William M. Briggs

Statistician to the Stars!

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Newcomb’s Paradox And Probability

This article was suggested by reader JH who saw it discussed at Massimo Pigliucci’s site.

When he was at the Lawrence Livermore Laboratory, William Newcomb devised the following puzzle, which some say is a paradox.

You will play a game against an evil entity that can perfectly predict your future actions. Just for the sake of giving the Evil One a name, let’s call him “Bill”. Bill is evil because he likes to taunt you with the possibility of making money, only to jerk that chance away from you at the last moment.

Here’s what Bill does, as traditionally described. Later, we add clarifications and twists. Bill puts $1,000 in a clear box, and then also presents you with an opaque box inside of which might contain $1 million. You will be allowed to take both boxes or just the opaque one. To clarify: you may not take the $1,000 without also taking the opaque box. Obviously, you may keep the contents of whatever box or boxes you take.

Now for the evil part. If Bill predicts—and remember, he’s never wrong—that you will take just the opaque box, he will leave it full of money. But if he predicts that you will greedily take both boxes, then he will put nada in the opaque box, which, after mandatory donations to our betters in Washington, nets you only about $550.

Why Bill would ever want to play this strange game is never mentioned. Anyway, the easiest way to short his pockets by a cool million is to decide now and forevermore to take just the opaque box. Because he’s never wrong, Bill will figure you’d do just this, and thus you’d walk away to find new messages on your answering machine from your brother-in-law asking if he could drop by for a chat about this new fishing boat he’s had his eye on.

By the premises of the game, there is no way you can out-think old Bill and collect the million and the thousand simultaneously. You cannot, for example, declare to the world, “I’m only taking the opaque box!” and then, at the last moment, grab both, because old Bill will have anticipated this. Nor can you attempt a crash course in hypnosis to convince yourself that you’re only taking the opaque box, only to be awakened to discover yourself picking up both. Bill would have predicted this perfectly, too.

Not much of a paradox, really. (Though there’s always someone who thinks he’s discovered a way to cheat Bill). Using just brain power and no external devices, the best you can do is a million—which would be good enough for anybody but a politician. So, in honor of our money-thirsty betters, here’s what they can do when next confronted by Bill and his boxes.

When Bill lays out his choices, take out a coin and flip it. If it comes up Heads, take both boxes; tails, take just the opaque one. As long as you are not the sort of politician who would cheat, then your actions cannot be predicted ahead of time by Bill. Since there is only a 50% chance of you taking both boxes, this is what Bill must predict.

He must, of course, come to a decision and not continuously fly between the horns of the dilemma. How Bill does this, how he, that is, comes to a definite prediction is his business, but come to one he must if he is to play his weird game.

There are problems with this. Coin flips are only “random” because it is difficult to know what the initial conditions of the flip are. But if you did know them, then the coin flip is perfectly predictable. And since it’s you who will flip the coin, and old Bill has the lock on your mental actions, we could say that he knows how you will flip the coin. Which, of course, means he knows if you’ll take one box or two.

Regardless whether this is so—you can always have a pal flip the coin, removing Bill’s prognosticative abilities, because the rules do not say Bill can predict anybody’s actions, just yours—predicating your actions on a coin flip can actually be worse for you than just picking the opaque box, because you run the chance of ending up with only $1,000. This happens when the coin lands Heads and this is what Bill predicted. The chance of this—assuming Bill follows the probabilities—is 0.5 x 0.5 = 0.25.

The chance Bill predicts Heads and you Tails is the same: meaning you will decide to take just the opaque box, but you’ll come away broken-hearted. The chance that Bill predicts Tails and you Heads is also the same, meaning there’s a 25% shot at making $1,001,000. Finally, the chance that Bill and you both go Tails is the same, meaning a 25% chance of scoring a million.

Homework: use a quantum number-maker-upper (QNMU), a device whose outcome Bill cannot prefigure, and which spits out Heads with probability p. You can either just take the opaque box, or use the QNMU to decide what to do. What strategy is best and why? If you use the QNMU, what value of p are you picking, and why?


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Are Student Athletes Worse Than Other Students? Deadspin Contest

Ambrose Bierce, as usual, summarized it best for us in the Devil’s Dictionary:

ACADEME, n. An ancient school where morality and philosophy were taught.

ACADEMY, n. (from academe). A modern school where football is taught.

As evidence for the disheartening, inexorable slide into the abyss, we have this “essay”, supposedly written by a DePaul basketball player in his introductory writing course (be sure to read all of it):

Favorite Song

The topic I choose is number four because I like to listing to music especially the love songs because it gets you in the mode for a lot of things. It gets you in the sex mode or even just a chilling mode if you are just relating some where. Love songs some times help people in there relationships some times to because people tend to play songs that’s similar to what they are going through or how they might fill about that person but is afraid to tell the other person, so they let the song say how they really fill about that person.

I don’t really have just one love song I really like because I don’t really listing a lot of slow music. But I have a couple I do listing to when ever I am about to get in to that romance mode or just trying to relaxes in my room. One of the songs I will listing to if a lady friend is over is probably Pretty Ricky song, “Honey” because it sets the mode off right away.

Another song I like is R.Kelly, “filling on your booty”. Now this one is for the one night stand girls because it gets right to the point of what I want to go down. The song starts with chorus and he starts to sing and it goes like this, …

This essay features in a contest by the website Deadspin: “The Search For America’s Dumbest Student-Athlete.” They ask that professors—and many of you are such—send entries to tips@deadspin.com.

Word of the contest is spreading (pace this post). Even the Chronicle of Higher Education mentioned it. It was from them that I learned of the site Rate Your Students (which has since ceased posting new material).

All professors like confirmation that they do not suffer alone, but the hope was soon exhausted on the Rate Your Students site because it became readily apparent from where many students learn their bad habits. The writing from teachers is poor and laced with profanity. They doubtless feel this makes them hip, a quality they need to possess so that their criticisms of student shortcomings are not pedantic.

In any case, Rate Your Students proves that intellectual inadequacy is not confined to the courts or fields of the groves of academe. But perhaps it is worst there. The contest will tell.

It is often argued that a college’s sports teams—usually just the men’s football squad, the other groups providing only red ink—generate a steady stream of income; and for some schools, this stream is a torrent. True, the salaries of the coaches and athletic directors, plus the upkeep of the fields, buildings (always the newest), and equipment drains a healthy portion of the streams out of the university, but there is always something left over for administrators to play with.

It is not even an open secret, but a truism and a necessary consequence of the need to fill uniforms that most college athletes are poor students, and that if it weren’t for their facility with a ball, most would never meet the colleges’ entrance requirements.

A few are so dismally unable to multiply fractions, or to compose essays, that they wash out. But most glide through with a—thanks to grade inflation—gentleman’s B. This situation is tolerated because administrators, professors, and alumni desire that their schools rate high on ESPN. The football field skyboxes (or equivalent) also make lovely places for presidents and board members to entertain and raise funds.

This wouldn’t be so bad—even the kids who fail get to eat and sleep free for a few months out of each year—except for its effects on the remainder of the students (and some professors). For example, when last I taught, students in two classes expected that I would cancel class the day after the game with the traditional rival. The day after, mind. Other profs did as much for them. It was traditional.

I refused, of course, using the old-fashioned argument that their studies were more important, and that if I had to be in class, they did, too. Come the day after, the census was down a bit, but not substantially. Missing, of course, were two members of the football team. Presumably they were recuperating.


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Richard Rogers, Architect Versus Charles, Prince

The New York Review of Books, via an article submitted by a man appropriately named Martin Filler has “deconstructed” Prince Charles dislike of modern architecture.

Deconstruction, in case you did not know, is the postmodern literary process of discovering or inventing words or actions from your victim in order to uphold your preconceived beliefs.

Filler’s belief is that modern architecture, and those that create and design that architecture are good. By “good” he evidently does not mean “beautiful”, “useful”, or “lasting.” Instead, the word translates into “ability to win awards.” Awards which are created and doled out by men such as he.

Prince Charles, Filler was aghast to discover, disliked the works of architect Richard Rogers, a designer who, bucking tradition, is not a narrow-rimmed glasses wearing, clad-in-black German. Rogers looks like your grandfather, a jolly and elegant old man. You would never guess by looking that this man could have brought so many grotesqueries into the world.

Filler classifies the great Prince’s dislike of Rogers’s designs as “mental illness”, which itself is caused by “inbreeding.” Conspicuously, Filler fails to mention his own family tree, so one can only wonder what horrors hang from its branches.

Here is a typical Richard Rogers building. It evokes the feeling of an Edward Hopper painting. There is nothing out of place; everything is perfect; clean lines and a sound structure. And utterly depressing. You can actually feel your happiness leaking away the longer you stare at it. It is ugly.

Richard Rogers design

This entry is typical of modernist design. Almost entirely glass, with weird jutting angles and structures tacked on which appear to defy gravity. The building looks like a puzzle, one that the viewer will tire of after they have figured it out. It might also be the creation of a precocious nine-year-old, cobbled together from a set of building blocks your aunt picked up in the Amsterdam airport. It is also ugly and looks ridiculous and ephemeral, especially when set next to brick and stone structures.

Richard Rogers design

This next attempt continues the erector-set theme, here evoking thoughts of a Japanese miniature found in a 1960s Godzilla movie. You look at that egg-shaped structure on the right and expect that, any moment, Mothra will emerge and start spraying silk over terrified citizens. At least Gojira would incinerate the shell of the cocoon with his atomic breath. The building is not so much ugly as it is silly.

Richard Rogers design

To contrast these purposely juvenile structures, we have those designed by Quinlan Terry, Price Charles’s “favorite living architect”. Filler calls Terrys’ work “soporific” and is miffed that Terry believes that beauty can be objectively defined. This, of course, is no less than the truth.

Here is an example of how to best incorporate the new with the old: by remembering the classical structures are common for a reason. Terry’s facade neatly hides the dull apartment building. It cleverly rides in front of and is not flush with the old structure, so that an effort has to be made to look up. The lines of the stone are neither too close nor too far apart. The detail is welcoming, particularly the homey “shutters” astride the second floor windows, the shape of which is echoed in the top layer of “attic” portals. The third floor’s mini balconies reinforce that idea that we are at home. This is a warm and comfortable place to live.

Quinlan  Terry design

This is a commercial building in Tottenham Court Road, London. Terry is not responsible for the asinine statue (of Elvis?) next door. There is nothing immediately remarkable about this building. It will not win an award. Indeed, you would hardly notice it as you walked by. It appears so solid and permanent it looks like it has always been there and, even stronger, always will be. At night, the windows will glow and tell viewers that “Lasting work takes place here.” It is a manly building, a gentlemanly building. It is not flashy, it does not draw attention to itself. It fits.

Quinlan  Terry design

This is an interior for the Royal Hospital, Chelsea, a building which particularly irritates Filler. This, of course, is the chapel, a room at least remarkable for its inclusion. The windows are exactly placed, the stiles are reminiscent of stained glass. The cross at the end of the room is not overwhelming, but neither can it be missed. The wood walls, wide chairs, and ceiling moulding lend a warmth which is needed to combat the austereness of the walls.

Quinlan  Terry design

Filler classifies Terry’s work as “neo-conservatism”—a self-contradictory term, incidentally. This proves that Filler has fallen prey to the belief that the only art that is “good” is that which is new, subversive, or controversial. Whatever other faults the handsome young Prince Charles has—and there are many—he at least knows that this attitude is bereft of logic.


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The Love Of Money Leads To Socialism

Most, with good reason, misremember the quotation. In entirety:

For the love of money is the root of all evil: which while some coveted after, they have erred from the faith, and pierced themselves through with many sorrows. —1 Timothy 6:10

And since we have that much, it does no harm to recall the words immediately before: “But they that will be rich fall into temptation and a snare, and into many foolish and hurtful lusts, which drown men in destruction and perdition.”

Paul was speaking of the actions of individual men, but he could just have easily meant conglomerations—now corporations, entities which are at once alive, incorporate, and yet not alive. Which, it will be noticed, are the same words we use to describe zombies, the undead. Money itself, and the act of accumulating it, is harmless, neutral; but the love of it, and the concomitant lust for ever greater piles, is the start of pain.

It is here that my sympathies with the Left are strongest. Like them, I dislike the word “capitalism”: a society based on businesses amassing “capital” to create “products” which “consumers” consume. We are content to let these ugly, distasteful words define the foundation of our society?

It’s still worse. Corporations, and those people that temporarily imbue them with life, constantly swear allegiance to stock holders, not to society. They will sell just about anything that boosts the bottom line: televised wrestling, rap music, a movie in which Captain America is “not a flag-waver” (they must consider foreign audiences), “Wonder” bread (it’s a wonder it’s called bread), “designer” jeans, and on and on.

The Left sees all this and, taking the part of the Russian KGB officer from a Cold War spy flick, says “Americans are decadent.” These are fightin’ words, and are what forces some of the Right to say, “It’s not so!” Well, it is so. The charges are true.

Only they’re not true for all. But even if they were, it does not follow that the standard solution of the Left, government proscription, should be implemented. What the Left does not see is that deep inside their ideal of removing freedom and replacing it with top-down rule, lies the same tendencies of the right: to create and to have “consumers” consume. Corporations would still churn, but instead of figuring out for themselves what to produce, a mousy bureaucrat in a windowless office hundreds of miles away would decide for them.

As proof of the Left’s same-mindedness, we have their official organ giving us an article recently “on what makes consumers happy.” Not people, mind, but consumers. They Left knows no other vocabulary but the Right’s. Incidentally, the Times discovered—though they didn’t say so—that “consumers” are happiest when not consuming.

Central control does not work because those at the top are just as fallible and prone to ignorance, bad taste, and idiocy as those in charge at the local level, only centralized leaders are less likely to acknowledge their failings. Instead of lots of different mistakes spread all over in capitalism, proscription (a.k.a. socialism) insures that everybody everywhere makes the same mistakes, with the added benefit that the possibly of innovation is removed. Capitalism at least can make many people happy, but socialism, aiming to make The People happy, insures that only party leaders are.

And neither of these systems fix the fundamental problem, which is the decreasing understanding on what it means to live the good life. Which is to say, we now feel the effects of lack of a classical education.

This is hardly the first time this lack has been noticed. Russell Kirk wrote of it in 1957 in, of all places, Fortune magazine. Even then, Kirk said that businessmen were “largely ignorant of the humanities, which, in a word, comprise that body of great literature that records the wisdom of the ages, and in recording it instructs us in the nature of man. ”

It was about then that colleges began emphasizing the practical and eschewing the eternal. This had consequences. Kirk:

A people can live upon their moral and intellectual capital for a long time. Yet eventually, unless the capital is replenished, they arrive at cultural bankruptcy. The intellectual and political and industrial leaders of the older generation die, and their places are not filled….The result of such bankruptcy is a society of meaninglessness, or a social revolution that brings up radical and unscrupulous talents to turn society inside out.

People awake to the arguments of the Left and see their force. But in doing so, in lacking a fund of historical knowledge upon which to draw, they fall prey to the false dichotomy that “It’s either capitalism or socialism.”

But Paul taught us there is a third way, “For we brought nothing into the world, and we certainly can’t carry anything out. But having food and clothing, we will be content with that.”

Update I’ve been away from the computer all day during which time the spam filter rank amok. All comments lost have been restored. Spam has been increasing dramatically of late (as have hits, and the two go together). I’ll work on it. Apologies to those who thought their comments lost.


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