On Growth and Form

This is a delightful book. I shall give some sample highlights. First some things from the particularly enjoyable chapter 2, "On Magnitude". Raindrops come in the sizes 2^n (p. 59, Dover ed.). Proof: As they leave the cloud the rain drops are all of the same size. If two rain drops meet they make one raindrop of twice the mass, as so start falling faster than the singles. Thus it will never merge with a single to make a size 3 drop, but it may join another double to make a quadruple drop. Of course the quadruples fall faster than the doubles and the singles, so they will only merge with other quadruples, and so on. Many results are derived from "dimension theory". A simple illustration is the following "paradox" of constant-temperature animals (pp. 33-34). "The heat lost must ... be proportional to the surface of the animal: and the gain must be equal to the loss, since the temperature of the body keeps constant. It would seem, therefore, that the heat lost by radiation and that gained by oxidation vary both alike, as the surface-area, or the square of the linear dimensions, of the animal. But this result is paradoxical; for whereas the heat lost may well vary as the surface-area [i.e., as l^2], that produced by oxidation ought rather to vary as the bulk of the animal [i.e., as l^3]". Thus one is "driven to the conclusion that the smaller animal does produce more heat (per unit mass) than the larger one, in order to keep pace with surface loss; and that this extra heat-production means more energy spent, more food consumed, more work done." Another illustration of dimension theory: the maximum jumping height of an animal is constant under scaling (p. 37), for "the work done in leaping is proportional to the mass and to the height to which it is raised, W proportional to mH. But the muscular power available for this work is proportional to the mass of muscle, ... W proportional to m. It follows that H is ... a constant. In other words, all animals, provided that they are similarly fashioned, with their various levers in like proportion, ought to jump not to the same relative but to the same actual height." It follows that "neither flea nor grasshopper is a better but rather a worse jumper than a horse or a man." Yet another illustration of dimension theory: the maximum velocity of a fish is proportional to sqrt(length), "For the velocity (V) which the fish attains depends on the work (W) it can do and the resistance (R) it must overcome. Now we have seen that the dimensions of W are l^3 [muscle volume], and of R are l^2 [surface area friction]; and by elementary mechanics W is proportional to RV^2, or V^2 proportional to W/R. Therefore V^2 is proportional to l^3/l^2=l, and V proportional to sqrt(l)" (p. 31). For land animals, however, velocity is constant under scaling (p. 38), as we se by considering "the momentum created ... by a given force acting for a given time: mv=Ft. We know that m is proportional to l^3 and t=l/v, so that l^3v=Fl/v

A great book, to be read by all biophysicists-to-be. The modern follow-up to this book is Thom's Structural Stability, which shows that the logical conclusion of Thompson's ideas is both exciting and dubious. We probably can't just 'look' at stuff, we need to make (useful) predictions or the theory won't last. The interested reader should also pick up, if briefly, Mandelbrot's Fractal Geometry of Nature. Two notes of interest. 1) Morphology has indeed proven successful in proving physical theory: in the aggregation of dust particals, measuring the gross fractal dimension allows you to predict the type of noise involved in creating it. 2) The logarithmic spiral, together with the fibonnaci sequence and the golden ratio, show up quite surprisingly in synchronized chaotic loops. PS: to these I can add three more. 3) Shipman and Newell at the University of Arizona have shown that the Fibonnaci sequence in phylotaxis arises from buckling of pressurized skin (e.g. in a cactus or young sunflower) 4) Goldstein, also at UA, has shown that a broad variety of cave patterns (from ripples on the wall to bumps on stalagtites to wonderful crystaline snowflakes) all arise as a result of a single cause, the diffusion-reaction equation. 5) the late Winfree (also at UA!) has quite conclusively shown that heart beating and defribrillation are non-equilibrium sprial patterns similar to the BZ reaction. The whole business of form has been taken up by the Sante Fe institute, see Kauffman's At Home in the Universe. Anyone who likes this book would inevitably also love Wilson's Insect Societies. So, hopefully you understand that Thompson's book is not an island, but a visionary precursor of active research.

This book is a classic, no two ways about it. It is really the first credible attempt to start taking a quantitative approach to biology, and despite the developments of the past century (molecular biology, etc), the problems raised in this book are just as pressing as they were when thompson wrote it. Anyone working in cell biology nowadays will immediately see applications of the ideas in this book, for example to organelle morphogenesis. The genius and erudition of thompson shine through on every page, making the book inspiring to read.

It's about so much more than the limits our minds create from standard reviews & categorizations. Shows how to organize your thinking to tackle something new. On the surface, it's a turn of the century survey & application of physical scientific knowledge. On a higher level it communicates how to effectively organize knowledge as a tool & pathway to inner understanding as only the CLASSICS can do. I was required to read it for my Brandeis Ph.D. in Biophysics, but have recommended it to home schoolers as the best single book to inform a teenager about physics, chemistry, biology, & practical thinking. The Latin roots of the title words, Form & Function, are utilized, rather than specialized contemporary jargon.