probability: systems are more likely to proceed from ordered to disordered
states, simply because there are a lot more disordered states than ordered
ones. The second law of thermodynamics explains why clean rooms left
unattended become dirty, but dirty rooms left unattended don’t become
clean: there are many more ways for a room to be dirty than for it to be
clean. The first and second laws of thermodynamics seem to appear in so
many diverse environments that they have become part of our collective
understanding of life: the first law says you can’t win, and the second law
says that it’s not possible to break even.
Carnot, Joule, and Boltzmann came at thermodynamics from three dif-
ferent directions: the practical (Carnot), the experimental (Joule), and the
theoretical (Boltzmann). They were linked not only by their interest in
thermodynamics, but by difficult situations bordering on the tragic. Car-
not died of cholera when he was only thirty-six years old. Joule suffered
from poor health and a childhood spinal injury all his life and, though
the son of a wealthy brewer, became impoverished in his later years.
Boltzmann was a manic depressive who committed suicide because he
feared his theories would never be accepted; ironically, his work was rec-
ognized and acclaimed shortly after his death.
The Ultimate Resource
There are striking parallels between energy and money. Each is the ulti-
mate resource in its own particular arena. Money is how we evaluate and
pay for goods and services, and energy is the measure of how much effort
is necessary to produce those goods and supply those services. Just as dif-
ferent currencies can be exchanged for each other, various forms of en-
ergy can be converted into each other.
The first law of thermodynamics, as described earlier, states that there
are no free lunches in the universe—energy cannot be created from noth-
ing. Nor, and this is often ignored, can energy be destroyed, but it can be
transmuted. The second law, which addresses the transmutation of en-
ergy, also has a monetary analogue: in real life, money is never used with
perfect efficiency. There are always middlemen extracting money for
making arrangements, and nature does the same thing whenever energy
is used. Energy can never be used with perfect efficiency; this is one of
the reasons that perpetual motion machines can never be built.
Recent developments, though, have made it appear that there may be
chinks in the laws of thermodynamics. One such chink is a consequence
of a topic discussed in an earlier chapter: only gravity (of the four forces)
is capable of exerting an extra-dimensional inf luence. We can never di-
188 How Math Explains the World