Sokal found such a view abhorrent—as would most scientists, whose job
it is to investigate reality. As he put it, “I’m a stodgy old scientist who be-
lieves, naively, that there exists an external world, that there exist objec-
tive truths about that world, and that my job is to discover some of
them.”^3
Failure to pay attention to the realities of the external world has been the
cause of numerous tragedies, from Icarus to Challenger. As Richard Feyn-
man remarked during the investigation that followed the disaster that
occurred when the shuttle Challenger was launched under unsafe condi-
tions, “For a successful technology, reality must take precedence over
public relations, for Nature cannot be fooled.”^4
Among the great objective truths that we have learned about the exter-
nal world is that not all things are possible. One plus one will always
equal two, no matter whether we give 110 percent or resort to wishing on
a star^5 —because, at bottom, arithmetic is not a social or linguistic con-
struct. If we add up the numbers in our checkbook correctly and the bal-
ance is $843.76, that’s what we’ve got. Unfortunately, never more, if we
want to buy a Lexus without resorting to five years of monthly payments,
and fortunately, never less, if we want to go to dinner and a movie without
worrying that we will be thrown in debtor’s prison if we can’t pay for it.
Nature supplies us with the raw materials from which the universe is
constructed. Some of those raw materials are, well, material: the matter
from which every thing in the universe is made. Some of those raw mate-
rials are less substantial, such as energy. There are relationships between
and among the raw materials of the universe that dictate what is and
what is not possible. This was first glimpsed by the French chemist Anto-
ine-Laurent Lavoisier, who discovered that in a chemical reaction, the to-
tal mass of the products of the chemical reaction was equal to the total
mass of the substances that reacted. This result, known as the law of
conservation of mass, marked the beginning of theoretical chemistry. A
trio of nineteenth-century scientists would significantly expand upon
this result, extending to energy what Lavoisier did for matter.
The Heat Is On
In the summer of 1847, William Thomson, a young Briton, was vacation-
ing in the Alps. On a walk one day from Chamonix to Mont Blanc, he
encountered a couple so eccentric they could only be British—a man car-
rying an enormous thermometer, accompanied by a woman in a carriage.
Thomson, who was later to become one of the greatest of British scien-
tists and be granted the title Lord Kelvin, engaged the pair in conversa-
186 How Math Explains the World