An evening in wonderland by Bhumkiti Panwannakul

An Evening In Wonderland

A Brief Story Of Maths, Physics & The Universe Jacqueline Koay

Copyright An Evening In Wonderland A Brief Story Of Maths, Physics & The Universe Copyright ÂŠ Jacqueline Koay, 2016 All rights reserved in all media. No part of this book may be used or reproduced without written permission, except in the case of brief quotations embodied in critical articles and reviews. The moral right of Jacqueline Koay as the author of this work has been asserted by her in accordance with the Copyright, Designs and Patent Act of 1988. Published in the United Kingdom by Sun Yoga Press 2016 Cover drawings by Embla Ester Illustrations by Kerry Robinson Paperback ISBN: 978-0-95564

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The Sheldonian Theatre, Oxford

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For my youngest child, Georgina, I wish you beautiful encounters.

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I would like to thank Professor Carlo Rovelli of Centre de Physique ThĂŠorique de Luminy at Aix-Marseille University for reading through the manuscript of An Evening In Wonderland â&#x20AC;&#x201C; A Brief Story of Maths, Science & The Universe and for giving me his invaluable encouragement. Professor Rovelli is the author of the book, Seven Brief Lessons on Physics, which explains the heart and soul of physics in seven beautiful chapters.

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The conversation between Professor PW Vanderleyden and his eight-year-old son, Piet: Piet: “Pa, what are dinosaurs and people made of?” PWV: “Atoms.” Piet: “What are atoms made of?” PWV: “Electrons, protons and neutrons.” Piet: “And these electrons, what are they made of?” PWV: “Fields, my son.” Piet: “What are fields made of?” PWV: “I don’t know yet, son, and when I do, I will come home.”

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Of Einstein, Space & Time They stood at the steps of the Sheldonian in the dying light of day. Though it was midJune, there was light snowfall in Oxford that year. PW Vanderleyden looked skywards and fleetingly thought about his beloved Drakensberg Mountains in South Africa where he went for his honeymoon twenty-two years ago. Then, it had snowed too, but ah, that was so far away and so long ago. Like many, he had left his home to come to Oxford searching for the point of existence, in particular, for the meaning of his own life. We are always searching for the meaning of life. “Human beings are a species that needs and wants to understand who we are.” He had said that just now, sometime during his inaugural two-hour lecture on the existence of higher dimensions. He couldn’t be sure, but he thought he mentioned sea squirts in his lecture (though they were completely unrelated to his topic). These sea squirts were 9

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born with brains to allow them to travel, but when they arrived at where they wanted to be, they ate up their own brains because they didnâ&#x20AC;&#x2122;t need brains anymore! Not being a biologist himself, PW found it intriguing that brains might have evolved solely to orchestrate and express active movement. For movement is life. Yet she - Alice - had told him something altogether diametrical to his belief system, a belief that was solidified by his two decades of being a physicist. Maybe he never really understood physics. She had told him that movement is an illusion. The distance between any two galaxies grows with time, giving the illusion of mechanical motion, but the galaxies themselves never move. They just sit there, watching the unfolding of space. Itâ&#x20AC;&#x2122;s like baking a Christmas cake: the raisins, currants, candied peels and cherry pieces themselves donâ&#x20AC;&#x2122;t actually move, but when the cake batter rises, it gives the illusion that all the bits in a Christmas cake have moved further apart from each other. 10

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“We need an absolute point of reference for movement to exist, and wherever you look in the universe, my dear Professor, that absolute point of reference does not exist,” she said with the total conviction of youth. “Heck, we don’t even know where the centre of the whole universe is, because we don’t know how far its outer edges stretch to!” He thought about his sea squirts but said nothing. How the young seem to think they know everything, he thought to himself. I was once like that, too. But that’s the beauty – and torment - of science: we don’t know things for sure, and that is the reason why we soldier on, to discover new things with each rising sun, with each discovery bringing us one step closer (maybe) to knowing the unknown. She, Alice, was his postgraduate student here at Oxford, one of the many signed up for the three-year programme of research in his department. He had not met her personally until this evening, when she accosted him at the end of his lecture.

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Precocious and brilliant, she had completed her doctoral thesis at only twenty years of age, and she wanted him to defend her viva. Viva - or to be more accurate, viva voce - means “with the living voice” and is the culmination of the Doctor of Philosophy programme of study and research. It is an oral examination, where an internal academic staff, though not the immediate supervisor of the student, often acts as a champion for the thesis, the so-call defender, alongside an external examiner who typically plays the hard cop. Alice’s thesis was on Precision & Accuracy. Precision is the quality that tells us how ‘sharp’ a measurement is, whilst accuracy is about how close to the ‘truth’ a measurement is likely to be. They are two very different things. Take this example: the distance from the centre of the earth to the centre of the moon. 240,000 miles would be accurate but imprecise. 289,562 miles would be precise but inaccurate. 238,857 miles is both accurate and precise. For theoretical physicists like PW who are trying to find imaginary particles with their massive space-age detectors, both precision and accuracy are very 13

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important qualities indeed. Thus, PW could not say no when Alice asked him to defend her thesis. Maybe some part of him did not want to say no. When she had cornered him just now in the empty theatre after his lecture, he had felt like he was falling down the proverbial rabbit hole, hurtling headlong into the unknown. But PW, ever the adrenaline junkie, was hooked from that moment on. Presently, standing on the steps of the Sheldonian, he reached out and caught a snowflake delicately on his fingertip. “Your blerrie country,” he said instead, just for something to say, as he and Alice stepped outside, “snows at the height of summer.” Alice merely shrugged, her eyes fixed on the snowflake melting on his fingertip. “It’s always snowing somewhere in the world in June, Professor, so why not in Oxford? We just have to rotate space, tilt it away from the sun, right? Then we enter wintertime in June here.”

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PW wanted to say something in rebuttal, for she had turned everything on its head with what she had just said. Again! Everything she said seemed to turn things upside down, including his brain. He wanted to say to her that we can link two events happening in the same place at a different time - we can predict what will happen in the same place but at a different time - but we cannot predict what is happening at the same time in a different place. Because in a different place, time might be totally different, depending on the gravita15

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tional force experienced in that place (as well as other factors). Gravity is a huge deal yet we take it for granted, most likely because it never changes in our world. It is always the constant in our daily life. You jump, and it brings you down to earth at a speed of 9.8 metres per second. You never fall up, because gravity doesnâ&#x20AC;&#x2122;t do surprises in our world. But in the weird and very real universe that our world sits in, gravity doesnâ&#x20AC;&#x2122;t make things fall downward every time at the fixed speed of 9.8 metres per second. In Wonderland, which models our universe very aptly, events are more perplexing. For example, gravity is not constant and nor is it predictable in Wonderland. When Alice tumbled down the deep rabbit hole that resembled a well, her descent was slow enough for her to read the labels on potion bottles on the shelves along the way. She even had time to reach out to grab one and drink its contents before she reached the ground. If gravity in Wonderland had been as strong as it should have been, in all probability Alice would have broken most of the bones in her 16

body from falling down the deep rabbit hole at such great speed. Thus, it was fortunate for Alice that in Wonderland, this force leaked out into the other dimensions that overlap ours, the way a blob of ink seeps through the pages of a book. And fortunately for us, we are here by the grace of gravity being just as it is. If gravity had been too weak at the moment of the birth of the universe, stars, and therefore human beings, would never have been able to form because there would not have been enough force pulling stuff together. If, on the other hand, gravity had been stronger than it is, galaxies and their stars would have collapsed into themselves; itwould have crunched up space-time like a ball of paper destined for the wastepaper basket. So, as you can see, gravity is not a straightforward force. It is geometry rather than straight lines pointing downwards. It is all tied up with space, and its Siamese twin, time. You meld space and time together, and you get this wonderful, stretchy fabric called space-time, where all magical things â&#x20AC;&#x201C; including life â&#x20AC;&#x201C; happen. The gravitational constant, G, though may not be measured with the precision of other constants, is well-defined.

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Philosophers and scientists have long debated about the nature of space-time. Do they exist independently of the things and processes in them? Or is space-timeâ&#x20AC;&#x2122;s existence totally dependent on these things and processes? Is space-time like a blank canvas onto which an artist paints her picture; does it exist whether or not the artist paints on it? Nobody quite knows the nature of this living creature all that well, only that it moves, folds, twists, and bends and has holes in it. And it does so, in order for the universal laws of nature to work as splendidly as they do. But what is known about gravity is that it distorts the fabric of space-time. If you put a heavy ball on a piece of stretchy fabric, it will warp the fabric to the extent that when you roll a small marble across the fabric, the marble will move towards the heavy ball due to the warping of the material by the heavy ball. The heavy ball deforms space-time to draw the marble towards it. In our galaxy, the sun is the heavy ball and it affects the trajectory of objects passing close to it; indeed, it even distorts the path light takes when light passes close to the sun. 18

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Similarly, you couldn’t fly in a straight line across the universe – rather, your trajectory will be curved – because of the effects of gravity caused by the lumps and bumps created by the presence of mass and energy, drawing you towards them. And this space-time, it is also known as the fabric of reality, though it is only chalk lines on the blackboard.

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A Game Of Croquet There is nothing new or radical about this view of gravity and the mixing together space and time. It is eschewed in Albert Einstein’s General Theory of Relativity, unleashed to the world in the earlier parts of the twentieth century. Before Einstein came along, space and time used to be straightforward. Space exists so that everything doesn’t happen in one place. And time exists so that things don’t all happen at once. The world ran on these straightforward laws of Sir Isaac Newton for almost three hundred and fifty years. We still use these high-school laws to land spacecraft on the moon. Reality according to Newtonian mechanics began when the infamous apple purportedly fell on Newton’s head. This was the second most momentous Eureka! moment in the history of science (the first was Archimedes jumping out of his bathtub and running stark naked down the streets of ancient Syracuse, 21

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but that’s another story altogether), because the apple that fell on Newton’s head made him realise that the same force, namely gravity, that had brought the apple falling down to earth also kept the moon falling towards the earth and the earth falling towards the sun. That explained a lot of things, but not everything. Newton’s simple laws work to high precision, but they do not work not all the time. And for a theory to be accepted, it has to be able to explain everything and works every time. Gravity was not really understood until Albert Einstein’s General Relativity almost three hundred and fifty years later, though we are far from completely understanding of this strange force. Lately, there have even been murmurs in some quarters that gravity does not exist, that it is no more than side effects of something else, born from the laws of heat and gases. But going back to Einstein, one of the first things he stated was that nothing can travel faster than the speed of light. He then mixed space and time together to come up with 22

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something called space-time, which can be warped by gravity. Einstein’s General Relativity still remains our best large-scale theory of the universe. PW taught it at Oxford. Some would go as far as say Professor PW Vanderleyden from South Africa was the successor of Einstein’s crown as The Greatest Thinker of Our Time.

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Einsteinâ&#x20AC;&#x2122;s General Theory of Relativity 1916: How it was constructed

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But the great Professor PW Vanderleyden eyed Alice warily, for she was Alice Liddell who came to his physics fiefdom via a firstclass degree in mathematics. Alice did not know that much physics, but many would argue, physics is a child of mathematics. She understood things he couldn’t, because her brain was wired differently from his. He could never understand numbers; they frightened him like the monsters from his childhood that grew larger and larger with the years. And that’s the thing with numbers: you have to face down the monsters because they will not go away. PW was shy as a boy and did not dare to speak up in class when he didn’t understand something, and so, the monsters of long divisions grew into the many-headed creatures of differentiation as well as scary-shaped beings called integration. Is everything really made of numbers? If so, he was doomed. Setting aside his troubling thought, PW said loudly, “I’m hungry. Giving lectures always makes me hungry.”

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“Let’s go for high tea,” Alice replied eagerly, clapping her hands together in delight. Though twenty years of age, she still had the appearance of a young girl with puppy fat on her cheeks and her small stature. It was as if she never really grew up despite the advancing years. PW raised an eyebrow. “Six o’clock? Isn’t that a bit late for high tea?” And then he laughed merrily, discarding his inbuilt rigidity and getting into the spirit of the moment. “I guess not. We are in Oxford after all, and I am sure The Grand Café serves high tea at all hours, eh?” The Grand Café was built on the site of the oldest coffee shop in England, according to Samuel Pepys Diary 1650, and high tea was still on the menu in the twenty-first century. It was indeed the perfect place for scones, strawberry jam and clotted cream at six o’clock on June evenings when it snowed in Oxford. In his country, they would be getting ready for dinner at this time of the day, not taking 26

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high tea. His father believed that eating after sunset was bad for digestive health. Early to bed and early to rise had been the creed of generations of his ancestors who farmed in the Eastern Transvaal. In the depths of Africa, time was not the mechanical hands on a face of a clock, but the stirring of the land and its inhabitants, namely the insects and noisy birds that collectively stretched and woke human beings up from their nightâ&#x20AC;&#x2122;s rest. Life was lived closer to the earth, on the parched land irrigated with water from ancient rivers feeding thousand-year-old baobab trees. As a boy, PW used to climb inside the trunks of dead baobab trees and be in his own magical universe. His universe inside the baobab trees was one that was populated by he alone and the colourful birds of the Transvaal, from fierce parrots to owls which laid chalky-white eggs to spiny forest birds and those with glossy green feathers and black wings with monochrome spots, all flying free in the endless African skies. But life was altogether different in Oxford. It was as if the city existed in its own spacetime, full of old honey-coloured buildings, 27

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silent quadrangles, million-dollar machines and high tea at six o’clock on snowy June evenings. “This is blerrie madness,” PW muttered. “We are all mad here,” Alice grinned at PW, her tiny teeth showing in two perfect rows. “And you must be too, my dear Professor, or you wouldn’t have come here.”

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It’s Always Six O’Clock! Alice linked her arm through PW’s and they headed towards The High. It was a beautiful evening, though Oxford was strangely deserted. It was the night of the Magdalen College Ball, and maybe that was where everybody went: to the halls for dinner, the girls getting ready to step into their ball gowns like exotic birds with flamboyant plumage and the boys shoring up their braggadocio with low-priced alcohol whilst propping up the Student Union bars across the colleges. Alice knew there would be fairy lights, fireworks and bucking broncos at the Ball. She had seen the shimmering white marquees being set up on the lawns of Magdalen that afternoon. “Why aren’t you at the Ball?” PW asked suddenly. Though they had only met less than two hours ago, they were unusually in sync with each other. It was as if their respective world-lines had entwined and become enmeshed together somewhere back in time 29

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long before this first meeting. She shook her head. “Balls are not my sort of thing.” Truth was, Alice did not have any friends to go to the Ball with, and no boy had asked her. Moreover, she was awkward in company and was often tongue-tied. PW stole a curious look at her. He did not know enough of the English language to be able to place her accent, and so, he asked guilelessly, ‘Where do you come from, Alice?” “Oxford,” she replied. “Oxford? No, really?” He shook his head a little and laughed to himself. “Nobody comes from Oxford. We all come to Oxford.” And then hastily correcting himself, PW muttered, “We all come up to Oxford. I have a Scottish postgraduate from Outer Hebrides who told me that he came up to Oxford. I told him, c’mon, man, you are so blerrie far up north in the North Sea that your closest neighbour is the North Pole and you are telling me you come up to Oxford?”

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Alice laughed. “We do indeed have our own language here.” He grinned back at her. “Tell me about it! Buttery and battels, staircase and scout, rusticated and sent down. And blerrie sub fusc. I’m always forgetting mine. I look like a blerrie giant crow in sub fusc.” He took a closer look at her. Though she had the archetypal English look, her eyes were dark and strange. “Are you really from Oxford, Alice?” “Yes,” she replied, smiling at him with those eyes. “I was born here. I lived here in Jericho all my life; that is, apart from the six months that I was away.” He looked at her curiously. There was something very unusual about this girl that he could not quite place his finger on. “Where did you go?” He asked, intrigued. “Wonderland. You might have read the books about my childhood adventures.” He was poleaxed. No, he had not read those books – he grew up in South Africa, for heavens’ sake, deep in Eastern Transvaal 31

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and spoke only Afrikaans for the first seven years of his life – but he knew of those stories, written by an Oxford Professor of Mathematics. His blerrie books were everywhere in Oxford, even though he had been dead for over a hundred blerrie years! “Ah, the girl who fell down the rabbit hole,” he teased but a sense of unease rose in his esophagus like bile as he stared at this postgraduate of his with unusual eyes and dressed in an old-fashioned dress. But maybe she was dressed for the Ball, he reassured himself, for tonight was the night of the Magdalen Ball. “Professor, I did not fall down the rabbit hole. I followed the rather strange rabbit down the rabbit hole,” she corrected him primly. What a strange girl! But then, everything in Oxford was blerrie strange to PW. He stole another sidelong look at her and her long blue dress with buttons marching all the way down her back like a row of soldiers. They had walked through the narrow, enchanted alleyways of Oxford and had arrived at The Grand Café on The High by then. Maybe it was the unexpected snow or the 32

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Magdalen Ball, but the cafĂŠ was empty apart for a table of Japanese tourists in the corner. This establishment had, over the years, been rebuilt, renovated and transformed several times. In its current guise, it was full of mirrors, which gave PW the heebie-jeebies. Through The Looking Glass somehow came unbidden to his mind, that book he often saw in bookshops all over Oxford. Mirrors brought back scary memories of his nightmares. As a boy, PW used to be terrified of monsters and dead people living in the unending netherworld behind mirrors until his Oupa told him that our reality itself is nothing but an image in two opposite mirrors. And now, at forty-two years old, he was in Oxford, trying to understand this. Alice greeted the proprietress with familiarity and led PW through a narrow passage towards the rear of the cafĂŠ, as if they were going to the kitchen or the loo. Bemused, PW followed this strange girl. The walls on both sides of the narrow passage were lined with mirrors, giving an illusion of a world trapped within a world. Again, the heebie-jeebies had sneaked up on PW and cold fingers danced down his spine. He was reminded of the old 33

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tales once again. In his culture, all the mirrors in a house had to be covered up whenever someone dies so that his or her soul does not get trapped in the mirrors for all eternity. And it was exactly for this reason that folks don’t buy old mirrors. PW looked at the many antique mirrors hanging on the walls and shivered involuntarily, Eeeee! To his surprise, the passage opened into a small room dominated by a big, old-fashioned clock. The clock’s hands pointed to a twelve and a six respectively. “That can’t be!” PW exclaimed in disbelief. “It was six o’clock when we left the Sheldonian. I know, because I remember checking my watch as we left!” He looked at his watch, and to his utter amazement, it was showing six o’clock too! “Time is not welcome here, Professor, but please do take a seat,” Alice told him. Perplexed, PW sat down on the armchair with elaborate velvet upholstery. His eyes darted round the table. All the chairs were different from one another – Alice picked an uncomfortable bar stool – and there were 34

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already teapots, teacups and saucers on the table, laid out for a tea party. “I’m sorry, some of them are dirty.” She gesticulated at the messy, haphazard table. “We just have to sit where there are clean cups and saucers. Service is not very good here, I’m afraid. The serving staff is all focused in the front parlour. Have more tea, please, Professor.” PW grinned. “I can’t have more tea, because I haven’t had any yet. See, there’s nothing in my cup.” When PW was a boy of six or seven, he often sat on the stoep at night and wondered what his lunchbox would be filled with if he were to take it to outer space, open its lid and scoop up whatever was surrounding him. What would be in his lunchbox? If he did it here and now, he knew the box would be filled with air, but what if he were to go to outer space? Would he be able to fill his lunchbox with stars? Oupa told him that, if he did not go out far enough, the box would still only be filled with air, though air is in itself interesting. But PW did not want air. So Oupa 35

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replied, if they could get so far away from the heavenly bodies and nebulae, they could fill the box up with â&#x20AC;&#x153;interesting thingsâ&#x20AC;?. As a physicist, he now knew that the interesting things Oupa had alluded to would make an invisible soup of low density atomic particles, neutrinos, electromagnetic radiation, magnetic fields, cosmic rays and the mysterious dark energy. But right now, he just wanted some tea in his rather large bone china teacup.

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“Take some more tea,” the March Hare said to Alice, very earnestly. “I’ve had nothing yet,” Alice replied in an offended tone, “so I can’t take more.” “You mean you can’t take less,” said the Hatter: “it’s very easy to take more than nothing.” ― Lewis Carroll, Alice in Wonderland

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Six Impossible Things Before Breakfast PW shook his wristwatch - a present from his Oupa - but the hands refused to budge even a little. And through the skylight above the small tearoom, he saw snow falling abundantly from the ink-black skies. He looked round the room wildly, and saw that the assortment of pictures that hung on the walls were all askew, as if someone had gone round the room messing them up for a joke. PW jumped up to his feet. No, this can’t be happening! The girl, the clock, and now this! He looked down at the floor and noticed that it was slightly tilted. “Dit is mal!” He exclaimed. This is crazy! “The world and the whole universe, are crazy, Professor,” she chided him gently. “You 38

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should know, you teach it. Snow in Oxford in June. You think it’s crazy? I told you, it’s just a case of rotating 3-D space, all part of the movement thing you are so fond of. Your sea squirts. To move is life, remember? So if sea squirts, human beings, and all creatures in between sea squirts and human beings can move freely, why not the space we live in? That’s what we do in Wonderland. Sometimes, it is the space that moves instead of peoples and clocks.” PW was perplexed by the concept of moving spaces, especially floors that looked as if he had drunk a gallon of moonshine. When he was a boy, he had asked his Ouma, “ Did God make everything?” Ouma had replied yes in her uncompromising manner, but her answer did not satisfy the young PW. “But Ouma,” PW had persisted doggedly. “If God made everything, what did He stand on then before He made the floor?” PW’s brain raced feverishly as he thought 39

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back to that conversation with his Ouma of long ago. So what did God stand on? He couldn’t take his eyes away from the tilted floor that his feet rested on uneasily. “Quaternions,” Alice said gravely, observing the queasy look on PW’s face. “Discovered a long way back. In 1843, actually. They are stunningly beautiful. Unreal stuff, many great brains thought at that time, but guess what, we use quaternions a lot for rendering digital animation these days. Even your smart phone uses quaternions to figure out its orientation; flip your phone and the quaternions get to work frenetically. Oh, we can have lots of fun with rotation of space, my dear Professor, on paper and also in the real world, because as I have said over and over again, movement is an illusion.” PW sat down. “What is the meaning of this?” A quaternion is a complex number of the form w + xi + yj + zk, where w, x, y, z are real numbers and i, j, k are imaginary units that satisfy certain conditions, and provides a convenient mathematical notation for representing orientations and rotations of objects in three dimensions (to rotate objects in three dimensions, we need a four dimension number, hence the name quaternion). Pure quaternions have properties similar to ordinary three-dimensional vectors. As a matter of fact, quaternions were discovered before vectors, but when vector operations were defined, quaternions were largely buried.

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He gesticulated his hand wildly around the room that seemed to have rotated on itself by several degrees, with mirrors, pictures and shelves askew, as if to illustrate Alice’s point on blerrie quaternions. PW fixed his eyes on the large, silent clock which stared back beadily at him. At least the clock was straight and righteous, though it told the wrong time. ‘You’re turning my brain upside down, Alice. You have been doing just that from the moment we met.” He cast her a surly look. “And not in a pleasant way, either. You are blerrie mad.” “All the best people are, my dear Professor, as I told you before. Because the quantum world that we live in is indeed very, very mad. To make sense of it, it seems that you must believe in six impossible things before breakfast,” Alice said gravely, and then with the seriousness of a zealous postgraduate, she continued, “You taught us that there is no up and there is no down in the universe. Up and down exist only for us. We need one absolute point of reference for up and down to exist, like more and less relative to something. But that absolute point of reference 41

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does not exist, does it Professor? Who says floors have to be flat on the ground, or indeed, on the ground. Ditto time. You taught us that fundamentally, time does not exist. It exists only for us.â&#x20AC;? What is time, away from the physics and mathematics?

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“Alice: How long is forever? White Rabbit: Sometimes, just one second.” ― Lewis Carroll, Alice in Wonderland

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Time is the passing of seasons, the waning and waxing of the moon, the flow and ebb of time and children being born, skins getting wrinkled and weary human organs shutting down. It is the heartbeats, moments, seconds, minutes, hours, days, months, years and decades that we lived through, like the stills of old-fashioned negatives run through a projector to make a movie. PW thought back to his honeymoon of twenty-two years ago with the nineteen-year-old girl he married in the small church in the middle of the veld. In his culture, back in those days, people married young. You marry your first love and stay together until you die, and this concept was very fine with PW. He had known her, his wife Karin Van Achterberg of Eastern Transvaal, for almost all his life. When he was about four or five-years old and she a toddler, the Van Achterberg family had moved into the homestead next to his. They had inherited the smallholding with the happy house called Sondela, which 44

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meant Welcome, come in! in Zulu. PW had great memories of the times he spent in Sondela as a boy, eating condensed milk from the tin and koeksusters in the cosy kitchen, and adoring Karin with all the love his boyish heart could hold. For I have always loved Karin. Karin of Eastern Transvaal. He had immortalised that sentence in every single book he had written. The passage of time had seen Karin grow from a young girl playing with dollies with his sisters into a matured woman nearing forty-years of age and the mother of his three sons. He realised with a sudden pang that she had become a stranger to him in the intervening years, in the years that he crossed oceans and vast tracts of land seeking the meaning of life. Now, it seemed like they didnâ&#x20AC;&#x2122;t even speak the same language. But maybe Forever-Love is like that; it flows and ebbs like the tide but always same-same. PW felt a sudden longing to be home with his wife, to renew his closeness with her all over again, to have her head resting on his chest, listening to his heartbeats as they slept in each otherâ&#x20AC;&#x2122;s arms. Because what is 45

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the meaning of life other than the passage of time counting down to last minutes of this finite life, without the heartbeats of our loved ones to give meaning to the years? For PW, his wife had always been his absolute point of reference. She was his six o’clock in a world of quantum uncertainties. Sensing PW’s melancholy, Alice said quite loudly, “Whatever you start with, that’s what you’ll end up with. Ashes to ashes, dust to dust. That makes life easier to fathom, doesn’t it, Professor? In fact, this is an is incredibly useful way to think about time, and everything in the universe: imagine how much trickier it would be to manage your time if the total number of hours in the day changes constantly and is not conserved at twenty four. There has to be some order at the heart of chaos, eh?” She grinned mischievously at him. “Don’t lose sleep over it though, Professor, for one of the few certainties of life on earth is that all is conserved. As my old friend the Mad Hatter would say, ‘It’ll all come out in the wash’. Or at least, they appear to be.” 46

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Ah, that made PW’s head hurt. The numbers involved in everyday life are so huge that fluctuations are easily absorbed without us noticing the little blips. Time, if there was such a thing, had been going for 13.8 billion years, or thereabouts. People started using numbers when life got too complicated to be counted with fingers and toes. There are so many zeroes these days. So twenty-four hours is rather puny by comparison. You wouldn’t notice it. It’s rather like a drop of dye in an ocean of seawater. But take twenty-four hours down to the quantum world where events happen at the nano-second timescale and you begin to see just how crazy it is trying to figure it all out from one end to the other. PW sighed. “That’s always the big problem when we try to bring the very large and very small together within the same framework. It’s like talking about bugs and blerrie hippos in the same breath. I was helping my son Piet with his schoolwork, and you know, it is impossible to draw bugs and hippos in proportion to each other on the same piece of paper? In physics, we encounter the same problem. 47

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The set of equations to describe the cosmos clashes so blerrie badly in form and in content with the ones used to describe what’s happening at the smallest scales. Relativity and quantum theory. Yet both are about the same blerrie universe!” Einstein’s theories of relativity remain the best framework we have for describing the universe at large. It also covers that perplexing force called gravity, which we still haven’t figured out in its entirety yet, even after all these years of trying. But to Einstein’s big hippo is the tiny bug, namely quantum theory to describe the world at the minutest scale. PW had to fit the hippo and the bug on the same piece of paper to win the Nobel Prize for Physics, the Holy Grail that he had spent the last twenty-two years chasing without an end in sight. PW’s fist thumped the table unexpectedly, making the teacups, teapots and saucers jump. “They just don’t blerrie fit!” His sudden, uncontrolled outburst reflected the many hours he went round and round in his head trying to find a bridge between the two discrete realms 48

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but coming face-to face with an insurmountable brick wall instead at every turn. He hated not knowing the way, though not knowing was what that drove him, from the days when he was a little boy who asked his Oupa what lay beyond the universe. PW wanted to make the small bug disappear from the face of the earth so that he didn’t have to worry about his drawing not fitting on a piece of paper. Before its inception, there was an uneasy truce between Newtonian mechanics and Einsteinian relativity, and the universe was somewhat peaceful. Things sort of fitted back in those days, though admittedly, the fit between the two world-views was far from perfect. But like Pandora’s Box, once opened, the wave functions of quantum theory flowed out and gave civilisation too many amazing things in its wake – lasers, smart phones and quantum computers to name but a few – thereby changing people too irrevocably for it ever to be unwritten. Like the bell, it cannot be un-rung once its music had been heard; it was the impossibility of putting the one thousand butterflies back into the tiny 49

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cardboard box that once housed its one thousand caterpillars. No, PW didn’t quite know how to deal with quantum theory. Quantum theory is more often than not at odds with common sense and with the certainty of the everyday world we live in. For the boy who grew up in the veld, magic was to be found in living things – in the vivid sunsets, colourful birds and thousand-year-old baobab trees – rather than in non-existent numbers and unseen phenomena. How is it possible to be in two places at the same time? How is it possible to be in one place and then in a blink of the eye, magically appear in a totally different location? How is it possible to influence each other simultaneously from afar, without any form of connection? How is it ever possible to be alive and dead at the same time?

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Yet these are all tenets of quantum theory. Heck, there is so much quantum weirdness that no one understands! PW comforted himself with that thought. It’s all blerrie crazy! It’s a blerrie crazy world we live in. But if there is no up and no down, then what is crazy and what is sane? He took a sip of the cold milky tea in an oversized baby-blue teacup with multi-coloured polka dots. “Yissis!” He exclaimed in disgust. “This tastes like blerrie washing up water! Do you have sugar?” ‘No, but have some treacle instead.” PW settled back into the big armchair, drinking tepid treacle tea and commented, “Life was simpler when we all believed in Sir Isaac Newton’s laws, when there was nothing else. Then, the world ran like clockwork, tick tock tick tock, to the hands of some heavenly clock. Newton treated time like the solid walls of the house.” “Haha, I know why you like clocks!” Alice 51

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teased PW. “It’s all about movement, isn’t it? Like your sea squirts. Some parts must always move in clocks, be it an oscillating quartz crystal or the ejection of a particle from a radioactive atom. Either, any which way, there must be movement. But my dear Professor, motion is an illusion. To try to catch anything would be like catching infinity.” She stood up with flourish and PW stared at her with great interest. What is she up to now? He wondered curiously. With deft fingers, she unraveled the black velvet ribbon from her hair and tied one of its ends to the handle of a large, pink teacup with hearts painted all over it. She got up and went round the table looking for an identical teacup from the medley of un-matching ones that were strewn across the table haphazardly. When she found the teacup’s identical twin amongst the rabble, she grinned triumphantly and attached its handle securely to the other end of her ribbon. She then climbed onto the table, being careful not to step on any of the china crockery 52

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and cakes sitting on the saucers. Holding the midpoint of the ribbon delicately between her thumb and forefinger, Alice began swinging the two cups over her head. Round and round the cups went, like helicopter blades above Alice’s head, pulling the ribbon taut. At one stage, the teacups were going so fast that PW got worried that they were going to break free from their velvet tether and fly off across the room. “Slow down,” PW warned Alice. The teacups went on spinning round and round in their fixed orbit, a blur of pink in the colourful, charming room. But Alice merely grinned at him. The teacups were spinning ever so fast over her head. “Slow down?” She laughed gaily. The teacups were going faster and faster. “But my dear Professor, they are not moving relative to each other, are they?” PW’s eyes were drawn to the length of Alice’s velvet ribbon. It was taut and constant, holding the two teacups at a fixed distance from one another as they flew round and 53

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round in their fixed orbit. He held up his hands in mock surrender. “OK, OK, you proved your point! Motion is relative. The teacups are not moving relative to each other.” Slightly breathless, she caught the teacups deftly in her hands, bringing an end to the illusion of motion. She bowed mockingly at him. “At last, my dear Professor!”

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“But relativity does not seem to work on me in this instance. Time might have stood still in this room, but my gut has not. I am blerrie hungry! I could eat a blerrie rhino!” “I am sorry, Professor, but there’s only cake here, and they’re a bit stale. The shop may have run out of scones, jam and clotted cream as I saw the Japanese tourists ordering a rather large number of those when we came it. Perhaps we should wander down The High and see what we can find there?” ‘Good idea!” PW enthused and stood up. He didn’t really fancy being in this claustropho55

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bic little room for a minute longer if he could avoid it. He was far too large for this twee room, standing at six feet and five inches tall. Reading his thoughts – again – Alice grinned at him and pointed at an array of colourful bottles sitting on the wooden shelf. Each bottle bore a handwritten label around its neck that read, ‘Drink Me!” “Any one of those will shrink you,” she told him. “It might make you feel more comfortable in this room.” “I don’t want to be shrunken, thanks,” he answered hastily. “Now, now, Professor, that’s what ignorant people say. Your absolute size doesn’t matter ultimately, does it? Ultimately, it is the relative proportions of your body parts that matter. You’d be no good if your head is too small or if your legs are too long,” she gave his long legs a pointed look. “If you understood mathematics properly, you would know this. But we’ll leave that for another day, shall we?”

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She wanted to say, I may be small in stature, but my love for you is greater than the love your tall wife has for you. Instead, she fumbled into her purse and retrieved some coins. She left £4 on the table. PW eyed the money quizzically. “Well, it is not civil not to pay for one’s tea, is it?” she retorted. These blerrie English, PW thought to himself with a shake of his head, I’d never understand them in a million years. “OK, I’ll buy you a kebab,” he grinned easily at her instead. “I was rather hoping we’d go to the Fowl & Foetus,” she replied primly, closing the clasp of her purse with a decisive snap.

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“Would you tell me, please, which way I ought to go from here?’ ‘That depends a good deal on where you want to get to,’ said the Cat. ‘I don’t much care where -’ said Alice. ‘Then it doesn’t matter which way you go,’ said the Cat. ‘- so long as I get SOMEWHERE,’ Alice added as an explanation. ‘Oh, you’re sure to do that,’ said the Cat, ‘if you only walk long enough.” ― Lewis Carroll, Alice in Wonderland

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Cats’ Tails: Cheshire Cat & Schrödinger’s Cat Outside, it had stopped snowing and the night was crisp and cold. PW shivered in his thin summer jacket and wondered why Alice was impervious to the cold, seemingly in a world of her own, in a place where life played by its own rules. Maybe her world, a multiverse of all possible worlds, was someplace that had no rules and no laws, or conversely, her world could well be the birthplace of all rules and all laws. But what are rules and laws? The laws of physics gave us our universe whose laws it itself abides. In his flashes of insight, PW had seen the solid foundations and mega structures of the universe crumbling into dust that blew away in the strong Transvaal wind. And in these vivid dreams, he had stood there in the sandstorm until there was nothing left but emptiness. Eventually, even the fine threads that held everything together returned to their 59

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pre-creation state, namely to nothingness. But PW knew that there was more to nothing than meets the eye. She, Alice, stood in the epicentre of the universe’s 0, telling him this: “So long as the potential is there, life will always be trembling at the edge of creation. Because it was from nothing that everything and all possibilities were created.” By their own volition, Alice and PW’s feet turned left on The High and took them towards the River instead of through the back alleys of the city towards The Eagle & Child pub. By turning left instead of right took Alice and PW into a completely new reality. Events of the night would have turned out rather differently had Alice and PW chosen to turn right on The High, which they did in the mother-book, Catching Infinity. Indeed, how many times in our lives have we wondered, what would have happened if we had taken the left turn instead of right; what would have happened if we had stayed instead of walked away?

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In the quantum world, all the infinite possibilities are poised at the scalpel-edge, waiting for a choice to be made. At that precise moment when a choice is made, all other possibilities dissolve into nothingness, and the path we choose becomes the only real one … to us, that is. Some say that the other worlds that would have existed - had they been chosen - continue to unfold along their own disparate paths, taking our other selves along in their flow. Thus, we live an infinite number of lives in an infinite number of worlds. The Cheshire Cat from Alice’s Adventures in Wonderland had come back to our reality as the cat of the physicist, Erwin Schrödinger. Schrödinger’s cat was placed in a sealed box with some radioactive material, a Geiger counter (to detect radiation) and a poison trigger. When the Geiger counter detects radiation from the radioactive material, it releases the poison and kills the cat. We only know whether the cat is alive or dead when we open the box; until the box is opened, the cat is both alive and dead. To put it simply, nothing happens until someone looks, until someone makes something happen, and until then, Schrödinger’s cat exists in ma61

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ny-worlds where it is both alive and dead simultaneously. So yes, your every decision matters, because it is up to you to create what happens next. Note: This was just a little thought experiment and the fate of SchrĂśdingerâ&#x20AC;&#x2122;s cat remains unknown right this moment in time. We can only talk about probabilities until an observation is made.

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“Well! I’ve often seen a cat without a grin,’ thought Alice ‘but a grin without a cat! It’s the most curious thing I ever saw in my life!” ― Lewis Carroll, Alice in Wonderland

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Maths Is Magic PW wanted to mention this to Alice, to tease this thought out with her, but half-suspecting an equally incomprehensible or nonsensical rejoinder, he asked instead, “Is everything really made of numbers, you think?” Mathematics was PW’s weakness for he had never really understood it. For years he had managed to stay in the game by the grace of his one true gift, which was storytelling. He had sought exciting, new knowledge from those who really understood the heart of the matter – like Alice – and exploited their brilliance with his gift of creating strong, believable and attention-grabbing parables out of the filched knowledge. Without language, numbers make no sense whatsoever, he would retort defensively whenever challenged, a line of thinking that he had carefully developed over the years. In his defence, he had used his gift to build co65

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operation between disparate research groups in several different countries and had produced some of the most awesome results in theoretical physics, results which brought humankind one step closer to understanding itself. But this girl, she knew! “Why do you fear maths, Professor?” She said guilelessly. PW hesitated for a moment, and decided to be candid to Alice. He was tired of pretending after all these years. And so he began telling her. He was seven years old again, back in the hot airless classroom. Numbers scared him, because there could only be one right answer. No maybes. No what ifs. No “possible”. Just right, or wrong. A wrong would earn PW a painful rap on his hand with the wooden ruler followed by being made to stand in the corner facing the wall wearing the dunce’s cap. The humiliation of getting the wrong answer was often carried into the playground, where his classmates for being stupid hurled abuses at him. His father would hit him with the sjambok for being 66

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stupid. Thus, PW had always been afraid of numbers, very afraid indeed. And the worst thing about maths is, if you fall behind, you stay behind. “It’s silly, rite?” he said with a self-deprecatory shake of his head. “Numbers are after all just 0 to 9. Just ten blerrie fellas, rite?” Alice smiled up at him. How she wanted to hold him in her arms and comfort him. But she mustn’t. Yet. For she was only twenty and had never been kissed. “No, Professor, just two, actually. 1 and 0. You can reduce your ten bloody fellows and everything else to 1 and 0. The whole universe is built entirely on 1 and 0, don’t you know? You teach it, after all. Everything we have in 4-D, we can compress it into 1’s and 0’s, just like when we take a 2-D photograph about a particular event in time and store it in our computer. And when we delete that graphics file, we scatter the 1’s and 0’s back into circulation in the universe again, to be reconstructed in other combinations at future dates.” She grinned at him. “So yes, reality exists in numbers. 67

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“You said before, movement is life. You talked about sea squirts moving until they find the perfect spot. I don’t know what sea squirts look like, but when I heard your words, I saw instead the beautiful calculus behind it. I saw movement thorough the oceans. The sea squirts must have followed the gradient of their senses, or the direction that gives the highest rate of increase, to take them to wherever they felt compelled to go. That’s calculus. For calculus is the just language of change, not some scary entity of your childhood nightmares.” PW closed his eyes and sought out his inner eye, as Alice had taught him. He saw, within him, the hues of the sea, from the palest blue to the darkest turquoise, its colour changing frame by frame, getting progressively deeper. That was calculus. “The great Galileo himself said ‘the great book of nature is written in mathematical language’, adding that ‘its characters are triangles, circles and other geometrical figures, without which one wanders in vain through a dark labyrinth’, didn’t he?”

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Alice shrugged and smiled tenderly at PW. How sweet he is, she thought, like a small boy seeking to please. “And before Galileo there were Pythagoras, Archimedes and Euclid on algebra and geometry, five hundred years before the birth of Christ. But numbers are just numbers, my dear Professor. Don’t place too much importance on them. Yes, I know, the language of our universe is written in numbers, but numbers come down to nothing. 0=0, Professor….pooooft! All disappears! It’s like the Cheshire Cat. It’s there all the time; it’s just that sometimes, we don’t see it. It’s a bit like negative numbers, like what does it mean to subtract five hippos from three hippos.”

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“Mad Hatter: “Why is a raven like a writing-desk?” “Have you guessed the riddle yet?” the Hatter said, turning to Alice again. “No, I give it up,” Alice replied: “What’s the answer?” “I haven’t the slightest idea,” said the Hatter” ― Lewis Carroll, Alice in Wonderland

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Uncommon Nonsense “Will you play a game with me?” Alice asked PW. He nodded, brimming with curiosity. Ever since meeting her, PW had been on fire. She removed his scarf and used it as a blindfold to tie it round his head. She began spinning him round and round. Whoa! He got nervous, because they were standing on The High, and there were cars going by. He was wearing a dark suit and he was afraid the drivers wouldn’t see him if he were to stumble onto the road accidentally. He didn’t particularly want to be run over by a car, or several cars. But just as he was about to ask her to stop spinning him round, she stopped and pulled off his blindfold. He staggered momentarily, and like a drunk, he first saw spheres of light 71

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of varying sizes and luminosity when the blindfold was removed. Sphere upon sphere, one into another, endless and infinite, illuminated from within. The spheres then dissolved into irregular shapes before evaporating into the thin air, as buildings, streetlamps and familiar things came back into focus … including Alice’s face with its dark unreadable eyes, as the last of the ethereal spheres dissolved into the night. Alice watched the play of emotions across PW’s face and their eyes met. Though she had never met him until this evening, she had loved him since she was fourteen. “Magic!” He exclaimed. “Open any maths book and most of the equations in it don’t correspond to what you have just experienced, nor to any tangible object or physical process,” Alice commented, striving for composure whilst her heart thumped like the beat of African drums. She passed a hand, which was not quite steady, lightly over PW’s eyes. “See with your inner eye, my dear Professor. Your inner eye is in you. The two eyes sitting in your eye 72

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sockets are just the megapixel digital cameras that connect to the billions of neurons and trillions of synapses in your brain. And when the neurons and synapses fire up, thatâ&#x20AC;&#x2122;s when magic happens. If you close your eyes, go inside yourself and use your inner eye, you see the fireworks. You see the neutron stars and the supernovae happening all around you, within you.â&#x20AC;? They were at the Bridge by Magdalen College and there they stood, looking at River Cherwell. He stared into the river in silence. From here, they could see and hear the revelries of the Magdalen Ball in full swing, but it was the strong essence of the Magdalen Deer Meadow beyond that drew their deepest awareness. PW was beginning to use his inner eye that Alice spoke about, and he saw something infinitely more magical beyond the fairy lights and colourful dresses of the Ball. He saw a violet land shimmering in the luminescent glow of the moon. For though it was already early summer, the greenish-purple flowers were still abundant in the meadow that year. The Snakeshead Fritillary has been growing here since 1785, and once its flowering season is over for the year, deer 73

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are moved in for the summer and autumn months. “My dear Professor, you don’t really understand gravity and Einstein’s General Relativity, do you, because you don’t really understand geometry. And you don’t really understand geometry, because you are fearful of mathematics.” They began walking towards the meadow. A sweet scent assailed them. “Let’s start with 0,” Alice began. “It’s the most beautiful number of all, because the whole universe is contained within it. The early Greeks and Romans thought it self-evident that zero did not exist. It took thousands of years for its existence to be recognised. Isn’t it obvious that nothing can’t have existence?” She paused for him to process this before continuing, “Thus, you need to make that insightful leap, Professor, from this prison of a framework that you hold so dear into Wonderland, which is the real universe in its full glory.” “How do I do that?” He asked. 74

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She paused before replying. PW bent down to pluck a Snakeshead Fritillary and brought the flower to his nose. There was something about Oxford, about its enchantment. Like right now, walking in Magdalen Deer Meadow close to midnight with this child-woman in a field carpeted with eerie, purplish flowers. The flowers’ distinct shape resembled the bells once carried by lepers to announce their fearful presence. “You have to forget you were ever the plasjaapie from Eastern Transvaal who was humiliated by his teachers and peers for not coming up with the right answer. Numbers are just numbers. Yes, numbers do tell us things about the universe that we did not know, but to glean higher knowledge from numbers, you have to feel with your intuition. You need to be reflective. And ambitious. Like seeing with your inner eye.” She continued, “Let’s try, Professor. Let me tell you something about geometry. It is nothing more than a study of points, lines and circles in the plane. And it’s beautiful. Geometry is all about symmetry and beauti75

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ful shapes. Like the snowflake you captured on your fingertip outside the Sheldonian earlier this evening. Chances are that the snowflake was a six-fold hexagonal star, simply because of the way water molecules join together when they freeze, their unique shapes determined by temperature. You don’t need equations to understand that. Don’t get lost in the numbers. It is just this: a thing is symmetrical if there is something you can do to it so that after you have finished doing it, it still looks the same as before.” He cast his eyes heavenwards to look at the stars above them, as if searching for the circles of light he saw on The High. Alice watched him tenderly. Maybe one day he will speak with great love of the stars hanging above Oxford as he did about those in his beloved African skies, Alice hoped, to give immortality to this magical night. “The universe, in its entirety, is symmetrical. It is more or less the same whichever way and whatever direction you look,” she said softly. “Life runs on symmetry, from the biology of a virus, due to its symmetrical shape, and the growth pattern of pine cones, 76

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to the behaviour of elementary particles and the clustering of galaxies, to smart phones and the Internet. Thus, if we understand symmetry, we begin to understand life, because from this sphere, we grow. “I want to tell you why this is important, Professor. Look into the skies and see what’s up there. Because shapes and geometry, gravity and physical forces, collectively hold the answer you are seeking. The answer is in the way they come together. From water molecules arranging themselves to give symmetry to snowflakes, to the cluster of stars forming galaxies, all of them are products of nature’s formula sheet. The shapes and symmetry that you see, sculpted from the dance between gravity and its opposing force called cosmic expansion, hold within them what you seek. That’s why human beings are intuitively drawn to nature, the reason why you talk all the time about stars in the African skies, wildebeest in the veld and thousand-year-old baobab trees. “Earlier this evening, during your lecture in the Sheldonian, you said, human beings are a species that needs and wants to understand 77

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who we are. But later, in The Grand Café with me, you talked about the impossibility of fitting a hippo and a bug on the same piece of paper if you were to draw both to scale. Forget the paper and the computer. Go back to nature, my dear Professor, and use your inner eye to see the snowflake that you held on your fingertip on the steps of the Sheldonian and the superclusters of galaxies out there. Close your eyes and see.” PW closed his eyes and he saw. At last, he was beginning to see. “A circle is less scary if one doesn’t think of it in terms of πr2, 2πr or trigonometric functions, hey?” He looked at the round moon high above them in the Oxfordshire firmament and added, “My Oupa used to say, the world is round, so that all human beings can be from the same family. I didn’t believe him, of course, but I kinda want to.” Symmetry, circle, family, love. The way space and time fold up into themselves – the so-called warping of space-time – all solely for the purpose of obeying the universal 78

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laws. Oh, he is so sweet, Alice thought to herself. He remained the six-year old plasjaapie from Eastern Transvaal beneath his expensive Savile Row suit, still struggling with maths lessons in his backwater school in the Eastern Transvaal. But lessons are called lessons, because they lessen each day, until the ultimate truth â&#x20AC;&#x201C; which is simplicity â&#x20AC;&#x201C; is revealed in its stark glory, within the heart of terrifying numbers and breathtaking shapes.

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Madness Of The Red Roses In the beginning of chapter eight in Alice’s Adventures in Wonderland, Alice stumbled upon three gardeners painting the white roses that grew in the royal garden a vivid shade of red. “Would you tell me please,” she asked. ‘Why are you painting those roses?” The gardeners, who had planted the wrong type, were performing this ridiculous task of painting roses red to appease the Queen and therefore (hopefully) avoid decapitation. The universe we live in is but an illusion, a holographic projection. Look at the strip of hologram at the back of your credit card and its play with light to understand.

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The world is an illusion.

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In The Magical Garden Snakeshead Fritillary, not red roses. Alice and PW sat down on the meadow, amongst these ancient flowers of England. He had taken off his light summer jacket and laid it on the grass for her to sit on, an affectation he had adopted since moving to Oxford. He had watched the film Shadowlands many times, enchanted by the romance of Oxford and the love affair between another Oxford academic, C.S. Lewis, and his Joyce. Oxford and life here were literally a universe away from his existence in the Eastern Transvaal, and PW was beginning to fall in love with its shimmering meadow, silent river and dreaming spires. As they sat in silence on Magdalen Deer Meadow that June night, a meteor shot across the night sky in a blaze of colour. PW instinctively genuflected himself and then laughed self-consciously as he felt Aliceâ&#x20AC;&#x2122;s 82

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eyes on him. “Shooting star,” he shrugged self-deprecatingly. “Make a wish and your wish will come true.” Those dark eyes of hers regarded him steadily. “What did you wish for, Professor?” “I can’t tell you! If I do, my wishes won’t come true!” He had, at the height of folly and crazy impulse, wished that he could kiss this girl just this once. He wanted to taste her wide lips and know her adolescent body, just as he was beginning to know her deep, fathomless brain. He wanted to plunder her, if only for one blerrie crazy Oxford night. She knew what he had wished for, for those eyes of hers ate him up slyly, daring him to make his wish come true. He decided to tell her a story instead. “My Oupa came from faraway,” PW began deeply, his consciousness reaching for the safety of the familiar shores of his childhood. “He came to South Africa to work in the mines of Luanshya. He was full of mystery, like the man from nowhere. He didn’t 83

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bring much with him, just his Bible and a very small cloth bag; you know, the type of purse tied with a leather string. The small bag was filled with little stones, and each stone was of a different shape and a different colour. My brothers and sisters used to play with Oupa’s stones. It seemed like Oupa had spent his entire life collecting them. “Tell us where these stones come from,” we would ask, and each time, he would patiently tell us the beautiful stories associated with each stone. He made the world sound like a very magical place. One evening, as Oupa and I were walking home from the veld, I saw him genuflect and bend down to pick a stone up. There wasn’t anything special about that particular stone, but as I took my eyes away from Oupa’s hand, I saw the most amazing falling star ever shooting across the skies. It was then I realised, Oupa’s stones were a record of all the falling stars he had witnessed in his lifetime.” By the time PW finished his story, the meteor had disappeared completely from the heavens above them. Alice opened her palm and in it sat the most exquisite stone. The stone had faint purplish veins from the Snakeshead 84

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Fritillary threaded into its surface. There were also specks of white in the stone, reminiscent of the June snowfall in Oxford. “We are rewriting shapes, PW,” Alice said, using his name for the very first time. “Just as we are rewriting everything we know. Atoms in periodic table that we learned at school are now being written in shapes without edges to capture their flow and their true state of being.” Nothing in the world is ever as it seems. Wonderland nonsense, unphysical sciences and arcane mathematics have all turned out to correspond to the true state of the universe. Look as hard as you may with the two eyes sitting in your eye sockets and you will never be able to find the square root of minus one. But it exists in the heart of nature, this so-called imaginary number. But imaginary numbers have been shown to be real because they describe the behaviour of elementary particles in our universe that our space-age machines are just beginning to see. And Non-Euclidean shapes, such as falling stars and Cheshire Cats that Alice talked 85

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about, have showed up as gravity that affects us all. Thus, it seems ironic to Alice that so many people are seeking spiritual experience in life when in actual fact, we are massless, ethereal beings here for the human experience. The internal war that rages within us arise from the conflict between what reality truly is and what we believe it should be. If you stop believing, it will go away. â&#x20AC;&#x153;I hope you will always think of me whenever you search for the meaning of life, PW. For I have shown you tonight that space and time fold into one other to create the most beautiful shape imaginable, all just so that the fundamental laws that keep our universe going can be obeyed, like light travelling at a finite speed irrespective of the motion of the person measuring it. This law was Einsteinâ&#x20AC;&#x2122;s Special Relativity. He put space and time together in a way that people had not thought of before, but putting space and time together is not crazy, because they are quite the same, really, if you look at life in a freer way. The only difference is that in space, a straight line is the shortest distance between 86

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two points, whereas in time, it is the longest. “Tonight, we talked a lot about shapes, because Einstein could only take his incomplete picture of the universe further when he learned some mathematics, namely the mathematics of geometry. With this new maths, he could work out the energy contained within space-time, and with that, he began incorporating gravity into this framework. Is gravity always the same? … uh, someone falling freely through space will not be able to feel his weight! When Einstein put these two tenets together a hundred years ago, he came up with our best working model of the universe. His General Theory of Relativity is the best framework we have to date, one hundred years after its conception. Its predictions are spot-on. “But gravity is yet to be fully explained; it is our last mystery. Why is gravity so weak compared to other fundamental forces of nature? I think it’s because it seeps into higher dimensions, like a blob of ink spreading through the pages of a book. Close your eyes and use your inner eye instead to see these dimensions, PW. Remember the orbs 87

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of light you saw when I spun you around on The High; the geometry of space-time acts as a lens that focus the light to give us magical images. See in these magical images the many-worlds that exist within ours. Look for the patterns in our quantum world as well as in the stars, wherever you are, for therein rests your answer, waiting. And think always of this moment and of me, PW.” Finally, PW picked up the stone that was meant for him from her outstretched palm. The stone had travelled thousands of light years – from a time dinosaurs still walked on earth - to come to him on this enchanted twenty-first century June evening in Magdalen Deer Meadow, Oxford. “That’s beautiful,” PW breathed, enchanted. It was a small piece of meteorite from the asteroid belts of Jupiter before arriving here in Magdalen Deer Meadow, Oxford. The diamonds within the stone glinted in the moonlight like a million micro pieces of hologram. The meteorite felt cool against his over-heated skin, despite the blazing fires in its past. And overtaken by an emotion larger than he, 88

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PW reached out to take Alice into his arms. He had wanted to do this ever since they stood on the steps of the Sheldonian in the light falling snow. He had wanted to kiss her wide lips and to know her adolescent body as he was beginning to know her fathomless mind, for she was the answer-bearing, mythical creature that he had been hunting for since he was a boy. In his other many-worlds, PW got up and walked away from Alice. He walked through Magdalen Deer Meadow, hundreds of Snakeshead Fritillary crunching under his feet, as he retraced his path back to The High, from thence he caught the last bus to the airport for his flight back to South Africa. But here and now, he stayed and kissed Alice. The taste of his lips on hers, his very essence, sent a thousand supernovae exploding within Alice, and she thought with absolute certainty, I know I have lived, because I have known love.

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Footnote: The mathematics of Gรถdel postulated that any sufficiently powerful system must contain statements that are true but which are not provable. This is beautifully demonstrated at that precise moment in time when love comes into being. From the inner spaces of non-existent elementary particles to the outer spaces of distant galaxies, it is all here and now, coalesced and tangible. For love is the nothingness that governs all physical and non-physical laws which compelled the universe to come into existence, quod erat demonstrandum.

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“Lastly, she pictured to herself how this same little sister of hers would, in the after-time, be herself a grown woman; and how she would keep, through all her riper years, the simple and loving heart of her childhood: and how she would gather about her other little children, and make their eyes bright and eager with many a strange tale, perhaps even with the dream of Wonderland of long ago: and how she would feel with all their simple sorrows, and find a pleasure in all their simple joys, remembering her own child-life, and the happy summer days.” ― Lewis Carroll, Alice in Wonderland

Full story in: CATCHING INFINITY by Jacqueline Koay www.catchinginfinity.com 92

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Einsteinâ&#x20AC;&#x2122;s Puzzle Let us assume that there are five houses of different colours next to each other on the same road. In each house lives a man of a different nationality. Every man has his favorite drink, his favorite brand of cigarettes, and keeps pets of a particular kind. 1. 2. 3. 4.

The Englishman lives in the red house. The Swede keeps dogs. The Dane drinks tea. The green house is just to the left of the white one. 5. The owner of the green house drinks coffee. 6. The Pall Mall smoker keeps birds. 7. The owner of the yellow house smokes Dunhills. 8. The man in the center house drinks milk. 9. The Norwegian lives in the first house. 10. The Blend smoker has a neighbor who keeps cats.

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11. The man who smokes Blue Masters drinks beer. 12. The man who keeps horses lives next to the Dunhill smoker. 13. The German smokes Prince. 14. The Norwegian lives next to the blue house. 15. The Blend smoker has a neighbour who drinks water. The question to be answered is: Who keeps fish? ... the answer is on the next page.

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Author’s Note: The answer to Einstein’s puzzle is the German keeps the fish. I hope you enjoyed it and your evening in Wonderland with Alice and PW. An Evening In Wonderland - A Brief Story Of Maths, Physics & The Universe is a small window into the full-length novel, Catching Infinity. The novel was inspired by my three years at Oxford and is a story of our universe, obsession and Forever-Love. It took me twenty years to write this story. It is now ready. www.CatchingInfinity.com

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“Time does not exist” – Catching Infinity

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Je liefde voor mij is de allerhoogste wet. Het is de wet die alle andere dingen mogelijk maakt. Met liefde en eeuwige dankbaarheid, mijn hart.