IEEE Spectrum July, 2012 - 25

reflections

By roBert w. lucky

curiosity

A

GreG Mably

recent conversation
with a friend turned
to the wonders of GPS.
"How could we have ever
lived without it?" he asked.
I agreed, and began to
explain how GPS worked
and how the critical clock
correction was done. But
I quickly saw a blank
expression on my friend's
face, and an averting of eyes.
"You're an engineer, and
you care about things like
that," he said dismissively.
The conversation left a
strange aftertaste. Do you
have to be an engineer to
care about how things work?
Do engineers have an innate
sense of curiosity that is
largely absent elsewhere?
Shortly thereafter,
I brought up the question
with two engineering
friends. They looked at each
other with an expression
of collusion that excluded
me. "No," said one, while
the other nodded and said
in agreement, "We don't
have any special curiosity."
Nonetheless, I'm still
curious about curiosity.
This sense has always been
a powerful stimulant for
creativity and innovation.
I have a mental image of
Isaac Newton watching the
apple fall. According to a
contemporary biographer,
Newton asked himself, "Why
should that apple always
descend perpendicularly to
the ground?" Had no one
ever been curious about
this before? After all, apples
had been falling since Eve.
Newton's curiosity led
to his law of gravitation.
spectrum.ieee.org

But asking "Why?" is often
a recursive exercise, like
opening nested dolls. Two
centuries later, Einstein
asked himself why being
in an accelerating elevator
is similar to the effect of
gravity. His curiosity led
to the theory of general
relativity. And even today
physicists are curious about
gravity. How does the apple
know that Earth is pulling
it downward-or perhaps
I should ask, how does
space get warped by mass?
Recently I read something
that mentioned the Monty
Hall paradox. Some years
ago I had worked out an
explanation in my mind,
but now I had forgotten it.
I lost sleep over it-I went
to bed with my curiosity
reverberating and wasn't
satisfied until I worked it
out again the next morning.
Still wondering if there
was a curiosity meme that
I could inflict on others,
I tried the paradox on a
dozen friends. The result
of my small experiment
was that no one else had
any curiosity about it.
However, I'm not giving
up yet, and I'm about to
try it on you, dear reader.
Years ago Monty Hall
was the host of the TV
game show "Let's Make
a Deal." Contestants on
his show could win a new
car if they guessed which
of three doors it was
hidden behind. Behind
the other two doors were
goats. Presumably, they
preferred the car to a goat-
even if the show and their

local ordinances allowed
them to take a goat home.
Let's say you chose door
No. 1. Instead of directly
revealing whether you
were right, Monty, who
knew where the car was
hidden, would open one of
the other doors, say door
No. 3, to reveal a goat. Thus
the car was either hidden
behind door No. 1 or door
No. 2. So far, so good, but
then Monty would offer
you a puzzling alternative:
"Do you now want to switch
your choice?" he would ask.
Apparently, almost no
one ever switched from the
door they chose to the other
remaining one. Among the
dozen friends on whom
I tried the experiment, no
one switched. After all, it

still appears an even bet,
whether or not you switch.
Moreover, the pressure is
on, and if you switch and it
turns out that the car was
behind your original choice,
you'll feel like a goat yourself.
However, it can be shown
that switching doubles your
probability of winning.
This seems completely
counterintuitive. Surely the
probability of winning for
either of the two remaining
doors is the same. But
it isn't. When I told my
friends that they had missed
the chance of doubling
their chances of winning,
they all denied that was
the case and evinced no
subsequent curiosity.
So I wonder. Are you curious about this paradox?
o

July 2012 * IEEE SpEctrum * NA

25
http://spectrum.ieee.org
Table of Contents for the Digital Edition of IEEE Spectrum July, 2012
