“Fair Quiet, I have found you here” / “Mistaken long, I sought you then / In busie Companies of Men. / Your sacred Plants, if here below, / Only among the Plants will grow. / Society is all but rude, / To this delicious Solitude.” Andrew Marvell, The Garden / Epicurus' Garden was once located outside the walls of Athens and its Dipylon Gate. It has come to seem a metaphor for the retiring and non-political character of his philosophy. According to Seneca, who thought that Epicurus secluded himself outside Athens to avoid notice, there was an inscription at the entrance to his suburban garden. It read: 'Stranger, your time will be pleasant here. Here the highest good is pleasure.' (In Seneca's Latin: hospes hic bene manebis hic summum bonum voluptas est, Ep. 79.15.) Epicurus' Garden would seem to be the prototype of Rabelais' Abbaye de Thélème. The inscription must be an invention, but it stands in pointed contrast to the inscription that led into the garden and groves of Plato's Academy, which was also located outside the walls of Athens: 'Let no one unversed in geometry enter here.' In his move to Athens from the Greek East in 307/306 BC Epicurus acquired this garden located not far from Plato's Academy. The sum seems large: 80 minae (or 8,000 drachmae, DL 10.10), but his sworn enemy Timocrates of Lampsacus claimed that he spent a mina a day on food (DL 10.7).

Like other Hellenistic philosophers, the Epicureans assume that the principal goal of philosophy is to secure one's happiness, and that that result can be achieved only by removing the principal causes of human suffering, namely the vices (kakiai) and certain emotions or passions (pathē). Considered in the light of a normative conception of nature and psychic health, these are diseases of the soul that philosophy must cure and thus restore the soul to its healthy natural state, much as medicine treats the ailments of the body aiming to restore its unimpeded functioning. Therapy consists in purging from the soul the elements of moral disease, in putting into the soul the right elements, and often in both. However, from the practical perspective, the important aspect of the therapy is purgatory: the removal of features that cause disturbance and unhappiness rather than the replenishment of whatever knowledge we lack. Epicurus is the first member of the school to compare philosophy to medicine and the philosopher to the medical doctor (221 Us.). Lucretius (first century BC), Philodemus (first century BC), Diogenes of Oinoanda (second century AD) and other Epicureans are also wedded to the so-called medical analogy. They too perceive the philosopher as a kind of doctor who cures disturbance and anxiety and helps us achieve the supreme good, pleasure (hōdonō) or the absence of pain (aponia). The medical model suggests that philosophical therapy is an ongoing activity integrated into the context of ethical praxis.

The recovery of Epicurus' natural and moral philosophy in the Renaissance and its dissemination in the early modern period had a significant effect on the evolution of philosophy. The theses of the plurality of worlds, their self-formation, the non-existence of any god or gods concerned with the affairs of men and women, and the centrality and validity of the hedonic motive in human life, came under extended scrutiny in the seventeenth and eighteenth centuries. Although it was once customary to regard Epicureanism as a fringe movement represented in the seventeenth century almost uniquely by the enigmatic Pierre Gassendi, it is now increasingly recognized that Epicurus' letters and sayings, and his follower Lucretius' Latin poem, On the nature of things, contributed to the formation of a rival image of nature - the corpuscularian, mechanical philosophy - that replaced the scholastic synthesis of Aristotelianism and Christian doctrine, and that found special favour in the new scientific academies of Europe.

The Epicureans held that perceptions serve as a foundation of scientific inference and, further, that all perceptions are true. This is a unique position among ancient philosophers, and it provoked vigorous attacks. Lucretius defended the Epicurean position with an image: just as a building will collapse if the initial measuring rod is crooked, so reason will collapse if it starts out with false perceptions (DRN 4.513-21). This chapter considers perceptions within the context of Epicurus' methodology as a whole. Epicurus proposed two basic rules of investigation: a demand for initial concepts as a means of formulating problems; and a demand for perceptions and feelings as a means of inferring what is not observed. He discussed the rules in a book called Kanōn, literally, a 'straight rod' or 'measuring stick'. The subject, called 'canonic', was considered by the Epicureans to be an adjunct of physics rather than a separate part of philosophy. Canonic is tied to physics in two ways: first, the rules of investigation serve as a preface (or 'approach', DL 10.30) to the physics, and, second, the rules are defended on the basis of the ensuing theory. The Epicurean spokesman in Cicero's De Finibus (1.64) sums up this procedure: 'Unless the nature of things is recognized, we shall not be able in any way to defend the judgments of the senses.' Our sources tend to mingle the pre-theoretical understanding of the rules with their subsequent justification. It is important, however, to keep the two kinds of understanding separate.

Epicurean thoughts about politics contrast sharply with those of other prominent Greek and Roman philosophers. Plato, Aristotle and the Stoics agree that human beings are naturally political animals, by which they mean that to realize fully our natural capacities and be perfectly successful as human beings, we need to contribute to the polis. Accordingly, they believe that humans should start a family and should, at least if circumstances are favourable, engage in politics. These philosophers also agree that justice exists by nature and not by convention, by which they mean that standards of right and wrong for social life do not depend upon any particular agreements or customs. The Epicureans differ. They discourage starting a family and engaging in politics, and they deny that justice exists by nature. It would be a mistake, however, to infer that Epicureanism is apolitical. First, these sweeping contrasts need some qualification: the Epicureans do not absolutely reject ordinary politics and do not think that justice is whatever a society decides it is. Second, and more importantly, the Epicureans' pursuit of pleasure requires that they cultivate their own just community of friends, apart from the madding crowd.

A widely publicized trait of ancient Epicureanism was its opposition to paideia, the set of disciplines or subjects of instruction which instilled culture and bestowed prestige on the Greek elite and included the so-called 'liberal' arts, usually: grammar or literature, rhetoric, dialectic, geometry, arithmetic, astronomy, music. Epicurus was said to have turned to philosophy when he could not learn from his grammar teacher about 'Chaos', at the beginning of Hesiod's theogony (DL 10.2). Later, he wrote to his pupil Pythocles to 'Hoist the sails of your skiff and avoid all of paideia' (DL 10.6=163 Us.; cf. Plutarch, Non posse 1094D), and to another pupil he said: 'I call you blessed, Apelles, because you have set out for philosophy undefiled by any paideia' (Athenaeus Deipn. 13.588a=117 Us.). Epicurus' attitude to the arts is conditioned by the privileged position he accords philosophy: you should do philosophy all your life because it is never untimely to care for the health of your soul (Ep. Men. 122). Other disciplines do not meet this high standard of necessity and are criticized for it. Sextus Empiricus notes that two groups attacked the arts: the Epicureans did so because the arts 'contributed nothing to the perfection of wisdom' (or else in order to cover up Epicurus' ignorance in such things), while the Pyrrhonians avoided a dogmatic attack of this sort (and did not suffer from the ignorance of an Epicurus), but found the same sort of controversy and puzzles in the arts as they did in philosophy too (M 1.1 and 1.5).

Is there such a thing as 'Epicurean philosophy of language'? There was, of course, no division or discipline so labelled within the Epicurean system. But that is a merely superficial objection: almost since there have been philosophers at all, they have been reflecting on many of the phenomena and problems now staked out as their territory by today's philosophers of language, although what earlier philosophers thought was worth investigating about language will not necessarily chime with modern priorities. Thus when we ask of any classical text the sorts of questions pursued by today's philosophers of language - such as how we manage to talk about the world, and to say true and false things about it; how language is related to thought; what a theory of meaning should look like - what we do not find may be at least as significant as what we do, just as what their contemporaries may have thought valuable or vulnerable in Epicurean theorizing need not coincide with our judgements. The deep problem may be that Epicurean contributions derived importance from their role in some other enterprise than that of pursuing an interest in language per se. Epicureans, like Stoics, could be powerful arguers, resourceful, subtle, dogged (cf. Cic. Fin. 1.63) - but the school's insistence on keeping one's eyes on the prize was more powerful still.

Pleasure is the goal of life for an Epicurean. But it is pleasure of a particular kind that represents this goal, namely lack of pain in body (aponia) and lack of distress in soul (ataraxia). It is clear that, for Epicurus, to be free from bodily pain and mental distress is, in and of itself, to be in a state of pleasure. He does not recognize a neutral state of neither pleasure nor pain; for a percipient subject, being without pain is already pleasant. Equally, however, Epicurus does not hold that the only pleasure to be had is freedom from pain. The pleasures of the profligate, which he tells us do not represent the Epicurean goal (Ep. Men. 131), certainly are pleasures as far as Epicurus is concerned, since he calls them that, though he adds that such pleasures do not generate a pleasant life - it is 'sober reasoning' that does so (Ep. Men. 132).

Any account of philosophy in the Roman Republic must start from the events of 155 BC. The city of Athens, appealing to the Roman senate against a fine levied for its sack of Oropus, sent as ambassadors the current heads of three leading philosophy schools - the Academy, Stoa and Peripatos. The excitement generated by these philosophers during their stay in Rome was sufficient to ignite the long Roman love affair with philosophy. Roman patronage became in time a factor that few Greek philosophers could afford to ignore. Many Romans travelled, or sent their sons, to Athens to study in the metropolitan schools. But, conversely, many of the philosophers migrated towards the new centre of power, typically joining the entourage of a powerful Roman. By the mid first century BC, Rome itself had become one of the leading philosophical centres. This shift of the centre of gravity away from Athens was a gradual one, but was intensified by Sulla's crippling siege of Athens during the Mithridatic War, 88-86 BC, a critical period which, for example, saw both contenders for the headship of the Academy move the scene of their operations elsewhere - Philo of Larissa to Rome, Antiochus to Alexandria. The leading Stoic of the first century BC, Posidonius, who was frequently to be found in Rome, did not succeed to the headship of the Stoa in Athens, but eventually set up a school on the island of Rhodes.

The Epicureans set the absence of mental disturbance, ataraxia, as the goal of human life and claimed that it is identical with the greatest mental pleasure. They can be expected, therefore, to offer an account of the psychology of mental disturbance and the proper methods for managing and eradicating it. Their basic conception of value, that pleasure is the only good and pain the only bad, is supplemented by the assurance that we should feel no anxiety about our chances of living a good life since pleasure is easy to obtain and pain is easy to avoid. In addition, they identified two major sources of common mental disturbance: fear of the gods and the fear of death, and they dedicated considerable effort and philosophical ingenuity to the removal of these. Before we come to consider their arguments in detail, it is important to look at the general Epicurean account of the sources and nature of mental disturbance since this provides the general framework for their understanding of how mental disturbance should be tackled.

THE SPHERE AND CYLINDER: MOTIVATING THE DISCUSSION

The Stomachion lies at the edges of our knowledge of ancient mathematics, hardly figuring in any of the modern histories of mathematics. This may represent a more modern bias (the game it studies was called in antiquity “the box of Archimedes,” which suggests that Archimedes' treatment of it became widely known), but even so, no one would suggest this represents the core of Archimedes' fame. For this we have to turn to the Sphere and Cylinder. After all, there is the famous report by Cicero, according to which Archimedes chose those two figures for his tombstone – defining them as his crowning achievement. And one can easily see why. With all we have seen in the previous chapter concerning the fascination shown by Greek mathematicians towards the complex and the unwieldy, nothing could beat sheer elegance. And what elegance in this result! The cylinder (defined as having its height equal the diameter of its base) is one-and-a-half times the sphere it encloses. Exactly so – in other words, the two objects are like the harmonic notes of the fifth. And is not the sphere as elusive as the circle, with the added complexity of the third dimension? To compare the sphere with the simpler cylinder is to measure it, in a sense, and this result obtained by Archimedes is the closest that Greek mathematicians – or any other since – have ever come to squaring the circle.

So this book is going to be about the style of mathematics. Does it mean I am going to ignore the substance of mathematics? To some extent, I do, but then again not: the two dimensions are distinct, yet they are not orthogonal, so that stylistic preferences inform the contents themselves, and vice versa. For an example, I shall now take a central work of Hellenistic mathematics – Archimedes' Spiral Lines – and read it twice, first – very quickly – for its contents, and then, at a more leisurely pace, for its presentation of those contents. Besides serving to delineate the two dimensions of style and content, this may also serve as an introduction to our topic: for Spiral Lines is a fine example of what makes Hellenistic science so impressive, in both dimensions. For the mathematical contents, I quote the summary in Knorr 1986: 161 (fig. 1):

The determination of the areas of figures bounded by spirals further illustrates Archimedes' methods of quadrature. The Archimedean plane spiral is traced out by a point moving uniformly along a line as that line rotates uniformly about one of its endpoints. The latter portion of the treatise On Spiral Lines is devoted to the proof that the area under the segment of the spiral equals one-third the corresponding circular sector … The proofs are managed in full formal detail in accordance with the indirect method of limits.

THE STOMACHION: MOTIVATING THE DISCUSSION

My moment of revelation – indeed, the starting point for writing this book – was while trying to make sense of Archimedes' Stomachion. This treatise, surviving on a single parchment leaf containing the introduction, a preliminary proof, and one stump of a proof – all mutilated and difficult to read – has gained little scholarship since its first publication by Heiberg in 1915. I would have never paid it much attention myself – it did not appear to be a “serious” work – but it is after all a page out of the Archimedes Palimpsest, and just looking at the parchment one could not resist the temptation to work on it. The page looked to be in such a bad shape, surely Heiberg did not manage to read it satisfactorily!

My reading did not add many words to those read by Heiberg. But I was probably the first person in many years to have read, slowly and attentively, the introduction to the Stomachion. I quote a tentative translation:

As the so-called Stomachion has a variegated theoria of the transposition of the figures from which it is set up, I deemed it necessary: first, to set out in my investigation of the magnitude of the whole figure each of the <figures> to which it is divided, by which <number> it is measured; and further also, which are <the> angles, taken by combinations and added together; <all of the above> said for the sake of finding out the fitting-together of the arising figures, whether the resulting sides in the figures are on a line or whether they are slightly short of that <but so as to be> unnoticed by sight. […]

The overall structure of the argument is simple. First, we have covered, in the first three chapters of this book, a substantial body of evidence pointing to a certain style of Hellenistic mathematics. Its three major constituents are: (1) mosaic composition, (2) narrative surprise, (3) generic experimentation (a more specialized phenomenon is that of the carnival of calculation). Second, we have briefly noted, in chapter 4, how such stylistic features may also be typical of the major literary works of the same period (with the carnival of calculation paralleled by the carnival of erudition). The minimal claim of the book, then – the one backed up by evidence – is of a certain homology of style between the exact sciences and poetry in the Hellenistic world. In the conclusion to the preceding chapter I have already pointed beyond, to much more tentative claims. It is tempting to postulate a historical force underlying the homology. More than this: if indeed we suggest that a certain historical process led to a Hellenistic interest in generic experimentation, then it becomes very tempting to suggest that the rise of the exact sciences as a major cultural phenomenon should be seen as part and parcel of this practice of experiment in genre, where a hitherto minor genre suddenly gains in prominence.

All of this, however, is highly tentative, largely because our evidence can support such historical interpretations only with difficulty. In this section I acknowledge and address the limitations imposed by our evidence.

The claim of the following chapter is twofold, looking at how poetic practices are (i) complementary to those of the exact sciences, and (ii) parallel to them. Section 4.1 makes the case for (i) complementarity. It shows how Greek poets turned to scientific concepts and contents, weaving science into their poetry just as the scientists were weaving poetry into their science. Sections 4.2–4.3 make the case for (ii) parallelism. Section 4.2 takes a central example of the practices of mythography in Hellenistic poetry as a starting-point for an analysis of the familiar role of “erudition” in this poetry – now considered in light of the scientific practices discussed in this book. Section 4.3 broadens the discussion to look at the poetic parallels to the scientific practices seen throughout this book, as a whole: the narrative surprise and the mosaic text. Of course, the complementarity and parallelism are tightly connected. Section 4.4 offers a brief summary, with some tentative conclusions.

The Hellenistic world was, for generations, the least intensively studied of all ancient periods, its culture alien and uninviting for classicists inspired by Greek glory or by Roman grandeur. With changes in contemporary taste, as well as with the overall explosion of academic writing, considerable and sophisticated studies of Hellenistic civilization have appeared over the last couple of decades. Even this scholarship, however – as is not surprising – concentrates on Hellenistic literature to the exclusion of science.