Hello people....Happy New Year!.
Was I dreaming a few weeks back...or did I note somewhere that JC is dabbling with the Vesica?
Cool...especially as I also detect more `depth` in general, in questions posed and the replies offered here these days.
I'm kinda hoping that 2011 will see many more folk investigating that which is quite possibly under our noses but so difficult to see...none so blind etc.
IMHO the odds on the Vesica being at the heart of any solution are so short that it simply must be, so say's my logic....not my lunacy.
I've spent too much time dwelling on the thing, that's for sure.......but something odd continues to baffle me.
Perhaps I'm simply not looking at it correctly, perhaps I'm crap at web research or something?
Here's one of many similar quotes, translated from some Holy Book or other;
In the beginning the universal mind of God created from a total void or nothingness from the focal point of God’s awareness a single central sphere. The first sphere was all around God on the first day of creation. The next day God created another sphere, the center of this sphere is located on the surface anywhere of the first sphere.
The Vesica Piscis is must commonly represented 2D...the eye shape between two intersecting circles. It's also available in glorious 3D...in the shape of an American/Rugby football.
But this isn't the 3D Versica surely??
I follow God's simple steps, in my equally simple mind...and the shape I end up with is the classic flying saucer shape....two woks stuck together?
It's a third of a regular football glued to its other third...isn't it?
A circle, from sideways on?
Strange though...much as I'm convinced, can I find one single reference to this on the web...no.
So I'd sure appreciate it if any of you's can put me straight, one way or the other.
Regards/Gill
[/i]
Fish Bladder?
Moderator: scott
Fish Bladder?
"Everything you know will always equal the sum of your ignorance"
Gill...
1) take the inner, over-lapping part of two 2D circles (vesica pisces), and you have a 2D lens. Now if you rotate the LENS (through the third dimension) you get one thing... a rugby ball.
2) but if you take the inner, over-lapping part of two 3D spheres , you have a different structure... one also in 3D.
3) the structure from #2 is identical to the structure from #1... EXCEPT that you not only rotate the 2D lens through the horizontal, but also the vertical... this results in the desired structure/form.
Hiccupalypse
PS - continuing forward, if you proceed to rotate the resultant product through another angle of rotation... you wind up with a...?
Take ANY 2D object, rotate it (on the plane) and you get a? Take any 3D object and rotate it. If it's a cube you get a cylinder. So 3D is a bit more interesting than 2D in this regards.
1) take the inner, over-lapping part of two 2D circles (vesica pisces), and you have a 2D lens. Now if you rotate the LENS (through the third dimension) you get one thing... a rugby ball.
2) but if you take the inner, over-lapping part of two 3D spheres , you have a different structure... one also in 3D.
3) the structure from #2 is identical to the structure from #1... EXCEPT that you not only rotate the 2D lens through the horizontal, but also the vertical... this results in the desired structure/form.
Hiccupalypse
PS - continuing forward, if you proceed to rotate the resultant product through another angle of rotation... you wind up with a...?
Take ANY 2D object, rotate it (on the plane) and you get a? Take any 3D object and rotate it. If it's a cube you get a cylinder. So 3D is a bit more interesting than 2D in this regards.
re: Fish Bladder?
Thanks for your input Rasselas....not sure though if you've confirmed my point or the opposite?
The 2D Vesica can indeed be turned in the 3rd dimension, resulting in a Rugby ball.....entirely legitimate as a geometric exercise....and, as an exercise in geometry, then it can indeed be expanded upon as you suggest.
But the Vesica, above all other, is revered as the Holy Grail of Sacred Geometry and I have to repeat.....nowhere in any Sacred account does `God` intersect two circles to create a 2D lens and then turn it through the 3rd to create a Rugby ball....only the mathematician does this. God starts with two spheres, simply stuffs one into the other....and the 3D form that results at the centre is not a Rugby ball.
It appears as though the mathematician, intent on proving that number equates to `God`.... something that I can wholly identify with, has come up with this Rugby ball thing as the Sacred form above all others to express this....whereas `God` offers no such thing.
If anyone should entertain the notion, as I do, that this Sacred 3D space is quite likely to hold the geometric properties/secret to enable some cool, hitherto unrecognised, movement to be conducted within it, then it would be prudent surely to first ascertain the actual shape/dimension of that 3D space.....and according to `God` it's a flying saucer...NOT the Rugby ball?
Cheers/Gill.
The 2D Vesica can indeed be turned in the 3rd dimension, resulting in a Rugby ball.....entirely legitimate as a geometric exercise....and, as an exercise in geometry, then it can indeed be expanded upon as you suggest.
But the Vesica, above all other, is revered as the Holy Grail of Sacred Geometry and I have to repeat.....nowhere in any Sacred account does `God` intersect two circles to create a 2D lens and then turn it through the 3rd to create a Rugby ball....only the mathematician does this. God starts with two spheres, simply stuffs one into the other....and the 3D form that results at the centre is not a Rugby ball.
It appears as though the mathematician, intent on proving that number equates to `God`.... something that I can wholly identify with, has come up with this Rugby ball thing as the Sacred form above all others to express this....whereas `God` offers no such thing.
If anyone should entertain the notion, as I do, that this Sacred 3D space is quite likely to hold the geometric properties/secret to enable some cool, hitherto unrecognised, movement to be conducted within it, then it would be prudent surely to first ascertain the actual shape/dimension of that 3D space.....and according to `God` it's a flying saucer...NOT the Rugby ball?
Cheers/Gill.
"Everything you know will always equal the sum of your ignorance"
Gill... I'm interested in what "religious text" you are using (especially as it seems you refer to multiple ones). If you're referring to the Bible... I'm not sure how genesis and you're translation thereof line up... care to explain a bit further or provide a link?
As to Sacred Geometry... besides the vesica pisces there are some other neat things as well. Some of my favorite geometrical forms are what are termed "optical illusions" even though they are "irregular" structures and typically ignored in geometrical "circles"... geometricians refer to people who dabble in such eccentricities as being "square". :p
But seriously....
Take a vesica lens (with vertical height greater than horizontal width), rotate it in 3D (through the horizontal) and you have a rugby ball. Now rotate the rugby ball in 3D again (through the vertical this time) and you have the shape you are after. If you put the rugby ball in sand up to it's halfway mark, then rotate the football (though through either the vertical OR horizontal from this experiment)... you are left with an indentation that is half the structure you seek. (easier technique to visualize with sand imo)
In short, your structure is two truncated hemispheres stuck together at their base... BUT, it's ALSO a lens rotated into a rugby ball, then rotated into a flying saucer (wich still has a lens appearance from some perspectives).
Pi everyone nearly agrees is formed from comparing the ratio of a circle's diameter to it's perimeter. BUT that is only one way of generating Pi. So to say that God created the obvious way, and the mathematicians the other ways... i'm not sure.
You can create the Star of David by intersecting two oppositional triangles... but you can also create it by placing an equilateral triangle on each side of a hexagram.
I'm not saying that there isn't a preferred pathway, only inquiring into reality, between what is subjective and what is object-ive.
As to Sacred Geometry... besides the vesica pisces there are some other neat things as well. Some of my favorite geometrical forms are what are termed "optical illusions" even though they are "irregular" structures and typically ignored in geometrical "circles"... geometricians refer to people who dabble in such eccentricities as being "square". :p
But seriously....
Take a vesica lens (with vertical height greater than horizontal width), rotate it in 3D (through the horizontal) and you have a rugby ball. Now rotate the rugby ball in 3D again (through the vertical this time) and you have the shape you are after. If you put the rugby ball in sand up to it's halfway mark, then rotate the football (though through either the vertical OR horizontal from this experiment)... you are left with an indentation that is half the structure you seek. (easier technique to visualize with sand imo)
In short, your structure is two truncated hemispheres stuck together at their base... BUT, it's ALSO a lens rotated into a rugby ball, then rotated into a flying saucer (wich still has a lens appearance from some perspectives).
Pi everyone nearly agrees is formed from comparing the ratio of a circle's diameter to it's perimeter. BUT that is only one way of generating Pi. So to say that God created the obvious way, and the mathematicians the other ways... i'm not sure.
You can create the Star of David by intersecting two oppositional triangles... but you can also create it by placing an equilateral triangle on each side of a hexagram.
I'm not saying that there isn't a preferred pathway, only inquiring into reality, between what is subjective and what is object-ive.
re: Fish Bladder?
Oh dear...nuch as I appreciate your efforts to solve my confusion here I must confess that I'm getting ever more confused!
Firstly; The religious context is by the by....let's just say, for instance, that you have commissioned me to make you a solid Versica.
I take a box of level sand and into it I press a globe until it sits one third of it's diameter into the sand. I remove the globe and completely fill the indentation with a resin liquid. When hardened I remove it and then repeat the process to create a second. I then glue together the two flat, circular surfaces of each together.
Happy with my creation I rush to the Post Office to send it to you.
Upon receipt are you going to be just as happy to have this flying saucer....or are you gonna be mailing me to demand why I haven't sent you a rugby ball?
Gill
Firstly; The religious context is by the by....let's just say, for instance, that you have commissioned me to make you a solid Versica.
I take a box of level sand and into it I press a globe until it sits one third of it's diameter into the sand. I remove the globe and completely fill the indentation with a resin liquid. When hardened I remove it and then repeat the process to create a second. I then glue together the two flat, circular surfaces of each together.
Happy with my creation I rush to the Post Office to send it to you.
Upon receipt are you going to be just as happy to have this flying saucer....or are you gonna be mailing me to demand why I haven't sent you a rugby ball?
Gill
"Everything you know will always equal the sum of your ignorance"
Gill... nice attempt at working with the sand-box, I hadn't thought of working with images of resin as well... neat.
1) you're sticking of the spheres(globes) 1/3 of the diameter into the sand is only approximate. Pi is transcendental, and the point of intersection of the globes won't be exactly rational (but irrational, or non-integeral instead).
2) Try this... take one of the spheres, cut a section off, with the cut mark being parallel to the diameter (ie, not a conic-section, or elliptical shape, but will result in a circular shape). See, like an orange that has been cleaved, and can now rest easily upon a flat table. Now scoop the insides of the sphere/orange out. Now place another sphere against the first, so that part of the second projects into the first. In other words, we're purposefully and helpfully removing part of the complexity to more easily see what the shape might look like (although incomplete).
3) Try this... take an orange, and instead of cleaving off a section (producing a circular flat), take a knife and just try to cut off a lens shaped section. Can you? Can you explain what the result of that test means?
I believe that you've misunderstood what I said about a rugby ball. Imagine a stick spinning very quickly about a fulcrum. It will be like a fan. It will take on the appearance of a solid object, both to the sight and to the touch (if spinning fast enough). So is it a stick... or is it instead a disk/circle? In our case, we are imagining a rugby-ball undergoing a lengthwise rotation to form a double-saucer...
So whether we take a circle and rotate it once to create a sphere, and then take another circle and rotate it once to create a sphere (summing to two rotations) OR we instead take the intersection of two circles, and rotate that once to create a rugby-ball, then rotate it once more (now along its length) to create a double-saucer... we have started both times with the same basic shapes, and both times we used the same number of rotations to produce the correct result.
If you are like me, you won't be satisfied until you can visualize it with certainty for yourself, so I hope you appreciate the demonstrations I've given (rather than just a blunt answer).
But in addition, I'd like to inquire again as to the religious context you earlier presented. I personally don't see why you consider that to be the story of creation. Is that a Pythagorean doctrine maybe? Also, why do you consider it the most sacred shape... vs something simple like the pentagon, or something complex like the 3D mandelbrot (known as the mandelbulb):
http://www.skytopia.com/project/fractal/mandelbulb.html
http://www.skytopia.com/project/fractal ... -small.jpg
1) you're sticking of the spheres(globes) 1/3 of the diameter into the sand is only approximate. Pi is transcendental, and the point of intersection of the globes won't be exactly rational (but irrational, or non-integeral instead).
2) Try this... take one of the spheres, cut a section off, with the cut mark being parallel to the diameter (ie, not a conic-section, or elliptical shape, but will result in a circular shape). See, like an orange that has been cleaved, and can now rest easily upon a flat table. Now scoop the insides of the sphere/orange out. Now place another sphere against the first, so that part of the second projects into the first. In other words, we're purposefully and helpfully removing part of the complexity to more easily see what the shape might look like (although incomplete).
3) Try this... take an orange, and instead of cleaving off a section (producing a circular flat), take a knife and just try to cut off a lens shaped section. Can you? Can you explain what the result of that test means?
I believe that you've misunderstood what I said about a rugby ball. Imagine a stick spinning very quickly about a fulcrum. It will be like a fan. It will take on the appearance of a solid object, both to the sight and to the touch (if spinning fast enough). So is it a stick... or is it instead a disk/circle? In our case, we are imagining a rugby-ball undergoing a lengthwise rotation to form a double-saucer...
So whether we take a circle and rotate it once to create a sphere, and then take another circle and rotate it once to create a sphere (summing to two rotations) OR we instead take the intersection of two circles, and rotate that once to create a rugby-ball, then rotate it once more (now along its length) to create a double-saucer... we have started both times with the same basic shapes, and both times we used the same number of rotations to produce the correct result.
If you are like me, you won't be satisfied until you can visualize it with certainty for yourself, so I hope you appreciate the demonstrations I've given (rather than just a blunt answer).
But in addition, I'd like to inquire again as to the religious context you earlier presented. I personally don't see why you consider that to be the story of creation. Is that a Pythagorean doctrine maybe? Also, why do you consider it the most sacred shape... vs something simple like the pentagon, or something complex like the 3D mandelbrot (known as the mandelbulb):
http://www.skytopia.com/project/fractal/mandelbulb.html
http://www.skytopia.com/project/fractal ... -small.jpg
re: Fish Bladder?
Rasselas....Straigh off, your praise re the sand/resin is most unwarranted in light of the fact that I suggested pushing a sphere into the sand one third its diameter....I'm sure any lesser a fool than I could take one look and see immediately that it's one quarter.
Regadless, I really can't, nor want really, to tax my logic with the irationalities of mathematics. Intrigueing as it may be, the fact that the circumference of a circle/sphere cannot be precisely defined mathematically doedn't prevent me from holding a definativel circle/sphere in my mitts...and what I seek here is no more than that, a 3D Vesica in my hands.
As before I must admit that your valiant and much appreciated efforts to help me are to little if no avail.
Perhaps flipping the script might be more productive?
Pushing two spheres into each other to the point whereby the outer circumference of both touches the centre of both results in an overlap.
Should I offer you a reward large enough to spur you into action
1; Could you produce a solid 3D representation of this overlap for me?
2; How would you achieve it?
3; Would I get a flying saucer or a rugby ball?
My logic, despite all this complicated stuff, still simply insists upon a saucer!
Keeping to this simple approach then I really now regret having ever mentioned the God reference.....I do not consider `that` to be the story of creation above any other story of creation. I consider all stories of creation to be exactly that...stories...theories....and like all other mortals I am in no position to give preference to any one of them over any other?
Furthermore I didn't say, or mean to suggest, that I personally view the Vesica as the most sacred, only that it is and throughout time has been, hailed as such. My only definitive view on the thing is the `fact` that all of geometry, be it 2 or 3 dimensional can be derived from it and that this fact suggests that it might be the best basis from which to start, where no other, obvious/likely, starting point currently exists.
Pythagorean doctrine?
For sure I am convinced that if this impossibility should actually be possible then there has to be something amiss in the way we imagine this reality to be. The fact that number/mathematics throws up irrationalities, seems to be a likely culprit and again, a good point therefore at which to start any search for a solution.....I wouldn't wish to attach the term doctrine to it though...it's a hunch and nothing more.
Thanks again for your assistance.....Gill
Regadless, I really can't, nor want really, to tax my logic with the irationalities of mathematics. Intrigueing as it may be, the fact that the circumference of a circle/sphere cannot be precisely defined mathematically doedn't prevent me from holding a definativel circle/sphere in my mitts...and what I seek here is no more than that, a 3D Vesica in my hands.
As before I must admit that your valiant and much appreciated efforts to help me are to little if no avail.
Perhaps flipping the script might be more productive?
Pushing two spheres into each other to the point whereby the outer circumference of both touches the centre of both results in an overlap.
Should I offer you a reward large enough to spur you into action
1; Could you produce a solid 3D representation of this overlap for me?
2; How would you achieve it?
3; Would I get a flying saucer or a rugby ball?
My logic, despite all this complicated stuff, still simply insists upon a saucer!
Keeping to this simple approach then I really now regret having ever mentioned the God reference.....I do not consider `that` to be the story of creation above any other story of creation. I consider all stories of creation to be exactly that...stories...theories....and like all other mortals I am in no position to give preference to any one of them over any other?
Furthermore I didn't say, or mean to suggest, that I personally view the Vesica as the most sacred, only that it is and throughout time has been, hailed as such. My only definitive view on the thing is the `fact` that all of geometry, be it 2 or 3 dimensional can be derived from it and that this fact suggests that it might be the best basis from which to start, where no other, obvious/likely, starting point currently exists.
Pythagorean doctrine?
For sure I am convinced that if this impossibility should actually be possible then there has to be something amiss in the way we imagine this reality to be. The fact that number/mathematics throws up irrationalities, seems to be a likely culprit and again, a good point therefore at which to start any search for a solution.....I wouldn't wish to attach the term doctrine to it though...it's a hunch and nothing more.
Thanks again for your assistance.....Gill
"Everything you know will always equal the sum of your ignorance"
re: Fish Bladder?
Hello, guys!
It's hard to 'see' this rugby ball.
Easier to 'see' is the figure that appears at a 2 spheres intersection! ()
See?
Cheers!
M.
It's hard to 'see' this rugby ball.
Easier to 'see' is the figure that appears at a 2 spheres intersection! ()
See?
Cheers!
M.
Gill, let's try one more perspective game.
1) take two spheres and overlap them so that their circumference touches each other's centers... that's your typical 3D vesica... and we are trying to definitively determine what it's shape is.
2) since we couldn't figure that out, let's take the same two spheres and push them so that they merge more and more. At each step we can stop and ask ourselves... "Does this help me to see the structure of a spherical OVERLAP?"
You see... spherical overlaps all look pretty much the same, the way that all rectangles look pretty much the same. Or the way all triangles look pretty much the same.
3) take our two spheres and overlap them to the extreme amount that they coexist in the same space (ie, as much overlap as possible... so much so that there appears to only be one sphere). NOW Gill, ask yourself, "Does this help me to see the structure of a spherical OVERLAP?"
So you see (as you instinctively intuited), the structure of the (or ANY) spherical overlap is TWO (often truncated) hemispheres conjoined together. Is a rugby-ball two conjoined hemispheres (even truncated ones)?
No. So, rather the shape we DO produce in a spherical vesica pisces IS a double-saucer (ie, a prototypical ufo, as you yourself believe).
Gill, hope you enjoyed the Mandel-bulb links.
1) take two spheres and overlap them so that their circumference touches each other's centers... that's your typical 3D vesica... and we are trying to definitively determine what it's shape is.
2) since we couldn't figure that out, let's take the same two spheres and push them so that they merge more and more. At each step we can stop and ask ourselves... "Does this help me to see the structure of a spherical OVERLAP?"
You see... spherical overlaps all look pretty much the same, the way that all rectangles look pretty much the same. Or the way all triangles look pretty much the same.
3) take our two spheres and overlap them to the extreme amount that they coexist in the same space (ie, as much overlap as possible... so much so that there appears to only be one sphere). NOW Gill, ask yourself, "Does this help me to see the structure of a spherical OVERLAP?"
So you see (as you instinctively intuited), the structure of the (or ANY) spherical overlap is TWO (often truncated) hemispheres conjoined together. Is a rugby-ball two conjoined hemispheres (even truncated ones)?
No. So, rather the shape we DO produce in a spherical vesica pisces IS a double-saucer (ie, a prototypical ufo, as you yourself believe).
Gill, hope you enjoyed the Mandel-bulb links.