On Growth and Form: The Complete Revised Edition
By addebook • Jun 24th, 2008 • Category: Biology •
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On Growth and Form: The Complete Revised Edition
On Growth and Form: The Complete Revised Edition
By D’Arcy Wentworth Thompson
Publisher: Dover Publications
Number Of Pages: 1116
Publication Date: 1992-06-23
ISBN-10 / ASIN: 0486671356
ISBN-13 / EAN: 9780486671352
Binding: Paperback
First published in 1917, On Growth and Form was at once revolutionary and conservative. Scottish embryologist D’Arcy Wentworth Thompson (1860-1948) grew up in the newly cast shadow of Darwinism, and he took issue with some of the orthodoxies of the day–not because they were necessarily wrong, he said, but because they violated the spirit of Occam’s razor, in which simple explanations are preferable to complex ones. In the case of such subjects as the growth of eggs, skeletons, and crystals, Thompson cited mathematical authority: these were matters of “economy and transformation,” and they could be explained by laws governing surface tension and the like. (He doubtless would have enjoyed the study of fractals, which came after his time.) In On Growth and Form, he examines such matters as the curve of frequency or bell curve (which explains variations in height among 10-year-old schoolboys, the florets of a daisy, the distribution of darts on a cork board, the thickness of stripes along a zebra’s flanks, the shape of mountain ranges and sand dunes) and spirals (which turn up everywhere in nature you look: in the curve of a seashell, the swirl of water boiling in a saucepan, the sweep of faraway nebulae, the twist of a strand of DNA, the turns of the labyrinth in which the legendary Minotaur lived out its days). The result is an astonishingly varied book that repays skimming and close reading alike. English biologist Sir Peter Medawar called Thompson’s tome “beyond comparison the finest work of literature in all the annals of science that have been recorded in the English tongue.” –Gregory McNamee
Classic of biology and modern science sets forth seminal “theory of transformation”—that one species evolves into another not by successive minor changes in individual body parts but by large-scale transformations involving the body as a whole. Rich literary style. Over 500 photographs and drawings. Index.
Summary: Mathematical-biological gems
Rating: 5
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, or v^2=F/l^2. But whatsoever force be available, the animal may only exert so much of it as is in proportion to the strength of his own limbs, that is to say to the cross-section of bone, sinew and muscle; and all of these cross-sections are proportional to l^2, the square of the linear dimensions. The maximal force, F_max, which the animal dare exert is proportional, then, to l^2; therefore F_max/l^2=contant. And the maximal speed which the animal can safely reach … is also constant.”
Geodesics: “an instructive case is furnished by the arrangement of the muscular fibres on the surface of a hollow organ, such as the heart or the stomach. … In fact we have a right to expect that the muscular fibres covering such organs will coincide with geodesic lines … For if we imagine a contractible fibre … to be fixed by its two ends upon a curved surface, it is obvious that its first effort of contraction will tend to expend itself in accommodating the band to the form of the surface, in ’stretching it tight,’ … and it is only then that further contraction will have the effect of constricting the tube and so exercising pressure on its contents. Thus the muscular fibres … arrange themselves automatically in geodesic curves: in precisely the same manner as we also construct complex systems of geodesics whenever we wind a ball of wool or spindle a tow, or when the skilful surgeon bandages a limb” (pp. 742-744).
Comparative anatomy of bridges. A parabolic arch bridge is designed to distribute stress uniformly. Its shape is determined by a “stress diagram”: if we imagine the bridge as a beam on two pillars and plot the stress as a function of position on the bridge then we get precisely the arch needed to equi-distribute this stress. More generally, “Every diagram of moments represents the outline of a framed structure which will carry the given load with a uniform horizontal stress” (p. 996), and “to precisely those stress-lines has Nature kept in the building of the bone” (p. 995). So, for example, “whenever the head and neck represent a considerable fraction of the whole weight of the body, we tend to have large bending-moments over the fore-legs, and correspondingly high spines over the vertebrae of the withers … The case is sufficiently exemplified by the horse, and still more notably by the stag, the ox, or the pig.” (p. 1003).
Summary: a classic compilation of very neat gems
Rating: 4
This book is a *classic*; an adventure into abstract mathematical properties of nature. The author rambles on about many topics concerning natural manifestations as viewed from near human and cellular scales, with the tools of the early 20th century. It’s that enigmatic space between Biology and Geometry, presented in a very accessible manner by an author whose love and knowledge of the subject shines through well.
Summary: Canto: An unfortunate redaction of a timeless classic
Rating: 2
Don’t get me wrong — “On Growth and Form” is one of my absolute top favorite books of all time. Possibly my favorite book, in fact. This review is a warning to make sure you get the right imprint.
Unfortunately some publishers think that they know better than D’Arcy Thompson, and cut out more than half of the original material. After all, nobody these days actually looks at equations, right? Well I do, and the pathetic edition by Canto (368 pages) weighs with less than 33% of the material in the modern unexpurgated reprint by Dover (1116 pages).
Amazingly enough, the redacted Canto version costs nearly the same as the Dover complete. If you care about this material, take care to get all of it.
Summary: On Growth and Form
Rating: 5
On Growth and Form written by D’Arcy Wentworth Thompson is a classic and should be found on the bookshelf of any well read person.
This book sets our mind up for an education in physics, chemistry, mathematics, and physiology with form and function. Language skills are needed for reading this book as the author uses the original Greek in places for explaination and emphsis. Aristotle comes to mind and German is used for emphsis.
If you want to get the full extent of the text and you are not up to speed on the subjects mentioned or you’ll find it hard to read this book. This could be read by a junior or senior in high school. But, I think it would be more appropriate for college.
This book is the study of organic form using methods found in the physical sciences. This book is a challenge to read, but it is very logical and straight forward.
Summary: A misunderstood classic
Rating: 5
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.
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A Highly Acclaimed book ever written in the history of mankind. Arcy Thompson saw numbers and only numbers in every living and nonliving thing on this earth. A great work throwing light on various aspects of mathematics as applied to the variety of natural phenomena ranging from plant cells to the shells on the seashores…..
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