26 March/April 2022
GETTY^ IMAGESDeep Math
5The board game Chutes and
Ladders involves players racing
up a numbered path according to
the sum of a dice roll. If you land
at the bottom of a ladder, you
climb farther up the board, while
landing atop a chute slides you
backward. The game ostensibly
hinges on chance due to its reliance
on dice, but in actuality, Chutes
and Ladders is a stochastic system
called an absorbing Markov chain,
meaning just a portion of the
system contains randomness.
Absorbing Markov chains
are “memoryless.” Past dice rolls
in Chutes and Ladders don’t affect
the results of the next move, but
the current position of each player
does. Rolling a seven might move
you forward seven spaces in oneThey found that an erroneous layer—one that was
too thick or too thin—affected layers up to 5.5
microns (5.5 millionths of a meter) away, creating
repetitions over distances of 8.5 microns that, all
together, formed a near-symmetrical pearl. Mol-
lusks appear to be accounting for irregularities
that occur while constructing pearls. Nacre layers’
thicknesses varied by up to 40 nanometers on aver-
age, but not in a haphazard way.
The layers mirrored what often happens in a
mathematical system known as a Markov pro-
cess, says Hovden. Markov processes include an
element of randomness—in this case, the thick-
ness of the outermost nacreous layer—but one that
can be inf luenced by the system’s history. (“Mem-
oryless” Markov systems also exist—see sidebar.)
In a pearl, the thickness of the nacreous layers
depends somewhat on the thickness of the layers
preceding it; thick layers will sometimes beget
compensatory thin layers around them, and the
correlation is strongest between layers that are
close by. This pattern is typical of systems involv-
ing a Markov process.
Markov processes are widespread in nature. “It’s
the same structure you find in heartbeats, in earth-
quakes, the crumbling of sandcastles, economic
markets, and now we add to that list, the structure
of pearls,” Hovden says. This fits what scientists
already knew about pearls, says Landman: Changes
in the outside world, such as seasons, appear in a
pearl’s layers. “Pearls are like tree rings,” he says.
“If you cut up the pearls, you could reconstruct what
is going on in the area where the pearls were form-
ing maybe hundreds of years ago.”
These findings intrigue engineers and
researchers looking to recreate desirable natural
materials without human manufacturing. Mother
Nature can make pearls under “physiological con-
ditions,” says Shenqiang Ren, a professor at the
State University of New York at Buffalo. “I mean
neutral pH, room temperature, and ambient pres-
sure.” The hope is for humans to achieve the same
results with the same sustainable methods.
When humans build with bricks, they plan the
construction to avoid irregularities. “A skilled
mason measures every layer, and any mistakes
that could disrupt the periodic order are corrected
through premeasured lines and templates,” says
Hovden. Mollusks, however, don’t seem to need
planning to create near-perfect pearls: “They’re
pretty unintelligent things. Yet [pearls] have
incredible periodic symmetry.” Hovden says.
Scientists don’t yet understand all the nuances
of pearl making, but Ren and his lab are using
nacre as one source of inspiration for a strong,
light material that can be used in gear such as
armor and helmets. “Before we replicate those
material[s] artificially in man-made structure[s],
[we’ve] got to understand what processes deter-
mine their microscopic physical properties,” Ren
says. Other possibilities include diatoms, a type of
algae, and materials inspired by bones.
But you won’t find nacre-inspired armor any-
time soon. Producing an object the size of a pearl
is quite different from producing suits of armor,
Ren says. “There are still some fundamental ques-
tions that need to be addressed in order to make
this commercially viable,” he explains.
In the meantime, there is plenty to appreciate
about pearls and other natural materials as they
already are. “Serendipity is just wonderful,” says
Hovden. “We’ve been [studying biomaterials] on
the side for five years now, and I’m yet to have a
project where you don’t open up this material and
just get shocked with wonder.”