{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

Who was he to doubt the work of a leading professional which had been accepted by the psychological elite? What gave him the right to suggest that the emperor had gone naturist?

"The answer," says Brown when I meet him in a north London cafe, "is because that's how it always happens. Look at whistleblower culture. If you want to be a whistleblower you have to be prepared to lose your job. I'm able to do what I'm doing here because I'm nobody. I don't have to keep any academics happy. I don't have to think about the possible consequences of my actions for people I might admire personally who may have based their work on this and they end up looking silly. There are 160,000 psychologists in America and they've got mortgages. I've got the necessary degree of total independence."

Armed with that independence, he went away and looked at the maths that underpinned Fredrickson and Losada's ratio. Complex or non-linear dynamics are not easy for an untrained mathematician to understand, much less work out. Losada, who claimed expertise in non-linear dynamics, was working as a business consultant and making mathematical models of business team behaviour when he first met Fredrickson.

"Not many psychologists are very good at maths," says Brown. "Not many psychologists are even good at the maths and statistics you have to do as a psychologist. Typically you'll have a couple of people in the department who understand it. Most psychologists are not capable of organising a quantitative study. A lot of people can get a PhD in psychology without having those things at their fingertips. And that's the stuff you're meant to know. Losada's maths were of the kind you're not meant to encounter in psychology. The maths you need to understand the Losada system is hard but the maths you need to understand that this cannot possibly be true is relatively straightforward."

Brown had studied maths to A-level and then took a degree in engineering and computer science at Cambridge. "But I actually gave up the engineering because the maths was too hard," he says, laughing at the irony. "So I'm really not that good at maths. I can read simple calculus but I can't solve differential equations. But then neither could Losada!"

He went back over Losada's equations and he noticed that if he put in the numbers Fredrickson and Losada had then you could arrive at the appropriate figures. But he realised that it only worked on its own terms. "When you look at the equation, it doesn't contain any data. It's completely self-referential."

Unfortunately, while his grasp of maths was strong enough to see the problem, it wasn't sufficiently firm to be able to mount an academic takedown of Fredrickson's and Losada's work. Yet that was what he wanted to do. Once he knew to his own satisfaction that their research was fundamentally flawed, he was not going to be content to let things pass. So he decided to seek the help of an academic mathematician. Not just any academic mathematician either, but one who had made a name for himself by puncturing the bogus use of maths and science in another discipline.

Losada had derived his mathematical model from a system of differential equations known as the Lorenz equations, after Edward Lorenz, a pioneer of chaos theory.

Sokal did a little research and was amazed at the standing the Fredrickson and Losada paper enjoyed. "This theory is not just big in academia, there's a whole industry of coaching and it intersects with business and business schools. There's a lot of money in it."

Then there was the lucrative lecture circuit. Both Seligman and Fredrickson are hired speakers. One website lists Seligman's booking fee at between $30,000 and $50,000 an engagement. In this new science of happiness, it seemed that all the leading proponents were happy.

But then Nick Brown started to ask questions.