Books — hermiene.net

This is a collection of essays by Asimov on numbers and mathematics. It discusses how we got the concept of zero (from India via the Arabs), exponents, factorials, aleph numbers (there are actually different kinds of infinities), pi, imaginary numbers, huge numbers (like googol, but that doesn't even scratch the surface), the metric system (yum), and a host of other stuff. It also has an essay on animals and their sizes.

As with most essay collections from Asimov, this one is a sure-fire good read. Asimov explains in detail (but not too painful detail) a lot of difficult mathematics, step by careful step. Unlike a lot of his other collections, this one feels a little miscellaneous, but that doesn't at all detract from its quality.

Flatland chronicles the adventure of A. Square, a being in Flatland. Flatland consists of only two dimensions, as opposed to Pointland, which consists of zero dimensions, Lineland, which consists of one dimension, and Spaceland (the one we inhabit), which consists of three dimensions. It describes at length the society in Flatland, and how they go about tasks that we Spacelanders find trivial. For instance, everyone is a Polygon. The more equal all its angles and the more sides it has, the higher its social rank. Lowest are women (or the Frailer Sex, as they are often called) who are mere Lines and have no chance of rising in rank. Then come the Triangles, which are men. Then Squares (of which the narrator, A. Square, is naturally a member), Pentagons, Hexagons, Heptagons, Octagons, etc. The more sides a Polygon has, the closer it gets to being a Circle. They're the top leaders of every aspect of Flatland's society.

Flatland is a classic, and even though it's written in the 1880s in Victorian English, it's still eminently readable (and funny). You might have to read a little carefully at first to get used to the age of the language, but once you've picked it up you'll have no trouble enjoying this excellent story.

Flatterland is sort of an unofficial sequel to Abbott's classic Flatland, written in modern non-Victorian English. Although Victorian English gave the original a pretty classy feel, Flatterland doesn't disappoint. Its aim is similar to that of the original: To explain new mathematical concepts to lay people in lay language.

The book succeeds brilliantly. It's filled with illustration to help visualize the concepts, and the stories around which the concepts are introduced are reminiscent of Alice's Adventures in Wonderland (well, the fact that chapters have names like The Topologist's Tea-Party and Along the Looking-Glass probably helps), and this gives the book a whimsical tone (that's a benefit). Here's a sample:

"Is Planiturth's universe built from mathematics? Or is mathematics built by the minds of Planiturthians? Planiturthian mathematicians would like to think that their universe is built from mathematics, but that's only natural, after all. Planiturthian physicists would like to think that the Planiturthian universe is built from physics. Planiturthian biologists would like to think that the Planiturthian universe is built from biology. Planiturthian philosophers would like to think that the Planiturthian universe is built from philosophy. (Let me tell you a secret: it is. The fundamental unit of the Planiturthian universe is the philosophon, a unit of logic so tiny that only a philosopher could hope to split it.)"

The book also ventures a little into physics, explaining things like the Schrödinger's cat, the double-slit experiment, time travel, and forces. But the meat of the book is mathematics.

Based on articles written for Scientific American, every chapter has an addendum, explaining further points or elaborating new ones, and some chapters have letters from people sent in after the article in question was published.

An awesome book with lots of interesting things. Read the chapter titles in the Structures for a preview.

This book is written in the same vein as Mathematical Puzzles and Diversions.

I truly loved this book. My favorite chapters are The Five Platonic Solids, Mazes, and Eleusis: The Induction Game.

Somewhat of a sequel to Flatland, Sphereland continues in the same vein, explaining three dimensions to two-dimensional creatures. The pace and mode of writing is pretty similar to the original, and I very much liked that. The novel things that Sphereland does is two-dimensional space exploration and explaining a curved line to a one-dimensional being (and thus setting up the explanation for why two-dimensional beings would have problems understanding a plane curved into a sphere, and by extension how three-dimensional beings would have trouble understanding how to curve a sphere around a hyper-sphere).

Letters to a Young Mathematician is written as an update on G. H. Hardy's classic A Mathematician's Apology, but the book is not an exercise in apologetics.

"Attitudes change. No longer do mathematicians believe that they owe the world an apology."

It follows an imaginary girl, Meg, from her school years through her ensuing career, and each chapter is a letter to her at crucial steps in her career. Some parts are musings on math (pure vs applied) while others are specific career tips (solitary work vs collaboration). The book is virtually devoid of any actual math, so I think it's safe for mathophobes. In fact, for this very reason, it might even help to partially cure the phobia of those unfortunately inflicted.

I really liked the light-hearted way the book is written. Perhaps someone who is planning on embarking on a mathematical career would enjoy it even more.