C4| Saturday/Sunday, April 4 - 5, 2020 **** THE WALL STREET JOURNAL.
ThePowerof
Exponential
Growth
EVERYDAYMATH
EUGENIA CHENG
TOMASZ WALENTA
FIGHTING A PAN-
DEMIClike Covid-19
requires experts in
many fields: epidemi-
ologists who study
the spread of disease, doctors who
treat the sick, scientists who work
on finding a vaccine. There is math
involved in all of these specialties,
but math can also help us to make
sense of the barrage of information
that we’re receiving daily.
The starting point is the math
of exponential growth. The word
“exponential” is sometimes used
informally to mean “really fast,”
but mathematically it means
something very specific: that a
quantity is repeatedly multiplied
by the same number. When a vi-
rus spreads, each infected person
goes on to infect a certain number
of other people, on average; this
is called the reproduction number
or R0. Then each newly infected
person goes on to infect R0 peo-
ple, again on average.
Exponential growth is danger-
ous, because if each person infects
more than one other person, the
spread of disease quickly becomes
overwhelming. Multiplying by 3,
for instance, it only takes 21 steps
to reach 10 billion, more than the
current population of the world.
We start with very low numbers
that seem insignificant, but it’s
not the absolute numbers that
matter, it’s the rate at which
they’re increasing, which also in-
creases exponentially. Waiting un-
til an infectious disease feels like
a problem is too late to start ad-
dressing it.
One important feature of expo-
nential growth is that it’s not help-
ful to look at the number of new
cases each day. Exponentials in-
crease by multiplication, so it’s
more relevant to look at the per-
centage increase each day. This is
what “flattening the curve” is
about: reducing the rate of multi-
plication. Eventually we need the
rate to be less than one, so that
each infected person infects fewer
than one new person, producing
exponential decay instead of
growth.Contrary to optimistic hopes,
there is no guarantee that the coro-
navirus will just peter out on its
own—at least, not until so much of
the population is already infected
that there’s simply a lack of new
people to infect. That is the worst
case scenario. The aim of interven-
tionistoreduceR0beforethat.
While experts seek a vaccine, the
best thing we can do is reduce the
amount of contact we have with
others. That is the point of staying
at home and trying to reduce the
chance of infection if we do go
out—by washing our hands fre-
quently, keeping a distance from
other people and wearing a mask
(ideally homemade, so as not to de-
prive medical professionals of
masks). We don’t know how much
any of these things reduces R0, but
they definitely do reduce it, and
any decrease in R0 helps even if it
remains above 1.
Math can’t accurately predict
the future of the Covid-19 pan-
demic, partly because we don’t
have accurate data about the true
number of infections and partly be-
cause so much beyond math is in-
volved. We can’t predict how hu-
man beings will behave, nor can we
quantify how much difference that
makes. There is a range of possible
outcomes, and the one that we end
up with is almost certain to be bet-
ter than the projected worst-case
scenario—that’s the whole point of
a worst-case scenario. How much
better depends in part on our be-
havior, and our behavior should
take the math of exponentials into
account.REVIEW
BYAUGUSTINESEDGEWICKLeft, a poster for a German
cafe, 1910s. Right, an ad
with a woman drinking
coffee over a landscape of
Rio de Janeiro, circa 1900.A man cupping coffee
beans in Ethiopia.concluded that caffeine increased
the body’s capacity for muscle or
cognitive work within 15 minutes
of consumption.
Prescott’s lasting contribution
was to rebrand coffee’s apparent
contradiction—generating work
without calories, output without
input—as a kind of miracle. Coffee
was better than food, he con-
cluded: a form of instant energy, a
work drug not subject to the limits
of appetite and the delays of di-
gestion. The implication was that
the human body on coffee was lib-
erated from the laws of energy
consumption and expenditure that
governed the rest of the universe.
Based on these findings, the coffee
planters and roasters began to
push a novel proposal: a pause in
the workday for coffee, especially
late in the afternoon.
After five centuries, we stillhave questions about coffee, but we
agree on what we need it to do.
Most of us drink coffee not because
we have a finely calibrated under-
standing of its role in blocking the
adenosine that makes us feel tired
and increasing the dopamine that
makes us feel good. Instead, we
drink coffee because we
have adopted (in part
from the coffee business
itself) a way of under-
standing ourselves and
the world that makes it
look like a godsend when
we have no choice but to
keep working—or even
the fulfillment, for a mo-
ment, of our bottomless
desire for more ideas,
more talk, more energy,
more time, more life.Prof. Sedgewick teaches
history and American
studies at the City Uni-
versity of New York. His
new book, “Coffeeland:
One Man’s Dark Empire
and the Making of Our
Favorite Drug,” will be
published on April 7 by
Penguin Press.C
offee is so ubiquitous
that it’s easy to for-
get how unusual it is.
Its defining, name-
sake ingredient, caf-
feine, is not only the world’s most
popular mind-altering drug—used
regularly by perhaps 90% of the
planet—but also, as Michael Pollan
has noted, the only one we rou-
tinely serve to children. This nearly
universal acceptance is all the more
striking considering that, for much
of its 500-year history, coffee
drinking was viewed with confu-
sion, suspicion and disgust.
What changed? Once used to
fuel extraordinary acts of worship
and creativity, coffee has become a
necessity we rely on to meet the
everyday demands of modern cap-
italism.
Coffee is native to Ethiopia, but
Sufi monks in Yemen seem to have
been the first to consume the
brewed form, probably in the 15th
century. According to many ety-
mologies, “coffee” is derived from
the Arabic wordqahwah, which
carried several meanings, includ-
ing “to make unappealing,” “dark”
and “wine.”
This raised some early ques-
tions. In 1511, officials in Mecca,
suspicious of the drink’s intoxicat-
ing effects, decreed a coffee ban.
Police torched the city’s supplies,
but that hardly settled the matter.
A century later, around the time
that European travelers recorded
their first encounters with coffee,
the beverage was so widespread in
the Ottoman Empire that, accord-
ing to the scholar Markman Ellis, it
appeared “the perfect symbol of Is-
lam.” Marked with foreignness, cof-
fee entered Europe through a scrim
of prejudice. In 1610, the British
poet George Sandys judged it
“blacke as soote, and tasting not
much unlike it.”
Like alcohol, coffee changed
people who drank it, but there was
no consensus on how. Some women
in London claimed that it made
men impotent and lazy, but the
city’s employers disagreed. Morn-
ing draughts of ale rendered ap-
prentices and clerks “unfit for busi-
ness,” but coffee helped them “play
the good-fellows,” wrote court his-
torian James Howell in 1657.
Europeans didn’t understand
why. The medical thinking of the
age emphasized balancing the
body’s four humors—blood,
phlegm, black bile and yellow
bile—by using foods as drugs.
Foods were classified within one of
four prescriptive categories: hot,
cold, wet and dry. Yet coffee, along
with tea and chocolate, didn’t fit
neatly into any one quadrant. It
was hot and stimulating but also
cooling and diuretic, confounding
ideas of the human body that had
been fixed for 1,500 years.
The picture wasn’t clarified by
the chemical isolation of caffeine
in a German laboratory in 1819.
“Coffee acts on the diaphragm and
the solar plexus, where it spreads
to the brain via immeasurable em-
anations that escape all analysis,”
Honoré de Balzac wrote 20 years
later. “However, we can presume it
is the fluids of the nervous system
that conduct the electricity which
this substance releases, and which
it either finds or stimulates in our
bodies.” Balzac himself drank cof-
fee in prodigious quantities as he
wrote his nearly 100 novels. By
some accounts, he
downed 50 cups a day,
exacerbating his heart
disease.
Balzac died in 1850,
but if he had lived just
a few more years, he
might have seen a
breakthrough. A new
concept of the body was
then emerging in the
West to take the place
of the humoral system,
one based not on the
balance of fluids but on
cycles of input and out-
put. The analogy was
no longer a scale but an
engine.
The crux of this shift
was the discovery, in
part through analysis of
steam engines, of en-
ergy: the overarching
force unifying what had
been thought of as dis-
crete phenomena, in-
cluding motion, heat
and light. The first law
of thermodynamics,
stating that energy is
neither created nor destroyed but
rather converted from one form to
another, posed a fundamental
question: Were human beings ex-
ceptional creatures, or did theyoperate on the same principles as
machines? Hermann von Helm-
holtz, commonly credited as the
author of the first law, suspected
the latter.
By 1900, the new science of nu-
trition had applied thermodynam-
ics to human physiology via the
calorie, a unit of measure that ex-
pressed the needs and abilities of
the body in common terms—in-
puts and outputs, food and work.
On its own, the calorie didn’t re-
solve questions about coffee,
which contains very few calories
per cup. But the calorie did pro-vide a stable framework for under-
standing coffee’s physiological ef-
fects since it made work look like
the basic function and natural con-
dition of a living body, much like
an engine. This ascendant biology
of drudgery informed a new con-
sensus on coffee: It was lubricant
for the “human machine.”
That idea was translated into
advertising in the 1920s. Brazilian
coffee growers and American cof-
fee roasters cosponsored research
to contest the claims of John Har-
vey Kellogg and C.W. Post, who,
peddling trademark breakfast sta-
ples of their own,
blamed coffee for an
American epidemic of
enervation and frailty.
Samuel Prescott, an
MIT biology professor,
ran the study from 1919
to 1923, drawing heav-
ily on earlier research
funded by the Coca-
Cola Company whichFor much of its 500-year history, drinking
the beverage was viewed with confusion,
suspicion and disgust.How Coffee
Became
A Modern
Necessity
‘Coffee...
spreads to the
brain via
immeasurable
emanations
that escape all
analysis.’
HONORÉDEBALZACGETTY IMAGES (3)