Boltzmann, the architect of statistical mechanics, who realized that when
one talks about order and disorder, about the number of microstates associ-
ated with a given macrostate, the concepts being discussed related to the
information one had about the system. Let’s look again at the example of
the loafers and sneakers above. The most ordered macrostate is the one
where every shoe is in its correct box, the least ordered one is the one where
no pair of shoes is in its correct box, and the number of microstates corre-
sponding to each varies inversely with the precision with which we can lo-
cate the shoes if all we know is the macrostate.
The more microstates that are associated with a given macrostate, the
less we are able to say with precision about the individual components of
the system. When we know that both pairs of shoes are in the correct box,
we know with certainty where the left loafer is. By checking the table on
pages 193–194, if we know that only one pair of shoes is in the correct
box, the left loafer is in the loafer box in 4 out of 6 microstates—a proba-
bility of 2/3. However, if no pair of shoes is in the correct box, the left
loafer is in the loafer box in only 3 of the 9 microstates, a probability of
1/3. This analysis is typical; as entropy increases, the information that we
have about the system decreases. Since the second law of thermodynam-
ics tells us that entropy is on the rise in the universe as a whole, the inexo-
rable progress of time is increasing what we cannot know. The heat death
of the universe is also an information death; the universe is tending to-
ward a state in which there is nothing left to do, and very little of a physi-
cal nature to know.
This is the exact opposite of what our everyday experience tells us. Every
day science gathers more and more information about the universe
around us; but that is because entropy is still capable of suffering local
defeats. There is still lots of information to be gathered, and there will be
into the far distant future. But even as we are greedily sucking up expo-
nentially more information, in the far, far, far distant future we will head
inexorably toward a universe in which we cannot know almost anything,
because there will be almost nothing to know.
Black Holes, Entropy, and the Death of Information
As science progresses, many of its important ideas traverse a common
path. The first stage is the formulation of a hypothetical construct (the
Sokal article now has me using that term), an object whose existence ex-
plains certain phenomena. The next stage is indirect confirmation; experi-
ments or observations suggest that the construct does indeed exist. Finally,
we hit the jackpot, a direct observation of the object under consideration.The Raw Materials 195