Obituary Notice

Fast, Image-free, contents page for Bill Burke's website.

Ph/Ay 259 General Relativity Class Webpage

What's new. and What's history. Last change January 11.
Note changed URL for this homepage:

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 Geomview available for their browser.

Differential Forms

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

Rough draft 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.

16-Body Problem

Searching for Truth on the Green Felt

Here is some material on the Physics of Pool

Fourier Optics

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. Explain. 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 fall quarter: 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 sample, 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 class group.

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 picture.

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 smallest interval.

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 the reals.

Notable Puzzle:

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.


Notable Quotes:

Notable Sites: