Free Fear of Physics by Lawrence M. Krauss Page A

of QCD and asymptotic freedom. Even though no one has yet been able to perform a complete calculation in the regime where QCD gets strong, the experimental evidence in the high-energy regime is so overwhelming that no one doubts that we now have the correct theory of the interactions between quarks. In fact, Gross, Wilczek, and Politzer were awarded the Nobel Prize in 2004 for their discovery of asymptotic freedom, and with it, the ability to verify QCD as the theory of the Strong Interaction. And without some dimensional guide for our thinking, the key discoveries that helped put the theory on a firm empirical foundation would not have been appreciated at all. This generalizes well beyond the story of the discovery of QCD. Dimensional analysis provides a framework against which we can test our picture of reality.
     
     
    If our worldview begins with the numbers we use to describe nature, it doesn’t stop there. Physicists insist on also using mathematical relations between these quantities to describe physical processes—a practice that may make you question why we don’t
use a more accessible language. But we have no choice. Even Galileo appreciated this fact, some 400 years ago, when he wrote: “Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.” 3
    Now saying that mathematics is the “language” of physics may appear as trite as saying that French is the “language” of love. It still doesn’t explain why we cannot translate mathematics as well as we might translate the poems of Baudelaire. And in matters of love, while those of us whose mother tongue is not French may labor under a disadvantage, most of us manage to make do when it counts! No, there is more to it than language alone. To begin to describe how much more, I will borrow an argument from Richard Feynman. Besides being a charismatic personality, Feynman was among the greatest theoretical physics minds in this century. He had a rare gift for explanation, I think due in part to the fact that he had his own way of understanding and deriving almost all the classical results in physics, and also in part to his New York accent.
    When Feynman tried to explain the necessity of mathematics, 4 he turned to none other than Newton for a precedent. Newton’s greatest discovery, of course, was the Universal Law of Gravity. By showing that the same force that binds us to this sphere we call Earth is responsible for the motions of all the heavenly objects, Newton made physics a universal science. He showed that we have the potential to understand not merely the mechanics of
our human condition and our place in the universe but the universe itself. We tend to take it for granted, but surely one of the most remarkable things about the universe is that the same force that guides a baseball out of the park governs the sublimely elegant motion of our Earth around the sun, our sun around the galaxy, our galaxy around its neighbors, and the whole bunch as the universe itself evolves. It didn’t have to be that way (or perhaps it did—that issue is still open).
    Now Newton’s law can be stated in words as follows: The attractive force that gravity exerts between two objects is directed along a line joining them, and depends on the product of their masses and inversely as the square of the distance between them. The verbal explanation is already somewhat cumbersome, but no matter. Combining this with Newton’s other law—that bodies react to forces by changing their velocity in the direction of the force, in a manner proportional to the force and