Hobbes, Thomas (1588–1679)

4. Geometry, optics and physics

First philosophy is a preliminary to natural science proper, and the first of the natural sciences is geometry. Geometry is a natural science for Hobbes, because it studies the effects of moving bodies. It studies the properties of straight lines, for instance, and straight lines are the effects of the motion of a small material thing – a point. He rejects the idea that the geometrical point is an abstraction distinct from some small material mark or other. Being a body, a geometrical point is divisible and not, as Euclid had it, ‘that which hath no part’. A point could no more lack quantity than a line could lack breadth and be constructed by motion. The bodies whose motions geometry studies may not have much quantity, and the quantity may not be relevant to what is being demonstrated of them, but they are bodies all the same. Though geometry is a science of bodies, it is also in a sense an a priori certain science, as physics is not, for the effects are produced by us, and we know in advance by what means they are produced. In this, Hobbes believed, geometry is like politics. In a sense, too, geometry is a very basic science – basic not in the sense that the objects it studies are higher or more real than those in nature, but in the sense that it studies bodies and motion at a very high level of generality, with much that is specific about the bodies left out of account. Hobbes thinks that geometry is also basic in another sense, for its methods of demonstration and analysis are the inspiration for the methods of the other demonstrative sciences.

Hobbes was self-taught in mathematics, and his friend and biographer, John Aubrey, says he did not encounter Euclid until he was middle-aged. Nevertheless, he was taken seriously by very able geometers in Mersenne’s circle, and is even credited with inspiring a proof by Roberval of the equality of arcs of a parabola and an ‘Archimedean’ spiral. He is much better known, however, as a mathematical failure whose attempts at expounding geometry in De corpore were ridiculed by the English mathematician John Wallis. Wallis’ attack was motivated by a wish to discredit the anticlerical passages in Leviathan, and its attack on the universities. In correspondence with Huygens, Wallis said that Hobbes ‘took his courage’ from mathematics, and so it ‘seemed necessary for some mathematician to show him how little he understands’. Wallis’ attack succeeded – it focused on Hobbes’ doomed enterprise of producing a quadrature of the circle – and was made the more effective by Hobbes’ persistent refusal to concede errors.

Although the geometrical parts of De corpore were supposed to present some new results, Hobbes did not claim any great stature for himself in geometry. In optics, on the other hand, he regarded himself as a major figure. It was certainly a subject he turned to early in his transformation from man of letters to man of science. As early as 1636, optical questions were featuring in his correspondence with the Earl of Newcastle, and the treatment of the sensible qualities was mechanical: ‘whereas I use the phrases, the light passes, or the colour passes or diffuseth itselfe, my meaning is that the motion is onely in the medium, and light and colour are but the effects of that motion in the brayne’. Perhaps more accurately, these effects were supposed to be the effects of the motion of the medium transmitted to the animal spirits in the brain.

Exactly how early Hobbes arrived at his conception of the workings of light is not entirely clear. A short treatise dated to 1630 and originally attributed to Hobbes has been claimed by some scholars to be the work of someone else in the Cavendish circle. It contains doctrines different from writings that are more certainly ascribed to Hobbes, and which probably belong to the 1640s: the Tractatus Opticus I and II. It also contains as ‘principles’ formulations that these later optical writings present as mere hypotheses. Whether the writings of the 1640s represent only a change of mind or whether they are Hobbes’ first extended publications in optics, they show him adopting a mediumistic theory of the propagation of light based on the idea of continuously expanding and contracting light sources. These displace contiguous parts of an ethereal medium of uniform density and set up a chain reaction to the eye. A resistance in the eye caused by a countervailing motion from the brain produces a phantasm of a luminous object – that is, in Hobbes’ terminology, light. Light is propagated instantaneously, as both luminous object and medium expand simultaneously. The account does without the postulation of an emission by luminous objects of species or replicas of themselves which subsequently inform the senses and permit perception. Instead, luminous objects illuminate by radiation: they, so to speak, send out rays or, more precisely, displace the medium along paths called ‘rays’. In their passage from luminous objects to the eye, rays are supposed to describe parallelograms. Hobbes used the properties of other geometrical figures described by rays of light passing through different densities to account for refraction. Colour he regarded as light perturbed by the internal motions of rough or coarse bodies on its way to the eye. The differences between the colours on the spectrum from blue to red he accounts for as the product of refraction plus restraint or reinforcement of the lateral motion of rays of light that goes with refraction.

At no point in the process that starts with the motion of the luminous objects and ends in the production of the phantasm does Hobbes depart from a mechanical model of the causes of sense-perception. His mature theory of optics is through and through an account in terms of matter and motion. But between the Tractatus Opticus I and the Tractatus Opticus II, he seems to have revised his ideas about the organs of sensory perception. Phantasms are said to come from the heart, rather than to result from the clash of incoming motions with motions from the brain. By 1646, when Hobbes produced A Minute or First Draught of the Optiques, the most polished of his optical treaties, the main lines of his doctrine were settled. In addition to material on light and its propagation, refraction and reflection, there are accounts of various kinds of sensory error.

Physics, understood as the theory of the causes of appearances to sense and of the nature of the objects of sense, is in part an offshoot of optics. It is expounded at the end of De corpore. By an ‘object’ of sense Hobbes means an external body that registers in experience as being the subject of certain qualities, and that sets off the process culminating in an ‘act of sense’. The object of sense is not an idea or a sense-datum or a mental image, though such a thing may be the medium in which the object of sense is registered. The greatest of the objects of sense is the world itself, as registered from some point within it. But only a few intelligible questions can be asked about the world, and these cannot be conclusively answered. One can ask whether it is of finite or infinite magnitude, whether it is full or contains empty space, and how long it has lasted. Only the second of these questions is open to a scientific answer, and even then only to a probable conclusion, while the others are for lawfully appointed churchmen to discuss. Hobbes thinks that probably there is no vacuum, that the world is full, but that some of the bodies that make it up are invisible: thus the ether and ‘the small atoms disseminated through the whole space between the earth and the stars’. He adopts Copernican and Galilean hypotheses in chapter 26 of De corpore to explain the order, motion and relative position of the planets. He also infers explanations of, among other things, the passage of the seasons, the succession of day and night and ‘the monthly simple motion of the moon’.

Hobbes goes on to consider the bodies between the earth and the stars. Foremost among these is ‘the most fluid ether’, which he proposes to regard as if it were first matter. He supposes that its parts only receive motion from bodies that float in them, and impart none of their own. The bodies in the ether are supposed to have some degree of cohesion or hardness and to differ from one another in shape, figure and consistency. Any more specific hypotheses about them Hobbes adopted only to explain particular phenomena. He is, however, willing to venture that many such bodies are ‘unspeakably little’ or minute, since God’s infinite power includes a power infinitely to diminish matter. Assumptions about intersidereal bodies inform his theories of the phantasms appropriate to the different senses, not only light but also heat, sound and odour.