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I continue quoting from Alan Lightman's, "A Modern Day Yankee In A
Connecticut Court and other essays on Science".

Conversations with Papa Joe

The Fourth Evening

"The next day I stayed home to prepare some lectures, but my heart
wasn't in it. I spent the time reading a novel instead, sitting in Papa
Joe's chair. That night the old gentleman returned as he had promised,
and wasted no time in getting to the topic of conversation.

"Now, I'm not afraid of numbers, young man," he began. "A fellow in
construction for forty years knows numbers." He paused. "But I don't
understand about equations. And I especially don't understand why you
put so much stock in them."

I got out a sheet of paper and wrote down:

C = 2 pi r

"Papa Joe, this says that the circumference of a circle equals its
radius times two, times pi, a special number close to 3.14."

"I remember that rule," my great-grandfather said.

"The real strength of equations is their logic," I said. "You start at
one point, and an equation tells you what has to come next, according
to logic. In the example here, you give the radius of any circle, and
this equation says what its circumference has to be. I think the
Babylonians or somebody figured the thing out first. They went out and
measured the radii and the circumferences of a whole bunch of circles,
of all different sizes, and gradually realized that a precise
mathematical law held every time. It saved them a lot of trouble when
they found it. Equations in science are all like this, except usually
what logically follows from the law, step by step. They give rules for
how things ought to behave."

"Does every single item in the world have an equation for how it

"Most Scientists would say yes--for the physical world, that
is--although in some cases we haven't yet figured out what the
equations are."

"So, if I understand you right, you believe that everything in nature
follows rules. Whatever the thing is, you'll eventually find an
equation for it, and it'll stand up and salute."

"But what's the alternative?" I asked. "To be constantly afraid that at
any moment houses might float off the earth, or stars might change into
wheelbarrows, or people might start talking backwards? The world we're
born into is strange enough as it is. We've got to believe that, at
bottom, nature is at least rational. Scientists might not discover all
the rules straight off, but we trust that we'll find them."

"I can see where that view might bring you some comfort," said the old
gentleman.

"What's changed in this century," I continued, "is that we don't have a
physical feeling for all of the rules we've been finding. The
Babylonians could draw their circles and measure them with string to
test their equations. Sir Isaac Newton could compare the prediction of
his law of gravity with the observed motion of the planets. But many of
the new rules deal with things we can't touch or see, and some of them
plain violate common sense."

"I gave up common sense a few evenings ago," said the old gentleman,
chuckling, "with the heavens all bursting apart and those things flying
around the earth looking at invisible light. Your new equations and
your new gadgets should be very happy together. But I still don't have
any idea of these new rules you've been talking about."

"Let me give some examples," I said. "The ones that come to mind are
from physics."

"Fine, but please hold to a slow trot, if you don't mind."

I got up to stoke the fire and pour us some tea. "In the first third of
the century," I went on, "physicists discovered a new set of rules,
brimful of equations, called quantum mechanics. Quantum mechanics
concerns the behavior of atoms, and particles even smaller than atoms.
One of the rules amounts to this: a subatomic particle can be at
several places at the same time."

"Young man, you're galloping."

"I can't help it. The difficulty is that all our experience with the
world is based on objects much larger than atoms. Golf balls and
marbles are things you can pick up with your hands. They have edges.
They stay where you put them. But as you go to smaller and smaller
sizes, matter begins behaving differently. When you get down to atoms
and smaller, your whole idea of a solid object falls apart. A particle
that size, like an electron, doesn't act like a little sphere with
sharp edges marking the boundary between itself and the rest of the
world. An electron acts like a haze, a blur covering all places it
might be at the moment. If you throw identical marbles with identical
aim at a wall, they'll all hit the wall in the same spot. But if you do
the same with electrons, they'll hit it in many different spots. That's
what the equations of quantum mechanics tell you. And those same
that have been measured and verified. So if you have faith in the
theory--and physicists these days do--then you have to accept this
slippery business with electrons. It goes against common sense, but
there it is."

The old gentleman had got up from his chair again. "I'm beginning to
get your meaning," he said. "Would you mind giving me some idea of how

"It's not much like the Babylonian method of trial and error. For many
phenomena, we'd never stumble on the right rules that way. There are
too many choices. Somehow, we've got to sniff out the trial."

I paused a moment, and Papa Joe took a deep, lingering whiff of the
aromas drifting his way from the pipe.

"Simplicity seems the best guide," I continued, "although nobody knows
why. Scientists these days are constantly searching for the fewest and
simplest rules possible. Two rules for a thing are better than three. A
short rule is better than a long one. I know I'm being vague. Let me
give an analogy. To scientists, nature is a vast game of chess. They
see the board every now and then with their experiments, study what
squares the pieces are on, and from this try to figure out the rules of
play. At first, they might guess that every piece moves one square at a
time, like a pawn. When this doesn't work, they'll try something
slightly more elaborate, and so on, but never anything more complicated
than the facts require. What's astonishing is that this kind of
approach works remarkably well. It seems that nature loves simplicity.

"Take the case of the electron," I went on. "The precise equations for
electrons were worked out by Professor Dirac fifty years ago. Now Dirac
was a theorist, a pure pencil-and-paper man. I suspect he'd never been
under the hood of a car in his life. But he had great faith in this
idea of simplicity. So for the electron, he figured out the simplest
and prettiest rules possible, consistent with the other rules he
already knew. And his rules have held up for fifty years, tested by
countless experiments. A more complicated theory would have been wrong.
Out of his theory, by the way, came an unexpected prediction of a new
kind of particle never before seen, a close cousin of the electron,
called a positron. Professor Dirac wasn't looking for positrons; they
just marched out of his equations for electrons. A few years after his
prediction, real positrons began turning up in the Lab."

"Remarkable," said Papa Joe.

"There are quite a few stories like that one. With every success,
scientists have gotten more sure of themselves. In recent years,
physicists have staked their reputations and millions of dollars
hunting subatomic particles predicted by their theories."

My great-grandfather whistled softly. "I'd hate to be ruined by a
positron that wouldn't come out of the brush," he said. "You know, I
reckon it would be easier for me to follow you if I knew more math."

"Well, I'm cutting some corners, it's true," I said. "But you've been
keeping up better than I would on something this new."

"What I admire most in these scientists," said Papa Joe, "is how
they're willing to trust their equations against common sense. I don't
believe I could follow the plans for a house that seemed upside down.
That takes faith."

"I agree. You'd want to be darn sure of your architect. And you
wouldn't move in right away." We sat for a time without talking,
listening to the faint bark of a dog down the street.

"Tell me about some other theories that seem contrary," said the old
gentleman.

"You remember the black holes from last night?"

"Yes, They were my favorites."

"Black holes were predicted by Professor Einstein's new theory of
gravity. According to the theory, if you went to live near a black hole
and then came back to earth, you'd be much younger than if you'd stayed
here. The gravity of the thing slows down time in its vicinity."

"Confound it," shouted the old gentleman. "I'll go along with your
fuzzy atoms and particles, whatever they're good for, But time is time.
A year is a year, isn't it? I must have misheard you."

"You didn't mishear me, Papa Joe, although I agree that the idea seems
preposterous. You see, Professor Einstein's theories propose that the
flow of time is not fixed, as it seems. Time depends on motion and on
gravity. The effect is tiny unless you're moving at extremely high
speeds or being pulled by a very high gravity, and that's why you don't
notice it. But sensitive instruments and clocks have verified the
effect. It's taken me years to get used to the idea."

"Now that I think of it, I remember a big commotion over one of
Einstein's predictions being proved."

I nodded. "You're probably remembering the famous experiment during the
solar eclipse of 1919. One of Einstein's theories predicted that light
should be attracted by the sun, the way a planet is. The effect is very
small, because light travels much faster than planets, but it's there
and it's measurable. To test the prediction, you examine some stars
just past the edge of the sun. According to Einstein, the starlight
should be deflected by the sun on its way to the earth, and the images
of the stars should be slightly distorted. Some astronomers did the
measurement at the first convenient eclipse, when stars could be seen
near the sun, and confirmed the effect. These days, most scientists
believe just about every prediction of Einstein's theories. even the
ones not yet proved."

"I wonder whether Professor Einstein was bothered by this odd business
with time slowing down," said Papa Joe.

"I don't think so," I replied. "From what I can tell, Einstein believed
that the new ideas were logical and natural, given certain facts. He
had this wonderful way of starting from scratch, without taking
anything for granted. And he never expected to experience all the
mysteries of nature with his body. To him, it was pleasure enough to
get a mental glimpse now and then, and imagine the rest."

As I got up to stretch, the church clock in town chimed eleven. The old
gentleman was back at his spot near the window, looking out at the
night. I joined him there. Sirius, the brightest star in the sky, was
in easy view, as well as half a dozen constellations--celestial
pictures of hunters and serpents and lions and dogs, ancient visions of
men and women looking for order.

"You know," said Papa Joe, "I believe your faith is contagious. These
last few nights I've felt so tiny I could fit inside an atom, and so
big I could step from one star to the next." He paused, staring out the
window. "I proposed to your great-grandmother on a night like this."
Papa Joe turned and took a long look around the room. "You take care of
that pipe."

I stood for a moment beside my great-grandfather, shoulder to shoulder,
and then he melted away.

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Conversations with Papa Joe appeared serially in "Science 84-86", which
was my first introduction to the writings of Alan Lightman. It was a
great joy to discover this story as one of many essays in the
collection titled, "A Modern Day Yankee In A Connecticut Court". I
chose to reproduce "Conversations with Papa Joe" over four months, in
its entirety, to treat you to a fine story--but also to a story that
teaches some very fundamental ideas about astronomy and how we do
astronomy and science. Papa Joe was certainly a likable character--a
curious man with a good head on his shoulders.

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