March 15, 2010

Dear Colleague:  

     In the beginning God created Heaven and Earth. Whatever it was like in Heaven, on Earth it was chaos. And so God had to introduce order by separating light from darkness and land from sea. When He had done that, He said that “it was good.” This is, of course, from Genesis. It is by now so familiar that God’s accomplishments no longer impress. I am led to wonder, Is there another way to tell about them that can still make us sit up in admiration? The answer is yes. All we need is a different creation story. Try this. In the beginning were random numbers. Of the many that are possible, the most famous is pi. Ahmes, an Egyptian scribe who lived around 1650 BC, was the first to refer to it. Around 200 BC, Archimedes of Syracuse found that pi is somewhere about 3.14. In 1991, two mathematicians, Gregory and David Chudnosvsky, computed pi to more than 2 billion digits, which, if they were lined up, would extend from New York to San Francisco. Today, they would reach China, for a Japanese mathematician has continued the computation to more than1 trillion digits. The pi digits are random, yet sequences of perfect order occur. For example, around the three-hundred-millionth decimal place, the digits go 88888888 in a row, and somewhere in the half-billion mark appears the sequence 123456789 (New Yorker, 2 March, 1992).

     Now, these digits represent chaos to me–not utter chaos, for that would appear to be impossible–but chaos with islands of order in it, like snowflakes in a dark night of random Browning movements. If this be reality, surely it is Godless or the work of a Madman. Think, therefore, how relieved I am to know that, far from being chaotic and senseless, all these trillions of digits “add up” to an object of singular beauty, namely, a circle with a diameter. What this means is that when I now see senseless randomness anywhere, I will say to myself, can there be a figure of elegant simplicity behind it? Of course, I have reversed the order of creation for my own purpose, the accepted one being, first, the circle and the diameter, then, the endless, random decimals. But why not imagine the order in reverse? This is a free country and I have free will, don’t I?

     We human beings are said to be made in the image of God. We too create, and the area in which we create most impressively is, to my mind, music. What is there of sound–beautiful sound--in the universe before we arrived on the scene? Silence reigned everywhere, with not even a squeak when galaxies collided. Noise, true enough, is common on Earth, and it ranges from the whisper of leaves to volcanic explosions, from the twittering of birds to the blood curdling screams of colobus monkeys. But where is the music? Is the sound of a bubbling brook really a match for Beethoven’s Pastoral symphony? Is even a concertina of nature’s sounds a match for the sublime works of Mozart? From chaos and randomness, come order and beauty, and from order and beauty, come an appreciation for mild exhibitions of chaos and randomness. Mozart loved nature, but five minutes before his death, he asked that the chirping canary be removed from his room, for it interfered with his composition of the drum passages in the Requiem.

Best wishes,



All text and essays on this site © Yi-Fu Tuan. Published irregularly. All rights reserved.
Terms of Use, How to Cite.
home Subscribe to Dear Colleague letters Publications and Research Dear Colleague