As a species, we don’t seem to be very good at dealing with nonlinearity. We cope moderately well with situations and environments that are changing gradually. But sudden, major discontinuities – what some people call “tipping points” – leave us spooked. That’s why we are so perversely relaxed about climate change, for example: things are changing slowly, imperceptibly almost, but so far there hasn’t been the kind of sharp, catastrophic change that would lead us seriously to recalibrate our behaviour and attitudes.

So it is with information technology. We know – indeed, it has become a cliche – that computing power has been doubling at least every two years since records of these things began. We know that the amount of data now generated by our digital existence is expanding annually at an astonishing rate. We know that our capacity to store digital information has been increasing exponentially. And so on. What we apparently have not sussed, however, is that these various strands of technological progress are not unconnected. Quite the contrary, and therein lies our problem.

The thinker who has done most to explain the consequences of connectedness is a Belfast man named W Brian Arthur, an economist who was the youngest person ever to occupy an endowed chair at Stanford University and who in later years has been associated with the Santa Fe Institute, one of the world’s leading interdisciplinary research institutes. In 2009, he published a remarkable book, The Nature of Technology, in which he formulated a coherent theory of what technology is, how it evolves and how it spurs innovation and industry. Technology, he argued, “builds itself organically from itself” in ways that resemble chemistry or even organic life. And implicit in Arthur’s conception of technology is the idea that innovation is not linear, but what mathematicians call “combinatorial”, ie one driven by a whole bunch of things. And the significant point about combinatorial innovation is that it brings about radical discontinuities that nobody could have anticipated.

In recent years, we’ve begun to see the results of this in information technology. The most dramatic case is probably the self-driving car, a development that most of us failed to predict and which was made possible by the sudden conjunction of a whole lot of different technologies. These include: the near-infinite computing power provided by Moore’s law; precise digital mapping; GPS; developments in laser and infrared sensor technology; and machine-learning algorithms plus the availability of massive data-sets on which to train them. Put these together using the kind of skilled engineering resources possessed by a company such as Google and you get the self-driving car.

The implications of this vehicle stretch far beyond the future of the automobile industry or even the future of transport. What it signals is that vast swaths of human activity – and employment – which were hitherto regarded as beyond the reach of “intelligent” machines may now be susceptible to automation. So we need to revise our assumptions about the future of work in the light of combinatorial innovation.

Last September, Dr Carl Benedikt Frey and Michael Osborne, two researchers at the Martin School in Oxford, published the results of a major study of the susceptibility of jobs to this new kind of automation. Their report, The Future of Employment: How Susceptible Are Jobs to Computerisation?, makes for a pretty sobering read. Frey and Osborne used machine-learning techniques to estimate the probability of computerisation for 702 detailed occupations, based on US government classifications of those occupations. Their conclusion? About 47% of total US employment is at risk from technologies now operational in laboratories and in the field.

There will be lots of technical argument about the methodology and the algorithms used in the Oxford study, but there’s little doubt that the main thrust of the research is accurate: lots of non-routine, cognitive, white-collar as well as blue-collar jobs are going to be eliminated in the next two decades and we need to be planning for that contingency now.

We won’t, of course, for two reasons. The first is that our politicians pay no attention to anything with a time-horizon longer than the five-year electoral cycle. The second is our innate inability to handle nonlinear change. “We’ve always been able to absorb mechanisation and automation in the past” will be the response to the challenge of the technology. “Automation has always created more jobs than it destroyed.” And so on.

All of which was true in the past, when innovation was incremental and society had time to absorb and respond to the shock of the new. Combinatorial innovation is a different kettle of fish, because it feeds on itself and grows exponentially. Given that we’re bound to lose this race against the machine, isn’t it time we began thinking of how we might harness it to improve the quality of our lives, rather than merely enrich the corporations that own it?