Friday, August 1, 2014

The Limits Of Metrical Argument

"Mathematics is a meaningless formal game." -- David Hilbert.

Mathematics, whether high or low, is inherently independent of any connection to objective reality. It exists in a realm of pure abstraction. (You might even call it a Realm of Essences.) Though mathematical techniques can be used to describe reality, they cannot be used to control reality. (For the use of the inverse assumption as the driver for a fantasy story, see James Gunn's The Magicians.)

That doesn't stop tendentious types with an axe to grind, of course.

The most insidious use of mathematics to deceive is by extrapolation of some identifiable pattern. The extrapolator draws attention to the pattern, then forecasts the future as if it could be relied upon to continue indefinitely, when such continuation is in fact dubious or worse. Mark Twain made humorous note of this practice:

In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old O├Âlitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact. [From Life On The Mississippi]

Somewhat more recently, the great Thomas Sowell lassoed, threw, and hogtied it in his masterpiece The Vision Of The Anointed:

[I]f the temperature has risen 10 degrees since dawn today, an extrapolation will show that we will all be burned to a crisp before the end of the month, if this trend continues. Extrapolations are the last refuge of a groundless argument. In the real world, everything depends on where we are now, at what rate we are moving, in what direction, and -- most important of all -- what is the specific nature of the process generating the numbers being extrapolated. Obviously, if the rise in temperature is being caused by the spinning of the Earth taking us into the sunlight, then the continuation of that spinning will take us out of the sunlight again and cause temperatures to fall when night comes.

Now and then, a tendentious extrapolator will resort to even worse deceits, such as picking his time base specifically to conceal the reversal of the trend upon which his argument is based. For example, a passionate advocate for increasing the number and visibility of police might pick a year -- say 1960 -- with an unusually low number of murders, compare it to the present number of murders per year, and thus imply that murder is increasing in frequency even though the murder count was higher in 1990 than it is today and has been declining steadily since then. He who fails to check the source data is vulnerable to being misled in this fashion.

Tendentious extrapolation is bad enough, but when we add the "apples to oranges" comparison -- i.e., inviting the audience to assume that the same rules and processes apply to greatly dissimilar situations -- it approaches criminality and should be treated with a comparable degree of contempt. That's what the "Global warming / climate change" evangelists do: they produce "simulations" of the atmosphere and biosphere that they claim "prove" that global warming -- and specifically anthropogenic global warming, at that -- is occurring and will have catastrophic effects in the reliably foreseeable future -- and then go on from there to scream that "the science is settled!" Yet as I wrote some time ago:

Science is entirely encompassed and defined by the scientific method. Scientific hypotheses must be confirmed or challenged by predictions about the outcomes of properly designed experiments that others can replicate. However, the anthropogenic global warming hypothesis cannot be confirmed or challenged by experiments of any sort, for several reasons:
  1. Earth is an "open system," with a multitude of feedback mechanisms that influence atmospheric and oceanic temperatures; thus, producing a replicable experimental setup is inherently impossible.
  2. There is no way to control or measure the amounts of the various "greenhouse gases" that are emitted per unit time.
  3. The Sun, which is the principal determinant of temperatures on Earth, is a mildly (4%) variable star.
  4. Temperature measurement itself is an inexact matter that's easily disturbed by environmental fluctuations of all sorts.
  5. Even the most careful measure of temperature is nevertheless a local phenomenon, pertaining only to the immediate region around the measuring device. Thus, the exact placement of those devices, which is inherently a matter of judgment, is far more important to the readings than any other aspect of the matter.

Which is why the warmistas rely on simulations. But simulations, as I have excellent reason to know, are relevant only to the exact conditions simulated -- and those conditions cannot, in the nature of things, match the far more complex dynamics of the Earth's atmosphere and oceans.

Perhaps the supreme irony that emerges from this deceit-by-numbers is that those who perpetrate it ceaselessly congratulate themselves on how much smarter they are than "those rubes." The irony sharpens still further when we discover that among them are many who've succeeded only in deceiving themselves. On that note, I will conclude by citing a pithy passage from a recent essay by Charles C. W. Cooke:

One part insecure hipsterism, one part unwarranted condescension, the two defining characteristics of self-professed nerds are (a) the belief that one can discover all of the secrets of human experience through differential equations and (b) the unlovely tendency to presume themselves to be smarter than everybody else in the world. Prominent examples include MSNBC’s Melissa Harris-Perry, Rachel Maddow, Steve Kornacki, and Chris Hayes; Vox’s Ezra Klein, Dylan Matthews, and Matt Yglesias; the sabermetrician Nate Silver; the economist Paul Krugman; the atheist Richard Dawkins; former vice president Al Gore; celebrity scientist Bill Nye; and, really, anybody who conforms to the Left’s social and moral precepts while wearing glasses and babbling about statistics.

There is no substitute for familiarity with the ground data -- the unmassaged, reproducible facts provided by agenda-free Nature herself, including when and where they were gathered, how, and by whom -- and skepticism toward those who claim to know better than you, no matter how many numbers they claim to have at their command.


Differ said...

I would venture to assert that most of the names in Cooke's list wouldn't recognize a differential equation if it took a finite bite out of them; they're merely self-presumed-smart-people (TM).

Francis W. Porretto said...

(chuckle) And as for a tensor or the Law of Cosines, well...!

RichJ said...

Excellent post today, Francis.

I am sending this one along to my brainwashed kids. I have made similar arguments to my eldest especially regarding the statistical extrapolation problem and cherry picking the data points.

Your post concisely expresses the issue. Thank you.

Wayne said...

They all think they are Hari Seldon when they are really Harry from One Direction.