Moore's Law: it is one of the most important drivers of innovation, but sometimes you need to sit back to fully appreciate it.

Maybe it is human nature. Most of us get the idea behind exponential growth. Put a grain of rice on the top left-hand square of a chess board, put two on the next square, four on the next, then eight and so on. By the end of the first row you have 128 grains. By the end of the second, you have around 32,000. And by the last square of the board you have something like 1,000 trillion grains. Many times more than global output.

So that's the idea, not hard to understand. But apply it to the story of progress, but extrapolated forward, and our logic seems to fall away.

Take renewable energy. Its cost is falling at a geometric rate. Yet, in 2010, when the Energy Information Organization projected coal output forward to 2050, it expected an increase in production of around 40 per cent. Those who had spotted how the cost of renewables was falling so rapidly said such projections were wildly too high. Well, in 2013, it revised those projections, this time it expected zero growth. Why such a revision? Because it forgot about the exponential effect. In fact, if the exponential effect can continue to apply to renewables for the next few years, expect coal output to fall and the Energy Information Organization to revise again.

Indeed, changes following an exponential course are more common, they apply to genetic science, battery technology and AI, that is why people keep underestimating the speed of innovation, why AI was able to defeat the world champion of Go or create autonomous cars much faster than people expected.

But the best example of exponential change is Moore's Law, so named after Gordon Moore, co-founder of Intel, who predicted that the number of transistors on an integrated circuit would double every two years.

But what does that really mean? If the average family saloon car had seen its top speed increase at a pace commensurate with Moore's Law since 1965, then today it would travel at the speed of light.

The esteemed economist, Brad De Long had been doing some number crunching. The iPhone X has 256 GB of memory, and 4.3 billion transistors in the A-11 processor.

He looked at the components and compared with what similar components cost in 1957.

It turns out that to build an iPhone X in 1957 would:

  • Have cost 150 trillion of today's dollars: one and a half times today's global annual product.
  • Taken up a hundred-story square building 300 meters high, and 3 kilometers long and wide.
  • And drawn 150 terawatts of power—30 times the world's current generating capacity.
So that's quite a significant change.

But let's forward wind the clock. Many argue that Moore's Law is slowing, but technologies such as quantum computing and super materials such as graphene may give it a new lease of life.

Just imagine that in 50 years’ time we all carry around with us a computer that in 2017 would have cost $150 trillion. And be bigger than all the skyscrapers in London, New York and Beijing put together. What would such a marvel be able to do? We have no way of knowing for sure, but suffice to say, we are not remotely prepared for the changes, even that a continuation of Moore's Law for another ten years might bring.