I’m no good at April Fool’s jokes myself, but I always enjoy having a look at them on the web. Check out NASA’s image of the stable hexagonal feature at Saturn’s North Pole. Clearly such a thing must be impossible, no?

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## L. Riofrio said,

April 2, 2007 @ 1:39 am

Great photo, and it shows us just how much is not understood. I was planning to put that photo on my blog, but I’ll just put a link back here instead.

## Matti Pitkanen said,

April 2, 2007 @ 3:47 am

I think that New Scientist article was week before April but who knows. I also heard about analogous discrete symmetries in other planetary objects when I visited Hungary in March.

If one accepts dark matter as a hierarchy of phases with increasing values of Planck constant, one must accept scaled up versions of various discrete symmetries. In particular, the discrete subgroups of rotation group appear as symmetries in arbitrarily large length scales. One might have analogs of zoomed up copies of molecular physics. Visible matter would reflect these symmetries. Perhaps even symmetries of snowflakes could represent examples of these symmetries.

One implication would be Bohr quantization of planetary orbits for visible matter induced by that for dark matter. The evidence for this quantization (googling “Nottale” probly gives links) was the stimulus which led to my own recent view about dark matter.

Matti

## Mahndisa S. Rigmaiden said,

April 2, 2007 @ 4:38 am

04 01 07

“If one accepts dark matter as a hierarchy of phases with increasing values of Planck constant, one must accept scaled up versions of various discrete symmetries.”(Previous comment deleted due to mistake that has been corrected).Yes, I agree. Heirachies come about in a p-adic context. Whenever there is clustering of minima,p-adic physics are present. These symmetries also can be thought of as being generated in a q-adic context. Number of vertices in a shape could be generated by a p or q-adic function. The hexagonal shape could be generated by taking a composition of the 2 coefficient and the power of three to the first power to keep things p-adic, or a coefficient of 1 composed with six raised to the first power for a q-adic flavor. I will ramble about this for my next post. I have been busy at the tutoring of good children this week, so had to disappear for a bit:)

Have a great upcoming week:)

## nige said,

April 2, 2007 @ 5:31 pm

Looks like a blackcurrant cheesecake. Yum!

## a quantum diaries survivor said,

April 2, 2007 @ 8:06 pm

I agree with Louise, we know so little of the internal dynamics of things we see and love… When one talks about dark matter and dark energy in the universe without having more than indirect clues is really a bit cocksure.

Cheers,

T.

## Doug said,

April 3, 2007 @ 1:11 am

This hexagon may have a mathematical explanation.

A pentagon was shown in News @ Naure ‘Geometric whirlpool revealed’ 19 May 2006

http://www.nature.com/news/2006/060515/full/060515-17.html

These may be two examples of a superellipse.

http://mathworld.wolfram.com/Superellipse.html

## CarlBrannen said,

April 5, 2007 @ 3:55 am

Hexagons appear naturally in the solutions to non linear differential equations. It’s a sort of soliton. To learn more about this sort of thing, look up the bifurcation diagram of the logistic map.

On another note, the powers of 3 that I’m going on about appear to have a relation to the Hawking temperature of black holes. Check out equation (54) of gr-qc/0212096.

In the above paper, the “tripled Pauli statistics” corresponds to the three colors of primitive idempotents that I call R, G, and B.