Free Fear of Physics by Lawrence M. Krauss Page B

inversely proportional to their masses—you have it all. Every consequence of gravity follows from this result. But how? I could give this description to the world’s foremost linguist and ask him or her to deduce from this the age of the universe by semantic arguments, but it would probably take longer than this time to get an answer.
    The point is that mathematics is also a system of connections, created by the tools of logic. For example, to continue with this famous example, Johannes Kepler made history in the early seventeenth century by discovering after a lifetime of data analysis that the planets move around the sun in a special way. If one draws a line between the planet and the sun, then the area swept out by this line as the planet moves in its orbit is always the same in any fixed time interval. This is equivalent (using mathematics!) to saying that when the planet is closer to this sun in its orbit it moves faster, and when it is farther it moves more slowly. But
Newton showed that this result is also mathematically identical to the statement that there must be a force directed along a line from the planet to the sun! This was the beginning of the Law of Gravity.
    Try as you might, you will never be able to prove, on linguistic grounds alone, that these two statements are identical. But with mathematics, in this case simple geometry, you can prove it to yourself quite directly. (Read Newton’s Principia or, for an easier translation, read Feynman.)
    The point of bringing all this up is not just that Newton might never have been able to derive his Law of Gravity if he hadn’t been able to make the mathematical connection between Kepler’s observation and the fact that the sun exerted a force on the planets—although this alone was of crucial importance for the advancement of science. Nor is it the fact that without appreciating the mathematical basis of physics, one cannot derive other important connections. The real point is that the connections induced by mathematics are completely fundamental to determining our whole picture of reality.
    I think a literary analogy is in order. When I wrote this chapter, I had been reading a novel by the Canadian author Robertson Davies. In a few sentences, he summarized something that hit very close to home: “What really astonished me was the surprise of the men that I could do such a thing.... They could hardly conceive that anybody who read . . . could have another, seemingly completely opposite side to his character. I cannot remember a time when I did not take it as understood that everybody has at least two, if not twenty-two, sides to him.” 5
    Let me make it a little more personal. One of the many things my wife has done for me has been to open up new ways of seeing the world. We come from vastly different backgrounds. She hails
from a small town, and I come from a big city. Now, people who grow up in a big city as I did tend to view other people very differently than people who grow up in a small town. The vast majority of people you meet each day in a big city are one-dimensional. You see the butcher as a butcher, the mailman as a mailman, the doctor as a doctor, and so on. But in a small town, you cannot help but meet people in more than one guise. They are your neighbors. The doctor may be a drunk, and the womanizer next door may be the inspirational English teacher in the local high school. I have come to learn, as did the protagonist in Davies’s novel (from a small town!), that people cannot be easily categorized on the basis of a single trait or activity. Only when one realizes this does it become possible truly to understand the human condition.
    So, too, every physical process in the universe is multidimensional. It is only by realizing that we can understand each in a host of equivalent, but seemingly different, ways that we can appreciate most deeply the way the universe works. We cannot claim to understand nature when we see only one side of it. And