http://www.extremetech.com/extreme/164050-discovery-may-make-encryption-exponentially-easier-to-break discusses a paper (view PDF) on the typical set and the probability distribution therefore. It contrasts that distribution with the uniform probability distribution and asks a question: is the distinction material to cryptanalysis?
Of course it is.
Or, in simper terms, do the statistics of averages lie? That is: would politicians [and spies] use statistics to lay a trail of deception?
So, in the spirit of de-math’ing math (so everyone can participate in the study of cryptanalysis), note that the “typical set” is a region of “point-space” where the electron spends most of its time – given the possible regions it might occupy. This means that it is at some point at the radius of its orbital’s (3d) egg-shell – that surrounds the nucleus. Called a virtual particle, the electron’s charge disappears from one point to appear at other. “Disappearing” means that the particle reached infinite action potential and was able to manifest in one of the troughs- created when waves superimpose (just as ripples on ponds so superimpose). Just as there are sounds and smells a dog can sense that you cannot, so there are the dark areas in the crests and troughs where waves are reinforcing and canceling; but where its hard for classical detectors to detect charge-in-phase-transition. Because of the plank action, as the discrete charge potential swaps between two states in phase-space it necessarily has infinite action for a non-time (infinitely small), which affects the whole system. Since it logically has infinite mass and is acting at the speed of light it has infinite reach – since time has compressed to nothing, It can thus “address” the entire space of combinatoric possibilities – no matter how large – simultaneously.
As I said to the missionary on the bus once to address his getting upsetting at my preventing him ranting on about some the claimed-significance of some or other biblical story: you REALLY ought not to be afraid of Science – since its all about the infinite.