Listening to debates pre-Brexit, there were familiar cries from the British public to politicians of "we need more information, a more informed debate", implying "tell us more accurately how our vote will play out, you must know!" but then when trends or figures were presented "you can't believe any expert".

Unpacking these sentiments is enlightening. Effectively the clamour was for a detailed model and computation of what leaving the EU versus staying in might mean, particularly in practical financial ways like affordability of housing.

The fact is, no-one knows, even approximately. In practice you can't predict it, not with today's methodologies. The ecosystem is too complex, with huge numbers of feedback loops and linked components, many of which even individually are almost unknowable.

Sometimes the error bars swamp the value. In the end there's too much variability to say anything much quantitative. You can surmise things like "there'll be a shock if we exit", but not its detailed consequence or even whether saying this is perturbing the consequence eg. is self-fulfilling.

What's amazing is that I'm having to say all this. I wouldn't have had to 100 years ago: there wouldn't have been any concept that such predictions could be computable. But in recent times, real-world maths and computation have in many ways been so successful for so many predictions that societally there's an assumption we can "compute anything" or always quantitatively predict with some accuracy how decisions will play out in whatever field.

"A key part of using any powerful tool—computation included—is knowing when it works and when it doesn't."

Don't get me wrong. I'm a keen advocate for computing answers, driving decision-making and optimising actions with computation; I spend much of my working life driving more use of computation; I think we're only at the start of where it can take us in increasingly broad swaths of life. Indeed, since the mid-twentieth century, I'd argue that the rise of mechanised computation continues to be the biggest underlying driver of human progress—particularly through engineering and hard science.

But a key part of using any powerful tool—computation included—is knowing when it works and when it doesn't. With no effective, general education in computational thinking, most people can easily be mislead, and they are.

This educational failure is a major part of what's caused "post-truth". Years of apparently precise, prominent predictions with at best over-stated accuracy or worse, that are just wrong. "Experts" push numbers to assume an importance beyond their ability to inform to the point where a sizeable fraction of our population, given no computational education to fall back on, no longer believes any logic, any number, any expert.

I remember a blind "belief in computation" starting to take hold in the 1980s crystallised in particular for me through a conversation with a friend at school. Some early global climate predictions were starting and I was sceptical that they were right, whether over or under estimating the effects. He argued that if the predictions "made a good point" and garnered attention, it was important that scientists en masse were simplistically presenting them whether or not they really could justify their veracity. I argued that in the end this would backfire: if any of the widely accepted expert predictions failed, science, computation and logic would suffer huge rejection. Perhaps to needle my (Catholic) friend, I pointed to his church's insistence that it knew the sun orbited the earth in a perfect circle—and the damage this had done both in actions taken (eg. against scientists) and to its own credibility.

" 'Experts' push numbers to assume an importance...
...beyond their ability to inform."

The promulgators of predictions—politicians, campaigners and experts—certainly bear responsibility for post-truth. They get more publicity for being definitive on a "big issue" with "evidence" even if they're massively overstating the claim or its precision and damaging long-term credibility of their professions. Instead they need to be prepared to give real answers like "we don't know" or "the only prediction we know how to make assumes xxx, which is probably wrong".

But a major responsibility also lays with the public and in particular their mainstream education. They need experience and developed instinct in questioning models, science, computation. They need measured scepticism that comes of experience with real, messy situations, today's computational tools, manifested by ready-to-use questioning to help them pick apart expert statements. Things like "What are your assumptions?", "Why do you believe this is the basis?", "Have you forgotten any effects?", "What happens if there's a small error in your opening assumption?" and so forth. They need to be versed in dangerous scenarios to look out for and take special care over. For example, often I am more likely to believe localised, short-term predictions than global long-term ones because the likelihood of massive errors in the model tend to grow very sharply with time and complexity; there's often no control scenario either; and it takes too long to see effects of the prediction. That's a small example of experience I've developed.

Why isn't STEM and specifically maths education—as the only mainstream computation subject—teaching these vital topics? They need to be central but aren't. They aren't because they can't be with subject's overwhelming focus on hand-calculating.

Look at today's maths curricula around the world and you'll find scant coverage of topics like these, and none with needed modern computer-powered analysis of messy scenarios that give real experience.

Therefore I think a crucial step in the long journey to fixing the post-truth problem is laying out what we want from mainstream maths—why we've developed our new "outcomes" list as part of our computerbasedmath.org project. Here's one snippet...

Only when our populations can't so easily be misled by maths will they re-engage with its power to persuade. This is vital individually, and societally, or we may start down a path of mysticism, a new era of Unenlightenment.

Post-truth: shocking indictment of today's maths education