International trade secretary Liam Fox has shown us what happens when one of the leaders of the revolution spends three subsequent years looking at paperwork. The fantasy lives – just – but must now inhabit a lever-arch file outlining everything the UK still doesn’t understand about global trade.

In recent weeks, dyed-in-the-wool Brexiter Fox has warned against no deal, explained why Boris Johnson cannot use Gatt article 24 to unilaterally implement a deal with the EU, and pointed out that we cannot negotiate a new package with the US before Brexit has taken place. The reason for his newfound pragmatism was perhaps revealed by Monday’s announcement that the government is seeking to train 12 new professional trade negotiators, and Fox’s declaration that trade should be taught on the national curriculum. So there we have it: the government has discovered that trade depends on rules, and almost nobody in Britain knows what they are.

The government has discovered that trade depends on rules, and almost nobody in Britain knows what they are

The UK’s ongoing lack of preparedness for Brexit is not news. The revelation that we are only now training new negotiators merely highlights the slapdash incompetence the government has been showcasing since the Brexit vote. But the demand for better trade education was revealing, because it illuminates one of the key problems with Brexit: it depends not on dreams but facts.

What, then, should we add to this new curriculum? The first lesson is that trade is not about taking back control. Indeed, the opposite is true. Unless you wish to force your goods and services on others, modern trade arrangements revolve around common laws and conventions. That champion of free-trade Brexiters, the World Trade Organization, is (unlike the EU) an unelected body that sets the basic rules of everyday commerce. Countries must, for example, set limits on tariffs and share quotas. Because discrimination is forbidden, the UK will have to apply its tariffs to all countries equally. These rules may be described as pooling sovereignty. Certainly, countries are free to organise trade deals in which they can eliminate tariffs altogether. These also require a legal agreement to prevent one country flouting shared rules or acting uncompetitively or unfairly, and this also limits sovereignty. If one member later “reasserts” it, by pulling out of the agreement, it must face negative economic consequences.

The second lesson is gravity. The flow of trade depends on both size and distance. The US and EU have similar GDPs, but we trade more with the EU because it is nearer. Indeed, our trade with individual EU countries is significantly greater than with many of the world’s largest economies. Our volume of trade with Ireland is more than 200% greater than that with India – 110% more with Germany than China.

The third lesson is that trade is about power, but the power you have now, not the one you remember. The EU as a bloc negotiates successful trade deals because it has the clout of more than 500 million consumers behind it and can afford to walk away from a deal rather than make overly painful compromises. Within the EU, power and resources also matter. Germany exports more to India, South Africa and Australia than we do, despite our Commonwealth and language ties, because it is larger, richer and produces more things that people want to buy – not because it imagines itself to be great or focuses on a mythologised history.

The fourth lesson is that trade is about reciprocity, and listening to the concerns of your partners. If you show a willingness to compromise on things you want, engage in good faith and allow others to assert their interests, you may be able to agree deals more quickly. If, however, you simply arrive with a checklist (a single market in goods, for instance) without taking into account the other partner’s wishes (upholding the basic principles of the EU and the Good Friday agreement, say), you may get stuck.

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Perhaps the most important lesson about trade is that there is more to life than trade. The UK’s most basic error was to assume that its status and statistics would speak for themselves. But in the end it didn’t matter that Britain was an important country, or that the EU had a trade surplus it wanted to preserve: Brussels still wasn’t going to give us the benefits of EU membership without any of its obligations. The fabled German car manufacturers didn’t, in the end, bail us out, because the EU is about more than mercantilism, commerce or a balance sheet. It is about the political cohesion of a group of nations which depends on shared rules, solidarity and trust. The British government thought it could trump the EU’s laws and values with the promise of 65 million customers, and it was wrong.

Fox’s idea about education illuminates the truth: the Brexiters were never interested in trade, but the idea of trade. Our future will not depend on the imagination, but on the cold, unforgiving realities of power, leverage and skill. It is right that schoolchildren should learn about it – so should our next prime minister. We may ultimately conclude that if our politicians had paid more attention to trade in the years before the referendum, we would never have conceived of Brexit in the first place.

• Jonathan Lis is deputy director of the thinktank British Influence