Manifest Form

"The harmony of the world is
made manifest in Form and Number,
and the heart and soul and all the
poetry of Natural Philosophy are embodied
in the concept of mathematical beauty.

...

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and confirmed... Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science."

- D’Arcy Wentworth Thompson (1860 - 1948)
On Growth and Form

Subjective Wholes

"As we analyze a thing into its parts or into its properties, we tend to magnify these, to exaggerate their apparent independence, and to hide from ourselves (at least for a time) the essential integrity and individuality of the composite whole. We divided the body into its organs, the skeleton into its bones, as in very much the same fashion we make a subjective analysis of the mind, according to the teaching of psychology, into component factors: but we know very well that judgement and knowledge, courage or gentleness, love or fear, have no separate existence, but are somehow mere manifestations, or imaginary coefficients, of a most complex integral."

- D’Arcy Wentworth Thompson (1860 - 1948)
On Growth and Form

Little Ripples

 

"The waves of the sea, the little ripples on the shore, the sweeping curve of the sandy bay between the headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology.

...

Our own study of organic form, which we call by Goethe's name of Morphology, is but a portion of that wider still Science of Form which deals with the forms assumed by matter under all aspects and conditions, and, in a still wider sense, with forms which are theoretically imaginable.

...

We rise from the conception of form to an understanding of the forces which gave rise to it... in the representation of form we see a diagram of forces in equilibrium, and in the comparison of kindred forms we discern the magnitude and the direction of the forces which have sufficed to convert the one form into the other.

...

We have come to the
edge of a world of which
we have no experience, and
where all our preconceptions
must be recast."

- D’Arcy Wentworth Thompson (1860 - 1948)
On Growth and Form

Mathematical Beauty

"The harmony of the
world is made manifest
in Form and Number,
and the heart and soul
and all the poetry of
Natural Philosophy are
embodied in the concept
of mathematical beauty."

- D'Arcy Wentworth Thompson (1860 - 1948)

Postscript. As may be the case with many of you, my day-job constraints leave me precious little time to devote to purely aesthetic pleasures (notwithstanding those that occasionally overlap with more mathematical pursuits). Sometimes, as now, even my weekend time is filled mostly with staring at gibberish on a computer screen, and pounding away at my keyboard to produce picture-less reams of technical reports (even as I day-dream of month-long photo-safaris in far-away lands). Thus, the short walks my wife and I take through our neighborhood after breakfast each day have become immeasurably important physical and spiritual oases for me. The simple pleasure of encountering beautifully haphazard arrangements of natural forms rejuvenates and nourishes my soul. The images in the triptych above were taken no more than a few minutes apart during a walk that itself lasted less than a half hour. But what a joy it is to stumble upon such humble transcendent beauty hiding in plain sight! The great polymath Thompson's book, On Growth and Form (the first edition of which came out in 1917, and which to this day remains an extraordinarily beautiful book to read) is essentially a 1100+ page erudite argument that biology can be reduced to mathematics (a sentiment that a much younger version of myself would have been happy to accept): "It behooves us always to remember that in physics it has taken great men to discover simple things. They are very great names indeed which we couple with the explanation of the path of a stone, the droop of a chain, the tints of a bubble, the shadows in a cup. It is but the slightest adumbration of a dynamical morphology that we can hope to have until the physicist and the mathematician shall have made these problems of ours their own." For those of you interested in exploring (taking a deep-dive, really, into) the broader entanglement of art and science, here are some slides I used for a 2017 presentation at a Humanities and Technology Association conference (held that year in Newport, RI). This lecture is one of three I've given in (relatively) recent years during which I wore both of my hats, as physicist and photographer. The other two lectures were given at the American Center for Physics (College Park, MD in 2009) and at the Morrison House (Alexandria, VA in 2011).