Fast, Image-free, contents page for Bill Burke's website.
Ph/Ay 259 General Relativity Class Webpage
What's new. and
Last change January 11.
Note changed URL for this homepage: http://www.ucolick.org/~burke/
Temporary Address during Earthquake Retrofit: 439A Kerr
Class Material for the year
Fall: Applied Symplectic Geometry
Winter: Applied Differential Geometry
Spring: Applied Riemannian Geometry
First Meeting: Wednesday 2:00-3:10 Rm 68 Kerr Hall, not at the
time listed for Ay 259.
Postscript file for notes from last year's
class (120 pp)
Interactive 3D Diagrams
For those who have
available for their browser.
Differential forms are taking over the world.
I don't use vectors, Fortran, or Roman numerals, all for the same reasons.
Here are some resources useful for those trying to form their unformed minds.
Div Grad and Curl Are Dead
I have a draft of this completed and I am looking for volunteers to test
it out. Stop by my office. Table of Contents,
and a few sample sections.
Also an index is now available.
Differential Forms Samizdat
A reading group on differential forms.
Drawing Vectors: The Eight Icons
of a paper/section of Div Grad Curl are Dead,
giving a gentle introduction to differential forms from the standpoint
of the descriptive geometry of tensors. Hardcopy available for
perusal in my office.
Searching for Truth on the Green Felt
Here is some material on the
Physics of Pool
Want to understand egyptology? Consider
PH 109 in the winter quarter. And see below.
Do Try This At Home
Immerse a light bulb in a round jar of water. Look at how thick
the glass envelope appears to be.
Available in my office.
Thanks to Jeff Wilkinson for showing me this.
Want to know more? Take my Ph 109 Optics in the spring.
The Geometry of Perfect Phase
Dispersive Wave Packet Dynamics
Here is some material that supplements my Non-Linear Lecture in the
Mathematica Code for Wave Diagrams.
Here is a picture of the pattern of waves behind a moving boat.
The shading indicates the amplitude with a logarithmic scale.
Kelvin Ship Waves Pattern
and see next:
Large Scale Structure in Random Noise
The Ring Spectrum Puzzle
A random function with applications to cosmology, quantum chaos,
radio astronomy, oceanography, and so on: Gaussian random function
with a power spectrum confined to a ring in two dimensional frequency
space. Here is a
and two magnifications by factors of four
of such a random function. The long range order is interesting
and not explained. A large poster of this function is on my office wall.
This winter I would like to make my class in Applied Differential Geometry
available over the net. At present I am trying to collect the resources
that would be useful for this; in particular, the transmission of
graphical information is a thorny issue. I would like to be able to
transmit "live" pictures rather than just dead PostScript. Except for
the expense, mathematica notebooks would be one such "live" graphical
format, although the platform independence leaves something to be desired
as well. If you have any thought on this I would be delighted to receive
email from you.
The idea would be to do this "without adult supervision." If telefolk
wanted credit, say as an independent study, for the class,
this is something they would have to arrange
with their local university. I would be willing only to provide
a minimal letter of evaluation for their electronic submissions to the
This first attempt will be orgainized as an email mailing list, which
I will call the
Differential Forms Samizdat.
Random Dot Stereograms
Stop by and chat if you are interested in making these. One of mine
with heavy aliasing is attached:
explanatory text and
Where is GO played in Santa Cruz?
Saturn Cafe Tuesday and Thursday 8 to midnight
Santa Cruz GO Club 684-2433
The Interval Game
Recently developed at a party given by Mike Beeson.
Two players each compete to acquire a larger part of the unit interval.
Each player claims a connected subinterval of the unit interval. Parts
claimed by only one player are awarded to the player. Parts claimed
by both are awarded to the player with the least greed, who claimed the
This was developed to model scientific measurement, in which both
accuracy and precision were to be rewarded. It is only vaguely relevant
to that in its present form.
Example: If Alice claims the entire interval and Bob claims (1/8,7/8), then
since Bob was the least greedy, he gets 3/4 of the interval, while
Alice gets the remaining 1/4. Bob wins.
There is no pure winning strategy, but I think there is a mixed strategy.
The three person game is wide open, and may not even be soluble over
You are in the hall outside a room with a closed door. There are
three light switches in the hall connected to three light bulbs
in the room, one to each light bulb. Switch up = light bulb on,
switch down = light bulb off. You are allowed to manipulate the
switches, THEN open the door and go into the room, but not
come out again (hence you can't touch the switches after entering
the room). Problem: How can you determine which of the three
switches controls which light bulb?
Normal puzzle assumptions apply, e.g. you are not allowed to
take the switches apart and fiddle with the wiring, etc.
- Computing is full of second-rate physicists.__R.W. Hamming, quoted by
- Hands down, man's best friend is the goose.__WLB
- The most significant event of the 19th century will be judged as
Maxwell's discovery of the laws of electrodynamics. The American Civil War
will pale into provincial insignificance in comparison with this
important scientific event of the same decade.__R.P.Feynman
- The early worm gets the bird. __WLB
- Go is to chess as philosophy is to double entry bookkeeping. __Shibumi
- Man must sit with mouth open for a very long time before
roast duck flies in. __Chinese Proverb
- If you haven't found something strange during the day, it hasn't
been much of a day. __John Archibald Wheeler