Dr Faustus of Modern Physics - Department of Speech, Music and ...

220 CHAPTER 51. FINITE PRECISION COMPUTATION
51.2 Analog and Digital Computation
Finite precision computation has the following qualities:
• simple microphysics,
• basic assumption (of finite precision) possible to test directly,
to be compared with those of statistical physics:
• complex microphysics,
• basic assumption (e.g. equidistribution) impossible to test directly.
Note that Boltzmann’s basic microscopic assumption of statistical independence
in a gas with each mole consisting of 6×10 23 molecules, seems to be
beyond the possibility of any kind of conceivable experiment or mathematics;
only indirect evidence in the form of macroscopic observations seem to be
possible, which is far from enough. In fact, it is known that Boltzmann’s
assumption can only be (nearly) true in the very special case of a very dilute
gas with rare collisions, and the derivation of Boltzmann equations for more
general situations seems to pose unsurmountable problems.
In the above books I show that with finite precision computation it possible
to mathematically prove and thus theoretically understand, without
resorting to statistics,
• 2nd law of thermodynamics expressed in terms of kinetic energy, heat
energy, work and turbulent dissipation, with explicit reference to entropy,
• direction of time,
• Planck’s radiation law,
• basic aspects of turbulence including a resolution of d’Alembert’s paradox,
and also related other results traditionally approached by statistical arguments.
In short, finite precision computations opens to resolving some of the
basic mysteries of physics. You don’t have to dwell into this if you don’t feel
that you have to. In a way it is enough to understand that the old dead-lock