Promises delivered

The conclusion of The Golem, the first volume in this series, argued that the book had wide significance where science touched on matters of public concern. Here we deliver on that promise.

The chapter on the Challenger explosion shows the way that human error is taken to account for technological failure and shows how unfair it is to assign blame to individuals when the uncertainties are endemic to the system as a whole.

The Challenger enquiry is one case among many that reveals that when the public views the fruits of science from a distance the picture is not just simplified but significantly distorted. Nobel laureate Richard Feynman demonstrated on TV that when a piece of rubber O-ring was placed in a glass of iced water it lost resilience. This was at best trivial – the effect of low temperature on rubberwas alreadywell understood by the engineers. At worst it was a dangerously misleading charade – an acting-out of the most naive model of scientific analysis. The crucial question was not whether low temperature affected the O-rings but whether NASA had reason to believe this would cause them to fail. Feynman gives the impression that doubts can always be simply resolved by a scientist who is smart enough.

Horns

We have had so much to say on the subject of shell-spirals that we must deal briefly with the analogous problems which are presented by the horns of sheep, goats, antelopes and other horned quadrupeds; and all the more, because these horn-spirals are on the whole less symmetrical, less easy of measurement than those of the shell, and in other ways also are less easy of investigation. Let us dispense altogether in this case with mathematics; and be content with a very simple account of the configuration of a horn.

There are three types of horn which deserve separate consideration: firstly, the horn of the rhinoceros; secondly, the horns of the sheep, the goat, the ox or the antelope, that is to say, of the so-called hollow-horned ruminants; and thirdly, the solid bony horns, or ‘antlers’, which are characteristic of the deer.

The horn of the rhinoceros presents no difficulty. It is physiologically equivalent to a mass of consolidated hairs, and, like ordinary hair, it consists of non-living or ‘formed’ material, continually added to by the living tissues at its base. In section the horn is elliptical, with the long axis fore-and-aft, or in some species nearly circular. Its longitudinal growth proceeds with a maximum velocity anteriorly, and a minimum posteriorly; and the ratio of these velocities being constant, the horn curves into the form of a logarithmic spiral in the manner that we have already studied.

Spirals in Nature

The very numerous examples of spiral conformation which we meet with in our studies of organic form are peculiarly adapted to mathematical methods of investigation. But ere we begin to study them we must take care to define our terms, and we had better also attempt some rough preliminary classification of the objects with which we shall have to deal.

In general terms, a Spiral is a curve which, starting from a point of origin, continually diminishes in curvature as it recedes from that point; or, in other words, whose radius of curvature continually increases. This definition is wide enough to include a number of different curves, but on the other hand it excludes at least one which in popular speech we are apt to confuse with a true spiral. This latter curve is the simple screw, or cylindrical helix, which curve neither starts from a definite origin nor changes its curvature as it proceeds. The ‘spiral’ thickening of a woody plant-cell, the ‘spiral’ thread within an insect's tracheal tube, or the ‘spiral’ twist and twine of a climbing stem are not, mathematically speaking, spirals at all, but screws or helices. They belong to a distinct, though not very remote, family of curves.

Of true organic spirals we have no lack. We think at once of horns of ruminants, and of still more exquisitely beautiful molluscan shells—in which (as Pliny says) magna ludentis Naturae varietas.

This chapter (and the beginning of the next) possesses a curious blind spot: it is primarily concerned with the effect of surface-tension on the form of cells, yet it completely ignores all the beautiful experimental work, begun in the early 1930's by E. N. Harvey, K. C. Cole and others on the actual measurement of the surface-tension of cells. This is all excellently reviewed in a recent paper by Harvey; let me just state two of the important conclusions here. In the first place there are a number of clear demonstrations that the cell boundary primarily exerts membrane tension and not true surface-tension. In fact it is a composite of the two and the sum of all these tensions is referred to by Harvey as ‘tension at the surface’. The second point is that these tensions are extremely low, far too low to account by themselves for cell shape. Instead, then, we must look to the micro-structure of the cell periphery for an understanding of cell form. Despite the fact that no reference is made to this considerable body of experimental work, it must be admitted that D'Arcy Thompson seems, in certain passages, to be aware of the difficulties.

But this omission need not mar the value of the chapter if we think of D'Arcy Thompson's presentation as a model rather than a reality. The formula of Laplace remains a useful description of the sites of forces playing upon a cell, even though those forces are not surface-tension alone.

The Gulf War

In August 1990 Iraqi forces invaded Kuwait. The United States presented Iraq with an ultimatum – ‘withdraw or face a military confrontation’. The Iraqi president, Saddam Hussein, responded by threatening to stage ‘The Mother of All Battles’. Over the next four months the United States set about building up military strength in neighbouring Saudi Arabia with the intention of driving Saddam's army from Kuwait. Given Iraq's confrontational stance, this meant building a force capable of destroying all of Iraq's military resources.

Considering the scale of the imminent confrontation, and its distance from the American continent, the United States needed the backing of the United Nations and the military and political cooperation of many nations, notably Iraq's neighbours. A critical feature of this alliance was that a set of Arab states would side with the Western powers’ attack on a fellow Arab state. As the old saying goes, ‘my enemy's enemy is my friend’, and at that time all the Arab states except Egypt had an enemy in common – Israel. On the other hand, America was Israel's staunchest ally, while Iraq was viewed as an important player in the confrontation with Israel. Thus the political alignment that the US needed to hold in place was continually in danger of collapse. It was crucial for American policy in respect of the forthcoming Gulf War that Israel did not take part in the conflict. Should Israel attack Iraq, creating circumstances in which the Arab states would be directly supporting Israel in its attack on an Arab ally in the Middle East conflict, it might become impossible for the other Arab states to continue to support America. Iraq's strategy was clear: they would try to bring Israel into the confrontation that had started with their invasion of Kuwait.

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?