El Escritor Inglés: 2016

Monday, December 26, 2016

Black Swans Fly At Night

Few individuals are more annoying than those who are ‘smart after the event’. To put it more precisely, they are smart only after an event, but rarely prior to it. I am sure everyone can recall dozens of examples. Mainstream media outlets are bursting with them.

For instance, the UK’s recent pro-Brexit vote was hardly predicted before the summer referendum; but, ever since, hack journalists and self-appointed ‘experts’ have been falling over themselves to explain its inevitability. For me, post hoc wisdom verges on fraudulent. Anyone can do it. Of course, some did predict the outcome correctly and proceeded to broadcast their foreknowledge as loudly as possible, implying that ‘I was one of just a select few who, all along, could see it coming’. Even this is often disingenuous. If one makes enough predictions, however outlandish, some are statistically bound to be accurate. Does a stopped clock not tell the correct time twice every day?

The so-called ‘Black Swan Theory’ is a clever metaphor for a special type of surprise occurrence. It was first put forward by a Lebanese-American professor, Nassim Nicholas Taleb (Figure 101.1), in 1991. Taleb’s neat idea relates to a difficult-to-predict event which proves highly consequential and can be rationalized only with hindsight. Political analysts are some of the worst offenders. They explain so many events, with great authority and eloquence, as if everything were blatantly obvious from the beginning (when they never thought to say so). The 2008 financial earthquake is another excellent case in point. Before the crisis, hardly any analysts foresaw it; afterwards, almost all of them supposedly did.

Figure 101.1: Nassim Nicholas Taleb (1960-) is a former mathematical trader and Distinguished Professor of Risk Engineering at New York University’s Polytechnic Institute.

The black swan reference originates from ancient folk wisdom: black swans (Figure 101.2) were believed not to exist because no one had ever seen one. Eventually, when such birds were identified, the presumption was instantly falsified. As the saying goes, absence of evidence does not equate to evidence of absence. (That said, please read Irving Copi’s Introduction to Logic if you feel inclined to disagree.)

Figure 101.2: A rare sighting of Cygnus atratus

Taleb’s subject is a fascinating one to explore. Why, then, do black swans – the events, not the biological species – exist? I would say that nearly all individuals are hoodwinked by psychological bias, where they are more likely to accept new evidence if it concurs with their existing beliefs. Individual bias is then compounded by collective confirmation bias, because individuals tend to surround themselves with those that share similar views. Thus, even patently false or ridiculous beliefs can become entrenched.

It is said that we see only what we want to see. I would disagree: we see what we expect to see, as a result of psychological bias, whatever the extent of its veracity. If something did not exist yesterday, why be on the lookout for it today?

The night sky is full of black swans. A few will be sighted in 2017, and myriad know-alls will emerge from the woodwork and claim to have seen the birds’ invisible flight paths. I suspect, though, that the vast majority will continue to fly unseen. Some truly audacious ones might even repeatedly swoop and dive right in front of our faces – and still remain unnoticed. Food for thought, anyone (Figure 101.3)?

Figure 101.3: Do you see?

Saturday, October 29, 2016

Dying Of The (US) Light

My first visits to the United States of America, in the late 1980s, were the happiest of times. I had never felt so liberated. The summer sun shone every day; the Ohio countryside stretched to a hazy infinity; stars and stripes flags hung in silent majesty from the covered bridges of Ashtabula County (Figure 100.1); and, each night, I would fall asleep listening to the sound of crickets chirping in the grass outside. This was, quite evidently, the land of the free.

Figure 100.1: Root Road Covered Bridge in Northeast Ohio, USA

These were also the latter days of the Cold War, where the democratic, freedom-loving USA stood toe-to-toe with the authoritarian, clapped-out socialist republics of the Soviet Union. It was an easy dichotomy to grasp: USA good, USSR bad.

After two decades of reduced tension between West and East, the old foes are once again squaring up to each other. Today’s potential battleground is Syria, and Western propaganda is being ratcheted up to new levels. USA still good, Russia incurably bad – or so we in the West are being led to believe. This time, however, it is a lie.

The facts speak for themselves. The stand-off revolves around the supply of natural gas. Europe depends on Russian gas, and the USA is desperate to reduce Russian power over European nations. Two new gas pipelines have been proposed, linking the Persian Gulf to Europe. One is designed to transport gas from Qatar (where the USA has a military base), the other from Iran, a Syrian ally. In order to access Europe, both pipelines would need to pass through Syria. Understandably, Syrian president, Bashar al Assad, refused the first (Qatar) but accepted the second (Iran) (Figure 100.2). This wholly legitimate strategy reassured Russia but infuriated the USA, and Syria has since morphed into the horrific geopolitical chessboard that we see every day in the news.

Figure 100.2: The two proposed trans-Syrian gas pipelines

Since the turn of the millennium, the USA has shown itself to be a psychopathic brute on the world stage. When Saddam Hussein threatened to trade oil in Euros, as opposed to US dollars, the Americans launched an illegal war, and subsequent occupation, of Iraq. When Muammar Gaddafi proposed a gold-backed pan-African currency, in defiance of the petrodollar standard, it was Libya’s turn to be ransacked. Thanks to the USA’s megalomania, both have become failed states. Millions have been killed.

True to form, proposals to invade Syria, and remove President Assad from power, were put forward a couple of years ago. Only with Assad gone could the USA get its way with regard to the Qatari pipeline. The proposal, endorsed with mindless enthusiasm by the UK’s former prime minister, David Cameron, was rejected by people who were at last beginning to see the USA for the hideous bully that it has become.

A different strategy was demanded. Instead, but also true to form, the USA covertly armed terrorists to do their dirty work in blatant defiance of international law. Thus, ISIS was born, and it quickly turned into an uncontrollable monster. US president, Barack Obama, then pretended to change his tune: military action in Syria was necessary to defeat ISIS, he claimed. This was simply a clumsy pretext, and anyone with more than a single brain cell could see that his sole aim was in fact to remove Assad.

Under siege from ISIS, Assad consulted Russian president, Vladimir Putin, and invited Russian military assistance to help Syrian forces to defeat the USA’s proxy of murderous Islamists. At this juncture, Western propaganda went into overdrive. The evil Russians, led by the evil Putin, were now massacring innocents in rabid pursuit of their unlawful aims. How any intelligent person could believe such a transparent untruth is beyond me by some distance.

Recently, US Secretary of State and presidential candidate, Hillary Clinton, has even proposed the (illegal) establishment of a no-fly zone within Syrian airspace to resist Russian forces. President Putin, however, is standing firm (Figure 100.3). He knows that his forces have every right to be where they are, and that the USA is yet again breaking all manner of laws in order to get its own way.

Figure 100.3: The intellect gap between Vladimir Putin and his Western tormentors should be obvious to all.

Why, America, why? It is an easy question to answer, but one that pains me to admit it. This once-beautiful nation, founded by the likes of Thomas Jefferson (1723-1826) and helped on the road to greatness by Abraham Lincoln (1809-65), is in its death throes. Today, it rages against the dying of its own light. Economically, it is beyond redemption. Its national debt has doubled (to $20 trillion) in the last ten years; it has printed its precious paper currency like never before in order to stave off national bankruptcy; and a huge proportion of its inhabitants could not survive without welfare support.

Desperate predicaments bring about desperate survival measures. As the USA’s predicament deteriorates terminally, what measures might it take? On November 8th, hundreds of millions of Americans must ask themselves: Is Hillary Clinton spoiling for a fight with Russia? It is a fight she would not win, but might she nevertheless be sufficiently delusional to try?

God bless you, America.

Friday, September 02, 2016

The Spectre Of Bernoulli

I used to know an elderly man who had taught Latin in a prestigious fee-paying school in the east of England. ‘Many of my pupils,’ he recalled, ‘would wonder, quite reasonably, why they should compulsorily read a language which no one speaks.’ He smiled to himself. ‘My reply was always the same: when you leave my tutelage, I doubt that any of you will retain anything but a tenuous grasp of Latin. However, your English should be exemplary.’

He must have had the ‘dead language’ argument bowled at him from every conceivable angle for forty years; and yet, that same straight bat of his always dealt comfortably with it. Even so, I am certain that almost all students have come up against a subject which they were not only thrilled to see the back of, but also confident that they would never need to revisit in later life. I was one. I studied ‘Further Physics’ – even the name is scary – just prior to my first spell at university. One of its constituent topics – Bernoulli’s principle (Figure 99.1) – practically drove me nuts, not least because it seemed to fly in the face of common sense. Luckily, my Physics teacher, who was much smarter than he looked, forced the penny to drop just in time for the exam.

Figure 99.1: Bernoulli’s magnum opus (pardon my use of Latin), published in 1738, was the first ‘bible’ of fluid mechanics. Readers fluent in Latin will be able to translate its front cover without too much difficulty.

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That was thirty years ago. Since then, I have morphed into a multidisciplinary life scientist, and Bernoulli’s principle had, thankfully, never raised its contrary head – until this year. While sponsor confidentiality forbids me to elaborate on current research, I think I am at liberty to state that it involves something called hydraulic conductance, which appertains to the behaviour of pressurized fluids permeating biological tissues.

Like nearly all laboratory kit these days, the analytical equipment I am using is entirely computer-controlled. An ingenious microfluidics system controls fluid pressure through a digital sensor and records subsequent tiny changes in flow rate. I have spent most of this year conducting a comprehensive validation program, proving that this rather expensive toy does what it says on the tin. If I increase the system pressure, the fluid flows faster in direct proportion.

Last week, the plot thickened. If I exchanged the sensor for one with different optimal settings, the flow data came out different. According to the computer, the fluid movement had slowed. How come? Surely, given that only the sensor had been changed, it should have yielded the same results as before.

Then came an ominous ‘Eureka’ moment: Bernoulli had returned to haunt me. He had also solved the puzzle. Daniel Bernoulli (1700-82) (Figure 99.2) was a Swiss mathematician who studied fluidic movement under controlled pressure. His world-renowned principle states that if there is a pressure reduction in a system of steady fluid movement, its flow rate will increase, and vice versa (Figure 99.3). I discovered that the tubing passing through the second sensor had a larger cross-sectional area than that of the first. A-ha! This had increased the internal pressure and thus reduced the speed of flow (Figure 99.4).

Figure 99.2: The godfather of hydrodynamics

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Figure 99.3: This simple schematic demonstrates the relationship between system pressure and fluid flow.

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Figure 99.4: A theoretical chart showing my recent findings. I had initially expected the two curves to be more or less superimposed on one another. Bernoulli put me right.

As we still say in Latin: Quod Erat Demonstrandum.

Monday, August 01, 2016

The Blue Kite

There is an uncelebrated stretch of coastal road, somewhere in England, but nowhere in particular, along which I first walked half my life ago. Today, I feel the need to be here again.

A rectangular green field leads to the water’s edge. In the middle of it lies a bright blue, parachute-shaped kite. A faceless man struggles to get it airborne. A few seconds later, he tries again. He is foiled again but refuses to give up. A young girl waits, with equal patience and frustration, at his side. Her dress is the same colour as the kite. The choice was probably his.

I wander along the roadside overlooking the water. The tide is in but beginning to ebb (Figure 98.1). A few seagulls hover overhead. Alongside me, I notice a silver-coloured dog lead, twinkling in the sunlight. At one end of it is a white, short-haired terrier. It is eager, perhaps overeager, its eyes wide and tongue hanging out at the side. At the other end is an elderly man. He walks too slowly for the dog’s liking. Time passes too quickly for his own. A lone barbecue puffs away behind a striped canvas windbreak.

Figure 98.1

Beyond the field’s paved edge are some plush bistros. I count nine. Not one is more than a year old. Their terraces are empty. Further along, in embarrassing contrast, is a scruffy corner café. Lime green paint peels from its exterior woodwork. Inside, varnished chairs and tables are set in fixed rows. They look as old as I am. Most of the clientele are older still and mostly silent. On a polished shelf, behind the counter, is an old whisky bottle full of copper coins. Next to it sits a compact analogue radio. The muffled sound of Tracy Chapman’s Fast Car miraculously conveys every human emotion in less than five minutes. I sit alone and anonymously, drink hot tea from a cup with a saucer, then up and leave without speaking to anyone. No one notices.

Turning another corner, the breeze drops. I begin the feel the sun’s warmth. The war memorial (Figure 98.2) is still decked with poppy wreaths from last November. A young boy pedals by on a small bicycle with crooked stabilizers. I climb the twenty-odd steps leading inland.

Figure 98.2

Next, Berkeley or Brackenhurst? It is no matter: I know that both short roads lead to the same junction. I choose Berkeley. On the other side of a black fence, four old-timers, cacooned from the world, play bowls (Figure 98.3). The timber-framed pavilion is lovingly preserved. Their friendship is no doubt the same.

Figure 98.3

Another right turn sets me on the way back to where I set out. Near the hilltop, there stands a tall, dark-haired man. Even in khaki overalls he appears dignified. He is replacing a wooden gatepost. Everything he does is thorough. I watch him check verticality over and over again with a well-used spirit level. Across the road is a car dealer’s forecourt. Coloured balloons are tied to second-hand cars. Opposite, a small, brick-built Baptist church bears an ‘All Welcome’ sign on its closed doors. A brown paper bag drifts in front of the gates like tumbleweed. An hour has passed.

Different individuals react to, and try to cope with, bitterly sad news in different ways. Here, today, this is mine. I am back at square one and feel a little more composed. The sun is lower. Above the field, that same blue kite now soars and flutters without effort (Figure 98.4). At a certain angle, its colour matches the clear summer sky. On the grass below, the young girl now holds the strings. Her father is elsewhere. His work is done.

Figure 98.4

The circuit is complete. Everything changes with time – and yet, the essence of this place will forever remain the same.

In dear memory of Len (1934-2016).

Saturday, July 30, 2016

Bold Dogs Indeed

Take a look at the picture below (Figure 97.1). There is nothing fake about it.

Figure 97.1: Is it a bird? Is it a plane? Is it E.T. going home?

If I zoom in a little (Figure 97.2), you can see man and machine with greater clarity.

Figure 97.2: No, it is a member of the Bolddog Display Team.

Freestyle Motocross (FMX) is one of the most recent examples of extreme sports. Throughout the summer, across the UK and Europe, three intrepid riders (from Norfolk, England) are on tour, entertaining the public by jumping 25-yard (23-metre) gaps while performing mid-air stunts and tricks. I witnessed one of their many shows last week. Sponsored by Honda, ‘those magnificent men in their flying machines’ have been honing their FMX skills for more than twenty years. There is little I can add to the photographs below (Figures 97.3, 97.4, 97.5, 97.6 & 97.7).

Figures 97.3, 97.4, 97.5 & 97.6: Each stunt is more incredible than the previous one. I could not help but wonder just how many of their practice sessions went wrong.

Figure 97.7: Full details of Bolddog history and current schedule can be found at www.bolddog.com

Tuesday, June 21, 2016

Vote LEAVE

The day after tomorrow, the British people will give to the world their view of the European Union. Yesterday, a pharmacology publication, Drug Target Review, to which I subscribe, asked a group of life scientists, including myself, to offer ours (Figure 96.1). I have published a selection of replies (Figure 96.2 & 96.3).

Figure 96.1: The full list of replies can be found at

http://www.drugtargetreview.com/12470/content-type/drug-target-review-extra/eu-referendum-tell-us-think/?utm_medium=email&utm_campaign=DTR%20-%20Brexit&utm_content=DTR%20-%20Brexit%20CID_c1c69b2f7a4f418b268bfd0ea9f38c31&utm_source=Email%20marketing%20software&utm_term=CLICK%20HERE%20TO%20SHARE%20YOUR%20VIEWS

Figure 96.2: I suspect that most of the views have come from non-British scientists.

Figure 96.3: Thank you, Professor.

Without being disrespectful to my own branch of work, the future of life sciences is of microscopic importance compared with the major political issues. Former Soviet leader Mikhail Gorbachev (1931-) had it right: why has the EU leadership been so keen to recreate, with all its failings, the old USSR?

With or without the UK, the EU will one day implode, as all such vainglorious empires do. I have been willing it to happen ever since I read Margaret Thatcher’s seminal ‘Bruges Speech’ 28 years ago. When it does, the pan-European relief will be as palpable as when the Berlin wall was torn down – and millions of ordinary individuals will ask themselves: ‘How did we come to be hoodwinked and subjugated for so long?’

Let us Brits bring forward that day. Vote LEAVE.

Saturday, June 04, 2016

Next Generation Roses

When I was ten, I dreamt mainly of cricket. At thirty, I dreamt of having young cricket-loving sons to take to cricket matches. At about forty, I had two sons. Yesterday, with my fiftieth birthday just gone, I took them to their first proper game (Figure 95.1). It was not just any old encounter either: this was a ‘Roses’ match, contested by counties Yorkshire and Lancashire since 1849, and whose associations refer to the 15th-century ‘War of the Roses’. It remains the greatest rivalry in English cricket.

Figure 95.1: The ‘Twenty20 Blast’ is currently English cricket’s most popular brand.

As a young boy, cricket meant white flannels, a game of slow-building tension, and strategy and tactics akin to those from the game of chess. It was, for me at least, a relaxing spectacle, something in which I could lose myself from morning till dusk, day after day. No sport or pastime gave me anywhere near as much boyhood peace and pleasure as cricket did.

However, to quote L.P. Hartley (1895-1972): the past is a foreign country; they do things differently there. We arrived at Old Trafford, home of Lancashire County Cricket Club, on a smooth, electric ‘Metrolink’ tram, which cruised to a gentle halt right outside the ground. I know the place well – or rather, I used to. In the last few years, the ground has changed as much as the game itself. The new spectator stands are state-of-the-art (Figure 95.2). The ramshackle ‘M’ enclosure, where I watched England battle with Australia in the famous 2005 Ashes series, is long gone, and even the 22-yard pitch runs in a different direction.

Figure 95.2: If I could have seen this picture ten years ago, I would have recognized nothing.

Once inside the turnstiles (Figure 95.3), speaking to the boys became a waste of time. There was too much for their eyes to absorb for their hearing to kick in. Behind the magnificent new stands, we came across a rock band on a custom-built stage (Figure 95.4), grown men dressed as furry animals, promotional stalls, glossy merchandise stores and multiple beer gardens drenched in the 20°C evening sun. There was pre-match entertainment for all, and we made the most of it (apart from the beer).

Figure 95.3: Only £46 for tram and admission combined

Figure 95.4: Even the band performed at a frenetic pace.

At 6:30 p.m., the floodlights came on and the players – Lancashire in bright red and Yorkshire in cool blue – took to the field. Fireworks exploded from the boundary (Figure 95.5) and giant flame-throwers blasted fire into the air (Figure 95.6). We could actually feel the heat in Row 11. (I remember attending a Cleveland Indians v Chicago White Sox baseball match on U.S. Independence Day in 1989, and I believed then that American-style razzamatazz would one day prove irresistible to the English audience, if given half a chance to embrace it.)

Figure 95.5: So many outdoor events these days begin with either these …

Figure 95.6: … or these.

The greatest change, though, has been the philosophy of the game itself. Five-day Test matches, for all their cerebral and aesthetic appeal, have been pushed to one side. The requisite attention span seems too demanding for the present audience. Today’s favoured format lasts a mere three hours, perfect for today’s youngsters but way too brief for me. (At the Edinburgh Festival Fringe, I once saw Shakespeare’s Othello performed in fifteen minutes. Although very clever, and hilarious, most serious theatre-lovers would have preferred the real thing.)

My boys – along with thousands of other kids in a capacity 26,000 crowd – lapped up every high-octane moment (Figure 95.7). They waved their freebie flags and danced to Pharrell Williams’s Happy, hoping that the ‘Dance-Cam’ would project their moving images onto the ground’s two giant screens in real time. A breathless affair from first ball to last, the cricket did not disappoint. Lancashire batted first, racking up an imposing total of 204 in their allotted hour-and-a-quarter. Back in my youth, such a score would have taken at least twice as long to post.

Figure 95.7: Party time in Stand ‘B’

After a fifteen-minute break, Yorkshire chased the total (Figure 95.8). Only the sublime Joe Root, arguably the world’s best batsman today, offered resistance, scoring an unbeaten 92 runs, albeit in vain. The excitement ended on schedule at 9:15 p.m. with a convincing Lancashire victory (Figure 95.9). By 9:25, we were back on the southbound tram – and able to catch our breath.

Figure 95.8: The names might be different – substitute my heroes, Boycott and Gower, with my sons’ favourites, Root and Bairstow – but their inspiration to youngsters to love the game remains exactly the same.

Figure 95.9: Story of an English cricket match, as told by two young brothers

Some occasions in life simply have to be memorable. Mission accomplished.

Saturday, April 30, 2016

Los Locos Vivos

I have always believed the correlation between personal wealth and intelligence to be somewhat tenuous. An email I received last week strained the link beyond its elastic limit.

Throughout the developed world, the super-rich are fleeing cities like proverbial ship rats. Chicago and Paris are cases in point. Their actions seem to conform to the narrative accepted by many observers – myself included – that world economic collapse cannot be forestalled for much longer. When the debt-based currency system inevitably implodes, civilized society might well go with it. Other possible triggers range from natural disasters to chemical, biological or nuclear incidents.

The email included a link to a website http://www.terravivos.com. This is the online home of an American company called Vivos, which specializes in the construction of elaborate underground shelters, designed to keep the insanely rich secure should surface life become apocalyptic. These well-stocked subterranean sanctuaries are fortified by thick walls and blast doors, thereby providing a full year of autonomous survival (Figure 94.1).

Figure 94.1: I have no idea who designed, built and furnished this particular shelter. I love the plastic picnic chairs. Some ‘elite’. More like the Beverly Hillbillies. Pass them there big ole sugar cookies and ginger ale, Ma!

A sensible strategy? Not according to World War Two U.S. General George S. Patton (1885-1945) (Figure 94.2), who insisted that ‘fixed fortifications are a monument to the stupidity of man’. I think he was right. First, static isolation would be dangerous: communications would be difficult; and a conspicuous, immobile target is always an easy one to hit.

Figure 94.2: General Patton knew, from a lifetime of military service, that mobility and manoeuvrability were crucial to survival.

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The longer I thought about it, the more convinced I became that any such structure would be an underground prison, with the term of confinement possibly becoming a life sentence. Combine the inevitable cabin fever with a well-established sense of entitlement, and I expect most of them would go stir crazy within a week or two (Figure 94.3). I once lived in a gated community, long enough to learn that the real dangers come from within the gates, not beyond them.

Figure 94.3: Back in 1991, I was given a guided tour of this British nuclear submarine, HMS Unseen, in dry dock at Birkenhead’s Cammell Laird shipyards. My submariner pal informed me that all potential service personnel are subjected to extensive psychometric testing to ensure that only those with infinite patience and a readiness to cooperate and compromise are considered for a life of long-term seclusion.

Imagine, then, dozens of psychopaths cooped up together in a confined space. There would be bloody murder in no time. The place would resemble the set of a ’70s horror movie. (Still, the crisis would have the potential to resolve itself quite neatly.)

I forwarded the email to a few friends throughout Europe. Here are some of the replies:

‘They won’t be able to stay down there forever. When they come up for air, you can bet the natives won’t be terribly friendly.’

‘Someone would find the air vent and pour petrol down it.’

‘They’re stupid. More money than sense = constant paranoia about the Morlocks coming over the garden wall. The company will make a fortune out of these rich dumb f*****s.’

‘What if there was a leaky tap – or the toilet broke? Plumbing skills, anyone? Oh dear …’

‘One of them developing a nasty contagious illness would spice things up.’

If these people are trying to buy a stairway to heaven, someone ought to remind them that they are going the wrong way.

Sunday, March 27, 2016

Kids’ Gravitational Physics

‘I read very, very little fiction as a kid. All the books I can remember are junior science books.’

These are the words of English writer Mark Haddon (1962-), whose award-winning 2003 novel The Curious Incident of the Dog in the Night-Time captivated my younger son, both in print and in a recent stage production. It is a story to which my son can readily relate, for he and the novel’s young protagonist share a defining trait: Asperger’s syndrome. My son even bought a commemorative Curious Incident pencil case, bearing the phrase: ‘I like Maths and being on my own.’

For this reason alone, and writing from a scientist’s angle, it gives me tremendous pleasure to see that science museums the world over are now laying great emphasis on interactive exhibits designed to captivate ‘Aspie’ youngsters, who see their world in extraordinary detail, identify patterns where their peers see only randomness, and generally analyse everything to the nth degree.

There are around fifty such science museums in Britain alone. Alongside these are play facilities aimed primarily at children, such as The Puzzling Place, in Keswick and Techniquest (Figure 93.1), based in Cardiff. I took Junior to the latter this Easter weekend. The interactive exhibits, demonstrating sound, optics, anatomy and magnetism, kept us occupied for hours. One particular piece practically mesmerized him. It was, at first view, a plastic bowl with two identical holes at its deepest points (Figure 93.2). Kids of all ages took turns dropping plastic balls into the bowl, watching carefully as each one swirled round and round, often circling one hole before switching, at the last moment, to the other. To the unscientific eye, the eventual destination of each ball was random. It was simply fun to watch a moving object with (apparently) a will of its own.

Figure 93.1: Further details are available at: http://www.techniquest.org

Figure 93.2: Watching the ‘magic’ of gravity

Junior, to his credit, saw things his own way. After studying the sweeping movements of ball after ball, he remarked: ‘Dad, why is it, when they slow down a bit, they sometimes start going round like a number eight?’

It was an astute observation. Of all the questions he might have asked, though, this was perhaps the most difficult for me to answer. Still, as Einstein once said: ‘If you can’t explain it to an eight-year-old, then you don’t understand it yourself.’

So here goes. Whenever a ball rolled deep into one of the holes, it would move along a circular path, round and round, in a downward spiral, until it disappeared from view. However, if a ball were moving with sufficient speed at a high enough point, then it might have the energy required to roll across to the other hole. Then, if it had lost too much energy by so doing, it would stay there and eventually drop through that hole. If sufficient energy remained, it might be able to switch back again, and so forth until its energy finally ran out. This two-hole arrangement is called a ‘binary system’ and plays a crucial role in gravitational physics.

Why a figure-of-eight? If a ball were to ‘escape’ from one orbit in, say, a clockwise movement, it would necessarily join the other orbit in an anticlockwise movement (Figure 93.3).

Figure 93.3: This simple graphic shows a figure-of-eight orbital pathway operating within a binary system.

The so-called Roche lobe is a region around a star, within a binary system, where the orbiting object is gravitationally attracted to that star. The lobe is shaped like a teardrop, and, when conjoined to its corresponding lobe, forms a figure-of-eight. The orbit takes its path along a line of equal gravitational potential, which is analogous to a geographical contour line or a meteorological isobar. The crossover point from one Roche lobe to the other is called the L₁ Lagrangian point of the orbital system.

Perhaps – just perhaps – many years from now, there will be a banknote bearing the image of a world-renowned scientist whose inspiration stemmed from playing with a toy of such supreme scientific elegance.