Good Approximations

Abstract

Every measurement, whether the naked result of an impression on the human eye or ear, or the product of a sophisticated measuring instrument, is merely an approximation. We can know, and our computing machines can know, only a finite number of decimal places in the numerical representation of a distance or a weight or a force or a temperature.¹ The eye has limited resolving power, the ear a limited frequency response, and comparable limitations hold for all other instruments whether biological or “mechanical.”These limitations are not merely due to poor “manufacturing technique”; as Heisenberg’s Uncertainty Principle tells us, they are inherent in the essence of things. Life and the universe depend on approximations. And so, too, does technology.