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Someone once asked Albert Einstein what he considered mankind’s most powerful discovery. Without hesitation he replied, “Compound interest.” The world’s numerati have long been fascinated by the awesome power of geometrical growth, and to prosper in the economy of the future, or what I call the exponential economy, today’s leaders must go beyond simple fascination and embrace the extraordinary possibilities that exponential growth portends.

The distinction between linear growth and exponential growth is not merely a matter of degrees. It can literally be the difference between life and death, as the following story demonstrates.

According to legend, the emperor of China, after being presented with the game of chess, was so impressed with it that he offered the inventor–a seemingly humble man–a gift of his choosing. The inventor made a request that on the face of it seemed innocent enough. He requested that he be granted a single grain of rice on the first square of the chessboard, two on the second, four on the third, and so on until all the board’s squares were accounted for. The emperor glanced at the board, noted it had only sixty-four squares, and readily granted the man his request.

The story abruptly ends with the emperor severing the inventor’s head after only the thirty-second square. This is because, although only halfway through the deal, the emperor was already committed to providing the inventor the equivalent of forty acres worth of rice. Had he lived up to the terms of the agreement, the emperor would have been put in the untenable position of having to supply 18 million trillion grains of rice. To appreciate this predicament it helps to understand that it would take an area approximately twice the size of the earth, including all of the oceans, to produce that much rice.

You Ain’t Seen Nothing Yet!

Like most fables, the story holds a powerful and valuable lesson and it is one that is especially relevant today: If you think change is happening fast today, you haven’t seen anything yet. Consider just the first of many such real-world equivalents of exponential growth: computer transistors. For the past forty years the number of transistors that could be placed on a computer chip has doubled every eighteen to twenty-four months. This development is widely known as Moore’s law and is named in honor of Gordon Moore, the former CEO of Intel, who in 1965 accurately predicted this progression.

For years so-called experts have been predicting the imminent demise of Moore’s law. Undeterred by such prophecies, talented engineers and technology geeks have ignored their warnings, and in 2007 Intel Corporation and others achieved the twenty-ninth iteration of this doubling. In so doing they successfully squeezed mreo than 500 million transistors onto a single chip. This astonishing achievement has dropped the cost of one megahertz of computer processing power from $7,000 in 1970 to just fractions of a penny today.

According to the semiconductor industry, there is still clear sailing for Moore’s law for at least the next ten years. This means, among other things, that by 2018 computers will become a minimum of thirty-two times more powerful than those existing today.

Using the earlier analogy of the chessboard, with regard to the modern transistor era of computers we have not even approached the halfway point in the doubling game. To put it another way, this means that society is but a fraction of the way into the computer revolution. The really big changes are still before us.

The time to begin contemplating what computers thirty-two times more powerful will mean for your business is now. To do this you will need to learn to ”jump the curve.”

Jack Uldrich is a writer, futurist, public speaker and host of jumpthecurve.net. He is the author of seven books, including Jump the Curve and The Next Big Thing is Really Small: How Nanotechnology Will Change the Future of Your Business. He is also a frequenter speaker on future trends, innovation, change management and executive leadership to a variety of businesses, industries and non-profit organizations and associations.