Einstein at the Bus-Stop
For the purposes of plain getting on with things – keeping warm, staying fed, making babies – there is no reason on earth, or off it, why anyone not actively engaged in the world of science should comprehend the underlying workings of physics. All we really need to know is that, accurate or not this week, relativity, cosmology, quantum mechanics don’t concern us in our everyday lives. Let the quantum physicist panic because she knows the floor she walks on is almost entirely empty space with a few widely scattered molecules dotted here and there. The rest of us stomp around in blissfully ignorant confidence that – barring unforeseeable acts of God – a floor will continue to do what a floor is supposed to do. Or as the New York Times for 10 November 1919 put it, ‘Einstein Theory Triumphs. Stars Not Where They Seemed or Were Calculated to Be, but Nobody Need Worry.’
But still. But still. Quantum theory suggests that there is a vanishingly small chance that a kettle full of water on the hob will freeze rather than boil. This is disturbing, if only in a vanishingly small way. And if the stars are not where they seemed to be, then where are they? And to whom did they seem to be where they are not? Are they not where they seem to be to me? Or are they not where they seem to be to someone else to whom they seem to be somewhere quite different because they are looking at them from another point of view? In which case, are they nonetheless where they seem to me to be, or were there those who knew that they were not where they seemed to me to be, but who were as it turned out wrong about what they thought they were right about? And does that make me right? Almost certainly not. But it is an awful thought that people who know something you don’t know might after all be wrong, and that when their error is discovered, you will not understand the new solution any better than you understood the old. It’s no good being told not to worry, these things are a worry, even if not of such a pressing kind as the question of when the bus you are waiting for will arrive. Moreover, there is always the sneaking suspicion that if you knew what they knew, you would also have a special insight into the arrival of the bus (because things always turn out to be linked in some unexpected way), and you would then be able to conclude that it would be much better if you gave up and went home to bed.
So it has always bothered me to be told that E=mc2 contains a vital truth about the world and not to be able to grasp what that truth is. There are, I know, those who think that science is a special kind of truth that I’ve no business trying to grasp if I don’t have the mathematical tools to understand it, because not understanding it in scientific terms is not to understand it at all, but David Bodanis, the author of E=mc2, is not one of them. As someone to whom science has always been a black hole, I see Bodanis and those who bother to try to explain to the likes of me what they understand mathematically as therapists of a sort. Not to understand something and to know you don’t understand it is distressingly akin to being post-Freudian: like being aware of the existence of your unconscious and knowing that it is forever withholding from you what you really need to know about yourself. Actually, to be mathematically illiterate is worse than being an unanalysed post-Freudian, because what is not understood is palpably there in the form of stars or floors, whereas my unconscious exists, if it does at all, in the realm of thought and can, thanks to its own devious workings and my willed collusion, be ignored.
But scientists are always telling us that E=mc2 is of the utmost everyday importance while at the same time berating writers and artists for taking half-understood scientific ideas and applying them to fiction and works of art. It is, I suppose, some sort of bad thing if poorly digested concepts become common currency, but I rail at being disallowed whole playgrounds full of metaphor and generalisation just because tears of failed arithmetic past spring to my eyes at the merest glimpse of an equation. A little knowledge may be a dangerous thing, but so is a lot of knowledge that only a few magisterial types are permitted by their own obfuscations to understand. Compare and contrast a novel that misapplies quantum theory with the building and dropping of a nuclear bomb.
And what about the extraordinary and inalienable human pleasure of getting something that you haven’t grasped before? There are, of course, various degrees of getting things. There is the pinprick of light at the end of the hopelessly murky tunnel, when you can see how you might comprehend something if only the fog would clear. Or there is that three in the morning blaze of insight, when you give up trying to sleep, open the Tractatus and see exactly what Wittgenstein was on about – though the blaze begins to flicker by the time you turn the lamp off, and is quite dead as you scan the page again by morning light. And there is the bolt from the blue, where you understand with complete clarity what you were sure you would never understand – and what you can’t understand now, no matter how hard you try, is how you ever didn’t understand it. But, oh, the delight of grasping an idea, the sheer rush of endorphins, the irrepressible desire to leap up and pirouette around the room. What else, apart from sex and drugs and rock ‘n’ roll, is there in life better than getting it? And what is more important in the world, apart from great lovers, honest drug-dealers and fine musicians, than good teachers?
Bodanis gets a gold star for good teaching, and for understanding that with this reader at least there is no level of explanation too low. I’ve gone the explanatory route of the man travelling in a train with a torch, a watch, a pair of dividers and wellington boots, being observed by a man standing on a platform and another with binoculars on the other side of the galaxy. So this appears like that to him, and like something else to the other, and someone gets older than someone else, or fatter, but what’s that got to do with E=mc2 or nuclear fission or even the price of wellington boots? It may be that the man-in-the-train explanation is elementary to someone who already knows what they are talking about, but if you haven’t got the basic skills to use the analogy it takes you down quite the wrong alley. I remember reading about Schrödinger’s imaginary cat – the one in the box who both is and isn’t dead if it has or has not been poisoned and the lid remains shut. Wondering what they would make of the equivocal world of quantum theory, I put this fairytale to my six-year-old and her friend as a bath-time story. All hell broke loose, waves of bathwater soaked floor, walls, towels and myself as the two outraged little girls flung their arms about and stamped their feet demanding to know who this cruel and evil scientist was who locked cats dead and undead in boxes and was not punished for such behaviour. I feel a little like that with the man in the train. I become more interested in the narrative than the point. Where is he going? Has the bloke on the platform missed his connection? Were they going to meet? And why? Running off together, or plotting world revolution? And why is the guy on the other side of the galaxy so interested in the 11.10 from Euston? Looking for hot tips on privatising the railways of Betelgeuse, I dare say.
Bodanis begins at the very beginning, taking the equation itself as his structure, and nothing for granted as to the possible ignorance of his reader. If you are me, this is not patronising, it is a great relief. E, =, m, c and 2 each have a chapter to themselves. E is for Energy. I gave up science decades ago: I really do want to know the history of the concept of energy and be taken back to Faraday, have my hand held through the law of conservation of energy, and be led gently towards Einstein. I’m delighted to learn about the development of the equals sign and what exactly the idea of mathematical equivalence is. And pathetically grateful that mass, the speed of light and the squaring of the speed of light are explained to me step by step, towards the notion that nothing can go faster than the speed of light and how exactly it is that energy transforms into mass and vice versa. ‘Visualise the equals sign in the equation as a tunnel or bridge. A very little mass gets enormously magnified whenever it travels through the equation and emerges on the side of energy.’ No, I really don’t mind being asked to see an equation as a choo-choo train, in fact, on the contrary, suddenly I see the whole point of equations.
So there I am, thinking I get it, and I’m squeaking with pleasure. Bodanis leaves the equation and discusses the development of the idea in the real world. The splitting of the atom and the making of bombs, the discovery of black holes, the creation of our galaxy, the Big Bang. At last I see how they are connected and why everyone makes such a fuss about Einstein’s little equation. It all depends on the absolutely limiting speed of light and what happens when any mass is sent across the = of the equation at 448,900,000,000,000,000 mph: the c (constant) squared. I even see why c has to be squared. And then, smug as anything, I turn on the TV to watch Horizon where a devastatingly confident young Portuguese physicist from Imperial College pours scorn on the narrow assumptions of his peers and announces that the constant speed of light is not constant at all. Light, he says, travelled faster in the young Universe. Einstein got it wrong. The laws of the conservation of energy may not be unchanging laws at all. The void, he announces with all the clarity of a mystic, which existed before there was anything was not nothing. I no longer know what he is talking about, but it is clear that I haven’t the faintest idea what energy, mass, the speed of light, the Universe or even equals means. On the other hand, whether I think I know or I think I don’t know, the world goes on in a remarkably similar way, as it does if the speed of light is or is not a constant. Is this relativity?
Relativity is about the only thing left that I think I might understand. In the singular universe of me sitting in my living-room with Bodanis’s book, I can grasp his explanation of how everything works. In the parallel universe of the outside world and its neighbouring galaxies, I don’t have a clue what any of it means. I both do and do not understand it, just as Schrödinger’s cat is both dead and not dead, to say nothing of entirely imaginary. This is not necessarily a tragic insight, or even a bad thing. It confirms what I have always suspected, which is that I should stay home and not wait for buses, and that it is perfectly all right for me to take E=mc2 or any other set of letters and play with them to my heart’s content, provided I do not inform the world that I am a competent physicist. Not, as it happens, easy in our category-crazed times. Recently I was phoned by a researcher for Newsnight and asked to participate in a discussion of global weather change. Some years back I published a novel entitled Rainforest, set to some extent in a rainforest, but mostly inside the psyche of an ecologist studying one. I also wrote a book with the word ‘Antarctica’ in its title, though it was a memoir, not a natural history. These titles were enough, apparently, to give me an aura of meteorological expertise.
‘We’d like your opinion on global warming and its likely effects.’
I quite fancied the idea of babbling uninformed nonsense on TV about forthcoming ice ages or the roasting of the planet, but I pulled myself together and declined the invitation. Remember this next time you see or hear someone pontificate publicly about the state of the world.
On the other hand, at home, armed with Bodanis and other kindly souls, I can pace up and down and chatter to my cats and the four walls on the nature of the Universe. I can turn my half-understood ideas upside down and inside out and half-bake them if I choose. And what harm can I do if I publish them in the form of fictions and fancies, when as far as I can see, this year’s truths turn out to be next year’s old hats? The hard-core scientists can keep their secret knowledge, and I will continue not to know what I can’t know and to do with my lack of knowledge what I will.