Dehydrated Elephants

Not Even Wrong noted the recent passing of mathematician Robert Hermann 1931-2020.

In that blog post, Peter Woit wrote:

Being ahead of your time and mainly writing expository books is unfortunately not necessarily good for a successful academic career. Looking through his writings this afternoon, I ran across a long section of this book from 1980, entitled “Reflections” (pages 1-82). I strongly recommend reading this for Hermann’s own take on his career and the problems faced by anyone trying to do what he was doing (the situation has not improved since then).

The reference is to Robert Hermann's book, "Cartanian Geometry, Nonlinear Waves, and Control Theory, Part 2", which you can read in Google Books. This is where I first encountered dehydrated elephants.  To quote:

5. INTUITION AND LOGIC OF POINCARÉ AND THE DEHYDRATED ELEPHANTS OF MARK KAC

As I have already mentioned, I feel  very attracted to the mathematical attitudes of the late 19th century France...Of course, the greatest scientific figure of this period is Poincaré.  A chapter in his book "The Value of Science", titled Intuition and logic in mathematics, has always seemed to me to be the ultimate statement in mathematical philosophy by which I have lived.  Since it is not well-known today, here it is:....

Go to the link above if you want to read Poincaré's chapter.  I'll just note that Poincaré too has an elephant ("....should a naturalist who had never studied the elephant except by means of the microscope think himself sufficiently acquainted with that animal?").   I continue with Hermann:

Now, perhaps the reader can understand why I believe it has been all down hill since 1900.  Leaving t he sublime, let us turn to consider a representative opinion of today, a statement made by Mark Kac.  Here he starts off arguing for a view of "applied mathematics" transcending "practical" considerations, but most of his essay is a warning about producing "dehydrated elephants".  He objects strongly to the views of Saunders MacLane, who he calls a "leader and eloquent spokesman for the strongly abstract trend in mathematics."   He particularly objects to the following statement by MacLane:

Just as each generation of historians must analyze the past again, so in the exact sciences we must in each period take up the renewed struggle to present as clearly as we can the underlying ideas of mathematics. . . . Many cumbersome developments in the standard treatment of mechanics can be simplified and better understood when formulated with modern conceptual tools, as in the well-known case of the use of the "universal" definition of tensor products of vector spaces to simplify some of the notational excesses of tensor analysis as traditionally used in relativity theory.

Kac claims that MacLanes's program of reexamining physics in the light of conceptual advances in mathematics would, without checks, constitute the broadest license for the creation of "dehydrated elephants".  He says that "it would also add a kind of self-delusion that one is contributing to a subject when in reality all one is accomplishing is discovering that all the time one has been speaking prose."  Kac then goes on to cite Caratheodory's "subtle and elegant axiomatization" of thermodynamics as a prime example of such a "dehydrated elephant".

Woit's take on this controversy is here.  We get to "On Applying Mathematics: Reflections and Examples", by M. Kac, Quarterly of Applied Mathematics, April 1972, and we find Kac's dehydrated elephants:

...and here I cannot resist referring once more to a wartime cartoon depicting two chemists surveying ruefully a little pile of sand amidst complex and impressive-looking apparatus.  The caption read: "Nobody really wanted a dehydrated elephant but it is nice to see what can be done".  I am sure that we can all agree that applying mathematics should not result in creation of "dehydrated elephants".

(Kac returned to the theme in Dehydrated elephants revisited, American Scientist, Vol 70, No. 6, November-December 1982), pp. 633-634.)

So of course, I want to see this cartoon.   Fortunately one can find a reference:

Elworthy, P. H. (1997). Dehydrated elephants and other matters. Journal of Pharmacy and Pharmacology, 49(6), i-x.

A shortened version of the text of Professor Elworthy's Science Chairman's Address to the British Pharmaceutical Conference in 1971 in Glasgow reprinted, with permission, from the Pharmaceutical Journal 1971 207: 265–269.

Elworthy begins: 

The title that I have chosen may seem very strange.  It comes from a cartoon in Hein's book where two academic powder technologists are studying a little heap of powder, and remarking: 'Of course, nobody really wanted a dehydrated elephant, but it's nice to see what we can do'.

and he kindly gives the citation, which leads us to Die Pharmazie in der Karikatur, Wolfgang Hagen Hein, C.H. Boehringer Sohn, 1964.

And here, finally, is the cartoon: