One of my favorite books is Fantasia Mathematica, edited by Clifton Fadiman, a collection of stories, articles and verses about mathematics and science. (I lost my copy a few years ago, but recently obtained another from Amazon.com.) And one of the delights in it is a reprint of a New Yorker Magazine short story by Russell Maloney.

Briefly, on one particular night, NYC police are overcome by nearly every one in the City trying to go across The George Washington Bridge at the same time. Then all the people dining out each night are trying to go to a few restaurants. Other such anomalies plague the City, and similar stories emanate from other parts of America. It's suddenly realized that THE LAW OF AVERAGES HAS BROKEN DOWN!

However, clever bureaucrats find tactics for compensating with this failure of The Law of Averages. For example, a Law is passed mandating that only people whose surname begins with letters A, B, or C can go dining on a Monday night, and they must go to a restaurant whose name includes that letter. Etsettery.

But just as ORDER seems restored, DISORDER breaks out in another way and in other directions. From the woods of West Virginia and Appalachia and the Ozarks, hillbillies and tenant farmers come riding out in limousines. THE LAW OF DIMINISHING RETURNS HAS BROKEN DOWN!

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Elsewhere, I've a file, "LEAKY NAMES LOSE DECISION-GAMES!", complaiing about any word that has two or more divergent meanings. The word "law" is very LEAKY. It has a legal or social meaning, which is very different from its scientific meaning, which is very different from its mathematical meaning. You can pass or repeal a social law; but not a scientific or mathematical law. You may find an exception to a scientific law, but properly not to a mathematical law.

The humor in Maloney's story is that he makes a mathematical or scientic law sound like a social law. And, before going to my main point of this introduction, I must correct any misunderstanding about "The Law of Averages".

This jargon refers to a superstition that, say, for tosses of a FAIR coin, a run of heads must be COMPENSATED by a CHANGE TO TAIL or TAILS. As another example, a friend of Esther, who had 4 sons, was sure that "by The Law of Averages, the next one must be a girl".

(The book, Mathematics (1963), in the LIFE Science Library, by David Bergamini, on pages 144-5, contains a photograph of a family with a run of 6 girls followed by a run of 5 boys, which seems to bear out the compensation idea. But this is belied by another photograph of a family with 13 boys, no girl. And another photograph with a family of 8 girls, no boy.)

The noted Russian-American probabilist, William Feller -- I wrote my Master's Thesis on his paper, "The Law of the Iterated Logarithm"" -- once said, "The Law of Large Numbers [the proper term for this] works, not by compensation, but by swamping." That is, in a large sample, "inequities" diminish or disappear. (And the economic Law of Diminishing Returns is thought to work similarly.)

But I really mentioned the New Yorker story's anomalies to introduce the subject of "aberrations in history".

One of these is the story of Paracelsus (1493-1541), who spent much of his career as a typical medical quack, then began to achieve some real healing, and is sometimes called "The Father of Modern Medicine". Whahappen?

The distinguished French historian, Jules Michelet (1798-1874), wrote a book providing evidence that Paracelsus stole his remedies from contemporary women, known as "The Sagas", healers among the poor. The Sagas were very knowledgable about herbs. Thus, another name for the plant, nightshade, is "belladonna"", which means "beautiful lady"in Italian. Poisonous in significant amounts, it has healing power when judiciously used. Those who benefited from this and other nostrums praised these drab old women as "beautiful".

(Incidentally, prior to publication of this book giving credit to The Sagas, Michelet was considered the leader of the French historical school. But he was denounced by his peers for this publication, which was considered a betrayal of his profession as well as of his gender. If I were a girl, I'd take up Michelet's cause and enquiry!)

Another example is the one that involves my title. Just as Renaissance medicine seemed to change quality ABRUPLY, so did certain parts of Renaissance mathematics, particularly in numerical algebra and number theory.

But, recently, some scholars found evidence that European mathematicians, particularly Italian ones, may have copied, and sometimes built upon, work of Islamic and Jewish mathematicians working before the Renaissance. In fact, a few of their writings actually credit such contributions, but mainstream mathematicians have chosen, up until now, to ignore this.

Correct history is always important. Due credit should always be given. And, if I were of Islamic or Jewish heritage, I'd certainly wish to CORRECT DISORTIONS OF THE RECORD or OMISSIONS IN IT. How about you?