The discrete paradigm

Sharada, the six-year-old, was thrilled when I gave her a gift, a box of candies, after she finished her homework. "Thatha, can I share this with Babu," she inquired. "Of course," I encouraged.

She sat on the floor, spilled the candies, made two equal piles, kept one for herself and one for her friend Babu. She soon found there were five in each and seemed to be mildly disturbed by the discovery. I asked what was worrying her. She said she would like to have a little more than Babu, not much.

I moved one candy from one pile to the other and said, "There you are, take the big one and give Babu the other." She counted the lots again and found six and four, beamed and relaxed for a while, but not for long. Shortly after that, with knitted eyebrows, she was a figure of distraught. "Now, what?" I asked.

"I can’t have so much more than Babu. I just want a little more, that’s all," she added rather meekly. Very fair minded for a kid. Unable to handle her math, I suggested, we shall bring to five each, unwrap one candy, cut a small portion and put it in the other pile. Of course she will have nothing of that as it unsettled the discreteness of the whole sharing business. That in any case did not see the last of Sharada that evening.

As I was preparing to go out in the evening, I saw Sharada by the iron gate looking at the long shade, the gate was casting on the velvety grass.

"Thatha, the shade was there, now it is here. Slowly it does not move in steps." I was stunned. After all Newton broke the centuries old paradigm of discrete thinking, when he noticed on a quiet late English country evening the slow and continuous movement of the moon and the stars. Then he went in and studied the subject close at home, the pendulum in the clock. He goes on and develops Calculus.

How can language, an invention for convenience explain, let alone to a six-year-old, the two great manifestations of nature. What is discrete for years became continuum when mind evolved. They became discrete again as in quantum mechanics. There is also the postulate that Radiations behave as continuous waves or quantum, either way as the observer chooses to set his experiment for.

I turn to the following quote by David Berlinski, (A tour of the Calculus) 'Words and numbers are, like human beings who employ them, isolated and discrete; but the slow and measured movement of the stars across the night sky, rising and setting of the sun, … the thoughts and emotions that arise at the far end of consciousness, lingers for moments or for months, and like barges moving on some sullen river, silently disappear — these are, all of them, continuous and smoothly flowing processes. Their parts are inseparable. How can language account for what is not discrete, and numbers for what is not divisible?'