Bees Know Best
Humans have long suspected what honeybees seem to have known for millions of years - that the honeycomb is indeed the most efficient way to pack liquid in an array of cylinders. We'll talk with a mathematician about honeycombs - after this on Earth and Sky.
Date
JB: This is Earth and Sky, on the subject of honeycombs. If you wanted to know the most efficient way to store honey, just look to the bees. But if you don't trust the bees, ask a mathematician. We spoke with mathematician Dr. Keith Devlin about what's known as "the honeycomb conjecture":
(Tape 0:01:58-0:02:25) Even way back in the time of the ancient Greeks, it was conjectured that the familiar honeycomb shape we see, which is a repeating hexagonal pattern -- they're cylinders, hexagonal-shaped cylinders, stacked one against the other in an endless array -- even in the times of the ancient Greeks it was conjectured, I think it was Pappas in fact who conjectured that that was the most efficient way of storing honey -- efficient in the sense of it uses the minimum amount of wax to store a certain volume of honey.
JB: But it took a long time for humans to prove the wisdom of what the bees had been doing for millions of years.
(Tape 0:02:33-0:02:51) Oddly enough, this was one of those cases -- and they happen from time to time in mathematics -- that proving something rigorously that seems obvious or at least intuitively clear can take a long time. In the case of the honeycomb conjecture, the conjecture that the shape of the honeycomb uses the least amount of wax - that conjecture took two thousand years to prove. (Tape 0:03:11-0:03:24) It was rather tricky mathematics - the proof takes about 30 or 40 pages as I recall - quite heavy-duty mathematics in order to do something that the natural world had just done through ordinary evolutionary processes.
JB: Thanks to Dr. Keith Devlin for speaking with us. And with thanks to the National Science Foundation, I'm Joel Block, for Deborah Byrd, for Earth and Sky
Author: Beverly Wachtel.
Thanks to the following individual for aiding in the preparation of this script:
Dr. Keith Devlin
Dean of Science
St. Mary's College
Moraga, CA
Senior Researcher
Center for the Study of Language and Communication
Stanford University
Menlo Park, CA
Devlin@stmarys-ca.edu
If you enjoyed this program, you may be interested in the following:
The Language of Mathematics: Making the invisible visible, Keith Devlin. W.H. Freeman, 1998.
Life by the Numbers, Keith Devlin. John Wiley, 1998. (The companion to the PBS television series by the same name.)
Goodbye Descartes: The End of Logic and the Search for a New Cosmology of the Mind, Keith Devlin. John Wiley, 1997.
Mathematics: The Science of Patterns, Keith Devlin. W. H. Freeman, Scientific American Library series, 1994.
Science News Online: The Honeycomb Conjecture:
http://www.sciencenews.org/sn_arc99/7_24_99/bob2.htm
Frank Morgan's Math Chat - HALES PROVES HEXAGONAL HONEYCOMB CONJECTURE:
http://www.maa.org/features/mathchat/mathchat_6_17_99.html
The Honeycomb Conjecture:
http://www.treasure-troves.com/math/HoneycombConjecture.html
Author's notes:
Dr. Devlin adds:
It was only in 1999 that Thomas Hales, a mathematician at the University of Michigan finally proved what everyone had suspected for a long time - that the honeycomb is indeed the most efficient way of packing any kind of liquid in an array of cylinders