Dave Benson moved to Aberdeen (Scotland) to take up a 6th Century Chair of Pure Mathematics in September 2005.

The new front page is here. Please change your lookmarks and binks.

Dave Benson's home page is here
The Groups, Representations and Cohomology Preprint Archive is here
The music page is here
The DX7 page is here
The mathematics page is here
The mathematics and music page is here

Dave is being carried off to the ward for the terminally sarcastic. He expects to have a rollicking time; more fun than a human being should be allowed to have.

The latest exciting thing:
Peter J. Lu and Paul J. Steinhardt,
"Decagonal and quasi-crystalline tilings in mediæval Islamic architecture",
Science 315 (2007), 1106-1110.

The Islamic quasi-periodic tilings described in this paper predate Roger Penrose's 1974 discovery by more than 500 years.

Math problems?

Call 1-800-e^π√163

Saddam Hussein was taunted and then executed. And you tell me that taunting him was wrong?

The box said "requires Windows 98 or better" so I bought a Macintosh.

If God really wanted us to believe in him, he could go to the trouble of existing.

- Linda Smith

The A-Z of phobias.

aibohphobia: Fear of palindromes.
alephobia: Fear of the infinite.
anachrophobia: Fear of time travel.
chromophobia: Fear of Morava K-theories.
clustrophobia: Fear of cluster algebras.
cohomophobia: Feared by gays.
Deligne sesquiphobia: SGA fear and a half.
enneëkbolophobia: Fear of casting out nines.
homophobia: Fear of representable functors.
luposlipaphobia: Fear of being pursued by timber wolves around a kitchen table
    while wearing socks on a newly waxed floor. (Gary Larson)
microphobia: Fear of windows.
Möbiophobia: Fear of loss of orientation.
monophobia: Fear of injections.
Neophobia: Fear of matrix multiplication.
octophobia: Fear of the Cayley numbers.
onomatophobia: Fear of sudden occurrences of the word "bang".
phobophobia: Fear of self-reference.
sinomodulophobia: Fear of Chinese remainders.
tetragonocyclophobia: Fear of squaring the circle.
TeXnophobia: Fear of typesetting.
topophobia: Fear of the Grothendieck site.
Vennophobia: Fear of sets.
Zenophobia: 1. Fear of Buddhists; 2. Fear of convergent series.

I crashed an eighties party the other day.
It wasn't very good, it turned out that it was for people in their eighties.
Sadly, nobody noticed that I was a gate crasher.

Divorce rates in the USA (percent who have been divorced among various groups)

Born again Christians: 27%
Other Christians: 24%
Atheists, Agnostics: 21%

Source: Barna (conservative religious group) research report, Dec 1999.
Barna seem to be trying to distance themselves from this report: they have removed all traces of it from their website.

Kill the ads. I don't want ads. Get them ouda me bleedin' life. Vamoosh.

Stop Press:

Mathematician stripped of Fields Medal after testing positive for the performance enhancing drug tetrahydroconjecturone.
What gave the candidate away was the characteristic p. Read all about it in New Theorem Weekly.

Epitaph

Here lies John Dunn;
He was killed with a gun.
His name was not Dunn, but Wood.
But Wood would not rhyme with gun, Dunn would.

Microhydrodynamics: The study of the movement of small wet things.

Go here to find out what it is like to be an Arab/Muslim in the USA these days.

I may disagree with what you say, but I will defend to the death your right to mis-attribute this quote to Voltaire.

- Avram Grumer

On Thu, 18 Aug 2005, Official UGA Announcements wrote:

> Gov. Sonny Perdue invites all to join him for a prayer vigil
> and moment of silence honoring Georgia's soldiers and their
> families.  A ceremony will be held in the North Wing of the
> State Capitol from 12:30 - 1:30 p.m. today, Thursday, Aug.
> 18, 2005, with a statewide moment of silence to be observed
> from 1:00 - 1:02 p.m. today.  Flags at all state facilities
> have been lowered to half-staff for the observance.
>

Coming from the University Administration, this is unprofessional in the extreme.
I bet I won't get messages from the University of Aberdeen extolling me to pray to their gods!

What did the Buddhist say to the hot dog vendor?

"Make me one with everything."

In Scotland, an average of two people per year are killed by guns.
Of these three quarters are in the Glasgow area, which can be a bit rough in places.

In Fulton County, Georgia, an average of 400 people per year are killed by guns.

Das Ästhetische Wiesel

Ein Wiesel
saß auf einem Kiesel
inmitten Bachgeriesel.

Wißt ihr,
weshalb?

Das Mondkalb
verriet es mir
im stillen:

Das raffinier-
  te Tier
tats um des Reimes willen.

- Christian Morgenstern

Sudden prayers make God jump.

- Musrum, by Anthony Earnshaw whose father, according to Wikipedia, died before he was born. Presumably there was an accident with a contraceptive and a time machine.

Sudoku

"Sudoku" means "Number Place". So while English speakers say "Sudoku", Japanese speakers normally say "Number Place".

This fact is far more interesting than the puzzle itself, which is as tedious as a tale twice told.

Also more interesting than the puzzle is the following exercise in group theory.

Exercise: define and find the structure of the symmetry group that acts on the set of Sudoku solution grids. I can see at least 9! . 6⁸ . 2 symmetries (beware that some symmetries of the square have the same effect as suitable permutations of the rows and columns).

First, let me explain that I'm cursed
I'm a poet whose time gets reversed
  Reversed gets time
  Whose poet a I'm
Cursed I'm that explain me let, first

Nothing is so powerful as a bad idea whose moment has come

I wonder whether there will ever come a time when delivery companies realise that there are more precise measurements of time than "between 8AM and 6PM on the day of delivery".

Foundations sometimes matter

The projective dimension of C(x,y,z) as a module over C[x,y,z] is:
two if the continuum hypothesis holds and three otherwise.

(I kid you not)

My light shines in the darkness whenever I forget to switch it off 

∫ ₀¹ x⁴ (1 - x)⁴ dx / (1 + x²) = 22/7 - π

You can find a lovely story illustrating exactly what's wrong with Microsoft Word's .doc format, and how it bit Tony Blair in the rear end at http://www.computerbytesman.com/privacy/blair.htm. Serves him bloody right!

You can also go to http://www.slothmud.org/~hayward/mic_humor/nt_navy.html and find out what happened to the US Navy when it tried using Microsoft NT as the operating system aboard USS Yorktown. A divide by zero error brought the entire ship to a standstill, and it had to be towed into dock!

Motor mechanics' chat up lines (ISIHAC, 28 Jun 1999):

Those who would give up liberty for the sake of security will probably end up with neither

The Reals and Complexes

Here are some hints about why this is true: A nonzero real number has a square root if and only if it is positive, so every field homomorphism on the reals takes positive numbers to positive numbers. Therefore it preserves order. It also fixes the rationals, and is therefore the identity. [The instinctive reaction is: can't I just take √2 to - √2? But if you do that, where will you take ^₄√2?]

On the other hand, the abstract field of complex numbers is just the algebraic closure of a pure transcendental extension of the rationals of transcendence degree 2^ℵ₀. Every permutation of the transcendence basis extends to a field automorphism.

There was a young man from Dunoon
Who always ate soup with a fork.
  For he said, "Since I eat
  Neither fish, fowl nor flesh,
I should finish my dinner too quick."

Puritanism:
The haunting fear that someone, somewhere, may be happy.
(H. L. Mencken)

Last night I dreamt I had insomnia. Woke up totally exhausted, yet too well rested to go back to sleep.

Yan, tan, tethera, methera, pip;
Sethera, lethera, hovera, dovera, dick.

Yanadick, tanadick, tetheradick, metheradick, bumfit;
Yanabumfit, tanabumfit, tetherabumfit, metherabumfit, jiggot.

- Counting sheep in Cumberland; nobody in Cumberland has more than 20 sheep.
Actually more accurately, on "jiggot" you transfer a stone from one hand to the other and start again.
Presumably at the end of the process, you count the stones:
Yan, tan, tethera, ...

"Would it be too bold to imagine that, in the great length of time since the earth began to exist, perhaps millions of ages before the commencement of the history of mankind would it be too bold to imagine that all warm-blooded animals have arisen from one living filament, which the great First Cause endued with animality, with the power of acquiring new parts, attended with new propensities, directed by irritations, sensations, volitions and associations, and thus possessing the faculty of continuing to improve by its own inherent activity, and of delivering down these improvements by generation to its posterity, world without end!"

Erasmus Darwin, grandfather of Charles Darwin

"Whoever thinks his problem can be solved using cryptography doesn't understand his problem and doesn't understand cryptography."

Attributed by Roger Needham to Butler Lampson, and by Butler Lampson to Roger Needham.

If you think abortions are immoral, the remedy is simple: don't get one.

There was a young man from Dundee
Who was stung in the neck by a wasp.
  When asked, "Does it hurt?"
  He said, "No it doesn't,
It can do it again if it likes."

What's purple and commutes?
An abelian grape.

What's pink and commutes?
An abelian semi-grape.

What's yellow and equivalent to the axiom of choice?
Zorn's lemon.

What's yellow, linear, normed and complete?
A Bananach space.

Okay then, what's all the colors of the rainbow, perfectly round, and commutes up to all higher homotopies?
An E_∞ ring spectrum.

The world is divided into two classes of people:

those who say the world is divided into two classes of people, and
those who say: "The world is divided into two classes of people:

those who say the world is divided into two classes of people, and
those who say: "The world is divided into two classes of people:

those who say the world is divided into two classes of people, and
those who say: ...

The Jerusalem Artichoke is an interesting specimen.
It is neither an artichoke nor connected with Jerusalem in any way.
Reminds me of the Moral Majority.

La piccola Moffita
  S'assit un jour bien vite
  Die Süßspeise zu essen.

Es kam eine Spinne
  Which fell in her dinner,
  Und gleich war die Speise vergessen

- Jack Benson (some time in the 1930s?)

"What is conceivable can happen too,"
Said Wittgenstein, who had not dreamt of you...

- William Empson

I rather enjoyed reading the FAQ of the London Vampyre Group here, especially the email exchange in Q9. Priceless!

Umwelt schützen: Einrad benützen

Conway's Fractran

A program in Fractran consists of a finite list of fractions, the last one having denominator 1. The input is an integer, and the output is a sequence of integers. The first integer in the output sequence is the input. Thereafter, each integer in the sequence is obtained from the previous one by multiplying by the first fraction in the list that gives an integer answer. Conway proved that Fractran is a Turing machine.

To illustrate this, he wrote down the list:

17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/14, 15/2, 55/1.

This list has the property that if the input is 2, then after the first term, the powers of two that appear in the output have as their exponents the sequence of prime numbers, in ascending order: 2², 2³, 2⁵, ....

(Just for a check, the first few entries in the sequence are 2, 15, 825, 725, 1925, 2275, 425, 390, ... and the twentieth term in the sequence is 4=2²)

References:

J. H. Conway, FRACTRAN: a simple universal programming language for arithmetic, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 4-26.

R. K. Guy, Conway's prime producing machine, Math. Mag. 56 (1) (1983), 26-33.

A yak from the hills of Iraq
Met a yak that he'd known a while back.
  They went out to dine,
  And talked of Lang Syne:
"Yakkety, Yakkety-Yak!"

There's an old and somewhat time-worn palindrome that goes:
A man, a plan, a canal - Panama!

A beautiful skit on this is the following palindrome by James Lindon:
A dog, a pant - a panic in a Patna Pagoda!

The prize for the ultimate take-off, though, must go to Guy Steele:
A man, a plan, a canoe, pasta, heros, rajahs, a coloratura, maps, snipe, percale, macaroni, a gag, a banana bag, a tan, a tag, a banana bag again (or a camel), a crepe, pins, Spam, a rut, a Rolo, cash, a jar, sore hats, a peon, a canal - Panama!

Not working out with your analyst? Try a topologist.

I've been mad for farking years,
Absolutely years,
Been over the edge for yonks,
Been working me buns off for calculus students.
- Pink Floyd, Dark Side of the Moon (revised and remastered)

Me with a brain the size of a planet, and they get me
teaching calculus to undergraduates. Do you call that
job satisfaction? Because I don't.
- Marvin the Paranoid Android (revised and remastered)

   ...sì lunga tratta
di gente, ch'i' non averei creduto
che calcolo tanta n'avesse disfatta.
- Dante Alighieri (revised and remastered)

The Laws of Thermodynamics (revised and remastered):

1. You can't win.
2. You can't break even.
3. You can't get out of the game.

Question:  Find an anagram of Banach-Tarski

Answer:  Banach-Tarski-Banach-Tarski

Man tut was man kann, Mann! - Tutankhamen

There was a young fellow named Tate
Who dined with his girl at eight-eight.
  But I'd hate to relate
  What that fellow named Tate
And his tête à tête ate at eight-eight.

Forty-seven percent of adult americans think the human race was created by god in pretty much its present form some time in the last 10,000 years.
Twenty percent think the sun orbits the earth.
Seventeen percent believe the earth revolves around the sun once a day.
Fifteen percent have no health care coverage. Ouch!
Wake up, America!

René Descartes was sitting at a local tavern when the bar tender came and asked him whether he would like yet another beer. He said "I think not" and vanished in a puff of logic.

The mathematician David Hilbert noticed that a certain student had stopped attending classes. When he was told that the student had given up mathematics to become a poet, he said, "Good! He doesn't have the imagination it takes to become a mathematician."

The song of canaries
  Never varies.
And when they're molting,
  They're pretty revolting.

      - Ogden Nash

Papa Ratzi and the Spanish Inquisition!

    - Ratzinger, speech made in Parma, Italy, March 15, 1990.

Question:   Name a cardinal greater than the pope.

Answer:    2^pope

Ounce
Dice
Trice
Quartz
Quince
Sago
Serpent
Oxygen
Nitrogen
Denim

From Ounce, Dice, Trice, Alastair Reid, 1958.

An extroverted mathematician is one who looks at your shoes rather than his own when talking to you.

A terrible poet was Jenny
Her limericks weren't worth a penny.
  As prose they were sound,
  Though often she found
Whenever she tried to write any
She always had one line too many.

There was a young man from Hibernia
Who rhymed himself into a hernia.
  He became quite adept
  At the practice, except
For occasional anticlimaxes.

A limerick fan from Australia
Regarded his work as a failure
  His verses were fine
  Until the fourth line.

A limerick writer from Shrop-
shire wrote poems that tended to stop
  When they got to line three.

There was a young lady from Crewe
Whose lim'ricks would end on line two.

There was a young man from Verdun.

Let ε < 0.

Some are wise.
Others are otherwise.

"Got a light?"
"Yeah, but I keep it under a bushel."

Bring out the meatballs, Mother, we've come to a fork in the road.

Eighty-seven percent of all statistics are made up on the spot to win an argument.
Six people out of every five don't understand statistics anyway, so what's the point?

Two intuitionists are alone in a room, and one of them farts and denies it.
The other one doesn't know who did it.

Santa Cruz Students a "Credible Threat" to National Security

The Pentagon has labelled the students at UC Santa Cruz a credible threat to national security. This is apparently on the grounds that the students held a counter-recruitment demonstration because the military are breaking California state law with their anti-homosexual stance. So now the Pentagon is involved in acts of surveillance, spying and repression at UCSC, thereby destroying the very freedoms they claim to be protecting.

Bombs through Scotland

So the US thinks it can send supplies of bombs to Israel via Scotland, does it?! What an appalling cheek! Keep your dirty laundry out of here, we don't want it. It's about time Britain stopped playing lapdog to the US and got a mind of its own. (Blair, wake up - Blair, Blair, are you listening?)

A British historian was recently arrested and assaulted by police in Atlanta for jaywalking, then jailed for eight hours in filthy conditions.

It's almost that we'd prefer to believe something like this instead of the prosaic reality.

- Rowan Williams, The Archbishop of Canterbury

He was speaking of a book by Dan Brown, not about religion in general, but I wonder why he thinks reality is prosaic? Maybe he doesn't know anything about particle physics, music, homotopy theory, sporadic groups, ...

What's gelatin made of?
Boiled bones and hide of dead cows and pigs, that's what.
"Tuck into your yogurt."
"Hmmm, I don't think I can finish this."

Reminds me of a Calvin and Hobbes cartoon where Calvin asks his mom
whether they make hamburgers out of people from Hamburg.
His mom comes back with:
"Don't be disgusting. They're made of ground beef."
"You mean I'm eating a cow?"
"Yes."
"I don't think I can finish this."

What's Coca-Cola made out of?
Caramelized battery acid.
What's Diet Coke made out of, then?
Caramelized battery acid, with the nutritional value removed.

"I don't think I can finish this."

There's an interesting game, called "the ingredient game".
The rules are quite simple.
There are two players, and one is holding a prepackaged food item.
The other player's task is to guess the ingredients listed on the package.
A sure guess on many items bought in the USA is high fructose corn syrup,
which just happens to be strongly associated with type 2 diabetes.
We all knew it was in fizzy drinks, but
I've often wondered what that item is doing in the ingredients of:

bread
corn flakes
baked beans
yoghurt
crackers
peanut butter
granola bars
jam
cranberry juice
Starbucks "Frappucino"
pancake mix

"I don't think I can finish this."

You want to know how they make milk in the USA?
Because of the appalling conditions under which cows are kept,
the milk is full of cows' white blood cells (pus), as well as the
usual diet of hormones, pesticides and antibiotics.

"I don't think I can finish this."

This rant was brought to you by the Fried Okra Marketing Group of Georgia - "A wholesome dish, and pure."

Journals

It doesn't have to be like this.

The policies of Illinois Journal of Mathematics show how things can be done. This journal is not only one of the cheapest, but also have free online access whether or not you subscribe. I would have cited Annals of Mathematics in this regard if they had a better turnround time for papers.

If you work at the University of Georgia, you can find out your salary
(and that of the blighter in the office next to you) here.

Calculators

Should we be worried by Osama Bin Liner's video tape broadcasts?

WTC and the Spanish Inquisition

$f \colon X \to Y$

${^3}D_4(q)$

$M{\uparrow^G}$, $N{\downarrow_H}$

\begin{proof}
......
\begin{equation*}
......
\qedhere
\end{equation*}
\end{proof}

\reversemarginpar
\font\manual=manfnt
\newcommand{\dbendsign}{{\manual\char127}}
\newcommand{\dbend}{\marginpar{\hfill\dbendsign}} 
\newcommand{\ddbend}{\marginpar{\hfill\dbendsign\ \dbendsign}} 

\usepackage{graphicx}

\begin{center}
\includegraphics[scale=0.5]{filename.eps}
\end{center}

jpeg2ps filename.jpg > filename.eps

\begin{center}
\includegraphics[scale=0.5]{filename.jpg}
\end{center}

\iffalse
This text just doesn't appear
in the final output.
Imagine seventy-six more lines here.
\fi