Precision

A certain monk approached Java master Bawan at the end of the evening meal and demanded:

“Is it not so that a computer’s memory is, essentially, a finite sequence of bits?”

“It is certain,” said the master.

“And if all computers in the world were brought together to labor on a task, then still the number of bits would be finite?”

“Even so,” said the master.

“Then we can never hope to calculate perfectly with common irrational numbers such as pi or the square root of two, for they possess an infinite number of digits! Our approximations yield error upon error with each mathematical operation. The exquisite profession of floating-point computation is but a fortress built upon quicksand!”

Master Bawan rose to his feet, stared thoughtfully at the monk’s waist for a moment^*, then hurled his wooden rice bowl hard at the monk’s stomach. The monk doubled up.

“Radius, five centimeters,” said Bawan, indicating the bowl. “What is the circumference?”

“10π,” gasped the monk.

“Astonishing,” said Bawan. “How unthinkably vast your brain must be, to juggle an infinite number of digits and arrive at an exact answer.”