Babylon had in all probability the earliest written language.
At the same time, an elegant system of weights and measures kept
the peace in the marketplace. Their method of counting was in some
ways better than our present one! We look at some ancient math
tables, and ideas about Pythagoras' theorem 1,000 years before
In the ancient port city of Miletus, there took place a "discovery
of nature": philosophers tried to understand natural phenomena
without invoking the supernatural. The Greeks imported basic geometric
ideas from Egypt, and developed them further. Members of the Pythagorean
cult announced the famous theorem, and the (to them) alarming
discovery of irrational numbers! The Greeks had some ideas
about elements and atoms. Hippocrates looked for non-supernatural
causes of disease. Plato formulated a rationale for higher education,
and thought about atoms.
A brief review for moderns of facts familiar to almost everybody
in the ancient world: how the sun, moon and planets move through
the sky over the course of time.
A brief look at the beginnings of science and philosophy in Athens:
Plato's Academy and Aristotle's Lyceum. On to Aristotle's science:
"causes" in living things and inanimate matter, Aristotle's
elements, and laws of motion.
We look at some startlingly good measurements by the Greeks of
the size of the earth and the distance to the moon, and a less
successful (but correct in principle) attempt to find the distance
to the sun.
Strato understood that falling bodies pick up speed (contrary
to Aristotle's assertions). Aristarchus gave a completely correct
view of the solar system, anticipating Copernicus by 2,000 years
or so. Science flourished for centuries in Alexandria, Egypt:
Euclid, Apollonius, Hypatia and others lived there, Archimedes
studied there. Archimedes understood leverage and buoyancy, developed
military applications, approximated Pi very closely, and almost
invented calculus! (See also the next lecture.)
Nailing down the square root of 2. Zeno's paradoxes: Achilles
and the tortoise. Proving an arrow can never move - analyzing
motion, the beginning of calculus. How Archimedes calculated Pi
to impressive accuracy, squared the circle, and did an integral
to find the area of a sphere.
The universe is like an onion of crystal spheres: Plato, Eudoxus,
Aristotle. More earthly ideas: Eudoxus and Aristarchus. Understanding
planetary motion in terms of cycles and epicycles: Hipparchus
and Ptolemy. These methods were refined to the point where they
gave accurate predictions of planetary positions for centuries
(even though Ptolemy believed the earth was at rest at the center
of the universe).
Copernicus challenged Ptolemy's worldview. Evolution of the telescope.
Galileo saw mountains on the moon, and estimated their height
- the first indication that the moon was earthlike, not a perfect
ethereal sphere at all.
A few facts and anecdotes to try to give something of the flavor
of Galileo's life and times, plus references to books for those
who would like a more complete picture.
One of Galileo's most important contributions to science (and
engineering): the realization that since areas and volumes scale
differently when the size of an object is increased keeping all
proportions the same, physical properties of large objects may
be dramatically different from similar small objects, not just
scaled up versions of the same thing. We explore some of the consequences.
Galileo argued against Aristotle's assertions that falling bodies
fall at steady speeds, with heavier objects falling proportionately
faster. Galileo argued that falling bodies pick up speed at
a steady rate (until they move so fast that air resistance
becomes important). He constructed an experiment to prove his
point (and we reproduced it).
This lecture presents the core of Galileo's analysis of motion
in free fall, which he referred to as "naturally accelerated
motion". This is challenging material if you're new to it,
but crucial in progressing from an Aristotelian or medieval
worldview to that of Galileo and Newton, the basis of our modern
understanding of nature. Galileo used his new-found understanding
of falling motion to prove that a projectile follows a parabolic
path, if air resistance can be ignored.
A simple introduction to the modern way of describing motion using
arrows - "vectors" - to indicate speed and direction.
Galileo (and, later, Newton) made heavy use of Greek geometry
in analyzing motion. It's much easier, and just as valid, to use
These two colorful characters made crucial contributions to our understanding of the universe: Tycho's observations were accurate enough for Kepler to discover that the planets moved in elliptic orbits, and find some simple rules about how fast they moved. These became known as Kepler's Laws, and gave Newton the clues he needed to establish universal inverse-square gravitation.
This lecture links to more detailed lectures I gave
previously, and to a neat NASA simulation of Kepler's laws.
A brief account of Newton's life, followed by a discussion of
perhaps his most important insight: that a cannonball shot horizontally,
and fast enough, from an imagined mountaintop above the atmosphere
might orbit the earth. This tied together Galileo's understanding
of projectiles with the motion of the moon, and was the first
direct understanding (as opposed to description) of motion in
Newton's famous Laws of Motion generalized and extended Galileo's
discussion of falling objects and projectiles. Putting these laws
together with his Law of Universal Gravitation, Newton was able
to account for the observed motions of all the planets. This lecture
gives a careful development of the basic concepts underlying Newton's
Laws, in particular the tricky concept of acceleration in a moving
body that is changing direction - essential to really understanding
Aristotle thought it was infinite, Galileo tried unsuccessfully
to measure it with lanterns on hilltops, a Danish astronomer found
it first by observing Jupiter's moons. Rival Frenchmen found it
quite accurately about 1850, but a far more precise experiment
was carried out in 1879 in Annapolis, Maryland by Albert Abraham
By the late 1800's, it had been established that light was wavelike,
and in fact consisted of waving electric and magnetic fields.
These fields were thought somehow to be oscillations in a material
aether, a transparent, light yet hard substance that filled the
universe (since we see light from far away). Michelson devised
an experiment to detect the earth's motion through this aether,
and the result contributed to the development of special relativity.
Galileo had long ago observed that in a closed windowless room
below decks in a smoothly moving ship, it was impossible to do
an experiment to tell if the ship really was moving. Physicists
call this "Galilean relativity" - the laws of motion
are the same in a smoothly moving room (that is to say, one that
isn't accelerating)as in a room "at rest". Einstein
generalized the notion to include the more recently discovered
laws concerning electric and magnetic fields, and hence light.
He deduced some surprising consequences, recounted below.
The first amazing consequence of Einstein's seemingly innocuous
generalization of Galileo's observation is that time must pass
differently for observers moving relative to one another - moving
clocks run slow. We show how this comes about, and review the
experimental evidence that it really happens. We also show that
if times pass differently for different observers, lengths must
look different too.
Another essential ingredient in the relativistic brew is that
if I synchronize two clocks at opposite ends of a train I'm on,
say, they will not appear to be synchronized to someone
on the ground watching the train go by. (Of course, the discrepancy
is tiny at ordinary speeds, but becomes important for speeds comparable
to that of light).
At first sight, it seems impossible that each of two observers
can claim the other one's clock runs slow. Surely one of them
must be wrong? We give a detailed analysis to demonstrate that
this is a perfectly logically consistent situation, when one remembers
also to include effects of length contraction and of lack of synchronization
- special relativity makes perfect sense!
Some famous paradoxes raised in attempts to show that special
relativity was self-contradictory. We show how they were resolved.
An elementary review of these basic concepts in physics, placed
here for the convenience of nonscience majors who may be a little
rusty on these things, and will need them to appreciate something
of what relativity has to say about dynamics - the science of
A straight forward application of the new relativistic concepts
of time dilation, length contraction etc., reveals that if you
walk at exactly 3 m.p.h. towards the front of a train that's going
exactly 60 m.p.h., your speed relative to the ground is not 63
m.p.h. but a very tiny bit less! Again, this difference from common
sense is only detectable if one of the speeds is comparable with
that of light, but then it becomes very important.
How the very general physical principle of momentum conservation in collisions, when put together with special relativity, predicts that an object's mass increases with its speed, and how this startling prediction has been verified experimentally many times over. The increase in mass is related to the increase in kinetic energy by E = mc2. This formula turns out to be more general: any kind of energy, not just kinetic energy, is associated with a mass increase in this way. In particular, the tight binding energies of nuclei, corresponding to the energy released in nuclear weapons, can be measured simply by weighing nuclei of the elements involved.