The Most Symmetrical Objects in the World

I think the part about the kilogram is missing the point -- it's not that a pure silicon crystal sphere is a better artifact to be the kilogram than the platinum-iridium cylinder. The idea is that they are defining a reproducible process to manufacture an object of known mass without reference to some artifact at all. They are proving by demonstration that anyone can manufacture such an object and then test it for chemical purity, perfection of crystal lattice, size, and sphericity. This allows you to form a counting argument based only on math and the physical laws of the universe that the produced object has within some small error exactly n silicon atoms in it, which will then be the definition of the mass unit (any sphere of n silicon atoms, not any particular one).

On a more pedestrian scacle...

There are some extremely smooth and round objects available for ornamental purposes. Finnish company Sorvikivi [0] has been making such granite balls for 20 years, and their products are so accurately manufactured that the balls can be supported by a hydroplane between the ball and an equally smooth support bowl.

I remember seeing one of their products at the lobby of a hotel. Because the ball was effectively floating on water, you could rotate it by hand. And we did.

[0]: http://www.sorvikivi.com/eng/index.html

I had a friend who worked on a very deep sea drone. He told me that it was better to flood as much of the drone as possible to minimize the strength of the pressure vessels they had to build. The one exception to this was the buoyant components, which had to be hollow to work. These were made of hollow ceramic spheres of exacting sphericity. A sphere provides maximum enclosed volume and strength for a minimum amount of structure, so was a good choice for the pressure vessel shape. They had to be so perfectly spherical to force the pressure to be balanced across the sphere and distribute the compression evenly.

Not sure if this was the exact drone he worked on, but the spheres look like what he described.

http://www.whoi.edu/oceanus/feature/floating-without-implodi...

The incredible precision with which the two spheres mentioned in the article have been manufactured sure is mind-boggling. But I think the article itself is a good example for what I find pretty annoying in popular presentation of quantitative results in science.

- "off by anything larger than one one-hundred-billionth of a degree"

- [normal gyroscopes] "are over ten-million times less accurate"

...and to a lesser extent, because people in mechanical engineering or metal-working are actually used to measure in micrometers:

- "three ten-millionths of an inch away"

- "only 25 nanometers away from being perfectly round"

The precision is presented as a very impressive sounding, but to the typical reader pretty meaningless number, because in our normal lives we don't have any reference for hundred-billionths of anything, and frankly many people have difficulties writing up 100-billionths correctly, anyway.

I'd really like to see the general notion of "order of magnitude" be used for these kinds of achievements, which can be presented as a "number of digits" figure easily:

- To measure the relativistic frame-dragging, Gravity Probe B had to measure the degrees of rotation of its gyroscopes with a precision of 11 digits after the decimal point whereas (military gyroscopes) only are accurate up to 7 digits.

- three ten-millionth of a inch -> Diameter (in inch, let's assume it's 3 inches) specified with 8 digits of accuracy, similarly for the "25 nanometers away from being round)

> The problem is that the current IPK has lost a tiny bit of weight, in comparison with 40 similar cylinders held in other countries, which is a significant flaw in an object used to define a unit of mass. So the Avogadro Project has created two softball-sized, near-perfect spheres, made entirely of silicon-28 atoms, that should remain exactly one kilogram in perpetuity.

I seem to remember reading a while ago that no-one was quite sure why the reference kilogram was losing mass. Why should one therefore be confident that the new spheres will not do so?—or is this another 'distortion for convenience' of the article, like:

> Lie group E8, for instance, is a set of 248 different forms of symmetry that apply to a theoretical 57-dimensional object.

E_8 as a Lie group is 'continuous', and therefore infinite, and E_8 as a Weyl group has size much, much, much bigger than 248. The number 248 presumably comes from the dimension of the Lie group E_8 (and I suppose that one could twist words to accept that the dimension of the Lie group is somehow a reflection of the "number of different kinds of symmetries" that it contains); I'm not sure (but am not an expert on this, and so might just not know) whence comes the 57.

> According to the Guinness Book of World Records, these are the roundest objects ever made.

What a shame they didn't specify that these are the most spherical objects ever made. "Round" can, and usually does, refer to two dimensions, while "spherical" refers to three.

They forgot to mention this beauty: http://en.wikipedia.org/wiki/Red_Square_Nebula