & leave it to your imagination...suffice to say that the top sphere, sat on its petal, is now also sat in a shoe of the second disc placed over...the bottom sphere likewise but in reverse....and the two spheres between, either side, are held...errr?

Let's just say, held in a very special & uniquely `balanced` way between four petals, two from each disc.
In truth, the whole geometry at play is very special & unique...quite Divine!

Now...I can't possibly discern...but the two disc are either turning against each other & this `solid disc` that currently slants towards you will begin to `gyrate`....the four spheres will each flow back & forth, towards/away from your nose to facilitate this gyrating motion around.
And viewed anywhere around, from the side, a swinging/wagging, as already said, from side to side.

Or...the two discs oscillate against each other to facilitate the gyration.

Also, In addition to this....(see later)

Bessler's Engraving...

I kinda hate to say it but should this all be correct then the fella simply employed a gyrating square! (FIG 3)
A somewhat different design/geometry to his discs to accommodate a square rather than a circle but going back to FIG 1 you would have a square, set diamond shape, as you view. The top tip of the square is nearest your nose, the bottom tip furthest from your nose...& the two tips, left/right, equal distance from your nose, behind the top, in front of the bottom.

Lengthy consideration, that I need not bore you all the more with, suggests to me that this square would be required to collapse/flop...all four points able to collapse/expand from their 90 degrees...as per Toys Page C/D perhaps?

This is also the case with the four spheres above...viewed face on then this `square` of four must collapse/expand an amount...as two spheres appear to move closer so the other two appear to move further apart...& visa versa.

In truth, then no amount of thought will suffice...imagining the precise mechanism, via geometry, that generates this motion by way of two wheels turning against each other in either suggested manner is clearly unimaginable...it's a see it to ever be able to believe/understand it kinda thing for sure.

However...it's not too difficult to imagine it potentially likely to be true, we can `glimpse` at the geometry involved well enough to be convinced of the possibility.....two unique `wheels` that by way of their geometric design facilitate a Euler's Disc in motion, gyrating about a fixed point on a fixed axle in the gravitational field.

Or, as Bessler perhaps viewed it...the true solution to the squaring of a circle?!!

[agor95]

...
Or, as Bessler perhaps viewed it...the true solution to the squaring of a circle?!!

Hello Gill

I have given your geometry some thought over the years.

That including the tetrahedron interacting with a Sabu Disk.

I have considered the Sabu Disk as a response by stone craftsmen to the arrival of metal worked artefacts.

This change of materials is also seen in bronze axe heads made too follow stone axe head designs.

A bronze axe head can be made to have a thinner cutting angle.
It appears that was too radical to the stone axe using community of the time.

The Sabu Disk most likely held oil with reeds or flax linen placed around the edge; to act as wicks.
So it is in effect a standing lamp.

Connecting the Sabu Disk to Bessler's inspiration requires some evidence that Bessler knew the existence of the Sabu Disk. The date when the Disk was found is after Bessler's death.

Remember it was found 100 years ago.

Saying that a geometric principle exists forever and only awaits a person too become aware of it's existence.

I have had an understanding of your tetrahedron interaction to a Sabu Disk.
It's hard too explain or visualise. In fact that is why I have spent so must time learning how too create visual models.

The best I can say is a tetrahedron on top of a Sabu Disk. The tetrahedron follows the contours of the disk.

However the sphere as they drop into a hollow flex out pulling the centre of gravity from the centre
of rotation.

Saying rotation here means in all three dimensions of cause.

As the flexed sphere moves on the upward contour the stored energy is returned too cause a pumping of the rotation.

There are only two spheres interacting at any time. However they are swapped with the other two as the
tetrahedron tumbles.

Note.

As I have illustrated this year the tetrahedron can be seen as four points of a cube that has eight corners. So another tetrahedron can be use with the spare four corners. The main observation is the diagonal links that connect the four points of the tetrahedron when mapped onto a cube wire frame.

They make up four triangles.

So we have a half a cube [square with depth] having a three point footprint.
That then can interact with a third symmetry form below.

P.S. The conjecture is the deformation by flexing and stretching could be a possible source of energy.

Regards

[eccentrically1]

Here is a paper showing the sabu disc was for mixing beer mash.

https://www.scirp.org/journal/paperinfo ... rid=114435

It would be interesting to know how they discovered this was a good shape to craft it in, if that's really what it was. Perhaps by accident; maybe trial and error; or an epiphany from observation of natural motion.

[agor95]

Here is a paper showing the sabu disc was for mixing beer mash.

https://www.scirp.org/journal/paperinfo ... rid=114435

It would be interesting to know how they discovered this was a good shape to craft it in, if that's really what it was. Perhaps by accident; maybe trial and error; or an epiphany from observation of natural motion.

All though I would not criticise the creation of a more efficient method of producing beer. Even if it appears a perpetual one. It is noted the finding of the device was in 1936. Therefore again after Bessler's demise.

I feel obliged too add a little on the subject regarding the tumbling of a tetrahedron.
Seriously for not do so would mean I have not got a leg too stand on with regards this thread.

Yes I would be legless.

I am thinking a rotating object where the rate of rotation follows a three phase sine wave should do the trick. If this was employed then the tetrahedron using a sine wave rate control of the three axis should produce the effect we are looking for. There is only one way too find out and that is to build it.

Cheers

[Gill Simo]

Thank you agor95 for your input re the tetrahedron.
My newer thread on the matter might appear to suggest that I've abandoned the tetrahedron/Sabu disc concept but that's not the case at all...I'm merely attempting to keep things as simple/understandable as possible in that newer thread....for the moment.

Can't grasp your reference to Bassler not having knowledge of the Sabu disc...whilst entirely correct of course I've never thought to assume otherwise...Bessler presumably got `there` by his own means alone?

This leads nicely onto the paper re beer mashing....it seems forever the case that we completely ignore the elephant in the room when coming up with all these proposed uses of the Sabu disc.
That being that the disc is considered to be at least 5,100 old...at least.
By current understanding that would make it at least 1,400 years prior to the invention of the wheel.
The invention of the wheel, more precisely, was the revelation/understanding of placing an axle through the centre of a disc...and any theory suggesting that the Sabu disc, complete with central hole, sat there for 1,400 years before some bright spark had the revelation/understanding that this rope maker, oil lamp, beer masher etc could be better employed as a wheel is, of course, utterly absurd.

[agor95]

The invention of the wheel, more precisely, was the revelation/understanding of placing an axle through the centre of a disc...and any theory suggesting that the Sabu disc, complete with central hole, sat there for 1,400 years before some bright spark had the revelation/understanding that this rope maker, oil lamp, beer masher etc could be better employed as a wheel is, of course, utterly absurd.

I think we need to leave the date and time open. The first log rolled down a slope is a wheel.
That could have been done by anyone in the past with an axe or a hungry beaver.

If one tumbles a tetrahedron and trace the vertex path then one chooses the motion so the trace tends towards the Sabu disc contours.

Regards

[Gill Simo]

Not that it's of any great importance agor but with respect...the inventive step that gave rise to the wheel was, as already mentioned, the notion of placing an axle through the centre of that log rolling down the hill, in no way the rolling log in/of itself.
I must continue to insist therefore that the very idea that someone had that inventive step to then conceive of the Sabu disc...to then only conceive of a beer musher or the like, is utter nonsense.
This old UK tv commercial makes the point perfectly

https://www.youtube.com/watch?v=xmpM2iKMea0

[agor95]

You are correct the Sabu disc is a work of art and it's original function is not known.

Therefore it can be many things that the material it is made of will allow.

Regards

[Gill Simo]

Here is the perfect example of the motion that I'm suggesting is induced into four spheres held between two Sabu discs turning in opposition.

https://www.youtube.com/watch?v=e7kb6ZuDPmw

[JUBAT]

Video unavailable and private.

[Gill Simo]

Oooops.....how about

https://youtu.be/e7kb6ZuDPmw

In addition...the following Bessler comments may add weight to my proposal?

"Children play with my pm principle in the streets" ... plus his notated image of a spinning top on his toys page which translates as "Children's game in which there is something extraordinary for anyone who knows how to apply the game in a different way".

[Trev]

Still private:

Private video
Sign in if you've been granted access to this video

[Gill Simo]

Deary me...sorry.
3rd time lucky I hope!

https://youtu.be/e7kb6ZuDPmw

[agor95]

Hello Gill

The YT video is operational

I found this yesterday while looking for matrix rotation.
https://eater.net/quaternions/video/stereo3d

The point that jumped out to me was the image below.

P.S. Your video arrived here at the right time. For it's a subject that involves current developments.

Regards