Describe Everything...Use No Words

Despite what many of us may have thought when we were taking math class, the equations we were required to learn did not spring fully-formed from the sadistic minds of our instructors. Though some are ancient and some are recent, all of them "came into being," so to speak, when someone happened upon a principle and expressed it in terms that developed into the formulas we are used to (or maybe not so used to) today.

According to mathematician Dana Mackenzie in The Universe in Zero Words, the history of humanity's understanding of the world around us can be found in looking at some of the very same equations we may have cursed in the classroom. Mackenzie selected 24 equations, starting with antiquity, and with brief vignettes, sketches the role each played in the development of human thinking and understanding the universe.

And he does start with the basics -- the very first equation he considers is ye olde 1 + 1 = 2. Perhaps self-evident in the modern world, but as Mackenzie notes, until you have the relationship between objects thus coded in some way, you don't have a system for manipulating numbers and you don't even have basic arithmetic. Take one apple and add another and you have two apples, but what about pears? Are they the same? Or what about groups of different objects? Do they behave the same way as the apples? Without the expression 1 + 1 = 2, you are left with having to count them all of the time. But with that expression, you can state a general rule that frees you from counting everything in order to see how many you have. We have no idea when this basic arithmetic was first used or where it came from, but there was a time before it, and without someone figuring it out we are pretty much stuck with stone knives and bearskins.

Mackenzie goes through the history of mathematics this way, touching on famous equations like the Pythagorean Theorem (probably not discovered by Pythagoras) or Albert Einstein's E = mc². He also explores lesser-known formulas that the blogger interface can't reproduce properly, but which have proven vital to understanding the universe as well as the infinitesimally small world of quantum mechanics. First by outlining the basic arithmetic and geometry that let people begin to think in abstract as well as concrete terms, then through the times of Newton and Liebniz, Gauss and Galois and into the 20th century with Gödel and Dirac and Einstein himself, Mackenzie offers the story of humanity's ability to know the world around us -- or at least parts of it -- through the development of the equations that describe the planets, the atoms, the particles of which they are all made and the way they behave.

Mackenzie doesn't load the book with a lot of formulas and mathematical arcanum -- it takes algorithm-phobes such as myself some time to puzzle out the different symbols and their meaning, but it can be done. And doing so is worth the trip for a fascinating view of how human beings have sought to find -- and in some cases impose -- order on the world in which we live and move and have our being.