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.