This chapter is a discussion of ‘direct adaptations’, instances where mechanical forces operate upon a living structure in such a way as to modify it and make it mechanically efficient. There immediately arises the question, rather carefully avoided by D'Arcy Thompson, of the relations of these adaptations to the problem of inheritance. That there is a relation follows not only from the requisites of the Darwinian conception of evolution, but also from direct evidence.

In some instances a particular structure may not be inherited (such as the configuration of bone trabeculae in a poorly set broken leg), but the sensitivity of the cells to physical forces surely is a factor capable of inheritance and obviously of adaptive value.

In other cases, a structure is both stimulated into existence by mechanical factors and present in the embryo before the mechanical factors could possibly have operated. The soles of the feet are already thickened in the human foetus, although clearly the abrasion of walking barefoot vastly exaggerates the embryonic beginning. We have already suggested an explanation of how the organism might inherit a reactivity to the environment that would possess adaptive value, and now comes the question of how the structure itself could be directly inherited without use.

The simplest possibility (sometimes referred to as the Baldwin effect) is that if certain gene combinations appeared that produced a structure that was identical to the one produced by mechanical factors, obviously it would be advantageous and be retained by the population.

We always remember where we were when we first heard about a momentous event. Those over forty-five years old know what they were doing when they heard that John F. Kennedy had been assassinated. Similarly, anyone who was watching television remembers where they were at 11:38 a.m. Eastern Standard Time on 28 January, 1986 when the Space Shuttle Challenger exploded. The billowing cloud of white smoke laced with twirling loops made by the careering Solid Rocket Boosters proclaimed the death of seven astronauts and the end of the space programmme's ‘can do’ infallibility.

Unlike the inconclusive Warren Commission that inquired into Kennedy's death, the Presidential Commission chaired by William Rogers soon distributed blame. There was no ambivalence in their report. The cause of the accident was a circular seal made of rubber known as an O-ring. The Challenger's Solid Rocket Boosters were made in segments, and the O-rings sealed the gap between them. A seal failed and the escaping exhaust gas became a blow torch which burned through a strut and started a sequence of events which led to the disaster.

There are two justifications for a new edition of D'Arcy Wentworth Thompson's On Growth and Form: One is that a shorter version might make the work more available, at least to the general reader, and the other is that the 1942 edition contains many passages that are now out-of-date. If the book is to retain its importance, which it has maintained since its first publication in 1917, a mild freshening in the form of commentary does not seem out of place.

Of its importance there is no doubt, but I must agree with Medawar when he says that its considerable influence ‘has been intangible and indirect’. I will shortly mention some of the facets which make the book so distinctive and unique, and all of these have contributed to its success. But I believe that the cardinal point is that D'Arcy Thompson was consistently able to examine subjects of significance in biology from a fresh point of view, and the mere fact that there was another point of view (sometimes one first imagined in early antiquity) comes as a shock, and therefore a stimulus, to those who so easily fall into the scientific fads and fashions of our day, and make little effort to look beyond the horizon of the ‘current views’.

The most conspicuous attitude in the book is the analysis of biological processes from their mathematical and physical aspects.

Shortly after the Second World War, an engineer from New Zealand, ‘Bill’ Phillips, working at the London School of Economics, built a model of the economy. The marvellous thing about this model was that it ran on water. Phillips's model was a set of tanks, valves, pumps, pipes, baffles and cisterns. If, say, the flow into some cistern increased while the cross section of the output remained the same, the water in the cistern would rise. The new level might increase the flow of water into another cistern, raising its level, or it might be enough to trigger a valve and restrict the flow somewhere else. The whole thing, which stood about seven feet high, weighed a good part of a ton, and was prone to leakage and corrosion, was meant to represent the flows of income around a national economy. Changes of levels were linked by indicators to scales which represented measures of economic performance such as price indices, stocks of money, or Gross National Product. It was even possible to link one of these gurgling monsters to another, thus representing the interaction of two national economies, or the interaction of one economy with the rest of the world. Phillips's hydraulic model of the economy has been restored recently and can be seen at the Science Museum in London.

Nowadays no one would dream of building a model of the economy that ran on water. Nowadays one would use a computer and the relationships would be represented by interacting mathematical equations. Using a computer and equations one can build the equivalent of many more pipes, tanks, and valves than one could ever construct with plumbing. This is what macroeconomic modellers do; they use equations to build a model of the economy. They model not only theoretically derived relationships but quantities based on observations of how this or that change has appeared to affect the economy in the past. Modern models may have hundreds of equations and variables arranged in a big tree-like structure representing everything from world interest rates to levels of business and consumer confidence; the output of some equations will count as variables in other equations, while these effect still other equations and so forth. A modern model rendered hydraulically in the style of Phillips would be big enough to flood the LSE and the surrounding streets.

The fact that I set little store by certain postulates (often deemed to be fundamental) of our present-day biology the reader will have discovered and I have not endeavoured to conceal. But it is not for the sake of polemical argument that I have written, and the doctrines which I do not subscribe to I have only spoken of by the way. My task is finished if I have been able to show that a certain mathematical aspect of morphology, to which as yet the morphologist gives little heed, is interwoven with his problems, complementary to his descriptive task, and helpful, nay essential, to his proper study and comprehension of Growth and Form. Hic artem remumque repono.

And while I have sought to show the naturalist how a few mathematical concepts and dynamical principles may help and guide him, I have tried to show the mathematician a field for his labour—a field which few have entered and no man has explored. Here may be found homely problems, such as often tax the highest skill of the mathematician, and reward his ingenuity all the more for their trivial associations and outward semblance of simplicity. Haec utinam excolant, utinam exhauriant, utinam aperiant nobis Viri mathematice docti.

On 24 April 1984, Margaret Heckler, US Secretary of Health and Human Services, announced with great gusto at a Washington press conference that the cause of AIDS had been found. A special sort of virus – a retrovirus – later labelled as HIV, was the culprit. Vaccinations would be available within two years. Modern medical science had triumphed.

Next summer, movie star Rock Hudson died of AIDS. The gay community had lived and died with the disease for the previous four years. Now that the cause of AIDS had been found and scientists were starting to talk about cures, the afflicted became increasingly anxious as to when such cures would become available. Added urgency arose from the very course of the disease. The HIV blood test meant lots of seemingly healthy people were facing an uncertain future. Was it more beneficial to start long-term therapy immediately or wait until symptoms appeared? Given the rapid advance in medical knowledge about AIDS and the remaining uncertainties (even the cause of AIDS was a matter of scientific debate), was it better to act now with crude therapies or wait for the more refined treatments promised later?

From Falstaff to the Ring of the Nibelungen, great constructions and great works of art have paid a price for amplitude beyond usual standards. D'Arcy Wentworth Thompson (1860–1948), Professor of Zoology at Scotland's University of St. Andrews, and perhaps the greatest polymath of our century, was scarcely homo unius libri (a man of one book). He composed two volumes of commentaries on all birds and fishes mentioned in classic Greek texts; he prepared the standard translation of Aristotle's Historia animalium; he labored for years over statistics for the Fishery Board of Scotland; and he wrote the section on pycnogonids (a small but fascinating group of arthropods) for the Cambridge Natural History series. But his enduring (indeed evergrowing) fame rests upon a glorious (and very long) book that served more as the active project of a lifetime than a stage of ontogeny—On Growth and Form (first edition of 793 pages in 1917, second edition enlarged to 1116 pages in 1942).

Much as it must pain any scholar and publisher of integrity to abridge such a work (for such an act does resemble the dissection of a body), one must not, as Jesus told us, light a candle and then place it invisibly under a bushel (Matthew 5:14–17). On Growth and Form is one of the great lights of science (and of English prose); it must be available at an affordable price and a totable heft: “Let your light so shine before men, that they may see your good works.”

‘Science seems to be either all good or all bad. For some, science is a crusading knight beset by simple-minded mystics while more sinister figures wait to found a new fascism on the victory of ignorance. For others it is science which is the enemy; our gentle planet, our slowly and painfully nurtured sense of right and wrong, our feel for the poetic and the beautiful, are assailed by a technological bureaucracy – the antithesis of culture – controlled by capitalists with no concern but profit. For some, science gives us agricultural self-sufficiency, cures for the crippled, a global network of friends and acquaintances; for others it gives us weapons of war, a school teacher's fiery death as the space shuttle falls from grace, and the silent, deceiving, bone-poisoning, Chernobyl.

Both of these ideas of science are wrong and dangerous. The personality of science is neither that of a chivalrous knight nor pitiless juggernaut. What, then, is science? Science is a golem.

A golem is a creature of Jewish mythology. It is a humanoid made by man from clay and water, with incantations and spells. It is powerful. It grows a little more powerful every day. It will follow orders, do your work, and protect you from the ever threatening enemy. But it is clumsy and dangerous. Without control a golem may destroy its masters with its flailing vigour; it is a lumbering fool who knows neither his own strength nor the extent of his clumsiness and ignorance.

A golem, in the way we intend it, is not an evil creature but it is a little daft. Golem Science is not to be blamed for its mistakes; they are our mistakes. A golem cannot be blamed if it is doing its best. But we must not expect too much. A golem, powerful though it is, is the creature of our art and our craft.’

With the exception of most of Chapter 1 and the whole of Chapter 3, the substantive parts of this book are largely expositions of others’work; in this we follow the pattern of the first volume in the Golem series.Thefull bibliographic references to the works discussed both in this Preface and the other chapters, as well as additional reading, will be found in the Bibliography at the end of the volume.

As for the substantive chapters, Chapter 1 is Collins’s redescription of the argument over the success of the Patriot missile. It is heavily based on the record of a Congressional hearing that took place in April 1992, and on two papers written by principal disputants, Theodore Postol and Robert Stein; it also draws on wider reading. Though this chapter is not a direct exposition of anyone else’s argument, and though it uses a new analytic frame-work turning on different definitions of success, it must be made clear that the account was made possible only because of Postol’s prior work. Also, Postol was extremely generous in supplying Collins with much of the relevant material and drawing his attention to more. Collins has tried to make sure that the account is not unduly influenced by Postol’s views and that the material on which it draws represents the field in a fairway. Itwill be noted that the chapter does not repeat Postol’s expressed position – that no Scud warheads, or almost no Scud warheads, were destroyed by Patriot missiles – but stresses the difficulty of reaching any firm conclusion while keeping open the strong possibility that Postol is right.

These words were uttered in 1984 by the late Sir Walter Marshall, chairman of Britain's then Central Electricity Generating Board (CEGB). The CEBG used the rail system to transport spent nuclear waste from its generating plants to its reprocessing plants. In spite of the fact that the fuel was contained in strong containers, or flasks, the public was not happy. The CEGB therefore arranged for a diesel train, travelling at a hundred miles per hour, to crash head-on into one of their flasks to show its integrity. Sir Walter's words were spoken to the cameras immediately following the spectacular crash, witnessed by millions of viewers either on live television or on the nation's televized news bulletins. Sir Walter was claiming that the test had shown that nuclear fuel flasks were safe. (The source from which Sir Walter's quotation was taken and of the basic details of the train crash is a video film produced by the CEGB Department of Information and Public Affairs entitled ‘Operation Smash Hit’.)

Surface-tension

We pass from the solitary cell to cells in contact with one another—to what we may call in the first instance ‘cell-aggregates’, through which we shall be led ultimately to the study of complex tissues. In this part of our subject, as in the preceding chapters, we shall have to consider the effect of various forces; but, as in the case of the solitary cell, we shall probably find, and we may at least begin by assuming, that the agency of surface-tension is especially manifest and important. The effect of this surface-tension will manifest itself in surfaces minimae areae: where, as Plateau was always careful to point out, we must understand by this expression not an absolute but a relative minimum, an area, that is to say, which approximates to an absolute minimum as nearly as the circumstances and material exigencies of the case permit.

Let us restate as follows, in terms of Energy, the general principle which underlies the theory of surface-tension or capillarity.

When a fluid is in contact with another fluid, or with a solid or with a gas, a portion of the total energy of the system (that, namely, which we call surface-energy) is proportional to the area of the surface of contact; it is also proportional to a coefficient which is specific for each particular pair of substances and is constant for these, save only in so far as it may be modified by changes of temperature or of electrical charge.

The accident at the Chernobyl nuclear power plant in the Soviet Union on 26 April 1986 is one of the defining moments of the nuclear age. It is the worst nuclear accident ever: a melt-down of the core of a reactor, followed by an explosion and fire releasing tons of radio-active debris into the atmosphere. The accident not only killed nuclear workers and firemen who fought to save the doomed reactor, but also condemned many others who lived under the path of the fallout to illness and premature death or a life of waiting for a hidden enemy. The weather, no respecter of nation states, carried its deadly passenger far and wide.

Of the chemistry of his day and generation, Kant declared that it was a science, but not Science—eine Wissenschaft, aber nicht Wissenschaft—for that the criterion of true science lay in its relation to mathematics. This was an old story: for Roger Bacon had called mathematics porta et clavis scientiarum, and Leonardo da Vinci had said much the same. Once again, a hundred years after Kant, Du Bois Reymond, profound student of the many sciences on which physiology is based, recalled the old saying, and declared that chemistry would only reach the rank of science, in the high and strict sense, when it should be found possible to explain chemical reactions in the light of their causal relations to the velocities, tensions and conditions of equilibrium of the constituent molecules; that, in short, the chemistry of the future must deal with molecular mechanics by the methods and in the strict language of mathematics, as the astronomy of Newton and Laplace dealt with the stars in their courses. We know how great a step was made towards this distant goal as Kant defined it, when van't Hoff laid the firm foundations of a mathematical chemistry, and earned his proud epitaph—Physicam chemiae adiunxit.

We need not wait for the full realisation of Kant's desire, to apply to the natural sciences the principle which he laid down. Though chemistry fall short of its ultimate goal in mathematical mechanics, nevertheless physiology is vastly strengthened and enlarged by making use of the chemistry, and of the physics, of the age.

In this chapter and the following ones D'Arcy Thompson is straggling against the notion that all form can simply be explained by heredity, and that therefore changes in form inevitably map out phylogenetic relations. Instead he repeatedly suggests that physical forces (such as those which produce the variations of shapes of snow-flakes) are of prime importance and relationships of shape may not justify any family tree or a sequence in time, but simply show mathematical kinship. Today we are inclined to combine the two and say that the genes, the units of heredity, do control shapes, but that the activities of genes are constrained by the physico-chemical properties of the chemical substances and the configuration of these substances present in the organism. This does not touch upon the question of whether or not all the shapes produced are adaptively significant. D'Arcy Thompson's strong arguments that they are not is a reaction against those who see a selective advantage to all structures. But this issue cannot be resolved without an ecological study of each example, a Gargantuan task that is unlikely ever to be achieved. All we can say at the moment is that there is no a priori reason why some structures, which have been initiated by mutation and formed within the confines of physico-chemical laws, should not utterly lack any adaptive significance, and yet remain fixed in the population. It might even be argued that a particular gene-change produced other effects that were adaptively significant and these less obvious gene-effects elicited the selection pressure which preserved the adaptively inert structure in the population.