
Homepage / Publications & Opinion / Silicon.com Peter Cochrane's Uncommon Sense: Exponential growth  so misunderstood Yet our leaders are always talking about it... The economist Adam Smith was wrong. He was just too linear in his thinking. So says Peter Cochrane in his latest column, where he explodes the myths surrounding exponential growth... There are two commonly misunderstood expressions used by the media and politicians that mildly amuse me for their inaccuracy. The first is quantum leap  which 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 (what you pay on a loan or overdraft) I find that the vast majority still don't understand. They have a mortgage and a bank account but they don't really don't understand compound interest and therefore, exponential functions. The function ex (which = EXP(x) in computer speak) is so delightfully simple and so very deceptive! Here is a simple explanation. Suppose you to work for me on the following basis: on day one I pay you $2, on day two I pay you $4, on day three $8, day four $16 and so on. How much will I pay you on the tenth day? The answer is $1,024. This is counter intuitive outcome, even more so on the twentieth day I will pay you slightly over $1m and the thirtieth day slightly over $1bn. This is exponential growth. Lets look at it another way  if you were to invest $1 at 10 per cent interest compounded for 10 years, you would receive $2.59, but if it were $1 for ten years at 100 percent, then you receive $1,024. An old conundrum says a king is asked to pay for work by placing a grain of wheat on a square of a chessboard and then on day two two grains, on the third four grains and so on. By the last square of the chess board the grains of wheat more than fill a throne room. This, by the way, is how a viral infection rapidly becomes an epidemic  sneezing or skin contact is an exponential spreading mechanism! And so is a computer virus that can now span the planet in much less than a day via the internet. 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 by the advancing wave and you will die. Similarly, driving a car at great speed sees our perception framework distorted and we become unbelievably tolerant and confident on an open road. 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. Moore's Law is the most celebrated exponential law in the IT industry. It accurately predicted that integrated circuit density, and hence computer power, would double in power every 1218 months from 1960 onwards. But there are other, similar laws for optical fibre bandwidth, network capacity and so on. In fact it is difficult to find anything in IT that isn't governed by exponential growth. 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 not today, 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 nonlinear channels involving fixed and mobile networks, computers and people networks  eyes and ears. How different to 100 years ago  and how dangerous when planners, politicians, decision makers and leaders do not understand the most fundamental of functions that now governs the growth of trade, communication, wealth and risk. This column was typed on an Apple G4 Laptop and sent from a car on the M25 Motorway heading to Heathrow Terminal 4 very early on a Sunday morning  but I am not driving! 