Something is killing conventional economics and it’s probably an inside job. Reliance on abstract mathematics and absurd assumptions has brought the discipline into disrepute, even if politics and policy are guided by the ghosts of its teaching.

Nobody was surprised recently to learn that the price of the overdue and over-budget HS2 high-speed rail project could rise by another £30bn. People were surprised to learn, however, that in the cost-benefit analysis used to justify the original project, planners assumed that no passengers work while on a train. That made the times savings on the new line look more valuable than they really were.

But curiosities like that are nothing compared with the epic, conceptual departures from the real world made by the economics mainstream in recent years. Risk models used by the investment bank Goldman Sachs suggested that the financial crisis of 2007 should have been in effect impossible. And have you ever wondered why privatisation continues in the face of repeated failures from care services to railways, and in spite of pledges to rein them in?

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It’s because neoclassical economics has so deeply entrenched the notion that markets are better than all other ways of organising life, that decisions escape rational scrutiny. Academic economists will tell you that their discipline offers a far more complex picture of the world. But, at the policy level, what tilts a spending decision one way or the other is the simple power of the seeming “folk wisdom” that markets are best. It becomes the rule of thumb.

They might look less good if the assumptions on which the equilibrium models that got us here were more widely known. The idea of perfect markets under perfect competition, for example, asks us to believe in a world where everybody knows everything, there are an infinite number of companies, no barriers to setting up a business, where any product can stand in for any other (say, a banana for a tractor) and, crucially, there are no “externalities” (economic speak for “consequences”) from production or consumption.

Facebook Twitter Pinterest ‘[The economist] William Nordhaus came to the conclusion that an “optimal” economic approach would allow global heating of at least 3C – a level that climate science shows would cause catastrophic, irreversible change.’ Photograph: Michelle Mcloughlin/Reuters

All models use a few simplifying assumptions, but those underpinning mainstream economics more often distort and detach from reality. It’s one of the reasons why students have rebelled, forming groups to demand that universities take a more pluralistic approach to teaching economics. Katie Kedward left a banking job in the City for ethical reasons and sought a degree that would make sense of economics. Despairing at the unreality of mainstream courses, she found a rare exception: a master’s in ecological economics at the University of Leeds. The course, though, isn’t even taught in the economics department but the School of Earth and Environment. That’s why new groups are emerging to promote heterodox economics, which draws on the insights of the study of complexity, neuro and behavioural science, ecology, feminism and the core economy of family, mutualism and community.

But there’s an awfully long way to go. Late last year, on the day that the Intergovernmental Panel on Climate Change released its starkest warning yet on the importance of holding global heating below 1.5C, William Nordhaus was awarded economics equivalent of the Nobel prize. Nordhaus is famous for applying conventional economic models to environmental issues. Using his toolkit on climate breakdown, infamously he came to the conclusion that an optimal economic approach would allow warming of at least 3C – the level that climate science shows would cause catastrophic, irreversible change.

For anyone outside economics that might seem bewildering, but the blase disregard of the economy being a wholly owned, and utterly dependent, subsidiary of the biosphere is perfectly symbolic.

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Economics has a reputation for being dismal because it seems to delight in making itself confusing and inaccessible. Real progress, and better decision making, is hard to imagine without demystifying the discipline and breaking the singular grip of old school, neoclassical teaching.

For that reason, my colleague David Boyle and I dared to write a beginners’ guide for the complete non-expert. In it we ask some heretical questions that that could get us expelled from most university economics departments, such as: is the price mechanism so clever, or rising productivity always a good thing? We talk about the trouble with growth, and why working less might be better. Our common starting point is that the economy should serve rather than dominate people, and that it must work within planetary ecological boundaries.

Roasted by heatwaves, this year the world went into ecological overshoot on 29 July, the earliest yet. Unless we begin again with economics, understanding and letting go what has gone wrong, and letting more of the real world in, one day soon everything will have fallen apart and nobody will quite know why. But the answer will be: it was the economy, stupid.

• Andrew Simms is co-author with David Boyle of Economics: A Crash Course, published this week