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Bees, basalts, and hexagons

The geometry of nature

By Jack Souther, Whistler Naturalists

Mathematicians call it "hexagonal close packing" and can prove by means of sophisticated formulae that it is absolutely the most efficient way to divide a space into a number of smaller "rooms." This remarkable flash of human insight was in fact discovered by the lowly honey bee long before Thales and Pythagoras invented geometry.

But even before the first bee evolved from some speck of primordial ooze – when the earth was still cooling from its cosmic origin – the columnar jointing of lava flows was governed by the mathematical principles of hexagonal close packing.

From the bee's perspective hexagons make eminent sense. They allow the storage of a maximum amount of honey in convenient sized containers that require a minimum of wax to construct. If we were to adopt the same principle to say, beer cans, making them hexagonal rather than round, the space now used to hold a six-pack would suffice to hold a seven-pack.

Tourists seeking to view the hexagonal marvel of columnar jointing are lured to such exotic destinations as Devils Postpile in California or Giants Causeway in Ireland. Here at Whistler we need go only as far as the BC Rail quarry to find basalt lava flows with pretty good columns. A little farther up Cheakamus Valley, the long slender columns from lava near Loggers Lake are prized by landscape gardeners who have gathered them up and transplanted them to incongruous spots throughout the Lower Mainland.

Columnar jointing forms when molten lava cools, solidifies, and shrinks. As a flow cools it solidifies from the top down and the bottom up. Depending on its thickness the process may take days, weeks, or months before molten lava in the centre of the flow becomes solid. As the lava cools it continues to shrink even after it is solid, setting up stresses that cause the rock to fracture. The first shrinkage cracks develop as soon as a solid crust has formed on the cooling lava. These are propagated upward and downward as successive layers of the flow become solid enough to fracture and ultimately these cracks become the columnar joint surfaces. Because the fractures progress in a succession of short breaks the resulting column may exhibit horizontal "chisel marks" each representing a discrete mini-fracture.

Computer simulations of column development are, not surprisingly, consistent with the obvious. As the first random fractures on the surface of a cooling flow propagate inward to a more uniform thermal environment they gradually re-organize and rotate into a pattern of hexagonal close packing. Like the hexagonal efficiency of the honeycomb the hexagonal fracture pattern of columnar jointing is the most efficient way to relieve the internal stresses in a cooling mass of shrinking lava – uniformly distributing the volume change with a minimum of fractures. Like so many things in nature the bees and basalts got it right without the help of Greek geeks or computer freaks.

Upcoming Events:

Friday, October 25th, 7:30 p.m. — The Milky Way and Other Galaxies , with John Nemy of the Pacific Observatory. Millennium Place. The talk goes from the Mount Wilson Observatory, California to The Space Telescope on this galactic journey of our Universe. The presentation is suitable for all ages and follows humanity’s quest to understand the spiral nebulae. John will present images from Star Hill, New Mexico, Torrance Barrens Dark Sky Reserve, Ontario, and Manning Park and Mount Kobau, B.C.

Sightings: NatureSpeak is prepared by the Whistler Naturalists. To report noteworthy bird sightings any time of year, please contact Michael Thompson (604-932-5010; email:

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