30 November/December 2020
COURTESYPARAMOUNT^ PICTURES8
Science
at Budapest University of Technolog y.
To understand how rocks break down this way,
the team then used supercomputers to create a
series of mechanical simulations. Here they stud-
ied a molecular model, where a brittle rock-like
material was modeled, using what looks like virtual
gumdrops and toothpicks. The gumdrops repre-
sent the rock-like substance while the toothpicks
represent the bond holding it together, including
a weighted failure criterion—which measures the
force that can break each segment. In these simu-
lations they studied the fault lines that shatter open
when they break, like if you dropped a plate onto
the f loor. The simulations found that as you broke
apart natural materials, on average, most pieces
conformed, on average, to a cube-like shape.
The research could eventually help scientists
identify regions on Earth’s surface that are sus-
ceptible to rock falls. As rocky outcrops are exposed
to the elements, inherent f laws in the rock slowly
grow into large cracks. When these fissures meet,
they form unstable blocks of rock that can be loos-
ened by an earthquake or by gravit y over time. “The
size and structure of the crack networks determine
the size of the blocks that are produced, which ulti-
mately determines, to a large extent, the hazard
created when they fail,” Jerolmack says. Their
work, he adds, could eventually help to forecast how
these rock blocks form on both 2D and 3D surfaces.
The discovery also supports an improbable
theory that’s nearly 2,400 years old. Before the dis-
covery of chemical elements and atomic structure,
Plato and his fellow natural philosophers—the
forebears of modern scientists—came up with
the classical elements of earth, water, fire, air,
and cosmos to explain what the world was made
of. In Plato’s dialogue Timaeus, he theorized that
the classical elements were each composed of a
three-dimensional shape where all angles are
equal, as are all sides. Of these five shapes, known
as Platonic solids, he believed the cube was linked
with Earth due to its ability to seamlessly fill space.
Jerolmack and Domokos both pointed out that
their results are a twofold representation of Plato’s
work, first as the Platonic solids, but second, and
arguably more interesting, in combination with the
philosopher’s allegory of the cave.
In Plato’s Republic, he tells a story about pris-
oners in a cave. They can only observe strange
shadows on the wall, never what’s casting the
shadows. Plato suggests that for people with no
additional information, the shadows are reality,
but that doesn’t imply that the shadows are the full
reality. In an analogy straight out of calculus, he
suggests that there are additional stages of reality
with more dimensions of understanding. “Plato’s
idea was that what we see with the naked eye are
just distorted shadows of the true reality, so the
reality which we perceive is a distorted version,
and the ideas are the reality,” Domokos explains.
By studying the rock fragments and the
“shadow” created by taking their probabilis-
tic and arithmetic averages, Jerolmack says, the
researchers inadvertently brought both of Pla-
to’s ideas together. “What we’ve demonstrated is
that on average, rock or earth is made up of cubes,
but you never see the cube,” he says. “It exists
only when you take all these distorted shards
and bits and average them together.” Domokos
adds: “It is so much in the spirit of Plato—
there are too many coincidences to say that it is
just coincidence.”At the crux of Mission:
Impossible—Fallout, Tom
Cruise’s character, Ethan
Hunt, and antagonist
August Walker, played
by Henry Cavill, come
to blows atop Norway’s
famed Pulpit Rock.
The granite cliff
caught the eye of studycoauthor Gábor Domokos,
a mechanics professor at
Budapest University of
Technology. “Somebody
took me to see the movie
and, at the end, I said ‘My
god! Look at those frac-
tures!’ ” he says.
Domokos asked one
of his assistants to runan analysis on an image
of Pulpit Rock to see
whether the outcrop’s
fracture patterns fit
Plato’s theorized cuboid
average. “I didn’t tell him
what it was. I just told him
to do it,” Domokos says.
“And, of course, he got the
right numbers.”PLATO’S
CUBES ON
THE BIG
SCREEN