Borromean Triangles and Prime Knots in an Ancient Temple - Indian ...
Borromean Triangles and Prime Knots in an Ancient Temple - Indian ...
Borromean Triangles and Prime Knots in an Ancient Temple - Indian ...
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The universality of<br />
the <strong>Borrome<strong>an</strong></strong><br />
symbol is very<br />
remarkable as it is<br />
found <strong>in</strong> disparate<br />
cultures <strong><strong>an</strong>d</strong> times.<br />
An example of a<br />
situation where a 2-<br />
body configuration is<br />
not stable, but a 3-<br />
body one is, is<br />
provided by ‘halo<br />
nuclei’ with some<br />
neutrons loosely<br />
bound to a core.<br />
GENERAL ARTICLE<br />
International Mathematical Union adopted a three component<br />
<strong>Borrome<strong>an</strong></strong> l<strong>in</strong>k, which m<strong>in</strong>imized the l<strong>in</strong>k length when tied with<br />
a rope of unit diameter, as their logo <strong>in</strong> August 2006. The<br />
Australi<strong>an</strong> artist John Rob<strong>in</strong>son has made <strong>Borrome<strong>an</strong></strong> sculptures<br />
us<strong>in</strong>g various shapes <strong>in</strong>clud<strong>in</strong>g tri<strong>an</strong>gles. It is <strong>in</strong>deed a lot of fun<br />
<strong><strong>an</strong>d</strong> challenge to take some cardboard <strong><strong>an</strong>d</strong> create ones own threedimensional<br />
version of the <strong>Borrome<strong>an</strong></strong> tri<strong>an</strong>gles whose projection<br />
is found <strong>in</strong> the temple. Once created it is <strong>an</strong> object that is often the<br />
nucleus of conversations on <strong>Borrome<strong>an</strong></strong> matters! The universality<br />
of the <strong>Borrome<strong>an</strong></strong> symbol is very remarkable as it is found <strong>in</strong><br />
disparate cultures <strong><strong>an</strong>d</strong> times. One of my personal favourites is a<br />
<strong>Borrome<strong>an</strong></strong> configuration <strong>in</strong>volv<strong>in</strong>g a doughnut, a coffee mug <strong><strong>an</strong>d</strong><br />
a computer mouse with cable which forms the logo of the Topological<br />
Qu<strong>an</strong>tum Comput<strong>in</strong>g project at Indi<strong>an</strong>a University. This<br />
<strong><strong>an</strong>d</strong> other logos, as well as a considerable wealth of <strong>in</strong>formation<br />
on <strong>Borrome<strong>an</strong></strong> l<strong>in</strong>ks is available <strong>in</strong> the website http://<br />
www.liv.ac.uk/~spmr02/r<strong>in</strong>gs, which is one of several sites that<br />
deal with matters <strong>Borrome<strong>an</strong></strong>. <strong>Ancient</strong> Indi<strong>an</strong> uses of the symbol<br />
which must <strong>in</strong>deed be quite prevalent however do not seem to be<br />
documented.<br />
<strong>Borrome<strong>an</strong></strong> Metaphors <strong>in</strong> Physics<br />
The adjective <strong>Borrome<strong>an</strong></strong> is <strong>in</strong> use <strong>in</strong> few-body qu<strong>an</strong>tum systems<br />
– it describes the situation where a 2-body configuration is not<br />
stable, while a 3-body configuration may be. An example is<br />
provided by ‘halo nuclei’ with some neutrons loosely bound to a<br />
core, such as <strong>in</strong> the case of 6 He, which is stable aga<strong>in</strong>st dissociation<br />
while 5 He is not. Thus while the 3-body configuration<br />
<strong>in</strong>volv<strong>in</strong>g (,n,n) is stable (there exists a bound state), the 2-body<br />
ones (,n) <strong><strong>an</strong>d</strong> (n,n) <strong>in</strong>volv<strong>in</strong>g a Helium nucleus () <strong><strong>an</strong>d</strong> a neutron<br />
(n) or just two bare neutrons are unstable (there are no bound<br />
states).<br />
Another use of the <strong>Borrome<strong>an</strong></strong> l<strong>in</strong>ks as a descriptive metaphor <strong>in</strong><br />
qu<strong>an</strong>tum physics is <strong>in</strong> the study of ent<strong>an</strong>gled states. Ent<strong>an</strong>glement<br />
is a peculiar qu<strong>an</strong>tum correlation that we do not observe <strong>in</strong><br />
our everyday ‘classical’ world, but which could be a crucial<br />
44 RESONANCE May 2007
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