Many of the foundation principles of mathematics are not well known among the general public. A case in point is "exponential growth."

An illustration of the principle is this problem: I give you a penny today, tomorrow I give you twice as many, two pennies. On the third day I give you four pennies, the next day eight pennies, and so on, doubling each day. How much will I be giving you on the 30th day? The answer is just short of $11 million.

An icon is a symbol to which we give meaning. Our letters and numbers are icons that probably developed from writing with a rock on cave walls. In the digital world, an icon in its simplest form is represented by a graph paper-like grid of squares in which each square may be white or black. It's called a monochrome bitmap.

The problem is that the number of possible patterns in such a grid exhibits exponential growth. It's 2 (white or black) to the power of the number of squares in the grid. Digital artist John F. Simon Jr. explores this in his "Every Icon" Java applet. He starts with a 32 x 32 grid and runs through each possible pattern at the rate of 100 per second (on the average PC.)

The entire exercise will take, get this, trillions of years! During one of those .01 second intervals, the letter A in the font Bookman Swash Italic will certainly flash across the screen. I hope I don't blink and miss it. ;-)

Favorites: Law of Diminishing Returns * Patently Absurd * Sir Arthur C. Clarke * W. Daniel Hillis * Claude E. Shannon -2 * The New York Times * The Buckminster Fuller Institute * Chautauqua * LuLu Press * Dan Bricklin * William Dunk