Book mathematics--Part 1.
I would like to think that anyone who enjoys mathematics also enjoys reading (although the converse of this may not be true, alas). I know I do; but this does not necessarily mean that what I read is exclusively mathematical or about mathematics. Indeed it is comparatively rarely that I find myself pausing, while reading, to consider the mathematical implications of some point in a book. Yet when this does happen, it is especially arresting--and potentially the start of some interesting mathematical thinking. Moreover, my enjoyment and understanding of the book is enhanced by this detour into mathematics.
Of course there is more to mathematics than arithmetic (numeracy numeracy Mathematical literacy Neurology The ability to understand mathematical concepts, perform calculations and interpret and use statistical information. Cf Acalculia. > numberacy). Consider such aspects of a book as:
* when: time-lines, and historical relationships;
* where: maps, and journeys;
* logical reasoning The three methods for logical reasoning, deduction, induction and abduction can be explained in the following way: 
Given preconditions α, postconditions β and the rule R1: α ∴ β (α therefore β). : cause-and-effect and deductive de·duc·tive
1. Of or based on deduction.
2. Involving or using deduction in reasoning.
* spatial orientation, and geometric attributes;
* family relationships: family trees This is an index of family trees available. It includes noble, politically important and royal families as well as fictional families and thematic diagrams. Europe
* scale and proportion and ratios;
* units of measurement Units of measurement
Values, quantities, or magnitudes in terms of which other such are expressed. Units are grouped into systems, suitable for use in the measurement of physical quantities and in the convenient statement of laws relating physical quantities. : distance, time, money, mass;
* probability and randomness; and so on.
Alex Kasman's website, Mathematical Fiction (http://math.cofc.edu/kasman/MATHFICT/ (last accessed 21 September 2007)) provides a large list of books that deal with mathematics, mathematicians or scientists (for example, Kasman includes Bertold Brecht's play The Life of Galileo Life of Galileo (Leben des Galilei), also known as Galileo, is a play by the twentieth-century German dramatist Bertolt Brecht. The first version of the play was written between 1937 and 1939; the second (or 'American') version was written between ), or that have some mathematical term in their title (for example, Kasman includes John Cheever's short story The Geometry of Love, although this simply mentions geometry as a hobby of the central character).
Each of the following excerpts from books offers a mathematical challenge. Each of the books is itself worth reading, for different interests or purposes.
I would be glad to have further examples from other keen readers.
Mr Midshipman midshipman: see toadfish. Hornblower (C. S. Forester Noun 1. C. S. Forester - English writer of adventure novels featuring Captain Horatio Hornblower (1899-1966)
Cecil Scott Forester, Forester , 1950)
In Chapter Two: A Cargo of Rice (pp. 51-55), the young midshipman (junior naval officer NAVAL OFFICER. The name of an officer of the United States, whose duties are prescribed by various acts of congress.
2. Naval officers are appointed for the term of four years, but are removable from office at pleasure. Act of May 15, 1820, Sec. 1, 3 Story, L. ) has been put in charge of a captured French cargo ship, full of rice. The ship has been damaged in the fight that led to its capture. A cannonball struck the hull, below the water-line, while the ship was heeled over under a full-spread of sail.
Rice would absorb every drop of water taken in by the ship, so that no leak would be apparent on sounding the well [the bilges]... Dry rice soaked in water would double or treble its volume. The cargo was swelling and bursting the [wooden] seams of the ship open.
This is a thrilling twist to an exciting story, threatening young Hornblower's first independent command; but does dry rice really swell that much? (What about lentils, or dried lima beans?)
There is a great deal of incidental mathematics, or mathematical stimuli throughout the Hornblower books, including frequent use of old British and European units of measurement (quintals of salt and hogsheads of rum, for instance, in The Happy Return), and necessary attention to maps, as well as time-lines for Napoleonic history. It should be noted that (like Patrick O'Brien's naval captain Jack Aubrey in a sequence of novels, partly filmed as Master and Commander with Russell Crowe) many of the exploits of Hornblower are actually based on a real-life Napoleonic era naval captain Thomas Cochrane.
The Stinky Cheese Man and Other Fairly Stupid Stories (Jon Scieszka & Lane Smith, 1992)
In the Introduction, Jack, the narrator NARRATOR. A pleader who draws narrs serviens narrator, a sergeant at law. Fleta, 1. 2, c. 37. Obsolete. , is explaining the difference between traditional "fairy tales" and "fairly stupid tales," such as "Goldilocks gold·i·locks
pl.n. (used with a sing. or pl. verb)
A European plant (Aster linosyris) having narrow sessile leaves and dense corymbs of small, bright yellow, discoid flower heads. and the Three Elephants," in which Goldilocks breaks into the home of the three elephants, but is unable to climb into any of the chairs (elephants' chairs, even those for baby elephants, are rather large), and so she goes home. Jack then urges the reader:
... you should definitely go read the stories now, because the rest of this introduction just kind of goes on and on and doesn't really say anything. I stuck it in here so it would fill up the page and make it look like I really knew what I was talking about. So stop now. I mean it. Quit reading. Turn the page. If you read this last sentence it won't tell you anything.
Think about it. Does that last sentence tell you anything?
This is a very funny, fairly stupid (or brilliant) book (as are all the books by Jon Scieszka and various colleagues, especially The Maths Curse, which is arguably the most mathematics-intense picture-story book ever written--and one of the funniest). On the back cover, the egocentric egocentric /ego·cen·tric/ (-sen´trik) self-centered; preoccupied with one's own interests and needs; lacking concern for others.
adj. , talkative Little Red Hen asks, "Who is this ISBN ISBN
International Standard Book Number
ISBN International Standard Book Number
ISBN n abbr (= International Standard Book Number) → ISBN m guy?" The story that Jack tells (under extreme threats from the Giant) is in the great tradition of the dark and stormy night where a story is called for, so the narrator begins telling a story about a dark and stormy night where a story is called for, so...
Recursion In programming, the ability of a subroutine or program module to call itself. It is helpful for writing routines that solve problems by repeatedly processing the output of the same process. See recurse subdirectories. , and self-referential statements are important concepts in mathematics logic. The famous case of Epimenides (6th century BC), the Cretan who declared that all Cretans are liars, was one of the first of these paradoxes. Douglas Hofstadter's classic (non-fiction) Godel, Escher, Bach: An Eternal Golden Braid (1979) explores recursion and other aspects of mathematics in music, logic and art, circling recursively around Kurt Godel, Maurits Escher, and Johann Sebastian Bach--and, most appropriately, Lewis Carroll (the pen-name for a major nineteenth century mathematician). Raymond Smullyan also explores these fascinating topics: one of his book titles plays on self-reference: What is the Name of This Book? Compare this with the name-ambiguity of the Abbott and Costello Abbott and Costello (kŏstĕl`ō), American comedy team of William Alexander "Bud" Abbott, 1895–1974, b. Asbury Park, N.J., and Lou Costello, 1906–59, b. Paterson, N.J., as Louis Francis Cristillo. vaudeville and film routine "Who's on first?" and Odysseus using a nom-deguerre to boast to the blinded Cyclops that "Noman has hurt you!"
Editor's note: In this occasional series, John Gough presents the many mathematical possibilities found in books/stories that are not deliberately mathematical in nature.
with John Gough
Deakin University * <firstname.lastname@example.org>