Mr Miles Davis may not have invented cool, but it may have peaked with him, and with one of his most famous albums, Birth Of The Cool, from 1957. I mean, what is cooler than showing up to the recording sessions with some rough sketches in your head (never written down, of course), as he did, and just letting your horn blow, man? Cool is inviting in a bunch of your favourite musicians into the jam sessions, as he did, and not giving them any direction, just letting them do their thing and it somehow still sounding great. Cool is being captured in the studio with your leg over the back of a chair and an ascot tie tied around your neck just so. And cool is also sticking the landing, coming out of it all with one of the greatest albums of all time; that part seems essential. That part brings with it some cool cash and a lot of cool clout to go with it, both of which Mr Davis flaunted in spectacularly uncool fashion.

But then, what is cool really? Apart from being like pornography in the sense that we know it when we see it, how are we to define or quantify coolness? In a new PBS documentary about Mr Davis, also titled Birth Of The Cool, airing and streaming on its platform now, we get a little insight into the musician’s process and projections, about his background and behind-the-scenes behaviour that cannot help but dispel some of his aura. But, that’s sort of the thing about “cool”, isn’t it? It’s a kind of quantum quicksilver that dissolves under any amount of investigation and doesn’t break down into parts that might be reverse-engineered into an equation.

One thing cool certainly is – no matter how under-analysed – is relevant in the marketplace. As consumers, we fetishize cool, both in the brands we buy and in the personal brands we buy into. As people trying to find our way in the world too, we may look to cool as a kind of beacon, an example of the life we’d like to live, and the way in which we’d like to do it. Which means that cool is powerful and dangerous, a siren song.

In Mr Davis’s case, the cool he projected was incredibly calculated. Throughout the documentary, we hear both him and his friends talk about the ferocity with which he protected his image (for various political reasons, it was immensely important to him that he never left the house looking anything short of “sharp as a tack”, as he liked to brag). Behind closed doors, of course, he was anything but cool – the musician’s past was stained with serious addiction issues and incidents of domestic violence – which may be the best tell on the substance of cool there is: that it isn’t about substance at all, but all about artifice.

So, what is the lesson here? Projection is everything if not the only thing? Well, yes. That’s the thing about faking it till you make it, it is a kind of promise to yourself, a bet placed on yourself based on the belief that ultimately you do have the substance (or talent, or whatever it takes) to back up the stylish exterior. It is a cart-before-the-horse tactic, sure, but in that cart ride our better angels, the best versions of ourselves we might become. So, definitely get yourself a cool and silky ascot, if only to look as good now as you ultimately would hope to be.

Miles Davis: Birth Of The Cool is on PBS on 25 February