An arm’s reach or the orbit of Mars

An arm’s reach or the orbit of Mars

Exponential growth is easy to understand in theory but almost impossible to comprehend in practice


MOST OF US alive today will live to see something so extraordinary, so monumental, so counterintuitive that it is almost incomprehensible.  Yet, maybe because it is so difficult to get our heads around, there has been no serious public debate about it, no coordinated political action. As a result, most people are left unaware of just why it is that a handful of nerdy-looking trends is set to dominate everyone’s lives and transform our world.

The largely-hidden mechanism behind this inexorable takeover is actually pretty straightforward to illustrate. Imagine you are stretching apart two markers – the further apart they are the greater the complexity of a single computer chip at any given date. The first integrated circuit was manufactured in 1958 so you can start in 1960, just as The Beatles are forming, with your markers 1mm apart (that is about 1/25th of an inch). By 1961 your markers are 2mm apart. By 1962 they are 4mm apart. 1963 it is 8mm. This is all comfortably slow. By 1965 your markers are still only 32mm apart – just over an inch. Acceleration at this rate everyone can comprehend. But it is all about to go counterintuitive.

By 1970, only five years later when The Beatles have just broken up, your markers are already a meter apart (more than a yard). In memory of the Fab Four, if you visualize standing at the entrance of The Cavern in Liverpool where they used to perform and keeping one of the markers beside you, then by 1975 the second marker is on the other side of the street, by 1980 it is thirty seconds’ stroll down the road, by 1990 it is fifteen minutes’ walk away on the outskirts of town. By the Millennium celebrations it will take you about an hour by cab to reach your marker. Ten years later it will take you a few hours on a jet aircraft to reach your second marker because it is already part way across the Atlantic. The prototype chips currently in advanced development indicate that your marker will reach John Lennon’s memorial garden in the Big Apple in a couple of years’ time.

Now see what happens if the complexity of computer chips continues to accelerate at that same rate. In reality, that prediction is far more likely than many forecasters have assumed – but for now just accept it. You will need a virtual spaceship. If the predicted rate of growth continues, then your marker will reach the moon in less than a decade-and-a-half (by 2025). By 2040 you will be way past Mars and entering the asteroid belt.



After the initial prototypes of the 1960s, the figures that everyone quotes for the ‘complexity of a computer chip’ typically relate to the maximum number of transistors that could be built onto the most complex yet still cost-effective commercially available integrated circuit. By this measure, the trend of increasing-complexity has remained steady since the early 1970s, with the transistor count doubling every two years. There are already several billion transistors crammed onto a single chip. If this long-established trend continues, it implies by 2040 slightly more than a thirty-thousand-fold increase on today’s figures, corresponding to approximately 150 trillion transistors on a chip.



That is from New York to Mars in less than thirty years. And yet after the first thirty years you could walk the distance between your markers in a quarter of an hour. And if from 1960 up to 2040 the markers had merely kept progressing at the same rate as they moved in the first year or so, then the distance they would have reached after the full eighty years would still be so small that you could move your finger from one marker to the other – by simply reaching out with one arm.

The difference between an arm’s reach and the orbit of Mars is the difference between ‘linear’ and ‘exponential’ growth. Most progress is linear. The five trends that will dominate our future are all exponential.