Inquire about purchasing the book | Table of Contents | Annotated Bibliography | Class on Nature of Mind

**These are excerpts and elaborations from my book "The Nature of Consciousness"**

The trick is
that Boltzmann assumed that a gas (a discrete set of interacting molecules) can be considered as a
continuum of points and, on top of that, that the particles can be considered
independent of each other: if these arbitrary assumptions are dropped, no
rigorous proof for the irreversibility
of natural processes exists. The French
mathematician Jules Henri Poincaré (“Sur le problème des trois corps et les équations
de la dynamique”, 1890), for example, proved just about the opposite: that
every closed system must eventually revert in time to its initial state (the
“recurrence theorem”). Thus everything that can happen “will” happen, and will
happen infinite times. Poincaré proved eternal recurrence where Thermodynamics
had just proved eternal doom. The
German mathematician Ernst Zermelo immediately (“On a Theorem of Dynamics and the Mechanical Theory
of Heat”, 1896) noticed that this would violate the law of entropy, as the
return to a previous state would imply that entropy at some point must decrease
in order to return to its original value. Boltzmann could find only one rational reply: that there might be universes
in which entropy decreases to compensate for universes like ours in which
entropy can never decrease. It took the
Belgian (but Russian-born) physicist and Nobel-prize winner Ilya Prigogine, in the 1970s, to provide a more
credible explanation for the origin of irreversibility. He observed some
inherent time asymmetry in chaotic processes at the microscopic level, which
would cause entropy at the macroscopic level. He reached the intriguing
conclusion that irreversibility originates from randomness which is inherent in
nature. Boltzmann’s reformulation of the second
law was probabilistic: it explained the entropy of the system as a property
about a population of particles, not just one particle. The second law does not
claim that every single particle is subject to it, but that closed systems
(made of many particles) are subject to it. An individual particle may well be
violating the second law for a few microseconds, but the millions of particles
that make up a system will obey it (just like one person might win at the
roulette once, but that episode does not change the statistical law that people
lose money at the roulette). In 2002 Australian researchers, in fact, showed
that microscopic systems may spontaneously become more orderly for short
periods of time. Back to the beginning of the chapter "The New Physics" | Back to the index of all chapters |