OUR world is beautiful; but also very boring. I am writing this in Florida, once an untamed tract of mangroves and marshy rainforest, full of wildness and surprising beauty, but now a huge, bleak grid of turnpikes and motorways, endlessly scored across with lines of concrete and wire. Unlovely barrack-like buildings and a tangle of advertising signs offer a rare splash of colour. The roads are congested; as cars dawdle alongside you, you see angry and frustrated faces flinching at the red lights ahead. Everybody is on the move. Everybody, it seems, is anxious to be somewhere else. Time is sliced into harried segments.

That is one person's impression of life in one place, but there is a more general point. Almost wherever we are, our experience of life is often of boredom and frustration. We are glued into time, the fourth dimension, and yet there is never nearly enough of it. And this, for me, is the point of art. Art helps us to stop off and remind ourselves that we are making but a brief visit to a beautiful world. Remembering this regularly is probably a way to be happy.

Painting is a system of communication with only one message, the sensation of being alive more intensely than normal.

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For around 40 years, from my early teenage years to the age of 53, I painted like this: I would take a small box or a grimy bag of tubes of gouache or oil paint, a foldaway easel and a pre-prepared board to a hillside or a flat rock or to the side of the road. Then I would sketch our roughly what I saw in front of me, and paint it in colours. I would do this when I had a holiday or over a few free days – not very often. Over time and not surprisingly I became slightly more skilled, learned a few tricks and became, therefore, more artful. Then I had a stroke, which paralysed the left-hand side of my body, and I had to give all that up.

I now recognise that I've been telling a deceitful story about what happened next. I've said that because of the practical difficulties of being unable to paint outside, I was forced to start again in a studio, where I could control my environment. There, I was obliged to find a new way of painting because I didn't want to do still lifes of flowers or oranges, or indeed nudes.

Though all of that is true enough, it leaves out the most important thing. After coming close to losing my life, I had a more intense sense of how little time I had left – the "shortness of life" thing, running alongside the "beauty of life" thing. I realised that, more than anything else, I'd always wanted to paint well, but that I'd put it off because I was frightened of not being good enough. Now I thought to myself, Andrew, you're in danger of running out of time. How would you feel if you found yourself too old and simply too frail to paint – and you'd never tried, not seriously? You'd never risked it?

I knew I would feel mightily hacked off – a coward – miserable. So I told myself to get on with it. Try to paint properly. That's what I have been doing, and it isn't really much to do with physical disability. And I have never enjoyed myself more.

Well, enjoyed? Sometimes, with my back aching and after several hours of intense concentration, I find myself weeping with frustration. Why don't I have that innate understanding of shape and form that Kandinsky had? Why, after hours of trying, can't I draw a single line with the honesty of Matisse? There are no answers beyond the vagaries of differently distributed human skills and characters. But at least I know where the gaps are.

What's it really about? My wife and children ask me that. They find it odd and, I'm afraid, slightly irritating when I trail off, yet again, to the painting studio round the corner. I should be doing something more normal, like watching television, or eating buttered toast. "What are you doing it for?" they want to know.

What is this compulsion to leave something behind? What is this rather pathetic reaching for some sort of immortality? The interrogative banter starts to have an edge to it. Painting might be a reasonable thing to do if you are a lifelong, full-time and professional painter who can actually earn a living by making pictures that people want. For somebody like me, who has a perfectly good job doing something else, it seems to smell of delusions of grandeur. What do I do it for?

It's a reasonable question. It deserves an answer. I am not completely deluded. I don't think I am Camden's Caravaggio, or the Picasso of Primrose Hill. I can tell the difference between great paintings and the rest and I know perfectly well that the pictures I make will never change the course of anything and may well be quickly forgotten just as soon as I shut up about them. I started on this journey far, far too late in life. There are important painters. I am not, and to my eternal regret, will never be.

Yet there is something inside that seems to have to fight its way out. What it feels like to be me and alive now is something I want to explain, and I can do so only through paint. I'm in my late 50s, not particularly well, and time is running out.

And I know enough to see that sometimes the pictures are successful as communication and sometimes they aren't. The ones that work are postcards. They are messages sent outside my immediate circle of friends and family, and even into the future. And all I really want is that they stay alive.

Paintings don't all live. On Monday, you can be putting your everything into a picture, thinking hard, working hard, and leaving the studio feeling that you have made something that earns its place, that's alive. And then you come in feeling chirpy on Tuesday ... and the poor beast has died in the night. Yes, there are just the same colours in just the same places, but it's a dry corpse. If you hung it on a wall, you couldn't keep coming back to look again, except with mounting distaste and horror.

The line between this dead picture and another picture which, against all the odds, despite some terrible bodging and moments of despair, seems to stay alive, is a tiny, flickering thing. It isn't a line you can touch with your finger. But it's the fatal division between transcendence and boredom. It's the only thing that matters.

This is an edited extract from A Short Book About Painting by Andrew Marr, published by Quadrille on November 2, £15