William M. Briggs

Statistician to the Stars!

Page 395 of 728

“For who are a free people? Not those, over whom government is reasonably and equitably exercised, but those, who live under a government so constitutionally checked and controuled, that proper provision is made against its being otherwise exercised.” —John Dickinson, Letters From a Farmer in Pennsylvania (1768).

Stats On Extra-Terrestrial Life

From the mailbag comes this question.

Dear Professor Briggs,

Thanks for your astutely iconoclastic posts. I’m very interested on your opinion as regards the “there’s an infinite number of planets so there must be more intelligent life” meme. Disclosure: I am an Anti-Dawkins, “meme”-hating big fan of the late Stephen J. Gould, who thought the odds were greatly against anything like us on other planets, based upon the unlikelihood of so many crucial events in our evolutionary history. Thanks.

Michael Felong

Hey, me too! I also think memes are stupid, except as synonyms for “goofy ideas du jour“. As a scientific explanation for human behavior, they are at best asinine and useless and at worst a scurrilous, unjustified attack on human intelligence.

And I too enjoyed Stephen Gould’s writing and was with him all the way in his criticisms of the risible just-so stories “evolutionary psychologists” tease each other with.

But to your question. If there were an infinite number of planets, and given what we know about physics and biology as it pertains to evolution and so forth, then there would indeed be an infinite number of planets with life. Whether that life is “intelligent” is a separate question requiring the additional premise that all we (a sample of intelligent life) are is the result of “blind” forces. However, suppose that premise is true for the sake of this argument. Then given the other premises, there would be an infinite number of other planets with intelligent life, with “many” (by which I mean an infinite number) of these planets having life that looks and acts like us.

Depressing, no?

All this follows easily from simple probability calculus. Let the chance human-like beings evolve from scratch be some number, and let that number be as small as you like as long as it’s greater than zero. (It cannot be infinitesimally small given we already see us.) Then as long as we’re multiplying this small number against an infinite number, we must end up with infinity.

That means we must have an infinite number of planets that look just like ours (but are not ours) which contain beings who look us, who speak and act as we do, who are our doppelgangers in every respect, even to the point that there must exist at least one (other) plant where a being named “Felong” writes to another being named “Briggs” asking him questions about infinity.

There: An argument only a multi-worlds physicist could love. But also a demonstration that infinities are dangerous creatures not to be trifled with.

Anyway, there are not an infinite number of planets; in this universe there are not a infinite number of anything. I leave open the question whether there really are an infinite number of universes (with which no communication is possible). But inside this one, everything is finite. All is countable and limited.

This being so, it becomes crucial to nail the probability with which sentient life evolves. With an infinite number of planets, its size was irrelevant; here, it is everything. We can still say this probability is non-zero, and we can say this because we can say this. It is here that Gould’s observation that we are highly complex becomes relevant.

And we are complex; I’d say indescribably so, or at least incomprehensibly so. By which I mean that no one person can understand all that it is to be human, or can delineate the exact processes which were the causes of our evolution (an event which I do not deny). The best we can say is that there is nothing else like us; no other animal is even similar to us, especially with regards to thinking—and how that thinking relates to our ability to make tools which would make other intelligent life aware of our existence.

Since even identifying the premises which give us the probability our of evolution is difficult (or impossible), we can’t say with any certainty how many other planets with intelligent species exist. This remains true even if we could unambiguously say how many other planets there were which could support life and can support it for some identifiable length of time (for the universe is also finite in time).

The best we can do is to make the numbers up whole cloth, à la the Drake equation and its variants. This of course makes for a certain amount of fun, and for innumerable Star Trek episodes. But that’s about it.

Spanking Good For Future Education, Income: Researchers

                   Spanked as a child?

A new peer-reviewed paper in the journal Pediatrics shows that girls are luckier than boys in avoiding spankings, that those who were spanked as children went on to greater education than those unfortunates biffed on the butts, and that those spanked had higher incomes as adults.

Yet in the paper’s abstract, we read

Harsh physical punishment in the absence of child maltreatment is associated with mood disorders, anxiety disorders, substance abuse/dependence, and personality disorders in a general population sample. These findings inform the ongoing debate around the use of physical punishment and provide evidence that harsh physical punishment independent of child maltreatment is related to mental disorders.

And then there are these summary headlines in the popular press:

The paper is “Physical Punishment and Mental Disorders: Results From a Nationally Representative US Sample” by Afifi and others. What Afifi did was to have a browse through the the National Epidemiologic Survey on Alcohol and Related Conditions and gleaned from that data those who had self-reported mental maladies and those who self-reported being spanked as a kid. This data was the result of face-to-face interviews with U.S. Census workers (surely government workers probing for intimate for-the-record details was no bar to honesty?).

Afifi, a Canuk, starts by telling us that, “The parent or caregiver’s right to use physical punishment has currently been abolished in 32 nations.” And is there a hint of lamentation when she continues, “Canada and the United States
are not included among these countries”?

Adults who answered at least “sometimes” to the question, “As a child how often were you ever pushed, grabbed, shoved, slapped or hit by your parents or any adult living in your house?” were classified as “having experienced harsh physical punishment.” Before questioning the use of harsh for something as small as being “grabbed”, let’s recall that Canada is a foreign country and they use words differently up there, eh?

A more rough-and-tumble interpretation of harsh would be “severe physical abuse, sexual abuse, emotional abuse, physical neglect, emotional neglect, or exposure to intimate partner violence” But we can’t use this definition because the poor folks who admitted to suffering this kind of “harsh” treatment “were excluded from the current sample.” Sigh.

Afifi and crew then checked off whether each remaining individual scored highly on various questionnaires for “major depression, dysthymia, mania, hypomania, any mood disorder, panic disorder with or without agoraphobia, social phobia, specific phobia, generalized anxiety disorder, posttraumatic stress disorder, agoraphobia, any anxiety disorder, any alcohol abuse/dependence, and any drug abuse/dependence.” She even grouped various of these into “clusters.” According to Tables 2 and 3 in the paper, they have 25 separate ways to be (to use a common Canadian phrase) a jelly donut short of a filling.

Anyway, the whole lot was fed into a series of logistic regression models, first adjusting for this, and then later adjusting for that. We can be grateful that Afifi eschewed the normally sacrosanct 0.95% confidence intervals and instead called “significant” those results which had p-values less than 0.01.

Unfortunately, after this promising start, Afifi forgot to adjust for all the different tests she ran. Using (for example), the Bonferroni method, to maintain that “0.01” level of significance, actual p-values would have to be 0.0004 or lower. That means a lot of the mental maladies Afifi thought were associated with mental maladies actually weren’t. Ah, well.

Then it appears she has sometimes mixed up the idea of confidence intervals and p-values. For example, in Table 1, “Widowed/divorced/separated” are given three asterisks (supposedly significant) with a confidence interval that includes 1 (which is not significant). And this happens in Table 2, too.

There were 20,607 individuals in the database (after culling). But only 1,258, or 6%, reported having remembered, or were willing to report to a government worker, “harsh” treatment. Only 6%? Really? I emphasize this to show that measurement error is in play here, which means (in frequentist theory) that p-values are too high.

The mean age of these folks was 48.4 plus-or-minus 0.2 years. Odd, that. And, for example, of those 1,258 “harshies” just 53 reported “Schizoid personality disorder”, yet this was “significantly” higher than the “un-grabbbed.” Small numbers here.

The authors also try to forget those results which appear at the start of this post: effects which show that “harsh” treatment can be good for some (the first link recognizes this). The big question any defender (even you) of this study must answer is: what other effects were positively associated with “harsh” treatment?

It is a disservice (at the least) to go into a database and look only for what you hope to find, to ignore evidence which does not support your theory. Yet that is what appears to have happened here.

July 4th: It’s Summer And It’s Hot

[To be sung to the obvious tune]

I have a sad story to tell you
It might upset you a bit
Last night I walked on the sidewalk
And it was hot.
Pity me!

Not exactly poetry, but it has a certain je ne sais quoi to it. The pathos encapsulated by the last line brings a tear to the ocular orifices every time I sing it. Doubtless you are welling up, too.

And that’s because it’s obvious this song of woe is a tale spun from reality. It actually happened to me! Yes. Last night I did walk out onto the sidewalk…and it was hot! Heat—raw heat—covered me instantly, soaking me, drenching me in waves of unwanted electromagnetic radiation. Layers of humidity, one upon the other, attached themselves to my clothing and my skin, making me feel as slimy as a Chicago alderman.

This went on block after block. The heat did not abate; no, not even in the shade. If anything, it grew hotter. And when I finally reached the bodega in which lay the amber, life-giving well-hopped fluid which my body so desperately craved, I realized to my horror that the air in the place was not conditioned! Avert your eyes if you don’t like graphic descriptions of bodily functions—but this final serving of blistering heat actually caused me to sweat!

I tell you the truth: I have never before suffered such minor inconveniences as this.

I should have listened to the radio, to the television, to the newspaper, to the media in every form which had dispatched scores of reporters to the far corners of the city, where to a man each of them reported that it was hot. These dedicated newsmen warned me to stay inside. They cautioned me to stay where the air was electrically cooled. They told me that sure death awaited me if I dared venture forth without saturating my bodily fluids.

Not satisfied with telling me the temperature, the journalists invented something called a “heat index.” I discovered (via statistical calculation) that this was actual temperature multiplied by three. The heat index isn’t therefore the temperature, but is a number to show what the temperature would be were it hotter than it is. It is a kind of maybe temperature, a temperature that isn’t, an index which can be adjusted up or down according to the importance the journalist gives the story.

When I went out onto the street, I naturally expected to see piles of bodies which had succumbed to the heat. But there were none. This was curious. Perhaps those that were to die had died already; their corpses efficiently removed by the Soylent Corporation. Still, I began to question if there was an element of exaggeration in the repeated dire warnings.

As I walked I recalled how I had lived for three years in San Antonio, Texas (average August high of 96 with liquid skies), and again in Okinawa, Japan (a degree or two cooler, but always wetter), and never had air conditioning. As far as I could ascertain, I had not died from this lack. I also remembered that in all the cars I ever owned, there was no air conditioning. Again, this did not kill me.

There may have been lasting damage, however, because I was for years after this an atheist (I have since recovered). Anyway—full disclosure—there was an air conditioning unit in the apartment in San Antonio, but the (so-labeled by Danny Stiles) blonde bombshell with whom I shared the rent would not allow me to turn it on because she was deathly afraid of contracting Legionnaires disease, which she was sure lurked in the recesses of the machine. Yes.

Who knows where the truth lies. But if there’s anything to this global warming we hear about, it’s likely to stay summer until at least September. Worse, sophisticated computer models say the whole cycle could repeat next year.

It’s the glorious 4th. Happy Birthday, America! Be careful, it’s Summer out there and hot. And since it’s never been Summer and hot before, heed the warnings of your elected and unelected leaders and stay away from any activity in which you might find enjoyment.

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