This is a typical school maths question.
  1. Two buses leave the same bus station at noon. One travels west at a constant 30mph, the other travels north at a constant 40mph. What time will it be when the buses are 100 miles apart?

This is a typical real life problem.

  1. I need to catch a plane leaving Gatwick at 8am. How should I get there (by train, taxi or car) and at what time should I leave the house?

The slightly odd thing about the human mind is that many people would find the first question difficult, but find the second question easy. Yet the second question is computationally much more complex.

The fact that most of us find the second problem easy and the first problem difficult says much more about the evolution of our brains than it says about the difficulty of the problem. The reason is that the first question is tailor-made for computation: it is what you might call a “narrow context problem”. It assumes an artificially simplified, regularised world (where buses miraculously travel at a constant speed); it involves very few variables, all of which are numerically expressible, and allows for no ambiguity: it has one single, incontrovertibly correct answer (2pm).

The second question - how to get to Gatwick - is what you might call a “wide context” problem. It allows for vagueness and multiple right answers, and doesn’t demand absolute adherence to any precise rules. There is no rigorous formula governing the solution, and it allows scope for all kinds of possible “right-ish” answers. All kinds of information can be taken into account in coming up with an answer. These are the problems we seem instinctively better equipped to solve, but which computers find hard.

If I were to delve into my unconscious and uncover some of the variables at play in my brain when I next have to get to the airport, it might include “Is it raining?” “How much luggage do I have?” “How long am I going to be away for?” “What is the average time via the M25 versus taking the A25?” What is the variance of journey time on the M25 versus the A25?” and “Does my flight leave from the North or South Terminal?”

If you think of getting to Gatwick as a narrow problem the way your satnav does - a question only of getting to the airport as quickly as possible - you may think some of these factors are irrelevant. But all of them are important in real life. If I am going away for two weeks rather than one night, it affects the car-park I can use and the relative cost of going by train or car or taxi. The variance of travel time on the M25 matters - I usually use the A25 to get to the airport and the M25 to get home: this is because, although the M25 is faster on average, on it might be so gridlocked that I miss my flight. Heavy luggage makes the train less appealing, especially if you are using the more distant North Terminal.

What’s interesting is that we find solving complex problems such as this so easy. This suggests that our brains have evolved to answer wide-context problems because most problems we faced historically were of this type. Blurry “pretty good” decision-making has simply proven more useful in the ancestral environment than precise logic. (If narrow rationality had been valuable in evolutionary terms, accountants would be really sexy).

Now I accept that the need to solve “narrow context” problems is much greater today than it was a million years ago: there’s no denying the contribution that rational approaches have made to our lives. But I would also contend that our environment has not changed all that much: most big human problems are still “wide context” problems. Most business decisions are, certainly. The problems occur when people try to solve “wide” problems using “narrow” means - “treating clouds as though they were clocks” in Karl Popper’s unforgettable phrase. Keynes once said “It is better to be vaguely right than precisely wrong.” Evolution seems to be on Keynes’s side.

The risk with the growing use of cheap computational power is that it encourages us to pretend that wide problems are narrow: to take a simple, mathematically expressible part of a complicated question, solve it to a high degree of mathematical precision, and then assume you have solved the whole problem. So my Satnav answers a narrow question brilliantly “How long will it take to drive to Gatwick?” But the wider questions “How should I get there and when should I set off?” still remain.

In the same way I can optimise my digital adspend to a huge degree of precision. But this does not necessarily mean that I have contributed anything to the wider marketing questions - “why should people trust me enough to buy what I sell?” for instance. We fetishise precise numerical answers, because they make us look scientific - and we crave the illusion of certainty. But the real genius of humanity lies in being vaguely right.

This article first appeared in the Leader – the journal of the Marketing Society