When Dominic Cummings arrived in Downing Street, some of his new colleagues were puzzled by one of his mantras: “Get Brexit done, then Arpa”. Now, perhaps, they have some idea of what that meant. On 2 January, Cummings published on his blog the wackiest job proposals to emerge from a government since the emperor Caligula made his horse a consul.

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The ad took the form of a long post under the heading “We’re hiring data scientists, project managers, policy experts, assorted weirdos…”, included a reading list of arcane academic papers that applicants were expected to read and digest and declared that applications from “super-talented weirdos” would be especially welcome. They should assemble a one-page letter, attach a CV and send it to ideasfornumber10@gmail.com. (Yes, that’s @gmail.com.)

It was clear that nobody from HR was involved in composing this call for clever young things. Alerting applicants to the riskiness of employment by him, Cummings writes: “I’ll bin you within weeks if you don’t fit – don’t complain later because I made it clear now.”

The ad provoked predictable outrage and even the odd parody. The most interesting thing about it, though, is its revelations of what moves the man who is now the world’s most senior technocrat. The “Arpa” in his mantra, for example, is classic Cummings, because the Pentagon’s Advanced Research Projects Agency (now Darpa) is one of his inspirational models. It was set up in 1958 as part of America’s response to the Soviet space satellite programme and was charged with generating and executing research and development projects to expand the frontiers of technology and science.

Arpa, as it was then known, was the agency that funded the arpanet, the precursor to the internet, and is famous for the lavishness of its funding, the speed with which it operates and its decisiveness. When Bob Taylor had the idea of funding the arpanet, for example, it took him just 20 minutes to get his boss to agree to it. Other Cummings inspirations are the Manhattan Project, which built the first atomic bomb, and the Apollo mission, which first put men on the moon.

Note that all these inspirational projects have some interesting things in common: no “politics”, no bureaucratic processes and no legal niceties. Which is exactly how Cummings likes things to be.

One of Cummings’s abiding obsessions over the past few years (often aired on his blog) is his conviction that “SW1” – his term for the entire government machine and its political masters – is totally unfit for purpose in the modern era. In a way, his job ad is a 3,000-word articulation of this belief. SW1, as he sees it, is scientifically and technologically illiterate, stuffed with Oxbridge humanities graduates, generalists, amateurs, etc. When mounted on this particular hobbyhorse, Cummings sounds like CP Snow on speed.

I have some sympathy with these views – as do some of the younger civil servants I meet. The problem is that the thinking implicit in Cummings’s blog post is flawed in two ways. The first is that he has swallowed the Silicon Valley delusion that data (and data science) provide the key to life, the universe and everything. The second is that his recruitment wheeze is strategically naive. The idea that the huge bureaucratic machine of the British state can be transformed by the injection of a cadre of disruptive young geniuses is, to put it mildly, bonkers. The civil service has a powerful immune system for rejecting outsiders and Cummings’s stated ambition – that his new hires will make him redundant in a year or two – is therefore daft. What he has are ideas when what he needs is a strategy.

Which is odd, because his main claim to fame from the Vote Leave campaign and Johnson’s election victory is as a gifted strategist. Deep down, Cummings is what the economist Tyler Cowen calls a “state capacity libertarian”. This sounds like an oxymoron (a libertarian who believes in a strong state), but what it appears to involve is a conviction about the need for a capable state. In this regard, writes Cowen, “sometimes the problem is too much government, sometimes the problem is not enough government. Most often, the problem is the wrong sort of government.”

If this is indeed what Cummings believes (and much of his derisive blogging about the stupidity and incapacity of SW1 suggests that it is), then he needs a more sustained strategy to make the British state more capable of handling the challenges of governing a 21st-century society. In other words, a state that would never have screwed up on a universal credit scale.

In some ways, Cummings is his own worst enemy (though David Cameron might retort: “Not while I’m around”). Many people are repelled by the way he interweaves radical insights with what looks like vulgar abuse. He mixes understanding with wacky afterthoughts and lets his compulsive autodidactism run away with him.

But he also has an acute sense (which most Brexiters seem to lack) that a UK outside the EU will need to become a much more capable and creative state if it is to escape becoming either a gigantic imitation of Singapore or the sandpit for private equity envisaged by Jacob Rees-Mogg and his cronies. Given Cummings’s role in Number 10, and the elective dictatorship bestowed on his master by the rackety British constitution, he has a real opportunity to do some good. Let’s hope he takes it.

• John Naughton writes the Networker column for Observer New Review