1. Deleuze (1983a), 23–7; Deleuze and Guattari (1994), 38. The latter draws a link between νόος (‘thought’) and φύσις (‘nature’) with specific reference to Heraclitus. Writing of the plane of immanence, that ‘image of thought’ populated by philosophical concepts, they assert, 38: ‘When Heraclitus’ thought becomes polemos, it is fire that retorts. It is a single speed on both sides…The plane of immanence has two facets as Thought and as Nature, as Nous and as Physis.’ As I shall argue, Heraclitus’ conception of νόος seems to point towards this same ability to fold apparently disparate phenomena into a connected, yet ever mobile, plane of thought and being.

2. The reading of Heraclitus as a philosopher of time and becoming, with radical things to say about the limitations of our human subjective experience, is a central aspect of Nietzsche's analysis in his Pre-Platonic Philosophers. Borrowing the hypothetical experimentation of the natural scientist Karl von Bar in which he postulated that the perception of change in various animals was relative to their heart rate, Nietzsche (2001), 61, extended Bar's insight to imagine the differential experience of change if our lives were lengthened such that: ‘We would experience as much in one year as we now do in eight to nine hours; then every four hours we would watch winter melt away, the earth thaw out, grass and flowers spring up, trees come into full bloom, and then all vegetation wilt once more.’ Among modern interpreters of Heraclitus, it is Dilcher (1995) who most stresses Heraclitus’ innovative and enduring contribution to the theorization of time. For recent analysis of the relationship between Nietzsche and Heraclitus, see Lambrellis (1989), Przybyslawski (2002), and Fink (2003).

3. Deleuze (1988a), 28.

4. This is the overarching thesis of Long (1999b). The limitation of the Milesians’ subject matter to purely physical questions is, of course, a simplification. To take one example, Anaximander of Miletus: his political theorizing on equality has been well-analyzed by Naddaf (2005), just as Hahn (2001) has recently explored the material and historical context behind the lineaments of his cosmological model as being responsive to the context of monumental temple building techniques and the presence of Egyptian architectural knowledge in Miletus in the late seventh century.

5. I employ the traditional numbering system of Diels and Kranz (1952) for the fragments of Heraclitus. All translations are my own, unless otherwise noted.

6. See Kirk (1949), Nussbaum (1972).

7. Kahn (1979), 108.

8. The opposition Heraclitus draws here in DK.B40 between πολυμαθίη and νόος is later replicated by Democritus DK.B64: πολλοὶ πολυμαθέες νόον οὐκ ἔχουσιν (‘many of those who have learned much do not possess understanding’). Furthermore, Democritus extends this distinction with the form πολυνοΐη (‘thinking much’): πολυνοΐην, οὐ πολυμαθίην ἀσκέειν χρή (‘it is necessary to practice thinking much, not learning much’, DK.B65). It is clear that for Democritus, as for Heraclitus, there is a qualitative difference between these two forms of knowledge.

9. Fritz (1945). Among recent analyses, Graham (2008), for example, remains indebted to Fritz's work.

10. Subsequent studies of Heraclitus’ epistemology have stressed a linguistic model of mind, marked by a process of rational deliberation; see Nussbaum (1972), Dilcher (1995), and Hussey (1999). Heraclitus’ interest in language, signification, and the slippage of meaning between word and world is undoubtedly a key component of his philosophical practice. But it is my contention that his model of mind advocates a movement beyond the head to where meaning is constructed through the encounter with the materiality of the world, where thought correctly practiced can take one beyond the boundary of the self into other things, be they animals or rivers, whose rhythms and being in time are at once disclosed by the perceiving self, but also serve to enclose that self in new assemblages of meaning.

11. Barnouw (2004), 94–7, in which he details how visceral thinking in Homer's Odyssey is exemplified in words such as φρήν (‘heart’), νόος (‘mind’), and θυμός (‘spirit’), can provide a powerful interlocutor here, noting how, for example, θυμός paints the physical act of thinking like seething oceans.

12. Fritz notes that the fundamental etymological meaning of νόος is related to smelling, or sniffing. Plutarch's reading of a theory of psychic anathymiasis, the exhalation of souls, in Heraclitus preserves a fragment in which souls are said to smell in Hades (DK.B98); elsewhere, Heraclitus’ valuation of the olfactory is indicated in DK.B7, where we are told that ‘If everything that exists become smoke, the nostrils would provide a diagnosis’ (εἰ πάντα τὰ ὄντα καπνὸς γένοιτο, ῥῖνες ἂν διαγνοῖεν).

13. Naddaf (2005), 133, agrees with McKirahan (1994) in adopting the view of logos as a divine objective structure and states that '[t]he single most important thing to realize is that there is an impersonal, supreme cosmic principle (logos) or law (nomos) that regulates all physical phenomena (or conversely, all physical phenomena are manifestations of the one; see [DK.]B10) and which should be the basis or blueprint for all human laws, political, and moral᾽. Kirk, Raven, and Schofield (1983), 212, speculate that the divine one is identical with the logos as ‘the formulaic constituent of the cosmos’ and that human laws can manifest this principle through the material connection of human lawmakers possessed of the element of fire (cf. DK.B118) that grants them a tenuous connection with the fiery logos.

14. Dilcher (1995), 46, traces a balance between this objective aspect, as the result of logos, and the subjective performance of logos that is tied as a ‘principle of deliberation and reflection’ to a specific occasion.

15. Many scholars of Heraclitus resort to a linguistic model of mind (Nussbaum [1972]; Graham [2008]), that can overlook the embodied and extended model of cognition that one can trace in Heraclitus.

16. So Fritz (1945), 235, argues, ‘The man who learns by (very often unpleasant) experiences learns the hard way, and his knowledge is determined by objects which he not only studies but with which he often collides…There is no room for different and subjective viewpoints.’

17. Badiou (1997) writes with regard to Lacan's assertion of Heraclitus as a predecessor for his own theory of the death drive: ‘Among these aphorisms, the most useful is the one which states the correlation of the Phallus and death…The authority of difference allows Heraclitus to perceive, in the identity of the god of the dead with the god of vital ecstasy, the double investment of the Phallus.’

18. See Nussbaum (1972).

19. Fritz (1945), 232, glosses the targets of DK.B40 as follows: ‘All the persons whom Heraclitus mentions were men not so much of practical experience as of prominence in various fields of theoretical knowledge. What is common to them all is an unusually broad and detailed knowledge in specific fields.’ This combination of overspecialization along with broad learning seems to raise Heraclitus’ ire in the way it produces conceptual generalities and resemblances that fail to properly think through the encounter with the material world.

20. Ansell Pearson (2002), 3, writes that ‘as a thinker of time Deleuze is both profoundly Bergsonian and radically different from Bergson’. Deleuze's work on Bergson, especially his Bergsonism (1988a, orig. publ. 1966), is not an act of philosophical hagiography, but an attempt to rescue Bergson from himself, to clarify certain key concepts, and draw the ultimate evolution of these ideas into a workable form for future philosophical endeavor. It is not so much that Deleuze reads Bergson against Bergson, though he is often on the lookout for hints in Bergson's analyses that he has overlooked something he later intends to remedy, such as the extension of duration to objects; rather, he wants to clarify with more precision Bergson's insights, such as the status of the virtual and the essential difference between the concepts of actualization and realization.

21. See in particular the analyses in Bergson (1960), 110f., and (1983), 306f.

22. Deleuze and Guattari (1988), 13.

23. Deleuze (1988a), 13.

24. Deleuze (1988a), 13.

25. Bergson (1991), 48.

26. Ansell Pearson (2002), 12.

27. Deleuze (1988a), 37.

28. Bergson (1983), 13.

29. Deleuze (1988a), 31f.

30. Deleuze (1988a), 32.

31. Bergson (1999), 36.

32. Graham (2008). Heraclitus is not talking of sameness here, whether of human or river, but rather highlighting the constitutive process of difference that flows from the encounter between them. Indeed, in their creative overlap we gain a foreshadowing of the strong contrast Deleuze will later draw between repetition and resemblance at the start of his Difference and Repetition. In it Deleuze (2004b), 1, writes that ‘repetition and generality must be distinguished in several ways. Every formula which implies their confusion is regrettable: for example when we say that two things are as alike as two drops of water’.

33. See Deleuze and Guattari (1988), 551, Deleuze (2004b), 45f.

34. On the history of this question, see most recently Levine (2002). Kirk (1950) is still useful.

35. The unusual frequency with which children appear in the fragments of Heraclitus confirms the value of a hermeneutic approach to the Heraclitean corpus that emphasizes connections across fragments, paying attention to what Kahn (1979), 89, has termed the principles of ‘linguistic density’ and ‘resonance’ throughout Heraclitus’ oeuvre. Of course, such a reading, whereby fragments neither complete one another, nor exist as unfinished ruins, and instead forge affiliations that resist the sequential orderings of any putative book structure is fundamentally Deleuzian and Guattarian in its approach, see their work (1988), 12. Kahn does, though, attempt to capture the ‘original order of the fragments’ based on their literary qualities. The question of the original book of Heraclitus is a vexed one, of course, and it must suffice here to note that the doxographical tradition (Theophrastus preserved in Diogenes Laertius Vitae 9.6) argues that Heraclitus’ works are always already fragmented, and that even Socrates is unable to plumb their depths (Vitae 2.22).

36. See in particular Heidegger's important reading of the ‘upsurgence’ characteristic of physis (1975), 112.

37. Deleuze and Guattari's emphasis upon the connective flows of ‘desiring-machines’ across the natural and psychical worlds actually seeks, in somewhat Heraclitean fashion, to reveal the mutual imbrication of human and nature as ‘one and the same essential reality, the producer product’ (1984), 5. Such an insight, they write, can be gleaned only by ‘the being who is in intimate contact with the profound life of all forms or all types of being’ (1984), 4. Heraclitus’ children at play represent just such a deep materialist engagement with the natural world and its various forms of being, whereby their youthful productions can couple seemingly fragmentary material into new, and potentially subversive, arrangements.

38. Multiplicity in this sense means more than just a unified collective of apparently disparate entities. Deleuze's understanding of multiplicity is born out of his engagement with Bergson's distinction, itself developed from the mathematician G.B.R. Riemann, between discrete and continuous multiplicities. The former are numerical in essence, represented by space and exteriority, wherein the figures of juxtaposition, location, and order are used to trace differences of degree in homogeneous terms; the latter are non-numerical, and are to be understood, rather, in temporal, or durational, terms, as the location for differences in kind, marked by qualities of fusion and heterogeneity. While a discrete multiplicity can be divided up without changing the fundamental nature of the multiplicity (as in the case of units of number), a continuous multiplicity changes in kind during the process of being divided up. Deleuze (1988a), 39–41, discusses Bergson's adaptation of Riemann, as well as his engagement with Einsteinian relativity. See also the summary in Ansell Pearson (2002), 15–18.

39. Deleuze and Guattari (1988), 11.

40. Bergson (1991), 97.

41. As Deleuze and Guattari (1988), 16, write of the disruptive play of the child: ‘In the case of the child, gestural, mimetic, ludic and other semiotic systems regain their freedom and extricate themselves from the “tracing”, that is, from the dominant competence of the teacher's language—a microscopic event upsets the local balance of power.’

42. Bollack and Wismann (1972), 195, argue, ‘Le mot de peux, en grec, signifiant destructeurs (phteir-, sur phteirein) les garçons tuent ce qui tue. Les deux termes sont juxtaposés.’

43. Weyl (1987), 87.

44. Among the twenty-two passages of Heraclitus that Hippolytus, the fourth-century Bishop of Rome, quotes is one he introduces to expose the relativism of Noetus, such that a child and god might seem to be interchangeable, along with their associated qualities of mortality and infinitude. In glossing DK.B52, Hippolytus claims that Heraclitus is here asserting that the totality is a child. Lucian of Samosata's deployment of DK.B52 in his satirical Philosophies for Sale (Vit. Auct. 14) is remarkable for the work he makes it do in order to encompass the many avenues of flux within Heraclitus’ kosmos: the ‘exchanges’ (ἀμειβόμενα) of the child's play are made to represent the physical alterations of location and magnitude, the emotional categories of ‘enjoyment’ (τέρψις) and ‘displeasure’ (ἀτερψίη), and the epistemological antinomies of ‘insight’ (γνῶσις) and ‘ignorance’ (ἀγνωσίη). The catalyst behind these changes is once again αἰών and it is this dynamism that the child at play explicates. Recent work on Lucian, e.g. Schlapbach (2010), has also foregrounded the philosophical nature and import of his presentation and manipulation of earlier philosophers and schools.

45. On the difficulty of identifying the nature of this game and with a suggestion for resolving the uncertainty, see most recently Schädler (forthcoming).

46. Coubaritsis (1989), 104–13. Bollack-Wismann (1972) translate αἰών as ‘life’, Conche (1986) chooses ‘time’, while Kahn (1979) opts for ‘Lifetime’.

47. A passage in Euripides’ Heracleidae gestures in this same direction of a creative and dynamic αἰών that is linked to childhood: πολλὰ γὰρ τίκτει Μοῖρα τελεσσιδώ-/τειρ᾽ Aἰών τε Χρόνου παῖς (‘Fate that brings completion and Aion, the child of Chronos, brings many things to pass’, 899f.). Coubaritsis (1989) considers this mythological genealogy to be authentically archaic, and as indicative of the historical reversal Plato initiated in making χρόνος the mimetic child of an eternal αἰών.

48. Interpretations that emphasize the randomness of children's play as somehow synonymous with the putative scatterings that inadvertently produce cosmic order in DK.B124 overlook the important oppositional role that the ludic child and children play to traditional structures of thought and modes of understanding throughout Heraclitus’ work.

49. Kurke (1999), 270.

50. Massumi (2002), 3. Indeed, Diogenes of Laertius’ doxographical gloss on DK.B121, which advocates leaving the rule of the Ephesian polis to the young (anēbois), guides us towards the way that childhood gameplay in Heraclitus can be seen as having a politically performative force, rather than representing a cipher for existing modalities of political organization and ideology (Vit. Phil. 9.1.2f.).

51. The embodied child at play thus represents a form of creative distribution that precedes the subsequent stratifications and limitations imposed by the state-organized board. The idea that the child αἰών enacts a playful open-ended distribution accords well with Deleuze's writing upon the etymology of nomos, which he borrows from the Indo-European linguist Emmanuel Laroche (Deleuze [2004b], 85 n.6). Deleuze (2004b), 46, terms this distribution of space as one that is ‘nomadic, a nomad nomos, without property, enclosure or measure. Here there is no longer a division of that which is distributed but rather a division among those who distribute themselves in an open space—a space which is unlimited, or at least without precise limits…Even when it concerns the serious business of life, it is more like a space of play, or rule of play’.

52. Deleuze (1988a), 25–7.

53. The potential of the kingly child at play thus seems to disrupt the stability of a state-controlled space. Deleuze and Guattari's discussion (1988), 389f., of the difference between the games of Go and Chess provides a useful interlocutor here. For them, Chess represents that which is institutional, coded, where the pieces possess ‘internal properties from which their movements, situations and confrontations derive’, whereas in Go the pieces ‘are elements of a nonsubjectified assemblage with no intrinsic properties, only situational ones’. Space in Chess is fundamentally closed and striated; in Go it is open, such that the pieces maintain ‘the possibility of springing up at any point’. It is the unpredictability of Heraclitus’ collective of children at play that threatens to deterritorialize and reterritorialize existent organizations of power from within.

54. If anything the virtual is the dimension of the past, understood as a force constantly exerting pressure on the present, bringing it into being.

55. See discussion in Deleuze (1988a), 42.

56. The psychical, marked by a duration that is virtual, does not correspond to space, or fit the presiding models of ‘closed system’ thinking represented by mathematics and logic. Its features are those of what Deleuze (1988a), 42f., terms ‘the open’, vibrant with potential, other without being several, defined by its continuous movement of actualization, and the production of difference. Deleuze and Guattari's later concept of ‘schizoanalysis’ with its notion of the productive multiplicity of the unconscious where ‘there are only populations, groups and machines’ (Deleuze and Guattari [1984], 283) takes this blurring between the psychological and ontological still further.

57. Ansell Pearson (2005), 1113.

58. Bergson (1983), 258.

59. Kahn (1979), 227, argues that the participle μεταπεσόντα can reference game-playing, perhaps those involving dice, as can other verbs that are commonly used to describe the moving of pieces on a board, such as μετατίθημι (‘place among’) and μεταβάλλω (‘throw into a different position’).

60. Kahn (1979), 227.

61. Hussey (1999), 107.

62. Bergson (1960), 100, asserts that time, understood durationally, and on the level of consciousness, encloses both past and present in virtual co-existence, rather than as separated states marked by the spatial notion of succession.

63. Bergson (1983), 11.

64. Deleuze and Guattari (1988), 7. Ansell Pearson (2002), 36, notes how Deleuze uses Bergson's own musings as the fertile ground for his own Bergsonism, for example by quoting in (1988a), 48f., a passage from Bergson (1960), 227, in which Bergson wonders: ‘Although things do not endure as we do, nevertheless there must be some incomprehensible reason why phenomena are seen to succeed one another, instead of being set out all at once’.

65. Bergson (1960), 233.

66. See in particular Deleuze (2004b), 152–6.

67. I follow Graham (2010), 156, in the reading of χρεών, since this produces a more balanced phrase with the singular ἔριν, as opposed for the χρεώμενα used by Diels-Kranz.

68. Dilcher (1995), 108, observes that Heraclitus’ opposites are not the traditional static ones employed by Pythagoras, for example as here between male and female, or between odd and even, termed enantia (ἐνατία) in Greek. Instead, Dilcher asserts that Heraclitus’ opposites ‘all imply transition and change’, that is to say, their present state contains future states within it, that only become visible when one plots their mutability over time.

69. Bergson (1960), 101.

70. Vlastos (1993), 132. Hussey (1999), 97, argues that the functioning of the unity of Heraclitus’ kosmos demands an acknowledgement of temporal process, whereby only through time do diametrically opposed opposites reveal their ‘transformational equivalence’.

71. Hussey (1982), 56.

72. Deleuze (1988a), 28.

73. Deleuze (1988a), 28f.

74. Kahn (1979), 201. Dilcher (1995), 129, claims that Heraclitus was not suggesting an etymology, but deliberately using a homonymic play to provoke awareness of the wavering nature of the world: ‘language reflects in its ambiguity correctly the inherent ambivalence of the corresponding reality’. Dilcher's analysis privileges deliberate misreading too much, and resorts ultimately to a model of language as representation.

75. In this context, we might also note that Aristotle's subsequent use of σύλληψις to indicate ‘pregnancy’ (Hist. an. 582b11) could also be read through Heraclitus’ lens to represent the bodily involvement in the gestation and birth of new knowledge.

76. Deleuze and Guattari (1994), 38. See n.1.

77. βαθὺν λόγον is perhaps best translated in the sense of a Homeric opacity, a dense thickness befitting a mist (Il. 21.7) or luxuriant growth (Il. 5.555), as well as in the Aeschylean aspect of a complex intellectual capacity (Supp. 407).

78. Deleuze (1986), 59.

79. Ansell Pearson (2002), 42.

80. The authenticity of this fragment has been the subject of much debate, especially in comparison with the more widely accepted river fragment DK.B12. See discussion in Kirk (1954), 369, and Kahn (1980), 167. Graham (2010), 158, selects only the following phrases from the fragment as authentically Heraclitean in style: σκίδνησι καὶ πάλιν συνάγει and συνίσταται καὶ ἀπολείπει, καὶ πρόσεισι καὶ ἄπεισι.

81. Indeed, ἕξις (‘possession’, ‘state’) can have both a physical and mental connotation. For the former with reference to the body see Plato Theaet. 153b; for the latter Plato Leg. 650b.

82. This can help clarify the import of Heraclitus’ critique of his sleepwalking audience at the end of DK.B1: τοὺς δὲ ἄλλους ἀνθρώπους λανθάνει ὁκόσα ἐγερθέντες ποιοῦσιν, ὅκωσπερ ὁκόσα εὕδοντες ἐπιλανθάνονται. (‘What they do while awake escapes the notice of other men, just as they are forgetful of what they do when asleep’.)

83. The keen Stoic appreciation of Heraclitus makes it likely that if such concepts were evident in Heraclitus the Stoics would have been at pains to emphasize them, as Vlastos (1993), 136, adroitly points out. On the underexplored relationship between the Stoics and Heraclitus, Long's study (1996) remains the best, though Dilcher (1995) contains excellent observations, especially his discussion of the authenticity of the psyche as spider image (DK.B67A) preserved in Stoic sources.

84. In claiming that this connection is preserved through a ‘drawing off via respiration’ (δι᾽ἀναπνοῆς σπάσαντες, Adv. Math. VII.129), Sextus gestures toward the concept of ‘exhalation’ (anathymiasis) that is ascribed by Aristotle to Heraclitus in considering the relation of the soul to the surrounding cosmos (De Anima 405a25–9 = DK.A15). On the question of anathymiasis and its possible place in the authentic doctrines of Heraclitus see Kahn (1979), 256–60, and also Dilcher (1995), 172–83.

85. Deleuze and Guattari (1988), 5–7.

86. Vlastos (1955), 347, argues that the commonality of φρόνησις in DK.B113 is not just observational but prescriptive, acting as a model for how one should think.

87. We find a similar conception in Empedocles DK.B103: τῆιδε μὲν οὖν ἰότητι Τύχης πεφρόνηκεν ἅπαντα. (‘Now everything has a share of thought through the will of Chance.’) Indeed, Empedocles’ view of a transmigratory soul, traversing genders, crossing between fauna and flora, and moving from land to sea, could support this idea of the extension of duration to all things, albeit vectored by the preservation of the human soul as it journeys through various stages. Intriguingly, though, there is also the idea in Empedocles that thought itself possesses movement and growth, and will, if it is not nurtured appropriately by an individual, fly off elsewhere (DK.B110). For Empedocles, thought properly wielded seems to allow the wise individual to ‘reach’ (ὀρέξαιτο) across time, across ‘ten or twenty generations of men’ (δέκ’ ἀνθρώπων καί τ’ εἴκοσιν αἰώνεσσιν) to behold each existent thing (DK.B129).

88. Fink (2016), 51.