Then again John Baez is the dude who very nearly explained General Relativity to my satisfaction, long after I got my PhD in physics.
Physics, Topology, Logic and Computation: A Rosetta Stone
Permutation City: People can run simulations of themselves or entirely migrate their consciousness into computer programs, but existence is often limited to the amount of computation that you can afford, leading to slow existences that stretch time into fractions of realtime. That premise had me hooked, but the book has fantastic thought provoking plot points throughout. Highly recommended.
Then in my grad school work, I randomly ran across his name and have subsequently read most of his books.
Diaspora, however, remains my all time favorite novel.
He says with the same sort of casual tone that I would refer to my wife and I rearranging the living room last weekend.
I always wonder what it feels like to be able to do that. Even if, as Baez says, the formula wasn't actually "new", to be able to dive down and come back up with new to you must be very satisfying.
I certainly don't see any step in the outlined derivation that gains or loses the ability to be intuited simply due to a factor of two.
Pi is fundamentally wrong. A circle is defined by a point and a radius. Diameter is just something that has always been easier to measure, so now we're stuck with it :( The fact that Tau makes some formulas less "elegant" is irrelevant.
If you draw a typical star, the one you likely first learned to draw, each line is intersected by 1 to 1.618