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The elephant's trunk

January 31st, 2004

Via David Appell, I came across this marvellous quote from Freeman Dyson

In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?” I thought for a moment about our cut-off procedures and said, “Four.” He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”

It came to mind when I read this story in the NYT with the introductory claim What really stimulates economic growth is whether you believe in an afterlife — especially hell.The report is of some estimations done by Rachel M. McCleary and Robert J. Barro (the story notes that the two are married) published in American Sociological Review.

Barro is probably the biggest name in the field of cross-country growth regressions (a field in which I’ve also dabbled), and I’m sure he’s aware that thousands of these regressions have been run and that, with very limited exceptions, results that particular factors are conducive to growth have proved highly fragile. I haven’t read the paper, so for all I know, the results have been checked for robustness in every possible way. But my eyebrows went up when I saw this para

Oddly enough, the research also showed that at a certain point, increases in church, mosque and synagogue attendance tended to depress economic growth. Mr. Barro, a renowned economist, and Ms. McCleary, a lecturer in Harvard’s government department, theorized that larger attendance figures could mean that religious institutions were using up a disproportionate share of resources.

What this means is that at least two parameters have been used in fitting growth to religiosity and that the two have opposite signs – most likely it’s some sort of quadratic. In my experience, there’s always at least one arbitrary choice made in the pretesting of these models (for example once you have a quadratic, the scaling of variables becomes critical). That gives three free parameters, if not more.

I’m not John von Neumann, but with two parameters I can fit a dromedary and with three I can do a Bactrian camel.

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  1. February 1st, 2004 at 09:08 | #1

    Here’s one piece of insight for this sort of thing, that I heard a while ago.

    Suppose you have a curve with a nice broad hump (unimodal to you). This means it has a large “sweet spot”, where one thing is as good as another apart from immaterial higher order terms (if the curve has a narrow hump, either noise means you can’t hit it anyway or you can blur it with the noise to get a new curve with a broad hump that comes more from the bell curve of the noise than from the underlying process.)

    What all this means is that for many purposes the exact fitting curve doesn’t matter; a rough model will give you a recommended policy that is near enough as good as a true understanding would have given you.

    This doesn’t fit all cases of course – it certainly doesn’t guide the decisions of individual firms in cases where markets mean coming second is not good enough – but it does mean that, say, the last few tariffs aren’t worth the effort of getting rid of. (In directly practical terms – there may be a point of principle, to head off subsequent deterioration from conceding the principle and yielding the ground to rent seekers.)

  2. February 2nd, 2004 at 14:18 | #2

    Well speak of the devil! A cross-country comparison that picks up religious belief/attendance as the most powerful factor in economic growth.

    Socio-bio and comp-eco all in the one package.

    This is plain stupid, since it implies that priests would be richest people on earth, and pre-oil Saudi Arabia would be the richest country.

    What counts is not the formal fact that you believe in God, but the substance or your religious practices.

    THe Northern European Protestant societies emphasised capitalism and technology, whilst the Northern Asian Sagacious (Lao Tse, Confucius, Buddha, Basho) societies emphasised statism and technology.

    Both societies have northern latitudes and mechanical aptitudes in common.

    WHy doesn’t Barro plug those parameters into his equation and smoke them?

  3. February 3rd, 2004 at 08:53 | #3

    About “mechanical aptitudes” – when I was a child I lived in Iraq, where my father was running a date ranch in the marshes. He subsequently told me that the marsh arabs had a great deal of mechanical aptitude.

  4. rdb
    February 3rd, 2004 at 22:56 | #4

    Curve fitting and elephants trunks:

    from Dimensional analysis and scaling laws

    Brain size

    Interestingly, the brain mass also scales as body mass to the 3/4 power …

    And second, why is the human brain so much larger (1.5-2 time larger) than the empirical scaling would predict?

    Much of the brain’s computational power is devoted to muscular control. An elephant’s trunk, e.g. has 6 major muscle groups divided into about 10**5 individually controllable muscle units. Its brain weighs 3.6-5.4 kg. For comparison, there are only 639 muscles in the human body, and human brains weigh about 1.3 kg.

    Among mammals, apes, elephants and whales have brains larger than the M 3/4 fit would predict. When we examine the elephant brain we see it has massive temporal lobes and huge sections devoted to controlling the trunk muscles. The temporal lobes provide the proverbial elephant’s memory and the sections controlling the trunk musculature have to be enormous because this is the animal’s most vital organ. Not much brain is left over for abstract reasoning, and elephants do not seem to have such ability. The dolphin and orca (killer whale) are fast swimmers, and also possess extremely sophisticated sonar. They achieve their speed by constantly adjusting thousands of subcutaneous muscles that cancel out turbulence and thereby greatly reduce drag.

    The dolphin brain therefore devotes much of its computational power to the sensory and feedback control elements of the drag-reducing and sonar

    systems. Though their brains are moderately larger than humans’, dolphins’ intelligence ranks somewhere between wolves and chimpanzees.

    What 24 parameters/servomotors can do.

  5. February 4th, 2004 at 09:14 | #5

    Another odd one out for human beings is that we have a far longer life expectancy than would be predicted from our average body masses, metabolic and heart rates etc. I’ve heard speculation that evolution favoured keeping a grandparent generation around to help with child rearing (it doesn’t mean everybody has to last that long, just that breeding groups need a few oldsters).

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