William M. Briggs

Statistician to the Stars!

The Mathematics Of Santa Claus’ Present Delivery System

Truly, miracles are possible.

It’s that time of year for everybody’s favorite post.

It’s the time of year when people begin asking the very pertinent question: How does Santa Claus do it? How does he get all those presents to all those kids in just one night?

Some people think that the old man still personally hand delivers each and every toy—with the enthusiastic help of Dasher and others, of course. That used to be the case, a very long time ago, but there are too many kids in the world now, and the traditional sleigh-bearing method has become obsolete and even impossible.

About a century ago, Santa saw what was coming and began to devise new present-delivery techniques. Naturally, Santa, being the world’s greatest manager, knew that he couldn’t figure out how to do everything all by himself, so he hired outside consultants. I am one of these (not one of the first, of course; I came on only in the last ten years). My contributions are in the scientific field of present dynamics.

[Now a few] years ago, I was asked by the show Weird US to outline the modern mathematical ideas that Santa Claus now employs. The (then) History Channel episode in which I appear (near the end) is entitled “It’s a Wonderful Time to Be Weird.”

“A math and weather wiz at NYC’s Cornell University helps crunch the numbers [about Santa]…” (A heavily compressed clip: if anybody has access to a better rendition, please let me know.)

Many mathematicians go to great lengths to prove, using various theorems and lemmas, that there is no way Santa could physically deliver all those presents in just one night. Arguments begin by noting that there are tens to hundreds of millions of children, and there is not enough time, energy, or space to complete the task in this short a time. A typical analysis is this one, by an engineer. His math and reasoning are flawless.

In fact, any argument which attempts to show that Santa could do his job if he were only fast enough always ends disastrously. Santa would have to travel so fast that the reindeer would burn up like meteors entering the atmosphere. However, these mathematical results, while true, are answering the wrong question. And since those presents are delivered, so Santa must be doing something else. But what?

Have you see the movie Miracle on 34th Street? I mean the original, not any of the unnecessary (and simplified) remakes. There is a scene in the sanity trial of the old man who claims to be Santa in which the defense attorney calls to the stand the young son of the prosecutor. The prosecutor has previously argued that there is no Santa Claus.

The defense attorney, John Payne, asks, (words to the effect), “Johnny, do you believe in Santa Claus?” The kid replies, “Sure I do.” Payne: “Why?” Kid: “Because my daddy told me [there was a Santa Claus].” Payne: “And your daddy is a very honest man, isn’t he? He wouldn’t lie?” Kid: “My daddy would never lie, would you daddy?” The kid comes off the stand and whispers to Santa that he’d like a football helmet for Christmas.

Well, we all know what happens. The prosecutor concedes the existence of Santa and the court eventually decides that the old man in the dock is the one and only Santa Claus. But the key scene sneaks by unless you’re paying close attention. It’s when the case is over and people are noisily exiting the courtroom. We see the prosecutor suddenly realize that he’s got to run. He looks at his watch and says to his assistant, “I’ve got to get that football helmet!”

To be obvious: the kids asks Santa for the helmet, but it is the father who brings it. Do you see? Santa manipulated the events so that the kid got what he wanted for Christmas—Santa was responsible for the present—but Santa did not actually, physically have to bring the present! Here’s how it’s done.

Have you heard of chaos theory? This is the mathematical theory of how things move when they are under complex or unidentifiable forces. A common example: a butterfly flaps its wings in Brazil, and eventually a snow storm develops in Cleveland two weeks later. How? Well, the tiny puffs of air forced from the flapping of the butterfly’s wings cause other puffs of air to divert from their course, which in turn cause still others to change their course, and so on. The effect grows and magnifies so that the path and dynamics of a future storm is changed. Point is: a minuscule cause can grow into a macroscopic event later. You can imagine that the mathematics to track such events are difficult.

Now, Santa doesn’t do this math himself. His specialty is in toy making, not differential calculus, so Santa employs a group of consultants to help with the complicated computer code that is necessary to bring about the massive toy movement on Christmas Eve. I am one of those consultants and have been given permission to hint about how things work. The actual algorithms are, of course, secret and proprietary, so I can only give you a sketch here.

Santa’s sleigh ride is largely ceremonial at this point, though he does go out and personally deliver some presents. He does this in cases where the math indicates that certain children are unlikely to get exactly what they want. This is because the methods that we use are not perfect: Santa and his elves can only “flap their wings” in so many places and in so many ways.

There are two main branches of present dynamics mathematics: the physics of chaos theory, and the subtleties of probability theory. The first branch describes how the present “moves” through world, from its place of origin to its spot under the proper Christmas tree. This is described in the “Santa Claus Gift Momentum Equation”, shown below. The bold “V_gift” describes, in three dimensions, the actual physical location of the present at any moment in time. The parameters of that equations are the forces which govern that movement.

Now, the parameters in the momentum equation are decided by the probability equation, given next. The “p” in the equation is a probability, which should give you some hint that these methods are not perfect. Pay attention to the “I(Nice)” function. That is the “naughty or nice” indicator. Yes, Santa still keeps track of these things, so be careful! You can see that the coefficient on Age is negative, meaning that as you get older, you are less likely to get the present you want.

There is also a lot of “secret stuff” in these equations that I can’t show you. But if you are too curious and just need to know, the best thing is to study physics or math and then someday, if you get good at it, Santa may ask you to help him with Christmas.

Santa Claus Gift Momentum Equation

Gift momentum equation

Gift Probability Equation

Gift probability equation

Merry Christmas, and God bless us everyone!

Pascal’s Mugging Is Silly: Events Don’t “Have” Probabilities

Before we begin, see this similar article about a different mugging scenario, which demonstrated that all probability is conditional and that decision isn’t probability.

Here’s the serious version of Pascal’s Mugging (Eliezer Yudkowsky, or “Yud’s” from Less Wrong, makes little sense; paragraph breaks mine).

Blaise Pascal is accosted by a mugger who has forgotten his weapon. However, the mugger proposes a deal: the philosopher gives him his wallet, and in exchange the mugger will return twice the amount of money tomorrow. Pascal declines, pointing out that it is unlikely the deal will be honoured.

The mugger then continues naming higher rewards, pointing out that even if it is just one chance in 1000 that he will be honourable, it would make sense for Pascal to make a deal for a 2000 times return.

Pascal responds that the probability for that high return is even lower than one in 1000.

The mugger argues back that for any low probability of being able to pay back a large amount of money (or pure utility) there exists a finite amount that makes it rational to take the bet — and given human fallibility and philosophical scepticism a rational person must admit there is at least some non-zero chance that such a deal would be possible.

In one example, the mugger succeeds by promising Pascal 1,000 quadrillion happy days of life. Convinced by the argument, Pascal gives the mugger the wallet.

The previous article and the paragraph breaks should be a giveaway that the whole thing is silly. But if isn’t obvious, here’s the breakdown.

We’re trying to get inside Pascal’s head and form some list of evidence that is probative of the proposition, Y = “The mugger will another day give me X”, where X varies according to the deal. First, the mugger is always wrong: there is no probability for his promise. That probability only exists in Pascal’s head, deduced on the evidence Pascal decides to accept.

Some character comes up to you on the street and says “I’m a philosophical mugger. Gimme $100 and tomorrow I’ll give you $200”, and you’d form the evidence E= “This guy is a lunatic.” From which you’d deduce the probability of Y is 0; i.e. Pr(Y | E) = 0. Further, the higher the amount the mugger claims he’ll give you, the more you’d add to your evidence of the fellow’s insanity. “This guy is a lunatic. He has the power of granting 1,000 quadrillion happy days of life? Give me a break. And fetch me a straight-jacket.” From this, also you’d deduce the probability of Y as 0.

If you like, you can say the “weight” of the probability of Y has increased, in the sense each that addition to the evidence list would on its own lead to a 0 probability of Y (or close to that, depending on how you internally phrased each item of evidence). Learn more about probability “weight” in this fine book.

Anyway, why the interest in such a simple non-problem? Because of the mistaken belief that “events” have probabilities. The mugger insists Pr(Y) > 0, and therefore ups his offer so that whatever decision rule (see the first article about decision rules) Pascal uses, eventually the rule will say it’s optimal to hand over his cash.

This is true; it follows. But that is only because the false belief that events have probabilities. There is no such thing as “Pr(Y)”: it doesn’t exist. It is always wrong. Only Pr(Y | E) exists; so we must have evidence E.

Is Pascal’s Mugging salvageable? Suppose Pascal’s E is the proposition, “The mugger might pay me X”. But that’s logically equivalent to “The mugger might not pay me X”, which is equivalent to “The mugger might or might not pay me X”, which is a tautology. And which thus gives no information about Y.

No. The only way to save PM as a sensible problem is for Pascal himself to add evidence like, “I like the way this fellow looks; he has an honest face. People with honest faces keep their promises in bizarre situations like this sometimes, but not usually. He can keep his promise of giving me X if he really wanted to.” That’s a mouthful, but that’s how our minds work.

Still, there’s no reason to suppose anybody would think like that (except in fanciful, fantastic situations). If X is “Mugger will give me 1,000 quadrillion happy days of life”, nobody would believe it. I doubt anybody would believe it if the mugger promised a buck-fifty.

Russia As Salvation Of The West: Part I — Guest Post by Ianto Watt

If you please, I shall be bold. Bold enough to utter the word. The word that describes Russia in a nutshell. The one word. Because that one word is what is going to affect the entire world, now that Donald has won the Western Emperor’s crown. And then to share it with Vlad, the Eastern Emperor. The only question now is which of these two Caesars will be the actual Augustus? You do remember I told you this would happen, eh? And that as a result of Donald’s victory, there would be a new relationship with Russia, correct? A relationship based on peace. But not peace through strength. At least not on our part.

And so, what is this word? This word that describes Russia in her essence? The Russia described by Churchill as ‘a riddle wrapped in a mystery inside an enigma’? Well, it’s very simple, actually, and you’d think a man of Churchill’s dark brilliance would have understood it, if only he would have looked. But he was too busy destroying the evidentiary trail linking the Teutonic bonds that joined Angland and Germany for almost a millennium. He had to. Why? So no one would notice the similarity of their actions. Russia was just an afterthought to him. He thought the Great Game would last forever. The game Russia could never win. Winnie never saw that the Empire would one day have to reckon with the C-zar. Why? Because he thought Angland had already destroyed him, in the person of the K-zar, back in WWI. Bad move, Winnie. Clean your glasses, old boy. Kaiser Bill was only the warm-up. And Adolph was just a pretender to the would-be Anglo-Saxon world throne.

But now that Germanic chimera is gone. Berlin is not the locus. And neither is Berlin-on-the-Thames. Only Moscow matters now.

And so, back to our word puzzle. The word that unlocks the intentions of Russia. Don’t take my word for it. Listen to Nikolai Berdyaev. Just who was Berdyaev? Well, he was an intellectual, philosophical, religious Leftist Orthodox reformer who knew every Russian of importance, from Solovyev to Tolstoy to Trotsky to Stalin. In fact, when he was arrested by the Cheka (forerunner of the KGB), he was personally interrogated by Felix Dzerjinsky, the head of the Cheka. Attended by Lev Kamenev, if you know who he is. Huh? Well, Lev was one of the first seven members of the Politburo. Buddies of Lenin, Trotsky and Stalin. Here’s how Alexander Solzhenitsyn describes the interrogation in his opus The Gulag Archipelago:

[Berdyaev] was arrested twice; he was taken in 1922 for a midnight interrogation with Dzerjinsky; Kamenev was also there….But Berdyaev did not humiliate himself, he did not beg, he firmly professed the moral and religious principles by virtue of which he did not adhere to the party in power; and not only did they judge that there was no point in putting him on trial, but he was freed. Now there is a man who had a “point of view”.

Berdyaev later left Soviet Russia for the West, where he spent the rest of his life trying to educate the rest of us as to what Russia really is, and what she represents in the family of man. Not many have listened. But they didn’t listen to Solovyev either. It’s probably a cosmic joke on God’s part that these two Russian geniuses both wrote a book entitled The Russian Idea.

Nobody listened the first time (except Berdyaev). And nobody listened the second time. Oh well. They’ll listen this time. But it’s too late, of course.

Anyway, Nikolai Berdyaev, like Solovyev, Dostoyevsky, Tolstoy, Pushkin, Gogol and every other great Russian writer, says the defining term that describes all Russians is Sobornost. And that this word is untranslatable to any other language. Just as the concept of the orientation of the Orthodox Church towards the Holy Spirit is inexplicable to the West. And the reason it is inexplicable is that we in the West do not have the benefit of the experiences that gave birth to the nation of Russia. Or to Orthodoxy.

So just what does this term mean? What does it roughly equal in Western thought? Well, nothing really, but here’s a sampling of the attempts to find a Western synonym for Sobornost; togetherness; brotherhood; unity; one-ness; solidarity; communion; and so on.

And really, until you understand the real meaning of Sobornost, you will never understand the Russian mind. Because Sobornost is the heart of Orthodox ecumenism. Which is at the heart of most Russian philosophy, whether it be implicit or explicit. It is the soul of the Slavophiles and the Tolstoyan Universalists. Of Dostoyevsky and Solovyev. And of course, Berdyaev and Solzhenitsyn. In other words, all of them. And there is the key word, from our Western perspective. Them.

Just who is it that we mean when we talk about them? Well, let’s look at it from their perspective. When we say ‘them‘, they think ‘us‘. Us, as in all Russians. Every Russian, from serf to czar. From sinner to saint. From East to West and North to South. All bound together in one Holy Empire, each member having the same cosmic value as the other. Each member worth the ultimate sacrifice. As the Marines would say, ‘no man left behind’. This kinship is larger than the concept of family. It is nationality, writ large. It is hyper-nationality. Its people value the life of the criminal as much as the life of the judge. Which is why the Western notion of capital punishment is abhorrent to every Russian. Just ask Dmitri Karamazov if you don’t believe me.

But remember not to confuse the past actions of the Bolsheviks with the actuality of true Russian values, as Berdyaev says. Why is that? Because the commies weren’t really acting as Russians. They were acting as hyper-Internationalists, who also professed a belief that all men are equal. Equally worthless, actually, if you disregard their words and look only at their actions. No Russian worth his salt mine would conflate the value of a Left Bank pinko with the life of any true Russian, even a Kalmyk.

So here it is, Komrade. Here is what Sobornost means to a Russian. Every Russian. It means Us. All of Us. But this meaning does not exist in a vacuum, my friend. It’s not the religious concept of the All-One that was proposed by Solovyev. Nor is it the concept of a universal brotherhood of man proposed by Fedorov. And it’s certainly not the ‘Three Branch’ theory of Christianity posed by Palmer and Blackmore in their Oxford Movement pilgrimages to Russia in the mid-1800’s. No, Komrade. In the final analysis, it’s just Us. And furthermore, it’s Us against Them.

So there it is; they see themselves as separate from the rest of humanity. Why is that? Is it because they have suffered at the hands of every rapacious Horde of marauders from the East? Yes. Is it because they have suffered at the hands of every Scythian scourge from the South? Yes. And from every Viking overlord from the North? Yes. And of course, let’s not forget the Western waves of misery, whether it be Polish, Lithuanian, Swedish, Anglish, French or German. Yes, again. In other words, the defensive Russian psyche sees itself as having bravely borne the brunt of every unjust onslaught the world could throw at it, for a thousand years.

But there’s more to it than that. That’s the defensive part. There’s the converse of the coin as well. And the other side of the kopeck is this: that there was a reason, a divine reason, that Russia has survived, unchanged for a thousand years. And there is no doubt in their minds that it was truly divine protection that has kept them intact until today. Inert but intact. And here is the root of Sobornost; that the divine reason for this preservation of the Russian people is because of her faithful embrace of Orthodoxy. Eastern Orthodoxy, to be exact. As contrasted to all of those decadent and/or apostate fools in the West. Especially those silly Western Orthodox idiots that call themselves Anglicans and try to peddle their Three-Branch hokum to the Patriarch. And as a reward for their faithfulness, Russians will be God’s instrument of salvation to mankind. All Russians. To all of mankind. In other words, the Universal Salvation of all mankind.

But this is not The Russian Idea of Solovyev, or Berdyaev, or of the Father of Russian philosophy, Peter Chaadayev in his seminal work Apology of a Madman. No, this Orthodox Russian Idea means something completely different to the Russians. The idea is this; that Russia is divinely destined to be the source of the salvation of the world. The entire world. Period. Just listen to Nikolai Fedorov, in his Religion of Resusciative Resurrection. Listen to Berdyaev in his paean to Fedorv at his funeral in 1903.

Now I know this sounds crazy, but we’re talking about Russia, right? So it should sound crazy, no? And it wasn’t just Berdyaev that was influenced by Fedorov. Solovyev and Dostoyevsky and Tolstoy were all enthralled by the concept of this universal salvation. And a whole host of others. As long as it was brought about by Russia, of course. And let’s be clear; this salvation includes everyone, both past, present and future! Salvation for every last man, whether he be Orthodox, Muslim, Confucian or Shaman. And even those idiot apostate Westerners.

Well, how can this be? After all, if it’s us vs them (from either perspective), where is the unity of mankind in that? How can there ever be peace, let alone universal salvation in that kind of paradigm? Well, there can’t Komrade. At least not yet. We have to add the magic ingredient first, you know. And just what would that be, my friend? How can there be peace without unity? And how can there be unity without peace? Which must come first?

Now we’re at the tipping point. Chicken or egg. Which is it? Well, let’s slow down a bit. Let’s have a drink. Let’s have a think. If we accept (as every Russian does) that there is only One Humanity, then any subdivision of this body is equivalent to amputation. In other words, assuming the body is alive, this severing of limbs is a crime. A crime against humanity. A crime against the All-One. It must not be allowed.

Therefore, in the world of Slav-Think, there must be a cessation of thought that divides mankind. And of course, since the Slavs are the only ones who think this way (in spite of the horrific suffering they have undergone at the hands of the rest of mankind), they must be the ones God intends to choose as the nation that leads all other men to peaceful co-existence, right? Remember that term?

And this leads inexorably, in the mind of all Russians, to the conclusion that if mankind is a unified organic whole, with each nation having an organic (that is, systemic) role, then Russia must indeed be the head of this body. After all, she is the only one that seems to see this organic unity of mankind. She is the only one who really thinks! She must be the head. Get it, Komrade? The only problem, historically speaking, is this; this head has been asleep. This vision of human unity has only been a dream. A hesychastic dream. For a thousand years.

But now this putative head of humanity has awakened. And it seems to think it is the answer to all mankind’s problems. Can’t believe it? Then ask yourself this: does Vlad Putin seem to be animated by this spirit? Does Patriarch Kyrill seem to be animated by it as well? By this attitude of Russian-Orthodox chauvinism? So then, who is the crazy one here, me or Vlad? Or Kyrill? Or is it you, in your disbelief that this could possibly be the true portrayal of Russia?

I know, you think I’m rambling here. But remember, I’m talking about Russia, the riddle, the mystery, the enigma. Did you think this would be totally linear? Is anything of this size that simple? Well, actually, yes. Simple in the sense that the trajectory has already been set. The missile has already been launched. The question is, what were the launch co-ordinates? And who set them? Here’s a hint. The target is Rome. And the programmer, as Chaadyaev clearly saw, was Photius. The Father of Schism.

Statistician to the Stars For Hire!

Herein our semi-annual reminder that the purpose of this blog is mercenary. Filthy lucre is both impetus and goal of its daily readings. Moola, the spondulicks, the government’s glory, the geetis, the green stuff. Lettuce pray. Let it flow.

The burden is on you, Dear Reader. Let’s make it happen. Spread the good news: The Dancing Briggs is for hire!

Yours Truly is wholly independent. Think of the benefits! He has no schedule; he has no affiliations; he has no employer, only transient masters. He has no office: No clock no cubicle no concerns. No office gossip, no endless HR-mandated reviews. No inefficiencies.

These are, of course, the exact same freedoms possessed by those fellows who collect pop cans for remuneration. The same opportunities for advancement and for bonuses, too. The same retirement plan. But the sidewalk walkers have one additional benefit I do not. They don’t have to advertise. I do.

Folks don’t generally understand the wild life we statisticians lead. Why, only yesterday I was deeply involved in measuring trans-rectal diameters for diagnosing constipation. And then there was the time at the Med School I grabbed a slippery black tube off the wall in Dr Oz’s office (this was before he became “Dr Oz” or was famous) and said, “What’s this?”

How was I to know he specialized in colonoscopies?

One too many digestive anecdotes. I shouldn’t have read the Pope’s latest interview. Or had all that pizza. Never mind!

Switch instead to urology. I was recently asked, given my well known antipathy, did I give clients, when they requested them, p-values?

I am a great sinner (in this and in many other things). I do.

I won’t cop a plea of hypocrisy, though. I never give a p-value unless my arm has been twisted, and never without a lecture that there are no good uses of p-values, and that they only cause harm, and that they do not mean what it is thought they mean, and that they cannot prove cause or association or “links”.

So why give them? Because non-statistician journal editors always know more statistics than I. Most of my clients are academics pushing papers, and so they must bend their conclusions in the directions insisted upon by editors. And those editors always advocate doing things as everybody else does things. I have been lectured more times than our dear President has wagged his finger at the nation by editors telling me “The best test in cases like this is this-and-such.” (Hypothesis tests belong on the same pile with p-values.) The charge that peer review enforces mediocrity is true.

My strategy, then, is to provide the error, and also give the better or right answer using the predictive approach. At worst, it’s an opportunity. At best, we can slip in something new. And we had just such a success last week. Science, they say, is self-correcting. Which is, when you think about it, an admission that science is often wrong. Skip it.

What can I do for you? Eliminate the massive, cancerous over-certainty which plagues the old methods. Chances are, you have fallen prey to the Deadly Sin of Reification, or used pseudo-quantification, or have been misled into thinking you have identified the cause of some observation. Chances are, you won’t know the true definition of “chances are.”

The old ways tell you to be sure or nearly sure you’ve made the right decision. But this is almost always an exaggeration. Your confidence in some contingent conclusion should be curtailed if you rely on p-values and hypothesis testing.

Funny thing, though. People like the over-certainty which accompanies classical statistics. Indeed, it is the main reason for the great respect these methods enjoy. They make research a breeze! Want a “definitive” answer to some question? “Submit” your data to some software and out spits “the” answer. Just like a magic 8-ball. And just about as accurate, too.

What can I do for you? Analyses galore. Lectures, admonitions, seminars, classes, tutoring. You name it, I do it, then you pay. Preferably using large quantities of cash. Gold doubloons are always welcomed.

There is also Uncertainty: The Soul of Modeling, Probability & Statistics for those who would rather do it on their own.

Use the Contact Page to (what else?) contact me. Or use the Donate page to say Merry Christmas.

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