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Welcome,
Pilgrim. My name is Salviati. I will be your guide on
the first steps of this journey through Calculus. These
lectures are all about gravitation. They tell a small part
of the long story of how our ideas about gravity developed
over the years. And in that story is the germ of the story
of Science itself, because the simple but insistent questions
we have always asked, both about the cosmos, and about an
apple falling, have been the anvil on which our best understanding
of Nature has been forged.
My teacher, Professore Galileo Galilei, was one of those
giants on whose shoulders young Isaac Newton stood when
he first glimpsed the truth about gravity. But my teacher
did not know Calculus, nor even did he use algebra as we
know it today. He preferred the geometric and synthetic
reasoning of the Greeks and followed the example of Archimedes
in all things but Science. For it can be plainly seen that
of Science and of its Method, Galileo was the first true
architect.
And so, we shall begin our studies with Galileo in the Pre-Calculus
dawn of modern science. The questions he asked and the
answers he found will not require Calculus to understand,
but they will illuminate the path before you, especially
if you make them your own questions. My Master, a Copernican
to the end, died in the very year that young Isaac was born.
He passed the torch, in his writings, to the new Prometheus,
and we hope that these very writings, his Two New Sciences
among them, will serve to kindle a desire in you to know
Calculus, and to continue with the later Lectures to follow
the footsteps of Isaac Newton through that marvelous realm.
Too often, the laws of Nature, as we come to understand
them, are presented to us as "received wisdom,"
knowledge that is somehow graven in stone. But there was
a time when those ideas were fresh and ripe with possibilities
that were not yet imagined, not even by their discoverers.
My teacher, Galileo, came of age in such a time. And he
was skeptical of the "wisdom" that had been handed
down for generations, that was held to be true knowledge,
on the basis of authority alone. Like Copernicus before
him, and Descartes and Newton after, he chose to judge for
himself what was of value in the classical scheme of thought,
and to trust his senses and his imagination to fill the
gaps. You can begin to imagine what that was like in two
ways: You may discover some of those laws for yourself,
and we will attempt to help you to do that in our labs,
our exercises, and with our questions. But you should also
read the words of the ones who found them. Those words
are a treasure that tell the adventure of these ideas in
a special way. You had to be there.
You will find a little of what my teacher, Galileo, wrote
in his book called Two New Sciences, as I have said.
It will not be easy reading, because it comes from a different
time, from a mind occupied with different questions from
the ones you are familiar with. And you will find the thoughts
of Isaac Newton, as he penned them in his Principia,
his daring manifesto and joyous celebration of perhaps the
greatest discovery ever made. That book is well worth the
trouble to explore.
Today, the wisdom of these observations, capturing as they
do some of the best thoughts we have had about gravity and
its effects, are somehow dry and almost uninteresting, like
the dessicated and departed specimens on a museum
tray. But when they were born in human imagination, these
ideas were both youthful and fragile, playful and mischievous.
They were the dreams of lofty minds that came to roost in
a world that was hardly prepared to receive them. Hear the
voices of those dreamers, the "sleepwalkers,"
who taught us the secrets of the sky. I recommend them
to you!
These lectures are also about a wonderful unification of
what had seemed to be two separate questions. How do objects
fall? And how do the Moon and the Planets move? These are
really the same question. And the history of that question
is the subject of this book. We begin to ask the first
question in this introductory chapter. The second question
will lead us, following John Kepler and Isaac Newton, to
the Calculus itself. But you will use this book best if
you read it with your own questions. You will, in many
cases, be able to test your answers for yourself in the
laboratories.
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