11 January 2003, 12:34am IST
PRAVEEN B GAWALI
Though insentient, numbers perform important functions in our lives. Numbers do not have a physical entity of their own. They are just an abstraction. Notwithstanding, Galileo declared that nature can be read only through mathematics. Sadly, not many are comfortable with this language. An interesting story underlines the mundane-ness of our discomfort with numbers. The story in question involves the 18th century philosopher Denis Diderot and the Swiss mathematician Leonhard Euler. In response to Diderot's well- argued expositions on atheism, Euler placed before him an algebraic equation and announced that that parti- cular equation proved the existence of God. The equation put Diderot on the defensive and embarrassed, he fumbled with his scho- larly arguments. Because he did not understand the equation, he was unable to counteract it. Diderot lost the point even without a contest although what Euler did bordered on rubbish. There is something surreally natural to numbers that prompted people like Leopold Kronecker to announce, "God made the natural numbers; all else is the work of man". Kronecker is not the only one to have attached religious significance to numbers. Pythagoras discovered harmony in the pleasing sounds created by successive notes produced by strings that had lengths in simple ratios of one to the other. This 'harmonious' discovery led Pythagoras and his followers to deify natural numbers. They believed that the entire universe could be understood in terms of natural numbers and their ratios. According to them, the moving planets demonstrated the divine nature of these natural numbers by the play of 'the music of the spheres'. Some numbers even took on human qualities, and came to be recognised as 'masculine', 'feminine' and 'amicable'. The knowledge of the relationship between the ratios of natural numbers and the musical scale emboldened them to establish a belief system wherein they held the natural numbers themselves to be God. Pythagoras believed in the immortality of the soul, that there is a relationship between humans and animals; that the human soul can take birth in an animal. If humans led a disciplined life, it would prevent the soul from taking 'animal birth'. Pythagoras was the first to prove the theorem that says the sum of the squares of the shorter two sides of a right triangle is equal to the square of the hypotenuse. The Pythagoreans' belief — that everything was made up of natural numbers and the ratios of these numbers — was shaken by the proof which told them that there was no natural number whose square was two. The proof proved their religious beliefs to be miserably wrong. Religion based on 'numbers' is a verita- ble illusion. Investing dogmatic faith into some concept, which appears to be an inviolable 'truth', at a particular given time, may turn out to be a deviation. Pythagoreans put natural numbers on a pedestal and revered them as God. But, the fact that there exist other numbers in addition to the natural numbers unnerved them. The Pythagoreans put Hippassus to death when he dared to disprove the Pythagoreans' faith and belief in the universality of natural numbers. Truth is a derivative of the past and a product of the current 'time'. There is also a hidden truth, yet to be discovered, tucked into the womb of the future. The past viewed through whichever knowledge prism, seen from the vantage point of today, always reveals 'truths' gone awfully wrong. The future, because it keeps evolving and changing, always turns out right. On the other hand, the past has an incorrigibly static quality to it. When nature has never remained static, why should the most evolved species of the universe stagnate in the past?
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