On Prediction

Asimov’s “On Prediction” (1968), the introduction to a SF anthology entitled Future Tense, edited by Richard Curtis:
The matter of prediction is full of pitfalls.
For instance, if a new scientific theory is to prove a useful one, it ought to predict phenomena that are unexpected or even downright “impossible” by older theories. If the prediction is found to be accurate then that is a great point in favor of the new theory.
But is the prediction in itself sufficient to “prove” the new theory? — Not at all. Not if other aspects remain unacceptable.
For instance, I hereby propose a new theory to the effect that nylon is repelled by gravitational force and that anything made out of nylon will therefore fall upward. In line with this theory, I will predict that if you make a parachute of nylon and connect yourself to it by a harness and then jump from a plane, you will fall very slowly because gravitational repulsion will be pushing up against the nylon.
If you care to try the experiment you will find that this prediction is absolutely correct and goes flatly against old Galileo’s statement that all objects fall at the same rate. Does that mean that nylon is really repelled by gravitation?
Of course not. What Galileo really said was that all objects fall at the same rate in a vacuum and, by taking air resistance into account, we can explain the parachute effect without postulating gravitational repulsion. Besides the one prediction that comes true is balanced by others that emphatically do not. A nylon object left to itself will not fall upward.
Or take the predictions of Immanuel Velikovsky. He advanced a theory that at the time of the Biblical Exodus, Jupiter expelled a comet which passed close to the earth, caused the plagues of Egypt, stopped the Earth’s rotation, affected its orbit, and did many more things before settling down to become the planet Venus. In line with all this, Velikovsky predicted that Venus would be found to be hotter than astronomers suspected and, by golly, he was right.
Does that mean that because of this correct prediction, we must accept the whole of Velikovsky’s theories? Of course not. There remain many aspects of it (very many) which are extremely dubious in the light of modern theory. Astronomers will therefore try to explain Venus’ temperature in various non-absurd ways before accepting Velikovsky, and it is my calm prediction that they will suceed.
But then if Velikovsky’s theory is not correct, how did he know Venus was hot? Well, I know it’s very frustrating, but coincidences can take place and if an intelligent, imaginative man makes many predictions, some of them are bound to be close enough to the truth (usually in a very primitive way), to cause innocents to suspect that all the other predictions are true, too.
For instance, the alchemists thought lead could be transmuted to gold and nineteenth-century chemists laughed at the whole idea. Twentieth-century chemists, however, succeeded in carrying through numerous transmutations of one element into another.
Aha!!! Can we not deduce from that that those old alchemists were smart cookies; that they knew what they were doing; that they had access to ancient secrets we have lost?
But how about telling the whole story. Alchemists thought lad could be transmuted to gold by ordinary chemical procedures like heating and distilling and mixing and muttering spells. We do it now by particle accelerators and nuclear reactors. The two sets of methods bear no relationship and merely to dream of a goal is no sign of preternatural knowledge of the eventually discovered methods of reaching that goal.
And so it is with predictions in fiction.
One can finds lots of “predictions” in fiction if one looks assiduously enough and trustingly enough.
In the Greek myths, Daedalus invented feathered wings held together by wax, with which he and his son, Icarus, could fly through the air. Was that not a prediction of modern airplanes? Admittedly we use metal and welding instead of feathers and wax but isn’t the principle the same?
Again, in the Norse myths, the world was foreseen as coming to an end in the great Twilight of the Gods. And now science tells us that the world will come to an end when the Sun enters its red giant phase about eight billion years hence.
May we assume from that that the shaggy Norsemen of old had somehow figured out modern astrophysics?
Will anyone who believes that raise his hand?
And if we go through the fairy tales, we will come across flying carpets (helicopters?), seven-league boots (railroads?), magic (electronic instruments?), oracles (computers?), wicked demons (Nazis?), and anything else you want.
But, you know, the fantasts and mythmakers of the past were not trying for predictions. They were allegorizing or wishing.
Nowadays, though, we have science fiction, and what makes science fiction different from all previous types of fantasy literature, is that the science-fiction writer disciplines his imagination. Anything does not go. Only that goes that fits science as we know it today or as that science can be plausibly extrapolated. With that in mind, prediction really becomes prediction and not accident.
To be sure, it is not the first duty of the science-fiction writer to predict the future. His first duty is to write an entertaining story, which matches the structure of science or, at the very least, does not betray an ignorance of the structure of science.
In doing so, though, it is almost impossible for him not to draw a picture which is the equivalent of a prediction of some facet of future technology or sociology. And if an intelligent writer, with a competent understanding of science, does this, then, every once in a while, the prediction hews so close to the eventual course of history, as to come true.
This anthology is a sampling of stories in which the cloudy crystal ball cleared for a moment to allow a writer to look ahead and see what was to be — tanks, atomic bombs, television, communications satellites.
And as we read we must ask ourselves: What inventions or social phenomena being discussed in science fiction right now will come true a generation from now? Care to guess?

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Dan Brown parody

Dan Brown is a hilariously bad writer. The Da Vinci Code was an outrageously successful book.
So it was only inevitable that in addition to all the delicious criticism of Dan Brown’s writing,¹ there would also be a number of parodies of his books published, and indeed there have been several.² While looking for something in the library, I found The Da Vinci Cod: A Fishy Parody by “Don Brine” (real name Adam Roberts) and quickly proceeded to borrow it and read it. It was a good two hours spent, which is more than can be said for Dan Brown’s books themselves. Although the author is a professor of literature at London University, the book manages to remain true to the awful writing and plot of the original. I heartily recommend reading the book if you come across it; for a taste of what it’s like, some excerpts follow. You can also see parts of the book at Google Books.

Mathematics and notation: the Hindu-Arabic numeral system

Quick: What is CCXXXVII × CCCXXIX?

From page 15 of The Life of Pi by Jonathan Borwein:

The Indo-Arabic system came to Europe around 1000 CE. Resistance ranged from accountants who didn’t want their livelihood upset to clerics who saw the system as ‘diabolical,’ since they incorrectly assumed its origin was Islamic. European commerce resisted until the 18th century, and even in scientific circles usage was limited into the 17th century.

The prior difficulty of doing arithmetic is indicated by college placement advice given a wealthy German merchant in the 16th century: “If you only want him to be able to cope with addition and subtraction, then any French or German university will do. But if you are intent on your son going on to multiplication and division — assuming that he has sufficient gifts — then you will have to send him to Italy.” (George Ifrah, p. 577)

[The rest of the pages of the slides are also great and worth reading!]

Just to give some context of the time: The Hindu-Arabic system was introduced into Europe by Leonardo of Pisa (Fibonacci) — an Italian — in his Liber Abaci, written in 1202. Gutenberg (in Germany) invented the printing press around 1450. In Italy, Tartaglia lived 1500-1557, Cardano 1501-1576, Sturm 1507-1589, Giodano Bruno (1548-1600), and Ludovico Ferrari (1522-1565). (And outside Italy, Robert Recorde (as we’re talking about notation) (1510-1558) in Wales, François Viète (1540-1603) in France, etc. See this image.) Of course Galileo Galilei (1564-1642) was Italian too, but came later, as did Newton, Fermat, the Bernoullis, and all the others.

While on the topic of mathematics and notation, see also this post: Visual Clarity in the Naming of Variables.
[And while not exactly notation, Donald Knuth’s Calculus via O notation]