# Tales from the back of the eyelids

## Mathematics

### Overview:

- Edwin Hubble discovered that galaxies are moving away from each other (*1)

- Scientists have assumed this means the universe is expanding

- It is more likely, though, that the size of the universe stays the same

- Instead, everything inside the universe is shrinking

- Our solar system, our planet and its inhabitants will one day shrink to nothing

- We don't need to worry as this will happen billions of years from now

The professor was in full flow. He had his back to the class and was vigorously covering the whiteboard with green squiggles (that is to say, mathematical equations) from his marker pen. As he wrote he talked to the board, and here and there between his mumbles we could make out isolated words: integral, tangent, viscosity, parabola. Occasionally he would pause at an equals sign and give a little titter. Once or twice he let out a loud chortle. What the joke was amongst those algebraic proofs none of the students ever knew. We would give each other baffled sidelong glances - but not for long, in case we got left behind in the copying.

To keep up we had to write at a frantic rate. In the rush it was easy to lose our place and often by mistake we would recopy much of what we had already copied. The most precarious moment would come just after the professor reached the bottom right corner of the board. Then, with three or four merciless sweeps of the eraser, he would wipe out all the squiggles to make room for more. In the blink of an eye crucial formulae would be forever lost to us.

Unsurprisingly our lecture notes were completely incomprehensible. Of course we could have tried to decifer them later by cross-referencing with each other. But was there any point? We didn't even know what the course was about (apart from being about maths) as the professor never at any point announced either the subject or the individual topics. Any attempt to make sense of the notes would be a waste of time which would only lead to greater confusion. And there was so little time available to waste, what with drinking and the other enjoyments a student should have. In my view the best strategy was to cram from textbooks a week before the finals.

Even though I might seem sanguine about the prospect of the upcoming exams, this kind of dream is always filled with a heavy sense of foreboding. That's because I know what's coming next and I can't avoid it: soon I will find myself sitting in a big hall with the exam paper in front of me and I'll be trying to read what is written on it. I have three hours to answer five questions. But I am struggling to understand what is being asked of me. The problem is I keep on losing my place because the questions are constantly moving around on the paper. And when I do manage to pin one down, the letters are blurred and difficult to make out. Eventually I recognise some words here and there: integral, tangent, viscosity, parabola. At last I have some hooks on which I can hang my answer. I reel off calculations and draw elaborate diagrams. After a while, though, I realise I am in a hopeless muddle because I have forgotten what it is I'm trying to prove. I tell myself I'll go back and sort out the mess later. In the meantime I'll attempt another question. I look up at the clock and realise I have only half-an-hour left in which to answer four questions. In panic I jump from one question to another, covering the pages in squiggles, including in them everything I know which has anything remotely to do with the subject. Algorithms, functions and graphs swirl around in my head as I write. Everything is getting more and more confused and I am getting more and more frenzied - until the bell rings for the end of the exam, when I wake up covered in sweat.

That, anyway, is what usually happens. However on one particular night a couple of years ago the dream turned out differently. I am in the classroom again but for once I not trying to keep up. It has finally dawned on me that copying out squiggles is pointless. Instead I sit and gaze at the back of the professor as he mumbles into the board. For the first time I notice how scruffy he looks. He is wearing a baggy jumper and ill-fitting trousers and his unkempt white hair is sticking out in all directions. I am surprised to see he isn't wearing any shoes or socks. "He must be cold like that," I think. "If I saw him in the street I'd think he was a vagrant."

Suddenly, as if he could read my wandering thoughts, the professor spun round and wagged his forefinger at me. "Philip," he said. "You must pay attention! Why am I making all this effort to explain this to you, when you can't be bothered to concentrate?"

Astonished, I looked at the man reprimanding me and even more astonished I realised he was Albert Einstein.*2 Seeing that I was taken aback, he softened his tone and continued in a more friendly manner.

"You see," he said. "You must listen because I need you to tell the world about my new theory." In the long years since his death, he told me, he had had plenty of time to reflect in that other place and had come to some conclusions he had never reached while he was alive. It was all to do with the expansion in the first nanoseconds after the Big Bang and was fundamental to understanding all else in our universe from black holes and curved space-time to strings and extra dimensions. In those first moments of expansion lay the unified field theory and therefore, in essence, the link between all theories of the universe.

Einstein was bursting with excitement at his new ideas - and who would not have been? The answer had eluded him all his life and he was desperate to pass it on to me, in order that I, in turn, could pass it on to mankind. He turned to the board again and started to scribble down more equations. This time I made a serious effort to concentrate. Einstein's mathematical argument was a series of complex concepts and yet, despite this, his general drift was beginning to dawn on me. It was an amazing and pleasing feeling: I, who had always longed to understand the mathematics of theoretical physics and yet always found it mystifying was, at last, being let into its secrets. I was getting a glimpse and was beginning to see. I made copious notes, mostly for posterity, so that there would be a record, but also for myself, so that later I could refine my own understanding of the great man's thoughts.

Unfortunately, when the lecture was over and I woke up, all my notes were lost, as you might expect after a dream. I felt agitated, almost feverish: I had to remember what Einstein had told me, to pass his insight on to everyone. I went to the bathroom and sat down on the toilet. With my head in my hands, I recounted the main points to myself and tried to refresh the connections between them. But it was not easy; the dream was already beginning to fade.

"Damn it!" I cursed. "Of all the people he could have chosen, why did he choose me?"

Why indeed? It would not be accurate to call me a mathematical genius. Actually, it would be very inaccurate to call me that. I struggled with the subject throughout my education. That doesn't mean, though, that mathematics is beyond me. In fact Einstein might have picked me because the opposite is true:* I am beyond mathematics*. My mind is not stuck in a groove like an academic's and I am open to unconventional possibilties. Ask any mathematician what maths is and invariably you will be told it is truth. But ask them to prove that maths is truth, then they are stumped. Not that this failure will shake their faith in their assumptions – which is why, when the rest of us believe there must be a flaw in the theory, they will continue to insist that cats can be alive and dead at the same time.*3

"Ah," you might think to yourself. "If he is sceptical about mathematics, why does he think it's important to remember what Einstein told him? Einstein's theories also seemed barmy when they were first published and even today the notion of bending time is still hard to grasp. What's so special about Einstein?"

It's a valid point: if I didn't believe that Einstein has something significant to say, why would I bother to communicate his ideas? Let's suppose that instead of Einstein, my neighbour Mr Krumpflecker had disturbed me in the middle of the night, all excited, to explain how he had cracked the mysteries of time, space and matter. What would I have done? Of course I'd have called the psychiatric hospital and ask them to come and deal with him. But because it was Einstein I sat up and took note. When it come to theories of the universe, Einstein inspires in me more respect than Mr Krumpflecker does.

But why? If I have never fully understood either Einstein's or Mr Krumpflecker's theories, how come I value Einstein's more? The answer is not reassuring: I believe in Einstein because other people who I believe in, believe in him. In other words:* blind faith*. The same blind faith which causes societies to choose crooks as leaders. Hardly an adequate recipe for finding the truth. But what else can I do? You can't expect me to become an expert in theoretical physics. In any case, the most important thing is that Einstein's theories of General and Special Relativity have been proved to be true. (At least, that's what the people I believe in believe.)

So I sat on the toilet, trying to piece together what Einstein had told me. I had been given the daunting responsibility of revealing his new theory. Here's what I can tell you: the events of the early universe, in the first nanoseconds after the Big Bang, are determined by a quadratic equation (ie. of the type y = ax^{2} + bx + c). E is proportional to the component c^{2}-17m. In the quadratic form of the expression this component is found as (c^{2}-17m)^{2}. The number 17 is important because it is one of the early prime numbers.

There was more – quite a lot more – but unfortunately I've forgotten the rest. I'm sorry. All the same, it's a start: contemporary mathematicians and theoretical physicists have got something to ponder on. Perhaps that's Einstein's intention: life would be boring if there were nothing left to prove. That said, he realises scientists are stuck in the grooves of Quantum Theory, String Theory, Chaos Theory and Driving Theory and need a little prod to get them out.

Let's hope it works.

*1. Edwin Hubble (1889-1953) was an American astronomer. He made this discovery in 1929.

*2. Albert Einstein (1879-1955) is the most famous and influential theoretical physicist of the twentieth century. He won the Nobel prize in 1921.

*3. The quantum physicist Erwin Schrodinger (1887-1961) showed in a thought experiment how a cat can be both dead and alive at the same time. Einstein was dismissive of Quantum Theory and said "God does not play dice with the universe." Niels Bohr (1885-1962), who first applied Quantum Theory to atomic structure, is said to have replied "Don't tell God what to do!"

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