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THE US Navy should be preening itself. After all, it has just rolled out the
showpiece of its arsenal, the brand new Seawolf attack submarine. The fastest
sub in the world, it’s a technological marvel and a devastating weapon.

The Seawolf’s sophisticated store of electronic and acoustic equipment for
“seeing” underwater is pretty impressive, too. But unfortunately for the
military’s top brass, not quite impressive enough. What really rankles is that
in the seeing stakes, this world-class sub is beaten hands down by a certain
playful, warm-blooded, bottle-nosed creature—the dolphin.

Just by making sounds and listening for their echoes, dolphins can do
astonishing things. Through dark, murky waters cluttered with debris they can
detect fish the size of a golf ball some 70 metres away. And in seconds, a
dolphin can find its vitamin pill on the bottom of the pool. Researchers have
also filmed dolphins using their sonar in open waters to detect tiny eels and
other edibles squirming underneath the mud of the seabed. The dolphin listens,
then plunges into the muck up to its flippers, and comes up with a tasty
treat.

Tremendous stuff. But the US Navy is determined to catch up, and three years
ago, it enlisted Jim Kadtke, a theoretical physicist at the University of
California at San Diego, to help crack the dolphin’s secrets. Kadtke might bring
a seemingly inappropriate set of skills to the study of marine mammals. But his
unusual background is paying off because it seems that the key to understanding
the dolphin lies in the weird and sophisticated mathematics of nonlinear
dynamics and chaos theory.

Reading echoes

When it is swimming happily around the bay, hunting for fish or just playing,
a dolphin sends out intermittent bursts of sound known as “clicks”, each of
which lasts much less than a thousandth of a second, and contains frequencies
far beyond the range of human hearing. Special organs in the dolphin’s head make
the clicks and receive their echoes
(see “Sounding off”). All of this is well
known. The real struggle for dolphin researchers like Kadtke is to understand
how a dolphin extracts information from echoes. How does a hungry porpoise hear
“fresh seafood” in a garbled reflection from the ocean floor?

Getting to the bottom of this mystery isn’t easy, but after studying dolphins
in captivity for more than twenty years, researchers have a few solid clues for
Kadtke to work with. Patrick Moore of the Naval Command, Control and Ocean
Surveillance Center in San Diego, and Whitlow Au of the Hawaii Institute of
Marine Biology in Kailua, Hawaii, have developed some clever methods to study
dolphins much as a psychologist might study a human—by asking questions,
and waiting for answers.

The idea is to train a dolphin to use its sonar to identify a standard
object—an aluminium cylinder, for example, or a steel sphere or cone. Once
it knows the object well, then researchers can test the dolphin’s ability to
distinguish the standard object from another that is slightly different. On cue,
the dolphin—who wears blinkers so that it can’t cheat by
looking—faces the objects and sends out a stream of clicks. It listens to
their echoes, decides which object is the standard, and then pushes one of two
paddles to indicate where it thinks the standard is placed
(see
Diagram, p 37).FIG-20884701.gif

So how different, in terms of size, density, shape, and so on, do objects
have to be before a dolphin can tell them apart? In 1991, Au and Deborah
Pawloski of Science Applications International Corporation in San Diego
suspended two hollow metallic cylinders about a metre below the surface some 10
metres away from a dolphin. The cylinders were a few centimetres in diameter and
identical but for the thickness of their walls. But even when the thickness of
the walls differed by only a few tenths of a millimetre—about the
thickness of a human fingernail—an Atlantic bottlenose dolphin could tell
them apart more than 75 per cent of the time.

How? According to Au, when the dolphin sends a click out to the cylinder, it
reflects off the front edge and comes straight back. But some of the sound
energy also travels through the cylinder, reflects from the back edge, and then
travels back to the dolphin. The time delay between the two reflected pulses
depends on the thickness of the cylinder wall through which the second pulse
travels. “The difference in the intervals from the two cylinders was between 0.5
and 0.6 millionths of a second,” says Au.

These experiments testify to the amazing sensitivity of a dolphin’s listening
organs. But it still doesn’t explain their edge over the US Navy. With modern
electronics, it’s not difficult for subs to detect time differences of a
millionth of a second. No, the dolphin’s real prowess lies in recognising
subtler features of echoes. Au says that dolphins have no trouble telling a
fresh fish that their keeper tosses into the pool from one slightly older and
less savoury, even when they are blindfolded and kept at a distance. And when it
comes to detecting an echo in the midst of noise, here again the dolphin excels.
In comparison with man-made sonars, says Kadtke, the dolphin “does better than
us always.”

But Kadtke has an idea of how they might do it—and it involves chaos.
Since the early 1980s, the notion of chaos has been upsetting scientists’ views
on what is ordered and what is random. The lesson is—you can’t always tell
just by looking. The order in a signal is sometimes well disguised, and
uncovering it requires sophisticated mathematics.

It was Moore who first suggested that Kadtke, an expert in chaos theory,
apply his mathematical methods to search for hidden order in the routine clicks
of dolphins. Kadtke knew that just looking at the waveforms with the naked eye
wouldn’t be enough. As he points out, if you record the sound waves
corresponding to a set of clicks, and plot them out on some paper, you find that
“the clicks are spectral lumps, all looking much alike”.

But Kadtke set out with Michael Kremliovsky, also of the University of
California at San Diego and Mario Inchiosa of the Naval Command Control and
Ocean Surveillance Center, to see if he could find anything. Moore supplied the
data from experiments in which a dolphin looked towards a metal sphere or
cylinder from about 25 metres away. During each trial Moore recorded the clicks
that the dolphin emitted as it tried to identify the target.

The researchers treat each click as a waveform—it rises from nothing,
fluctuates up and down for a time, and then fades away
(see
Diagram, p 36). And
they decided to attach some descriptive numbers to these waveforms, by using
what they call a “global dynamical models”. This means, roughly, that for each
waveform they try to find the simplest conceivable mechanical system that would
generate the same pattern of ups and downs if it were set in motion.FIG-20884701.gif

This may seem like a strange way to describe a waveform, but it is a central
notion in a branch of mathematics known as dynamical systems theory. In the
early 1970s some of the very first work on chaos by the French mathematicians
David Ruelle and Floris Takens came up with a way to take a time series—a
simple record of some process, like a dripping tap, or a weather
pattern—and to use it to construct important features of the dynamical
system that gave rise to it.

The process is much like looking closely at some tyre tracks and then working
out what must have made them—a 1966 Ford Mustang, say, or a 1981 Volvo.
One of the most basic features of a dynamical system is its “attractor”, a
geometrical object that captures the long-term behaviour of the system.
Mathematically, it isn’t always possible to find the attractor because some time
series are truly random—so an attractor doesn’t exist. But Ruelle and
Takens showed that if there is order in a time series, it can be made apparent
by a procedure of “embedding” the time series in an abstract mathematical space,
which teases out the attractor.

Using this idea of embedding, Kadtke, Kremliovsky and Inchiosa took the
waveform generated by each click and estimated the attractor behind it. But then
they went further, to seek out a model for a dynamical (mechanical) system that
might produce that attractor. In the case of the dolphin data, the researchers
found that the best models for the click waveforms have six parameters, so six
numbers describe the shape of each click. These numbers don’t have transparent
meanings, but encode what Kadtke calls “nonlinear correlations” in the time
series—subtle bits of information that escape ordinary analyses based on,
say, measurements of pulse features like duration or amplitude.

Despite its abstraction, this way of looking at click sounds is well worth it
because it reveals an astonishing order, order that is far from apparent to the
naked eye. Plotting just three of the six parameters for each click (since six
is hard to visualise in our three-dimensional world), the numbers vary from one
click to the next in an orderly way
(see
Diagram, p 36). “Dolphins seem to be
able to tailor their clicks in a very detailed way,” says Kadtke.FIG-20884701.gif

Hidden order

Kadtke, Kremliovsky and Inchiosa suspect that the variations they observe
betray a delicate strategy on the part of the dolphin to tune its clicks to get
the best information. “The dolphin sends out a click and then tunes the signal,”
says Kadtke. “It usually takes about six clicks to do the optimal search.” That
is, the dolphin first sends out a fairly generic pulse, but then, depending on
what it thinks it has found—a fish, a boat, or whatever—it modifies
its next click.

This modification is so subtle that it can only be revealed by chaos theory,
although the dolphin, no doubt, has no problem hearing the differences. In the
experiments, the characteristics of the clicks often “settle” after six or seven
clicks, and then remain fairly similar thereafter—what Kadtke calls the
“six click rule”. “Based on the data we’ve analysed,” he says, “it appears that
the signal takes on a fairly stable structure that is distinct with respect to
target. The dolphin may be trying to pick out some resonances in the shape of
the target object.”

Another piece of evidence which seems to back this up is that a dolphin
doesn’t send out another click before it has heard the echo of the previous one.
It seems to use information from the previous echo to decide on the best pulse
to send next.

Not surprisingly, this way of homing in on the best kind of click for the
object being imaged is somewhat outside the experience of the US Navy. But it
presumably underlies the dolphin’s great capability with sonar. “It’s the task
requirement—detect, classify, can I eat that?—which drives a
dolphin’s emitted pulse structure,” says Moore. Perhaps the dolphin
distinguishes a fish from a clump of floating seaweed in just one click, then
tunes subsequent clicks to discover the kind of fish, whether it is live or
dead, and whether it looks tasty.

Listening by design

Armed with their new theory, Kadtke and Kremliovsky liken the final click
waveforms to a kind of “dolphin vocabulary” that helps the animal to identify
the target. As Kadtke points out, dolphins seem to vary the properties of their
clicks continuously. “But the final pulse shape seems to be target dependent,
and repeatable. In other words, there may be a fixed set of final, optimal
waveforms,” he notes. “That’s what we mean by a vocabulary.” Perhaps it also
reflects the knowledge the dolphin acquires about the kind of objects it sees
most frequently, and the hierarchy of crucial echo properties that lets a
dolphin gain sufficient detail about those objects to be able to distinguish
them quickly and reliably.

So it seems that at least one of the dolphin’s main tricks is finally being
revealed. And the US Navy is hoping to copy the dolphins’ strategy, at least in
a rudimentary way. In their work for the military, Kadtke and Kremliovsky’
general goal is to develop methods to characterise underwater signals, sometimes
of biological origin, and often cluttered by noise. “The hope is to build highly
sensitive processing software so that we can get information back from
low-amplitude pulses,” says Kadtke. “A Navy submarine, after all, wants to
remain clandestine in its operations.”

But naval technologists still have a lot to learn from the dolphin. For one
thing, hardly anything is known about how dolphins use sonar in the wild. Peter
Tyack, a dolphin expert at the Woods Hole Oceanographic Institution in
Massachusetts, says that the work of Moore, Kadtke and their colleagues “has
been very helpful and well controlled—a valuable start.” But he suspects
that dolphins in captivity may not show their full capabilities. “We need also
to study dolphin echolocation in relation to the problems for which it evolved
rather than in pens on spheres and cylinders,” he says.

Until recently, technical problems have stymied attempts to study dolphins in
the wild, but the miniaturisation of electronics is now at the stage that makes
such studies possible.

Doug Nowacek, a graduate student of Tyack’s, has been studying bottlenose
dolphins in the inshore waters off the coast of Florida. He uses a video camera
to study dolphins foraging for fish. By using suction cups to attach acoustic
recorders to the animal, Tyack hopes to monitor a dolphin’s use of sonar as it
hunts, during the stages of detecting fish, pinpointing them precisely and then
capturing them. His hunch is that dolphins’ tailoring of clicks should be much
more evident when studying dolphins in the wild than in pens.

If so, the US Navy might learn some new tricks. After all, the dolphin’s
sonar system has been under constant development by the forces of evolution for
tens of millions of years. No wonder it has the best sonar in the world. But one
day, perhaps, with a little help from mathematics, the US Navy may catch up.

* * *

Sounding off

DOLPHINS send out narrow beams of sound which they generate by blowing air
back and forth through a set of nasal passages. A fat-filled cavity in the
dophin’s head—called the melon—focuses the sound into a beam, which
the dolphin can direct where it likes.

By putting out a narrow beam, the dolphin directs more intense sounds on
interesting targets, and doesn’t waste energy elsewhere. Energy efficiency
probably also explains why the dolphin doesn’t send out sound continuously, but
as a series of short pulses or “clicks,” in a frequency range between 20 000 and
120 000 cycles per second, beyond the range of the human ear.

When Flipper is on TV making squawking noises, that has nothing to do with
sonar. “Dolphins don’t normally make noises out of the water,” says Chris
Sturtivant, a dolphin expert at Loughborough University, “but when around humans
they quickly learn that sounds made out of the water attract attention much
better than those made in it.” Squeaks and squawks may make you a star, but it
is the high-frequency underwater clicks that the dolphin uses in its day-to-day
navigation.

The dolphin also has some fancy equipment to listen for echoes. Anything that
uses sound to sense its underwater surroundings needs to hear only what it wants
to hear—the echoes—and not all the other sounds in the environment.
The dolphin solves this problem, oddly enough, with its jaws. Sound gets in to
the dolphin’s head through a thin “acoustic window” in the lower jaw—a
region where the bones are thinner and transparent to sound—and then
follows a fat filled canal to the inner ear.