by neufer » Wed May 15, 2013 3:27 pm
K1NS wrote:
This photo reminds me very much of a video posted on Science Friday
http://www.sciencefriday.com/segment/03 ... knots.html this last March. Physicists at the University of Chicago were able to tie water currents into a knotted vortex that looks very much like the Kepler's remnant.
Do the same physics apply?
- It's a mystery
- Hamlet, Prince of Denmark Act 1, Scene 5
Ghost: Make thy two eyes, like stars, start from their spheres,
- Thy knotted and combined locks to part
And each particular hair to stand on end,
Like quills upon the fretful porpentine:
- Love's Labour's Lost Act 1, Scene 1
FERDINAND: Now for the ground which; which,
- I mean, I walked upon: it is y-cleped thy park. Then
for the place where; where, I mean, I did encounter
that obscene and preposterous event, that draweth
from my snow-white pen the ebon-coloured ink, which
here thou viewest, beholdest, surveyest, or seest;
but to the place where; it standeth north-north-east
and by east from the west corner of thy curious-
knotted garden: there did I see that low-spirited
swain, that base minnow of thy mirth,'--
http://en.wikipedia.org/wiki/History_of_knot_theory wrote:
<<The early, significant stimulus in knot theory would arrive with Sir William Thomson (Lord Kelvin) and his theory of vortex atoms.
In 1867 after observing Scottish physicist Peter Tait's experiments involving smoke rings, Thomson came to the idea that atoms were knots of swirling vortices in the æther. Chemical elements would thus correspond to knots and links. Tait's experiments were inspired by a paper of Helmholtz's on vortex-rings in incompressible fluids. Thomson and Tait believed that an understanding and classification of all possible knots would explain why atoms absorb and emit light at only the discrete wavelengths that they do. For example, Thomson thought that sodium could be the Hopf link due to its two lines of spectra. Tait subsequently began listing unique knots in the belief that he was creating a table of elements. He formulated what are now known as the Tait conjectures on alternating knots. (The conjectures were proved in the 1990s.) Tait's knot tables were subsequently improved upon by C. N. Little and Thomas Kirkman.
James Clerk Maxwell, a colleague and friend of Thomson's and Tait's, also developed a strong interest in knots. Maxwell studied Listing's work on knots. He re-interpreted Gauss' linking integral in terms of electromagnetic theory. In his formulation, the integral represented the work done by a charged particle moving along one component of the link under the influence of the magnetic field generated by an electric current along the other component. Maxwell also continued the study of smoke rings by considering three interacting rings.
When the luminiferous æther was not detected in the Michelson–Morley experiment, vortex theory became completely obsolete, and knot theory ceased to be of great scientific interest. Modern physics demonstrates that the discrete wavelengths depend on quantum energy levels.>>
[quote="K1NS"]
This photo reminds me very much of a video posted on Science Friday [url]http://www.sciencefriday.com/segment/03/15/2013/physicists-tie-water-into-knots.html[/url] this last March. Physicists at the University of Chicago were able to tie water currents into a knotted vortex that looks very much like the Kepler's remnant.
Do the same physics apply?[/quote]
[list]It's a mystery :?
[list]Hamlet, Prince of Denmark Act 1, Scene 5[/list]
Ghost: [i][color=#0000FF]Make thy two eyes, like stars, start from their spheres,
[list] [u]Thy knotted and combined locks[/u] to part
And each particular hair to stand on end,
Like quills upon the fretful porpentine:[/list][/color][/i][list]Love's Labour's Lost Act 1, Scene 1[/list]
FERDINAND:[i][color=#0000FF] Now for the ground which; which,
[list] I mean, I walked upon: it is y-cleped thy park. Then
for the place where; where, I mean, I did encounter
that obscene and preposterous event, that draweth
from my snow-white pen the ebon-coloured ink, which
here thou viewest, beholdest, surveyest, or seest;
but to the place where; it standeth north-north-east
and by east from the west corner of [u]thy curious-
knotted garden[/u]: there did I see that low-spirited
swain, that base minnow of thy mirth,'--[/color][/i][/list][/list]
[quote=" http://en.wikipedia.org/wiki/History_of_knot_theory"]
<<The early, significant stimulus in knot theory would arrive with Sir William Thomson (Lord Kelvin) and his theory of vortex atoms.
In 1867 after observing Scottish physicist Peter Tait's experiments involving smoke rings, Thomson came to the idea that atoms were knots of swirling vortices in the æther. Chemical elements would thus correspond to knots and links. Tait's experiments were inspired by a paper of Helmholtz's on vortex-rings in incompressible fluids. Thomson and Tait believed that an understanding and classification of all possible knots would explain why atoms absorb and emit light at only the discrete wavelengths that they do. For example, Thomson thought that sodium could be the Hopf link due to its two lines of spectra. Tait subsequently began listing unique knots in the belief that he was creating a table of elements. He formulated what are now known as the Tait conjectures on alternating knots. (The conjectures were proved in the 1990s.) Tait's knot tables were subsequently improved upon by C. N. Little and Thomas Kirkman.
James Clerk Maxwell, a colleague and friend of Thomson's and Tait's, also developed a strong interest in knots. Maxwell studied Listing's work on knots. He re-interpreted Gauss' linking integral in terms of electromagnetic theory. In his formulation, the integral represented the work done by a charged particle moving along one component of the link under the influence of the magnetic field generated by an electric current along the other component. Maxwell also continued the study of smoke rings by considering three interacting rings.
When the luminiferous æther was not detected in the Michelson–Morley experiment, vortex theory became completely obsolete, and knot theory ceased to be of great scientific interest. Modern physics demonstrates that the discrete wavelengths depend on quantum energy levels.>>[/quote]