“A math and weather wiz at NYC’s Cornell University helps crunch the numbers [about Santa]…”

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 field of present dynamics.

A couple of 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. For example, 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. Those presents do get there, 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 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 normal 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 Probability Equation

Merry Christmas, and God bless us everyone!

Peer review—an institution a bare century old, and arising solely to control the page count of proprietary journals—is the weakest filter of truth that scientists have. Yet civilians frequently believe that any work that has passed peer review has received a sort of scientific imprimatur. Working scientists rarely make this mistake in thinking.

Here is an example of how the peer review process works—or rather, does not work.

The California Air Resources Board (CARB) met on 28 October to discuss the Jerrett report “Spatiotemporal Analysis of Air Pollution and Mortality in California Based on the American Cancer Society Cohort: Final Report (as revised)” by Michael Jerrett, Richard T. Burnett, and a host of others.

This is a study which claims to have found a statistical—not actual—relationship between dust (PM^2.5) and premature death for (at least part-time) California residents. I reviewed this paper and found several significant flaws in the use and interpretation of statistical methods. Here is the most significant: “I find further that the summary in the abstract—and therefore the only part of the report liable to be read by most—to be the result of either poor work or deliberate bias toward a predefined conclusion.”

The authors prepared and intensely investigated a series of complex statistical models. There were nine models in total, each having particular strengths and weaknesses. Each had several subjective “knobs” and “dials” to twist. Only one model of the nine (p. 108) showed a “statistically significant” relationship between mortality and PM^2.5, and that only barely; and in that model, only one sub-model showed “significance.” The other eight models showed no relationship. Some models even hinted that PM^2.5 reduced the probability of early mortality. With such a large number of tests and “tweaks”, the authors were practically guaranteed to find at least one “significant” result, even in the absence of any effect. Nowhere did the authors control for the multiplicity of testing, even though such controls are routine in statistical analyses of these sort.

You may even listen to the CARB meeting (mp3: 80 minutes).

There were seven separate critiques presented, all by peers with significant and lengthy expertise in relevant areas. Comments were provided by: Jim Enstrom, Matthew Malkan, John Dunn, Frederick
Lipfert, Gordon Fulks, Skip Brown (Delta), and yours truly (updated). A quote from each:

• Enstrom: “The results in the Jerrett Report do not support the authors’ claim.”
• Malkan: “[The] Abstract, Key Results, Key Findings, and Conclusion sections which do not accurately reflect, and are even contradicted by, the actual data analysis presented in this report.”
• Dunn: “[W]e have a modeling paper that looks a lot like the nonsense put out on global warming modeling, and it has the taint of data torturing in its presentation.”
• Lipfert: “I find that the consistent and overwhelming defect in this report is its arbitrary selectivity:…Selecting heart disease as the most important cause of death, while ignoring the apparently significant beneficial relationships with cancer.”
• Fulks: “With the apparent approval of the agency staff, the authors have refused to correct or even address mistakes.”
• Brown: “This ‘new’ report, whose entire purpose is to justify previously passed regulation, does not address the many scientific comments made rebutting the conclusions reached in the original report.”
• Briggs: “I find further that the summary in the abstract—and therefore the only part of the report liable to be read by most—to be the result of either poor work or deliberate bias toward a predefined conclusion.”

CARB had earlier implemented regulations based on the assumption that particulates kill. The story of how they came by that assumption is odd, but is not relevant here. The Jerrett report was meant to bolster the research that led to the regulations that were already in force. Therefore CARB was to decide only whether to accept or reject the Jerrett report. Despite the numerous flaws and objections given by Jerrett’s peers, after a few minutes discussion CARB voted to accept the report. In one sense, this was fine, because without this acceptance Jerrett could not claim that he fulfilled his contractual obligations.

But in the sense of approving the findings themselves, this peer review process clearly failed. This is true even if the large numbers of criticisms were wrong or inconclusive. This is because rebutting serious criticism takes time, thought, and effort. CARB did not attempt to rebut any of the criticism beyond saying because what Jerrett claimed was also claimed by other authors, therefore Jerrett’s findings should be accepted. Another commentator said that because science is imperfect, we may as well accept Jerrett’s findings.

Then the criticisms were not wrong, especially the “cherry-picking” critique cited above. The statistical mistake (choosing only the significant model which showed “significance” and ignoring the ones that did not, and for not correcting for multiple tests) made by Jerrett is enormous, and if addressed would have caused the claim of “statistical significance” to disappear. It is thus more likely that what Jerrett claims is false.

This is a (not at all unusual) failure of peer review.

Update My critique was commented on starting at 47 minutes in.

Larger Breasts Pay Off for Waitresses

Reader Katie sent in this breaking news: a professor from Cornell’s Hotel School finds that big busted, thin, blond women earn more tips that their opposites. The professor, a certain Michael Lynn, said, “Ugly people are not a protected class, legally. It is not in fact illegal to hire only attractive waitresses.”

To which, depending on your temperament, you shout either, “Injustice!” or “Amen!”

Shock: Race, Sex Matter

Reader Webbed Pete sent in this story from the ABA Journal: “Race & Gender of Judges Make Enormous Differences in Rulings, Studies Find“.

Two studies looked through trials ruled over by the men and women of different races; the studies concluded that the sex and race of a judge matter. The conclusions:

In federal racial harassment cases, one study (PDF) found that plaintiffs lost just 54 percent of the time when the judge handling the case was an African-American. Yet plaintiffs lost 81 percent of the time when the judge was Hispanic, 79 percent when the judge was white, and 67 percent of the time when the judge was Asian American.

A second study (PDF), looked at 556 federal appellate cases involving allegations of sexual harassment or sex discrimination in violation of Title VII of the Civil Rights Act of 1964. The finding: plaintiffs were at least twice as likely to win if a female judge was on the appellate panel.

Note the criterion of success switched between the two paragraphs: in the first, it was “plaintiff losing”; in the second “plaintiff winning.”

Your optimal strategy—if you’re the female plaintiff complaining of “discrimination”—is to seek out a sister: black female judges give you the best chance of sticking it to the man. But keep away from white or Hispanic male judges.

I have not read these studies, so I can’t comment on their veracity. But I would be shocked if there were no differences.

Uncertainty

Reader Sean Inglis sent in this link to the U.K. Royal Society’s “Handling uncertainty in science” series of lectures.

My favorite: Uncertainties of quantum mechanics – faith or fantasy? Sir Roger Penrose OM FRS, Mathematical Institute, University of Oxford, UK.

Incidentally, if you haven’t read any of Penrose’s books, you’re in for a treat.

Half of All People Make Less Than the Median Income!

Reader Jim Fedako sent in this curiosity: “Obesity as an Educational Issue.” Unfortunately, the period to view the article without paying has expired, but Fedako was able to copy this quote earlier: “Today fully one-third of children and adolescents are obese (having a weight to height ratio at or above the 95th percentile for age and gender) or overweight (85th percentile).”

That seem right to you? 33% are greater than 95% or 85%?

This is either another case of statistical hilarity, or the author of the study was using very old tables of percentages, or possibly those tables represented what some human agency decided was “optimal.” I was unable to discover which.

Balanced Education

Ryan Alexander, Campaign Manager for Balanced Education for Everyone, asked me to give a plug to that organization. He says:

The Independent Women’s Forum has launched the Balanced Education for Everyone Campaign that calls for balanced education of global warming in public schools. We’re encouraging encouraging parents and local activists who are interested in this issue to approach their schools. On Earth Day, schools often show films like An Inconvenient Truth or do some activity to suggest that humans are recklessly destroying the planet and will all die off if we don’t take drastic measures. Not all schools are like this of course, but we’ve heard enough alarming stories to realize this trend is happening in many parts of the country.

We’re just asking for a more balanced and appropriate treatment of environmental education. We’ve built a website that gives parents some resources and suggestions to approach their schools and ask for balance (www.balanced-ed.org). It also has a place for parents to share their stories/experiences.

EPA Posts Four New Fact Sheets on Climate Change

An anonymous reader alerted us to the EPA’s efforts to regulate anything to do with climate—-which, by logic, is everything. Start here.

I’ll let readers peruse the site: I don’t have the stomach for it.

Logical Nuns

Reader John Moore points to a National Review pleasant interview with Sister Prudence Allen, R.S.M. What’s the difference between a nun and a sister? This is the place to learn.

Statistical Models and the Census

Reader Al Perrella points us to this article in the Washington Post, in which author Jordan Ellenberg calls anybody who’s against statistical manipulation of census figures a mathematical Luddite.

Ellenberg is wrong: there are plenty of reasons not to trust us statisticians to fiddle with the numbers.

Budget Fantasies

Reader Nate Winchester shows us how paranoia can lead to bad math: Your Tax Dollars at War: More Than 53% of Your Tax Payment Goes to the Military. Sheesh.

Fun Fact: New York City Population

New York City (~8.3 million) has twice as many people as Ireland, about twice as many as Norway, a third more than Denmark. We have more folk than Israel, Finland, Ukraine, Bulgaria, Switzerland, and are about tied with Austria. In fact, NYC tops about 40% of other countries in the world in population.

Only 5 minutes!

A brief show today, containing one Earth-shattering announcement…

Big changes

…As of December 1st, you, my faithful audience members, will be my official bosses!

I am one of the few who honestly admit to not being a people person, and it was thought best by my overseers that I should be isolated from the rest of the population and conduct my labors independently. It will be so.

I am thus becoming a one-man think tank.

Because of this, I’ll be shuttling back and forth between San Francisco-ish and New York for some time. If you hear tell of some unfortunate who needs help with numbers, or they need a lecture, speech, or article or even a book, then please send them my way.

Those who acquire such referrals will be entered on my official Friends of Humanity list, which I need hardly tell you, is quite an honor.

Naturally, since I will find most of my work through this blog, you guys are in charge. So the first thing I’d like to talk about is a raise. Or at least a Christmas bonus. Give until it hurts.

Know anybody worth talking to?

If you are an author, or know one, of a book which you think I would either love or hate, then please send me an email at matt@wmbriggs.com. It’s time to schedule an interview for upcoming podcasts!

Since I am now a feelancer, I’ll be doing some traveling until just after the new year. Interviews and broadcasts will continue again mid-January. Blog posts will continue uninterruptedly.

No Climate Change

There isn’t any discussion about CRU climategate in this podcast. I recorded it before it happened. For an excruciatingly brilliant argument about why people mistakenly believe in man-made global warming, click here.

The best all-round summary I’ve read so far of the flap is here.

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Difficulties

I recently upgraded to Ubuntu 9.10, which included a new version of Audacity 1.3.9, a persnickety package that keeps locking up. Word on the ‘net is that it happens to the 64-bit version, but I have both a 32-bit and 64-bit machine and it locks up on both. I tried Ardour—a professional soundboard—but the thing is so complicated, that I haven’t figured it out in time to record this week’s lecture.

R is coming!

There have been requests for a series of podcasts on R. These are coming, probably in late January or February. R forms Chapter 5 of the class notes.

Conditional Probability

A recognition of logical probability is that all probability is conditional. Most books don’t come to defining “conditional probability” for many chapters, but it’s best to understand that all probability is with respect to, or given, or assuming that certain information is true. Think about the die example we have been using all along. The probability of seeing a 6 is conditional on our premises.

It was not a good habit for the old books to write probability such that it looks unconditional: this led to many misunderstandings. For a good example, grab any old book at look at the notation they use for gambling problems. If ever there was an argument for logical probability, it’s gambling. They will write, for example, the probability of dealing an “Ace” as Pr(Ace). They will give the premises separately: There is a deck of 52 cards, just 4 of which are labeled “Ace”; and just one card will be drawn. All that should have been listed in the evidence explicitly, to avoid confusion: pace Pr(Ace | E).

Agreement

Good news! All philosophies of probability agree on the following rules. As long as the events, propositions, and statements in which we have an interest are discrete and finite. Discrete means non-continuous; we’re not going to (yet) use real numbers, but integers and rational fractions. And we are going to limit our objects of interest to be of a finite nature. This is acceptable because (so far) all events of interest to us are discrete and finite.

Probability Rule #1

Conditional on some evidence, if some thing of interest can be broken into parts, and one of those parts must be true, than the probability of each of those parts (each conditional on our evidence) sums to 1. Take our die example: it can be broken in to the parts “a 1 shows”, “a 2 shows”, … , “a 6 shows.” The probability that some number (from 1 – 6) shows is 1.

Another way to state this is “Either a 1 shows or a 2 shows or a 3 shows…” The probability of that statement, conditional on our standard die premises, is 1. Something must show!

Probability Rule #1: ORs turns to +’s.

Probability Rule #2

Conditional on some evidence, if we have two (or more) events (or propositions, etc.) that can occur, and knowledge of the first event is irrelevant to knowing anything about the second event, then the probability of the first event and the second event occurring is the probability of the first event (given the evidence) times the probability of the second event (given the evidence).

Take throwing two dice and our standard premises. What is the probability (conditional on that evidence) of seeing two 6s? Knowing the result of the first throw tells us nothing about the second. Knowing the result of the second throw tells use nothing about the first. That is, the knowing about one or the other events is irrelevant to knowing about the other. Then the probability of the statement “a 6 shows on the first throw and a 6 shows on the second” given our premises is the probability of a 6 on the first throw times the probability of a 6 on the second throw.

Probability Rule #2: ANDs turns to x’s.

The classical way to state Rule #2 is that the events are independent. I prefer Keyne’s term of irrelevant because it keeps everything on the terms of knowledge. This can be very important in some situations; mistakes in reasoning are easier to make classically.

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Format change The regular and statistics podcasts are undergoing some changes. Stay tuned to this page for details. Today’s show is a little rushed because of this.

Randomness Why don’t we need to add “a fair die” or “an unbiased die” to our list of premises, “We toss a six-sided die, just one side will show, and just one side is labeled 6″? The probability of the conclusion “A 6 will show” is 1/6 without the addition of “unbiased”. If we add it, then our argument becomes circular, for “unbiased” means each side is equally likely.

We’ll talk more about the mysterious hold the word “random” has on experiments once we get to how to map our logical arguments to reality. That is, how do we determine whether a given die is biased or not?

Examples, finally! Give that three out of four dentists prefer Veldensteing Weissbier, what is the probability that your dentist prefers it? Obviously, 3/4. If you further know that your dentist is a teetotaler, then you must modify the entire argument to: “Given that three out of four dentists prefer Veldensteing Weissbier and my dentist is a teetotaler”, the probability that your dentist prefers that beer is 0—you have deduced it.

But you must always explicitly state your premises. You cannot criticize the conclusions of an argument for not including your favorite premises. Arguments stand on their own. Failure to heed this simple rule has led to more grief than anything else in understanding logic and probability. Research the sad story of Laplace’s Rule of Succession for an example.

Incidentally, in most of the arguments that matter to us (politics, religion, etc.), it is difficult to fully state our premises, a situation which makes it appear that probability is subjective. See the notes for more detail on this complicated subject.

Many multiculturalists are fond of saying, “There is no truth.” What is the probability the statement “There is no truth” is true? If the probability is 1, then the statement is false, for we have just found a truth. If the probability is 0, because there are no truths, then there are truths because the statement is false.

In other words, this is just another in a long list of asinine propositions put forward by half-wits who are anxious to get away with something.

But notice in our proof of the idiocy of that statement, we still used certain logical connectives, or steps, the validity of which we assumed true. We can never escape the fact that all truth eventually rests on our intuitions.

Last, my insurance company asked me to “prove that I do not have an additional policy with another company.” What is the probability I can prove this? Clearly state your premises.

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Review Logic: If our premises are that we have a six-sided die that we’ll toss, and that only one side will show on that toss, and that just one side of the six has six spots, then the probability that a six spot will show given these premises is 1/6. Probability, then, is a matter of logic. Usually non-deductive logic, and not necessarily inductive logic. Whew! We finally have that out of the way.

Frequentism The largest rival to logical probability is frequentism. This is the belief that the probability of some event is the limiting relative frequency of that event. Take an event, like a die roll, toss is a number of times which approaches infinity. Count the number of times it comes up “6 spot”, then divide by the number of throws. That limiting fraction becomes the probability. But only after we get to infinity. While this is a perfectly fine mathematical definition, it has nothing to do with reality.

What is the probability that “Hillary Clinton wins the 2012 USA presidential election”? This is a contingent event, and given that information, via logical probability, it is greater than a 0% chance and less than a 100% chance. Given other assumed information, like “She will be the Democrat nominee” then we can say, logically, the probability is 1/2 (implicitly, this assumes she has only one opponent). Incidentally, it is not pertinent that these assumptions are false in fact: assuming they are true, we can calculate a logical probability.

In any case, frequentism can never give a probability for any unique event, or any series of events that cannot, in theory, be infinite. And since those two classes encapsulate all real-world events of interest to humans, frequentism cannot deliver useful probabilities. Even if you wanted to embed the “Clinton wins” event into a set of events that can approach infinity, you are stuck with how. All women running for president of the USA? All women running for leader in democratic nations? All women whose husbands have been presidents? All women who take over any large organization? Each of these will arrive at difference answers—a theme that will often come back to haunt frequentist procedures.

Further, given the premise “Briggs was abducted by a green UFO”, the conclusion “Briggs was abducted by a UFO” has logical probability 1. But it can never have a relative frequency because, of course, it’s premise is false in fact. I think.

Subjective Bayesian The other name for logical probability is “objective Bayesian”, so you can imagine there is a lot of overlap with its subjective, willful brother. This is true: the math is, for all intents, identical; and in practice, nearly all subjectivists act like objectivists, so these objections are somewhat trivial.

However, a subjectivist is allowed to take, “If our premises are that we have a six-sided die that we’ll toss, and that only one side will show on that toss, and that just one side of the six has six spots” and announce the probability as any number he likes. He can say 0.01, or 0.987, or anything between 0 and 1—even including 0 and 1! However, as mentioned, hardly anybody does such a thing.

Next time Demystifying randomness. And finally some examples!

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Quick review All knowledge is conditional on evidence, which eventually leads back to our intuitions. The steps in an argument that make it valid are also assumed to be true. Probability and statistics are ultimately about making arguments to support certain propositions or statements.

Logic and arguments Probability is a matter of logic, so we review some simple logical arguments of the “All men are mortal” kind. We move from arguments that produce conclusions that are true to arguments that produce conclusions that might be true.

Arguments begin with a list of premises that are true, or are assumed to be true. A conclusion, which is related to these premises, is said to be “conditional on” or “given” or “based on this evidence” of the premises.

The simplest probabilistic argument is this: Premises “A die will be rolled; it has just six sides, only one of which will show, and only one of which is labeled ’6′.” The Conclusion of interest: “A ’6′ will show” has, conditional on, or given, or based on this evidence, the probability of 1/6 of being true.

Next time Other schools of probability and why I think they are insufficient or misleading. What “randomness” means.

These notes are not meant to be complete. See the class notes to the left (“Breaking the Law”), or search this site for “Chapter”, where you can find an early (somewhat crude) version.

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Science and skeptical bloggers A small article in last week’s Science magazine frets that skeptical bloggers are teasing climate scientists over their failed predictions. Bloggers are pointing out that actual temperatures have not been friendly to climatologists, and have failed to rise as predicted. Some climate scientists respond by effectively saying: have no fear, warming is on its way—and this time we mean it!

Climate forecast failures? Since 1999, most climate model predictions have been too high by a factor of about 3. Plus, actual temperatures have been decreasing, or at least not increasing. Yet the belief in the accuracy of future forecasts—all of which predict yet more warming—have not abated. Why is this? Why, that is, do scientists believe the opposite of the evidence and is it rational to do so?

Polka! Grab a beer and listen to Yosh and Stan Schmenge sing “Cabbage Rolls and Coffee”. Yum; or, rather, Mmm, Mmm, good. This is the rare live version! My first meal out was cabbage rolls—at Sanders (pronounced saw-n-ders) on Michigan Avenue in Dearborn (Sanders disappeared for a while, but are back, incidentally).

Evidence, Faith, and Belief To be useful, all models—climate, physics, statistics, whatever—must explain, or fit, previously observed data. Fitting that old data is always the first goal of the model-building process, but it is, or should be, far from the last. Climate models do fit, in a statistical sense, old temperature data.

But that old temperature data is sparse before about thirty years ago, and from heterogeneous sources before that, and some of it is even guessed at. There should be, therefore, but is not, tremendous uncertainty that the climate models have reproduced that old data faithfully. No climate model actually predicts past temperatures exactly; they only do so statistically, by simulating climates that “look like” the old data.

Explaining old data is a necessary but not sufficient condition for a model to be valid. To meet that standard, they must also predict new data accurately. So far, climate models have failed in this. Yet the powerful belief that is induced by a model happening to fit old data is almost overwhelming. The model fits, its owners say to themselves, so therefore it is valid. It also helps to know that nearly all statistical procedures—like the kind that are used to verify climate models’ performance—are designed to give measures of how well models fit old data. Overconfidence is an all too common result.

Climate models are built with the assumption that carbon dioxide is important, but only when it operates with a positive feedback mechanism. The truth of this is asserted and the models are built and tweaked, twisted, and tuned so that they fit old data well. Forecasts are then made, which invariably pronounce warming is on its way. And this forecasted warming is—incorrectly!—taken as evidence that the carbon-positive-feedback process is true. Again, this overconfidence stems from enjoying too much the co-incidence of the models fitting (statistically) the old data.

What needs to be done is this: a fully-funded, fully-dedicated team, skeptical of the carbon-positive-feedback process builds, tweaks and tunes, a climate model that does not contain this process. Forecasts from this model are made, and then compared with actual new data and with the forecasts from the standard climate models. (I realize this description is too brief, and even partly unfair—listen to the podcast for more.)

Glenn Beck-John Coleman call global warming a scam Coleman believes that climate scientists are forced to conform to the consensus and are engaged in a “scam.” I do not agree; “scam” is far too strong a word. It might apply to some, but it does not apply to the bulk of climate scientists. I know many of these people and I can assure you that they are not actively engaged in trying to fool the world into believing something that they themselves do not also believe. Using such an inflammatory word makes your enemies shut up their ears and rightly dismiss you as cranky, if not worse.

Nothing makes a scientist’s career faster than proving something that others either did not know or believed to be false. If a young scientist could prove that the carbon-positive-feedback process is false, he would be sitting pretty. But understand: climate models are enormous undertakings, dozens to hundreds of people working on them, building them through multiple years of effort. Vast sums are efforts are involved and no one person can play more than a small part in the process. Therefore, it is almost impossible for one person to go his own way; further, because of the sheer complexity, it is likely that everybody involved will tend to believe the same things. This is why there is a rough consensus of climate model workers.

And this explains why independent people, like your author, are the skeptics.

Polka again I found the outro song on YouTube, but I am unable to rediscover its source.

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I’m away to a conference this week, and so thought it would be fun to start a lecture series Understanding Statistics and Probability (this is posting automatically—I’ll be answering all questions by Monday, 12 October). They’ll be a series of brief chats about the meaning of statistical concepts. We’ll try and keep away from any formulas and concentrate on ideas. I’m aiming for 12-15 minutes for each lecture. Look for these every Friday.

I’ll be roughly following my class notes, which are linked to the left—the book Breaking the Law of Averages.

Feel free to ask questions. I never use canned examples—nobody ever remembers a canned example—so I’ll be relying on you, my faithful readers, to supply situations, and maybe even data.

All knowledge is conditional on evidence which follows a chain that least ultimately back to our intuitions. There are many things we know are true based on no evidence except that of our intuition. Another way to say this, is that our beliefs, all of them, are eventually grounded in faith. This is true for everybody.

While all knowledge is conditional, not all the information leads to certainty. Some propositions are thus known uncertainly. We use probability to quantify this uncertainty. Because of this, all probability, like all knowledge, is conditional. Probability, therefore, is a matter of logic, and we have to understand some basic steps in logic before we can go further. We’ll do that next week.

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