Between Mathematics and Transcendence: The Search for the Spiritual Dimension of Scientific Discovery

IN THE FOURTEENTH CENTURY, Nicole of Oresme tried to describe human emotions mathematically. Human psychic processes turned out to be too complicated for mathematical formulae and Nicole of Oresme's ambitious attempt failed. Seven centuries later, the language of mathematics in modern physics is used to describe the astonishing variety of physical processes, whether they take place in New York, Beijing, or Kinshasa. Why has the language of mathematics been so effective in the physical description of nature? And why can universal physical laws describe physical processes when they seem to be an uncoordinated mess? These questions may be regarded as counterparts to the classical philosophical problem: "Why does being exist where there could have been mere nothingness?" This question, criticised as trivial and meaningless by empirical positivists in the 1930s, can be expressed in a new form that is meaningful for empiricists as well: "Why are there mathematically described laws of physics when nature could have existed as uncoordinated chaos?"

The Mysterious Effectiveness of the Language of Mathematics

Mathematical language has been highly effective in describing natural phenomena. In the late seventeenth century, an important controversy arose between Isaac Newton, the author of the Philosophiae naturalis principia mathematica, the work containing the first theoretical exposition of modern physics, and John Flamsteed, the first Astronomer Royal and the founder of the Greenwich Observatory. Newton determined the positions of celestial objects on theoretical presuppositions underlying his principles of gravity. Flamsteed determined the positions of the objects on an empirical basis using the best observational equipment accessible at the time. Finally, after an emotional debate, Flamsteed had to correct his observational results. Mathematical formulae, worked out theoretically, revealed the structure of the physical world in our cosmic neighborhood better than observational evidence. ¹ Three centuries later, Eugene P. Wigner called the use of mathematics on the physical world "the unreasonable effectiveness of mathematics in the natural sciences." ²

Albert Einstein revealed the same "unreasonable effectiveness of mathematics" when, on the basis of field equations in his general theory of relativity, he discovered the expansion of the universe that was confirmed by observation several years later. In 1965, the same effect was illustrated by the discovery of the microwave radiation that originated fifteen billion years ago in the epoch of the big bang. The existence of this radiation had already been predicted in the late 1940s on the basis of mathematical calculations. How to explain that the language of mathematics is not only adequate to describe physical processes but also helps us to discover new phenomena unknown in the past? To understand this astonishing property of our world, let us refer to an analogy closer to our everyday experience. Let us imagine that someone had created a new language as a purely artificial product. Had he or she later discovered that an African tribe spoke this very language, such a coincidence would appear to be an amazing fluke. It would be as improbable as the existence of a tribe reciting fragments of Joyce's Ulysses or communicating in a language created specifically for computers. Such occurrences could not be considered obvious and natural.

Perhaps the people who either do not know computers or are always critical of Joyce would not find anything amazing about such a situation; for them any sequence of English or English-like words would be unintelligible jabber. A similar situation occurs among the people who do not understand mathematics and do not appreciate its role in the physical description of nature. Those who do understand the role of mathematics in science follow Paul C. Davies who, when awarded the Templeton Prize in 1995, expressed the essence of his philosophy by saying, "[i]t is impossible to be a scientist, even an atheist scientist, and not be struck by the awesome beauty, harmony, and ingenuity...