William M. Briggs

Statistician to the Stars!

The Mathematics Of Santa Claus’ Present Delivery System (With Video!)

Our favorite annual Christmas post, this time with New & Improved! video of my television appearance.

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.

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.”

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. 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! It’s the difference between primary and secondary causality. Here’s how it’s done.

The Math

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 completed by 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!

Summary Against Modern Thought: Speaking Of God Equivocally And Analogically

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

Equivocation is a danger, but it surely cannot be ever-present. If you disagree with that, you necessarily agree. Perhaps an argument by analogy would convince you?

Chapter 33: That not all terms applied to God and creatures are purely equivocal

4 Further. The use of equivocal terms breaks the continuity of an argument. Therefore if nothing were said of God and creatures except by pure equivocation, no argument could be made by proceeding to God from creatures, whereas the contrary is evidenced by all who speak of divine things…i

iWords have to mean something or nothing means anything. (Get it? Get it?)

Chapter 34: That terms applied to God and creatures are employed analogically

1 IT follows, then, from what has been said[1] that those things which are said of God and other things are predicated neither univocally nor equivocally, but analogically, that is according to an order or relation to some one thing.ii

iiWords, in other words, fail us at a certain point. We can only broach God, come at Him from a point of vast inequality and ignorance. Flaubert’s famous quote seems to fit here: “Human speech is like a cracked kettle on which we tap crude rhythms for bears to dance to, while we long to make music that will melt the stars.”

2 This happens in two ways. First, according as many things have a relation to some one thing: thus in relation to the one health, an animal is said to be healthy as its subject, medicine as effective thereof, food as preserving it, and urine as its sign.

Secondly, according as order or relation of two things may be observed, not to some other thing, but to one of them: thus being is said of substance and accident, in so far as accident bears a relation to substance, and not as though substance and accident were referred to a third thing.iii

3 Accordingly such names are not said of God and other things analogically in the first way, for it would be necessary to suppose something previous to God; but in the second way.

4 [You may want to first consult the footnote before reading this argument.] Now in this analogical predication the relationship is sometimes found to be the same both as to the name and as to the thing, and sometimes it is not the same. For the relationship of the name is consequent upon the relationship of knowledge, since the name is the sign of intellectual conception. Accordingly when that which comes first in reality is found to be first also in knowledge, the same thing is found to be first both as to the meaning of the name and as to the nature of the thing: thus substance is prior to accident both in nature, in as much as substance is the cause of accident, and in knowledge, in as much as substance is placed in the definition of accident.

Wherefore being is said of substance previously to being said of accident, both in reality and according to the meaning of the word.

On the other hand, when that which comes first according to nature, comes afterwards according to knowledge, then, in analogical terms, there is not the same order according to the reality and according to the meaning of the name: thus the healing power in health-giving (medicines) is naturally prior to health in the animal, as cause is prior to effect; yet as we know this power through its effect, we name it from that effect. Hence it is that health-giving is first in the order of reality, and yet healthy is predicated of animal first according to the meaning of the term.

5 Accordingly, since we arrive at the knowledge of God from other things, the reality of the names predicated of God and other things is first in God according to His mode, but the meaning of the name is in Him afterwards. Wherefore He is said to be named from His effects.iv

iiiSubstance? Accident? Here’s the Catholic Encyclopedia:

Substance, the first of Aristotle’s categories, signifies being as existing in and by itself, and serving as a subject or basis for accidents and accidental changes.

…Nothing is more evident than that things change. It is impossible for anything to be twice in absolutely the same state; on the other hand all the changes are not equally profound. Some appear to be purely external: a piece of wood may be hot or cold, lying flat or upright, yet it is still wood; but if it be completely burnt so as to be transformed into ashes and gases, it is no longer wood; the specific, radical characteristics by which we describe wood have totally disappeared. Thus there are two kinds of changes: one affects the radical characteristics of things, and consequently determines the existence or non-existence of these things; the other in no way destroys these characteristics, and so, while modifying the thing, does not affect it fundamentally. It is necessary, therefore, to recognize in each thing certain secondary realities (see ACCIDENT) and also a permanent fundamentum which continues to exist notwithstanding the superficial changes, which serves as a basis or support for the secondary realities — what, in a word, we term the substance. Its fundamental characteristic is to be in itself and by itself, and not in another subject as accidents are.

You are still the same you as yesterday even though you have changed by, for example, ingestion and excretion. You persist. The form into which the stuff which makes you is poured stays, but the stuff is rearranged or swapped out.

ivThis is much clearer (and briefer!) ni Summa Theologica (paragraphs added):

…Thus, for instance, “healthy” applied to animals comes into the definition of “healthy” applied to medicine, which is called healthy as being the cause of health in the animal; and also into the definition of “healthy” which is applied to urine, which is called healthy in so far as it is the sign of the animal’s health. Thus all names applied metaphorically to God, are applied to creatures primarily rather than to God, because when said of God they mean only similitudes to such creatures.

For as “smiling” applied to a field means only that the field in the beauty of its flowering is like the beauty of the human smile by proportionate likeness, so the name of “lion” applied to God means only that God manifests strength in His works, as a lion in his. Thus it is clear that applied to God the signification of names can be defined only from what is said of creatures.

But to other names not applied to God in a metaphorical sense, the same rule would apply if they were spoken of God as the cause only, as some have supposed. For when it is said, “God is good,” it would then only mean “God is the cause of the creature’s goodness”; thus the term good applied to God would included in its meaning the creature’s goodness. Hence “good” would apply primarily to creatures rather than to God. But as was shown above (Article 2), these names are applied to God not as the cause only, but also essentially. For the words, “God is good,” or “wise,” signify not only that He is the cause of wisdom or goodness, but that these exist in Him in a more excellent way. Hence as regards what the name signifies, these names are applied primarily to God rather than to creatures, because these perfections flow from God to creatures; but as regards the imposition of the names, they are primarily applied by us to creatures which we know first. Hence they have a mode of signification which belongs to creatures, as said above (Article 3).


[1] Chs. xxxii., xxxiii.

Do people like or not like the new footnotes? They look different in the emailed versus on-screen versions of the posts.

NYC Protesters: ‘What Do We Want? Dead Cops!’ Update: Dead Cops

“Comedy” (or perhaps “farce”) is a good word to describe the human predicament given events like Sony (the hacked company which revealed emails with lame jokes) studio head and noted progressive Amy Pascal having to “run to Al Sharpton next week to beg for forgiveness“.

Run to Al Sharpton next week to beg for forgiveness! AL SHARPTON!

Now if you don’t find that hilarious, then your imagination is stunted, your sense of history and proportion is sadly narrow, and your educational upbringing largely constituted of propaganda. You’re probably also a danger to yourself; at the least your mental well being is suspect, and you might, if you are exceptionally far gone, even be a danger to society.

Incidentally, it’s one thing to pretend to be “shocked”, “sickened”, “horrified”, suicidal or worse by these emails. So much is expected because of the certifiably insane, really quite lunatic, way race relations are in this country. But if you really are “shocked” etc., then baby, you are a — — — — —. I can’t say the word in an open forum. But you know damn well what it is. We’re raising a nation of mollycoddled half-witted hyper-sensitive snivelling weepy perpetual children. Sticks and stones may break their bones, but microaggressive names will plunge them into sickening (to witnesses) despair. Idiots.

Remember when we discussed herd immunity and the waning of Christianity? How plenty of folks, particularly young ones, safely ensconced in the remnants of Christian structures but ignorant of that fact, think everything will be fine, nay superior, once we throw off the final “religious shackles” and judge morality based on enlightened voting? And how, because few have any memory what Western civilization was like without the civilizing influence of Christianity (never being taught any history that wasn’t ideological), everybody is in for a rude surprise in, say, thirty to fifty years?

Same sort of thing applies to the idiot children (some of them fully grown) who marched through my backyard Saturday night chanting, “What do we want? Dead cops?” Dead cops, mark you. They also, further cementing the poop-filled diaper metaphor (or should I say reality?), chanted that they wanted it “now”. (Another contingent of mentally challenged did similar things in Berkeley. It’s unclear whether they received class credit for it.)

Some of them meant that “now.” Some officers were assaulted. The tweet above (linked here if you can’t see it) shows one bag of confiscated hammers, which some homicidal maniac (I speak literally) brought to use on the skulls of police (see this).

See if you can put yourself in the shoes of the cop who has just fingered the collar of the bloodlusting fool with the deadly weapons. The miscreant is probably foaming at the mouth and resisting arrest, probably shouting some standard activist slogan like “Kill! Kill! Kill!”. You get the idea.

If I were that cop and I thought nobody was looking, I’d be severely tempted to show that young man the kind of damage hammers can inflict. I’d call it a science demonstration. Tempted. I don’t think I’d do it unless the contemptible halfwit actually struck me and I felt I was defending myself.

Multiply this temptation across the hundreds to thousands of cops at these many “demonstrations” (demonstrating what? sublime unteachable ignorance?). Are you not as surprised as I that nobody has yet received what was coming to him? If the demonstrations continue, it’s bound to happen, and when it does the media will trumpet it as “brutality.” This will prove beyond any doubt any civilized person might yet cherish that journalists are among the least of us. But skip that.

Suppose these mental mole hills are granted their wish and we have a few dead cops and nobody does anything about it (like our self-styled communist mayor). Further suppose that cops, having had “sensitivity” grilled into them, pull back from black neighborhoods and stop the arrests. What will happen?

For whatever reasons, blacks commit far more crime than any other group (see the FBI stats here and here). This is just the raw statistics talking—and they’re talking an order of magnitude for violent crime, more for lesser crimes. Stop arresting criminals and the crime rate climbs. Where it peaks nobody knows.

The “demonstrators” don’t know now how good they have it. Herd immunity. The police have done these past few decades a marvelous albeit imperfect job (name one profession which is perfect). Remove police, lower their moral, let crime increase, and what happens? Nothing good.

One day these silly children are going to go too far and some authority is going to, as C Northcote Parkinson colorfully put it, “have the moral courage” to fire into the crowd. It’s at that point the “demonstrators” will get the exact opposite of their “demands.”

Update The fellow behind the hammers is—are you ready?—a CUNY professor and “poet”. What rhymes with (his words) “F*** the police”?

Update Although the points made here have nothing to do with it, let’s acknowledge racism does exist in America, and it sure is ugly. For instance this and this from a NYC official who said “Racist NYPD *******”.


Update This last week, the Police Benevolent Association “banned” the far left Mayor de Blasio from their funerals “if any”. I predict de Blasio, perhaps linking arms with Cardinal Dolan, will show at the service for the two “allegedly” (to use a favorite phrase of de Blasio) murdered men.

Update Not good. Cops turn their backs on de Blasio. Video.

Update People Take To Twitter To Celebrate NYPD Murders.

Update Make your projections. Will this finally be the incident that dooms Al Sharpton? I say no. Others think yes.

Update “Sharpton to have say over how Sony makes movies”. No civilization lasts forever.

Top 10 Health Scares Of 2014 From The American Council On Science & Health

Ahhhh! It's azodicarbonamide!

Ahhhh! It’s azodicarbonamide!

The American Council On Science & Health, longtime exposer of shoddy science, has released their 2014 list of the top scares. Below is a short summary and my comments.

10 Subway’s use of azodicarbonamide in their bread.

Some blogger named Vani Hari—and this is the good news: bloggers can be influential—a.k.a. The Food Babe, took against Subway, even though nobody was forcing her to eat there. She freaked out over the chemical (boo!) the chain uses in their bread.

“Even more ridiculous is Hari’s guidance that ‘if you can’t spell it or pronounce it, you probably shouldn’t eat it.’ It is unclear when spelling became a parameter for toxicological evaluation.” Relying on her own advice, Hari would starve in China. How do you spell “duck tongue” (yum!)?

Anyway, mice fed diets of azodicarbonamide in bulk developed cancer at higher rates than mice not so cruelly treated, which is all the evidence activists (and the ever-present “State of California”) need to conclude it must cause cancer in humans. It’s Science!

9 “Formaldehyde found in baby shampoo”.

Johnson and Johnson put Quaternium-15 in shampoo, which sounds like the maguffin from a science fiction movie, which breaks down into formaldehyde and which keeps shampoo from going bad.

But what about the children!

All of us are exposed to formaldehyde on a regular basis. It exists in a wide variety of food, especially fruits and vegetables, as well as ubiquitous products such as plywood, insulation, carpeting, and cosmetics.

And even if we were able to accomplish the impossible—remove all external exposure to formaldehyde—we would still be exposed to it, since it is made in the human body.

Even children human bodies.

8 Gluten! Gluten! Gluten! This post is certified 100% gluten free.

The dietary fads of rich Americans never fail to provide comedy.

7 Pesticides “linked to” Autism.

Got to love “linked to”. It has no definite meaning and given the low bar of “statistical significance”, almost anything can be “linked to” anything else. Prediction: once every child is routinely checked for autism, it will cease increasing. Think about it.

6 “Hydraulic fracturing (Fracking) pollutes drinking water”

It also causes bad breath, acne, an increase in UFO sightings, and a tendency to vote for Democrats. Increasing UFO sightings? Sure. The two series are statistical correlated. What more proof do you need?

The real concern is one of the fracking fissures caused by an greedy oil company will spread to the earth’s core, cracking it. We could literally split apart!

If that fear gains any traction, I want credit for thinking it up.

5 “Liquid nicotine used in e-cigarettes poisoning children”.

But what about the children!

Well, you can’t blame anti-smoking zealots. There is no “second hand” smoke with e-cigs; no, nor any “third hand” smoke, neither. Activists are so habituated to banning that they can’t stop themselves. And, dammit, those smokers look to be enjoying themselves. Thus the e-cigs must be dangerous. Dangerous to whom? How about the children? Yes!

But what about the children!

4 “Cancer epidemic from medical scans”.

See, this the exact reason metal leaf (thicknesses less than 0.2 mm) sheet-rolled aluminium was invented. It blocks all sorts of electromagnetic cancer causing rays, even those rays which come from outer space! Indeed, it is particularly apt prophylactically for rays which impinge on one’s cranium at direct vertical angles. Medical experts recommend fashioning a snug-fitting cranial-protection garment to avoid prob-scan cancer.

3 “GMOs not safe for use in foods.”

Frankenfoods. Of course, everything we eat has been genetically modified by farmers over centuries of careful breeding and care of stock. So the only way to avoid ingesting any GMO food is to head to the hills and stalk wild caribou using only an organic knife (particles from non-organic knives might cause cancer). Best way to lure these outsize deer is to pretend to be blades of juicy grass. Wear lots of green and brown. Go in November.

2 “Thimerosal in Vaccines poses threat to public health, says RFK Jr.”

I think most of know that after appear the words “says RFK Jr.” there is no need to say anything more.

1 “Prenatal exposure to phthalates linked to lower IQs in children”.

Boy, most of us can’t pronounce or spell that word, so it must be bad (see 10). Rich American parents have every right to expect their children to be above average, IQ wise. Why, if it weren’t for phthalates, azodicarbonamides, and fracking it follows it is near to certain we’d have a nation of near-to geniuses.

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