The Rubik’s cube, shown above, is used by Wikipedia to illustrate the area of mathematics known as group theory.
Tuesday, February 21, 2012

Monstrous Groups

Mark Roman has written an interesting book about the largest group known, The Monster, which operates in over 196,000 dimensions.

So what is a group? This may be an oversimplification and wildly inaccurate to boot, but the best way to think of it is as a series of moves, called permutations in mathematics, that affect the ordering of something. In the Rubik’s Cube you can rotate the individual pieces so that appear in billions and billions of ways. It is also possible to obtain algorithms, procedures, that will in a few steps restore the cube back to its original orientation.

Now you can also imagine an object that exists in more than three dimensions. A cube that exists in four spatial dimensions is called a tesseract, and you can find one featured prominently in Robert A. Heinlein’s story “And He Built a Crooked House.” The more dimensions the object exists in, the greater the number of sides, vertices, and so on.

Ronan does not give a great deal of math, and none beyond simple algebra, so you won’t learn how to construct a group. What you do get is a gentle introduction to group theory, its implications to the larger world around us, and brief background stories about some of the famous mathematicians.

It’s available on the Kindle, and makes for fast reading.

Next up, a book about the decision to drop the bomb.