Abstract
This article examines in detail the second-century CE polymath Claudius Ptolemy’s expression of the ‘desire for knowledge’, situating it against a wider backdrop of similar expressions in the Greek textual tradition. I argue that in his expression, Ptolemy creatively alludes to Plato’s Phaedrus, a practice that, surprisingly, here ties his work more closely to contemporary oratory and the ‘novel’ than to generic precursors in the exact sciences. The piece thus demonstrates how an author in the highly formalized genre of mathematics employs specific textual strategies held in common with his wider, contemporary literary culture.
I would like to thank the organizers of the Guangzhou conference for including me in the program, as well as for showing such wonderful hospitality over the course of the conference weekend. Acknowledgements are due, too, to audiences at Stanford and in Philadelphia who heard and commented on earlier versions of the paper. I am especially grateful to Geoffrey Lloyd, Reviel Netz, Anastasia-Erasmia Peponi, Susan Stephens, and the two anonymous referees, all of whom offered comments on earlier drafts that resulted in important clarifications and improvements. All errors of fact and interpretation remain my own.
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Notes
- 1.
Heisenberg 1971: 69.
- 2.
An early example is Fuhrmann 1960, a formalist account of ancient handbooks, but the last decade and a half, especially, have witnessed an acceleration in shorter scholarly publications on technical and scientific writing. An important methodological essay is van der Eijk 1997, but there are still relatively few monographs that account for formal or otherwise literary aspects of ancient scientific texts, though Netz 1999 and 2009 and Asper 2007 are crucial contributions. See also Fögen 2009 for a linguistic approach to Roman technical writing, and Mattern 2008 on the form and rhetoric of medical narrative across Galen’s works.
- 3.
The discussion here thus complements Matthew Leigh’s 2013 study of curiosity that focuses on πολυπραγμοσύνη. I hope, too, that this philological investigation of mathematical desire will dovetail with recent philosophical discussions of one object of that desire, namely, mathematical beauty; cf. Rota 1997, and Müller-Hill and Spies 2011.
- 4.
Netz 2002. On the apparently low mathematical productivity of the second century CE, see the tables in Netz 1997: 6–10. The Syntaxis, of course, is entangled to some degree with astrological practices of much wider popularity, but as Bernard 2010: 513 notes, even when an astrological theory was supported by geometric models, one did not need to comprehend those models in order to calculate horoscopes from, say, numerical tables.
- 5.
- 6.
- 7.
- 8.
Cf. Jones 2005a: 62.
- 9.
Olymp. In Phd. 10.4, granted some plausibility by Jones 2005a: 61–64.
- 10.
- 11.
Bernard 2010.
- 12.
- 13.
Tolsa 2013.
- 14.
Moving in this direction are Jones 2005b, which patiently maps out several of Ptolemy’s labyrinthine rhetorical strategies, and Mansfeld 1998: 66–75 and Feke 2012: 89, which consider some formal aspects of Ptolemy’s prologues. Tolsa 2013: 301–328 situates ‘Ptolemy’s epigram’ (possibly dubious but transmitted in the manuscript tradition of the Syntaxis) in literary context.
- 15.
For a plausible sequence of Ptolemy’s authorship, see Feke and Jones 2010: 200–201.
- 16.
- 17.
Ptol. Harm. III.3 [92.1–8 Düring], translation adapted from Barker 1989: 371.
- 18.
For a general account of this issue in Greek thought and literature up to (pseudo-)Longinus (not including Ptolemy), see Nightingale 2004: 253–268.
- 19.
Ptol. Syntaxis part 1, p. 7.25–26 Heiberg.
- 20.
Ptol. Syntaxis part 1, p. 7.21–22 Heiberg.
- 21.
Ptol. Syntaxis part 1, p. 361.11 Heiberg.
- 22.
To set out my search methodology more precisely: I used the TLG’s ‘Advanced Lemma Search’ function to locate combinations of each of the given terms for desire and knowledge occurring within one line of each other. For the ‘desire’ group, no formal constraints were set (on case, number, tense, mood, etc.), so as not to bias the search results to favor certain parts of syntax. On the other hand, since terms of knowledge are here specifically the objects of desire, certain constraints were set for this group in all searches: all noun-searches were limited to the singular genitive and accusative; verb-searches were limited to present and aorist, active infinitives, except for the cases of οἶδα, where I targeted the perfect, active infinitive, and the deponent πυνθάνομαι, where I targeted the present and aorist, middle/passive infinitive.
- 23.
Leigh 2013 develops an intellectual history of ancient curiosity which is naturally sensitive to form, but whose primary focus is on the valence of πολυπραγμοσύνη and related concepts.
- 24.
I treat cognate nouns, verbs, and adjectives (e.g., πόθος and ποθέω) as a single species, locating the defining features thereof at the linguistic root.
- 25.
Expressions based on βούλομαι number in the dozens, whereas I count only seven examples that feature ἵμερος/ἱμείρω. Uniquely in my searches, βούλησις produced zero results.
- 26.
The following is a representative, not exhaustive list of citations: ΠΟΘΟΣ/ΠΟΘΕΩ: θεάομαι: Ph. Jos. 204; Plu. Demetr. 6.5; Ptol. Harm. 3.3. ἀλήθεια: Ph. Aet. 2; S.E. M. Pr.6. οἶδα: S. Tr. 632; E. IT. 542; Pl. Men. 84c; Arist. PA. 644b26; Str. 2.5.18; Luc. Icar. 4. θεωρία: Th. 6.24.3. θεωρέω : not found. ἐπιστήμη: Ph. Op. 77; Plu Adv.Col. 1118b. γνῶσις: Str. 13.1.1; Plu. Adv.Col. 1118b. γιγνώσκω: Ph. Virt. 215; Plu. De genio 590a; Gal. MM. K vol. 10, p. 714.17. μανθάνω: E. Ion 1432; Ph. Fug. 8; D.H. 7.66.1; Max.Tyr. 8.4; S.E. M. 9.75; Luc. Trag. 209. σοφία: Ph. Op. 5; Max.Tyr. 25.1; Luc. Merc.cond. 25. πυνθάνομαι: Plu. Quaes.Rom. 266b. ΕΠΙΘΥΜΙΑ/Ε ΠΙΘΥΜΕΩ: θεάομαι: Pl. Ti. 19b; Arist. Rh. 1370a26; D.S. 13.9.3; Ael. NA. 16.39; Gal. PHP. 5.7.48. ἀλήθεια: Gal. MM. K vol. 10, p. 457.14. οἶδα: Ar. V. 86; Pl. Grg. 474c; Luc. VH. 2.20. θεωρία: not found. θεωρέω: Pl. Lg. 951a; Epicur. Ep. ad Pythoclem 94. ἐπιστήμη: Arist. Pol. 1288b17; Gal. Quod animi mores K vol. 4, p. 772.3. γνῶσις: D.H. 11.36.1. γιγνώσκω: LXX Is. 58.2; D.S. 10.8.3; Gal. Loc.Aff. K vol. 8, p. 144.7. μανθάνω: Ar. Nu. 656; Pl. Hp.Mi. 369d; X. Cyr. 4.3.15; Arist. Rh. 1371a32; Erot. 29.8; Plu. De Pyth. 395e; App. Pun. 430. σοφία: Ar. Nu. 412; Pl. Phd. 96a; LXX Wi. 6.20; S. 15.1.64; J. Ap. 1.111. πυνθάνομαι: Ar. Lys. 486; Is. 3.8; Plu. De comm. 1066d.
ΙΜΕΡΟΣ/ΙΜΕΙΡΩ: θεάομαι: Ph. Praem. 39; Ael. NA. 11.17. ἀλήθεια: S.E. M. 1.42. οἶδα: not found. θεωρία: not found. θεωρέω: not found. ἐπιστήμη: not found. γνῶσις : not found. γιγνώσκω: not found. μανθάνω: S. Fr. 314.134 Radt; Plb. 14.Pr.4; Ph. Cont. 75. σοφία: Ph. Spec.leg. 1.50. πυνθάνομαι: not found.
ΒΟΥΛΟΜΑΙ: θεάομαι: Ar. Th. 234; Pl. R. 327a; Plb. 7.12.1; D.S. 17.116.5; Ael. VH. 14.17; Plu. Cat.Ma. 17.4; Gal. AA K vol. 2, p. 630.8. ἀλήθεια: not found. οἶδα: Hdt. 1.86; Hp. Aph. 5.59; E. Alc. 140; Ar. Nu. 250; Th. 1.52.2; Pl. Lg. 629c; X. Cyr. 8.4.11; Isoc. 17.9; D. 19.227; Aesch. 3.199; Arist. EE. 1216b22; Plb. 4.38.12; D.H. Dem. 50; J. AJ. 1.325; D.Chr. 4.67; Gal. Dig.puls. K vol. 8, p. 955.17. θεωρία: not found. θεωρέω: Th. 5.18.2; Alc. Od. 86; D. Ep. 4.5; Arist. Cael. 300b20; D.S. 19.52.4; Gal. Dig.puls. K vol. 8, p. 944.8. ἐπιστήμη: not found. γνῶσις: not found. γιγνώσκω: S. Fr. 1130.3 Radt; Pl. R. 572b; X. Mem. 1.2.42; Arist. De an. 402a14; LXX To. 5.14; Plb. 1.1.5; D.S. 5.77.3; J. AJ. 12.100; D.Chr. 31.38; Gal. Lib.prop. K vol. 19, p. 9.1; Aesop. 50.6. μανθάνω: S. Ph. 233; E. El. 229; Ar. Nu. 239; Pl. Sph. 232d; X. HG. 6.5.52; D. 23.2; Agatharch. 14.6; Plb. 21.41.5; Str. 2.5.43; Ph. Jos. 56; D.H. 4.66.1; J. BJ. 7.454; Plu. Crass. 28.4; Ruf. Syn.puls. 3.3; Vett.Val. 8.8; S.E. M. 8.87; Ael. NA. 5.42; Gal. PHP 1.6.4; Luc. VH. 1.5. σοφία: not found. πυνθάνομαι: Hdt. 6.69; E. Hipp. 910; Ar. Nu. 482; Th. 8.19.1; Pl. La. 191d; X. Oec. 7.2; D. 4.10; Arist. Top. 161b5; Plb. 11.28.11; Plu. De genio 577e; S.E. P. 2.211; Gal. De semine K vol. 4, p. 527.18.
- 27.
I count only two instances of βούλομαι εἰδέναι in the Hippocratic corpus: Aphor. 5.59 and De semine 13.23, and one instance of ἐπιθυμέω θεωρεῖν at Epicur. Ep. ad Pythoclem 94.
- 28.
ΟΡΕΞΙΣ/ΟΡΕΓΩ: θεάομαι : not found. ἀλήθεια: Pl. R. 485d; Plu. De recta 48c; Ptol. Judic. p. 5 Lammert; Gal. De const. artis K vol. 1, p. 244.16. οἶδα: Arist. Metaph. 980a21. θεωρία: Alcin. Intr. 27.4. θεωρέω: not found. ἐπιστήμη: Arist. De an. 433a6; Gal. Syn.puls. K vol. 9, p. 431.2. γνῶσις: D.H. 1.1.3; Theon Sm. 1.11. γιγνώσκω: Gal. Diff.resp. K vol. 7, p. 889.1. μανθάνω: Gal. Ars med. K vol. 1, p. 224.3; Cels. Apud Originem 6.18. σοφία: Nicom. Ar. 1.2.3; Alcin. Intr. 1.1; Gal. MM. K vol. 10, p. 114.18. πυνθάνομαι: not found.
- 29.
ΕΡΩΣ/ΕΡΑΣΤΗΣ/ΕΡΑΩ/ΕΡΑΜΑΙ/ΕΡΩΤΙΚΟΣ: θεάομαι: Ph. Praem. 38; Ptol. Harm. 3.3 (with ποθεῖν). ἀλήθεια: Pl. R. 501d; Ph. Spec.leg. 1.59; Alcin. Intr. 1.2; Max.Tyr. 16.2; Gal. Nat.fac. K vol. 2, p. 179.13; Ael. NA. 2.11. οἶδα: not found. θεωρία: Ptol. Synt. 1.7; Gal. Dig.puls. K vol. 8, p. 860.5. θεωρέω: not found. ἐπιστήμη: Pl. Ti. 46d; Ph. Op. 77; Thess. Virt.herb. Pr.5. γνῶσις: not found. γιγνώσκω: not found. μανθάνω: E. Hipp. 173; Max.Tyr. 11.11. σοφία: Ph. Op. 5; Plu. Sol. 2.2; D.Chr. 36.40; Max.Tyr. 18.5; Ael. NA. Ep.1. πυνθάνομαι: S. OC. 511.
- 30.
Another might be found at E. Fr. 889.1 Nauck: παίδευμα δ᾽ ᾽Ἔρως σοφίας, but in context σοφίας is better construed quasi-subjectively with παίδευμα, rather than as the object of Ἔρως.
- 31.
Could the precedents from tragedy be yet further evidence of Plato’s appropriation of poetic discourse for his construction of philosophy, as argued by Nightingale 1996?
- 32.
- 33.
- 34.
μάθημα (R. 485b), τὸ ὂν (R. 501d), νοῦς (Ti. 46d), φρόνησις (Phd. 68a), τὸ ἀληθές (Phlb. 58d).
- 35.
The question of why other authors apparently avoid this complex of expressions until the Imperial period cannot be answered here; more searches are warranted and may of course qualify the result.
- 36.
See De Lacy 1974 and now Hunter 2012 for Plato’s influence on Imperial literary culture, and Trapp 1990 on the particular prominence of Plato’s Phaedrus, one of the key sources for Platonic ἔρως. Mansfeld 1994: 58–107 describes the pedagogical context. For Platonic influence on Philo, Maximus, and Galen, see Dillon 1977: 139–183; Trapp 1997: xxii–xxxii; and De Lacy 1972.
- 37.
The fact that he made any positive choice reveals something about the generic history of the exact sciences: we noted the apparent absence of the desire for knowledge from any Hellenistic mathematical works. As our survey was admittedly limited, we shall examine these texts in more detail below.
- 38.
See, for example, the editorial notes on Harm. 3.3–5 in Barker 1989: 373–377; Taub 1993, esp. 31–34; Feke 2009; Feke 2012; Tolsa 2013, esp. chapters 1–3. Like other Imperial writers, of course, Ptolemy is not swept entirely away by those currents, but demonstrates a notable degree of eclecticism; Feke 2009: 221 brands his philosophy ‘Platonic empiricism’.
- 39.
Hinds 1998: 40.
- 40.
Ph. Praem. 38. The result followed TLG Advanced Lemma Searches for combinations of ἔρως/ἐραστής/ἐράω/ἔραμαι/ἐρωτικός, πόθος/ποθέω, θεάομαι occurring within one line of each other. After Ptolemy’s Harmonics, the next instance is Ps.-Luc. Am. 53, perhaps from the early fourth century.
- 41.
See nn. 36 and 38 above.
- 42.
Tolsa 2013: 84 briefly notes lexical correspondence between the Harmonics passage and the Phaedrus.
- 43.
- 44.
Socrates asking whether Phaedrus ‘desires’ anything (Phdr. 234c); ‘beholding’ the writings of great writers (258c) and men of certain classes (271d).
- 45.
Or, in the case of ‘divine erôs’ alone, in Socrates’ recantation, which introduces the speech.
- 46.
A culture commonly referred to as the ‘Second Sophistic’, on which see Whitmarsh 2005.
- 47.
See De Lacy 1974: 6–8 and especially Trapp 1990, which includes an appendix that registers allusions to the Phaedrus (including the ‘soul of the lover’) from numerous authors and works; Ptolemy is not included. Cf. Hunter 1997; Hunter 2012: 151–184; and Rocca 2006 on Galen. Papyrological records from the CEDOPAL database (http://www2.ulg.ac.be/facphl/services/cedopal/), accessed on February 17, 2013, corroborate the dialogue’s popularity in the Imperial period: out of 105 fragments of Plato, 8 are from the Phaedrus (three of which, moreover, feature text from Socrates’ second speech). This number is exceeded only by the Republic (13), Phaedo (11) and Laws (10), but the Phaedrus’ tally is especially impressive given the substantially greater length (and therefore, the greater odds of survival) of those other works.
- 48.
Trapp 1990: 141.
- 49.
For a sizeable list of allusions, see Trapp 1990: 172; to this we might add Gal. Nat.fac. K vol. 2, p. 179.12–15.
- 50.
Feke and Jones 2010: 200–201 situate the Harmonics early in Ptolemy’s career; might its author be Trapp’s young pepaideumenos, eager to demonstrate his rhetorical-philosophical education? Tolsa 2013: 201–203 contends that Ptolemy frames another early work, On the Criterion, as a rhetorical exercise.
- 51.
On date, author, and title, see Hunter 1983: 1–15.
- 52.
On the Platonic aspects of this opening, see Hunter 1997: 24.
- 53.
Longus Pr. 2, translation adapted from Reardon 1989: 289.
- 54.
In Longus’ account, for instance, vision prompts desire, whereas for Ptolemy the desire is to see.
- 55.
Hunter 1997: 28.
- 56.
- 57.
For the general importance of sight and spectacle to Platonic philosophy, especially as they relate to Plato’s wider cultural context, see Nightingale 2004.
- 58.
- 59.
In this the allusion is unique in the Harmonics. It is also true that Ptolemy adduces another, more general Platonic figure—the `philosopher' (φιλόσοφος)—into his discussion at 3.5.70, but this is to illustrate further the concept of ‘harmonia’ (ἁρμονία); see Barker 1989: 377n50. In this passage Ptolemy does not use the philosopher to describe the practice of the theorist.
- 60.
In this it functions similarly to the ‘frame tales’ found in later mathematical commentaries that present famous mathematicians (e.g., Euclid) in moralizing episodes. These ‘deliver not the [mathematical] knowledge itself, but rather the way a mathematician is supposed to behave when putting the knowledge to practical use’ (Asper 2011: 96). A fundamental difference, however, is that Ptolemy is here not morally prescriptive, but emotionally so. He is idealizing the experience, not the behavior, of the harmonic theorist.
- 61.
Nicomachus’ Introductio arithmetica did register the expression σοφίαςὄρεξις (1.2.3), but this text is more a philosophical account of numbers than a presentation of geometric proofs (D’Ooge 1926: 16).
- 62.
Netz 2009: 92–107.
- 63.
- 64.
There are exceptions: below I examine Hipparchus’ ‘hybrid’ commentary on Aratus. But we especially miss the lost works of the polymathic Eratosthenes, whose nonextant Platonicus, for instance, might have offered interesting counterevidence. On this work see Geus 2002: 141–194.
- 65.
Ptol. Harm. 1.2.
- 66.
See Barker 1989: 28–52.
- 67.
On the connotations of ‘mathematics’ and ‘mathematician’ in antiquity, see Lloyd 2012.
- 68.
Reported in Porph. In Harm. 56.5 Düring.
- 69.
He is especially interested in defining the proper domain of the science of harmonics: see Aristox. Harm. 5.4–6.5 da Rios.
- 70.
Aristox. Harm. 40.14–16 da Rios, translation lightly adapted from Barker 1989: 148.
- 71.
Aristox. Harm. 40.16–41.2 da Rios.1 Cf. Barker 1989: 148n6.
- 72.
Netz 1999: 256.
- 73.
- 74.
- 75.
By Hypsicles’ time, as in our own, a term whose semantics had stretched to include more figurative meanings.
- 76.
σπουδή: Archim. Method vol. 2, p. 71, col. 1.33–34 Netz et al.; Apollon.Perg. Con. vol. 1, p. 2 Heiberg. φιλοπονία: Archim. Spir. vol. 2, p. 2.18 Heiberg; Eratosthenes, at Eutoc. In Archim. Sph. Cyl. 90.4 Heiberg (authenticity defended by Knorr 1989: 131–146). φιλοτιμία: Apollon.Perg. Con. vol. 2, p. 2 Heiberg. In Toomer’s translation of the Arabic copy of On Burning Mirrors, Diocles affirms that using gnomons requires ‘care’ (Toomer 1976: 42), which may have been σπουδή or something similar in the lost Greek original. The letter-form itself seems a natural vehicle to convey this attitude, since authors frequently offer their work expressly as the fulfillment of an eager correspondent’s personal request for more mathematics.
- 77.
The same language even expresses the attitudes that euergetic Hellenistic kings and their subjugated polities show toward one another: see Ma 1999: 191.
- 78.
On the hybrid form of this work, see Netz 2009: 168–171.
- 79.
Aischrion’s φιλομαθία: Hipparch. 1.1.5; ‘those who are fond of learning’ (τῶν φιλομαθούντων): Hipparch. 1.1.6, 1.10.25.
- 80.
The term appears frequently in the Phaedo and Republic, less so in the Phaedrus, Timaeus, and the Laws. Other Classical and Hellenistic instances include X. An. 1.9.5; Isoc. 1.18; Arist. EN. 1175a14; Plb. 1.2.8, etc.; Ps.-Scymnus 63; Aristeae.Ep. 1.6; Apollon.Cit. 3.15 Schöne. On its use especially in scientific texts, see Alexander 1993: 59, 100.
- 81.
This is the period of the philosophizing compiler Nicomachus: see n. 61 above. Cf. Cuomo 2000: 9–56 on the public profile of mathematics in the first centuries CE.
- 82.
This is the period Netz 1999: 284 describes as ‘a wilderness between two deserts’.
- 83.
Syntaxis part 2, pp. 30 and 33 Heiberg; apparently the same Menelaus is present for the dialogue in Plutarch’s De facie (930a).
- 84.
See further Krause 1998: 109–111.
- 85.
I am grateful to Alexander Key for his expertise and assistance on points of Arabic philology, which emerge in the following paragraphs.
- 86.
The extant manuscript is itself dated 1222 CE, but the translation apparently dates to the ninth or tenth century: see Akasoy and Fidora 2005: 1–2.
- 87.
Akasoy and Fidora 2005: 544n91.
- 88.
Does this indicate a convention shared among translators for rendering φιλομαθ- into Arabic?
- 89.
Krause 1998: 117n5.
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Wietzke, J. (2016). A Fashionable Curiosity: Claudius Ptolemy’s ‘Desire for Knowledge’ in Literary Context. In: Ju, S., Löwe, B., Müller, T., Xie, Y. (eds) Cultures of Mathematics and Logic. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-31502-7_5
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