Now combine the history of Hilbert’s “On The Infinite,” Godel’s Incompleteness Thm., and finally the birth of algorithmic information theory–and finally add General Relativity and Quantum Mechanics (intuited by Hilbert to an extent in “On the Infinite”), and voila–you can construct a convergent infinite series approximately modeling a finite interrelationship in physical reality.

That is, this math is the drawing of a finite algorithmic information target bullseye about the intersection of the previously shot arrow and the tree. However, if there is a law of physics–an empirical pattern in our sensory perception (what axioms really are, per Bertram Russell and Kurt Godel) to how arrows tend to hit a tree, such infinite series constructs can be a useful minimal shorthand to describe it.

]]>I must admit that this wasn’t discovered in the last five years; its first discovery was probably more than a century ago, and most recently discovered by someone working on the atomic weaponry of the US, an italian, and (most recently) Ed Parker and James Sochacki, published in Neural, Parallel, and Scientific Computations 4, 1996.

What does this do? It is incredibly effective at generating maclaurin Series solutions to systems of IVP equations and differential equations.

You can see more at wikipedia, or you can find a little tutorial at

]]>If you haven’t already encountered this great song perhaps it’s relevant to share it here for more people to enjoy! ]]>

On p. 157 (of the U.S. version), the book seems to be saying that a cube has 12 vertices:

Finally, count the number of corners, and denote that number by V (standing for vertices). For a cube V=12….

I believe it should be 8.

]]>Certainly many integers have been tested, but it appears that they start at a certain initial value

(close to 2,361,184,410,093,970,784,932), which raises the obvious question: “have all lower

values been tested?” Unfortunately, at least to me, that seems unlikely. ]]>

a lot. I personaly will miss him deeply. ]]>