» » Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life

Download Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life epub

by Robin Wilson

“A fine mathematical biography.”―John Allen Paulos, New York Times Book Review

Just when we thought we knew everything about Lewis Carroll, here comes this “insightful . . . scholarly . . . serious” (John Butcher, American Scientist) biography that will appeal to Alice fans everywhere. Fascinated by the inner life of Charles Lutwidge Dodgson, Robin Wilson, a Carroll scholar and a noted mathematics professor, has produced this revelatory book―filled with more than one hundred striking and often playful illustrations―that examines the many inspirations and sources for Carroll’s fantastical writings, mathematical and otherwise. As Wilson demonstrates, Carroll made significant contributions to subjects as varied as voting patterns and the design of tennis tournaments, in the process creating large numbers of imaginative recreational puzzles based on mathematical ideas. 60 b/w illustrations
Download Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life epub
ISBN: 0393304523
ISBN13: 978-0393304527
Category: Literature
Subcategory: History & Criticism
Author: Robin Wilson
Language: English
Publisher: W. W. Norton & Company; 1 edition (June 14, 2010)
Pages: 237 pages
ePUB size: 1982 kb
FB2 size: 1217 kb
Rating: 4.7
Votes: 363
Other Formats: docx lrf rtf docx

Although Charles Dodgson's literary works are of course very well known, his mathematical work is more obscure. In fact, his mathematics is notable not so much for its importance in the strict development of mathematics but rather for the algorithmic aesthetic that infused all of Dodgson's work. Dodgson was particularly interested in systematizing rules of thought, and he strove to do this in two areas, symbolic logic and linear algebra (notably determinants) that would not really yield to the power of the computer for generations. At the same time, Dodgson's interest in the paradoxes of systematization, in the interplay between algorithm and intuition, informed his fiction work and his work on puzzles as well.

This pleasant, easy-to-read book nicely captures the milieu of Oxford mathematics education in the nineteenth century generally and Charles Dodgson's life in that milieu in particular. Notable is the affection for scholarship for its own sake, and for a much more sedate pace of life, than obtains nowadays.

Even in political science, Dodgson was way ahead of his time in his interest in systematizing voting protocols; although he did not anticipate Arrow's theorem, he at least did some preparatory work.

As a strict mathematician, however, Dodgson did not have the deep technique of the great 19th century mathematicians. His work rarely exceeds very basic mathematics, what would now be learned, perhaps in less detail, in middle school. There is, at least in the book, no calculus, no complex variables, no power series, no abstract algebra, no non-Euclidean geometry, no infinite set theory, not even impossibility proofs. He deals with Euclidean geometry (plane geometry in the examples) and some basic linear algebra.

At the same time, with this limited palette, Dodgson addressed very important problems - the problems he worked on all wound up leading to major, important fields (computational logic, computational linear algebra, and voting theory).

Not only does this book give insight into Dodgson's work and character, it also has some fascinating old exam papers from that time period. Indeed, the book would have been substantially improved had it included more facsimiles of period-authentic examinations and textbooks (as well as, for that matter, a bit more explanation of the somewhat confusing system - to American readers - of exams and matriculation at Oxford). But what it does have is interesting.

An example of a nice puzzle by Carroll is from The Tangled Tale: a traveller walks along level ground and up a hill, then returns the way; leaving at 3:00 PM and returning at 9:00 PM that day; travelling at 3, 4, and 6 mph uphill, level and downhill respectively. How far did he travel and when, within a half-hour, did he reach the top of the hill?

A nice exam problem from Oxford at the time was to solve

(x+sqrt(a^2-x^2))/(x-sqrt(a^2-x^2)) = b ,

where one presumes this is over the reals. There is something relaxing about math before the high-powered modern machinery took hold, everything concrete and finite.
What was Norton publishers thinking? LCiN is a purely derivative book, part bare-bones biography of Dodgson/Carroll, part popular math collection. The biographical parts are completely pedestrian (Wilson is a mathematician, not a biographer, and it shows). Very able biographies and biographical studies of D/C have been written by others; this one adds nothing. The popular math parts -- which the title of the book gives some impression are its focus -- consist almost exclusively of lengthy direct quotations from Carroll's own books. If I had to guess, at least 30% of LCiN is copied wholesale. Had Wilson had anything at all novel to say about D/C's mathematics, or about the word, logic, and math problems he quotes ad nauseum, then LCiN might have been worth at least part of the price of admission. For the most part, Wilson simply plucks problems from D/C's books and supplies answers only in LCiN's (very confusingly structured) endnotes section. For worked out solutions, in the overwhelming majority of cases, he simply refers the reader to D/C's own treatments. There is barely a trace of popular mathematics exposition in this slim -- and crazy over-priced book -- and very little reflection on D/C the man above and beyond the bullet-points of his life story. Wilson did not undermine my very great esteem for D/C but neither did he teach me a thing. I can't imagine why this book was published. It's a colossally lazy effort.