William M. Briggs

Statistician to the Stars!

Another Drake Equation Paper Shows Why Drake Always Fails


We’ve seen the Drake equation in many forms, none of them very impressive. They all share the same failing, as we’ll see.

Two fellows, Frank and Sullivan, have another go. The lite version is (appropriately) in the New York Times with the title “Yes, There Have Been Aliens“. The full version is the peer-reviewed paper “A New Empirical Constraint on the Prevalence of Technological Species in the Universe” in Astrobiology. From the Times:

Instead of asking how many civilizations currently exist, we asked what the probability is that ours is the only technological civilization that has ever appeared. By asking this question, we could bypass the factor about the average lifetime of a civilization. This left us with only three unknown factors, which we combined into one “biotechnical” probability: the likelihood of the creation of life, intelligent life and technological capacity.

You might assume this probability is low, and thus the chances remain small that another technological civilization arose. But what our calculation revealed is that even if this probability is assumed to be extremely low, the odds that we are not the first technological civilization are actually high. Specifically, unless the probability for evolving a civilization on a habitable-zone planet is less than one in 10 billion trillion, then we are not the first.

You can already see that abuses of probability are coming up. From the paper:

We define the “A-form” of the Drake equation, which describes the total number of technological species that have ever evolved anywhere in the currently observable Universe:

A = [N* fp np][fl fi ft]

…where N* is the total number of stars, fp is the fraction of those stars that form planets, np is the average number of planets in the habitable zone of a star with planets, fl is the probability that a habitable zone planet develops life, fi is the probability that a planet with life develops intelligence, and ft is the probability that a planet with intelligent life develops technology (of the “energy intensive” kind such as that of our own civilization).

After this comes manipulations of the equation which aren’t especially interesting. There are no insurmountable problems in the leading elements of this or the modified equation. But there is a universe of trouble in the second terms in the brackets, [fl fi ft].

All of these elements are said to be probabilities. Skip whether we can discover unique numbers for each probability and instead focus on probability’s Golden Rule: All probabilities are conditional. From that simple and honest truth flows everything, including the proof that the Drake equation, modified or no, is meaningless.

To prove that, pick the element ft, “the probability that a planet with intelligent life develops technology (of the ‘energy intensive’ kind such as that of our own civilization).” That probability does not exist—no probability does—without premises, assumptions, givens, or conditions. And what might these premises be?

The point of the Drake equation is to count on or, in the modified form, to put a probability to the proposition “Rational creatures on other planets exist”. Yet a main element, fi, is very nearly that same probability. You might argue that it isn’t precisely the same, in an attempt to save Drake from circularity, but fi surely smacks of assuming what it set out to prove.

Even if circularity is missing, fi has no meaning. None. No probability in that equation is sensible. All probabilities need evidence, and these have none. The best we can do is infer the propositions of fi and so on are contingent, and therefore have any number between 0 and 1, which means, thus the final result (in the modified Drake) is itself between 0 and 1, and which is nothing more than knowledge that “Creatures exist” is itself contingent. Nothing has been gained.

In order to calculate fi, we need a list of accepted premises that unambiguously lead to a unique number, or at least to a tight interval. None exist: none that are acceptable and agreed to by all, I mean. Plentiful premises exist that might be used, of course. You might say, “7 out of 10 planets with life develop rational creatures” and thus fi = 0.7. But who would agree to these premises?

Since nobody has any idea of how life began (on Earth) nor do any know of rationality arose, premises which can fix fi just don’t exist. And that same is true for the other probabilities. The Drake equation leads nowhere.

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The Gambler’s Fallacy Proves Classical Statistics (Frequentist & Bayes) Fails


Everybody who’s anybody—which makes, as we’ll see, a lot of nobodies—knows the gambler’s fallacy. Gambler watches the roulette wheel come up red six times running and says to himself, “Black is due.”

It happens, too, these musings. Real people make real bets on black convinced that the Law of Averages will restore the black-red balance of the Roulette Wheel of the Universe. Somehow, fallaciers (yes, fallaciers) believe Fortuna herself, or anyway some occult power, reaches in and causes the wheel to adjust itself to maintain Balance.

We call these people frequentists. Bayesians, too.

And not just those people, but anybody who believes in physical probability embraces the Gambler’s Fallacy; frequentists are just their most visible representatives. Physical probability must be causative to make observed frequencies work out in balance. But since probability is only a state of mind, unless one is staunch Idealist, probability-as-cause makes no sense.

Now no frequentist, or at least none I’ve ever met, actually believes in the theory they espouse, which is limiting relative frequency. Probabilities are only defined, in that theory, at the limit: no probability can be known until infinite time has elapsed, and since we, sitting here in 2016, are well short of the mark of Infinity, yet we still see finite relative frequencies, and these observations are everywhere thought to be “well behaved”, it must be that, according to the theory, the Gambler’s Fallacy is operative. What is happening now is either being influenced by what has not yet occurred, or probability is physically real in the same way that mass or charge is. Yet there is, of course, zero evidence, and anyway its absurd, to think probability is material. Saying so is the Deadly Sin of Reification, and would be the same mistake a mathematician makes who thinks his equations are real.

(There is much, much more to be said about the absurdities that obtain in LRF: this wonderful exciting must-read #1 new best seller book has all the sober details.)

But like I said, no frequentist believes in limiting relative frequency in real life. In actual situations, frequentists behave like we pure probabilists do and believe probabilities are defined on evidence in the form of an argument: these premises imply the probability of this proposition. We know this is so because, again, of the Gambler’s Fallacy. How?

Merely state the fallacy. Every student is taught to chuckle at the foolishness of the gambler who believes numbers are “due”—yet numbers being “due” is exactly what LRF teaches. Still, the frequentist is right! We should pity the poor deluded gambler who believes probability is causative. And in that pity is the proof that probability is argument, that it is cause and essence which are of essence, and that probability is not subjective (as in Bayes) or physical (as in LRF).

Incidentally, as is clear, if probability is subjective, as Bayesians teach, then there is no Gambler’s Fallacy: it cannot exist. If probability is subjective, we should instead laugh at the theoreticians who don’t understand that everybody is free to believe whatever probability they like for any situation. Subjectivism makes the gambler right by default. The probability is his subjective belief! That we recognize the gambler is wrong is proof that subjectivism is false. So once more we have a theory that is touted but which nobody actually believes (consistently, anyway).

Why is it the Gambler’s Fallacy a fallacy? There are two points, both of which are of the utmost importance.

Point (1): we have the proposition of interest, “This ball lands black”, which has a probability m/n, a fixed, deduced number based on the evidence, “This ball must land in one of n slots, m of which are black”. This is probability-as-argument, which produces a number that all, frequentist and Bayesian alike, agree upon (look in any textbook for proof). In the fallacy, the gambler states some number (perhaps not strictly quantified) greater than m/n. But this departure alone is not the full fallacy.

Point (2): The evidence from which the probability is deduced is recognized as (observationally) true, because why? Because we know it is due to the essence, or nature, of the wheel to be this way. We know the causes which are operative have not fundamentally changed between spins of the wheel. This tells us the essence of the wheel is unchanged. It is in particular this second point which is held more strongly and which causes (!) us to recognize the fallacy; indeed, knowledge of the essential properties of the wheel and of cause is deeper and more fundamental than knowledge of probability; probability is a routine deduction, a deduction conditional on the knowledge of the essence and cause.

And there it is. Knowledge of cause and essence is at the base of every probability.

What’s that you say? “What if the wheel has gone bonkers or is worn? What of your fancy theory then?”

A Smiley Face to the reader who identifies the flaw behind this question.

There is more on the Gambler’s Fallacy in this book, which I know you’ve already pre-ordered.

Pride In Objectively Disordered Sexual Desires?

Yesterday was “Pride” day. Pride. Pride?

I know thy pride, and the naughtiness of thine heart.

No, surely not that kind of pride.

Pride goeth before destruction, and an haughty spirit before a fall.

Hmm. Perhaps not that either.

God opposes the proud, but gives grace to the humble.

That can’t be right. Newman?

I love the garish day, and spite of fear,
Pride rule my will: remember not past years.

Nope. But wait: Lewis often knows.

A proud man is always looking down on things and people; and, of course, as long as you are looking down, you cannot see something that is above you.

No. Maybe Sheen?

Pride is an admission of weakness; it secretly fears all competition and dreads all rivals.

On the other hand, there’s Ruskin.

In general, pride is at the bottom of all great mistakes.

Evidently we’re on the wrong path. It’s a cliché to quote Webster (1913), but we’re running out of options. So:

That of which one is proud; that which excites boasting or self-gratulation; the occasion or ground of self-esteem, or of arrogant and presumptuous confidence…

Aha! Self-esteem. That has a happier ring to it! This kind of pride, the unbridled love of self, carries the proper modern tone (Webster uses the old word) of self-congratulation for unaccomplished deeds, of trophies for participation, of awards for you being you, of rights and payments for just showing up.

Yes, and this must be the definition we’ve searched for, because the “pride” evinced in marches across the country was for the stated purpose of flaunting objectively disordered sexual desire.

Don’t be angry. The phrase “objectively disordered sexual desire” is proper, scientific, and true. It is proper because the truth is always welcomed, and it is scientific because engaging in any kind of sexual activity not directed toward procreation and the preservation of the species is by definition disordered, which itself is a truth. This conclusion is simple biology, indeed the simplest, and is indisputable.

Now having “pride” in a disorder is odd. A disorder is not an accomplishment, another truth with which even those who march would agree. Participants at these events did not scale mountains or build inventions or do mighty deeds. Instead, all they did was to admit to having a non-procreative sexual desires, desires which they intend to embrace and, as is well known, in which they insist you countenance—or else.

There must be something different about sexual from other disorders. For instance, there are no marches to espouse pride in congenital maladies like cleft palates or renal dysplasia. Nor are there demonstrations of pride for acquired disorders such as drunkenness and clogged arteries. For every other kind of malady or malfunction but sexual, there is sympathy and the very natural desire to heal.

Not all disorders can be healed, of course. Some departures from health are chronic, some fatal. Yet here is invariably found compassion by the healthy for the sufferers. The exception, a lack of sensitivity, if there is one, is for self-inflicted disorders. Imagine the reaction to a parade of drunks who flout their disorder and in which marchers tell the world they intend to remain drunk, that they encourage “straights” to experiment with drunkenness. Detractors would be denounced as drunkophobes and “Tsk tsk-ing” a man falling out of a bar classed as “hate speech.”

Same-sex attraction, even if that be inborn, and the evidence for this is dubious and is anyway false for all cases, is neither here nor there. Some have it, some lose it, some keep it. Non-procreative, same-sex acts are always a choice. “Pride” marchers are asking for two things. Respect for the attraction and admiration for the acts.

There is some justice in the first claim. Many who claim same-sex attraction would rather be rid of it, they say, but can’t. Even if these people enjoy their state, sympathy and compassion are anyway called for. But pride? That makes no scientific sense, as we saw, and no moral sense either. Because invariably pride in the state, instead of recognition that it is a disorder, leads to demands that the acts which follow from the state be seen as “good.” And that’s the case here. (The picture above is more than proof enough.)

What follows from denying the disorder is that, sooner rather than later, it will come to be seen as wrong and immoral to disparage the acts. Saying “Anal sex is always wrong and destructive” will be “hate” speech. And when that happens yesterday’s marchers will be proud.

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