Amy tells us William Sidis hated academia and spoke harshly
of a world of academics. (Upon reading his father's * Philistine
and Genius* , we can see why! See our review of P&G
nearby.) Using a Pirsig-like, MoQ perspective, Billy saw academia
as rigid, structured, bureaucratic, title- and .-centric, arrogant
folk of suffuse Static Quality. He saw them as stuck, proud,
content, and satisfied. They had to be! How else could
they 'teach' other people what they * need * to know? In
both * Zen and the Art of Motorcycle Maintenance* (* ZMM* )
and * Lila* , Pirsig rails about academics incapable of Quality
teaching because they do not know what Quality * is* ... Billy
Sidis certainly would agree. Genius in agreement with genius!

which is the same as eq. (8) with Φ =− Gm / r . For r inside the Schwarzschild radius, r s ≡ 2 Gm / c 2 , . inside the ‘event horizon’ of a black hole but outside the mass, the radicand is negative. So if a particle inside r s (but outside the mass) could be motionless, it would experience achronicity. However, most relativists think it is impossible for an object to have zero velocity inside the event horizon, partly because they want to avoid the possibility of the spacetime interval ds being imaginary, (. achronicity). 22

If we adopt these seemingly simple assumptions, the implications for the geometry of the universe are quite profound. First, one can demonstrate mathematically that there are only three possible curvatures to the universe: positive, negative or zero curvature (these are also commonly called "closed", "open" and "flat" models). See these lectures on cosmology and GR and this discussion of the Friedman-Robertson-Walker metric (sometimes called the Friedman-Lemaitre-Robertson-Walker metric) for more detailed derivations. Further, the assumption of homogeneity tells us that the curvature must be the same everywhere. To visualize the three possibilities, two dimensional models of the actual three dimensional space can be helpful; the figure below from the NASA/WMAP Science Team gives an example. The most familiar model with positive curvature is the surface of a sphere. Not the full three dimensional object, just the surface (you can tell that the surface is two dimensional since you can specify any position with just two numbers, like longitude and latitude on the surface of the Earth). Zero curvature can be modeled as a simple flat plane; this is the classical Cartesian coordinates that most people will remember from school. Finally, one can imagine negative curvature as the surface of a saddle, where parallel lines will diverge from each other as they are projected towards infinity (they remain parallel in a zero curvature space and converge in a positively curved space).