Do You Think You're Clever? (2 page)

(Law, Cambridge)

This is really a tormentor of a question! Answer, modestly, ‘no’ and of course the interviewer might take you at your word and deny you a place at Oxbridge where, naturally, only clever people are admitted (so rumour has it). Answer ‘yes’ and you risk suggesting that you are really quite a fool. For a start, the interviewer is bound to be, by virtue of his position (on the other side of the interview), cleverer than you – and by suggesting you might be on his level, you are heading for a fall! And for another thing, anyone who has too much certainty of their own cleverness is unlikely to be wise, or even open enough to learn, which is what, of course, the best students must do. And yet, if you hedge your bets with a non-committal answer, you look like someone who is too vacillating and lacking incisiveness to be an Oxbridge star …

Ever since the days of Ancient Greece, being clever has had rather negative overtones. Cleverness, according to Aristotle, was the mere capacity for figuring out how to achieve something, without the attending touchstone of virtue. It was impossible, he thought, to be wise without being good as well as clever. Plato was equally scathing, saying: ‘Ignorance of all things is an evil neither terrible nor excessive, nor yet the greatest of all; but great cleverness and much learning, if they be accompanied by a bad training, are a much greater misfortune.’ Ever since, cleverness has had the image of being a rather dubious quality, linked
with underhand cunning on one side and braggadocio on the other. Milton’s Satan was dubbed ‘clever’. So was Mary Shelley’s Frankenstein. The devil may be clever, but only angels are wise.

So admitting that you are clever can be tantamount to announcing that you are either devious or a braggart – or even a fool because no one who was wise would believe that they were clever, and no one who was really clever would openly admit to being clever. As Rochefoucauld says, ‘It is great cleverness to know when to conceal one’s cleverness’. In a hugely pompous tract on
Great Works of Art and what makes them great
, dating from 1925, F.W. Ruckstull summed up the general attitude to displays of cleverness: ‘Manet might have become a great artist, but moral myopia doomed him to remain in the ranks of trivial though clever craftsmen.’ So that’s Manet for you … Even the brilliant Oscar Wilde had to announce his cleverness with self-deprecating wit, saying, ‘I am so clever that sometimes I don’t understand a single word of what I’m saying’, which is probably the perfect answer to the question.

Of course, if the question had asked, ‘Do you think you’re intelligent?’ I might answer in a different way. Intelligence has far fewer of the negative overtones of cleverness. Cleverness is competitive. Intelligence has an image of objectivity. Yet actually, there are almost as many problems, because there is no universally agreed way of defining what intelligence is or of measuring it. Intelligence tests now have only a little more credibility than Trivial
Pursuit as true measures of intelligence, because they have been shown to be so much influenced by coaching – and the range of tests, too, is so culturally dependent. So if you were to be asked ‘Do you think you’re intelligent?’ and you answered, ‘Yes, I have an IQ of 155’, the tutor would be more likely to recommend you join Mensa than an Oxbridge college.

Of course, despite all this, my interviewer might be bowled over by the sheer panache of a candidate who said, ‘Yes, I’m as clever as you want me to be’ and then proceeded to demonstrate it with the wit of Cyrano de Bergerac celebrating his nose. After all, the clever minds of Oxbridge are already doomed to be viewed with some suspicion and envy, so why wouldn’t they welcome someone who was prepared to revel in the very thing that marks them out? According to Wordsworth’s niece Elizabeth in a little ditty from 1890, the die is cast anyway:

(Physics, Oxford)

You could answer this question in all kinds of ways – the humorous and human, the absurdly trivial or the grandly existential. But this was a physics question, so it makes sense here to address the science of formicine precipitation.

The first answer, then, might be to say that the ant, which if it’s the wingless kind can’t fly, falls to the ground – accelerating earthwards as it’s pulled down by the mutual gravitational attraction between the ant and the earth. Splat. But there is more to it than that. Ants are so small and light that their fall is considerably slowed on the way down by air resistance – by the collision of the ant with countless air molecules. So while a human skydiver can reach a maximum, or ‘terminal’, velocity of, say, 50–90 m/s, most ants are so light that their terminal velocity is slow enough for them to drift earthwards gently and for them to survive both the speed of the fall and the impact with the ground.

In fact, recent research in tropical Peru has shown that wingless worker ants are among the world’s flying, or rather gliding, animals. When an ant is dropped, it first tumbles vertically. But like a skydiver in the first stages of freefall, it splays its legs to increase drag and gain control. Eventually, by moving its legs to control direction through drag, it eases into a gentle glide at about 4 m/s. It apparently glides backwards because its hindlegs are longer than its forelegs.

The physics doesn’t stop here, though, because even in a simple action like dropping an ant, there is a complex assemblage of forces, reactions and consequences. We must remember, for instance, that gravity is a mutual force. So when you drop an ant it might fall towards the ground, but at the same time the earth is moving upwards to meet the ant. Of course, the mass of the ant is so small and the mass of the earth so great that the movement of the earth is immeasurably small, but we can be sure from other fine measurements that it really does happen. Moreover, as Newton’s Third Law of Motion makes clear, there is an equal opposite reaction to every action. So the act of dropping the ant will have its own, undetectably small, kick-back on your hand.

And as we talk about undetectably small movements, we are reminded of chaos theory and Edward Lorenz’s famous suggestion that ‘the flap of a butterfly’s wings in Brazil sets off a tornado in Texas’ – as the tiny movement of the air caused by the butterfly’s wings sets in train an escalating, multiplying whirl of movements in the air that culminates in a tornado far away. So, even such a small-scale event as dropping an ant could have manifold unpredictable consequences on every scale from the minuscule to the gigantic. So, actually, it’s impossible to say, on a certain level, what happens when you drop an ant.

Einstein’s General Theory of Relativity adds another aspect to this seemingly trivial event. Einstein explained gravity as working through the distortion of the fabric of
spacetime. So even a small movement of mass – the mass of the ant towards the earth – will minutely alter the fabric of spacetime. And of course the movement of the ant and the movement of the earth will, as Einstein’s Special Theory of Relativity shows, cause an (unimaginably small) shift in the time relation between you and the ant …

Ultimately, it all depends on what you want to know.

(Computer Science, Cambridge)

Even a kangaroo can’t get very high from a standing jump. That’s why both conventional high-jumpers and pole-vaulters use a run-up. Instead of accelerating against gravity from zero, the jumper uses the momentum of the run-up to boost upward acceleration. The vaulter’s pole enables the maximum possible momentum to be converted into upward acceleration. In terms of physics, it uses the leverage of the pole to convert the kinetic energy of the sprint run-up to combat gravity, or more specifically gravitational potential energy. And it’s in the physics that the limits to the heights that can be achieved by a pole-vaulter lie.

Ideally, a vaulter would convert all the kinetic energy of his sprint into vertical acceleration to combat gravity. Of course, in practice, even if he achieves the perfect lift-off
some energy will be lost to friction and in things such as the bending of the pole. So pole construction and design is important. Nonetheless, it is possible to calculate the maximum height a vaulter could reach in the ideal circumstances. The limit ultimately depends on the run-up speed.

You can calculate the maximum kinetic energy the vaulter has available from his mass (that is, his body weight) and his velocity, using the formula: half mass times the velocity squared, or KE = ½mv
²
. You can calculate, too, the gravitational potential energy that it has to be converted into using the formula: the acceleration due to gravity times the vaulter’s mass times the height, or PE = gmh, where g = 9.8 m/s
²
. The vaulter’s mass appears on both sides of the equation, and so cancels out. And so you can say the maximum height the vaulter can reach is half of the square of his velocity when divided by the acceleration due to gravity, h = (½v
²
/g). You’d have to make small adjustments according to the vaulter’s own height and centre of mass, but this way you can get a very rough figure of the height the vaulter could potentially reach.

Experts suggest the best that vaulters will ever achieve is about 6.4 metres, because of the limits to their run-up speed. The world record currently stands at 6.14 metres, set by Ukrainian Sergey Bubka on 31 July 1994. Altogether, just seventeen men have ever exceeded 6 metres in a vault. Women, who are generally shorter and able to reach slower run-up speeds, can vault less high. Just one woman, Yelena Isinbayeva, has ever exceeded 5 metres, and experts think the highest that women vaulters are likely to reach is about 5.3 metres.