Note: Copyright belongs to the publisher. This excerpt is posted here for the convenience
of the PHYS 1P21/1P91 students.
From Dance for Two. Alan Lightman. Pantheon Books. NYC NY. 1996.
Pas de Deux
In soft blue light, the ballerina glides across the stage and takes to the air, her toes
touching Earth imperceptibly. Sauté, batterie, sauté. Legs cross and flutter, arms
unfold into an open arch. The ballerina knows that the easiest way to ruin a good
performance is to think too much about what her body is doing. Better to trust in the
years of daily exercises, the muscles' own understanding of force and balance.
While she dances, Nature is playing its own part, flawlessly and with absolute
reliability. On pointe, the ballerina's weight is precisely balanced by the push
of floor against shoe, the molecules in contact squeezed just the right amount to counter
force with equal force. Gravity balanced with electricity.
An invisible line runs from the center of the Earth through the ballerina's point of
contact and upward. If her own center should drift a centimeter from this line,
gravitational torques will topple her. She know nothing of mechanics, but she can hover on
her toes for minutes at a time, and her body is continuously making the tiny corrections
that reveal an intimacy with torque and inertia.
Gravity has the elegant property of accelerating everything equally. As a result,
astronauts become weightless, orbiting Earth on exactly the same trajectories as their
spaceships and thus seeming to float within. Einstein understood this better than anyone
and described gravity with a theory more geometry than physics, more curves than forces.
The ballerina, leaping upward lightly, hangs weightless for a moment amid flowers she has
dropped midair, all falling on the same trajectory.
Now she prepares for a pirouette, right leg moving back to fourth position,
pushing off one foot, arms coming in to speed the turn. Before losing balance she gets
four rotations. Male dancers, on demi-pointe and with greater contact area, can
sometimes go six or eight. The ballerina recovers well, giving her spin smoothly back to
Earth and remembering to land in fifth position smiling. Briefly her feet come to rest,
caught between the passage of spin and the friction of the floor. Friction is important.
Every body persists in its state of rest or of uniform motion unless acted upon by outside
forces. Every action requires a reaction.
The ballerina depends on the constancy of the laws of physics, even though she herself is
slightly unpredictable. In this same performance last night she went only three and a half
turns through her first pirouette, and then took the arabesque several
feet from where she takes it now. Regardless of these discrepancies, the atoms in the
floor, wherever she happens to touch and at one millisecond's notice, must be prepared to
respond with faithful accuracy. Newton's laws, Coulomb's force, and the charge of
electrons must be identical night after night – otherwise, the ballerina will
misjudge the resiliency of the floor or the needed moment of inertia. Her art is more
beautiful in its uncertainty. Nature's art comes in its certainty.
The ballerina assumes one pose after another, each fragile and symmetrical. In the physics
of solids, crystal structures can be found that appear identical after rotations by
one-half, one-third, one-quarter, and one-sixth of a circle. Crystals with one-fifth and
one-seventh symmetries do not exist because space cannot be filled with touching pentagons
or septagons. The ballerina reflects a series of natural forms. She is first ethereal,
then lyrical. She has struggled for years to develop a personal style, embellished with
fragments from the great dancers. As she dances, Nature, in the mirror, pursues its own
style effortlessly. It is the ultimate in classic technique, unaltered since the universe
For an ending, the ballerina does a demi-plié and jumps two feet into the air.
The Earth, balancing her momentum, responds with its own sauté and changes orbit
by one ten-trillionth of an atom's width. No one notices, but it is exactly right.