Sayings of Chairman Pratt

Chairman of the Royal Australian College of Knowledge Prevention through Obfuscatory Terminology (off the record).

As collected over the years by recording secretary Alan Dratious.

(Depending on your background the following may contain offensive, disturbing, insulting, demeaning, sexist, sacriligious, racist, or just plain bizarre material. Treat anything that bothers you as hypothesis or speculation, restating every assertion of fact as a question.)

1. Epigrams

2. Science and Technology

3. Philosophy

4. Poetry

1. Epigrams

o One accurate measurement is worth a thousand expert opinions. --Grace Murray Hopper

o The religion of Moses avoids trichinosis. The religion of Jesus avoids other diseases.

o Was Sherlock Holmes good at thinking? Because if so, then according to Descartes Sherlock Holmes was more than merely Conan Doyle's fictional creation but actually existed.

o Ironically each side of the Bell Curve believes it is smarter than the other side, the left side because the right side seems to be talking incomprehensible gobbledy-gook.

o America has such strange politics. Democrats preach to the choir while Republicans preach to the gullible.

o Come up with an intelligent design for nitrogen-based life and it will write a book about you.

o Anyone can edit Wikipedia, but only the bold can be great. (Gusteau in Ratatouille: "Anyone can cook, but only the fearless can be great.")

o Life is a labor-intensive but fatal undertaking.

o 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.

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

o 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.

o 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.

o 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.

o How do you talk to the half of the country on the left side of the Bell curve without insulting their intelligence?

o A successful conspiracy is easily covered up with a hundred conspiracy theories. No need to do it yourself, they come out of the woodwork on their own.

o Can I be a Christian and a Muslim at the same time? If not, I do not wish to be either.

o When product marketing hands you lemonade, make lemons.

o Definition of democracy: Half the time the country is run by those of below average intelligence.

o 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.

o We do not fully appreciate the respect we accord logic in ordinary conversation until someone attempts to engage us without it.

o 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.

o Why do those preaching to the choir have to assume the others can’t carry a tune?

o Good comeback: "That's what you say."
Great comeback: "But that was not the original topic of discussion."

o Asking someone to repeat a joke is like asking a bee to sting you again. The bee died in the meantime.

o Judicial activism: a court decision that went against you.

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

o Why should there be no atheists in foxholes? One would expect the proportion of atheists among those in foxholes to be slightly higher than for the general population because atheists are less likely to trust in God and leap out of the foxhole.

o Boss's job description: to take the advice of your staff, the blame when it proves misguided, and at least twice their salary for agreeing to that cockamamie arrangement.

o The first religion to come up with the idea of attributing its writings to its own deity stole a march on the others.

o Democracy. n. A social program for getting the country's thousandaires to give what little they have to the country's billionnaires.

o Give me enough parameters and a suitable function of them and I will model the world.

o Who is likely to have accomplished more by the end of their life: one who has fulfilled their every ambition, or one who has only fulfilled half of them? What if the former had very few ambitions and the latter very many?

o One way to have the last word is to make it so boring it's the last thing anyone wants to listen to.

o Mathematical logic is more reliable for mathematical relations than human ones.

o God is never bigoted unless your religion makes him so.

o 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?

o 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.

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

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

o I have the following null hypothesis. There exists a Nobel prize winner whose prize was awarded on the basis of confirming a null hypothesis.

o 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.

o You may have noticed that it has become popular lately to claim that science is not about democratic consensus among scientists but about scientific truth. When confronted with such a claim, just ask whose truth they accept. Invariably it will turn out to be that of some fringe group whose pronouncements they accept in preference to those of the scientific establishment.

o I believe in Intelligent Design. Life was created by Natural Selection, the most intelligent designer known to science. Life is so complex that it is obvious it took more than six days. Natural Selection succeeded by allowing a realistic time budget for the project. Anyone who thinks otherwise has never had to budget time for a major project.

o Those with children who have ascended to greatness should feel pretty good that their children have descended from them.

o Oh to be young again, and be surprised by the surprising.

She: Why do you use algebra? Were you on acid or something?
He: Oh no, it's just that it's terribly comfortable. I think everyone will be using it in the future.

o Beauty before definition, definition before truth.
(Ugly definitions are hard to work with. And a proposition that contains an undefined term might be true with one definition of that term and false with another.)

o Having God as your copilot only works when air traffic control is on your side. If you're not tuned into Nature's channel back on planet Earth, your copilot can't help you.

o Hold your friends close and your hostages closer.

o Eccentric reasoning can lead to eccentric conclusions. To arrive at a false one takes circular reasoning.

o Spend the pennies on chocolate and the pounds will take care of themselves.

o Let civilization c have mass m. Then polarization P of the government of a civilization satisfies the law P = mc2.

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

o 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.

o Those who deny that mankind is responsible for the past half century of global warming don't hate science, they just hate the planet. How can anyone that loves the planet defend the amount of carbon we pump into the atmosphere? That's like the murderer that tells his wife he loves her just before he pumps her full of lead. Different position in the periodic table, same principle.

o A stopped clock is right twice a day. I wish my stock picks were as reliable.

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

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

o Why must there be beauty in truth? An ugly rumor confirmed by investigation remains ugly. And why must there be truth in beauty? Most beautiful stories are too good to be true. In life as in mathematics, judge definitions by their beauty and propositions by their truth.

o You can't feel someone else's oats. You'd get slapped down for it.

o The Equal Rights Amendment failed for omission of the right to leave the seat up.

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

o The language of Intrade Paddy Power is to truth as French is to love. Both games are better for having skin in them.

o 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.

o How can anyone who cannot define God be either an atheist or an agnostic? It is impossible to say of an undefined term that you do not believe in it, since it might turn out when defined to be something you do believe in. For example some define God as the universe, and I do believe in the universe, even devoutly.

o Seahorses are the only animals in the animal kingdom where the male gets pregnant and gives birth. If marriage is ever extended to other animals besides humans, should gay seahorses be permitted to marry?

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

o 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.

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

o A fallacy is worth a thousand steps.

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

o Retaining your password has much in common with retaining your virginity. However earnestly you are counseled early on to guard it at all times, and however diligently you heed that counsel, the time will come when you learn the hard way how social engineering works.

o Don't shoot the messenger. Exception: spam.

o 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?

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

o Arthur C. Clarke's laws of prediction (normal form):

  • Any sufficiently difficult goal is easier to prove impossible than possible.
  • Any sufficiently clear grasp of an obstacle will overcome it.
  • Any sufficiently advanced technology is indistinguishable from magic.
  • (People only remember Clarke's third law. He neglected to put the first two in normal form, making them impossible to remember.)

    o 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.

    o Blaming problems on ignorance is like a scoutmaster who holds nitrogen responsible for the inability of his troop to start a fire. Decreasing the amount of nitrogen around you so that the oxygen will accelerate combustion is a long term project−in the short term one can only work around the nitrogen. The same goes for ignorance.

    o 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.

    o The Nobel prize in physics should go to the first physicist to notice that the Sun is not a black body after all but bright yellow. Evidently experimental physics is a nocturnal occupation.

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

    o 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.

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

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

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

    o 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.

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

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

    o Live life one birthday at a time.

    o In means-end analysis, determinism serves the former, free will the latter. You are free to choose whatever end you want, but bear in mind that actions have consequences when choosing the means.

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

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

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

    o 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.)
    Other possible comebacks for the teacher:
    2. What would you prefer? y sheep? nsh sheep?
    3. Well, x is surely the number of something, so substitute that something for sheep in the problem, get the answer, and I bet that's also the answer for the case when x is the number of sheep.
    4. Yes, that could happen. We can solve the problem in two parts. First we solve it for my case, namely when x is the number of sheep. We can then easily reduce your case to mine by adding to x the difference between the number of sheep and x.

    o 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.

    o Our two eyes look outwards and see one world, our third eye looks inward and sees two minds.

    o 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.

    o 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.

    o What's all this "second coming" stuff I keep hearing about? Is this something to do with heaven, bed, or a delayed reaction to an obscure double entendre?

    o Things are in such a mess today because creation was such a rush job. If God had given himself more than six days he could have worked more efficiently and neatly by exploiting natural selection and letting nature do all the hard work.

    o Headlines: the last refuge of the bad pun.

    o He who dies with the most birthdays wins.

    o Cryptographic security: safety in numbers.

    o My mind does terrible things to my waist.

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

    o An erudite word is good to find.

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

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

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

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

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

    o The Poet: Nothing rhymes with orange.
       The Logician: Orange rhymes with orange.
       The Logician-Poet: Nothing rhymes with nothing.
    (This one has circulated without attribution so widely as to oblige me to mention here that every item on this website is original with me unless qualified otherwise.)

    o 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.

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

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

    o Contacts: glasses with wipers.

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

    o Waiter, another kettle of fish, please.

    o 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!

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

    o 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?"

    o Thank goodness one of us is on the same page.

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

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

    o Why can't spammers count? One caller just told me that their fifty-seventh notice concerning the factory warranty on my vehicle was the second.

    o 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.)

    o 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.

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

    o 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.

    o I was raised to be rigorous, not formal.

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

    o Negligence: the attitude to be worn with a negligee.

    o 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.

    o 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.)

    o 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.'')

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

    o 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.

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

    o 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.")

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

    o 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.

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

    o 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.")

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

    o 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.

    Previous epigrams here that I learned were not new with me.

    o [G.K. Chesterton] If it's worth doing it's worth doing badly.

    o [Brant Parker and Johnny Hart, Wizard of Id] The Golden Rule: He who has the gold makes the rules. (My version was not only later but a much clumsier formulation.)

    3. Science And Technology

    o A mnemonic for Domain,Kingdom,Phylum,Class,Order,Family,Genus,Species

    Donald Knuth Prefers Code Over Functions, Generally Speaking.

    o Newton on composition

    Analysis guides us to the composition, but true composition is not achieved before it is freed from analysis. Let even the slightest trace of analysis be present in the composition and you will not yet have attained true composition

    o The causal connection between CO2 and global temperature

    The argument is often heard that CO2 cannot raise temperature because temperature raises CO2. The usual basis for this argument is Milankovitch theory, which hypothesizes that the several deglaciations of the Late Quaternary were triggered not by CO2 but by warming induced by fluctuations in the eccentricity of Earth's orbit.

    This argument can be shown to be illogical by considering Tim and Cathy in balance at opposite ends of a seesaw, each holding a ten-pound weight. To raise Tim it suffices for him to drop his weight. The above argument obliges the conclusion that if Cathy drops her weight she will not rise.

    160 years ago Irish physicist John Tyndall invented the spectral photometer and used it to demonstrate in the laboratory that increasing CO2 could increase temperature. Those claiming that laboratory phenomena do not exist in the outside world are whistling in the wind with no supporting evidence.

    o Can a model of something tell us anything we didn't already know about it?

    Suppose some phenomenon happens to be following the shape of a gaussian or bell curve, but you can only see the top, between the two points of inflexion. It looks like the top of a gaussian to you. To be sure you do a least-squares fit and obtain an R2 of 0.98. This is sufficiently solid evidence for a gaussian so you infer from the phenomenon that it is a gaussian, and hence will decay to zero in due course.

    But then someone asks how you can distinguish that shape from a sine wave, pointing out that in that case it would not die out but keep oscillating.

    Interesting thought, so you try fitting a sine wave. This time you get an R2 of .9999. This would be amazing except that the phenomenon is so free of noise that such an R2 is not impossible.

    You furthermore realize that with the gaussian model there is not enough noise to account for the unexplained variance of 0.02. This casts doubt on the gaussian model, prompting you to switch to the sinusoidal model.

    Now was this inference made from the phenomenon? Well, you’d already inferred from the phenomenon that it was a gaussian. It wasn’t until you had a second model, and could compare the quality of fit of the two models, that you were in a position to infer that it is more likely to be a sinusoid than a gaussian, even though the gaussian at first seemed a perfectly reasonable inference.

    So I would judge the inference that the phenomenon was more likely to be sinusoidal than gaussian to have been drawn from the model, not from the phenomenon itself.

    o Gödel's second incompleteness theorem

    Gödel proved that any sufficiently powerful system of reasoning that assumes its own consistency is either inconsistent or becomes more powerful. Inconsistency therefore follows for any system that can prove its own consistency. The human mind that cannot prove its own consistency is therefore at liberty to assume it without running afoul of Gödel's theorem. Better yet, it can even assume that the assumption is consistent, so long as it counts this as a second assumption that is either stronger than the first or inconsistent.

    o The weight of US coins

    Although coins vary in weight according to both year of issue and degree of wear and oxidation, an easily remembered rule of thumb is that $10 worth of coins weighs 8 oz if silver (either quarters or dimes), 35 oz if nickels, and 90-100 oz if pennies (which vary according to year of issue).

    From this we can deduce the weight of a coin in ounces by multiplying the weight of $10 worth by the value of the coin in pennies and then dividing by 1000. Thus a quarter weighs 8*25/1000 = 0.2 oz, a dime 8*10/1000 = .08 oz, a nickel 35*5/1000 = 0.175 oz, and a penny 90*1/1000 to 100*1/1000 = 0.09-0.10 oz.

    In metric the corresponding weights are, to three decimal digits, 5.670 g, 2.268 g, 4.961 g, and 2.551-2.835 g. When the mint went metric in 1982 it used essentially these figures, officially taking 5.670 g and 2.268 g as the exact weights of the quarter and dime and rounding 4.961 g up to 5 g for the nickel and the rather variable penny down to 2.5 g.

    Translating these new metric weights back to British units, we have 0.2 oz, 0.08 oz, 0.17637 oz, and 0.088185 oz, all accurate to one part in 100,000. This is far more accurate than the actual weights of coins so more precision while possible is pointless---even the slight buoyancy due to the air displaced by coins makes a bigger a difference than that, as do corrosion and wear.

    $10 worth of silver coins still weighs 8 oz. However $10 in nickels now weighs 35.274 oz and in pennies 88.185 oz.

    Silver coins are worth $20/lb ($19.99966 to be more precise), nickels $4.536/lb, and pennies $1.814/lb (so 181 pennies weighs almost a pound).

    Before going metric the mint measured weights of coins in grains, there being 7,000 grains in a pound. The official weight of the Lincoln penny introduced in 1909 was 48 grains or .1097 oz during most of the 20th century with the exception of the latter half of World War II when it was reduced to 42 grains to free up metal for war transports and munitions.

    Don't use pennies to check your kitchen scale to better than 10%. Nickel is reasonable while silver is the most reliable though also requiring the most value in coins to achieve any given weight. But if you have a graduated container, weighing a pint of water at 4°C (40°F) to verify that it weighs a pound (remembering of course to tare the container first) should be more accurate. (At room temperature a pint of water weighs about 0.2% less than a pound.)

    o The Medieval Warm Period

    One often reads about the Medieval Warm Period as a time when temperatures were higher than now. The problem with this claim is that no one really knows how warm things were back then. The panel convened by the US Congress in 2005 on "Surface Temperature Reconstructions for the Past 2,000 Years" made this clear when they wrote as follows.

    "Less confidence can be placed in large-scale surface temperature reconstructions for the period from A.D. 900 to 1600. Presently available proxy evidence indicates that temperatures at many, but not all, individual locations were higher during the past 25 years than during any period of comparable length since A.D. 900. The uncertainties associated with reconstructing hemispheric mean or global mean temperatures from these data increase substantially backward in time through this period and are not yet fully quantified."

    In other words the reason some people are claiming the Medieval Ages must have been hot is because there is no evidence that they were cold. This is the meaning of "Medieval Warm Period."

    o The LCROSS mission: dropping a golf cart on the moon

    At 11:31 UTC on October 9, 2009, NASA dropped a probe the mass of a Humvee on the moon. Astronomers watching for some sign of the impact expressed disappointment that they did not see a cloud of dust or other indication at the moment of impact. Perhaps if the probe had driven around a few craters at 60 mph for a while it might have churned up a more visible dust cloud.

    The media has described this as the bombing of the moon by NASA. To put this in perspective, imagine that Britain were to bomb Dresden, or the US to bomb Hiroshima, by dropping a Humvee on it from a great height. What would be the outcry? That bombing Dresden or Hiroshima in this way would destroy Earth? Or that something larger needed to be dropped on Germany or Japan?

    Since the moon's gravity is only one-seventh that of Earth's, the LCROSS probe weighs only about as much as a golf cart. Ignoring differences in atmosphere, when dropped from a given height the energy LCROSS imparts to the moon's surface is that of a golf cart dropped from the same height above Earth.

    The public's response to NASA's "bombing" of the moon in this way has been a huge outcry: "Save the moon."

    I would say what really needs saving here is the economy, which has left the public with far too much free time and nothing better to do than worry about a golf cart hitting the moon. Meteors with more impact than a golf cart hit the moon at much higher velocities than the LCROSS mission every year. If the public wants to save the moon from such hits, instead of protesting LCROSS it should be demanding an anti-meteor shield to protect the moon from all future meteor hits. The government should set aside part of the stimulus money for a Lunadarity program which will employ all those in a position to help save the moon from meteors.

    The reason NASA added one more meteor to the millions the moon has endured in the past is to create a meteor impact at a known time (so we know when to observe it) and at a predetermined place (where NASA wanted to know what lay under that particular point). Meteor impacts are impossible to predict; the difference between NASA's one meteor and nature's many meteors is that NASA's meteor is the only one whose impact NASA can control (to hit the spot of interest) and observe (since we know when to watch it).

    Such an observation could add greatly to our understanding of the moon. The objections resemble the protests against stem cell research but without the added concern of the latter about human lives.

    o Amazon forums

    I love the give-and-take of Amazon forums, with their tone-deaf global warming skeptics and the constant bickering of atheists and theists. It's like Second Life with the difference that, for the scientific if not religious debates, one side of every conflict is grounded in reality.

    Those taking the other side are affectionately called nutters. The task of the nutter is to convince the unwary that he or she is actually the realist and that the other party is the nutter.

    It's a pleasant change of pace from my dry-as-dust academic writing, which even I find a boring read sometimes. Mystery novels serve a similar purpose for those unable to find entertainment in scientific crackpottery.

    o When did the message become the medium?

    When we talk about digital media we mean something different from mass media and news media. Digital media refers to technologies for the electronic representation of information. Mass media and news media refer not to the representation of information but to its content. With the latter usage the message has become the medium, opposite to Marshall McLuhan's observation that the medium is the message.

    Well, if the medium is the message, what's the harm in calling the message the medium?

    Only that the medium is *not* the message. McLuhan was too slick for our own good. When you make the medium the message you drag down communication to a level that dehumanizes it. When you accept the medium as the message you no longer need to think because the machines can now do your thinking for you. The medium is what the machines work with, the message is what we humans ask the machines to carry for us.

    When you can appeal to Google in its little search bar in the same way you appeal to a fellow human, maybe then the medium will have become the message. But we're still a long long way from that. In the meantime the medium is not the message, it is only the messenger.

    o Evolution

    Jonathan Wells, the author of Icons of Evolution, recently challenged the theory of evolution with the following "ten questions to ask your biology teacher." His tenth question states that evolution is based on misrepresentation, ironic given that most of his questions are based on misrepresentations. Here is a short summary of how biology teachers have been answering Wells's questions.

    Ten answers from your biology teacher

    Q: ORIGIN OF LIFE. Why do textbooks claim that the 1953 Miller-Urey experiment shows how life's building blocks may have formed on the early Earth -- when conditions on the early Earth were probably nothing like those used in the experiment, and the origin of life remains a mystery?

    A: Darwin's own opinion on the origin of life as expressed in a letter to his friend J.D. Hooker should be a sufficient answer here: "It is mere rubbish thinking at present about the origin of life: one might as well think about the origin of matter."

    Darwin's theory of evolution concerns the origin not of life but of species: how one species can gradually turn into another as it adapts to changing environments and competes with other species for scarce resources.

    Q: DARWIN'S TREE OF LIFE. Why don't textbooks discuss the "Cambrian explosion," in which all major animal groups appear together in the fossil record fully formed instead of branching from a common ancestor -- thus contradicting the evolutionary tree of life?

    A: This is incorrect. Mammals, fish, birds, and dinosaurs did not appear during the Cambrian explosion, but evolved many millions of years later, via many intermediate species, pretty much as originally diagrammed by Darwin. The Cambrian explosion strongly supports evolution.

    Q: HOMOLOGY. Why do textbooks define homology as similarity due to common ancestry, then claim that it is evidence for common ancestry -- a circular argument masquerading as scientific evidence?

    A: They don't claim that. The evidence for common ancestry is found in patterns arising in biological traits. "Homology" simply means the same thing as "similarity due to common ancestry." It makes no sense to say that two terms for the same thing can be used as "evidence for" each other.

    Q: VERTEBRATE EMBRYOS. Why do textbooks use drawings of similarities in vertebrate embryos as evidence for their common ancestry -- even though biologists have known for over a century that vertebrate embryos are not most similar in their early stages, and the drawings are faked?

    A: Actually vertebrate embryos do show those similarities, and modern textbooks use real drawings to illustrate this.

    Q: ARCHAEOPTERYX. Why do textbooks portray this fossil as the missing link between dinosaurs and modern birds -- even though modern birds are probably not descended from it, and its supposed ancestors do not appear until millions of years after it?

    A: Your supposed counterexample did not appear until two years after The Origin of Species, in 1861. How could the theory of evolution, which Darwin worked out between 1835 to 1859, be falsified by a species then unknown to Darwin?

    Although Archaeopteryx is not itself a bird, it is considered a close relative of the first birds. You are not descended from your uncle, but that does not preclude the possibility of a family resemblance.

    Q: PEPPERED MOTHS. Why do textbooks use pictures of peppered moths camouflaged on tree trunks as evidence for natural selection -- when biologists have known since the 1980s that the moths don't normally rest on tree trunks, and all the pictures have been staged?

    A: It turns out that "normally" here means that at any one time approximately 75% of peppered moths are high up in the branches, with only 25% down low on the trunks. Why should the photographers risk breaking their necks trying to photograph the moths high up when there are quite enough moths on the trunks to make the point?

    Q: DARWIN'S FINCHES. Why do textbooks claim that beak changes in Galapagos finches during a severe drought can explain the origin of species by natural selection -- even though the changes were reversed after the drought ended, and no net evolution occurred?

    A: That's easy. Species evolve in order to adapt to changing environments. If the environment changes back, the species change back along with it. How is this a problem for the theory of evolution? Just because you go to work and back home every day doesn't stop you from deciding to emigrate to Australia.

    Q: MUTANT FRUIT FLIES. Why do textbooks use fruit flies with an extra pair of wings as evidence that DNA mutations can supply raw materials for evolution -- even though the extra wings have no muscles and these disabled mutants cannot survive outside the laboratory?

    A: This is a reasonable objection. While the example shows that major changes are possible, it does not show that beneficial major changes are possible.

    A more convincing example would be a dog with a prehensile paw that could peel a banana. However no dog breeder has thus far pulled off that feat.

    What has been observed is the evolution of an e. coli population that can feed on citric acid in the growth media. For the bacteria world this is remarkable. For the human world it would be like breeding humans that could eat their floor boards the way termites do.

    In the long run evolution is the combined effect of many changes, minor and major. With enough time a dynasty of competent dog breeders could breed a barking triffid, which the dog breeders might call a dog on account of its ancestry but the biologists might prefer to classify as a vegetable.

    Q: HUMAN ORIGINS. Why are artists' drawings of ape-like humans used to justify materialistic claims that we are just animals and our existence is a mere accident -- when fossil experts cannot even agree on who our supposed ancestors were or what they looked like?

    A: They're not used to show we're "mere animals," they're used to illustrate our homology, or similarity due to common ancestry, with apes. Whether humans have a divine spark not possessed by nonhumans is an excellent question but not one that science is currently equipped to address (not that this has stopped scientists from speculating on the question). However fossil experts are in much greater agreement about our common ancestry with apes than you give them credit for.

    Q: EVOLUTION A FACT? Why are we told that Darwin's theory of evolution is a scientific fact -- even though many of its claims are based on misrepresentations of the facts?

    A: Look who's talking. Every objection to evolution raised by your questions was either not sustainable at all or depended for its sustainability on misrepresentation of the facts. Some biologists may have misrepresented some facts a century ago, but you are misrepresenting your facts today.

    o Your car: Gasoline or Electric?

    In the early 1900s the choice was between gasoline or electric vehicles. The latter eventually died out due largely to the much greater range of gasoline vehicles.

    Rising fuel prices along with increasing concern over emissions, especially the greenhouse gas carbon dioxide which cannot be controlled like other emissions, have driven a resurgence of electric vehicles, with GM's Saturn EV1 as a short-lived trial balloon, Toyota's RAV4 as a slightly longer-lived model, and now with Tesla taking the lead by adopting the more expensive but higher capacity lithium-ion battery, an improved technology driven by the widespread use of laptops and cellphones.

    In between we have seen the emergence of the hybrid, starting with the Toyota Prius and followed by the Honda Insight, the Ford Escape, and several others. Hybrids permit more efficient use of gasoline by allowing the gasoline engine to run at a more uniform speed, with the inefficiencies of braking and acceleration cushioned by a small auxiliary electric motor assisting the main gasoline engine.

    The refinement of the gas-electric choice created by the hybrid has now spawned its own refinement: small or large electric motor. GM's planned Chevrolet Volt reverses the hybrid's large-engine small-motor combination by powering the vehicle with a large 160 horsepower electric motor from a battery somewhat larger than the Prius's but much smaller and therefore much cheaper than the Tesla's. An overnight charge of the battery gives the Volt a 40-mile range, which while less than a fifth of the Tesla's more than 200-mile range is expected to cover more than 90% of all vehicle usage other than for vehicles in constant use throughout the day for law enforcement and ferrying people and goods. For longer range the Volt's smaller 85 horsepower gasoline engine kicks in to recharge the battery, sufficient for cruising at freeway speeds while simultaneously bringing the battery back up to full charge. As with hybrids the electric motor provides enough reserve power for the bursts of acceleration needed to overtake or enter freeways. The difference is that the electric motor is also the primary driver even at steady speeds, whether in city or highway driving.

    Given the high cost of high-capacity batteries today, the Volt seems an eminently sensible tradeoff in the power ratio between the electric and gasoline engines of hybrid vehicles. Pending any significant reduction in battery cost, expect to see many imitators adopting GM's combination of a large electric motor and a small gasoline engine.

    UPDATE mid-December 2016. The Volt was introduced exactly six years ago. At that time battery electric vehicles (BEVs) were still in their infancy, with no Tesla superchargers

    o My own position on evolution

    I am skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for any such theory should be encouraged. What I do believe is that the evident variations between individuals of any species, however caused, in combination with natural selection, are primary drivers of speciation, in accord with Darwin. Accounting for the complexity of life is a tremendously more challenging task that random mutation and natural selection cannot possibly accomplish on their own. Darwin never claimed his theory did so, and the vast amount we have learned since Darwin about molecular biology, cell biology, and ecology shows that it would have been wildly presumptuous for him to have done so.

    The above is my position statement. The first two sentences reproduce almost verbatim the wording of A Scientific Dissent from Darwinism signed by some 700 scientists. The only replacements are the obvious "I am" for "We are," and more importantly "any such theory" for "Darwinian theory" since Darwin did not claim to account for the complexity of life but for the phenomenon of speciation, whereby the characteristics of a population can change over time: the longer the time the greater the number and extent of possible changes. Speciation can contribute to the complexity of life, as Darwin pointed out with admirable clarity, but unless it is the only such contributor it cannot be said to account for it, and nowhere did Darwin claim to have done so.

    o Some one-sentence summaries of profound ideas in science

    Special relativity: The celebrated Michelson-Morley experiment in 1887 to measure the variation of the speed of starlight past the earth during its six-month journey halfway round its solar orbit inexplicably failed to produce not only the expected variation but any significant variation at all, which Einstein accounted for in 1905 with a theory of space and time in which the respective motions through space of both the source and the observer of the light dilated both space and time in a way that resulted in the same light beam having the same apparent velocity to all observers regardless of their velocities relative to each other and to the light source.

    Quantum mechanics: Physicists believed in the 18th century, thanks to Newton, that light was particles, and in the 19th, thanks to Young and Fresnel, that it was waves, but came to the gradual realization in the 20th century, via math that while in remarkable agreement with experiment seemed irreconcilable with our commonsense understanding of physics, that not only light but all radiation and all matter was simultaneously both waves and particles, which moreover are of an intrinsically probabilistic nature: however implausible, God does play dice, contrary to the intuitions of some of physics' greatest minds, for example Einstein.

    Evolution: Biologists used to believe that species persisted through time, but in the 19th century Darwin convinced the scientific community that the naturally arising variations between individuals in any given species allowed that species to adapt slowly but continuously, and in some cases dramatically in the long run, to environmental changes and competition from other species, by favoring the propagation of those individuals in the species that performed best for the prevailing circumstances of the species.

    Global warming: Although all constituents of the atmosphere act to one degree or another as a blanket to keep the earth from losing the warmth from the sun too rapidly, an effect significant not so much for day-to-day weather as for year-to-year climate, carbon dioxide or CO2 has in recent decades emerged as the most rapidly changing contributor to that blanket, making its increasing production from the generation of energy from carbon-based fuels potentially as great a threat to the stability of life on earth as some of the cataclysmic impacts of millions of years ago that radically changed the makeup of life on earth.

    (I'll be happy to field suggestions for other profound ideas in science if I can, let me know at .)

    o How potent is 200C?

    Among the commoner levels of potency found in homeopathic remedies is 200C, meaning 200 successive dilutions each performed by adding 99 parts of water or other diluent to one part of the substance being diluted. Now the number of molecules of water that can fit in a cup is very close to the fourth root of a googol. A googol is 10100, whence its fourth root is 1025, about 16 times as large as Avogadro's number, 6.023×1023. You may think molecules of water are very small, but they are very very very very small, so small in fact that even a line full of very's barely does justice to their incredibly tiny size. If that's hard to conceive, imagine how much bigger a googol itself must be.

    Compared to the dilution factor achieved by 200C potentization, a googol is tiny, being the fourth root of that dilution factor, which comes to 10400. The 200C dilution factor is as far on the high side of a googol as Avogradro's number (to be more precise, 16 times Avogradro's number) is on the low side.

    This should give you a better idea of just how incredibly potent 200C homeopathic remedies are. With potencies like that, the probability of finding one molecule of the original substance in the whole universe is way less than that of being abducted by aliens for the grand jackpot you just won in the lottery (which would be extraordinarily good luck compounded with extraordinarily bad luck).

    The Federal Drug Administration recognizes these small quantities and therefore does not consider homeopathic remedies a threat to public health. Even if the compounder of some homeopathic remedy started with the most toxic chemical in the universe, the probability that a 200C preparation of that remedy contains even one molecule of that chemical is so low by comparison to your odds of being struck by lightning or the wrath of Al Qaeda that the FDA can approve its distribution and sale with a clear conscience. Whether it is ethical to represent such a remedy as effective is apparently outside the FDA's jurisdiction.

    o Reflections on The Sokal Affair

    What Sokal ought to have going for him is what one might call the "natural consensus" among scientists, that teams working independently to understand the world should find themselves in agreement whenever they get together to compare notes, as at conferences. If they don't, some team must have committed either a mistake or a fraud, so goes that utopian view of knowledge and understanding.

    Ironically one of the biggest obstacles to consensus is hermeneutics, a term that Sokal seems to regard as pretentious but which is the accepted term in the business for what stuff means (along with semantics, a term with similar connotations but usually applied to smaller units−both terms are popular targets of ridicule). Were Sokal to complain that his objective has been misunderstood, as anyone under such strenuous attack is likely to do, he would be making a hermeneutic appeal. (He may well have so complained, but after reading his article starting this war and his subsequent "confession" I had no further interest in reading anything by him not in his own field as his motives and attitudes seemed perfectly clear.)

    It is all very well to say that the meaning resides in the mathematics, but for many people, even scientists, this breaks down when there is no accompanying intuition. Most people simply aren't capable of absorbing purely quantitative theories like quantum mechanics in the absence of accompanying reasonable interpretation. The saying in the business is, "shut up and calculate," but the physicists who can really do so are a breed apart. When quantum computation became a real subject, physicists who'd been researching and teaching quantum mechanics all their life didn't simply wade into that fray like ready-made experts, it was more like Mark Spitz learning to wind-surf and it took even the expert quantum physicists several years to absorb the mindset of quantum computation despite both being based on the same mathematics.

    Both technical and social intercourse is hugely dependent on interpretation. An excellent practice when encountering discrepancies, besides checking for errors and fraud, is to compare notes on the meaning of terms. Accounting should by rights be one of the most exact of disciplines, where inaccuracies of even a penny could be questioned were pennies in short supply. Yet accounting is notorious for its dependence on interpretation, which creates room for expensive misunderstandings on the one hand (you might prefer one stock over another and find later you'd picked the wrong one because their balance sheets meant different things), and frauds on every imaginable scale on the other. Translation between languages is another area presenting endless opportunities for misunderstanding through misinterpretation.

    I say Sokal's motives were clear because arguments of the kind he clearly enjoys have been going on for millennia, sometimes on purely religious matters, sometimes at the boundary of religion and ethics, or ethics and medicine (whether to save the mother or the baby when both is impossible), or ethics and war, or religion and science, etc.

    When arguing within a community that is largely in agreement with its interpretations, the discussions tend to be civil and productive. When people who interpret things differently meet, things break down much more readily and rapidly. Put simply, the arguers argue past each other. Each side feels it has valid concerns that the other side must be able to see (since they are so obvious) and is simply willfully ignoring. This gets both sides very angry with each other, and it becomes a considerable effort to keep the discussion civil. In such situations the odds of reaching consensus are vanishingly small. Not unlike divorce, where if you part amicably no lawyer is needed to perform division by two, but if your spouse hates you, you are foolish not to hire the most aggressive lawyer your estate can afford to be sure you aren't robbed by your spouse's lawyer.

    In this case Sokal launched a war on his own initiative as his way of arguing the case for his side. This has been a very popular tactic by military and religious leaders for as long as history has been recorded, and for all we know several times longer. The fact that many consider this debate tactic the height of incivility in bringing people to a meeting of the minds has done nothing to deter its practitioners. Expect to see many more Alan Sokals in future centuries. I place him in the shadowy underworld of physics agitators.

    Why should I care if I'm neither a physicist nor a philosopher myself? (Actually I'm a little bit of both, having originally trained as the former and having strong interests in the latter, especially the exact philosophies like logic.) Mainly I care because I don't want some spacecraft flown by a crew of postmodern philosophers into a spacestation occupied by my descendants in revenge for a crusade launched by some physicist errant centuries ago.

    o Trigonometry: A place where Pi = 3

    If you draw a circle on a sheet of paper you will find that π, the ratio of the circumference to the diameter, is pretty close to 22/7, or 3.142 in decimal. But if your circle is so big that your paper's curvature follows the curvature of the earth's surface, and if you insist on defining π as the ratio of the circumference to the diameter, then π might be a bit smaller when measuring the diameter along the surface.

    At the southern border of Canada's Yukon and Northwest Territories and Nunavut, where they meet British Columbia, Alberta, Saskatchewan, and Manitoba along their respective northern borders, π is exactly 3. Exactly! This is because that border is at latitude exactly 60 degrees north, and the length of that latitude around the world is exactly three times the distance from any point on that latitude heading north to the North Pole and then continuing on until you reach that line of latitude again, somewhere deep in Russia if you started from the Yukon border. That trip over the top is what counts as a diameter in spherical geometry.

    This assumes that the world is perfectly spherical. In practice nothing is that perfect, but as has often been pointed out, size for size the earth is smoother than any billiard ball. The exact latitude where π is 3 is for all practical purposes that border. And of course its Southern Hemisphere counterpart.

    o Medicine: The truth behind poisonous metals in vaccines

    Should you vaccinate your kid or not? Well, as everyone knows, for thousands of years physicians have been foisting on their patients cures that are worse than the disease. But as everyone also knows we are taller and run faster than a century ago, and our average life span is double what it was some centuries ago, or what it is even today in countries with inadequate medical infrastructure.

    So are doctors doing their job better now or not? Some say yes, they're obviously improving when you look at how strong and healthy we are today. Others say no, they're as bad as ever and it's gotten worse because now they're also beholden to big business.

    The nay-sayers tell us that big medicine is injecting our kids with dangerous metals, specifically mercury and aluminum. Are they just finding modern rationalizations for ancient superstitions that had more justification centuries ago, or is there more to this than meets the eye?

    We recently researched this question, and unearthed a shocking finding. Big government is behind the deadly metals in both vaccines and tuna sandwiches! And why? Because we are now living so long that social security will soon kill the budget. Mercury and aluminum are the government's none-too-subtle solutions to this coming crisis. Due to less oversight of tuna sandwiches by independent laboratories the government has been able to put a thousand times as much mercury in tuna sandwiches as in vaccines. But since not everyone likes tuna they have not completely neglected vaccines, nor dental fillings for that matter.

    So there you have it. Be a good little citizen now and eat up that tuna sandwich. Otherwise your descendants may inherit a fiscally bankrupt government when they would clearly be much better off with a morally bankrupt one, were they to survive the mercury.

    ----This secret revealed to you by Citizens for Thinning the Herd by Misinforming the Gullible.

    o Compression

    Q: Does it take more or less energy to double the pressure of a given mass of gas when starting from atmospheric pressure (14.7 psi) than when starting from a hundred atmospheres (1470 psi)?

    A: It takes the same amount of energy. Although compressing a hundred atmospheres takes a hundred times the force of compressing one atmosphere, the piston doing the compressing only has to move one-hundredth as far. Energy is force times distance so these factors cancel. In particular I calculate that at temperature T degrees Kelvin it takes 5.763 T joules to double the pressure of a mole (Avogradro's number of molecules) of any gas, no matter what pressure you start from, provided the gas remains a gas throughout. If it changes phase to a liquid or solid partway through, the energy required is less because the piston moves less than half the remaining distance when the pressure doubles. To my knowledge you first read this here: this constant has not previously been calculated or even considered.

    o Compressed Natural Gas -- Is it Worth It?

    The constant of 5.763 joules per degree Kelvin from the above section makes it easy to compute the additional cost (besides purchase in uncompressed form) of compressing natural gas to 3760 psi or 256 atmospheres, approximately the pressure used in the tank of a compressed natural gas (CNG) vehicle. This cost is of interest to those using a home compressor and natural gas from their utility company.

    To double the pressure of a mole of natural gas at a room temperature of 300 K requires 5.763 * 300 = 1730 joules. There are 28.3168/22.4 = 1.264 moles of any gas in a cubic foot at that temperature and 1 atmosphere pressure, whence to double the pressure of 100 cu.ft. of gas from 1 atmosphere to 2 atmospheres requires 1730*1.264*100 = 218700 joules or .219 megajoules (MJ). It takes 8 doublings to reach 256 atmospheres, requiring an energy of .219 * 8 = 1.75 Mj or 1.75/3.6 = .486 kilowatt-hours (KWH) assuming a compressor efficiency 100%. At 30% efficiency, which seems to be what is currently achieved by home filling stations, this rises to 1.6 KWH per 100 cu.ft. of gas.

    These calculations assume complete filling of an initially empty tank. Topping off a mostly-full tank each night is less efficient because all the new fuel goes in at high pressure (equivalently, more unusable energy stored in the compressed gas is lost when drawing fuel from a full tank than from a half-empty one, though arguably some of this loss is offset by the stronger turbocharger effect possible with a full tank). Hence to minimize compression cost, only refill when near empty. The resulting savings however are miniscule and hardly justify the inconvenience of not having a nearly-full tank at all times. However it does mean that long trips that do come close to exhausting the tank between refills result in a very marginally lower overall fuel cost. The following assumes the more economical fill-from-empty routine.

    At a nominal ten cents per KWH, 100 cu.ft. therefore costs $0.16 to compress. At $1.20 per 100 cu.ft., PG&E's rate for gas dedicated to CNG vehicle use, it follows that gas costs 1.20/.16 = 7.5 times as much to buy as to subsequently compress. Now 126.67 cu.ft. of natural gas at 1 atmosphere has the energy content of a gallon of gasoline (so 3.8 100-cu.ft. units equals exactly 3 gallons), whence the cost to buy and compress a Gasoline Gallon Equivalent (GGE) of natural gas is $1.36*3.8/3 = $1.72.

    To this must be added cost of the compressor. Initial purchase cost of the Fuelmaker Phill is approximately $4000 with a life sufficient to pump 2500 GGE and a replacement cost of approximately $2400 including deinstallation, shipping, and reinstallation. This therefore adds $1.60/GGE for the first 2500 GGE or 75,000 miles, and $0.90/GGE subsequently. However purchase and installation of each Phill is paid up front (unlike the gas and compression costs which are pay-as-you-go) so one must add an additional 10% in lost interest bringing these respective costs to $1.76/GGE and $0.99/GGE, dwarfing the cost of compression and exceeding the cost of the gas itself. The total cost per gallon then becomes $1.72 + $1.76 = $3.48/GGE dropping to $1.72 + $0.99 = $2.71 with the remanufactured unit after 75,000 miles.

    The overhead of owning your own refuelling station is therefore considerably more than buying from a gas station that charges say $2.50/GGE. But with gasoline dropping back to below $3/gallon even that price cannot justify the significant inconveniences of CNG.

    The principal benefit of CNG for passenger vehicles is therefore its reduction in emissions and an HOV sticker, not in fuel costs, at the expense of shorter range and less trunk space.

    The App Buying Experience

    I had an iPhone for a year. Naturally I bought Ratatouille from iTunes as soon as I got it, it was cool to watch it on a plane. And I downloaded a few apps such as Google Earth and the Ocarina, though most of the other apps didn't hold much appeal for me.

    This year I switched to the Blackberry Storm, which offered various features I was missing on the iPhone such as removable battery (which has since proved useful on several occasions), Bluetooth modem dialup (BT DUN), and stereo bluetooth headset. The Storm lacks WiFi but the experience with Verizon's 1 Mbit/s Broadband is not too different from the iPhone's WiFi. A really big hit for me was Garmin Mobile, a terrific app that is well worth the price.

    At a keynote speech by Electronic Art's Rich Hilleman I learned that Sim City could be downloaded to mobile phones. This sounded neat so I immediately tried doing so during the talk. I was directed to Handmark's website for the download. Nine days later I still had got nowhere with this. I still have no clue as to what is going wrong, and neither does Handmark. Here's the transcript of our joint efforts at debugging the problem (less occasional expressions of frustration by me, which Handmark has been very patient with).

    Customer (. .) 08/25/2009 01:59 PM
    I've been trying to order Sim City for $9.99 from my Blackberry 9530. I've filled in all the fields but I keep getting a message "Valid Postal Code is required to continue." I've tried both 94304 and 94304-1329 under ZIP but keep getting the same message.

    Auto-Response 08/25/2009 01:59 PM
    The Answers below were automatically selected for you by our system based on your question. If no solutions are listed or the solutions do not answer your question, click "Finish Submitting Question" below to submit your question to our Customer Care team.

    Response (Scott O.) 08/26/2009 03:15 PM
    Thank you for the information. Can you confirm for me where or what service you are using to try to place this order?
    Thank you,

    Customer (. .) 08/26/2009 04:58 PM
    > Can you confirm for me where or what service you are using to try to place this order?

    My Blackberry service is Verizon Wireless, and I was trying to order it directly using my Blackberry 9530 at the Handmark page offering it for Blackberry. I entered all the information requested by Handmark including my ZIP of 94304 and it kept saying "Valid Postal Code is required to continue" in bold white letters on a black background.

    Response (Scott O.) 08/26/2009 05:45 PM
    Are you sure that the United States is selected as your country? This may be preventing that postal code. Please try and let me know if you are still unable.
    Thank you,

    Customer (. .) 09/01/2009 11:55 AM
    I am still unable to get past this problem. It never asks me about a country, and there is no field on the form to indicate the country. What country does it think I am in? I am in the US, which should be obvious from both my phone number and my zip code.

    An additional problem is that your system forces me to reenter all the information on the Blackberry as though I were a new user, even though I already entered it all before and even though I already have a Handmark account, which I set up on my PC in the hope that this would help me buy SimCity for my Blackberry Storm. When I try to log in as an existing user it claims my phone number/password combination is invalid, despite the fact that my Handmark account has all that information.

    Customer (. .) 09/01/2009 12:01 PM
    Ok, now I'm getting a different error message. It says my email address is invalid. I typed Pratt@xxx.yyy.zzz , that's my email address, why does it say it is invalid?

    Customer (. .) 09/01/2009 12:05 PM
    On the possibility that your system was complaining about the space that the Blackberry likes to insert at the end of a field I tried deleting the space at the end of my email address. This had the effect of deleting all the information in the fields below.

    Response (Scott O.) 09/01/2009 12:26 PM
    We do not have anyone else reporting any of the difficulties that you have encountered in placing a purchase. I have added the Handmark credentials to your account. You should now be able to log in using your email address and the password: changeme

    Let us know if you continue to run into trouble with this.
    Thank you,

    Customer (. .) 09/01/2009 02:55 PM
    I tried logging in just now on the Handmark site from my Blackberry 9530. The only options are "New User" and "Returning customers." The latter has no field for email address. What now?

    I tried both my landline number and my cellphone number in combination with the changeme password and both were rejected. Couldn't find any other options.

    Response (Scott O.) 09/01/2009 03:24 PM
    Can you confirm for me what phone number you are entering?
    Thank you,

    Customer (. .) 09/01/2009 09:19 PM
    The two numbers I tried were xxxxxxx and xxxxxxx in that order, both prefixed with 650 (as in 6501234567 with no dashes).

    Response (Scott O.) 09/02/2009 10:56 AM
    I show that account under the phone number: 650xxxxxxx I have set your password to: changeme Please try this and let me know if you are still unable to log in.
    Thank you,

    Customer (. .) 09/03/2009 03:00 PM
    Tried 650xxxxxxx with password changeme and it still wouldn't let me in (not a valid combination).

    So I tried getting back to this customer help page and it wouldn't let me back in there either, either with my usual password or the changeme one.

    So then I tried resetting the password. Your system complained that "This webpage is not available."

    I started a whole new account in order to get back into communication with customer support. I was amazed to find that instead of complaining that this account name was already taken it connected me back to this page!! How is this not a security hole???

    Response (Scott O.) 09/03/2009 03:36 PM
    Hello, I'm afraid that I may be misunderstanding the nature of the issue so please forgive me if we are backtracking a little. You are attempting to log into the page through your device so that you can place purchases and it is not accepting your phone number at the time of purchase and gives you a log in error when you try to use the password "changeme"

    Is this correct? If you are attempting to log into another service can you verify that for me as I may not have set the correct credentials.

    Our apologies for the inconvenience. The error could be mine and if you can verify the above that will assist.

    Once again my apologies.
    Thank you,

    Customer (. .) 09/03/2009 04:17 PM
    Correct. I use the browser on my Verizon Blackberry 9530 to browse to then try to log in with phone number 650xxxxxxx and password changeme and I get the message "This is an invalid phone number and password combination. You can have your password reset using the 'Forgot Your Password' link below." When I click on that link I get the error message "650xxxxxxx does not appear as an account in our system. Contact support for further help in accessing your account."

    Customer (. .) 09/03/2009 04:20 PM
    Sorry, I meant I browsed to (I know I didn't browse to whatever that is because my Blackberry only has a record of, not

    Response (Scott O.) 09/03/2009 04:25 PM
    The web page that you are going to. is an AT&T web page and not a Handmark web page. We do not control the log in information for that service and you will need to contact them for assistance. We do offer products through that web service but we do not manage and I can not adjust your account log in for that service. My apologies at not having realized where you were trying to log in to earlier.
    Thank you,

    Response (Scott O.) 09/03/2009 04:33 PM
    Thank you for the update. I'm afraid that I sent my response before your email came in to our system. I have adjusted your account. Please try logging in using your phone number and the password: changeme

    Thank you,

    Customer (. .) 09/03/2009 07:01 PM
    Nope, still says invalid phone number.

    [at this point an SMS text message arrived on my cellphone with a URL for me to type in]

    Customer (. .) 09/03/2009 07:17 PM
    Well, that took ages to type in (have you ever tried typing random strings of characters like that on a 9530?--it's not a regular keyboard, it keeps trying to convert it into ordinary English). When at last I got it all typed in, the response was "We're sorry. Your change authorization is invalid. Please try again below."

    Customer (. .) 09/03/2009 07:34 PM
    PS. Just to clarify, my previous message was in response to the SMS message someone (Scott?) at Handmark sent to my cellphone as follows:
    Sep 3, 2009 5:01:19 PM:
    Vaughan Pratt, Please visit to change your site password.
    Thank you, Handmark, Inc.

    In the meantime I figured out how to get the link from the SMS message without typing it (tricky to do), but it still says "We're sorry. ... invalid." as before.

    Response (Scott O.) 09/04/2009 10:54 AM Hello,
    I'm sorry for the confusion. Where did you receive that last update? Are you receiving support from another source as well? Can you update me as to who and what they have recommended? I'm afraid I am unaware of who has sent you that link, can you provide some more information?
    Thank you,

    Customer (. .) 09/04/2009 01:29 PM Interesting. I'm not involved with any other support issues AFAIK, so if the SMS message didn't come from you I have no idea who could have sent it, or who would have even known to send it exactly at this time! The contents of the message and the time and date when I received it are all given in my earlier message, that's all the information I have about it, sorry.

    Response (Scott O.) 09/04/2009 02:58 PM Hello,
    I have tested logging into your account and was able to using the password: changeme
    Here are the steps that we used.

    1: Go to on device
    2. select "login" from the bottom of the page
    3. enter your phone number: 6507767728
    4. enter password: changeme

    This should allow you to log into the service.
    Let us know if you run into any trouble.
    Thank you,

    Customer (. .) 09/04/2009 05:07 PM Great. I did the same thing I'd done many times before and this time it worked! Whatever you did seems to have fixed the problem. Thanks very much for all the considerable time you put into this just so that I could download a game, it's greatly appreciated.

    Bottom line: all's well that ends well. But what a pain.

    o Chemistry One mole of air (Avogadro's number of molecules) weighs about an ounce. To be more precise, it weighs 28.97 g or 28.97/28.35 = 1.022 oz, an ounce being 28.35 g.
    o Logic

    There's an old puzzle, due to Raymond Smullyan, in which you meet three travelers one of whom always tells the truth, one who always lies, and one who answers at random, call them T, L, and R. The problem is to determine which is which by asking them three yes-no questions. Here's a harder version. Can you tell which is which by asking the one on the left the same yes-no question three times?

    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.

    o More logic

    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.

    o Optics

    Before asking why mirrors reverse right and left, one should ponder why a menu flat on a restaurant table being read by the person opposite you appears reversed to you not only right and left but also up and down. What mirrors really do is make the number of reversals odd.

    o Time

    If every year had February 29, and one year in every 230 also had February 30, a nanocentury would be √10 seconds plus the time it takes light to travel one cricket pitch.

    o Foundations

    After 756 pages of dense mathematics, Russell and Whitehead's Principia Mathematica finally proves 1+1 = 2 on page 83 of Volume II. If only they had used the same numerals for cardinal numbers that they used for volume numbers instead of those new-fangled Arabic numerals, and taken concatenation xy to abbreviate x+y rather than x×y, they could have left II = II as an exercise for the reader on page i of Volume I, with ii = ii as an easy corollary.

    o Analysis

    True or false? A stopped clock is right more often than one that moves at random.

    o Geometry

    Everyone knows that the area of a triangle is half the base times the height. Less well known, yet known to Archimedes, is that it's also half the perimeter times the inradius (the radius of the incircle).

    o Linear algebra

    If you think Rω is a countably generated vector space you are living in a state of sin. It is freely generated all right, but as a vector space it has uncountably many dimensions, i.e. generators, even though the set ω of natural numbers is countable.

    o Logic

    A Venn diagram consists of finitely many overlapping regions of space such that for every selection of regions the points lying inside the selected regions and outside the unselected ones form a connected space. In two dimensions Venn diagrams can be constructed having up to three circular regions (even with the restriction that they be the same size) but no more. Other shapes allow more possibilities: a Venn diagram with four square regions is possible provided tilted squares are allowed, but not five. More complicated shapes allow larger diagrams. It has recently been shown that for any finite n there exists a shape such that a Venn diagram can be formed with n equal-sized regions of that shape.

    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.

    o Electrical engineering

    In a capacitor C the phase of an alternating current I leads that of the voltage V by 90 degrees, and lags by the same amount in an inductor L. There are four types of electrical engineer.

    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.

    o Statistics

    As a remark on, or perhaps even a contribution to, the philosophy of statistics, the 1986 edition of Littlewood's Miscellany mentions on p.143 the Astronomer's Fallacy, that it is hard to select a star at random (with an eye say to estimating the average brightness of stars) when the brighter stars are more likely candidates for selection. Littlewood then goes on,

    ``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 be 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 as 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.

    o Number theory

    World's shortest rigorous proof of unique factorization: Let the least counterexample be pr = qs with p<q prime and r,s nonempty strings of primes. By leastness no prime occurs on both sides. Moreover p cannot divide q-p. Hence p(r-s) = (q-p)s yields a smaller counterexample.


    Music: The Harmony of the Continued Fractions

    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 2q. 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 2q, 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.

    o What is STENDEC?

    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.

    o Welcome to Doublemix (written January 1, 2018) The least prime is 2. The least four-digit prime is 1009, or MIX in Roman numerals.

    These being all and only the prime factors of 2018, I hereby declare today THE FIRST DAY OF DOUBLEMIX!

    Both primes are important in computer science.

    2 is the radix for almost every computer in the known universe. It was the first number to be discovered by humans, 0 and 1 having no obvious application to multiplicity. When there aren't two or more things, counting serves no obvious purpose. It was millennia before anyone even thought to generalize the concept of two things to just one thing, and several more centuries for 1 to catch on as an actual number.

    Tradition dies hard: even today many mathematics teachers superstitiously skip the 0 times table and the 1 times table due to Boolaphobia, fear of truth values (not to be confused with fear of bulls), the way architects skip the 13th floor due to triskaidekaphobia. Some of course fear all numbers and stick to creative writing the way Mongolian architects stick to yurts.

    1009 is the model number of Don Knuth's pseudocomputer, programmed in the pseudo-assembly language MIXAL in his Art of Computer Programming volumes. The books sold better than the computer, which appeared just as algorithm analysts were agitating for the big switch to higher level pseudocode.

    The least primes with either two or three decimal digits contain only 0's and 1's regardless of whether they are written in binary (1011 and 1100101) or decimal (11 and 101). This has sometimes caused confusion. One of the better known instances was when an order for five Dalmations, normally a one-digit prime number, was inadvertently printed in binary (101) instead of decimal (5). The dogs were delivered while the customer was out and were left at the door with a note helpfully suggesting that future orders of Dalmations be staggered. Hollywood soon got wind of the resulting chaos: you may have heard of or even seen the movie.

    Doublemix is especially important in the US, being an election year in which many Americans will be wondering what deed their deity has rewarded or punished them for by staffing the White House in such an original way, and resolving accordingly to do either more or less of it next time.

    On a happier note, everyone born on the last day of February of Doublemix will be entitled to as many birthday presents as other people. They should count their blessings: those born two years and a day later, or (looking further ahead) in Quadruplemix, won't be so lucky. They'll need to suck it up, life can be cruel. Many are betting that planet Earth won't get to see Quadruplemix. I have accordingly arranged an escrow where both sides can deposit their bets, and will be pleased to distribute it to the winners, with interest at half a percent (not to be sneezed at) when the outcome is known. Bitcoin only, please.

    4. Philosophy

    Justice vs. Politics Arresting Donald Trump for stealing nuclear secrets and lying about it to obstruct justice is a matter of justice. Not arresting him for those things is a matter of politics.

    The Constitution, infringing on personal rights

    In 1973 Roe v. Wade created a right for women, namely the right to an abortion if they wanted one.

    In 2022 the Supreme Court took away that right, basing their argument on the Constitution.

    American children are taught in school that the purpose of the Constitution is to protect the people by infringing on the rights of the government.

    American law seems to be the law of unintended consequences.

    The perfect knock-down argument

    Here is an argument from North Carolina applicable to every conceivable situation. All it requires is for you to match up the circumstances to what you feel is the most relevant article or amendment of the constitution.

    “Disregarding the facts, other politicians — from the White House to mayors to state capitals and City Council members and even our attorney general — have initiated and promoted conflict to advance their political agenda and tear down our state, even if it means defying the Constitution and their oath of office,”

    I may use it on my dental hygienist who keeps bugging me about my flossing.

    God and science

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

    Through faith, one knows God through personal conviction of His presence in the universe.

    Through personal experience, the private and gregarious alike know God through their perception of how He reveals Himself to them.

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

    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.

    An argument for more intelligent design

    Intelligent Design is the theory that complex structures on this planet such as trees and brains are too complex to have arisen by mere chance juxtaposition of their many components and must therefore have an intelligent cause.

    Intelligent design is advanced by its proponents as an alternative to the mechanism of natural selection at the core of Darwin's theory of evolution. Darwin postulated that every species arose from earlier species by natural selection of those individuals of the species best adapted to the prevailing circumstances.

    A prerequisite for evolution is that the species which is to evolve must contain some variation between its individuals; if all members of the species were identical, natural selection would have no way of selecting better-adapted individuals.

    Where I run into difficulty is with the idea that an intelligent designer would not exploit natural selection. Why laboriously design the universe by hand when the convenient mechanism of natural selection allows one to do the job automatically?

    Designing the universe by hand is as inefficient as washing laundry by hand. When the benefits of automation are available the intelligent designer avails himself of them. All He need say is, "Let there be diversity." Natural selection is a wonderfully efficient way to design the universe.

    The Omnipotence Paradox

    Can an omnipotent being create a stone he or she cannot lift? Those who try to argue that there is no paradox here on the ground that such a person may have been omnipotent before creating the unliftable stone but became less than omnipotent after doing so, are overlooking the point that anyone who can't retain their omnipotence while exercising their powers could not have been omnipotent to begin with.

    Free will

    Granted some events are beyond our control, but to claim so for all events on supposedly scientific grounds is defeatist. Free will is that which we exercise in the performance of those events within our control. To deny that there is free will is to claim that all events are beyond our control. A car without gas won't get far, and neither will those who have no control over their actions.

    Granted some thoughts spring unbidden into our minds, but to claim that our every thought is caused by something other than our free will is groundless speculation. Perhaps they are, and perhaps the number of gods is a perfect square, but these are articles of religious faith, not facts scientifically testable by current methods. A computer without software won't get far, and neither will those who have no control over their thoughts.

    The Supernatural in Religion

    Religion as a system of beliefs can be of benefit to both social cohesiveness and mental health, giving its believers a sense of worth, purpose, and community. Of questionable benefit however are its magical or supernatural aspects, those that contradict laws that we accept for all ordinary physical entities but for which we carve out exceptions for the entities of our religions.

    When religion asks its adherents to deny the self-evident, it risks both their clarity of thought and its own credibility.

    A case in point is the insistence of both Christianity and Islam that Jesus's physical body ascended into heaven. For many Christians this is a cornerstone of their faith.

    Yet the proposition that Jesus's body physically exists in heaven raises a number of awkward questions.

  • Size. Has Jesus become smaller or larger during the past two millennia, or has he remained more or less the same size?
  • Distance. How far away is he now? If as far away as the Sun, do our prayers travel to him faster than the speed of light, or do they have the same eight-minute delay as earthbound sunlight?
  • Direction. Where in the heavens does Jesus now reside? If we inadvertently pray to him in the wrong direction, are we being disrespectful?
  • One might expect the standard answer to such questions to be that Jesus's ascension into heaven was a purely spiritual one, and that his physical body remained on Earth following the same laws that govern all mortal bodies.

    This expectation was put to the test by the thesis that the Talpiot Tomb contains the remains of Jesus's body. The commonly raised objection that this was impossible because Jesus's body had ascended to heaven shows just how widespread is the belief in the physical reality of the ascension.

    While these believers cannot say precisely where this physical heaven is located, they are unable to accept that it is located at any tomb on Earth.

    So if Jesus's ascent was not merely spiritual but physical, where did his physical body go? Up, apparently. But if he went up, was he still up twelve hours later, or on the other side of the Earth?

    One might answer "both." But in that case I submit that what is being referred to here is not the physical body of Jesus but his spiritual body.

    The argument that what remains of the physical body of Jesus cannot exist on Earth because Jesus ascended into heaven cannot be reconciled with any sensible interpretation of the Ascension. To make sense of the Ascension we must regard it as spiritual. To view it as physical raises too many unanswerable questions.

    Pilate's excellent question

    John 18:28-38. Then led they Jesus from Caiaphas unto the hall of judgment: and it was early; and they themselves went not into the judgment hall, lest they should be defiled; but that they might eat the passover. Pilate then went out unto them, and said, What accusation bring ye against this man? They answered and said unto him, If he were not a malefactor, we would not have delivered him up unto thee.

    Then said Pilate unto them, Take ye him, and judge him according to your law. The Jews therefore said unto him, It is not lawful for us to put any man to death: That the saying of Jesus might be fulfilled, which he spake, signifying what death he should die.

    Then Pilate entered into the judgment hall again, and called Jesus, and said unto him, Art thou a king then? Jesus answered, Thou sayest that I am a king. To this end was I born, and for this cause came I into the world, that I should bear witness unto the truth. Every one that is of the truth heareth my voice.

    Pilate saith unto him, What is truth? And when he had said this, Jesus looked up and said, Father, when did you say I was also to be tormented by logicians?

    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.

    In Defense of Gopher Snakes

    The ecological world, like Gaul, is divided into two teams that eat, kill, maim, loathe, or send bills to, each other. Let Team X be the one with the gopher snakes and Team Y the other. This establishes for peacocks and mongooses, those desperate killers of snakes, membership in Team Y. And it establishes the same membership for gophers, those deserving victims of gopher snakes. Let us now consider, in turn and without prejudice, the vices and virtues of each of these creatures.

    The Gopher:

    As compelling as the blinding revelation to St. Paul is the recent ecological evidence that, from benevolent leviathan to meek snail darter, every creature great or small in these two teams plays an indispensible role in the continuing rotation of the earth on its axis. Every creature, that is, save the gopher. Members of Team Y know from birth the shame of their membership, and all know the root of their shame: the black sheep of their team, the gopher. Did I say "save the gopher?" Bite my tongue.

    Of course you may not own a lawn, in which case you may not have realized the extent to which the gopher has jeopardized the delicate fabric of the known ecological universe. Actually you used to own a lawn - you surely remember playing on it when you were little. How come you don't own it any more? Probably a gopher ate it.

    Now please let's not have any more of that "gophers don't eat lawns, they only kill them" poppycock. At the zoo live lawn sods are thrown to the milling gophers at the 4:00 pm feeding time. They had to move the 5:00 pm piranha feeding time up to 3:00 pm to get anyone to come.

    The Peacock:

    I wonder if my neighbor's peacock, as a killer of gopher-killing snakes, is devaluing both our houses?

    The Mongoose:

    If you look for this creature in your 1892 Webster's unabridged you will be disappointed. You will however find both the mongoos and the mungoos in your 1954 unabridged, who though spelled differently cannot tell each other apart even in broad daylight. In yet more recent editions it would appear that Noah capitulated to the British spelling, mongoose.

    The 1954 entry defines this beast as "a species of ichneumon of India." This entry reflects an era in which dictionary writers vied with each other for the longest path from a word to something the reader had a prayer of recognizing. If you allow yourself to be drawn into this game you will discover that the ichneumon is "a weasel-like digitigrade carnivore." The experienced player will at this point discount "digitigrade" as a noise word like "the" or "very" or "hypogynous" and call it a tie.

    Contributors to the downmarket Webster's New World Dictionary were denied the privileges accorded the contributors to the Unabridged and driven to the low fog-quotient entry, "a ferretlike, flesh-eating animal of India, known for its ability to kill rats, poisonous snakes, etc."

    You are by now asking yourself, what do I do when a neighbor frantically calls me up late at night to ask whether I think the animal chasing his cat around his lawn is a weasel or a mongoose. You instantly see his predicament: if it turns out to be a mongoose, bye-bye, gopher snakes and bye-bye, lawn.

    For such occasions it would be immensely helpful if you had had the foresight to tape the following extract from the Encyclopaedia Brittanica to your refrigerator.

    MONGOOSE, the name applied to weasel-like carnivores of the subfamily Herpestinae (see CARNIVORA), widely distributed in Asia and Africa, with a single species in southern Spain. The Indian mongoose is smaller than the Egyptian animal, with fur of a brownish grey colour, the hairs being largely white-ringed, while the cheeks and throat are more or less reddish. It is especially serviceable in India as a serpent-killer, destroying not only the eggs and young of these creatures but killing the most venomous adult snakes. The mongoose is not immune to the snake's poison, falling a victim as rapidly as any other animal when bitten. By its agility and quickness of eye, it avoids the fangs of the snake while fixing its own teeth in the back of the reptile's neck.

    Moreover, when excited, the mongoose erects its long stiff hair, and it must be difficult for a snake to drive its fangs through this and the thick skin which all the members of the genus possess.

    The mongoose is equally dexterous in killing rats and other vermin.

    For the effects of the introduction of the mongoose into Jamaica, see F. Finn, Wild Animals of Yesterday and To-day, 1st ed., London.

    Of course if mongooses recognized gophers as vermin it would be a different story. Since they are on the same team this is unfortunately mere wishful thinking.

    I must confess to some discomfort with this idea that mongooses do not eat what they kill. We have all been brought up to believe that animals honorably distinguish themselves from humans by refusing to be drawn into this immoral practice. I cannot find any reliable authorities willing to commit either way on the matter of whether they (the mongooses, not the authorities) eat the snakes they kill. So I have come up with my own theory, based on what I would imagine a Stanford football player would do in analogous circumstances hunting Big Game with his Axe in the California forest. A hungry player encountering a bear cub (of the type associated with UC) would follow his instincts and use his Axe to kill and eat the cub. (You and I of course would use a knife and fork for the eating part.) If the mother were to appear during the meal, he may find it necessary to kill the mother in self-defense, an act seen first only as a tragedy, but then shading into immorality as he realized that eating the mother was beyond even his capacity. Ursicide, but since it was in self-defence it was only a little white ursicide.

    Now I theorize that the unfortunate mongoose finds himself in just this predicament. There he is, joyfully driving up his cholesterol with irresistible snake eggs, and thinking of starting up a snake farm to keep up the supply, naturally giving a percentage to the snakes, when who should come back home but Mrs. Snake. The snake attacks the mongoose, and in an astounding flurry ... but no, we know that in life's big adventure the snake has to lose this one. Sigh, sighs the mongoose, killed the snake that lays the golden eggs. And I can't eat her 'cause she's too tough and I'm too (burp) full. Well, self-defence. My little white anguicide.

    If you have a better theory, or a better word than anguicide, I am sure the Encyclopaedia B. would be the ideal place to send it to.

    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. Assume the designer is intelligent. Then 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. This completes the argument by discharging the assumption in step 1.


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

    5. Poetry (so to speak)

    Why Satan missed the Ark

    The downpour was so great
    That Satan wanted to get on.
    But he didn’t bring a mate
    So Noah didn’t let him on.

    Anatomy lesson
    c. 1/1/15

    My head and heart were placed by Mom
    To keep one cool, the other warm.

    To be or not be an optimist?

    Neither an optimist nor a pessimist be,
    For optimism dulls the edge of scientific rigour
    And so does pessimism.

    Does CO2 poison or asphyxiate?

    Let me make it easy with this ABC o' Dyin'
    You just need to know the first letter of each line.
    When you've got it down and can say it back just fine,
    CO2's first letter is the way to jog your mind.

    Asps are full of poison, they're the dainty way to go.
    Boas merely smother, like your mother but more so.
    Cleopatra had an asp, e-i-e-i-o.
    Determined to outdo her, her boyfriend had a boa.

    (Then there's the more direct mnemonic CO2 and CObra, but that's reason without rhyme.
    If you replace the nitrogen in air with helium, leaving the oxygen at a constant 20% while breathing, your voice gets higher but you don't get dizzy because helium is even more inert than nitrogen. If instead of helium you use CO2, carbonic acid forms in your blood, you get metabolic acidosis, become dizzy, and die. Cyanide likewise gives you acidosis, just more strongly.)

    Will the real sword catcher please stand up?

    When asked who hurled King Arthur's sword
    Some say it was Sir Lancelot
    In sooth it was Sir Bedivere
    So named because he slept a lot.

    No place for a handkerchief

    When going out, to seem of note,
    It used to be you wore a coat.
    We've since come up with something better:
    Everybody wears a sweater.

    Yet another thanksgiving

    The day of giving thanks is nigh
    And so we must go out and buy.
    And some must shop, and some must chop,
    And some must make the apple pie.

    The day of giving thanks is here.
    Bring on the turkey, yams and beer.
    Around the table, while you're able,
    Eat enough to last the year.

    The day of giving thanks has passed.
    At what I ate, I am aghast.
    I huffed and puffed till I was stuffed.
    What better day to start a fast?

    Two theorems about cats provable by induction
    (Ray Balbes' Peano-cat metaphor, set to verse)

    Pray thee accept this verse upon
    The notion of induct-i-on.

    Hath every cat a different god,
    Itself a cat, which some think odd.

    If on each cat a bow you tie
    No matter then how hard you try,
    Should each cat's ribbon match its god's
    Then all cats' ribbons match. (The odds!)

    From these assumptions, tell me, son:
    Can two cats be a god to none?

    And if one mortal cat we see,
    Can cat who worships self there be?

    (The answer is no to both questions. Under the interpretation of "god of a cat" as "successor of a number," these negative answers correspond to the respective theorems that in Peano's axiomatization of the natural numbers, all but one number must have a predecessor, and no number can be its own successor.

    The hardest axiom in Peano's system is induction, because it needs somehow to say "for all properties." In place of the possible values of a predicate, the poem uses the possible properties of a ribbon that might be used in judging whether two ribbons match. Usually predicates are two-valued (true or false), but induction works just as well with multiple-valued predicates when expressed simply in terms of the predicate having the same value at n+1 as it does at n, the essence of mathematical induction.

    Although it is natural to assume that each cat has exactly one god, it turns out that both theorems remain true even if every cat is permitted to have any number of gods, including zero, two, and infinitely many gods.)

    The Book of Ruth, Verse One

    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")

    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

    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

    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

    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.

    The Duality Principle

    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…


    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?

    Lucida: A poem with few letters
    c. 1985

    When I was working on digital typography at Sun Microsystems in the mid-1980s, Chuck Bigelow and Kris Holmes sent me a few letters of Lucida, the font they were developing for use on computers, namely sixteen lower case letters, four upper case, and period. In order to get a feeling for how they worked together in a natural setting I composed the following poem using just those letters.

    Oh who would be a plowman a bowman a cowman.
    Oh who could plumb each wild and woolly wood
    and only place one windmill on each beach.
    How can one who whiled away a day
    become an onion by and by.
    Vain and venal vinyl will become alive in oil.
    Remind me how we pan an ounce and yield a pound in place.
    you need advice do you.
    you have a cow and need a bellboy.
    place a cowbell on a cowboy.
    wow boy.

    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.