- How did you end
up researching and working in Italy?
I was an undergraduate at Princeton University during its "golden age of
relativity" and met an Italian physicist
Remo Ruffini collaborating with John Wheeler (Feynman's advisor) on
black holes to do some independent work translating a long paper by
Luigi Bianchi from 1898 on homogeneous spaces for use in mathematical
cosmology. Some years later I then did a postdoc with Ruffini in Rome
never stopped returning.
- How would you
explain relativity to a freshman? (In other words, how would you explain it
to the layperson who has very little previous knowledge?)
Special relativity is relatively simple: the laws of physics show have the
same form for any pair of observers which are each moving at constant
velocity (inertial observers, as in inertial guidance systems for jets). For
example, if a laser gun on a jet fighter is shot in the forward direction,
the speed at which its beam arrives at the target should be the same as
measured on the ground or as measured by the jet fighter instruments.
General relativity is more complicated in that there are no preferred
inertial observers moving at constant velocity due to the curvature of
spacetime. I don't have a short answer for this. The presence of matter and
energy curves spacetime, and spacetime in turn tells matter how to move, in
the rephrased words of John Wheeler. But in any region small enough compared
to spacetime curvature, the laws of special relativity should apply.
- Can you say a bit more about the pasta metaphor? How
did you come up with it?
Pasta by Design is
a recent whimsical coffee table book reporting on the mathematical
description and classification of 90 types of pasta shapes by an
architectural design expert. The cavatappi shape is among the most
mathematically pleasing of these shapes and was a simple extension of the
donut geometry I had already
thoroughly studied, but even more whimsical
and certainly more complicated. The light bulb went off: this would make an
interesting way of describing spacetime curvature in a familiar setting,
while connecting the mathematical techniques to its Italian origins (Levi-Civita
gave Einstein the tool he needed to create his theory of gravity). And it
does not hurt that I am a big pasta fan.
However, as my talk will show, the so called "geodesics" of the helical
cavatappi surface surprisingly offer an incredible analogy to the helical
orbits in spacetime of the almost circular planetary orbits around the sun,
including the monthly oscillations in the Earth-Moon system about their
common center of gravity which correspond to the ridges on the cavatappi
surface. This I only realized after responding to these questions, showing
the power of human interaction to propel us forward in our thinking.
- What can students expect to take away from your
Mathematics is a beautiful and imaginative subject in its own right, but it
is also the most powerful tool we have to understand our universe and how
- Is there
anything else you’d like to mention?
None of this pasta geometry work would have been possible without a computer
algebra system: Maple is our choice here at Villanova University. It allows
the mathematically intelligent user to tackle calculational problems that
would never have been possible without such software. If only students (and
faculty) could recognize that both understanding concepts and having the
appropriate computational (software) tool to use those concepts to solve
realistic problems are equally important, but that promise of college
mathematics is not being fulfilled today---math is not just for taking
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