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I stumbled across an interesting paper last night.

Basically, it tries to see if mathematical equations have meaning by determining how well they "compress" the results. For instance, he says the equation $e^\pi-\pi = 19.9990999...$ is compressible (the equation generates more bits of $\pi$ than it takes up itself), and thus it is likely that there is some mathematical reason for this -- it's not just a coincident. On the other hand, $\frac{314}{100}$ gives an approximation to $\pi$ but does not compress its representation, so there is nothing intriguing about this formula.

I can't find much information on the guy that wrote the paper -- it may be someone doing math in his spare time. But I am interesting if there is something like this in "professional" math, where equations are analyzed this sort of way to determine if there is something meaningful about them. Can anyone shed some light on this?

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Related: Kolmogorov complexity. – dtldarek May 24 '12 at 20:14
up vote 2 down vote accepted

Maybe this would interest you:

Pieter Adriaans, Between order and chaos: the quest for meaningful information, Theory Comput. Syst. 45 (2009), no. 4, 650–674, MR2529741 (2010m:68066).

Quoting the first two sentences of the review by Vijay G. Subramanian,

In this paper, the author "studies the notion of meaningful information''. He then proceeds "to show that this notion is intricately connected with the idea of learning by compression''.

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