> "The shape of the bee cell does not have
> its celebrated regularity; its economy is a
> teleological myth...."
As early as 36 BC, Marcus Terentius Varro (aka "Varro Reatinus") disagreed -
he wrote down that a "hexagonal lattice lets you divide the plane into cells
of equal area with the least possible perimeter per cell", so the bees,
using the minimal amount of wax possible, are going to end up with a roughly
hex set of cells no matter how they start out by simply striving to conserve
wax and minimize surface thicknesses. There are multiple good videos
demonstrating this, here's one:
https://youtu.be/4Lt3b3rSjxs
Kelvin, Fejes Toth, Weaire, Phelan would also all disagree, and they all had
very solid math (based upon Navier-Stokes equations) and physical models
(using soap films and bubbles) to prove the point - both the math and the
experiments have shown that soap bubbles of equal size blown between two
sheet of glass (so as to constrain the bubbles as to length and keep the two
layers intact) form the exact same structural shape as an ideal bee-made wax
honeycomb cell. In fact, Weaire and Phelan found a very slightly more
"efficient" shape, beating Lord Kelvin's structure by 0.3% in terms of
surface area vs volume enclosed. They also found a slightly more efficient
variation than the bees could ever make, but this required a much less
viscous material than beeswax. So, the bees wax forms the most efficient
shape possible for that material.
The complete bee cell is harder to model with soap bubbles, and harder still
to get cells back-to-back to show the proper base configuration, but its not
impossible.
When the cells vary, it is localized variation due to physical constraints
imposed by the bees not making walls of the same thickness, the wooden frame
or nest walls, and transitions between the variations in cell-size between
"drone" and "worker" cells. More recently, Trinity College was able to
model the Weaire-Phelan structure using actual soap bubbles, rather than
software, like "Surface Evolver":
https://youtu.be/oS0XjwJ64GY
> "...The whole history of the bee cell in
> natural philosophy, geometry and
> philosophy is the story of a two
> hundred-years-old mistake."
Well, ascribing intent and great mathematical prowess to the bees was a
mistake, but the structures that result are none the less amazingly precise
and regular, due to the laws of physics, like the Young-Laplace equation,
subject to the understanding that while the bees will strive to minimize the
thickness of the walls of the wax cell, they will never have absolutely even
thicknesses of wax to produce "zero curvature" per Young-Laplace, so
beekeepers will always see some variation on each frame.
> Science is never settled.
In the "observational" sciences, like bio, this tends to be true, as a
sighting of one black swan (or at last noticing after 20 years that a
gazillion varroa are all oblong, rather than round) can change everything.
In the "analytical" sciences, the "hard sciences", (meaning "not soft or
fuzzy"), like physics, this tends to be a process of getting more data,
measured with sharper tools, which results in a more precise set of
statements about reality.
One could call these ever-more-precise values "unsettled", but they are tiny
improvements, better viewed as an expression of improved technology,
allowing better apparatus, and measurements that have smaller error bars.
> I've heard the universal constants are not all that constant
Paul Driac wondered back in the 1930s about the variation of things like the
gravitational constant over time. Variation in the constants would be
amazingly significant news if any evidence could be found, as it would shred
truckloads of studies and experiments, and prompt massive changes in the
consensus view of reality itself. So, there are people who choose to spend
their careers and lives addressing this issue, as it is a long shot, but
with a very large payoff if they ever get lucky.
The "CODATA Recommended Values Constants for 2010" (not published 'til 2012,
'cause they are just that careful):
http://physics.nist.gov/cuu/Constants/Preprints/lsa2010.pdf
http://tinyurl.com/2cnbty5o
includes the following statement - "Although the possible time variation of
the constants continues to be an active field of both experimental and
theoretical research, there is no observed variation relevant to the data on
which the 2010 recommended values are based". So, the term "constants"
still means what it says, at ever-more silly levels of precision that few
can afford the toys to verify.
The classic 1896 "Soap-bubbles and the forces which mould them" by C. V.
Boys is still being printed and sold, but a free pdf is here:
https://projecteuclid.org/download/pdf_1/euclid.chmm/1424377189
http://tinyurl.com/1pgrra27
I went down the soap bubble rabbit hole for a time, all math-heads do. I
recovered. Beekeeping is part of my ongoing therapy.
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