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Comment by jbyers | Hacker News Reader

If a Gömböc is built to 10 micron tolerances, does that mean I need a cleanroom and the world's flattest table to be assured it will work?

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According to Wikipedia, yes:

The balancing properties of a gömböc are affected by mechanical defects and dust both on its body and on the surface on which it rests. If damaged, the process of restoring the original shape is more complex than producing a new one.

So do the self-righting properties simply degrade or fail completely, if say an eyelash drops on it?

The self-righting properties degrade in imprecise environments -- from the level of "100% mathematical certainty it can right itself" -- to something sort of absolute mathematical certainty. Not from self-righting to complete failure.

Dropping an eyelash on it, and using a standard kitchen table probably won't make it fail, and it will probably still work -- but it does impact it at the theoretical absolute level.

I bet if that eyelash were on the stable equilibrium point, you'd now have two stable equilibrium points (one on either side of the eyelash, basically), and possibly an additional unstable point (balanced on the eyelash).

The self-righting property would be completely unaffected if the surface imperfection is smaller than a certain threshold value. This value is a function of the "equilibrium-ity" for any point of the surface.

Close to the stable and unstable equilibrium points, any imperfections create additional equilibrium points, like someone else mentioned.

The threshold will grow with the distance to equilibrium points, so in some places, an eye lash, a grain of sand or the inscribed logo makes absolutely no difference.

In the linked video they appear to demo it on a wood table which almost certainly doesn't meet the 10micron flatness.

For an interesting analysis of a practical application of this, namely turtles and tortoises righting themselves, there's a full text analysis of the dynamics involved available here: http://rspb.royalsocietypublishing.org/content/275/1630/11.f...

Not true: Here in the UK the BBC have a quiz show hosted by Stephen Fry - QI which featured the Gömböc. Fry placed it in front of him to show it in action, albeit on a mirror, but it certainly wsn't a dust free environment.

Here's the actual clip on Youtube http://www.youtube.com/watch?v=XCAg5_vHFmI

The article states that the machines are accurate to that tolerance, but not whether that level of precision is required.

Yeah that was a bit deceptive. A typical desktop CNC machine can easily do precisions in the thousands of an inch, or about 25 microns.

If you look at the close up of picture #2, they are nowhere near a 10 micron finish, which you would be able see your reflection in - all those tool marks (not to mention the logo) are an order of magnitude above 10 microns. http://www.gomboc-shop.com/app/urwfilter/catalog/do/action/S...

I wondered the same thing when I saw the wooden table, which surely has deviations > 10 microns. Possibly there are approximate Gömböc shapes that are "good enough" without being mathematically perfect.

The implication of the result is that all the real "Gömböcs" are really such "almost Gömböcs", since any deviation at all from the correct shape technically destroys it.

Not necessarily: the Gömböc-shape could be a envelope of similar shapes. Any object within that envelope is a Gömböc, and ones just outside it are "almost Gömböcs"

It could be, but it isn't, which is part of what's so interesting about it.

(And that's leaving aside the more fundamental point that the very definition of a Gömböc isn't applicable in the physical world, where objects do not have precisely defined edges and cannot be completely homogenous).

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