Thesis #3

Technological progress is in not linear, but exponential or combinatorial. That’s why we find it hard to cope with it

We humans are good at dealing with linear change — where things evolve in a fairly orderly way. Traffic increases by 3% a year, base salaries increment by a fixed percentage (if we’re lucky), and so on. Linear change means just that — you can graph it as a straight line that goes up or down over time. We like linear change because it gives us a basis on which we can plan.

And some technological change is like that. This year’s model of the Ford Focus or the BMW 5-series has a few new things that weren’t in last year’s model. Maybe it’s bluetooth integration with your smartphone, two-zone air-conditioning, more sophisticated cruise-control. But basically it’s still the same car.

With digital technology, however, change doesn’t proceed at an orderly, linear rate. For example, many years ago Gordon Moore, the co-founder of Intel, a big chip manufacturer, noticed that the number of transistors that could be fitted onto a silicon chip was doubling every 18 months. Since processing power is proportional to the density of transistors, that meant that the processing power of computers doubled every 18-24 months. This regularity became known as Moore’s Law.

For most people this doesn’t sound like a big deal. But it is, because doubling isn’t at all like linear growth.

The ancient fable about the man who invented the game of chess illustrates that. His friend was so impressed that he brought him to the Emperor to explain his wonderful invention to him. The Emperor was so impressed that he offered the inventor any reward that he desired. The inventor opened the chess board and asked that he be given a grain of rice on the first square, two grains on the second, four on the third, and so on. The Emperor, puzzled, readily agreed: it seemed such a modest request. What he didn’t realise was that by the time the 64th and final square on the chessboard was reached, the amount of rice required would be as big as Mount Everest.

Moores’s Law applies to just one component in a computer — the processor. Most of the digital technologies we use today use dozens of different technologies, some of which will also have been evolving at non-linear rates. That means that the rate at which the entire system changes will be a multiplicand of the individual rates of change. This produces what mathematicians call a “combinatorial explosion”. Which is why one of the most profound thinkers about this — the economist W. Brian Arthur — calls it “combinatorial innovation”.

Further Reading

Moore’s Law:

Combinatorial explosion:

W. Brian Arthur: The Nature of Technology: What it is and how it evolves, Penguin, 2010. Amazon UK:

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