William M. Briggs

Statistician to the Stars!

Author: Briggs (page 151 of 424)

Casino Deals Unshuffled Cards

As a break from things serious, consider this scenario:

In a New Jersey casino, you walk up to an electronic slot machine, stick in a buck and punch the buttons. You win fifty. It happens. Flush, you venture another buck. You’re still up a bunch. You win another fifty. Figuring why not, you bet again. Another win. Say, this is getting good. Another bet, another win. And so on for forty-one—that is 41—times in a row!

Ah, but then four beefy guys named Guido finger your collar, drag you back to your room and bounce you up and down a bit, hoping to dislodge a device you don’t have, a device which they imagine could have secretly controlled the slot machine. In saunters a pencil necked manager wearing an expensive but garish suit and says he’s not going to pay since he claims the machine is busted.

Out the door you go…straight into a lawyer’s office? Are you upset that you didn’t pocket the proceeds? Or do you figure that this is what happens when you flirt with fortune?

I say, write the whole thing off as a lesson in how not to gamble: viz. don’t gamble. Especially in New Jersey—New Jersey, for crying out loud.

The scenario painted above happened in a sort of way. In New Jersey at the Golden Nugget. According to the AP, several players at a game of mini-baccarat

kept seeing the same sequence of cards dealt, over and over and over again, their eyes grew wide and their bets grew bigger, zooming from $10 a hand to $5,000.

Forty-one consecutive winning hands later, the 14 players had racked up more than $1.5 million in winnings — surrounded by casino security convinced they had cheated but unable to prove how.

The Casino blamed their playing card source, Gemaco, Inc., which was supposed to send them the painted boards pre-shuffled. Only this time, they forgot. Also, this wasn’t the first time: “the Trump Taj Mahal Casino Resort used unshuffled mini-baccarat cards for 3 1/2 hours before realizing something was wrong.” You may wonder at the level of minds that take three-and-a-half hours to discover the decks of cards they’re using are unshuffled.

The Golden Nuggest, after they finally figured—after seeing forty-one straight hands with the same damn sequences over and over and over again—their cards were rigged, weren’t such bad sports about it. It “let nine of the players cash out $558,900 worth of chips.”

But poor Hua Shi of Brooklyn wasn’t one of them. He says he went back to his room after the game to knit the raveled sleeve of care, but then in busted a quartet of Planet of the Apes cast members “who pinned him against the wall and searched him and his belongings” and then kept him there overnight.

Hua Shi’s lawyer says he got the business because he was Chinese and that his treatment had nothing to do with the winnings he racked up from the stacked decks.

Recapitulation: forty-one—41!—consecutive winning hands are dealt, Casino realizes something fishy, notices unshuffled card; casino sues Gemaco, shakes down a player Hua Shi for winning too much; Hua Shi sues Casino.

I haven’t any idea how to compute the probability of 41 identical hands, because it would requiring knowing how many players played, the numbers of decks used per game, whether every player bet the same way each time, and so forth. But good grief, quantitative probability isn’t needed! Maybe, just maybe, after seeing the second hand identical to the first, we can imagine a pit boss saying, “Well, it could happen.” But after three? And then four, and even five?

The suspicion is either we’re not getting the whole story, or that casinos would not be the best hunting grounds to search for Mensa members.

If I were the judge, I’d throw out all the suits—and I wouldn’t apologize for the bad pun.

End Of The World Approaches—This Time Via A “State Shift”

Humans reproduce and multiply

“Humans,” the species nobody asked for, “now dominate Earth,” the brutes, “changing it in ways that threaten its ability to sustain us and other species,” for it is our duty to sustain other species. So goes, plus or minus, the opening strains of a melody we have been singing for lo these forty years.

This particular arrangement was conducted by Anthony D. Barnosky and his orchestra in the Nature article “Approaching a state shift in Earth’s biosphere.

Listen to the soothing lyric! “Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds.” Notice the sly use of forced: some thing is having its naughty way with Nature. What could that thing be? You know.

Historical examples of tipping points tipped? How’s a mass extinction grab you? Sure, the last one was 65,000,000 years ago, and took “2,000,000 yr to complete”, but it “could have been much shorter” (emphasis mine, and yours!). And then there’s the Cambrian explosion—an explosion!—half a billion years ago, with a bang extending over a mere 30 million years. (Let’s don’t mention the “explosion” was one of biological diversity.) Finally, glacial-interglacial transitions, the last of which was just the other day, about 11,000 years ago, and boy was it a whopper, causing the

extinction of about half of the species of large-bodied mammals, several species of large birds and reptiles, and a few species of small animals; a significant decrease in local and regional biodiversity as geographic ranges shifted individualistically, which also resulted in novel species assemblages; and a global increase in human biomass and spread of humans to all continents.

Now it is a fact that George Bush knew of each of these events, and did nothing to stop them! We’re in luck that our current administration is more caring. Just never mind the positive correlation that the coming of ice and thriving of Man were simultaneous: what matters is the transition killed off picturesque woolly mammoths.

Barnosky’s refrain is “past critical transitions occur very quickly”, meaning if they occurred very quickly in the past, they can do so again in the future. Sure, “quickly” is in thousands to millions of years, but why don’t you stop being critical and realize that “Critical transitions lead to state shifts, which abruptly override trends and produce unanticipated biotic effects.” Unanticipated, meaning we know exactly what will happen and it won’t be good.

And since we don’t know, we need to “improve biological forecasting” to anticipate “critical transitions” that can emerge; this would “minimize biological surprises that would adversely impact humanity.” This works because forecasts are an apt substitute for actual knowledge. Right, Gav?

Let me throw two more terms at you: “synergy and feedbacks.” Ha! These terms make tipping points realer when it dawns on you that individual geologic and biologic are not as absolutely, perfectly independent. Things interact: one thing changes another, which changes the first thing back, and so on synergistically. Sure, “Potential interactions between overlapping complex systems, however, are proving difficult to characterize mathematically, especially when the systems under study are not well known and are heterogeneous.”

By God, we don’t even know how many of these feedbacks and synergisms are out there! But they’re there, bet on it. And don’t you know that because we don’t know, you just know that changes in any of them caused by the likes of you, has to change things for the worse?

This is why we must “guide the biologic future.” After all, if we don’t, who will? We must keep the Earth as she is, in pristine purity, because however she is now (or was, just before the Industrial Revolution), is how she always was and always must be. Forgot those other tipping points: they’re in the past. The Earth of 1890, or 1850, or whatever, is our goal. Those climates are not in the past. They’re our future, as long as we act now.

Otherwise, “the biological resources we take for granted at present may be subject to rapid and unpredictable transformations within a few human generations.” Unpredictable: this is why we must predict them! As our last presidential election taught, change is not always for the better. Indeed, change is always involves “loss”, a word Barnosky loves. Why, if it weren’t for the last glaciation, we wouldn’t even be here to complain about it. Let that sink into your brain pans.


Incidentally, the same issue of Nature finds Paul “The End Is Near And This Time I Mean It” Ehrlich wielding his pen in service to the noble goal of “Securing natural capital and expanding equity to rescale civilization”. We’ll look at this tomorrow.

Statistics Of Drinking, Emailing, Pupil Size

Today, three studies from loyal readers.

Drinking Creatively

First up, the New York Post’s Kyle Smith with an anecdote:

Father O’Brien was driving home after lunch when a policeman pulled him over. “What have you been drinking?” asked the cop. “Only water,” replied the priest. “Then what’s that next to you?” said the policeman, pointing to the half-empty bottle of pinot noir in the passenger seat. “Good Lord!” said Father O’Brien. “He’s done it again!”

This broaches the worthy topic of civilized lunches. Seems that researchers set up a statistical study which got volunteers drunk and asked them to play

a game in which they were given a group of words, such as peach, arm and tar, and asked to come up with another word that could be used in combination with any of the above, such as pit.

Tipplers delivered more correct answers and delivered them more quickly. Drinkers solved nine problems on average, versus six for the sober group, and came up with answers in an average of 11.5 seconds as against 15.2 for the teetotalers.

Well, this is good enough for me. Statistics proves drinking at lunch is good for you. There must be a p-value joke in there somewhere, but it’s early and my glass of breakfast Chablis did not appear.

Control Your Pupils!

You might not be surprised to learn that ivory-tower researchers, who are not known to imbibe at their midday meals, find different ways to stimulate themselves. One of these is in measuring the “profound sex and sexual orientation differences in sexual response…based on measures of genital arousal.” Profound. This is a strategy which, interestingly enough, has “potential limitations” such as—are you ready?—“volunteer bias” (pause and reflect, dear reader, pause and reflect) plus the unacceptable circumstance that there are “differential measures for the sexes.”

Academics have now solved this discrepancy! Instead of wiring up the naughty regions of volunteers, researchers looked them right in the eye. Yes, a pair of Cornellians “assessed the pupil dilation of 325 men and women of various sexual orientations to male and female erotic stimuli.” Peer-reviewed result? “[S]elf-reported sexual orientation corresponded with pupil dilation.”

In research funded by the—drum rollAmerican Institutes of Bisexuality, academics discovered “Among men, substantial dilation to both sexes was most common in bisexual-identified men.” Oh, the work was also funded by you, in the form of the United States Department of Agriculture’s Federal Formula Funds. Which “Formula” we are never told. And don’t you think it’s just the USA: these tricks were first tried in the Great White North in the “1950s and 1970s.”

Another hard-core finding: “sexual attraction patterns of women are less affected by a partner’s sex and more by cultural, social, and situational variables.” Yes, truly, size matters: wallet size, that is.

How did they get their volunteers? The old-fashioned way: “from a web forum where men sought both men and women for sexual reasons.” What could go wrong? Once at the “facility”, volunteers “were seated in a dimly lit room facing a monitor.” Dimly.

Then came the data manipulation and statistical modeling, which produced one or two, but only one or two, p-values of the acceptable range. Must be a joke lingering there, too.

Email Me

More peer-reviewed research (pdf) tells us that “Depression is a serious mental health problem affecting a large population of college students.” To prove it, researchers asked some college kids how depressed they were and then measured their “average packets per flow, peer-to-peer (octets, packets and duration), chat octets, mail (packets and duration), ftp duration, and remote file octets.”

Lo! There was a positive statistical correlation, with publishable p-value, between some of these measures and the depression score.

Sure, were the Pearson r values between 0.06 and 0.28? They were, they were. And did “remote file octets” (perhaps accompanied with pupil dilation) have the best correlation with depression? It did, it did. Though the correlation between gloom and “average packets per flow” was nearly nil. That’s why they switched to the Spearman’s rho for this measure, where a successful p-value was finally found. There’s more than one path to a publishable p-value!

One conclusion: “Frequent email checking may relate with high levels of anxiety, which in-turn correlates with depressive symptoms.” Which in turn leads to the dismay of statisticians who read studies like these. Depression for everybody!


Thanks to Al Perrella for the first two tipples, and to Nate West for the last.

Bias Against Conservatives In Academia: Shocking New Study

Gander at this picture:

We are shocked to discover more leftists than rightists in academia

This shows self-reported political affiliation of a group of academic social and personality psychologists (this included some graduate students and post docs). The graph is difficult to read on-screen, so download the original, from the peer-reviewed paper “Political Diversity in Social and Personality Psychology” forthcoming in Perspectives on Psychological Science by Yoel Inbar and Joris Lammers.

Our authors asked, about Economics, Foreign Policy, and Social “issues,” this: “The following questions are about your OWN political attitudes. Please note: liberal is intended to mean ‘left/progressive’ and conservative is intended to mean ‘right/traditionalist.'”

Imagine our delight at finding more self-labeled moderates and conservatives than expected under Economics. Not every academic wants to take from them which have and then empower a government bureaucracy to dole back out a portion to support academic salaries. Celebrate this. And smile that the number of conservatives and moderates in Foreign Policy is not vanishingly small.

Matching the freshness of the headline “Pope Catholic”, however, is the finding of the near absence of conservatives, and even moderates!, on Social questions. In many Departments across the land, when traditional mores are mentioned we hear only the sound of one man clapping. Or no man. Especially if that man claps too vigorously.

For, can you imagine it?, academics preach tolerance and freedom, but they do not often practice it. The word you’re thinking of isn’t hypocrite, because the professor who professes “Tolerance!” has a theory which defines that word to mean something other than indicated in its dictionary entry.

Anyway, Inbar & Lammers also asked participants to self-report answers on these questions (they asked for participants’ own opinions and then for participants to judge the opinions of their departmental colleagues):

1. If you were reviewing a research grant application that seemed to you to take a politically conservative perspective, do you think this would negatively influence your decision on the grant application?

2. If you were reviewing a paper that seemed to you to take a politically conservative perspective, do you think this would negatively influence your decision on the paper?

3. If you were organizing a symposium, do you think you would be reluctant to invite a colleague who is generally known to be politically quite conservative?

4. If two job candidates (with equal qualifications) were to apply for an opening in your department, and you knew that one was politically quite conservative, do you think you would be inclined to vote for the more liberal one?

The proper answer to each, for those holding to academic freedom, open debate, intellectual honesty, and the like, is ‘No.’ We should expect, then, for the percentage saying no to be near 0, both for themselves and for their judgment of their colleagues.

But before we come to those numbers, recall that this survey is self-reported, and that human beings lie on self-reported surveys (to the questioner and to themselves), especially on topics which are contentious. Plus, the participants are sociologists and psychologists who use surveys continuously and know well how difficult it is to hide the intentions of the survey. Thus, we might expect, given our wide experience on the reporting of contentious questions, Inbar & Lammers’s results to underestimate the true propensities.

Let’s put the main finding in the words of our authors:

The more liberal respondents are, the more willing they are to discriminate.

Another Who Knew?: “We also found that women were more liberal than men in all domains” (this was in both of two datasets they used). This is academic women, dear reader, a population differing in many respects from civilian women.

For the four questions above, here are the percentages of those who answered being at least somewhat likely (I adapted this table from an Inside Higher Ed story, to align the answers with the same order of the questions):

Question Self Colleagues
1. Grant application 23.8% 36.9%
2. Paper review 18.6% 34.2%
3. Invite conservative speaker 14.0% 29.6%
4. Vote for liberal over conservative 37.5% 44.1%

About a one-fifth of academics admit they would hold a conservative’s views against him in the areas of grant applications, peer review, or in organizing symposia. This proportion doubles for voting for what an academic thinks his colleagues would do, and is therefore probably closer to the real percentage. Our authors put it this way:

The more conservative respondents were, the more they experienced a hostile climate, were reluctant to express their views to colleagues, and feared that they might be the victims of discrimination based on their political views. These fears are quite realistic: a sizeable [sic] portion of our respondents indicated at least some willingness to discriminate against conservatives professionally…

[W]e find that the more liberal participants are, the more likely they are to react negatively to work Political diversity taking a conservative perspective.

Obviously, quite obviously, these are “on average” results, with expected wide variability from institution to institution. Not much conservative discrimination, indeed probably its opposite, is expected at, say, Calvin College, where all professors must swear to the Nicene Creed. But lots and lots of discrimination is expected, and found, at places like Harvard—and there are many more Harvards than Calvins—where even a hint that one deviates (!) from the progressive line can send one packing. Buh bye, Larry.

Inbar and Lammers gave space for participants to write comments:

One participant described how a colleague was denied tenure because of his political beliefs. Another wrote that if the department “could figure out who was a conservative they would be sure not to hire them”. Various participants described how colleagues silenced them during political discussions because they had voted Republican. One participant wrote that “it causes me great stress to not be able to have an environment where open dialogue is acceptable. Although most colleagues talk about tolerance, and some are, there are a few vociferous voices that make for a closed environment.”

Even worse, one wrote “that (s)he once doubted that implicit measures really measure implicit racism, but felt too intimidated to openly ask that question.” In other words, don’t buck the consensus. If everybody uses a measure, it must therefore be right.

I gave this warning to junior faculty and graduate students a month or so back. I repeat it again today. As my old father says, Never pass up an opportunity to keep your mouth shut. If you don’t, you’ll end up with too much time on your hands, forced to take to something as low as blogging.

Reasoning To Belief: Feser’s The Last Superstition: A Refutation of the New Atheism — Part IV

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

It’s God All The Way Down

Talk about causality without foreshadowing a tie to God is coming and, if they can maintain an interest in the subject, people are receptive and willing to debate the argument on its merits. But hint that God is at the bottom of it all, as He will be here, and scholarly repose morphs into a sharp and anxious wariness. People tear into the argument with the zeal of Bill Clinton lecturing us about is. This is fine if the criticisms which arise from the increased scrutiny are valid, but usually they are not. In their suspicion that no good can come from tying causality to God, people are apt to convince themselves of objections which have long been refuted.

So I repeat the warning which I gave as we commenced this review: unless you are a specialist, it is unlikely the counter-arguments which occur to you are valid; further, it is highly probable that they are common and have well known rebuttals. This warning is not proof that the argument to come is valid, of course. It is instead a reminder that space is limited; I can only present a sketch while Feser offers chapters (in TLS and Aquinas). Dip into these volumes if you are convinced of a fallacy.

History, as it has been said, is one damn thing after another. Events which are one damn thing after another often form part of a causal series. Moe slaps Larry which causes him to slap Curly which induces him to slap Moe, etc. (start at 30 seconds). My great grandfather William produced a son William, my grandfather, who in turn produced my father William, who had a hand in me (William), and then I had a go with my number one son, William. This is where this time series stands at the moment.

Both of these are examples of causal series per accidens, first one thing, then another, etc. The object to notice is that my great grandfather, after he had done the work which resulted in my grandfather, no longer had to be present when my grandfather helped produce my father, and so on. And my grandfather need not have been alive when my father made me, etc. And this is so for all series per accidens: whatever set the chain in motion need not be present for the continuance of the chain.

This is not the only kind of causal series. There is another called per se, or essentially ordered causal series. This is the juicy kind, which when understood proves that God exists, and so forms Aquinas’s First Way.

Suppose you are incensed that the owners of Chick-fil-A have political opinions which dare to differ from your own. And so you buy up a bagful of chicken sandwiches and head over to the Family Research Council offices with gun in hand with the intent of teaching Chick-fil-A a lesson. You take out the gun and pull the trigger. Out flies the bullet, wending its way toward and eventually lodging itself into the arm of a security guard. So far we have a series ordered per accidens: you fire, the guard is eventually hit.

But consider the moment you squeeze the trigger. The movements of the hammer and of your finger happen simultaneously. The pressure of your finger is in turn simultaneous with the nerve impulses sending the squeeze signal to your muscles. The contraction of the muscles is simultaneous with the individual molecules in the muscles changing from one state to another, which in turn in simultaneous with the changing of the atoms in the molecules, which in turn is simultaneous with the changing of the forces operating to change the various sub-atomic particles, which in turn in simultaneous with whatever it is that operates on those forces which cause the change, and so on. But not “and so on” forever. This simultaneous, here-and-now series must come to an end: it cannot extend infinitely, otherwise nothing would ever get moving.

Now recall our earlier lesson: nothing that is a potential can be a cause, only something actual can be a cause. As Feser says in the article quoted below, “No mere potency can actualize a potency: only something actual can do so.” All those changes in the trigger-per se series are changes into potentials caused by something actual below them, and this series has to end in a first mover.

Now, a first mover in such a series must itself be unmoved or unchanging; for if it was moving or changing—that is, going from potential to actual—then there would have to be something outside it actualizing its potential, in which case it wouldn’t be the first mover. Not only must be be unmoved, though, it must be unmovable. For notice that, especially toward the “lower” levels of the series we were considering—the nervous system’s being actualized by its molecular structure, which is in turn actualized by its atomic structure, etc.—what we have is the potential existence of one level actualized by the existence of another, which is in turn actualized by another, and so forth…[T]he only way to stop this regress and arrive at a first member of the series is with a being whose existence does not need to be actualized by anything else. The series can only stop…with a being that is pure actuality. [Feser uses the example of a hand holding a stick moving a stone.]

And that being is, as Aquinas said, what we call God. Now I know that this example is too telegraphic to be convincing, or lastingly convincing. But let’s be clear what this argument is not saying. There isn’t one word here about the origins of the universe. For Aquinas, the universe could have begun at a single point in time, or existed forever, or even existed as a multiverse. Consequently, any physical discovery about branes or M-theory or cycles in big bangs, or whatever, have no bearing. This is not an argument about what caused things to be, or what set things moving as in a series per accidens, but about what causes any change whatsoever here and now.

To emphasize: the Unmoved Mover is an argument about what happens now, right now, this second, this very instant, about what is the first cause of every change. Anything that becomes actual is subject to a per se causal series, which must always terminate in a first cause, which is Pure Actuality. Feser continues:

[There cannot be] more than one being who is Pure Actuality [because] in order for there to be two (or more) purely actual beings, there would have to be some way of distinguishing them, some feature that one of them had that the other lacked…For to lack a feature is just to have an unrealized potentiality, and a purely actual being, by definition, as no unrealized potentialities…

A being of Pure Actuality, lacking any potentiality whatsoever, would also have to be immaterial, since to be a material thing entails being changeable…The Unmoved Mover is in any event that to which every motion or change in the material universe…traces back.

Besides monotheism, other traits of God can thusly also be deduced: like Omnipotence, Omniscience, Goodness, and so forth. Feser lays these out well, but in his discussion “privation,” which explains how God who has every perfection, relates to causing the absence of perfection, he stops short. It would surely be a privation to you if you were have your arm bitten off by a shark, but it would be a privation to the shark to miss his lunch. So there appears to be an order or hierarchy of privations (or perhaps this is only apparent due to my poor reading).

He also says little on the implications of the Unmoved Mover to us as rational creatures. Intrigued readers will be left with questions. Since God causes everything, at base, that seems to imply that God is with you as you err, even helping you pull the trigger, as it were. Is this God doing evil? Well, it was your will to do evil, not His. But since you’re dragging Him along in the per se trigger series, no wonder He’s not so happy about sin. Good grief! Can any of that be right?

True, Feser was not attempting to give us a complete theological treatise, but since his purpose was to show the errors of New Atheism, he might have expected to cause a few conversions, that some of his audience would want to know What’s Next?, where to go to resolve the tougher questions. Perhaps then in his second edition, he can provide a reading guide. It’s unlikely many will jump right to the Summa Theologica or Summa Contra Gentiles. A list of intermediate works would thus be of extreme utility.

Feser gives us two more of Aquinas’s Five Ways (in Aquinas, which he highly recommends, we get the whole package), each as compelling, but we’ll skip these and move on to his discussion of the soul.

Technical addendum

Here is a quotation from Feser’s article “Existential Inertia and the Five Ways” published in American Catholic Philosophical Quarterly. This version of the proof won’t be to everybody’s taste; but as somebody trained in mathematics and physics, I find its shape familiar and the chain of reasoning particularly compelling. Perhaps you will as well.

  1. That the actualization of potency is a real feature of the world follows from the occurrence of the events we know via sensory experience.
  2. The occurrence of any event E presupposes the operation of a substance.
  3. The existence of any natural substance S at any given moment presupposes the concurrent actualization of a potency.
  4. No mere potency can actualize a potency: only something actual can do so.
  5. So any actualizer A of S‘s current existence must itself be actual.
  6. A‘s own existence at the moment it actualizes S itself presupposes either (a) the concurrent acutalization of a further potency or (b) A‘s being purely actual.
  7. If A‘s existence at the moment it actualizes S presupposes the concurrent actualization of a further potency, then there exists a regress of concurrent actualizers that is either infinite or terminates in a purely actual actualizer.
  8. But such a regress of concurrent actualizers would constitute a causal series ordered per se, and such a series cannot regress infinitely.
  9. So either A itself is purely actual or there is a purely actual actualizer which terminates the regress of concurrent actualizers.
  10. So the occurrence of E and thus the existence of S at any given moment presupposes the existence of a purely actual actualizer.

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

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