Robin J. Wilson

Interesting, and well-presented. It's more about math and less about maps than I'd thought, but those are both interests of mine so it worked. The history of a math problem - not just "can every map be colored with no more than four colors so that no two countries that share a border have the same color" - but can that be _proved_. Chapter after chapter, he'd mention that it had been proved that the theory was true for any map with no more than...20, 50, 150 countries. But is it true for show more _all_ maps? The question kept getting more abstract - from maps, to geometric shapes, to graphs of connected points. There were a lot of proofs that were eventually shown not to be proofs - holes in their logic. The final answer (the question was first posed in the mid-1800s; the answer came in 1976) required a computer to work the proof, and was greeted with a good deal of skepticism thereby. Was it really a proof if a human hadn't done all the steps? I found that part particularly interesting. It's a question I'd heard of vaguely, and I'm glad I read this; I now understand the question, at least, though the details of the math began to escape me near the end. Definitely worth reading. show less

This is a relatively brief (228 pages with lots of illustrations) and coherent history of the 4-color map problem. A map is what you think it is, a surface with boundaries between regions. Other rules: the map may be on a sphere but it may not be on a torus (donut) or other 3D form with a hole, each region is independent (so not a map of the world in which some countries are split into parts that must be the same color), and the boundary is defined as more than a single point (n regions that show more meet in the center of a pie do not require n colors to be distinct). The problem made its appearance in 1852, when a student asked a professor, who asked a friend... and remained unsolved until 1976. It rose to notoriety because it's a simple question that was difficult to answer, and it was worth tackling because effort on any one problem can yield results that apply to other problems. One strategy was to prove the impossibility of a "minimal criminal": a minimal counterexample with a configuration of regions such that (a) the configuration _cannot_ be colored with 4 colors, but (b) any sub-configuration (the same configuration with one or more regions removed) _can_ be colored with 4 colors. A configuration might be a square (a region surrounded by four others), or a cluster of three pentagons (three regions each surrounded by five others), etc. Various mathematicians over decades contributed proofs regarding specific configurations of increasing complexity, and different methods of determining their properties. The strategy that eventually led to a proof was to find an "unavoidable set" (a set of regions one or more of which _must_ be in any map) of "reducible configurations" (configurations that may not be in a minimal criminal). The proof, by Kenneth Appel and Wolfgang Haken, consisted of nearly 2000 such configurations verified by a computer program, and was disturbing for its inelegance and non-transparency, to the extent that one math department deemed Appel and Haken a bad influence and barred them from meeting students. The proof has since been streamlined, but not fundamentally changed. The book is nicely presented in chronological order, with concepts succinctly explained and helpfully illustrated, especially in the earlier stages when things were still relatively straightforward. It becomes less clear in the later stages, but this is not the fault of the author, as the details are far too numerous for this sort of publication.

(read 27 Jun 2011) show less

Yes, really lovely. The D'Oyly Carte Opera Company ran for one hundred and seven years, from the moment in 1875 when founder Richard D'Oyly Carte [re]united two extremely different young luminaries of the British arts scene to create a one-act comic opera, Trial by Jury. The men's thirteen creations under D'Oyly Carte would prove the most lasting of all Victorian popular culture, rivalled only by the novels of Mr Dickens. Gilbert and Carte kept a firm hand on the staging of the works show more (Sullivan was somewhat more hands-off) until their deaths, after which time Rupert, Carte's son, led the company nobly, followed by his only child, Dame Bridget. Their performances upheld a remarkable tradition even if, dare I suggest, they threatened to protect Gilbert and Sullivan's operas in mothballs from time to time.

The company shuffled to its end in 1982. There had been a dramatic fall from grace since the celebrated centenary season of 1975. The cultural world was changing, as were the financial demands of taking a company on the road, and the Thatcher Government - despite public pressure - declined, through its Arts Council, to subsidise the company. An abbreviated last season was given in London, and the company went their separate ways, and a landmark of theatre was lost to time. Luckily they recorded all of the operas, some numerous times, and left an astonishing legacy.

This authorised picture book contains close to 500 pictures (largely black and white) from that first production of Trial by Jury through to the programme of the closing night. There is little text other than captions, and of course nothing that isn't out-and-out praise for The Company. But that's not to complain, given the gloriousness of the pictures and the nostalgia they conjure up. Treasures from a time long lost. show less

The title Four Colors Suffice refers to a simple mathematics problem that was first discussed in the 1850's. Namely, how many colors does it take to color a map so that no two bordering countries have the same color? The answer appeared to be 4 colors, but proving that took 150 years and required the use of computers. This book traces the history of the problem from the first publications to the proof of it in 1976, plus a discussion of the validity of a computer proof.

The writing overall show more was fine -- not brilliant, not poor, but somewhere in the middle. For some of the mathematics, the discussion was a bit unclear and hard to follow. (Yes, the methods used by various attempted proofs are difficult topics, but even having a decent mathematical background, I had to reread several pages to understand what he was trying to say.) The diagrams were terrific! The history was well researched with notes and a bibliography.

On the down side, the book lacked somewhat. As mentioned above, some areas were obtuse. Also some topics, such as why this is an important problem and not just a "let's see if we can prove it" type of problem, were alluded to but never really discussed. Wilson stated several places that the math used to solve this problem led to other important results, such as...well, he never says. Also, the final section as to whether or not the proof is valid felt like it was added later, without much enthusiasm. Proof by exhaustive computer search is a very interesting question -- is it really a proof? I understand that a thorough discussion would involve a lot of discussion of computer programming, but this book (as evidenced by the level of math when discussing the historic proofs) is aimed for a mathematical literate audience that could understand the basics of the computer issues.

Overall, the history part of the book was fine, but the "we have a proof" section was lacking. I will probably read it again at sometime, but not terribly soon. show less