You know that famous bit of chaos theory where a butterfly flutters its wings in the Amazon and a hurricane results in another part of the world? It’s the idea that a minute change in complex interlinking structures can have huge consequences elsewhere.

Well, forget butterflies in the Amazon and replace it with an electronic ankle tag put on a 70-year-old Brazilian bloke who was considered a flight risk, and the whirlwind it has produced thousands of miles north in Washington DC. The 70-year-old is Jair Bolsonaro, the former president of Brazil who is facing prison for his attempts to mount a coup to stop Luiz Inacio Lula da Silva from taking over the reins of power in 2023 after the Brazilian general election.

Donald Trump and Bolsonaro back in the day were kindred spirits: swashbuckling, anti-establishment wrecking balls who were going to make their respective countries great again, even if that meant refusing to accept the results of each country’s respective democratic elections.

Now this won’t be the first sentence written which has the words “Trump” and “chaos” alongside each other. The first six months of his presidency have given endless examples of surreal moments.

Some might argue that the tariffs policy, where import penalties have gone up and down with dizzying rapidity, is a prime example of chaos theory. Just look at what has unfolded this week. Dozens of countries have been punished for failing to reach agreement with the US.

We’ve seen a small section of Amazon rainforest felled for newsprint to explain the tariffs policy. The arguments have become familiar. America has been ripped off by its friends and neighbours for too long, with non-tariff barriers by all and sundry putting the US at a trading disadvantage. Only by the US imposing tariffs will those trade imbalances be corrected. And at Trump’s famous (or maybe that should be infamous) “liberation day” event in the White House rose garden the size of the tariff to be imposed was in direct correlation with the size of the trade deficit. It was a blunt instrument and terribly calculated, but you could see the theory.

So what has this to do with Jair Bolsonaro? Well, President Trump has now imposed Brazil with crippling 50 per cent tariffs on all goods exported to the US that will remain in place unless and until the charges against Bolsonaro are dropped.

But hang on, I hear you say, aren’t tariffs imposed depending on size of the trade deficit (and between Brazil and the US there is more or less no surplus or deficit on either side)? And what the hell business is it of Donald Trump to interfere in the judicial independence of another country? Isn’t this the independent supreme court in Brasilia going about its work – wheels of justice and all that?

Yes, I grant you, these are good questions. But this is becoming the preferred weapon of an authoritarian president: impose blunt-force trauma by thwacking over the head with devastating financial penalties if you don’t do what I want.

It’s not just Brazil. Canada too is now facing increased tariffs from 25 up to 35 per cent on certain goods. Why? Because it has announced that – like the UK – it will recognise Palestine if certain conditions aren’t met by the Israeli government. If your next question is “why isn’t he threatening the same to us seeing as we are in pretty much the same boat as Mark Carney’s government in Ottawa?” then all I can offer you is a shrug emoji.

The former US president, Theodore Roosevelt, used to talk about the ‘bully pulpit’ enjoyed by the inhabitant of 1600 Pennsylvania Avenue. By it he meant a president’s unrivalled ability to shape the national conversation. When you spoke from that pulpit you had the ability to command the nation’s attention and bully your enemies in a way they never could to you.

Trump has taken that to a whole different level. There isn’t much that is under-reported about the doings of Donald Trump in these first six months in the White House, but the shakedown – and it’s hard to know what other word to use – of some of America’s biggest law firms has had scant attention.

On the most spurious grounds Trump threatened to ban them from doing all government work worth billions of dollars unless they agreed to do pro bono work for causes dear to the president’s heart. A couple of firms have agreed to each do $125 million of free work for him. A lawyer I know at one of these firms said it was extortion, pure and simple.

Harvard University is looking to make peace with Trump for $500 million. A number of media companies who had big mergers in the balance have coughed up millions of dollars after the president sued them on the most vexatious grounds. CBS, to their eternal discredit, have axed The Late Show with Stephen Colbert – because Colbert has been a longstanding thorn in Trump’s side, and presumably executives at the parent company, Paramount, thought offering him up as roadkill would grease the wheels of their proposed multi-billion dollar -merger with Skydance Media. And guess what? It worked. The deal was given the go-ahead last week.

Trump crowed about the demise of Colbert on Truth Social. Colbert who is always punchy addressed his being cancelled by saying to the president: “Go f*** yourself”.

Brazil for the moment is using more diplomatic language, but it is not bending either; a rare example of a country that is prepared to stand up to Trump. Canada has also to work out what it intends to do.

Blackmail is an ugly word, but it does look as though regardless of whether you are a sovereign nation, an independent media company, an academic institution or a law firm, if you don’t do what Donald Trump demands then you’d better be prepared for the consequences.