Tin-Can Mystery

Copyright 2008 Paul Niquette. All rights reserved..

Natural environments do the work of selection. Holes pick the pegs, not vice versa. 

-- Paul Niquette ca. 1977
atural Selection determines the shapes and features of all living things commensurate with their overall size, according to John Burdon Sanderson Haldane (1892-1964).  He published a most informative and entertaining essay entitled On Being the Right Size in 1928 based on the Square-Cube Law, which may be summarized as follows:
As the linear dimension of an object varies, surface area varies according as the square while volume varies according as the cube.
For example, this table shows the effects of doubling and halving the linear dimension...
   Linear Dimension   1     2   1/2
   Surface Area   1    4  1/4
   Volume   1    8  1/8
   Weight   1    8  1/8
   Cross-sectional Area   1    4  1/4
   Strength   1    4  1/4
   Strength-to-Weight Ratio  R  R/2  2R

For survival -- rather, for successful propagation of genes -- living things, over wide ranges in size from amoeba to arethusa, baboon to beetle,... zebra to zebu have each accommodated the Square-Cube Law through distinctive shapes and structures, tissues and organs.  J. B. S. Haldane went on to observe size-imposed aspects of economic models and social institutions.

On the right, one sees two enclosed cylinders.  Despite their differences in size, these containers are nearly the same shape, with ratios of height-to-diameter of 1.5.  Linear dimensions vary between the two containers by a factor of eight (3.75 x 2.5 inches versus 30.25 x 20.0 inches). Thus, the surface area of the oil barrel is 64 times that of the soup can, and the volume is 512 times more capacious. 

ne might suppose that J. B. S. Haldane would be mystified by this apparent violation of the Square-Cube Law -- that with furrowed brow he would remark, "An elephant must manage 500 times the weight of a jackrabbit.  By virtue of natural consequences, these two creatures, unlike tin-cans and barrels, exhibit vast anatomical differences." 

Not likely.  Haldane's famous book, The Causes of Evolution (1932), a landmark work of modern evolutionary synthesis, applied the mathematics of Mendelian genetics to affirm Natural Selection.  Accordingly, he would cheerfully regard the Tin-Can Mystery merely as evidence of "intelligent design." 

These 'species' did not take millions of years to evolve, guided by "selective pressure" in the Darwinian sense.  Appearance of the tin-can dates back to only 1810 and its invention by Peter Durand.  One must wonder at the rationale guiding the mind of the "intelligent designer," such that a height-to-diameter ratio of 1.5 seems to be appropriate across an 8-to-1 range in size. 

One obvious consideration is the cost of materials. An enclosed cylindrical container with diameter D and height H has a surface area A D H + 2 (/4) D 2 square inches of tin (tin-coated steel, truth be known) to accommodate a volume V = (/4) D 2 H cubic inches. 

Is a height-to-diameter ratio of 1.5 especially economical?