快猫短视频

EARTHQUAKES, landslides, premature births, stock-market crashes and mass
extinctions鈥攖he more we find out about them, the more unpredictable they
seem. For years, people have been trying to understand what triggers
catastrophic events like these. Why, when everything is running smoothly, does
disaster strike out of the blue? Are there really no warning signs that would
let us take cover?

Most researchers have given up. They say these catastrophic events occur
because the Earth鈥檚 crust, financial markets and the world鈥檚 ecosystems are all
鈥渃ritical systems鈥濃�攁lways balancing on a tightrope. They are inherently
unpredictable because it is unclear how they will react to a nudge: sometimes
they keep their balance while at other times they topple off the rope. But
Didier Sornette, a geophysicist who splits his time between the University of
California, Los Angeles, and the CNRS in Nice, France, thinks they have given up
too easily. He claims to have found a subtle underlying signal, common to many
catastrophes, that can sound the alarm before it鈥檚 too late. Until now, these
whispers have gone unnoticed, but Sornette believes they could be the key to
forecasting catastrophe. It鈥檚 a hugely controversial claim, and has attracted
criticism from experts in all fields where Sornette has touted it.

It began in the early 1990s, when Sornette was developing a theoretical model
for predicting rupture in materials such as concrete, carbon fibres and certain
metal alloys (Physical Review Letters, vol 68, p 612). He modelled the
breakdown as a network of growing and interacting microcracks that finally
result in rupture. Sornette found that the rate at which these growing cracks
released energy was correlated with the time left before the material suffered
catastrophic failure. In other words, the cracks鈥攅ven the seemingly
insignificant ones鈥攇ive you a countdown to disaster.

So that鈥檚 the model, but would the same thing hold for real materials?
Working with engineers from Aerospatiale, the French aerospace company, Sornette
stretched Kevlar and carbon-matrix sheets to cracking point in pressure tanks,
while sensitive microphones recorded the pops and squeaks of the materials.
Careful analysis of all the frequencies revealed warbling trills and rumbling
bellows that no one had noticed before. 鈥淚t was like suddenly being able to pick
out the plucking of the double bass and the tinkling of the harp from the rest
of the orchestra,鈥� says Sornette. 鈥淭he secret was in getting a very clear
recording so that nothing was muffled.鈥�

They repeated the experiment using all sorts of different materials, and the
same pattern emerged every time. A little trill appeared at intervals in the
recording, a bit like the chorus in a song. Except it grew higher and higher,
with ever smaller gaps between repeats, until suddenly the material broke.

Sornette plotted these choruses against the time to failure, with the time
axis on a logarithmic scale. Remarkably, they appeared to repeat at perfectly
regular intervals so he called them 鈥渓og-periodic鈥� oscillations. By plotting
three or more choruses he could use the intervals between them to predict how
long it would be鈥攐r how much stress it would take鈥攂efore the
material suffered catastrophic failure.

As the experiments progressed, Sornette became increasingly confident that he
could accurately predict impending failure in materials. Aerospatiale patented
the method, citing Sornette as one of the inventors, and used it to
pressure-test the carbon-matrix tanks on the Ariane 4 and 5 rockets. After
applying a constant pressure to the tank for a short time, software picks out
the chorus in the cacophony of sound and gives a prediction of a tank鈥檚 rupture
pressure to within 3 per cent. 鈥淪ornette鈥檚 method made a big difference to us,鈥�
says Jean-Charles Anifrani, an Aerospatiale engineer who worked on the Ariane
project. Anifrani is now chief engineer at Eurocopter, the world鈥檚 largest
manufacturer of helicopters, and has begun using the same idea to test
helicopter gearboxes and parts of tail rotors. 鈥淣ow we can predict the pressure
at which the tail rotor tubes will rupture, and this means we can be confident
that each tail rotor tube is capable of doing its job,鈥� he says.

Sornette is not content to leave it there. Because it now looks as if
predicting certain catastrophic events may be possible after all, he feels that
he ought to be doing just that.

He has, for instance, studied landslides to see what kind of tune they sang.
First he and collaborators from the University of Grenoble, France, analysed
laser measurements and seismic data taken before the 1987 slip at the Tinee
Valley in southern France. It was a fairly minor event and no one was hurt, but
it did destroy a road, which had to be rebuilt on the other side of the
valley.

The seismic data from the slip lived up to Sornette鈥檚 expectations: there was
his pattern鈥攚ith the all-important chorus鈥攚ell before the slip
occurred. Sornette showed how the data could have been used to predict the
timing of the landslide鈥攖o within a month鈥攗p to a year in
advance.

Sornette has also looked at seismic data from landslides and rockfalls on the
volcanic island of R茅union in the Indian Ocean. Once again, he says his
method successfully predicted when the slips were due. 鈥淚 am really encouraged
by these results,鈥� he says. 鈥淚f I can verify the method on a few more landslides
then I hope to start putting this work into practice.鈥� He believes he will be
able to give enough warning to evacuate an area before a catastrophic slip
occurs.

If seismic rumbles can predict landslips, what about earthquakes? Sornette
has spent much of the past decade analysing seismic data from earthquake zones,
and says we should be able to spot danger coming here too. But, he adds, it鈥檚
not as straightforward as predicting landslides. 鈥淚dentifying the relevant data
really is a big problem here,鈥� he says. 鈥淓arthquake fault networks cover vast
areas and we can never be confident which fault the big earthquake will choose
to rattle.鈥� There are also problems in identifying the area over which to take
measurements. But even if his method can鈥檛 predict the timing and location of
earthquakes, Sornette says it can at least provide an all-clear. While most
researchers believe earthquake systems are in a dangerous state the whole time,
Sornette claims that most of the time they鈥檙e safe.

He believes that earthquakes follow seismic cycles in which small and
medium-sized earthquakes join up faults and create stress links across the whole
fault network. Eventually all the faults become connected鈥攖he critical
state鈥攁nd a small slip anywhere in the network can lead to catastrophic
failure. But until that state is reached nothing major will happen, and the area
can be declared safe. After a large quake the stress correlation is destroyed
and the whole process starts again.

This hypothesis cuts right across the received wisdom about earthquakes and
similar catastrophic events. The orthodoxy says that there鈥檚 no fundamental
difference between the mechanisms behind different-sized cracks. Most
researchers follow the model that crack networks in any brittle
material鈥攆rom a piece of concrete to the Earth鈥檚 crust鈥攁re 鈥渟cale-invariant鈥�
(快猫短视频, 8 November 1997, p 30).
Look at a stressed piece of concrete from half a metre away, and you might see a few large
cracks per square metre. Zoom in with a microscope, and you鈥檒l see smaller
cracks, but they鈥檒l look the same as the large ones: they have the same
distribution over the area that you can see. Whatever the scale at which you
look at the concrete, your view always appears the same.

That means a large crack is just a small one that didn鈥檛 stop growing (
Science, vol 275, p 1616). And this, the sceptics say, is what sounds the
death knell for predicting disaster: a big earthquake is simply a small
earthquake that didn鈥檛 stop. So, unless you鈥檙e willing to panic every time the
earth so much as shivers鈥攁nd in earthquake zones it does that a
lot鈥攖here鈥檚 no way to get out of town before the big one.

However, Sornette thinks that many systems have a special kind of
scale-invariance, called discrete scale-invariance, that might actually make it
possible to spot a breakdown coming. Ordinary scale-invariance leads to a
distinctive distribution of crack lengths: plot the length of a crack against
the number of cracks of that length and you鈥檒l get a smooth curve with small
cracks most common and big cracks least common. But from his analysis of real
and model systems approaching catastrophic failure, Sornette believes a system
under stress will actually show discrete scale-invariance. So, some crack
lengths will occur more frequently than for an ordinary scale-invariance
distribution. The details will be different for each system, but the signal data
will always be peppered with subtle signatures鈥攕uch as the log-periodic
signals鈥攖hat reveal when the whole system will go critical.

Sornette has begun looking at seismic data from the southern California fault
system, including the famous San Andreas fault. From an initial study of the
data, he thinks he can pick out a faint chorus signal among all the noise.
What鈥檚 more, the timing between seismic choruses has been diminishing fast
recently, and the southern part of the California fault system may be just
months away from the 鈥渃ritical state鈥�. He thinks that California is gearing up
for another big quake, measuring around 7.5 on the Richter scale.

But that doesn鈥檛 mean Californians should be panicking around Christmas. The
critical state is where the system is poised to fail鈥攊t doesn鈥檛 mean that
an earthquake will happen immediately.

Ian Main, an earthquake researcher at the University of Edinburgh and chair
of a recent set of Nature debates on earthquake prediction, feels that
Sornette may be stretching a good idea too far. A block of concrete or the side
of a mountain has clear edges to its fault network, he says. Earthquake zones do
not. 鈥淚t follows that it is harder to determine the location and maximum size of
the next big earthquake in advance,鈥� Main says. He is also concerned that
Sornette鈥檚 interpretation of the data makes some artificial, arbitrary
distinction between smaller and larger earthquakes.

Sornette acknowledges that a fault zone is not the same as a block of
concrete, but he is undeterred. In fact, he reckons that log-periodic
signals, and other indications of an impending critical point, will turn up in
many different systems that undergo sudden, catastrophic changes. He even
reckons they could help predict the timing of one of the most traumatic events
any of us face: birth.

In this instance, the equivalent of the Earth鈥檚 seismic vibes are the
electrical signals given out by uterine muscle. Sornette wants to look for
log-periodic signals in the muscle fluctuations, and translate them into a birth
forecast. 鈥淚 believe that this could be used to predict the day a woman will
give birth and that I could recognise unusual signals such as that of a
premature birth,鈥� he explains.

This claim has already caught the attention of Peter Bowen-Simpkins from
London鈥檚 Royal College of Obstetricians and Gynaecologists. Premature babies are
usually much smaller, weaker and more likely to suffer from problems in later
life. Many women are known鈥攆rom past experience鈥攖o be at heightened
risk of premature birth, so being able to monitor them and have advance warning
would be immensely useful, says Bowen-Simpkins.

They might not be able to stop the birth, but they could act to give the baby
the best chance of survival鈥攕teroids, for instance, to help mature the
fetal lungs. 鈥淭his would significantly reduce the risk of breathing problems
when the premature baby is born,鈥� Bowen-Simpkins says. And since the steroids
can have serious side effects for the mother, he would welcome any test to see
if and when they are necessary.

Sornette has collaborated with a team of Parisian obstetricians to produce a
mathematical model of the triggers for birth. He modelled the various tissue
layers of the uterus as oscillators. Before labour they are all unconnected and
behave independently, he says, but as the layers of tissue mature, their
behaviour changes. They start working together, in the same way that independent
cracks in concrete grow and form networks. And because of that, a repeating
chorus in the electrical signals from the uterine muscles should tell you when
the organisation will be complete and labour is set to begin.

Sornette and the obstetricians have already done some preliminary
experiments. They fitted pregnant women with an electronic belt that
continuously monitored and recorded their uterine muscle activity. Initial
results are promising, and there seemed to be a chorus, but logistical problems
such as the uncomfortable design of the belts halted the experiments before they
could gather enough evidence to tell for sure.

鈥淭he biggest difficulty is to find a sensible way of measuring the uterine
contractions,鈥� says Bruno Carbonne from the Port Royal Baudelocque maternity
hospital in Paris. 鈥淐urrently we are investigating non-invasive methods such as
using ultrasound.鈥� Once the problems have been ironed out, Sornette wants to
restart the project, and is looking for more obstetricians willing to
participate in a large-scale, long-term survey.

It鈥檚 odd enough that the same patterns should appear in apparently unrelated
natural signals, such as seismic data and muscle impulses. But Sornette believes
that exactly the same patterns also turn up in man-made systems. And that鈥檚 why
he wasn鈥檛 surprised to find his repeating choruses singing their way through the
financial markets.

Sornette, working with Anders Johansen of the University of Copenhagen,
claims to have picked out the choruses heralding the Wall Street crashes of
1929, 1962 and 1987, as well as the 1997 crash on the Hong Kong stock exchange.
He also heard the warning bells before the NASDAQ high-tech bubble burst in
April 2000 and correctly predicted a sudden upturn in the Japanese Nikkei index
for January 1999. 鈥淚n some ways it seems surprising that the same theory works
for epochs that are so different in terms of speed of communication and
connectivity,鈥� he says. 鈥淲hat this may show is that the stock market has always
been driven by human nature鈥攁nd this hasn鈥檛 changed so much.鈥�

However, that鈥檚 not enough to persuade James Feigenbaum, a physicist working
in the Tippie Business School at the University of Iowa. He believes Sornette鈥檚
vision of portentous periodic signals hidden in financial data could be
fundamentally flawed. 鈥淚t has not been convincingly established that
log-periodic oscillations are absent from times where no crash is evident,鈥�
Feigenbaum says. It鈥檚 possible that everything鈥攃atastrophic or
not鈥攑roduces subtle log-periodic signals. Sornette is undaunted by
Feigenbaum鈥檚 observation: he believes he has been thorough in the statistical
analysis of his data. 鈥淚 am confident that I am seeing a real log-periodic
signal, and that in certain situations this can be used for predictive
purposes,鈥� he says.

Yet the very fact that Sornette鈥檚 theory is so wide-ranging worries many
other researchers of critical systems. For them, the large number of phenomena
which he claims will be predictable makes the whole thing seem just too good to
be plausible, let alone true鈥攖hough so far no one has come out and told
him flat that he鈥檚 wrong.

Sornette is still working on his analysis techniques, unravelling new
signatures from the data and working out new ways to model critical systems. And
not everyone thinks he鈥檚 following a false trail. 鈥淭here may be some truth in
Sornette鈥檚 claims,鈥� says Neil Johnson, a director of the Oxford Centre for
Computational Finance. 鈥淚 do believe the answer to whether a large change is
coming up may somehow already be encoded in the make-up of the system.鈥�

Of course, Johnson warns, dramatic external events鈥攕uch as the attack
on America or a meteorite impact鈥攃an propel a system beyond the boundaries
of predictability. But in the normal course of events, everything required to
predict big changes could well be hiding within the data. All we need to do is
find the right way of taking a diagnostic X-ray. 鈥淭he question is: has Sornette
found the right X-ray?鈥� Johnson asks. 鈥淥nly time鈥攁nd an awful lot of
testing鈥攚ill tell.鈥�