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Preprints & Reprints The Nature of Exponential Growth There are two misunderstood expressions commonly used by the media and politicians that mildly amuse me for their inaccuracy and lack of understanding. The first is quantum leap - it is in fact an infinitesimally small change. The second is exponential growth. For the past three years I have been asking audiences of business leaders, planners, educators and politicians if they understand what an exponential function is? In an audience of 500 people I generally get less than 10 people put up their hands and the rest admit that they do not really understand. Surprisingly, when I move on to explain that an exponential function is exactly like compound interest I find that the vast majority still don't understand. Yes they have a mortgage and a bank account, but they don't really don't understand exponential functions. I then take audiences down this route. Suppose you to work for me on the following basis. On the first day I pay you $1, on the second I pay you $2, on the third $4, on fourth day $8 and so on. How much will I pay you on the tenth day? And the answer is $1,024. This is counter intuitive outcome, and even more so that on twentieth day I will pay you slightly over $1M, and the thirtieth day slightly over $1Bn. This is exponential growth. Let's put it another way - if you were to invest $1 at 10% interest compound for ten years, you would received $2.59, but if it were $1 for ten years at 100%, then you receive $1024. A old conundrum says a king is asked to pay for work by placing 1 grain of wheat on a square of a chessboard and then on day two - 2 gains, on the third - 4 grains and so on, by the last square of the chess board the grains of wheat more than fill a throne room. Probably the most frightening exponential experiences would be to sit on a beach and notice a wave on the horizon, but by the time you have realise it is a tsunami (a tidal wave) it is too late to run. You will be swallowed up and you will die. Similarly driving a car at great speed sees out perception framework distorted and we become unbelievably tolerant and confident on an open road, and only when we pull onto the off ramp do we suddenly perceive we are travelling extremely fast. Technology is the same. It may appear to be insignificant and on the horizon, but by the time it is perceived as a threat it is too late. Adam Smith was wrong in his own time and he is even more in error today. In his economic model of the universe there is a finite source of material with limited production, routes to market, finance and communication. This led to the linear channel model of economics with a finite population of limited appetite, expectation, and money. This was a model that worked well when the world was a slow moving place. But it is now apparent that in the new economy the source of raw materials is unlimited in term of bits, production, routes to market, finance and communication and there is no limit to what customers will purchase and use or expect and communicate. All are now linked by highly non-linear channels involving fixed and mobile networks, computers, people networks - eyes and ears. How different to 100 years ago - and how dangerous when planners, politicians, decision makers and leaders do not understand! Word Count = 593 |