On having multiple hypotheses which all fit the data

For every fact there is an infinity of hypotheses.” – from Robert Pirsig, Zen and the Art of Motorcycle Maintenance


‘I will read the inventory… First item: A very considerable hoard of precious stones, nearly all diamonds, and all of them loose, without any setting whatever… Second item: Heaps and heaps of loose snuff, not kept in a horn, or even a pouch, but lying in heaps… Third item: Here and there about the house curious little heaps of minute pieces of metal, some like steel springs and some in the form of microscopic wheels… Fourth item: The wax candles, which have to be stuck in bottle necks because there is nothing else to stick them in… By no stretch of fancy can the human mind connect together snuff and diamonds and wax and loose clockwork.’

‘I think I see the connection,’ said the priest. ‘This Glengyle was mad against the French Revolution. He was an enthusiast for the ancien regime, and was trying to re-enact literally the family life of the last Bourbons. He had snuff because it was the eighteenth century luxury; wax candles, because they were the eighteenth century lighting; the mechanical bits of iron represent the locksmith hobby of Louis XVI; the diamonds are for the Diamond Necklace of Marie Antoinette.’

Both the other men were staring at him with round eyes. ‘What a perfectly extraordinary notion!” cried Flambeau. “Do you really think that is the truth?’

‘I am perfectly sure it isn’t,’ answered Father Brown, ‘only you said that nobody could connect snuff and diamonds and clockwork and candles. I give you that connection off-hand. The real truth, I am very sure, lies deeper.’

He paused a moment and listened to the wailing of the wind in the turrets. Then he said, ‘The late Earl of Glengyle was a thief. He lived a second and darker life as a desperate housebreaker. He did not have any candlesticks because he only used these candles cut short in the little lantern he carried. The snuff he employed as the fiercest French criminals have used pepper: to fling it suddenly in dense masses in the face of a captor or pursuer. But the final proof is in the curious coincidence of the diamonds and the small steel wheels. Surely that makes everything plain to you? Diamonds and small steel wheels are the only two instruments with which you can cut out a pane of glass.’

The bough of a broken pine tree lashed heavily in the blast against the windowpane behind them, as if in parody of a burglar, but they did not turn round. Their eyes were fastened on Father Brown. ‘Diamonds and small wheels,’ repeated Craven ruminating. ‘Is that all that makes you think it the true explanation?’

‘I don’t think it the true explanation,’ replied the priest placidly; ‘but you said that nobody could connect the four things. The true tale, of course, is something much more humdrum. Glengyle had found, or thought he had found, precious stones on his estate. Somebody had bamboozled him with those loose brilliants, saying they were found in the castle caverns. The little wheels are some diamond-cutting affair. He had to do the thing very roughly and in a small way, with the help of a few shepherds or rude fellows on these hills. Snuff is the one great luxury of such Scotch shepherds; it’s the one thing with which you can bribe them. They didn’t have candlesticks because they didn’t want them; they held the candles in their hands when they explored the caves.’

‘Is that all?’ asked Flambeau after a long pause. ‘Have we got to the dull truth at last?’ ‘Oh, no,’ said Father Brown.

As the wind died in the most distant pine woods with a long hoot as of mockery Father Brown, with an utterly impassive face, went on: ‘I only suggested that because you said one could not plausibly connect snuff with clockwork or candles with bright stones. Ten false philosophies will fit the universe; ten false theories will fit Glengyle Castle. But we want the real explanation of the castle and the universe.” – from G. K. Chesterton, “The Honour of Israel Gow


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A History of Science in 12 Books

Here are twelve influential books covering the history of science and mathematics. All of them have changed the world in some way:


1: Euclid’s Elements (c. 300 BC). Possibly the most influential mathematics book ever written, and used as a textbook for more than 2,000 years.


2: De rerum natura by Lucretius (c. 50 BC). An Epicurean, atomistic view of the universe, expressed as a lengthy poem.


3: The Vienna Dioscurides (c. 510 AD). Based on earlier Greek works, this illustrated guide to botany continued to have an influence for centuries after it was written.


4: De humani corporis fabrica by Andreas Vesalius (1543). The first modern anatomy book.


5: Galileo’s Dialogue Concerning the Two Chief World Systems (1632). The brilliant sales pitch for the idea that the Earth goes around the Sun.


6: Audubon’s The Birds of America (1827–1838). A classic work of ornithology.


7: Darwin’s On the Origin of Species (1859). The book which started the evolutionary ball rolling.


8: Beilstein’s Handbook of Organic Chemistry (1881). Still (revised, in digital form) the definitive reference work in organic chemistry.


9: Relativity: The Special and the General Theory by Albert Einstein (1916). An explanation of relativity by the man himself.


10: Éléments de mathématique by “Nicolas Bourbaki” (1935 onwards). A reworking of mathematics which gave us words like “injective.”


11: Algorithms + Data Structures = Programs by Niklaus Wirth (1976). One of the early influential books on structured programming.


12: Introduction to VLSI Systems by Carver Mead and Lynn Conway (1980). The book which revolutionised silicon chip design.

That’s four books of biology, four of other science, two of mathematics, and two of modern IT. I welcome any suggestions for other books I should have included.


The Scientific Revolution and the Origins of Modern Science: a book review


The Scientific Revolution and the Origins of Modern Science by John Henry

I recently read the 3rd (2008) edition of John Henry’s The Scientific Revolution and the Origins of Modern Science – an excellent, though very brief, survey (it is 114 pages, not including the glossary and index).

Henry tends to see considerable continuity between the “natural magic” of medieval thought and the emerging scientific viewpoint, which was based on experiment and mathematical analysis. Personally, I think that he overstates the case a little. It is interesting that he never mentions Giordano Bruno, who was one of those who held on to the older magical view (then again, Bruno was not a scientist).


Replica of a van Leeuwenhoek microscope (photo: Jeroen Rouwkema)

Henry also puts emphasis on the emerging use of scientific instruments, such as the microscope and the telescope.


Galileo’s sketches of the moon, published in his Sidereus Nuncius of 1610

I was a little disappointed in the discussion of Galileo, which did not seem quite correct, but the main flaw in this book is its brevity. I’m giving it three stars.

* * *
The Scientific Revolution and the Origins of Modern Science by John Henry: 3 stars


Marching for Science #7

Interesting summary of the Science March from STAT:

  • Yes, it was a partisan anti-Trump event – “critics of the march who worried that it could turn scientists into an interest group to be isolated and ignored will likely feel their concerns validated after the event.”
  • It was mostly white – “There were [speakers] who were immigrants, trans, gay, Native American, black, Latino, young, and old. … But that audience itself was largely white.”
  • Industry science wasn’t there – “companies that are now marketing their ‘bold’ work in scientific discovery and developing new treatments largely lacked an official presence at the marches.”
  • People had fun – “lots of kids, dogs, and people dressed as dinosaurs. … and plenty of off-rhythm dancing to funk bands.”
  • What comes next is uncertain – “Will the march make a difference? Or will it end up as a historical footnote?”

March for Science, Washington, DC (photo: Becker1999)


Misquotes for Science

It’s a tough call, but the award for silliest statement at the March for Science has to go to the line “Dante said that the hottest places in Hell are reserved for those who remain neutral in times of moral crisis.” Dante never said anything of the sort, of course – the line is derived from something JFK said (“The hottest places in Hell are reserved for those who in time of moral crisis preserve their neutrality”), derived in turn from a chain of misquotes going back to Theodore Roosevelt. I’ve written before about Dante and Science, but suffice to say that in Dante’s Inferno, the worst regions are actually icy cold, and “neutrals” are not found there:

Please, let’s not have any “alternative facts” about Dante. The climate of the Inferno is important too.


Marching for Science #5

Further to my previous comments on the Science March, the graph below shows the (somewhat dubious) attendance estimates from Wikipedia for various cities (excluding vague counts like “thousands”), compared to the power-law predictor 0.47 D1.49 P0.78, where D is the fraction of the relevant state voting for Clinton last year (from Wikipedia), and P is the city population (also from Wikipedia).

The population P predicts 56% of the variance in turnout (not surprisingly), and D an additional 7%. Both factors were significant (p = 0.000000055 and p = 0.014 respectively). Prediction could probably be improved by using metro area population numbers for the cities, by using metro area election results (rather that state results), and by adding factors indicating the number of other marches in the relevant state (Colorado Springs, for example, was rather overshadowed by Denver) and the presence of universities (Ann Arbor, for example, is a university town). But the basic messages seem to be: Democrat voters do not like Donald Trump and Large cities attract large crowds. It would be interesting to compare the numbers here against other recent political marches which focused on different issues.