A SIDEWAYS GLANCE AT Euler's Disc
~~~~~~~~~~~~~
Thank you for taking the time to visit this `apparently` absurd page.......I hope nethertheless to present a logical arguement.
Nothing off the wall, nothing incomprehensable & hopefully, nothing you'll judge
a five or so minute, waste of your time.
A bit of geometry, nothing more....
To construct this device you will require:
Three equal spheres of some weight & of any diameter .
One larger, hollow, sphere, its diameter dependant upon the size of your chosen balls.
One thin/stiff disc.
Two short lengths of axle.....plus a third.
Cut one quarter off of the hollow sphere from one side, one quarter from the other
& discard the middle section.
Left with two bowls then attach an axle to each.... as per a stemmed wine glass or such.
Fit to an axle stand/s.... Connect the third axle through the disc,
bring the two bowls together with the three balls & disc between.
That's it...kids sorted for Christmas !!
This device is created as follows.
Based as it is on Sacred Geometry, then it goes without saying that a good degree
of accuracy is required in building it.
Draw a Vesica Piscis with two circles of the same diameter as the three balls being used.
From this derive the following geometry.
Your required disc is outlined in bold black.
.
~~~~~~~~~~~~~
Thank you for taking the time to visit this `apparently` absurd page.......I hope nethertheless to present a logical arguement.
Nothing off the wall, nothing incomprehensable & hopefully, nothing you'll judge
a five or so minute, waste of your time.
A bit of geometry, nothing more....
To construct this device you will require:
Three equal spheres of some weight & of any diameter .
One larger, hollow, sphere, its diameter dependant upon the size of your chosen balls.
One thin/stiff disc.
Two short lengths of axle.....plus a third.
Cut one quarter off of the hollow sphere from one side, one quarter from the other
& discard the middle section.
Left with two bowls then attach an axle to each.... as per a stemmed wine glass or such.
Fit to an axle stand/s.... Connect the third axle through the disc,
bring the two bowls together with the three balls & disc between.
That's it...kids sorted for Christmas !!
This device is created as follows.
Based as it is on Sacred Geometry, then it goes without saying that a good degree
of accuracy is required in building it.
Draw a Vesica Piscis with two circles of the same diameter as the three balls being used.
From this derive the following geometry.
Your required disc is outlined in bold black.
.
This same derivation also gives us a 2D template for the Cairo Flower Bowl.
Please search this/Tri-Lobed Bowl/Sabu Bowl for more details should you not be familiar with
this most perplexing of all `out of place` artifacts.
this most perplexing of all `out of place` artifacts.
Extended out by the addition of more circles layered around it gives us Bessler's engraving.
Again, please search Johann Bessler/Bessler's wheel for more detail
regarding this man & his apparent achievement/s.
Again, please search Johann Bessler/Bessler's wheel for more detail
regarding this man & his apparent achievement/s.
This engraving has a quote beneath which, thanks to the observant Mr John Collins in his book `Perpetual Motion....An ancient mystery solved?`
equates to 1717.
This appears to relate directly to the true Vesica.
equates to 1717.
This appears to relate directly to the true Vesica.
Refering to the geometry derived above:
The outer circle in red measures seven times greater in diameter than the length A/B,
the radius of each of your chosen three balls.
Use this outer red circle as the diameter for your two bowls.
I used three pool balls of 38mm diameter & a 16cm perspex ball that came as two hemispere.
Easily found on eBay UK at least, I cut each hemispere in half again, leaving me with two bowls,
each with an internal diameter at the rim of 133mm...perfect!
So.....
The 3D interpretation of the Vesica Piscis involves the intersecting of two spheres
as opposed to two circles & the intersection of two spheres results, in concept, in a quarter of one sphere joining with that of the other, to form a classic flying saucer shape.
The line C/D shown above represents its diameter & the line A/B its depth...
the distance between the centre's of the two, quarter spheres.
It's well known that the lines A/B & C/D of a Vesica, expressed as a ratio, equals sq/root 3.
Thus the diameter/depth of this flying saucer, this true 3D Vesica, is also set at a ratio of root 3.
The saucers DEPTH, line A/B, multiplied by seven, results in the DIAMETER of the red circle around,
This itself is but another Vesica but being seen head on this time...the Vesica you're gonna cut from both ends of your hollow ball in this case.
Hopefully you get the picture?.
That by applying geometry to the Vesica Piscis, in the simple manner that both the Cairo Bowl & Bessler appear to suggest, then the depth of one Vesica, multiplied by 7, gives the diameter of the next...1:7 1:7....
on & on/in & out....Vesica sideways on, within Vesica sideways on, etc, etc,....forever..
We measure from an assumed point....
Maybe others once saw this as too absurd an assumption upon which to base something as fundamental as measurement?
......it being an apparent fact that no point can possibly exist in a 3D reality.
The above suggests an alternative assumption and the trick here, for want of a better term, is to create a movement around a Vesica, within the larger Vesica that sorrounds it.
Having created the all important Vesica based on your three balls and the disc ,
now place the disc on an axle, its length equal to the depth (A/B) of the two bowls.
Assemble the device & grab the main axle.
Looking along the axle line........closest to you is a bowl, then a disc & further beyond another bowl.
See the disc in the Y position, with a cut out section at 6 o'clock.
Above the axle line, in cut out's at approx 2/10 o'clock sit two balls.
Both have fallen in towards the centre & in doing so they have both moved out of the disc/cut out.
One ball sits in front of the disc as you look, the other sits behind.
The third ball, in the six o'clock position, has fallen to the rim to sit centrally in the disc,
ready to fall next into the centre, either front/rear of the disc.
If we choose the two balls above to be front of disc at 2 o'clock & back at 10,
then the ball at 6 o'clock will end up forward of the disc turning clockwise
or back of the disc, anti-clockwise.
Hence, regardless of turn, the top two balls are always opposing
& that opposition toggles front/back as the thing turns......
the 2/10 o'clock positions switch from front to back to front etc.
Likewise the lower ball toggles front/back then back/front in its move through the disc.
The balls are always in touch with the bowls & the disc.
The balls can only reach their required position at the centre by easing/tilting the disc aside.
Thus, using the above example. (balls front of disc at 2 o'clock & back at 10)
.....Then the disc is twisted, as you look, back at 2 o'clock & forward at 10.
This twist is pivoted around the ball at 6 o'clock.
This is but a snapshot of course.
In motion,with the top two balls toggling position front/back & a falling third being
enticed/twisted correctly into one then the other, then you can hopefully envisage that this disc is
attached to no axle but its buckling/spiralling own.
The axle through the disc is performing a circular motion around the true axle, at the point where it touches the two bowls. This disc axle might be connected to the true axle by `cranks`....each equal to one half of length A/B.
Perhaps the disc axle needs to remain disconnected from the main axle...I kinda think so, it's more inventive.
The Sacred Geometry here leads to a wobble of the disc, around the cental line, that mirrors the tropics of Cancer & Capricorn around the Earth's Equator.....& the cranking circle mirrors that of the Earth's precession around its axle of rotation....no surprise?
The disc performs as per a Euler's Disk, with Omega thus evident me thinks.
Stationary then gravity dictates that the device will not turn, certainly not beyond the inverted Y position.
But this device will not move in any position....until it is moved from that position.
The balls are being forced out, around the bowls....arranged buckled around an axle.
The energy contained in that force lies within the buckled three balls.
The three energised balls attempt to sit centrally/straight around the axle, at the central position/out from the axle.. both left/right of the central position/in ....& all stops between, in their frustrated pacing back/forth in order to resolve the issue..
This energy remains trapped in the Vesica...regardless of the angle of its main axle
& it can be exercised likewise .
The Centre Position.
The Vesica Piscis, according to some, was seen symbolic of the 1st Day of Creation/Book of Genesis by the Ancients.
Here is their 2nd Day.
Here perhaps lies the answer, in essence.
This is a snapshot of the position reached by the three balls, head on, one after another, along the axle line.
This is only made possible by way of the balls alternating back & forth, the timing involved & the pushing of the disc aside.
The three balls within `drive` the crank by way of the disc.
It could be said perhaps, that the balls derive their energy from some `true point`.... that point achieved by the above positioning along the true axle line.
In essence the disc, by way of the Sacred Geometry applied, is forcing the three balls into moving
about the smaller Vesica, contained within the larger Vesica that contains those three balls.
If you're able to imagine the above device in motion, then you'll imagine balls spiralling out from/along an axle & then further along/back in.....back & forth.
Seen into the axle line then refer to current Black Hole research which suggests a dance between two Black Holes, a Cosmic Waltz.
See..... http://www.youtube.com/watch?v=bOtuJ3nM_qI .....for one.
From 23.00 minutes onwards you get to see this dance, the very same dance as performed in/by an atom, apparently.
It's the very same dance as that which I'm attempting to describe here....
the Dance that perpetuates the above device.
As ever though, this Cosmic Dance is being imagined/assessed in 2D,
despite the Cosmos appearing deceptively 3D.
As ever we work from our assumed point rather than simply imagining that it has another view....
& that seen from this view, these circles are moving/disappearing, in/out of the monitor.....
to a combined depth, which, expressed as a ratio to the diameter required around them, equals root 3.
A spiralling waltz between the centre `point` of one sphere & the centre `point` of its interlocked mate.
Movement through the Vesica they create.
As I've described matters, this movement is back & forth along an axle, from in at the centre,
along the axle & out, along further to back in.
This however is merely my option from two possible choices.....
in essence, your two bowls can be joined the reverse way around.
This motion can be extended along the axle ....in/out/in/out/in etc.
It can just as well be expressed....out/in/out....etc.
The Cairo Flower Bowl appears to favour this 2nd option.
This device/concept of course unites gravity & magnetism....possibly all forms of known energy?
North/South pole bowls, magnetic material for balls, stand well back & watch it dissolve I suspect...unless, like the Cairo Bowl, it's made from stone?
Needless to say, the Cairo Bowl is far more intricate in design than the
two smooth hollow bowls that I have suggested.
Their design suggests that the energy, possibly magnetic, is transfered to the two bowls
rather than cranked to any axle.
When understood in Principle then the truth of the Vesica can be derived/designed
in many a way for many a purpose I imagine....
The Cairo Bowl is likely to form part of some device well beyond the simple `in Principle` device I've outlined.
It's all currently just an absurd notion in itself of course.....but should this, or very similar, prove itself the motion then I would feel duty bound to point out Glastonbury's claim to fame here.
However much it denies me my logic.......however, even more absurd.......
"Here, on the mystical Isle of Avalon, there beneath Mount Zion, fountain of all knowledge & creation, lay the Holy Chalice.
Veiled ahead the well of a spring, to at once in time reveal its Divine Nature & herald forth the Holy Grail"
That Well has this at its head of course:
This is a snapshot of the position reached by the three balls, head on, one after another, along the axle line.
This is only made possible by way of the balls alternating back & forth, the timing involved & the pushing of the disc aside.
The three balls within `drive` the crank by way of the disc.
It could be said perhaps, that the balls derive their energy from some `true point`.... that point achieved by the above positioning along the true axle line.
In essence the disc, by way of the Sacred Geometry applied, is forcing the three balls into moving
about the smaller Vesica, contained within the larger Vesica that contains those three balls.
If you're able to imagine the above device in motion, then you'll imagine balls spiralling out from/along an axle & then further along/back in.....back & forth.
Seen into the axle line then refer to current Black Hole research which suggests a dance between two Black Holes, a Cosmic Waltz.
See..... http://www.youtube.com/watch?v=bOtuJ3nM_qI .....for one.
From 23.00 minutes onwards you get to see this dance, the very same dance as performed in/by an atom, apparently.
It's the very same dance as that which I'm attempting to describe here....
the Dance that perpetuates the above device.
As ever though, this Cosmic Dance is being imagined/assessed in 2D,
despite the Cosmos appearing deceptively 3D.
As ever we work from our assumed point rather than simply imagining that it has another view....
& that seen from this view, these circles are moving/disappearing, in/out of the monitor.....
to a combined depth, which, expressed as a ratio to the diameter required around them, equals root 3.
A spiralling waltz between the centre `point` of one sphere & the centre `point` of its interlocked mate.
Movement through the Vesica they create.
As I've described matters, this movement is back & forth along an axle, from in at the centre,
along the axle & out, along further to back in.
This however is merely my option from two possible choices.....
in essence, your two bowls can be joined the reverse way around.
This motion can be extended along the axle ....in/out/in/out/in etc.
It can just as well be expressed....out/in/out....etc.
The Cairo Flower Bowl appears to favour this 2nd option.
This device/concept of course unites gravity & magnetism....possibly all forms of known energy?
North/South pole bowls, magnetic material for balls, stand well back & watch it dissolve I suspect...unless, like the Cairo Bowl, it's made from stone?
Needless to say, the Cairo Bowl is far more intricate in design than the
two smooth hollow bowls that I have suggested.
Their design suggests that the energy, possibly magnetic, is transfered to the two bowls
rather than cranked to any axle.
When understood in Principle then the truth of the Vesica can be derived/designed
in many a way for many a purpose I imagine....
The Cairo Bowl is likely to form part of some device well beyond the simple `in Principle` device I've outlined.
It's all currently just an absurd notion in itself of course.....but should this, or very similar, prove itself the motion then I would feel duty bound to point out Glastonbury's claim to fame here.
However much it denies me my logic.......however, even more absurd.......
"Here, on the mystical Isle of Avalon, there beneath Mount Zion, fountain of all knowledge & creation, lay the Holy Chalice.
Veiled ahead the well of a spring, to at once in time reveal its Divine Nature & herald forth the Holy Grail"
That Well has this at its head of course:
God Bless
GillSimo/Glastonbury
2012
Please consider...
That everything we think we might know can never be anything more than the result of our ignorance...
.That in absolute truth, we can only ever `know` nothing.
Thank you for your time.
Footnote:
Having astounded myself in accurately cutting a Vesica from two hemisperes
I'm currently frustrated at cutting the disc.
Plastic isn't firm enough & I'm as useless at hacksawing an ali disc as I am at accurately
measuring out the required shape in the first place.
Still....I can confirm at least, that a ball will indeed move within in/around a bowl exactly as described.
However....place two halves of a Vesica together, with a ball inserted & you will see that the ball isn't able to drop down, all the way to the outer rim of that Vesica.
It gets pinched between the two bowls before that point & in order that a ball can do this & thus be able to slip through the disc, then a section of each bowl has to be removed around its rim....three sections per bowl.
Thus the balls must protrude through the two bowls when they are out from the centre & centrally in the disc.
This leads me to suspect that two smooth bowls might not be suitable, that the balls must in some fashion move/connect, in/out of the disc ...& in/out of the bowls as well to achieve our aim.
That in turn suggests that my bowls must be as equally innovative as the Cairo Bowl....
but in reverse ...kinda thing.
The three area's that need to be removed from each bowl are eye shaped....they corrispond exactly to the eye shape that is formed at the rim of the Cairo Bowl, by the overturned petals.
Cutting out these eye shapes & possibly needing to extend somehow inward, towards the centre of each bowl, such that a ball moves as smothly & progressively in/out of a bowl as it does in/out of the disc.....that's a tall order, a bit of geometry as unique & inventive as the CairoBowl for sure.
Furthermore....there is nothing set in stone here, I'm still of the view that I'm only seeing a greater part of the true action & not the complete picture.
For instance...In order that the balls always remain in contact with the disc cut out's, especially when in towards the centre, then this device really would have to be engineered to Nasa levels of accuracy. It would be far better to design the disc with guides along/around each cut out, on both sides.
Although I couldn't expect others to see the implications of this requirement it is self evident upon investigation that this would turn the required disc into something akin to a double sided Cairo Bowl.
This in turn suggests that the balls may very well move through the disc, in towards the centre/out of the disc....then through the centre & back out/into the disc via a different cut out.
It is beyond the imagination to `see` this action of all three balls juggling in, out, through, around, back & forth.
A simple enough action/movement once observed but next to impossible to imagine...
as one should expect in this instance.
Realising that the Vesica appears to provide a geometry for a very unique movement is a doddle, one only has to create the ball/disc/bowl arrangement outlined above & play around to see the obviousness of this.
Designing the geometry of the disc & bowls to accommodate & capture the movement requires much more careful consideration, trial/error & clever fabrication.
One look at the Cairo Bowl is enough to confirm this point & explain why
this simple truth sits hidden in plain sight.
GillSimo/Glastonbury
2012
Please consider...
That everything we think we might know can never be anything more than the result of our ignorance...
.That in absolute truth, we can only ever `know` nothing.
Thank you for your time.
Footnote:
Having astounded myself in accurately cutting a Vesica from two hemisperes
I'm currently frustrated at cutting the disc.
Plastic isn't firm enough & I'm as useless at hacksawing an ali disc as I am at accurately
measuring out the required shape in the first place.
Still....I can confirm at least, that a ball will indeed move within in/around a bowl exactly as described.
However....place two halves of a Vesica together, with a ball inserted & you will see that the ball isn't able to drop down, all the way to the outer rim of that Vesica.
It gets pinched between the two bowls before that point & in order that a ball can do this & thus be able to slip through the disc, then a section of each bowl has to be removed around its rim....three sections per bowl.
Thus the balls must protrude through the two bowls when they are out from the centre & centrally in the disc.
This leads me to suspect that two smooth bowls might not be suitable, that the balls must in some fashion move/connect, in/out of the disc ...& in/out of the bowls as well to achieve our aim.
That in turn suggests that my bowls must be as equally innovative as the Cairo Bowl....
but in reverse ...kinda thing.
The three area's that need to be removed from each bowl are eye shaped....they corrispond exactly to the eye shape that is formed at the rim of the Cairo Bowl, by the overturned petals.
Cutting out these eye shapes & possibly needing to extend somehow inward, towards the centre of each bowl, such that a ball moves as smothly & progressively in/out of a bowl as it does in/out of the disc.....that's a tall order, a bit of geometry as unique & inventive as the CairoBowl for sure.
Furthermore....there is nothing set in stone here, I'm still of the view that I'm only seeing a greater part of the true action & not the complete picture.
For instance...In order that the balls always remain in contact with the disc cut out's, especially when in towards the centre, then this device really would have to be engineered to Nasa levels of accuracy. It would be far better to design the disc with guides along/around each cut out, on both sides.
Although I couldn't expect others to see the implications of this requirement it is self evident upon investigation that this would turn the required disc into something akin to a double sided Cairo Bowl.
This in turn suggests that the balls may very well move through the disc, in towards the centre/out of the disc....then through the centre & back out/into the disc via a different cut out.
It is beyond the imagination to `see` this action of all three balls juggling in, out, through, around, back & forth.
A simple enough action/movement once observed but next to impossible to imagine...
as one should expect in this instance.
Realising that the Vesica appears to provide a geometry for a very unique movement is a doddle, one only has to create the ball/disc/bowl arrangement outlined above & play around to see the obviousness of this.
Designing the geometry of the disc & bowls to accommodate & capture the movement requires much more careful consideration, trial/error & clever fabrication.
One look at the Cairo Bowl is enough to confirm this point & explain why
this simple truth sits hidden in plain sight.