The Big and the Small of It

Even though the book I was reading was about the inherent limits of scientific knowledge, what caught my thoughts was some actual scientific information in the book.  The author, Sir Peter Medawar, winner of a Nobel Prize in Medicine, had been laying a foundation for the book's main point by first giving other examples of how some things have intrinsic limits.  He gave examples of two animals -- one big and one small -- whose sizes are confined by a principle of geometry.

one elephant
(two Homo sapiens in car)

That principle (sometimes called Spencer's Law) is that "if a three-dimensional body grows in size without change of shape, its surface area increases as the square of a linear dimension while its volume or mass increases as the cube."  Not being mathematically minded, I almost got lost following that sentence.  But fortunately, Medawar moved from that abstraction to concrete examples regarding animals, which I could understand:  "This principle sets an upper limit upon the sizes of land animals.  The weight of an animal increases as the cube of a linear dimension, while... the cross-sectional area of the limbs... increases only as the square.  An elephant's legs are pillar-like already.  If an elephant were much larger than it is, it might be difficult to see daylight between its legs [because they would have to be proportionally larger.]"

Etruscan pygmy shrew

Even more interesting, this principle regarding the ratio of surface area to body volume also forces a limit on warm-blooded animals on the opposite end of the scale.  That is, on little animals.  Again, Medawar provided me an example, in this case the opposite of that of an elephant:  "Weighing only 2 grams when fully grown, the Etruscan pigmy shrew has so great a surface area in relation to its volume that it is about as small as a free-living warm-blooded animal could be, having regard to the rate of loss of heat.  It must... eat almost uninterruptedly to maintain its body temperature."  Having never been as big as an elephant, I could not readily identify with it.  But I could empathize with that tiny shrew, whose work never seemed to be done no matter how fast it worked.

So, here I am, a human being caught on a mid-range between big and small.  That would have been the dilemma for all hominid species (even if they had been around at the time of dinosaurs, some of which would have pressed up against that upper body-weight limit even more forcefully).  It seems to me, however, that the greater limits most of us humans face are not ones of body size.  Instead they are limits involving abilities, wants, and hopes.  It is is in that sphere that the weight of heavy experiences in life can sometimes nearly crush us.

On the other hand, even while we recognize physical and environmental limits, it would not be good to set our hopes too low when we yearn for the good.  There is something about our human psychology that causes us to be sustained by visions of something greater than what we can usually accomplish.  As the 19th-century poet Robert Browning metaphorically put it,

"...a man's reach should exceed his grasp,

Or what's a heaven for?"

Similarly, the 20th-century theologian Paul Tillich pointed out that we are stronger when we want than when we possess.

~~~

Is there a good you yearn for, even though you know you may never see it completely?

(The Browning quote is from Andrea del Sarto [1855], l. 97.)
(The Medawar quotes are from The Limits of Science by P. B. Medawar.  © 1984.  [emphasis added] pp. 69 & 102.)

(Photo of shrew is by Trebol-a and is used under a Creative Commons Attribution-Share Alike 3.0 Unported license.)