Consider all the entities [stars, galaxies, or whatnot] in your study as points in 3-space. The descriptive length of the data is the total number of bits that describes the location of all points in your study.
If all points are random and evenly distributed, then the total number of bits required is (number of points)x(number of bits for 1 location).
Suppose you notice a clumping of points. Is this a structure or random variation?
Rework your data description as follows: for any point, use the first bit to determine whether a point is a member of the clump or not, and subsequent bits to complete the description, depending on whether the point is in the clump.
For this description, the total number of bits required is 1x(total number of points) + (number of points in clump)x(number of bits for location relative to clump) + (number of points not in clump)x(number of bits for general location).
If the 2nd description is shorter than the 1st description, then by Occam's razor the second description is more likely correct.
In fact, the number of bits directly tells the probability that the 2nd description is correct: if the 2nd description requires 10 fewer bits (total) than the 1st, then the 2nd description is more likely to be correct by a factor of 1024. Alternately, there is a 1/1024 chance that the 2nd description is *not* the correct description of the data.
If you have lots of data, it's not unusual for a descriptive length to be thousands of bits shorter than the baseline description; meaning, that it's virtually certain that the new description is correct and that the new structure does not arise from random variation.
I haven't seen the data, but I assume that describing all galaxies in the universe using the newly described "clump" as a categorical structure gives a smaller descriptive entropy than describing all galaxies without the extra category of "clump".
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/u4julZFK7bM/story01.htm
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