When Montaigne retired to his writing tower late in life, he first produced neat, closely argued disquisitions on this and that, based on well-known classical phrases and sayings, and carefully modelled on the sort of exercises the Greek and Roman rhetoricians had produced. One point followed the next, arguments were set up and knocked down until the one that had been intended from the beginning was shown, by logic and by citing the wisdom of the classical masters, to be right. That was how he planned to while away his time, calmly, until his death.

But well before his actual death 23 years later, he was advising his reader in mid-essay that digression was an integral part of what he was doing, that the reader should trust and follow him through the labyrinthine byways of his discussion, and that his subject was not the grand eternal truths, but the world as it seemed to be to him, Michel de Montaigne, the singular individual he knew better than anyone or anything else. Along the way he invented a new concept: the essay that wasn't designed to show the reader what a master of close reasoning the writer was but to test an idea, to elaborate on an abstraction, by seeing how it worked in his reality, using whatever came to hand and mind. To play. Not unrelated to his thoughts on the subject of writing and reading essays, Montaigne wondered whether, when petting his cat, he played with it or the cat played with him. The closed-endedness of the first kind of pieces he wrote had led him into a breakdown early in his tower time, from which he emerged with a brand new way of writing.

In his long essay Attention!, Joshua Cohen shows himself to be one of Montaigne's offspring, and has been given the leeway by his publisher to play with his subject over 60,000 words, right up until the last drop of blood has been squeezed from the stone of his subject. Undergraduate essays usually must, rather sadly, follow the classical method: know what you are going to say, say it, prove it using your elders and betters, and then conclude that you have said what you wanted to say to start with. That is a terrible way to educate a young mind. Cohen writes that he had always hoped to "write a book about nothing that was also a book about everything", but had lacked a subject until attention caught his attention. It's a brilliant definition of what writers should want to write, and echoes my own notion of the perfect book I am always failing to produce. He is a little disingenuous about having lacked a subject until now, because the point is that it really doesn't matter what the subject of such a book is. All good books are about nothing and (therefore the possibility of) everything, if you write them right.

Attention! isn't trying to disarticulate the whole idea of ordered writing. If writing weren't ordered in some way, no one would be able to read it, and all books would be 60-100,000 words in alphabetical order. Cohen sticks to chronology, beginning with attention as he observes it in ancient Sumer, in the language fixing of Babel and the rules of Eden, before moving on to Egypt, memory as attention, and the inability of Orpheus to keep his mind on what mattered. For the most part, attention is about words and what we think and do with them. The sweep and flow of Cohen's subject and where he takes it from and to are sometimes breakneck, and you race to keep up. How reliable is his information, you ask yourself, and then wonder whether you are prepared to give enough attention to his book to chase up the sources. He writes with the confidence and even arrogance that all good essayists should have. It's a way of securing the trust of the reader, but also assumes the reader can keep up and is as good at thinking as the author.

The one piece of information I wasn't inclined to check, because I have read it often before, was Cohen's reference to Augustine observing Ambrose reading silently and alone, and the suggestion that silent reading was virtually unknown in the middle ages. By chance, I read a review of a critical biography about St Augustine. It commented on the error of just that assumption, and led me to a paper by Myles Burnyeat that casts doubt on it. Happenstance and following up leads belong comfortably in the realm attention. Being wrong or having not perfectly up-to-date information isn't fatal in an essay (the term means "a testing" or "a trying out"). The unreliable essayist has a good pedigree. Montaigne often got his quotes wrong and was hit and miss about attributing them to sources. Readers should work, too, and decide how much they're prepared to take on faith.

It doesn't come as a surprise when Cohen confesses, "I have written half this book on psychostimulants both legal … and illegal." The book reads as if it's on speed as it winds up towards the end. The subjects that prompt the confession are ADHD and the extent to which computers can be programmed to function as if they were the human brain on amphetamines. Sometimes the leaps and diversions Cohen takes, by way of psychometrics, wave-particle theory, Buddhism, "neuroacademia", fiction, automata and computer notifications, require the reader to shut her eyes and squeeze them very hard in order to get the connection to attention.

But it's invigorating, as reading should be. And like Montaigne, he never really forgets what his subject is. He always manages to return his reader to the matter in hand, even if the matter in hand only looks like that for a page or two. Cohen is a cockily pyrotechnic writer; his essay is a show-off, but with something to show off about. It's a real attempt to make the subject his own and take a willing reader along with him. It's not what you want to read all the time, or the only thing you will want to read on attention (if only there were a bibliography – although that would spoil Cohen's flying-by-the-seat-of-his-pants style). Attention! will allow you to smile, argue, agree, refute or just go along for an engaging ride.