The Sayings of Chairman Pratt

As collected over the years by recording secretary Alan Dratious.

1. Epigrams

2. Politics

3. Technicalities

4. Philosophy

5. Poetry

1. Epigrams

Weather and climate are like gamblers and casino operators. Weather changes from day to day, like a gambler's ups and downs. Climate is longer term, like the monthly returns of operating a casino. Weather is hard to predict, climate is a lot more predictable. But even some casino operators unexpectedly fall on hard times.

Don't shoot the messenger. Exception: spam.

The difference between logic and mathematics is that in logic a proof is a mathematical object, whereas in mathematics it is a rhetorical device. All rhetoric pays at least lip service to consistency, but it is a sine qua non for the mathematician's variety.

Since "sesquipedalian" means "one and a half feet long" and a cubit is exactly that, how come no one's ever made the connection between the two?

If you don't like your town's pooper scooper law for dogs, imagine if they had one for cars. Even with your engine at 100% efficiency your exhaust emits 194 lbs of CO₂ as it burns through a 10 gallon tank of gas, more than the weight of the gasoline itself due to the oxygen added to the carbon by the burning process. CO₂ weighs about 1.53 times as much as air and so although some of that weight would be buoyed up by the displaced air, that still leaves a hefty 194 − 194/1.53 = 67 lbs pulling it down to the ground. Imagine having to carry a bag of that to a disposal facility after each fill-up. Dogs got nothing on cars.

In the beginning God worked for six days and rested on the seventh. Now it's the other way round.

Clarke's first law of prediction, short form: Any sufficiently difficult goal is easier to prove impossible than possible.

Einstein's thesis advisor Alfred Kleiner rejected Einstein's thesis as too short. Einstein added a sentence, resubmitted it, and Kleiner accepted it. Moral: don't take rejection as a sign of rejection.

Social structure is all about lawn ornaments. The proletariat seek to improve their lot so they can afford them. The bourgeoisie spread them around ostentatiously. And the intelligentsia decry the moral decay they bring about.

The Stanford Computer Science Department just met today to review and approve the latest syllabus revision. When it began over four decades ago computer science was not rocket science. The difficulty of fitting the new curriculum into four years made it clear that today rocket science is not computer science.

It used to be that on the Internet no one could tell you're a dog. Now they can target dog food ads to dogs.

Good science speaks for itself, bad science has to be defended by its perpetrators.

The self-evident is merely a hypothesis that is so convenient, and that has been assumed for so long, that we can no longer imagine it false.

Alice: I read that green tea can repair damaged brain cells.
      Bob: Why would I want to repair my old ones when my new ones can come up with such snappy comebacks?

Who said seeing is believing? When I look around I see that the earth is flat, nature abhors a vacuum, and time abhors the improbable. Yet I am persuaded that the earth is round, the universe largely vacuum, and life the improbable product of time. Persuading is believing.

Any sufficiently advanced mathematics is indistinguishable from gibberish. I went into technology because I didn't know anyone who preferred gibberish to magic.

Unlike mathematics, science and engineering are defined by their relationship to nature. While the scientist examines her minutely, the engineer exploits her passionately. It's too bad we can't ask her whether she appreciates either.

The rich may have a better home than the poor but not a better god.

Old dogs that can't learn new tricks but pronounce authoritatively on them anyway are speed bumps on the highway of knowledge.

Love is the mutual trust, respect, and understanding that keeps us from seeing each other as feral. To a feral cat, every human is feral.

Life is the opportunity to do something. Time enough to be somebody when you're dead.

All knowledge resides in the going odds. The odds improve as more people buy the proof.

The only thing we have to fear is the Homeland Security threat level itself.

Freewill or determinism? Surely both. Science is determined, scientists can only discover it. The engineers' inventions are the product of their own free will.

What is truth? Truth is a matter of opinion subject to review. The reviewers will take a hard look at the claim and a dim view of any sloppy thinking.

When you're the only one making sense, chances are no one else understands you. By all means stick to your guns, but just in case hedge your bets with a recalibration or two.

What is truth, if not just what we learn from proof? Proof is when your therapist confronts you with your demons. Truth is when they confront you themselves.

Silicon Valley was built by optimists. But behind every successful optimist is a pragmatic pessimist. The unsuccessful optimist has a rabid pessimist in front blocking the path.

Does my body love me, or is it just using me for food?

A fallacy is worth a thousand steps.

Time flies when you're getting old, whether or not you're having fun.

F1 is for students, H1 is in between.
     Damn the INS, it's not easy to be green.

Only is a contrarian. Optimists see the glass as only half-empty, pessimists as only half-full.

An itsy dent is only an incident when the car is new.

There exist fringe peer groups, but I'm not terribly sympathetic to these unless they include members who argue soundly, distinguish reliably between sound and unsound reasoning in the proofs of others, recognize and acknowledge any compelling alternatives to their viewpoint, and communicate articulately. Debate is easier for the majority, who can play the "as everyone knows" card whenever no better argument comes to mind.

Better those shivering by the warm pool jump in than that you bring the water to them in a bucket.

I'm not a lawyer, though I play one when arguing.

Live life one birthday at a time.

In means-end analysis, determinism serves the former, free will the latter.

Courting by going out to dinner is like playing chess: check, check, check, mate.

Who, me? Don't be ridiculous, I'm not argumentative.

The past is determined, and it has determined us.
    We are free to will the future, which is nondeterminous.

Teacher: Suppose x is the number of sheep in the problem.
Alec: But sir, suppose x is not the number of sheep.
Teacher: Good point. Let's each of us handle the case we brought up and see who finishes first.
(Corollary to a joke repeated in Littlewood's Miscellany.)

Do not confuse Boolean algebra with propositional calculus. One can translate between them even better than between French and German. But whereas Boolean algebra has all the moral ambiguity of film noir in according equal status to 0 and 1, propositional calculus is like your parents, demanding the truth and railing against falsehood.

Nature said, "I must set off my green jungle nicely," and painted the sky blue. Man said, "blue and green should never be seen," and made the jungle concrete.

Our two eyes see one world, our third eye sees two minds.

No analogy is exact or it would not be an analogy. To emphasize the dissimilarities in an analogy over its similarities is to deny analogy itself.

I don't understand this argument about evolution being false just because God didn't tell us about it in the bible. God didn't tell us about DNA either, and for good reason: we weren't ready for those details of his creation then. Now we are.

The electron is a genie that will only answer three questions. Its exact trajectory is given by the answers to six questions concerning its position and momentum in each of three axes, but the electron will only swear to tell the whole truth about one per axis. If you request its position and momentum in the same axis it will invoke the Heisenberg uncertainty principle and lie a little about both.

Headlines: the last refuge of the bad pun.

He who dies with the most birthdays wins.

Cryptographic security: safety in numbers.

My mind does terrible things to my waist.

I neither believe nor disbelieve the logical principle of excluded middle.

Today is not the best day to be doing what you should have done yesterday, but it's the best one that's left.

An erudite word is good to find.

When the can you've just opened has more worms than you can count, take another can.

Some day I'm going to shoot a movie. Only as a mercy killing mind you.

"Eureka" — Greek for "Oops, forgot my bathrobe again."

Quantum mechanics is true, I tell you, pay no attention to Einstein. We play dice, and are made in God's image, therefore God plays dice.

If you don't get it, don't sweat it.

Facts don't beg questions, questions beg questions. Facts just make it easier for questions to beg questions.

The Poet: Nothing rhymes with orange.
   The Logician: Orange rhymes with orange.
   The Logician-Poet: Nothing rhymes with nothing.

There is indeed a strong correlation between axioms and theorems, the only question is the direction of the arrow of causality. Logicians like to orient it from axioms to theorems. Mathematicians know better.

Deadlines: can't live with them, can't live without them.

God made only the positive numbers, zero was already there when he arrived.

Contacts: glasses with wipers.

For it has been said, judge not lest ye be judged. But I say unto you, judge lest ye lose the way.

Waiter, another kettle of fish, please.

Me: My brain must be out of its mind.
   My mind: I wish I'd said that.
   My brain: Ha, beat you to it again!

Education is not the same thing as training. If it were, schools would not be offering sex education.

My mind and my body keep playing tricks on each other. When I tell them to cut it out, they just say "Who are you?"

Thank goodness one of us is on the same page.

One of life's little challenges is constructively criticizing the ostensibly insane.

I wish I were a car burglar. Then I'd know how to avoid setting off my car burglar alarm.

Inlaws: can't live with them, can't get married without them. Even if it takes two weddings for the one marriage. (This was the recent fate of the brother of a coworker of mine: after getting married in Las Vegas his in-laws in India insisted on a proper wedding there.)

Alice: One can't make an omelette without breaking eggs, but the diner shouldn't have to pick out the shells.
   Bob: I'd be ok with the occasional bit of shell if that were the only extra price for twice as much omelette.
   Alice: That's the difference between a gourmet and a gourmand.

Logic separates by connecting: it separates the true from the false by connecting the conclusion to its premises.

A market correction does for investors what a correctional facility does for felons: it gives them time to reflect on their greed and bad judgment.

I was raised to be rigorous, not formal.

The square of the leech is the sum of the squares of the luff and the foot.

Negligence: the attitude to be worn with a negligee.

Bob: Did you notice that i and −i can be switched in the complex plane?
   Alice: Right, in fact if they turned it round 90 degrees it would have bilateral symmetry.
   Bob: Oh, so you'd have the two i's on either side. How appropriate.
   Alice: Yes, and the origin for the nose and −1 as a crooked grin.

Monotone functions respect order, group homomorphisms respect the group operation, linear transformations respect linear combinations, and the underworld respects membership in the Cosa Nostra, but what morphism has ever respected membership in a set? It is sheer hubris for a relation that can't get no respect to claim to support all of mathematics.
(Old argument of category theorist Mike Barr, new polemics.)

Google respects words like ``the", which is very helpful in searches for technical subjects such as ``the screw calculus.'' Try omitting ``the.'' (Some time after this was first posted, Google greatly increased the percentage of hits returning the technical meaning in the absence of ``the.'')

Experimentalist: "Theorist, prove thyself."
   Theorist: "Your proof is in the pudding, sir. Ours is but to reason why."

Alice: Pretty green terrorist if he couldn't get his belt to blow up.
   Bob: Green? I thought a green terrorist was one who insisted on recycled virgins.

Second only to how to lose weight is advice on how to save time. For that I have a simple answer: don't blog.

Some say that our mind is just a part of our body, but I say that you and I can be of one mind that John Kerry is of two minds. Try doing that with a body. (Or whichever hapless Democrat is next faulted by the Republicans for that sort of thing — before Kerry it was Clinton. Update 2008: switch "Republican" and "Democrat.")

Don't fix what's not broken. And don't tweak till you're twoken to.

Tom: Computers are just zeros and ones, so if you know zero about computers you're halfway there already.
   Dick: Even more than halfway, since there tend to be more zeros than ones.
   Harry: Oh, come on, if there were a million zeros for every one it would be obvious that mastery of computers involved understanding the ones.

Composition being an associative operation, what better way to realize a compositional architecture than with associative memories?

I thought computers were supposed to use Boolean logic. Mine just said "Your printer job was not unlinked." (Unlike intuitionistic logic, Boolean logic cancels double negatives; thus a computer based on Boolean logic should have rendered this as "Your printer job is (still) linked.")

DANGER: RADIATION HAZARD. This car's radiator can burn your hand.

T = Am where T is the time, in natural units, from the big bang to when the universe, by then having acquired mass m, collapses to a black hole of surface area A. Using seminatural units this relationship becomes T = 2Am, which is when I dreamed it up, and in hexanatural units T = 6Am, which is when it dawned on me.

2. Politics

Goat Busters

Dan Aykroyd is everyone's favorite ghost buster. But ghosts are for frightening kids, you can't frighten an adult with a ghost these days. For that you need need not ghosts but goats! Scapegoats, that is.

Four things in life are certain: death, taxes, problems, and haters. We eventually die, the government takes its cut, things go wrong, and some people are born to hate. When you pair up death and taxes you get the estate tax, for many a much bigger chunk of change than their annual income tax. And when you pair up problems and haters you get scapegoats.

Scapegoats work as follow. A hater with a sufficiently strong dislike of some group finds a plausible problem to blame on them and fabricates two piles of evidence: that the problem is far more serious than we'd realized, and that the group is the cause of this dreadful problem. Armed with these two stories the hater goes into business as: the goat buster! Who you gonna call?

The best goat busters are those skilled in the art of story telling. Weave a sufficiently compelling story about the problem and its cause and a good goat buster can inflame the passions of millions.

Goat busting has been practiced for thousands of years. Some instances have had consequences so horrific that it has become tactless to make comparisons with them. Recent examples that can be decently compared with each other include the following. The most famous comparison is of course between the first two, but the goat busters' modus operandi is the same in all cases.

In all of these cases many succumbed to the goat buster's stories at first, but as time went by more and more came to realize that their panic button was being pushed with fabricated stories.

Every threat is plausible for a while, but eventually loses its hold on our imagination and the goat busters have to find a new one to frighten, entertain, or annoy us according to our gullibility.

Goat busting has been a popular pastime for many centuries. Expect many more centuries of the same. There will always be new threats when the old ones wear out, and new suckers to be taken in by them as the old ones wise up to the goat busters' tricks.

The Reade Court Decision

The US routinely deports illegal immigrants without a proper trial. Since they don't have the right to live here this can hardly be called a violation of their civil rights. But that's not the same thing as having no civil rights at all. Prior to their deportation illegal immigrants have the same civil rights as legal immigrants and citizens. For example we can't kill them, or beat them up, or sentence them to a jail term without due process, merely on the ground that they're here illegally.

Justice Linda Reade has just sentenced 270 illegal immigrants to five months jail while denying them access to immigration lawyers, on the patently absurd ground that "The immigration lawyers do not understand the federal criminal process as it relates to immigration charges." She did allow a handful of court-appointed lawyers to represent them, but one fundamental civil right is the right to choose who will defend you. Any court denying that right is a kangaroo court. We often complain that other countries don't play by their own civil rights rules, but when we don't play by our own rules we can hardly complain about others who don't.

The US can plunge Iraq into civil chaos by withdrawing, or create economic chaos at home by staying. In advocating the latter Bush and McCain seem to think that the way to beat suicide bombers is with a suicide economy.

Geraldine Ferraro: Folks, you've been giving Obama extra points because he's black. This is racist. If you split them between him and my white friend here you won't be racist.
(Ferraro said that Obama is lucky to be black, and that he would not be where he is today if he were a white man or a woman. She insults Obama when she implies that his color rather than his talents got him to where he is today, she insults Americans when she accuses them of selecting their leaders on the basis of their race rather than their merits, and she insults everyone's intelligence when she refuses point blank to acknowledge that she insulted anyone.)

The staggering hypocrisy of Spitzer's program to round up prostitute patrons surely renders this ancient profession one of its greatest boosts in the past millennium or three. Spitzer's revulsion with payment for sexual services is distinguishable from Marx's revulsion with capitalist profiteering only in that Marx did not profit from capitalism. The attacks on prostitution down the ages are nothing but opportunistic prudery. The real victims here are those who are coerced into the trade, whose tragedy is only aggravated by the crude and ineffective attempts to stop the trade instead of the coercion.

Civilization approximates reality, and the government is its dominant error term.

The difference between Democrats and Republicans is that there's not a single Ann Coulter among those Democrats hoping to undermine Obama's candidacy. Coulter wouldn't pussyfoot around with hints that Obama might be Muslim, or that he once neglected to affirm Israel's right to exist, she'd come right out and say that Obama worships Satan, or to reach even more of the susceptible, that he is Satan.

Ralph Nader is a carmudgeon. Andrew Burnett is a curmudgeon.

The US government is defined by the relationship of its branches to the law. The judicial branch upholds the law by separating fact from fiction. The legislative branch holds up the law by generating friction from faction. And the executive branch defies both fact and faction by operating above the law.

Huckabee, 2/9/08: "I didn't major in math. I majored in miracles, and I still believe in them, too."
Might as well be frank, monsieur, it would take a miracle to get you into the White House, and the Democrats have outlawed miracles.

When paying for Iraq, it's hard for every dollar to count when they're surrounded by uncountably many.

Hartwig, Louisiana home insurers group: An insurer that is financially weak or insolvent is no use to anybody.
   Katrina victims: Your nonpayment enriches you by billions while crippling your customers financially.
   How does making your customers no use to anybody make you of use to anybody but yourselves?

Bush: Congress should not try to run the war.
   Congress: We don't want to run your war, we're just running out of money to keep funding it.

President Bush: The American people have got to understand the program is important and the techniques used are within the law.
The American people: Continuing to appoint attorneys-general who have no problem with procedures that almost all other countries view as abusive of human rights does not help the US maintain its standing as a pillar of the civilized world.

Ever-trendy California makes its move on the confession extraction business:

The US (vis a vis the Geneva Convention): We know you did it, confess or this is going to hurt.
California, vis a vis Schwarzenegger on Tookie Williams: We know you did it, confess or die.

("Is Williams's redemption complete and sincere, or is it just a hollow promise? Without an apology and atonement for these senseless and brutal killings, there can be no redemption." Arnold Schwarzenegger, in a written denial of clemency for Stanley Tookie Williams. Williams felt justice had been served in a roundabout way for his other crimes, while however maintaining to the end his innocence of the murders he was sentenced for.)

The alien meddling theory: Abraham Lincoln and George W. Bush are both Republicans, explained by the many UFO sightings during the 20th century.

3. Technicalities

Another variant: you're allowed to identify any of the three at any time, and they'll tell you if you're right and kill you if you're wrong. This time the requirement is that you ask the same yes-no question twice and identify all three without getting killed.

Hint: proofs that it can't be done should be taken with the same grain of salt as proofs that your antivirus software can't be compromised. I'll post solutions in a few weeks.

1. Show that in n dimensions a Venn diagram can be constructed with n+1 spherical regions of equal size. (A spherical region in n dimensions is an (n-1)-ball, that is, an (n-1)-sphere and its interior, e.g. when n = 2 a 1-sphere is a circle.)

2. Can this be improved? That is, in n dimensions, what is the largest number of equal-sized spherical regions that can be arranged as a Venn diagram? When n = 1, the line, regions are intervals and it is not hard to see that at most 2 intervals are possible. When n = 2, the plane, we noted above that the answer is 3. For n = 3 we can form a Venn diagram using 4 equal-sized balls; can one be formed with 5? And so on.

Type 1. Remembers all this with the help of such mnemonics as ELI the ICE man and CIVIL.

Type 2. Intuits that current lags voltage in an inductor by thinking of inductors as flywheels that respond sluggishly to an applied force. Doesn't intuit lead for capacitors (how could a capacitor predict the future?) but does remember that capacitors are the opposite of inductors.

Type 3. Is equally at home with voltage causing current and current causing voltage. An AC current applied to a capacitor causes the voltage to rise from zero when the current is at its peak and causes the voltage to reach its peak just when the current has dropped to zero and is starting to go negative. Hence in a capacitor the voltage lags the current by 90 degrees.

Type 4. Understands flywheels by analogy with inductors.

``A lecturer was once making the point that middle class families were smaller than lower class ones. As a test he asked everyone to write down the number of children in his family. The average was larger than the lower class average. The obvious point he overlooked was that zero families were unrepresented in the audience. But further, families of n have a probability of being represented proportional to n; with all this, the result is to be expected.''

One could quibble that a married respondent might write zero to indicate his or her childlessness--perhaps the question could have been better worded. But Littlewood's main point here is that the arithmetic mean of one plus the number of one's siblings provides the wrong estimate of the average number of children per family in the sampled population. That he does not think to ask for the correct estimate might taken as an indication that he does not think like a statistician (that, and that he came so late to martingales). It is a nice exercise to show that the correct estimate is the harmonic mean. Thus if three students reported respective family sizes of 1, 2, and 3, the average size of families in whatever (large) class those students are taken to represent should be estimated not as (1+2+3)/3 = 2 but 1/((1/1+1/2+1/3)/3) ~ 1.64.

But what does "correct" mean here? Littlewood's point about barren families remains of concern. The harmonic mean of a set of positive integers achieves its minimum of 1 when all integers are 1. If 99% of the class's families are barren and the remaining 1% have one child, the estimate of 1 that will inevitably be furnished by this method is not very impressive given that the actual average is 0.01. One answer might be that it is the best available estimate with this method. But since this experiment obviously has no access at all to the barren families, who have unlimited ability to drag the actual average down to zero, it would make statistics a more meaningful subject if the harmonic mean were taken to be an estimator of the average size of the nonbarren families. That is "correct." Taking control away from those over whom your statistical methods have no control levels the playing field.

What are the optimal music scales? Bach's well-tempered clavier divides the octave evenly into twelve notes, each stepping up in frequency by the twelfth root of two.

But why 12? Why not 11, or 17?

Twelve comes from the optimal rational scales, which arise as follows.

If we just want notes an octave apart, so we can sing the first two notes of "Over the Rainbow", life is easy, two being a well-known rational number.

But if we want more notes then we turn to 3/2 as the first possible refinement. This corresponds to going from C to G in the diatonic scale, where it is called a fifth, being the fifth white note on the piano if we count the starting point as the first.

Going up another fifth corresponds to squaring 3/2 to arrive at 9/4. The next note in that scale is 9/4, enough past one octave that we might (or might not) want to say it was recognizably different from an octave.

If we decide it is close enough for our kind of music to an octave then we can stop there and adjust things somehow to make it exactly an octave. If not then we keep going until we arrive at a note some number of octaves above our starting point that does sound close enough to that many octaves.

This can be made mathematical as follows. We are looking for integers p and q for which (3/2)^p is close to 2^q. That is, after going up p fifths we will have covered essentially q octaves as far as we're concerned. We won't have done so exactly, but if we adjust each step a little, not necessarily all by exactly the same amount, we can arrive exactly at q octaves past the starting point.

So for example if we'd picked p = q = 1 then we'd be saying that 3/2 was a fine approximation to an octave. That's terrible of course, 3/2 is only two thirds of an octave.

So we immediately move on to p = 2, q = 1. Here we're saying that 9/4 is close to an octave. It's closer, in fact we've overshot and the ratio is now 9/8 or 1.125. But that's still more than a semitone away, in fact a whole tone, so it's still pretty bad musically.

Where next? There are lots of choices of p and q, and some of them will be worse choices than p = 2, q = 1 even though they use bigger numbers for p and q.

Fiddling around for a while minding our p's and q's, we find that the next improvement to an octave comes at p = 5, q = 3. Here five fifths spans three octaves, to within an error of 243/256 = .95 or about a semitone, i.e. about a sixth of a tone per octave. Our classical diatonic or twelve tone scale can get very close to this with F C G D A F: taking five fifths upwards covered seven octaves. This is called the pentatonic system for two reasons, first that it leads to a natural division of each octave into five notes, and second that playing five fifths covers three octaves. The octave should ideally be divided into three white notes and two black notes, but we might just settle for the five fifths covering the three octaves and not try to hit each octave on the nose as we go past it.

The next best comes at p = 12, q = 7. Here the error after 12 fifths covering seven octaves comes to 531441/524288 = 1.0136, or .002 per octave. This is great: we split each octave into 12 notes, 7 of which are white and the rest black, and fiddle each of the 12 steps around to be a rational that is as close to a semitone as we can get.

Obviously we can do even better, but for what p and q? The next improvement comes at p = 41, q = 24. This tells us that our previous 12-tone octave turned out to be almost unbeatable, we had to go way up.

There is a beautiful theory that predicts this called continued fractions. Taking the log of each of (3/2)^p and 2^q, we get p log(3/2) and q log(2). That is, we are trying to make p/q = log(2)/log(3/2). It turns out that the ratio of two logs is the same regardless of what base you use for the logarithms (as long as you use the same base for both logs). For any base log(2)/log(3/2) turns out to be 1.709511, to six decimal places.

So at the end of the day, what we're trying to do is find numbers p and q that make p/q as close to 1.709511 as possible without ridiculously many octaves.

This number, 1.709511, can be expressed as the following continued fraction: 1 + 1/(1 + 1/(2 + 1/(3+ 1/(1 + 1/(5 + 1/(2 + 1/(23 + ...))))))), or more briefly 1,1,2,3,1,5,2,23,...). Don't look for a pattern, log(2)/log(3/2) as a continued fraction is not just irrational but transcendental and moreover inscrutable. (Not all transcendentals have an inscrutable continued fraction expansion, e.g. e = 2.718281828459... = 1,0,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,...)

The best possible rational approximation to log(2)/log(3/2) up to any point is obtained by lopping off an initial part of this continued fraction. 1 = 1, then 1 + 1/1 = 2/1, then 1 + 1/(1 + 1/2) = 5/3, then 1 + 1/(1 + 1/(2 + 1/3)) = 12/7, then 1 + 1/(1 + 1/(2 + 1/(3 + 1/1))) = 41/24, and so on.

But these are exactly the fractions we worked out the hard way before: the pentatonic scale with its three white notes and two black, and the twelve-tone scale with its 7 white notes and 5 black, and the 41-tone scale with its 24 white notes and 17 black, and so on.

This is the harmony of the continued fractions.

This was the final word in the final Morse code message sent by operator Dennis Harmer from the plane Star Dust before it crashed in the Andes on August 2, 1947 while flying from Buenos Aires to Santiago. The full message received in Santiago was "ETA SANTIAGO 1745 STENDEC". Two requests for retransmission still produced STENDEC. Then silence.

Hundreds of solutions have been proposed, ranging from STENDEC as a phrase with a secret meaning known only to a privileged few, to STENDEC as an acronym for STarting EN-route Descent or Severe Turbulence Encountered Now Descending Emergency Crash-Landing, to a scrambling of some other word such as DESCENT, to some mistranscribed sequence of call letters and abbreviations perfectly meaningful to the expert explaining confidently that such gibberish was standard operating procedure in his day, but never two experts with the same standard.

Having passed my Morse code test in 1961 (Australian ham licence VK2AUA for some years thereafter), I figured I should "have a go, mate."

My guess is that what Harmer sent was ETA SANTIAGO 1745 ST where by ST he meant Standard Time (since in August it would have been Standard Time in all Southern Hemisphere countries). He would then normally have sent the standard "procode" or logging abbreviation for End Communication, dit dah dit dah dit, normally written + and pronounced "cross" (not "plus"). This is sometimes written AR with a bar over it to indicate that it is formed by running A = dit dah and R = dit dah dit together. It is also sometimes sent as EC = dit/dah dit dah dit.

However while this is one of the seven punctuation and procode symbols required to be known for FCC tests, it is nevertheless not part of the International Morse Code and therefore not guaranteed to be recognized in all countries. On one or more of his previous flights into or out of Santiago that year Harmer may well have had Chilean operators read his + as EC without recognizing it as End Communication, and so this time preceded it with a clarifying END to avoid a repeat of that problem.

Unfortunately the result, ST END EC, when keyed fast enough to run together (Harmer may have seen no need to clearly separate them), would likely have made no sense whatsover to the receiving Chilean operator, for several reasons.

First, Chile hadn't used daylight savings time in 15 years (and didn't resume it again for another 21 years). Moreover when daylight time is used in Chile it is not called DT for Daylight Time but rather ST for Summer Time. (Chileans use CLT for standard time and CLST for daylight savings.) So ST used when it was not summer time would not have made the slightest bit of sense to a 1945 Chilean operator as a qualifier for the time.

Second END is not standard, being Harmer's improvised solution to his previous difficulty getting + or EC to be understood as anything more than just the two letters EC.

Third +/AR/EC is not in the original International Morse Code and therefore may well have been omitted from what was taught in Chile.

So the operator could well have failed to make sense of any of ST or END or EC and simply seen them as the meaningless word STENDEC.

London on the other hand would have spotted early on that ST had to belong to 1745, though they would have quickly agreed with the Chileans that this would have made no sense to the receiving operator. They should also have recognized EC as a variant of +.

But the extra END may have been the last straw for the ST END EC analysis, even for London. Harmer had sent EC, so why would he also send END? This can't be the solution, the ST was already a bit of a stretch.

But if someone looking at Harmer's record had noticed his six previous trans-Andean flights and drew the inference that Harmer might just have been compensating for a previous misunderstanding about EC identical to the one evidently encountered on this flight, then that would nail it! London could then show off how smart they were with their obvious-in-hindsight solution.

However there was considerable political tension between Chile and Great Britain just then. Rather than embarrass the Chileans in this way, London may have preferred to keep their better solutions to themselves and let a hundred inferior solutions bloom. By the time anyone else discovered as good or better a solution with which to embarrass the Chileans the political tension would have dissipated. And besides there would be so many solutions by then that no one would be able to spot the high-quality ones anyway. If anyone identifies this solution as a good one I'll take that back.

4. Philosophy

God and science

God is known through faith, personal experience, and shared experience.

Through faith, one knows God as the personal conviction of his presence in the universe.

Through personal experience, the private and gregarious alike know God by their perception of how he reveals himself to them.

Through shared experience the gregarious, if not the private, know God by meeting with like-minded believers for the purpose of sharing their personal experience of God.

Those who strenuously deny God as contrary to scientific knowledge at least do him the courtesy of granting that his existence is an important matter.

Some say God and those who believe in him do more harm than good. But one could make as strong an argument against science. In crusades and jihads God is the end, in Dresden and Hiroshima science is the means. In both, we are the agents of that destruction. To blame either the means or the end is to disavow our own responsibility.

When so much good is accomplished in the name of God or with the help of science, and sometimes both, who can say that either the means or the end is absolutely bad? If anyone can show that fire is absolutely good or absolutely bad, let them show some absolute truth about God or about science. Let others grant the benefit of the doubt to both.

Prejudice

Would you judge the author of the preceding article to be religious, an atheist, agnostic, or none of the above?

Strange laws of bygone times

Suppose a German Jew and a German Aryan do succeed in celebrating a marriage in Germany, e.g., because the Registrar and the parties by mistake assume that the Aryan party is not a German subject, while in fact he or she is. Assume further, the couple, after having detected the mistake and, threatened with a nullity proceeding, cross to England, can it really be said that the marriage is void or voidable, and that a decree of nullity is operating in this country [England]? We think for the reasons stated that it cannot.

Consequently a marriage celebrated in Germany, if otherwise valid, in this country should be on the same basis as a marriage celebrated in England; its validity should not be affected by a decree of nullity pronounced by virtue of racial prohibitions in accordance with the Nuremberg Laws.

  − Conclusion of "The Extraterritorial Effect of Some Foreign Marriage Prohibitions" by Hans Feist. In Transactions of the Grotius Society, Vol. 24, Problems of Peace and War, Papers Read before the Society in the Year 1938. (1938), pp. 81-103.

Facets of the mind

It is not uncommon to find the brain, consciousness, the will, emotions, and the soul being blurred together as simply facets of how we think. This does not do justice to the intuitive meanings of these notions, which can be distinguished as follows.

The brain is the gray matter in our head and surely the engine of the mind we associate with it.
Consciousness is a session of the parliament of the brain, where minutes and highly digested news dispatches from the subconscious mind and the unconscious sensory and other organs are read, and the issues they raise debated.
The will is the main ballot box of the brain, where the most important votes are cast, resolutions passed, and action recommended; break the will and you replace resolute democracy by aimless anarchy.
The emotions are a conventional set of distinctive heightened reflex responses of the consciousness, usually joint with certain characteristic physiological responses.
The soul is the part of us not permanently tethered to our body, a vague notion having several purposes some of which could be eliminated by fiat but not by sharpening the notion.

Not my theorem (but I wish I had thought of it first)

Theorem. All intelligently designed things are brought about by an intelligent designer through a process of intelligently conducted design.

Proof (in three steps)

1. Since the designer is intelligent, it follows that the design has been intelligently conducted.

2. Since the design has been intelligently conducted, it follows that we have been intelligently designed.

3. Since we have been intelligently designed, it follows that the designer is intelligent.

QED

Which part of this proof don't you understand? Please indicate the offending step.

5. Poetry

The Book of Ruth, Verse One
1/26/08

Pray tell what do the ruthless lack.
Has darling Ruth now turned her back?
Nay, ruthfuls pity show of course,
The ruthless merely lack remorse.

The saga of Alan Dratious
(to a tune from "Mary Poppins")
9/18/07

Superperiodic mystic expert Alan Dratious
Developed many theories of the temporal and spacious.
Such erudition earned him fame and cries of "oh good gracious!"
Until it came to light he'd been despicably mendacious.

Apropos of Seung-Hui Cho
4/17/07

The US Congress walks in fear;
The voters follow suit.
The former fear the NRA,
The latter those who shoot.

Yet Another Odd Sock Theory
2/7/07

When Tom and Harry learned that, lo these many years,
They both had odd-sock piles, they uttered many cheers.
But every silver lining has its cloud or so they say:
The silverfish had eaten all the older ones away.

War and Logic
4/10/06

Alexander lived a life of battles, dames and kings,
While his tutor Aristotle pondered over names and things.
But while Alexander's military followed him to wars,
Aristotle's syllogisms followed from his laws.

Darius and Alexander fought a mighty war.
The likes of such an argument had not been seen before.
But by Barbara and Celarent did Aristotle swear
As the mistresses of argument that never hurt a hair.

Some see it, some don't
July 2005

Fortune smiles upon the blind
And on his sighted brother.
Belief is given to the one
And seeing to the other.

Tao Jones (with apologies to Lao Tzu)
Words and music by Vaughan Pratt, November 1996
Performed by the Gerth Lane Choristers on 11/28/96

When I go out on the town the merry lads do sing so.
I can tell the charming ones are thinking of my ring though.
Down to the quay,
Jumping in the water clear,
Doing all the proper little
Things that Poppa taught to me.
Why do we dream? Doesn't ring a bell. I wish
I hadn't dived so quickly in the water with the jellyfish.

The Tao that can be told is surely not the Tao eternal,
And the name that can be named is not the name eternal.
What can't be named
Is real for eternity.
Naming is the origin
Of all particularity.
Free from desire,
You realize the mystery.
Caught in your desire,
You see nothing but your history.
Yet mystery and history together come from darkness both.
Darkness within darkness is the gate to everything we know.

Putting out the silverware before we fold the napkins,
Pouring oil upon the foil the turkey came all wrapped in.
Bread, wine, and thou,
Sitting down beside your lady,
Leaning back and squinting at
The sun when all the leaves are shady.
Why do we dream? Can't be the sort of fellow
Mama told me not to talk to just in case I got too mellow.

When some things look beautiful it makes some others ugly.
Some things looking very good leaves others looking badly.
Being and non-
Being create each other.
Difficult and easy are two
Things that can support each other.
High and low, depend upon each other.
After and before, follow each other.

Diving in the river from the bank I left my clothes on,
Breathing underwater through a reed I breathe in ozone.
Flop belly up.
Flop belly down.
Flopping up and flopping down
Like Molly when she paints the town.
Why do we dream? Can't be the busy river,
Rushing on and turning round and taking all the swimmers with her.

So it is the Master acts without a trace of action,
Teaching people everything in silent satisfaction.
Things arise,
And he lets them come.
Things disappear,
And he lets them go.
Have but don't possess,
Act but don't expect.
When his work is fully done it's what he can forget.
This is why the work he does will last forever yet.

Putting up the Christmas tree is part of what romance is,
Hanging out the ornaments on all the boughs and branches.
Presents for you,
Presents for me,
Presents for everyone
Underneath the Christmas tree.
Why do we dream? Maybe it's not a dream.
Pinch yourself and try to wake up, things aren't really what they seem.

When you praise important people others become weaklings.
When you buy expensive things then others try to steal them.
Master leads,
He empties out our minds,
Filling up our very core,
And weakening the drive that binds,
Sowing blind confusion in the minds of all who think they know.
Practice doing nothing so that everything will smoothly flow.

When I sing of spring and things the others all chime in. Though
Many of the dreamy ones are staring out the window.
Down to the quay,
This is where I want to be,
Doing all the proper little
Things that Poppa taught to me.
Why do we dream? Doesn't ring a bell. I wish...
I can't remember what I wish.
I can't remember.
What?

And, Or, Not
1995

The wind blows warm across the plain,
Chill antiwind blows back again.

The wind blows warm and friends do fly
Away, together, smiling. I
Return their smile and bid farewell
As on horizon's edge they dwell.

New friends breeze in on every side,
Conjunctively, from far and wide,
Converging to that distant plain
Where only memories remain.

But antiwind comes howling back,
Bearing thoughts with frown so black,
Each tutored in some learned course,
Demanding I their plank endorse.

Each of one mind — no, not true!
Looming near, they split in two.
``You must choose me!'' ``No, me!'' they shout
``Make up your mind, dispell the doubt.''

But then I wondered where the wind
Comes from. And whither antiwind?
Standing rooted to the spot,
I try to turn. So hard. I'm…

NOT

The wind blows warm across the plain,
Chill antiwind blows back again.

Working off your karma payments
(Tune: My bonnie lies over the ocean)

My karma ran over my dogma
My dogma is flat as can be
Nirvana is not till manana
Oh bring back my dogma to me

Chorus: Bring back, bring back, …

My grandpa has tied up my grandma
He's batty as grandpas can be
Oh please end this sad melodrama
Oh untie my grandma for me

My mama has earned her diploma
In veterinary dentistry
She's pulling horse teeth in Sonoma
Oh bring back my mama to me

Selma has a melanoma
All the way down to her knee
Thelma has a carcinoma
Oh please don't bring either near me

My uncle's pipe has an aroma
With auntie it did not agree
She's down for the count in a coma
Oh bring back my auntie to me

My father has caught emphysema
He caught it when skiing, says he
With mother he's now anathema
Whatever will happen to me?

Six Stanzas on Snoring
December 1962

Short Sam snorted and sat up on the sofa.
"Someone said something," said Sam, half asleep.
"Someone said something, I'm sure I sensed a sound.
Some sneaky so-and-so done woke me from my sleep."

Then spoke slim Sophie, sober Sophie by the sofa.
Sophie with a slightly shocked but supercilious smile.
"Shame, you silly simpleton, you sottish sluggard, you.
Stop your slimy sniveling, you've been snoring in fine style."

Short Sam snorted somewhat sourly then surrendered
To that sweet siren sleep, whose singing summons all.
Somnolently sighing, Sam started soon to snore,
Shaking soul and sofa with his seismic strident squall.

Up sprang Sophie, seething Sophie, scheming Sophie,
Sophie with a sudden sparkle shining in her eye.
She sped swiftly to the storeroom, stopped, and stooped, and searched,
Seeking somewhere, somehow, something — and a slab of soap she spied!

Smiling oh so sweetly she sat just next to Sam,
Seized the slippery soap suspended o'er Sam's snuffling snout.
She swiftly slipped the soap in, saw it slither down his throat,
Saw it stick in his oesophagus, heard a sharp and stifled shout.

Strangling, suffocating, seeing stars syncopating,
Sam was asphyxiating. Soon his struggles stopped.
Now Sam sleeps in a sound-proof sarcophagus
In the silence of a cemetery, a stone slab on top.