April 7, 1998, Tuesday
        Section: Science Desk
 
 
        Physicists Study the Honeybee For Clues to Complex Problems
 
 
        By MALCOLM W. BROWNE
        HOW doth the little busy bee improve each shining hour? By making
honey,
        of course. But also by prompting scientists to think about the deep
        significance of gooey coils that pile up when honey is poured on
toast,
        and how quantum mechanics might choreograph the dancing of bees.
        Two papers that recently came to light (one in the March issue of
        Nature, and the other not yet accepted for publication) celebrated
the
        humble honeybee, reminding readers that seemingly trivial problems
can
        lead to weighty insights.
 
        In the Nature paper, Dr. Lakshminarayanan Mahadevan, a physicist at
the
        Massachusetts Institute of Technology, revealed a formula he
discovered
        for predicting the frequency at which liquid coils form at the
bottom of
        a stream of honey (or a similar fluid). Assisted by experiments
        conducted by two Harvard University students, Dr. Mahadevan showed
that
        by taking into account the density of the fluid, its viscosity, its
flow
        rate, the gravitational force, the radius of the stream and the
height
        from which it descends, it is possible to calculate the frequency
and
        radius of the resulting coils, at least up to the point at which
they
        spread out (and are devoured).
        So what?
        ''At first I was just curious,'' Dr. Mahadevan said in an interview.
        ''This was one of the few problems that the late fluid dynamicist
Sir
        Geoffrey I. Taylor left the rest of us to solve. Taylor made many
great
        discoveries, including one he made while working on the first atomic
        bomb at Los Alamos. He discovered a way of predicting how the shock
wave
        from a nuclear blast would spread out. He also thought about weather
and
        climate, about how sperm swims, and many other things involving
fluid
        dynamics, but he never got around to solving the honey-coiling
        problem.''
        Dr. Mahadevan said that the problem seemed too complex to solve when
he
        first attacked it three years ago. Instead, he decided to
investigate a
        somewhat similar phenomenon: the spontaneous coiling of rope when a
        length suspended vertically falls to the ground. His successful
solution
        of the rope-coiling problem led to his new formula for honey
coiling.
        ''As we moved along,'' Dr. Mahadevan said, ''I found that there are
        people interested in this: in the glass industry, for instance, in
which
        glass fibers must be pulled from melted glass at just the right
speed,
        and in the textile industry, in which liquid polymer is pulled
through
        small holes to form fibers.''
        The investigation of honey coiling is far from complete, he said,
but it
        has led to another flavorful field of research: the study of how
sheets
        of falling honey (rather than thin streams) behave as they hit the
        ground.
        ''Sheets of viscous fluid do not coil,'' Dr. Mahadevan said. ''They
        buckle and fold. The behavior seems to be analogous to the buckling
of
        sheets of rock under pressure over geological time periods. The
        geological flow of tectonic plates -- the mechanism that creates
        mountain ranges -- may be similar in principle to the flow of sheets
of
        honey. We'll have to see how it pans out.''
        Bees, of course, are interested in honey too, and when a bee finds a
        good source of nectar it signals its hive mates where to look. It
does
        so by ''dancing.''
        Dr. Barbara Shipman, a mathematician at the University of Rochester,
is
        the daughter of a physicist who was interested in bees. Early in her
        career she became aware that bees returning to their hives do a
        stylized, curving ''waggling run'' with their heads pointed toward
food
        to guide others in the swarm.
        Dr. Shipman's special interest is the geometry of multidimensional
        spaces -- spaces that may have many more dimensions than the three
of
        everyday experience. While investigating patterns in a theoretical
        six-dimensional space (which cannot be visualized), she projected
them
        on a two-dimensional plane, and discovered to her surprise that the
        resulting curves resembled those that are traced by dancing bees. (A
        more easily visualized ''projection'' is that of a three-dimensional
        sphere. Projected on a two-dimensional plane, the result is a
circle.)
        Physicists have devised various theories based on multidimensional
space
        to find hidden relationships between different kinds of fundamental
        particles, all of which obey the rules of quantum mechanics. Dr.
Shipman
        suspects that quantum mechanics plays a role in biology and
behavior,
        and that there might be a link between the mathematics of
        six-dimensional space and the innate signaling behavior of bees.
        ''Lots of physics go on in the bee,'' she said. ''The bee doesn't
know
        what it's doing. Its behavior is programmed, not learned from other
        bees. Newly born bees do the waggling runs after their first flights
to
        find nectar, before ever seeing another bee dance.
        ''It seems to me natural that quantum mechanics must have some
        interaction with biology, which is the most complex of all physical
        systems.''
        Dr. Shipman has yet to persuade publishers to print the paper
outlining
        her ideas, but some physicists, Dr. Roger Penrose of Oxford
University
        among them, also believe in connections between quantum events and
        biological behavior.
        ''At least it's worth looking into, don't you think?'' Dr. Shipman
said.
 
 
        Correction: April 14, 1998, Tuesday
        An equation in Science Times last Tuesday for predicting the
frequency
        at which honey coils on toast rendered the exponents incorrectly. A
        corrected equation appears today on page F5.
        Correction: April 14, 1998, Tuesday
        An equation last Tuesday for predicting the frequency at which honey
        coils on toast rendered the exponents in the formula incorrectly.
 
        The formula is: [omega][wavy hypen]Q(to the 3/2 power)r(to the -7/2
        power)[nu](to the -1/2 power)
 
        Or: The frequency of coils is approximately equal to the flow rate
(to
        the 3/2 power) times the radius of the filament (to the -7/2 power)
        times the kinematic viscosity (to the -1/2/ power).
        Correction: April 17, 1998, Friday
        A picture in Science Times on April 7 with an article about the
coiling
        patterns of liquids like honey carried an incorrect credit. It was
from
        Felice Frankel, not Nature.
 
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