As soon as dawn breaks in your part of the world, we need you to start
running east, towards the Sun. Or take the car if you feel so inclined. The more
mass you move, the better—take the dog along too. If you live on an
eastern coast, get the boat out, or better still, hire a 747.

Now, keep going as fast as you can until the Sun reaches its zenith in
whatever part of the world you find yourself. Then go home. The closer you live
to the latitude where the Sun is directly overhead at midday, the more helpful
your effort will be. If you live anywhere that has permafrost, well . . . thanks
for turning out, but you needn’t have bothered. Everybody else, same again
tomorrow, please. In fact, keep on doing this until we tell you to stop.

Why this bizarre request? To save the Earth, oddly enough. By now, everyone
must have picked up an inkling of the doomsday asteroid—or
comet—that is lurking out there. It depends on who you talk to, but the
risk to interested parties here on Earth (us) seems to range from “a slight
possibility of a nick” to “a dead-cert wipeout situation”.

We’re not talking about the lunatic fringe here, who frequently claim that
something the size of Botswana is due to hit your locality at lunchtime next
Saturday. No, we’re talking about your respectable scientist here, who is simply
flagging up the theoretical risk, you understand, but at the same time subtly
implying that anyone who gets flattened in the initial impact can regard
themselves as lucky.

But to risk posing a simplistic question, shouldn’t we be doing something
about this? At the moment, we just seem to be looking. The next time we have a
near miss (and we’ve already had one or two) we can no doubt expect the
President of the US to go on network TV and explain how the world owes its
thanks to the country’s firm resolve and technical know-how. Likewise, in
Westminster, the Prime Minister will stand up to make a brief statement in the
House of Commons that will dwell largely on the fact that, had the opposition
been in power, we might not have got off so lightly. But then what?

Agreed, my plan to set up a longitudinal Mexican wave that peaks at the point
on Earth closest to the Sun may not be perfect—but hey, I’m just trying to
get the debate going here. We’ll assume that we get about 10 weeks’ notice that
an asteroid or whatever is set on collision course.

In order to dodge the blow, we need to speed up, or maybe slow down, the
Earth as it orbits around the Sun. Since the angular momentum of the Earth
around the Sun is conserved, if we redistribute some mass a little closer to the
Sun, the Earth should speed up a bit in its orbit to compensate. The spinning
ice-skater demonstrates the principle, although in this case we are considering
the angular momentum of the Earth about the Sun, not about its own axis.
Alternatively, we could all move westwards away from the Sun to slow down. Let’s
leave the details to the guys with the big telescopes.

Up until now, mind you, we’ve been leaving it all up to Jupiter—and the
Sun, which is the root cause of all the trouble anyway. Jupiter is “where it’s
at”, gravitationally speaking. This gives it the ability to suck up cosmic grit
like it’s going out of fashion, and that is just what it has been doing for
quite a while, with only the occasional careless lapse. But for how much longer
can we rely on such philanthropy?

Some of the probabilities quoted for a significant impact are surprisingly
high, such as “a few per cent” over the next 100 years. If you want a more
detailed analysis, you can look up The Spaceguard Survey, published in
1992 by NASA’s Ames Space Science Division. But even a rough estimate is enough
to tell you that your chances of being killed by this sort of thing in 1997
alone are reckoned to be greater, from what the Ames scientists seem to be
claiming, than your chances of being involved in an accident next time you fly
off on your summer holiday. Scary, eh?

So we’d better start thinking, though maybe we shouldn’t take the
Mexican-wave plan too seriously, especially when you can still fit the entire
population of Earth into Hong Kong if everyone breathes in. More significantly,
the total mass of humanity represents less than 1 billionth of one per cent of
the mass of the planet.

Nah. A better idea would be to vaporise the Moon with ray guns. Now you would
really be shifting some angular momentum with that plan . . .

Each child was handed a pair of hire skates and dispatched to the changing
area. They returned, swaying precariously on their skates and tightly clutching
their ÂŁ80 worth of designer trainers, complete with fluorescent laces.

‘Where d’ya leave ya trainers, sir?’ demanded the first one out of
the changing room. I looked around vaguely and motioned towards an open
area close to the entrance tunnel leading to the rink. Muttering under his
breath something about costing a bleedin’ fortune, and uttering dire threats
against any potential thief in the locality, the child followed my suggestion
and proceeded onto the ice. ‘Where d’ya leave . . . , uh?’ said number two
on exit from the changing room, and promptly deposited her trainers next
to number one’s. ‘Where . . ., uh?’ asked number three.

And so on. I watched the pile of trainers grow. What did we have here?
I traced back the recent history of these forty pairs of fetid footwear.
They had begun their journey from disparate parts of our school’s catchment
area. On arriving at the school bus park, they had formed a loose cluster
on the coach and travelled hundreds of miles across Europe in a sort of
blob of trainers. At the hotel they had loosened their clustering a little
further, although still densely packed relative to their journey’s starting
point, only finally to come together in this intimate dense cluster one
night in some mountain town in Austria. Why?

Well on the surface, of course, the answer is very simple – the children
put them there. But hang on, is it really that simple, or could there be
something deeper going on here? When I and my colleagues did a ‘room check’
towards the end of the week, we found the children’s bedrooms to be in a
terrible state. We could simply attribute this unremarkable discovery to
the fact that children are untidy. Then again, we could point out that the
untidiness of the bedrooms was an inevitable consequence of the second law
of thermodynamics – the tendency of the Universe towards disorder and gradually
increasing entropy.

Although recent developments in anti-chaos (the spontaneous eruption
of order out of disorder) may ultimately bring into question whether our
understanding of the second law is complete, it is self-evident in a general
sense, and particularly where children’s bedrooms are concerned. Is there
a similar deeper explanation as to why many like objects in the Universe
have a tendency to cluster together, either transiently or permanently?

It isn’t just trainers that are prone to it, nor even just matter generally
(into planets, stars, galaxies and galactic clusters). What, for instance,
is a classroom but a cluster of children. And is not a school merely a cluster
of classrooms? Looking down from my classroom I see a cluster of cars in
the car park, and farther afield, a cluster of trees in a distant wood.
In the adjacent field, sheep are a-clustering.

One can go on and become very boring. So let’s think of more interesting
examples. If I were to say old tyres, what does your mind conjure up? How
about wind turbines? Are your back copies of New ĐÓ°ÉÔ­´´ distributed uniformly
around your house in various nooks and crannies, or do they form a neat
cluster somewhere?

For every example quoted, there is of course the mundane explanation
as to why an item should be found alongside its kind, just as every article
out of place in the child’s bedroom can be attributed to some moment in
history when it was deliberately displaced from its usual location – but
the good old second law was driving it all.

Nor is it true that every object will cluster with like objects at some
point in its existence. But most things seem to. Anyway, what of it? Even
if there is some deeper truth driving it all, what use would such understanding
be? We can be sure that the first person to find a nugget of gold in a mountain
stream didn’t need some profound law of physics to tell them to go back
the next day and try again.

We might apply the principle ad hoc on the off chance, but it would
hardly be science. For example, we could decide to concentrate our search
for extraterrestrial intelligence on relatively nearby suitable star systems,
on the basis that if intelligent life forms are prone to clustering, then
(since we ourselves are here and supposedly intelligent) there ought to
be something worth having a good look for in neighbouring systems. But then
again, maybe intelligent life forms are one of those few entities that don’t
cluster.

Clustering, as a concept, is fine when we can also perceive the obvious
reason as to why those particular objects came together at that particular
time, but to appeal to it as a general principle in the absence of such
a reason is . . . well . . . you know. Still, next time you read in the
newspaper about an inexplicable leukaemia cluster, or something similar,
spare it a thought.

Chris Goy teaches maths at Wolsingham Comprehensive School, County Durham.