Wednesday, December 3, 2014

Simple Arithmetic

Back in the Seventies, there was a sporadic feature in Analog science-fiction magazine titled “Probability Zero!” Each segment of that series featured an “impending calamity” that actually had no significant chance of occurring...yet the piece would be written in the panic-style common to the doom-shouters of every era. There’s No Time To Waste!! The Governments Of The World Must Act At Once!! On their face they were humorously intended, but behind the laughs loomed a larger point about the readiness of so many persons to accept crisis-mongering if it comes with even a shred of pseudo-logical cover.

The one I have in mind this morning is “The Population Implosion.” The rationale behind that piece, which purported to demonstrate that the human race is shrinking toward extinction, was that since each of us requires two parents, four grandparents, eight great-grandparents, et seq to exist at all, the number of persons in each generation can only be half of the previous one at most. Why, pretty soon we’ll be down to just one of us...and what then, Gentle Reader?

Of course it’s nonsense. Even a child can see through it. Yet far older and more intelligent persons are regularly seduced by equally simple arithmetic, for an equally simple reason.

The reason, as Thomas Sowell and others have pointed out, is extrapolation in the absence of comprehension.

Consider the temperature of your neighborhood on a spring morning at, say, midnight. At noon, the temperature is virtually guaranteed to be higher, perhaps twenty or thirty Fahrenheit degrees higher. Would it be valid to extrapolate that trend forward by another twelve hours? By twelve hundred hours? Doesn’t it lead to inevitable calamity, specifically the roasting to death of everyone on Earth?

We can see this to be an absurd extrapolation because we grasp the reason for that midnight-to-noon temperature increase: the rotation of the Earth. Your neighborhood has rotated out of the Earth’s sun-shadow and exposed it to sunlight. Over the next twelve hours it will rotate back into the sun-shadow. The process is clear; the extrapolation is faulty because it doesn’t take it into account.

The simple-arithmetic method of forecasting has produced other absurdities as well. Consider “peak oil.” The very persons who in the Seventies predicted the imminent exhaustion of world oil supplies founded their crisis-mongering on simple arithmetic. The proven reserves at that time equaled about thirty years’ global oil consumption. Therefore, in thirty years the oil would all have been used up. Q.E.D., right? Right?

Of course not. Note that those folks are all silent today. Except for the ones who’ve “moved on” to other “crises” and those who are currently lamenting the supply-driven decline in fossil-fuel prices as a blow to their schemes for totalitarian control of the world economy, that is.

The poster-boy for simple-arithmetic forecasts is Thomas Malthus, he who endeavored to scare us into believing that the “geometric” increase of the world population would soon starve us all to death. Malthus was misled by his static views of both Mankind and technology. He made no allowance for the influence of industrialization and urbanization on birth rates, and even less for the possibility of massive improvements in food production technology. He admitted to those mistakes in a Second Essay on the Principle of Population, which isn’t nearly as well known as the first one. Yet the population-bomb doom-shouters of the Seventies repeated Malthus’s early mistakes virtually without deviation. Even as bright a man as Isaac Asimov was seduced by their pseudo-logic, which merely confirms Einstein’s observation that no one is so smart that he’s immune to gross blunders.

Robert M. Pirsig, best known for his book Zen and the Art of Motorcycle Maintenance, recounts therein a similar mistake by his early, pre-electroshock-therapy self, to whom he refers in the book as “Phaedrus.” Phaedrus was misled into the belief that scientific method – indeed, rationality itself – is inherently defeated by the infinite number of possible observations one can make and hypotheses one can form. That ignores the mind’s ability to filter irrelevancies and the efficacy of Occam’s Razor at winnowing through the possible explanations for the phenomenon under consideration. Yes, “the more you look, the more you see,” but that doesn’t mean that everything you see is therefore relevant to the specific mechanism you’ve set out to explain.

Phaedrus / Pirsig was rather young when he made his admittedly life-altering mistake, so perhaps we should cut him some slack. Then again, he did get a massive bestseller and international fame out of it, so perhaps it needn’t be very much slack after all. And he did piss in his own cornflakes with Lila, which lost him – deservedly – most of the admiration his earlier book had earned.

There’s a moral in there, somewhere.

If it sounds to you as if I’m about to say something like “Leave the simple arithmetic to the simpletons,” you’re not completely off base. Simple arithmetic is exactly that: simple. It attains its greatest relevance in simple situations. How many cookies are there in the jar? If you eat one per day, how long will they last you? That sort of simple arithmetic works – if we insist on the proviso that no one add cookies to the jar between your visits to it. It’s the failure to contemplate the possibility of such additional mechanisms that causes the forecaster’s problems.

The phrases that belong in all such proposed extrapolations are “Current trends continuing” and “All else being held constant.” Economists know this; the honest ones say it frequently and openly. But not all persons who award themselves the sobriquet of “economist” are honest.


Some simple arithmetic can go a long way toward explaining matters that others would prefer that we not understand. For example, consider the current, extremely long (by historical American standards) average period most unemployed Americans of working age remain in that condition. Granted that the economy hasn’t been good, though its condition varies regionally. Granted also that other factors, such as the explosion of financial burdens and legal hazards statutorily laid on employers, have something to do with the reduced pace of business expansion and consequent hiring. But there’s also an arithmetic component:

  1. Food stamps are available virtually for the asking;
  2. Unemployment insurance pays benefits for more weeks than ever before;
  3. It’s easier and safer to work “off the books” – i.e., without it becoming known to officialdom – than ever before;
  4. The difference in de facto income between persons in the “working class” economic segment and those exploiting conditions 1, 2, and 3 has been shrinking, and is now smaller in real terms than ever before.

Arithmetic of that sort reminds us of something quite a lot of activist types would rather we’d forbear to consider: people work to improve their lot in life. If work’s ability to improve one’s standard of living should decline, so will its appeal to potential workers. And thus shall it ever be.

Pretty simple, eh?

(Cross-posted at League of Outlaw Bloggers.)

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