Alternative Prime Spirals

The Ulam spiral is based on the idea of arranging integers in a rectilinear 2D spiral.

And noticing that certain diagonal patterns fall out that aren't explainable by simple equations that describe some of the "holes".

What other orderings might reveal interesting patterns? How about a 2D Hilbert curve?

Or maybe a 3D one? How might you continue a spiral in a cubic 3D space? Would you get diagonal planes describing the primes? How about a higher dimensional space — maybe higher dimensional planes?

Symbolically Guided Science

Einstein's famous equivalence e=mc² is a fairly simple symbol sequence. Given basic constraints such as unit agreement it could be discovered quickly using random search. The hard part is interpreting — the semantics. Assuming that some grand unified theory exists, one that's elegant, perhaps we can develop an automated search for it constrained by simple requiremenrs like unit agreement and some formal semantics describing observed behavior? The few theories that match observations but make unexpected predictions could be presented for further consideration by humans.

Engraved on the Palms of My Hands

A passion for infinity by any means possible: Ludolph van Ceulen, a German from the 1500s living in the Netherlands, spent his life solving for the perimeter of a 4,611,686,018,427,387,904 (2⁶²) sided regular polygon. With some modifications to an equation from eighteen hundred years earlier he calculated π to 35 digits, more than doubling the accuracy of his contemporaries. It took a century for anyone to usurp his effort, which was engraved on his tombstone.