How many ways can you arrange 128 tennis balls

[wolram]

http://www.sciencedaily.com/releases/2016/01/160127053413.htm

Researchers have solved an apparently overwhelming physics problem involving some truly huge numbers. In summary, the problem asks you to imagine that you have 128 tennis balls, and can arrange them in any way you like. The challenge is to work out how many arrangements are possible and – according to the research – the answer is about 10^250, also known as ten unquadragintilliard: a number so big that it exceeds the total number of particles in the universe.

 

[dipole]

So, without reading the paper, it seems like they are offering an approach to computing the entropy of a system where the Hamiltonian is dominated by steric interactions. In other words, for particles which don't interact much except due to collision.

This is very different than an ideal gas where, essentially, the gas molecules can pass through each other, or a better way of thinking of it, that collisions are rare due to low densities. In a pile of sand, collisions are frequent and are a dominant component of the Hamiltonian. You could also have some adhesion forces I suppose.

 

[wolram]

This is their research area.

Despite its complexity, this study also provides a working example of how "configurational entropy" might be calculated in granular physics. This basically means the issue of measuring how disordered the particles within a system or structure are. The research provides a model for the sort of maths that would be needed to solve bigger problems still, ranging from predicting avalanches, to creating efficient artificial intelligence systems.

I can not see where artificial intelligence comes from though.

 

[Rx7man]

They didn't say much about the constraints of the arrangement.. because if it's in 2 dimensions, it will be much different than in 3 dimensions... Technically the ways of arranging any two objects is infinite... Kinda like "where is there a flat spot on a circle"... the closer you look, and the more accurately you can measure, you keep coming to the fact it's always curved.

 

[dipole]

This is their research area.

Despite its complexity, this study also provides a working example of how "configurational entropy" might be calculated in granular physics. This basically means the issue of measuring how disordered the particles within a system or structure are. The research provides a model for the sort of maths that would be needed to solve bigger problems still, ranging from predicting avalanches, to creating efficient artificial intelligence systems.

I can not see where artificial intelligence comes from though.

The AI remark might be related to search. When you have some combinatorial search space, sampling it efficiently is very difficult. The concept of sampling a phase space, and search in AI are similar.

 

[256bits]

For anyone interested,
some more links of the problem of packing ( ie jam packing where anyone particular settled state can become lower in density )
https://www.newscientist.com/articl...-arrange-128-balls-exceeds-atoms-in-universe/
http://cherrypit.princeton.edu/disordered_packings.html
http://cherrypit.princeton.edu/torquato-aps.pdf

For the PDF, the first picture is probably the most descriptive of the problem.
They are attempting to calculate, ( or guestimate ) the area shaded grey.

The lowest density would be a completely ordered crystal structure.

For AI, the best description I can think of is: ( As I see it )
If one wants an answer to a problem, or make a decision, should one take a long time to determine the perfect answer ( the crystal packing ) , or take less time for at least a reasonable answer ( and how far off from the perfect answer would that be ).
To function in the real world, an AI would have to choose the latter.

 

[OrangeDog]

I had a thought about solving a similar problem using integer partitions. I got similar numbers for the problem I was looking at actually. I wonder what approach they used.