Today, we learn to keep track of our money. The
University of Houston's College of Engineering
presents this series about the machines that make
our civilization run, and the people whose
ingenuity created them.

You're a medieval
businessman -- trading wool, pepper, cloth. Money
is owed you, you have debts, and it all needs to be
recorded. But there's a problem. You track it with
a diary, using Roman numerals. For arithmetic you
have only some finger-counting methods. Your
records would curl a modern accountant's hair.

We talk of many inventions on this program --
engines and airplanes, art and literature. I doubt
you ever expected to see double-entry bookkeeping
on our list, but it is a profoundly important form
of mathematics in our trade-driven world.

Alfred Crosby writes about an explosion of trade in
the High Middle Ages. No longer was European trade
a mere matter among farmers and villagers. By 1400,
after the Plague, Europe was enormously
capital-intensive -- its ships moved goods
internationally. None of that could happen without
bringing money under control.

And so there developed, according to one historian,
an atmosphere of calculation. Scholars were
learning the new mathematics of algebra -- that
game where quantities are balanced across an equal
sign -- where quantities are positive on one side
and negative on the other.

So Crosby goes looking for the invention of the new
algebra of record keeping -- the method called
double-entry bookkeeping, where we list debits on
one side and credits on the other. It's the method
marked by the absolute requirement that those two
columns sum to zero. It's the basis for tracking
all our vast financial affairs today.

He finds that, in 1300, a Florentine bookkeeper
began listing debits and receipts in different
ledgers. In 1340 a Genoese accountant listed
payouts and receipts on the left and right sides of
a single page. For two centuries, the method slowly
evolved.

Finally, another Italian, Luca Pacioli, formalized the
procedure. Pacioli grew up with the first printed
books. He became a Franciscan monk and a noted
mathematician. The year after Columbus's first
voyage, Pacioli wrote a ponderous book titled
Summa, and it included the first
printed textbook on modern accounting.

The rest of Pacioli's pretentious mathematical
summation was soon forgotten. But the section on
double-entry bookkeeping was reprinted and
translated, and it continued teaching accountants
well into the 19th century. This formal method was,
in the words of an early 16th-century accountant,
"a magic mirror in which the adept sees both
himself and others."

Crosby reminds us that it's also the mirror in
which we see ourselves today. This uncelebrated
invention -- this peculiar division of all money
into plus and minus, black and red -- is a tool
without which all the money-fueled engines of the
modern world -- would simply grind to a halt.

I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.

(Theme music)