Most fundamental pictures of the physical world assume that the basic notions – fields, space, and time – are continuous entities rather than discrete bits.

Quantum tunneling processes, which are familiar to physicists and routinely observed, correspond to transitions which do not have a classical path.

[T]he pure mathematical research literature is virtually impenetrable to outsiders.

At present, physicists … search only for continuous pictures of fundamental physics. Maybe, one day, they will be motivated to look at possible structures of a fundamentally discrete world.

[T]he entropy level at the beginning of the expansion of the Universe must have been staggeringly small, which implies that the initial conditions were very special indeed.

Whereas most physicists regard the second law of thermodynamics as a reflection of the improbability of certain types of initial conditions, there are others who regard it as a far more fundamental idea that is prior to the laws of nature themselves.

There is one qualitative aspect of reality that sticks out from all others in both profundity and mystery. It is the consistent success of mathematics as a description of the workings of reality and the ability of the human mind to discover and invent mathematical truths.

The traditional view that initial conditions are for the theologians and evolution equations for the physicists seems to have been overthrown―at least temporarily.

The message seems to be this: reality is non-local, so get used to it.