* Binary thinking — right for computers, wrong for the real world

Conrad Wolfram is chief executive of the Wolfram Group Europe. Jon McLoone co-wrote this article

George Boole was born 200 years ago — and whether you celebrate or lament the mathematician’s life de­pends on your point of view. Yes, he made a profound contribution to today’s technological society; but one can also argue that he helped to entrench a damaging way of thinking that permeates society.

One of his lasting contributions came in his 1854 book, An Investigation of the Laws of Thought, introducing what we now know as the Boolean algebra crucial to most computers. This applied the systematic language of algebra to the field of logic — a unification of two disparate fields into something much more powerful. It centres on the simple idea of statements that are true or false.

There is an appealing simplicity about true versus false, and it is this characteristic that makes Boolean algebra so useful for computer engineers, who can work in “on” and “off” rather than exact voltages with all their variability. Boole’s logic predicts what happens for each of these binary states.

What is so unexpected is that “true”, “false” and a few simple logical operations such as “and”, “or” and “not” can be combined to make an equation that can add, multiply, compare, remember and much more. Indeed 80 years later Alan Turing — the British mathematician who developed the first electronic computer — would prove you needed only these simple operations to compute anything (if it was at all computable). From the great simplicity of base logic, we have built the most complex of machines.

However, this same attractive simplification is commonly behind poor decisions in other fields. We should not really blame Boole. Human nature has always tried to reduce the world to binary states — good and evil, friend or foe. But Boole gave strength to such thinking at a time when seemingly exact laws of physics promised to make the universe simple and predictable.

Politicians argue their policies are the “right thing to do”, that their opponents have the “wrong” ideas. We worry about which foods are “good” or “bad”; lawyers demand yes or no answers. Yet few situations are black or white. Medicines do “good” and “harm” simultaneously; wars do not just involve “good guys” and “bad guys”; political decisions are often less about what to do than how to do it.

The problem with binary thinking is that it leads to binary decision-making. We are drawn into reductive “if this, then that” reasoning. The UK’s In or Out debate on EU membership will leave little room for creative ways forward.

Perhaps the fight-or-flight approach to decision-making served humanity well in our evolutionary past but leaves us ill equipped to handle today’s multidimensional problems without the tempting reduction to binary versions.

Paradoxically, Boole’s legacy also gives us the tools to escape our human limitations through the automated computation of rising tides of data. But to use the tools well we also need to adjust our binary mind set.

One focus for change should be the “key targets” culture that pervades organisations. This reduces multidimensional data to the “true or false” test of whether a single arbitrary value has been reached.

Stripping out complexity makes it easier to direct people to a common goal. But this in itself creates problems. Hitting a waiting time target in the accident and emergency department may prove detrimental to quality of care, staff retention or funding preventive treatment. Targeting carbon reduction in cars has arguably resulted in more nitrogen oxide pollution from the switch to diesel vehicles, not to mention opportunities for cheating when incentives are attached to a single measure.

An alternative is a world of agile metrics. We can hold big data on a situation — but instead of those responsible for originating the data pre-computing the metrics, decision makers can, with agility, invent their own measures.

So how can we change our thinking? Maths education is pivotal. Rather than use modern computing to allow open-ended, complex problem-solving it in­sists on reducing complexity to the point that all problems can be solved with pencil and paper to yield an answer that is right or wrong. The real world is not like that. We need a curriculum that accepts practical problems do not necessarily have a single correct answer. Just as Boole combined maths and logic, we need to combine the power of computer-based maths with our natural intuition for a nuanced world, a project that I am deeply involved in.

Ultimately, is Boole the hero or villain of this story? No. Something in between.