Feeling a Little Derivative

I knew a mathematician who had a recurrent dream. He dreamt that he was a partial derivative.

[Jeremy Bernstein, A Theory for Everything (Singer-Verlag, New York, 1996), p. 263.]

This quotation no doubt tells you more about me than I expect, but when I read it I found it terribly funny. I also have the strong conviction that it’s saying “partial derivative” that makes it so funny; “He dreamt he was a derivative” barely provokes a smile. I doubt, though, that it would be at all funny to someone who has no idea what a partial derivative is.

Primates & Judicial Philosophy

Despite my proddings, some of you may still not read Bob Park’s “What’s New”. But that’s okay, since I tend to put the best bits here anyway.

Recently he solicited readers’ questions that might be suitable for appropriately probing the thoughts and positions of Supreme Court nominees regarding science. This week he revealed “the question that best captured the consensus of our readers’ views in the fewest number of words was from Abi Soffer at SLAC:”

How does being descended from a monkey affect your judicial philosophy?

Frontiers of the Mind

New frontiers of the mind are before us, and if they are pioneered with the same vision, boldness, and drive with which we have waged this war [i.e., World War II] we can create a fuller and more fruitful employment and a fuller and more fruitful life.

– President Franklin D. Roosevelt, in a letter to his science advisor Vannevar Bush asking for recommendations that led to the creation of the National Science Foundation, 17 November 1944; the letter is reproduced in Vannevar Bush, “Science — The Endless Frontier: A Report to the President on a Program for Postwar Scientific Research”, July 1945, three months after Roosevelt’s death.

Ascent of Science

I recently finished reading the massive but excellent book The Ascent of Science, by Brian L. Silver (Oxford University Press, New York, 1998). I had noted many passages that caught my eye as I read, and have shared some. As usual, I got behind, so here are the remainders.

Linnaeus, in 1735, commented, “It is remarkable that the stupidest ape differs so little from the wisest man, that the surveyor of nature has yet to be found who can draw the line between them.” [p. 269]

Just as true, it seems, going on 300 years later now that the genes of the chimpanzee have been sequenced.

Now this following example I have yet to see put forth as fundamentalist support for creationist doctrine:

Lamarck’s belief in the inheritance of acquired characteristics ws anticipated by Charles Darwin’s grandfather Erasmus, and has in fact persisted for centuries. It is part of the folklore of many societies and has been around too long to be killed by ugly facts. One example of the effect on their offspring of what their parents see is about 4000 years old. Genesis 30:37–39 reads: “Jacob then got fresh shoots of poplar, and of almond and plane, and peeled white stripes in them, laying bare the white of the shoots. The rods that he had peeled he set up, in front of the goats, in the troughs, the water receptacles, that the goats came to drink from. The mating occured when they came to drink, and since the goats mated by the rods, the goats brought forth streaked, speckled, and spotted young.” [p. 288]

Einstein’s feelings about relativity and religion — which should not come as a surprise:

Einstein was much concerned with questions of morality and meaning. When asked what effect relativity had on religion, he replied, “None. Relativity is a purely scientific theory, and has nothing to do with religion. Nevertheless, there is a long history of fruitless attempts to relate the specifics of mathematics or physics to man’s religious and moral life. This is the wacky side of the Pythagorean heritage. The most general lesson that man can learn from science is the need to apply the highest standards of reason to those problems to which they can be applied. [p. 400, emphasis in original]

About the events that put Einstein’s name on everyone’s lips:

Einstein’s theory predicted that the path of light would be bent near massive bodies. Newton had also believed that his light corpuscles would be attracted by gravity, and Faraday looked unsuccessfully for the effect of gravity on light. Einstein’s prediciton was tested in 1919, during an eclipse of the Sun. The man who organized the experiment, which involved sending observers to Brazil and Principe, an island in the Gulf of Guinea, was the English cosmologist Sir Arthur Eddington, who was an early convert to relativity. [...]

The experiment had been on a grnd scale. An account of the observations was presented at a joint meeting of the Royal Society and the Royal Astronomical Society, in London, and the announcement of the results by the astronomer royal, Sir Frank Watson Dyson, was a dramatic high point in the history of science. The deviations recorded by the two expeditions were 1.61 and 1.98 seconds of arc, although the experimental error was rather large. Einstein had predicted a deviation of 1.74 seconds of arc. The chairman of the meetings, J.J. Thomson, proclaimed, “This is the most important result obtained in connection with the theory of gravitation since Newton’s day [and] one of the highest achievements of human thought.” That was on 6 November 1919. The following day there was an announcement in the London Times, and within days Einstein’s name became known to more people at one time than that of anyone else in the history of science. [p. 431]

The heading to Chapter 33 on “Cosmology” [p. 442]:

The discovery of a new dish does more for the happiness of mankind than the discovery of a star.
– Jean Anthelme Brillat-Savarin, early nineteenth-century gastronome

A curious footnote to scientific history and theory that I’d never heard before:

Before Galileo turned his telescope to the night sky in 1610, the universe was a much smaller place. There are fewer than 5000 stars visible to the naked eye, although it must have been assumed that there were many more, in view of the common European belief that each person had his own personal star. [footnote:] In the fifth century, Bishop Eusebius of Alexandria asked if “there were only two sars at the time of Adam and Eve.” [p. 451]

Finally, a remark that has not lost its defining utility:

In the early 1920s the automated production line turned America into an object of mass envy and admiration. Technology, not art or basic science, was confirmed as civilization’s status symbol. Few heeded the words of Dean Inge, in the 1920 Romanes Lecture: “The European talks of progress because by the aid of a few scientific discoveries he has established a society which has mistaken comfort for civilization.” [p. 488]

Science as Nuisance

From the beginning, the Bush White House has treated science as a nuisance and scientists as an interest group�one that, because it lies outside the governing conservative coalition, need not be indulged. That’s why the White House-sometimes in the service of political Christianism or ideological fetishism, more often in obeisance to baser interests like the petroleum, pharmaceutical, and defense industries-has altered, suppressed, or overriden scientific findings on global warming; missile defense; H.I.V./ AIDS; pollution from industrial farming and oil drilling; forest management and endangered species; environmental health, including lead and mercury poisoning in children and safety standards for drinking water; and non-abstinence methods of birth control and sexually-transmitted-disease prevention. It has grossly misled the public on the number of stem-cell lines available for research. It has appointed unqualified ideologues to scientific advisory committees and has forced out scientists who persist in pointing out inconvenient facts.

[Hendrik Hertzberg, "Mired", The New Yorker, 22 August 2005.]

Miller’s Skepticism

But science is more than the sum of its hypotheses, its observations, and its experiments. From the point of view of rationality, science is above all its method–essentially the critical method of searching for errors. It is the staunch devotion of science to this method that makes the difference.
[...^*]
It took Popper’s genius to realize that what is central to rationality is criticism, not justification or proof; and to scientific rationality, empirical criticism. To rescue science as a rational enterprise, perhaps the rational enterprise par excellence, there is accordingly no need to attribute to well-tested scientific hypotheses a security or reliability that they do not possess. Scientific hypotheses are not trustworthy or reliable, except in the sense of being, in some instances, true; and they are not in any interesting respect based on experience.

[David Miller, "Being an Absolute Skeptic", Science, 4 June 1999.]
———-
^*The bit that I excised between the parts I quoted was not uninteresting, it just didn’t seem to carry the flow of the idea that I wanted to note by quoting Miller. Here are the words represented by the elipsis belonging, in the original, to the first paragraph:

What is wrong with pseudoscience is the manner in which it handles its hypotheses, not normally the hypotheses themselves (though if they are designed to be unassailable and unfalsifiable, then unassailed and unfalsified they doubtless remain). But although a hypothesis that survives all criticism thrown at it is preferable to a hypothesis that dies, it does not become a better hypothesis through being tested. It may have been a better hypothesis from the outset, of course; it may be true. True hypotheses are what we seek.

What Gödel Didn’t Say

What is it about Gödel’s theorem that so captures the imagination? Probably that its oversimplified plain-English form–”There are true things which cannot be proved”–is naturally appealing to anyone with a remotely romantic sensibility. Call it “the curse of the slogan”: Any scientific result that can be approximated by an aphorism is ripe for misappropriation. The precise mathematical formulation that is Gödel’s theorem doesn’t really say “there are true things which cannot be proved” any more than Einstein’s theory means “everything is relative, dude, it just depends on your point of view.” And it certainly doesn’t say anything directly about the world outside mathematics, though the physicist Roger Penrose does use the incompleteness theorem in making his controversial case for the role of quantum mechanics in human consciousness. Yet, Gödel is routinely deployed by people with antirationalist agendas as a stick to whack any offending piece of science that happens by. A typical recent article, “Why Evolutionary Theories Are Unbelievable,” claims, “Basically, Gödel’s theorems prove the Doctrine of Original Sin, the need for the sacrament of penance, and that there is a future eternity.” If Gödel’s theorems could prove that, he’d be even more important than Einstein and Heisenberg!

[Jordan Ellenberg, "Does Gödel Matter? The romantic's favorite mathematician didn't prove what you think he did." Slate, 10 March 2005.]

Herps, Gait, & the Invention of Clothes

Today’s reading from Richard Dawkins’ The Ancestor’s Tale (Houghton Mifflin, Boston, 2004) touches on several topics (as I catch a bit on the lunch-time notes).

[Speaking of naming types of animals:] Yet another informal grade name, favoured by American zoologists, is ‘herp’. Herpetology is the study of reptiles (except birds) and amphibians. ‘Herp’ is a rare kind of word: an abbreviation for which there is no long form. A herp is simply the kind of animal studied by a herpetologist, and that is a pretty lame way to define an animal.[^*] The only other name that comes close is the biblical ‘creeping thing’. [p. 250]

[About the "authoritative 'Tree of Life' project founded by the Maddison brothers":] This excellent resource is continually updated at http://tolweb.org/tree. The website has a delightful disclaimer: ‘The Tree is under construction. Please have patience: the real Tree took over 3,000,000,000 years to grow.” [footnote, p. 250]

The Human imagination is cowed by antiquity, and the magnitude of geological time is so far beyond the ken of poets and archaeologists it can be frightening. But geological time is large not only in comparison to the familiar timescales of human life and human history. It is large on the timescale of evolution itself. This would surprise those, from Darwin’s own critics on, who have complained of insufficient time for natural selectin to wreak the changes the theory requires o fit. We now realise that the problem is, if anything, opposite. There has been too much time! If we measure evolutionary rates over a short time, and then extrapolate, say, to a million years, the potential amount of evolutionary change turns out to be hugely greater than the actual amount. It is as though evolution must have been marking time for much of the period. Or, if not marking time, wandering around this way and that, with meandering fluctuations drowning out, in the short term, whatever trends there might be in the long. [p. 257]

The head louse, Pediculus humanus capitus, infests only the hairs of the head. The body louse, P. h. humanus, is a subspecies in the same species as the head louse which, interestingly, is believed to have evolved from it only after we began to wear clothes. Some workers in Germany have looked at the DNA of head lice and body lice to see when they diverged, with a view to dating the invention of clothes. They put it at 72,000 years, plus or minus 42,000. [p. 266]

…it is undoubtedly true that styles of walking have a kind of contagiousness and are imitated because they are admired. The boarding school that I attended, Oundle in central England, had a ritual whereby the senior boys paraded into the chapel after the rest of us were in our places. Their mutually imitated style of walking, a mixture of swagger and lumbering roll (which I now, as a student of animal behaviour and a colleague of Desmond Morris, recognise as a dominance display) was so characteristic and idiosyncratic that my father, who saw it once a term on Parents’ Day, gave it a name, ‘the Oundle Roll’. The socially observant writer Tom Wolfe has named a particular loose-limbed gait of American dudes, fashionable in a certain social sector, the Pimp Roll. At the time of writing, the abject sycophancy of the British Prime Minister to the US President has earned him the title ‘Bush’s Poodle’. Several commentators have noticed that, especially when in his company, he imitates Bush’s macho ‘cowboy swagger’, with arms held out to the sides as though ready to reach for two pistols. [p. 269]

[The extinct] Moas are extreme among flightless birds in that they have no trace of wings at all, not even buried vestiges of wing bones. They thrived in both the North and South Islands of New Zealand until the recent invasion by the Maori people, about 1250 AD. Thy were easy prey, no doubt for the same reason as the dodo. Except for the (extinct) Haast’s eagle, the largest eagle ever to have lived, they had known no predators for tens of milions of years, and the Maoris slaughtered them all, eating the choicer parts and discarding the rest, belying, not for the first time, the wishful myth of the noble savage living in respectful harmony with his environment. [p. 280]

———-
^*I’m not rushing to agree with Dawkins that it’s a “lame way” to “define an animal”. True, he would like names that imply some sort of fundamental biological or evolutionary connection between the members of the group, which seems desirable, but since I incline to the view that “science is what scientists do”, I’m less troubled by the idea behind the name ‘herp’.

Platypus Billsight

Two selections from today’s reading in Richard Dawkins’ The Ancestor’s Tale (Houghton Mifflin, Boston, 2004)

The point is that the platypus bill is not just a pair of jaws for dabbling and feeding, as in a duck. It is that too, though it is rubbery rather than horny like a duck’s bill. But far more interestingly, the platypus bill is a reconnaissance device, an AWACS organ. Platypuses hunt crustaceans, insect larvae and other small creatures in the mud at the bottom of streams. Eyes aren’t much use in mud, and the platypus keeps them tight shut while hunting. Not only that, it closes its nostrils and its ears as well. See no prey, hear no prey, smell no prey: yet it finds prey with great efficiency, catching half its own weight in a day.

If you were a skeptical investigator of somebody claiming a ‘sixth sense’, what would you do? You’d blindfold him, stop his ears and his nostrils, and then set him some task of sensory perception. Platypuses go out of their way to do the experiment for you. They switch off three senses which are important to us (and perhaps to them on land), as if to concentrate all their attention on some other sense. And the clue is given by one further feature of their hunting behaviour. They swing the bill in movements call saccades, side to side, as they swim. … [pp. 235--236]

Platypuses have about 40,000 electrical sensors distributed in longitudinal stripes over both surfaces of the bill. …a large portion of the brain is given over to processing the data from these 40,000 sensors. But the plot thickens. In addition to the 40,000 electrical sensors, there are about 60,000 mechanical sensors called push rods, scattered over the surface of the bill. Pettigrew and his co-workers have found nerve cells in the brain that receive inputs from mechanical sensors. And they have found other brain cells that respond to both electrical and mechanical sensors (so far they have found no brain cells that repond to electrical sensors only). Both kinds of cell occupy their correct position on the spatial map of the bill, and they are layered in a way that is reminiscent of the human visual brain, where layering assists binocular vision. Just as our layered brain combines information from the two eyes to construct a stereo percept, the Pettigrew group suggests that the platypus might be combining the information from electrical and mechanical sensors in some similiarly useful way. [p. 238]

Polygyny and Anteaters

Two selections from today’s reading in Richard Dawkins’ The Ancestor’s Tale (Houghton Mifflin, Boston, 2004), mostly to confound fundamentalists and creationists:

The Ethnographic Atlas of G.P. Murdock, published in 1967, is a brave compilation. It lists particulars of 849 human societies, surveyed all over the world. From it we might hope to count numbers of societies that permit harems versus numbers that enforce monogamy. The problem with counting societies is that it is seldom obvious where to draw lines, or what to count as independent. This makes it hard to do proper statistics. Nevertheless, the atlas does its best. Of those 849 societies, 137 (about 16 per cent) are monogamous, four (less than one per cent) are polyandrous [females having more than one male partner], and a massive 83 per cent (708) are polygynous (males can have more than one wife). The 708 polygynous societies are divided about equally into those where polygyny is permitted by the rules of the society but rare in practice, and those where it is the norm. [p 208]

The anteaters don’t seem to have made it into North America, but three genera survive in South America, and very unusual mammals they are. They have no teeth at all and the skull, especially in the case of Myrmecophaga, the large gound-dwelling anteater, has become little more than a long, curved tube, a kind of straw for imbibing ants and termites which are chivvied out of their nests by means of a long sticky tongue. And let me tell you something amazing about them. Most mammals, like us, secrete hydrochloric acid[*] into our stomachs to aid digestion, but South American anteaters don’t. Instead, they rely upon the formic acid from the ants that they eat. This is typical of the opportunism of natural selection. [p. 215]

———-
^*In particular, I want to draw towards this point the attention of those Splenda alarmists who are so concerned that a tightly bound chlorine atom in the sweetner is going to get loose, shoot through their bodies, and mutate them out of existence. The human body, to which salt (sodium + chlorine, recall) is essential and hydrochloric acid is in everyday use, is rather adept at dealing with a chlorine radical should it actually manage to get loose.