At least right from the time of Pythagoras in the West, we can see that there is a close connection between God and mathematics. In India, we may have discerned this link much earlier as mathematics grew in the arms of Vedic religion and helped it to calculate auspicious time and the shapes and sizes of the agni kandas ( fire places of the sacrifices) that were believed to be viewed by God with favor. Johanes Kepler thought that God is Geometer par exellence. Galileo has taught us that God has given us two books: book of God’s word and the book of God’s work. Book of God’s work, he said was written in alphabets of numbers, triangles, squares, circles etc. We can trace an interesting anecdote within this tradition of mathematics and the divine. Although, Richard Feynman confessed that he was an atheist, once in conversation with a fellow novelist Herman Wouk, is said to have posed Wouk a pointed question that asked Wouk if he knew Calculus. When Wouk admitted that he lacked the knowledge of calculus, Feynman pithily told him, ‘you better learn it. It is the language that God talks’. There is truth in this Feynman statement. For reasons we cannot explain, our universe is somehow deeply mathematical. May be God made it that way because non-mathematical universes cannot harbor intelligent life that will then pose this question.
Calculus and the Cosmos
Our universe obeys laws of nature that are expressed in the language of differential calculus. We live in a dynamically evolving universe. Therefore, we require calculus, the mathematics of change. Differential calculus assists us to understand the difference between something right now and the same thing an instant latter or the difference between something right here and the same thing infinitesimally close. This means there seems to be an underlying code of the universe that works like an operating system that animates everything from moment to moment and place to place. It is calculus that taps into this blue script and expresses it. It appears that Sir Isaac Newton was the first to come to terms with this secret of nature. He found that the orbits of the planets, the trajectory of the cannon ball, and the rhythms of tides could be best described by differential equations. Today we know them as Newtons laws of motion and gravity. Ever since then, we have found that the same pattern seems to hold everywhere we try our hand to understand the universe. From the ancient describtions of elements of earth, water, fire and air to the latest electron, quarks and blackholes, everything bows before the rule of differential Equations. This is why Feynman is somewhat right. God does speak the language of calculus!
Calculus and the Modern World
Calculus does not just describes our world, it has assisted us to build the world that we inhabit today. The universe runs on calculus and we have also made cellphones, microwaves ovens, computers, radios, televisions, ultrasound, GPS etc., on its basis. Without it, we may have not split the atom, put man on the moon, or unravelled the human genome. Most of us are a mathematical ignoramus and handle all these technological marvels without reflecting on the mathematics that has gone with it to make those marvels possible. It is true that calculus did not produce all of these wonders by itself. It is a tool with other things that humans engaged to build the world that we live in. Thus, for instance, let us take the case of wireless communication that has made our life so easy. It all began with the experimental work of Michael Faraday and Andre-Marie Ampere. Without their careful experimental findings the crucial facts of electric currents and their invisible force fields would remain a terra incognita and consequently, we may not have wireless communication. This suggests experimental physics was necessary and so too calculus. It was in 1860s, when a Scottish mathematical physicist James Clerk Maxwell recasts the experimental findings into a differential equation using calculus. When Maxwell calculated the speed of his electromagnetic field / wave, he predicated that there was another an electromagnetic wave that his equations were unraveling . It was later experimentally proved by Heinrich Hertz in 1887 that light was that electromagnetic wave/ radition. A decade later, Nicola Tesla built a radio communication system and five years later, Gulielemo Marconi transmitted the first wireless message across the Atlantic. This instance sufficiently indicates that calculus lays behind the world that we have built.
The Wonder of the Mathematical Match
Calculus is powerful system of reasoning. It is definitely deeply logical. It helps us build long chains of logical inferences which then give us those that are scientifically revealing. One requires ingenious creativity to listen to the messages that are spoken by the differential equations. Calculus is an imaginary world of symbols and nature is an actual realm of forces, fields and phenomena. Yet there is a wonderful match between the two worlds . Calculus wonderfully mimics nature. The logic of differential calculus can help use one real world truth to generate another through the application of right logical manipulation. This means calculus is not just tool of describtion of our cosmos, it is also a tool of discovery of other facts of the universe that we did not know till then. Thus, calculus does help us to pip into the future and predict the unknown. This is why it is a powerful tool for science and technology. But why should the universe respond to calculus? Maybe we have to ask the Hawking question: ‘who puts the fire in the equation?’ The answer is certainly someone powerful. Most of us know that someone as God. Perhaps even Albert Einstein alluded to it when he said, ‘the eternal mystery of the world is its comprehensibility’. Eugene Winger makes it clearer when he says, ‘ the miracle of appropriateness of the language of mathematics for the formulation of laws of physics is a wonderful gift which we neither deserve nor understand’.
Our universe speaks the language of mathematics. Hence, we have the challenge to dream to decode the hidden harmonies of our universe. The mathematics of change has changed our world and we can join this revolution of change.