William M. Briggs

Statistician to the Stars!

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Gay “Marriages” In Prison: A Dialogue

Teacher: “Why is it that only two people are married at once—couples, that is to say—and not three, four, or more? Why not triples, quadruples and higher?”

Student: “Well, history has always shown it takes two to tango.”

Teacher: “Are you sure you want that as your official answer?”

Student: “Well, yes. There have been cases of one man marrying several wives, but the wives weren’t also married to each other. To a far lesser extent, I have heard of the same thing reversed. One wife and several husbands; but again, the men in those situations weren’t married to each other; just to the wife.”

Teacher: “Then I’m afraid I have to mark you incorrect. That only two people are married at a time, or rather marriage was in pairs, even though some of the pairs were shared, must and could only be the result of irrational animus, bigotry, and hatred.”

Student: “You are the teacher, so you must be right. But could you explain?”

Teacher: “Certainly. You see, when it came to pass in our culture that two men or two women wanted to claim to be married to each other, they had no logical argument to support their desire. They could not point to biology or science, for instance, for those harsh realities insisted that families were for procreation, as that subject is understood writ large. Same-sex pairs could not use history to support their desires, either. For, you see, history did support the idea that only pairs could be considered married, but history also insisted that it was only men and women who could marry each other. History is thus prejudiced. And you have to take it whole. Picking and choosing which bit of history to rely upon is arbitrary and illogical.”

Student: “I take your point. Or points.”

Teacher: “Yes. So since science was of no help, and neither history, it was judged that both reality and history were bigoted, hateful things, and that any who called to these subjects were themselves filled with irrational animus and were thus bigots. Do you see?”

Student: “Yes, I think I finally do.”

Teacher: “Now it will make sense that even prisoners—male prisoners—will be able to declare their marriages to one another. Still only in pairs, of course.”

Student: “Can you quote from a competent authority for that claim? I ask with all respect. Plus I need footnotes for my thesis.”

Teacher: “I can. I quote from the Newsmax article “Gay Marriages Now in Prison“. Ahem:

British inmates Marc Goodwin and Mikhail Gallatinov became the first men to marry one another in the British penal system last year, despite serving life sentences for “hate crimes targeting homosexuals,” the Standard reports.

According to The Guardian, Gallatinov is a convicted pedophile who was convicted in 1997 of murdering a man he met through a gay chat line. Goodwin was sentenced in 2007 for killing Malcolm Benfold, 57, in what was described by police as “a savage, senseless homophobic attack that resulted in the death of a harmless man.”

Gallatinov’s mother, Christina Williams, said she was “glad he’s found love again,” after an earlier ex-boyfriend was moved by prison officials.

Writing for the Standard, Jonathan V. Last questions if “the homophobic murders [could] have been committed by gay men — in which case, they weren’t really “homophobic,” then, were they? Or did Goodwin and Gallatinov’s sexuality evolve in prison?

End quote.”

Student: “Would you classify this as Love at First Sight?”

Teacher: “The evidence supports that view, but I’m afraid without knowing more we cannot say for certain.”

Student: “You don’t find that this article is, well…a tad homophobic? After all, pointing out one of the new ‘husbands’ was a pervert and murderer might lead people to think there is something wrong with homosexual acts.”

Teacher: “Oh, no, I don’t think so. It is only irrational animus, bigotry and, of course, hatred that would lead somebody to fail to praise the many benefits of, for instance, sodomy. For, you see, if sodomy is not bad—and we mustn’t say it is—then it must be good. And what is good must be praised, supported, and even encouraged. All can see this simple point, which is why the news report has done no harm in reporting the facts.”

Student: “I see. Truly you are a wise teacher.”

Probability Three Points On A Line & Measurement Paradoxes

Reader Neil Taylor points us to the video above, which is a jumping point for the larger question (be sure to watch the video first):

In [the video] Professor Stankova makes a statement along the lines that the probability of having three points form a line is zero.

I was fascinated by this statement — I presume it simply comes from a point being a genuinely insignificant part of a continuum.

What confuses me though is that given any two points we can construct a third which is guaranteed to lie on the line between them — via an Euler line for example.

The first two points form a triangle “centred” (via different definitions of centre) by these two points and then the third “centre” can be constructed which will by definition lie on the line through the first two points.

A certain way to reconstruct an event with zero probability.

What a wonderful paradox.

It’s not quite a paradox, because the Euler line is constructed via set rules. That the Euler line exists is proven (graphically and loosely in the video) via simpler arguments. Those three points, and all the other points on the line are there on purpose, if you like. And it is only one example of how to construct a line, which is defined as having infinitely many points which “lies equally with respect to the points on itself”, as Euclid said.

Now any two points can be said to lie on a line (mathematically—we’re not talking physics here). Take a third point and “drop it”, as suggested by the video. What is the probability that this interloper lies on the line?

Well, it’s a bad question. We don’t have enough information to discover. One of our premises is “drop it”. What exactly does “drop it” mean? We need to be rigorous in our definition since this is mathematics. Let’s start with a simpler problem and figure it out, and see how it fits in with this harder one.

Imagine a grid, size N x M, with both N and M finite, with slots which may or may not be equally sized, into which we can either place a wooden pin or nothing. Pick any two slots and place a pin in each. Needed next is the definition of a “line”, made by a path along the pins, on this grid. This line will be porous, and possibly jagged, because we don’t have infinitely many points. Use the same definition your computer screen uses in drawing lines with lighted pixels instead of pins (which are jagged, porous lines). Screen-lines only appear like mathematical-lines because N and M are large and your eyes small.

Anyway, with this definition in hand (whatever it is its premises will be about finite, discrete points) it’s now easy to calculate the probability of filling an unused slot that lies along the grid-line—as long as we have “drop it” defined. Perhaps the most natural definition is, “There will be X unused slots along the line as defined by the two present pins, and the third pin can be in any slot on the grid”. X of course is finite, too. The probability, conditional on all this evidence, is X/(NM – 2), where the subtraction is due to the initial two pins. (Some pedant out there will be situations where NM < 3.)

The next step is to increase N and M, not to infinity, but so that they are very large indeed. X will still be defined, because our grid-line and “drop it” are still defined. The probability is still X/(NM – 2). Finite can be very large indeed. N and M can be googols to the googol to the googol to the googol to the googol to etc. and still be finite. The probability will always be X/(NM – 2) no matter how large N and M grow, as long as they are finite (X depends on N and M and the definition of the grid-line).

Isn’t that interesting? Since N and M (and X) can soar to the heights, there doesn’t seem to be much need (or desire) for infinity. So there are two considerations. (1) What happens when N and M, and perforce X, go to infinity? (2) What if we confuse “drop it” with physics?

To infinity and beyond

Things do not just “go to” infinity, they go there via certain route and at a certain pace. Here, three things are heading off into the great beyond, and we need to be careful to specify with excruciating precision the route and pace of all three items, N, M, and X. We simply cannot rely on intuition because Infinity is too bizarre a place. It will bamboozle you every time. See Chapter 10 of Jaynes’s probability masterpiece for how infinity plays tricks on the finest minds.

One form of intuition suggests that our trio, N, M, and X, journey together at an even pace, in which case the probability X/(NM – 2) scoots toward zero, which is what the video suggested. But there are many other possibilities, and in some of these the probability changes.

Physics and measurement

Any system of measurement—and I go into this (and infinity) in more detail in Uncertainty: The Soul of Modeling, Probability & Statistics—is necessarily finite and discrete. Also remember probability is not physical, i.e. it is not ontic but epistemological, a matter of thought only. Probability can be used to speak about infinity, but measurement which confirms projects will only be finite and discrete.

Any real life physics problem should and must start with how we can measure it, thus we’re in the realm of finite and discrete, where calculations of probability involve only counting. If we think, based on other arguments, there is an infinite-continuous reality beneath the measurements (or a finer, and larger discrete one than our coarse measurements), then we have to suppose a path and a rate at which our measurements head towards this reality. Else, as we saw above, our probability calculations will be wrong.

Don’t be confused about “drop it”, or “drop randomly”, or “drop fairly” or some such other distraction. All that “random” and “fair” business leads to tautological arguments, or which reassert the probability above. On the other hand, if you’re imagining a physical pin bouncing around, you have to specify forces and equations of motion and so on, which if they don’t lead back to the original probability, will lead to something else easily countable—once the definition of these forces are in hand (and where “easily” is relative).

“Random”, “change”, “fair”, and all the rest are like Infinity. They are places where the intuition goes to die.

A Coincidence: Coyne Zinged Me Before I Him — Or, The Coyne Fallacy Redux

Ain’t I pretty?

After posting yesterday’s article, Jerry Coyne Doesn’t Have Free Will (poor fellow), I immediately saw hits coming to my place from Coyne’s. It turned out that, unbeknownst to me, the afternoon before, Coyne had published his own article “I am honored by theologians: there’s now a ‘Coyne Fallacy’!!!“, in which Coyne promotes me to the level of theologian. A fun coincidence and unexpected accolade.

Coyne was interested in his own encomium, the Coyne Fallacy, a neologism which appeared in my review of David Bentley Hart’s The Experience of God.

Let’s get one popular fallacy out of the way. This is the most-people-believe-what’s-false-therefore-it’s-false fallacy, or the Coyne fallacy, named after its most frequent user, Jerry Coyne. This fallacy is used to reject a proposition because most people misunderstand or hold false beliefs about that proposition. So that if the average church or temple goer has a definition of God that suffers certain inconsistencies, therefore God doesn’t exist. If you accept that then you’d have to believe that since the average citizen has mistaken ideas about evolution (holding to Intelligent Design, say), therefore evolution is false. Truth is not a vote.

Straightforward, yes? An obvious fallacy, is it not? Embarrassing to be caught using it, wouldn’t you say?

Suppose an individual proposes God is made of pressed farina and egg. (Well, people do say these kinds of things.) Would that curious proposal therefore prove, or even hint, that God does not exist? God as defined in careful and deliberate prose by Hart as the ground of being itself, the necessary being; the God of Aquinas, as laid out in this series. I mean, wouldn’t it be farcical if somebody in earnest said, “Because some people hold that God is made of pasta, therefore the God of Aquinas etc. does not exist”?

Coyne takes pains to show a list from some poll which says, among other things, that some 57% of Americans believe “Jesus was born of a virgin.” The most one could draw from that would be observations like 43% of Americans have some reading to catch up on, or we’re not doing a good job conveying dogma, and so on.

The Coyne fallacy would be committed if one were to try use the errors of Americans to hint or to attempt to prove that God does exist. Right? Here is Coyne’s answer to the Coyne Fallacy. He first quotes me, then says this:

That’s about the dumbest thing I’ve ever heard. The fallacy, ascribed to me, is to claim that because a group misunderstands the nature of something, that thing doesn’t exist. So it’s just as false to say God doesn’t exist because some Christians (or atheists) have a “false” notion of who He is as it is to say that evolution doesn’t exist because many people misunderstand it.

If what I said was the “dumbest” thing he’s ever read, then it proves Coyne doesn’t get out much. The rest of that paragraph is a restatement of the fallacy. He then says:

And yes, many people do misunderstand evolution. But there’s a difference between evolution and God. Do I need to point out that we have evidence for evolution but not for any kind of god, from Demiurge to the Ground of Being? That’s a big difference. So we can correct misunderstandings about evolution because, as evolutionary biologists, we know how it works. David Bentley Hart has only a knowledge of what other theologians said and whatever revelations strike him when contemplating the Numinous.

Clever readers will have noticed old Jerry (may I call you Jerry, Jerry?) never answered the charge. He instead claims that scientists have no business using mathematics because—wait for it…wait for it—there is no empirical evidence for mathematics! Ha ha! Ain’t that rich.

Sorry, Jerry, old son. It won’t do. First, you stand guilty as charged. You have used the Coyne Fallacy before, and you use it in your attempt to claim innocence of its use. That so many Americans do believe in a Demiurge (Hart explains this term at length; see the review), or something like it, and have false notions of God, does not hint at nor does it disprove God Himself exists.

Second, as for your strange ideas about empiricism you—what’s that? You didn’t say anything about mathematics? Oh. How silly of me.

There is no empirical proof of mathematics, nor of logic, yet I’d wager Coyne (and other atheists) are happy to use, rely on, and trust both. (If you disagree, email me the infinite subsequence of an infinite sequence; any sequence will do; be sure your email client allows large files.) Logical positivism, and the extreme empiricism which accompanied it formed, as the late great David Stove said, an episode of “black comedy in philosophy.” Somehow the word about the failures of positivism did not get back to scientists. Well, these things take time. Been about a century now. Still. Grants proposals and such can distract one so.

Anyway, arguments about the nature of God are necessarily metaphysical, philosophical, and, yes, theological. About the first two, like in mathematics, empirical proof will forever be lacking, but about the last, why, there is loads of empirical evidence! The resurrection of Jesus alone, an empirically verified event, i.e. a whopping piece of observational evidence, has kept authors busy for two thousand years. So, please, no more carping about “lack of evidence.”

About me

In his post, Coyne pointed to my “Who is WMB?” page, which excited many of his readers. Many were in awe of my status as Thought Leader (Slogan: “Have your thoughts led by me”). I recall well the press release announcing this lofty post:

FOR IMMEDIATE & PERPETUAL RELEASE

It can now be revealed that my recent secret trip was to secure a reverse MBAectomy, a painful operation which has frappéd my cranial capacity a statistically significant 342.7%. I am now qualified to be, and do hereby accept the title of, Thought Leader…

Coyne’s readers were, to say the least, impressed by my achievement. One, overcome by the discovery, wrote, “Thought leader? —omfg.” (That woman gets a discount when she wants her thoughts led.)

Several commenters, examining closely the picture Coyne used of me, thought that I was attempting to spin so as to fly, like a helicopter. These people were wrong. There was one night experimenting with some Irish homeopathists with achieving lift off, but I can report no success. Above, the photographer caught me demonstrating the Fourth Position in ballet. Ballet beats the skintight pants off of yoga. Besides, I look wonderful in a tutu.

I don’t know who Ken Phelps is, but clearly this fellow knows me well:

I am once again unable to resist the image of a small boy, dressed in his father’s shoes and fedora, overcoat trailing on the ground behind him, clomping about the house, waving a felt marker about as if it were a cigar, and he a tycoon.

It is human nature, I suppose, to ape those we are not. But really, inventing fallacies? Perhaps in the future you should check to make sure the cap is on the marker, Mr. Briggs, your lips lips are bright yellow.

I’m not old enough for real cigars: I substitute lemon lollipops instead. This explains the lip color.

Someone calling himself infiniteimprobabilit asks the important question, “‘Statistician to the Stars’ — wtf? Why would the stars need a statistician?” Because, of course, the Stars would never be caught dead discussing their own wee p-values.

Ed Kroc, perhaps an investigative journalist, finds it “extremely suspicious” that Cornell does not list me among its Adjunct Faculty. Well, Ed, now that you’ve read me, would you admit to knowing me? (About my book, perhaps “skimming” isn’t helping you; try reading. Your brother-in-ink Jeremy Pereira might try the same: I have an entire Chapter on the different kinds of Induction which he missed.)

Finally, Bruce Lyon suspects I might be a “climate change denier”. Let me set your mind at ease, Brian. I have never denied the climate has changed.

Jerry Coyne Doesn’t Have Free Will

Be sure to read the caption.

Edge is at it again, asking named persons “What scientific term or concept ought to be more widely known?” Many interesting things to discuss, so consider this the launching of a new series. (I was directed there, via this site, which linked to me.)

My eye was caught by the never-disappointing Jerry Coyne, author of Faith Versus Fact: Why Science and Religion are Incompatible. Coyne wrote to tell us that he has no free will. This is terrific news, because we’d hate to think he was responsible for that book. Far better to put it down to the determinism, and poor sense of humor, of genes and the laws of physics.

Coyne is at the bottom of a long line of thinkers who tell us the world would be a better place if we knew we could not make choices, because then we’d make better choices.

Profound, n’est-ce pas?

A concept that everyone should understand and appreciate is the idea of physical determinism: that all matter and energy in the universe, including what’s in our brain, obey the laws of physics. The most important implication is that is we have no “free will”: At a given moment, all living creatures, including ourselves, are constrained by their genes and environment to behave in only one way—and could not have behaved differently. We feel like we make choices, but we don’t. In that sense, “dualistic” free will is an illusion.

This must be true from the first principles of physics. Our brain, after all, is simply a collection of molecules that follow the laws of physics; it’s simply a computer made of meat. That in turn means that given the brain’s constitution and inputs, its output—our thoughts, behaviors and “choices”—must obey those laws. There’s no way we can step outside our mind to tinker with those outputs. And even molecular quantum effects, which probably don’t even affect our acts, can’t possibly give us conscious control over our behavior.

One wonders who this “we” is. It appears, according to Coyne, there is a person above and beyond the body or flesh robot whose actions are determined with full rigor by genes, chemistry, and physics. This ghost-in-the-machine, as it were, notices what’s happening, it has desires and wants, but it is powerless to have its way. This ghost can see the “mind” of the robot, but can’t influence it. Meaning, of course, the ghost is a person with free will but who is ever shackled. So there is free will after all, but only for ghosts.

Why is it important that people grasp determinism? Because realizing that we can’t “choose otherwise” has profound implications for how we punish and reward people, especially criminals. It can also have salubrious effects on our thoughts and actions.

First, if we can’t choose freely, but are puppets manipulated by the laws of physics, then all criminals or transgressors should be treated as products of genes and environments that made them behave badly. The armed robber had no choice about whether to get a gun and pull the trigger. In that sense, every criminal is impaired. All of them, whether or not they know the difference between right and wrong, have the same excuse as those deemed “not guilty by reason of insanity.”

The armed robber had no choice but to pull the trigger, yet somehow—more mysterious ghosts?—the person who punishes the robber does have free will in choosing to punish! Thus the punisher is the real bad guy.

But wait a moment, wait just a moment or two. Let’s read that passage again at a more sedate pace. What’s this about robbers behaving “badly”? Did Coyne say badly? As in not goodly?

No, Jerry, it won’t do. If people are machines responding by fixed rules to external stimuli, in the same was as the photocopier or electric mixer does, then there is no bad, there is no good, there is nothing. There is no possibility of right or wrong. No morality, no ethics. No nothing. Somebody can only act badly when they had the possibility of acting goodly, and vice versa. Under determinism, as Coyne-the-meat-machine envisions, there are no possibilities, only unbreakable rules.

When the mixer fails to break up a chunk of butter and flour we do not say it “sinned.” In the absence of free will, we cannot even say it “malfunctioned”, because that would be to assign purpose to the machine, and purpose implies intellect and will.

I choose to let Coyne have the last (explanatory) word, and will leave it as homework for the reader to analyze.

Beyond crime and punishment, how should the idea of determinism transform us? Well, understanding that we have no choices should create more empathy and less hostility towards others when we grasp that everyone is the victim of circumstances over which they had no control. Welfare recipients couldn’t have gotten jobs, and jerks had no choice about becoming jerks.

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