Crates & Mathematical Geography

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Transactions of the American Philological Association 142 (2012) 295–328
Crates of Mallos and Pytheas of Massalia:
Examples of Homeric Exegesis in Terms of
Mathematical Geography
tomislav bilić
Archeological Museum, Zagreb
summary: Crates of Mallos, a Hellenistic grammarian and geographer, is
known to have combined Homeric exegesis and mathematical geography into
a comprehensive world-view. His views appear to have influenced a tradition
of map-making, as evidenced by an unusual late antique map that locates parts
of Odysseus’s voyage from Aeaea to Hades according to Crates’ geography. This
essay elucidates Crates’ geographical accounts of the Homeric Laestrygonians
and of the constellation Draco and his understanding of the arctic circle in light
of the map and of earlier geographers, particularly Pytheas of Massalia, who
similarly incorporated Homeric references into his theorizing about the fixed
arctic circle.
introduction
crates of mallos, aristarchus’s “arch-enemy,” was a second-century
b.c.e. grammarian (he would have prefered the title kritikos),1 whose contribution to Homeric exegesis is increasingly acknowledged and studied
in its own right.2 His contributions to geography, however, are in general
not judged favorably: he is described “bestenfalls als interessierter und ver-
Fr. 94, cf. T 1, 20; fr. 59. Crates’ fragments are generally cited according to Broggiato
2001 (fr., T); otherwise, according to Mette 1936. Broggiato is currently preparing a new
edition of Crates for FGrHist 5 (Brill online), and I would like to thank her for giving me
the opportunity to study the section of her manuscript pertaining to the subject of my
paper (cited as Broggiato forthcoming). On the terms grammatikos/kritikos/Homerikos
with reference to Crates, see Asmis 1992: 138–39; Porter 1992: 85–86, cf. 87–88; Broggiato
2001: xx, 249–50.
2 See, e.g., Kroll 1922; Mette 1936; Quinn 1982: 97–108; Asmis 1992; Porter 1992,
2003; Broggiato 2001: xiii–lxix.
1
© 2012 by the American Philological Association
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gleichsweise gut orientierter Laie.”3 It could be argued that this is a generally
accepted opinion, though a few scholars have been rather more sympathetic
to Crates’ contributions to the science of geography.4 His geographical work
is an excellent example of his eclectic, but still highly selective,5 intellectual interests, and his contribution to physical allegorizing, especially in the
form of the so-called sphairopoiia (“the sphericity of the cosmos”), is well
recognized.6 Furthermore, his geographical teachings—their shortcomings
notwithstanding—survived down to late antiquity, including his theory that
the four great land masses were divided by equatorial and meridian oceans.7
Since a number of authors, among them Strabo, Geminus, and Macrobius,
show significant familiarity with his works, it would not be an exaggeration
to claim that both his geographical and his allegorizing teachings were well
known both in antiquity and the Middle Ages (cf. Romm 1992: 130).
Crates’ interpretation of the Homeric epics is usually styled as “Stoic,” but
this notion is unsubstantiated (Asmis 1992: 140; Porter 1992: 85–86). It is
also a regular feature of both ancient and modern criticism to charge Crates
with reading either Stoic or his own idiosyncratic principles into Homer,
taking his poems as cosmic allegories (Asmis 1992: 141; Porter 1992: 72; cf.
Graf 1993: 194, 198). A good example of this practice is offered by Geminus
of Rhodes (fl. first cent. b.c.e.), who in his Introduction to the Phenomena accuses Crates of “fabulously distorting” Homer’s descriptions (Porter 1992: 87)
or simply “speaking in marvels” about them (Evans and Berggren 2006: 215)
and, further, of reading his own theory of sphairopoiia into what Homer had
actually said.8 A similar accusation is found in Philodemus (P.Hercul. 1676 fr.
2 = fr. 99) and Heraclitus (All. 27.2 = fr. 3). Such charges are, on the whole,
3 Abel 1974: 1052.4–5. Generally, “his reputation is not very enviable ... he is regarded
as something of a crank” (Asmis 1992: 138). He is referred to as “a highly eccentric
geographer-critic” by Romm 1992: 179, while Thomson 1948: 202–3 calls his Homeric
geographical exegesis a “strange aberration” and his theory of oceans “hardly better than
an idle fancy of misguided scholars.”
4 E.g., Aujac 1987b: 162–64. Cf. Mette 1936: xx, 66–67, 90–93; Uhden 1936: 106–15.
5 This description of Crates’ range of activities is found in Porter 1992: 87.
6 Frr. 37, 99; cf. fr. 50. For Crates’ sphairopoiia, see Mette 1936: vii–viii, xx, 11–12,
30–42, 55–58; Asmis 1992: 141; Porter 1992: 87–89; Broggiato 2001: lii, lxii, 217–18, 257.
7 Fr. 37, compare Macrob. In Somn. 2.9.1–6 (= fr. 35f Mette). See also Mette 1936: 77–78;
Uhden 1936: 106. Possible representations of this theory can be found on the denarii of T.
Carisius (Crawford 1983, 464.3a–c, Pl. LIV, 46 b.c.e.), L. Aemilius Buca (Crawford 1983,
480.6, Pl. LVII, 44 b.c.e.), and L. Mussidius Longus (Crawford 1983, 494.39a–b, Pl. LX,
42 b.c.e.); cf. Berger 1903: 458; Thomson 1948: 203; Aujac 1987b: 164.
8 Geminus’s work will be abbreviated hereafter as “Gemin. Elem. Astron.” For the final
charge, see Asmis 1992: 141; Porter 1992: 87; Gemin. Elem. Astron. 16.27 = fr. 37.
Crates of Mallos and Pytheas of Massalia
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correct. Crates’ approach to Homer and his interpretative method were thus
highly idiosyncratic, with his belief in the Poet’s “wide learning” allowing him
to interpret Homer’s stories as “scientific hypotheses.”9
the map
Given Crates’ reception and influence, it comes as no surprise that there is
an ancient map based on his geographical and allegorizing teachings. It is
a unique graphical representation, embodying not only his geographical
conceptions, but also his allegorizing interpretation of a section of Homer’s
narrative. The existence of the map supports the tradition that Crates made a
model, a terrestrial globe or a sphairopoiia, “presumably as a visual analogue
to his Homeric exegeses” (Porter 1992: 88).10
A version of the map was first published by Neugebauer 1975a (cf. 1975b:
735). Jacob 1988: 2 suggested that the influence of “a theory recognized by
Hellenistic thinkers,” especially Crates of Mallos, concerning the four quarters
of the earth, might have been at work in the making of the map, as evidenced
by the presence of the antoikoumenē. He also recognized (at least) three levels
of knowledge employed in the making of the map (geographical, cosmological, eschatological: Jacob 1988: 4), but did not further develop his thoughts
in this direction.
The map is preserved in three copies as a part of an astrological compendium and in nine further copies accompanying the anonymous scholia to
Theon’s commentary on Ptolemy’s Procheiroi kanones (Edson and SavageSmith 2000: 27).11 All twelve examples show a great similarity with one
another, albeit with minor differences.12 The map depicts a zonal division of
Ἐπιστημονικὰς ὑποθέσεις: Strabo 3.4.4 = fr. 75; cf. Broggiato 2001: lv.
Cf. Kroll 1922: 1636.34–40; Mette 1936: 60; Broggiato 2001: 284–85; see Strabo 2.5.10
(fr. 134), Gemin. Elem. Astron. 16.22 (fr. 37). In the words of Romm 1992: 189, “Crates
sought to ‘map’ the Homeric poems on the enormous globe he devised to illustrate Stoic
geographical theory.”
11 The following MSS contain copies of the map (list from Edson and Savage-Smith
2000: 27): Berlin, Staatsbibliothek, MS Phill. 1479 (fol. 28v); Oxford, Bodleian Library,
MS Barocci 94 (fol. 118v); Oxford, Bodleian Library, MS Marsh 42 (fol. 4r/156b); Florence,
Biblioteca Laurenziana, Cod. gr. 28.1 (fol. 177r); Florence, Biblioteca Laurenziana, Cod.
gr. 28.7 (fol. 107r); Florence, Biblioteca Laurenziana, Cod. gr. 28.12 (fol. 296v); Florence,
Biblioteca Laurenziana, Cod. gr. 28.47 (fol. 271v); Venice, Biblioteca Marciana, Cod. gr.
314 (fol. 222v); Oxford, Bodleian Library, MS Canon. Gr. 32 (fol. 17r); Paris, Bibliothèque
Nationale de France, fonds gr. 2390 (fol. 155v); Escorial, Bibl. Monasterio de San Lorenzo
el Real, MS (Φ I 5 = gr. 183 (fol. 31v); Vatican, Biblioteca Apostolica, Cod. gr. 183 (fol. 21r).
12 Neugebauer 1975, Pl. III.2; Jacob 1988: 3, Fig. 1; Edson and Savage-Smith 2000: 8,
Fig. 1; 9, Fig. 2; 10, Fig. 3; 11, Fig. 4.
9
10
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Figure 1. The Map of Crates. From Edson, E. and Savage-Smith, E. 2000. “An
Astrologer’s Map: A Relic of Late Antiquity.” Imago Mundi 52: 7-29. Figure 5 (p.
12). Reproduced by kind permission of Imago Mundi Ltd.
the earth’s surface and/or the heavens, together with the line of the ecliptic, a
meridian connecting the poles, and several geographical terms (see Figure 1).
South of the equator there is a depiction of a “fiery unnavigable sea” or the
“ocean towards13 antoikoumenē.”14 This sea/ocean extends to approximately
midway between the equator and the winter tropic, that is, in the sections
Κατά, surely not “below,” as in Edson and Savage-Smith 2000: 27, cf. 12, Fig. 5. Hiatt
2008: 42–43 simply translates “the sea of the ....” Cf. Neugebauer 1975a: 313: “Ocean of
the ...” and Jacob 1988: 2 and his no. 23 on Fig. 2 (p. 3): “Océan de l’antoekoumène.” For
discussion on the semantic range of κάτω, see Nicolai 1984: 103–12.
14 No. 23 on the schematic map in Neugebauer 1975a: 313, Fig. 1; Jacob 1988: 3, Fig. 2;
and Edson and Savage-Smith 2000: 12, Fig. 5, reproduced here as Figure 1 by kind permission of Imago Mundi Ltd. Designations of this body of water are found only on the maps
in the scholia accompanying Theon’s commentary (Edson and Savage-Smith 2000: 27).
13
Crates of Mallos and Pytheas of Massalia
299
close to the eastern and western borders of the map; approaching the central
meridian, however, the coast veers from both sides tapering towards the
south, traversing the winter tropic and joining the meridian approximately
halfway between the tropic and the antarctic circle or circle of permanent
invisibility. Within the “bay” thus formed, there is an inscription: the “sea
towards15 antoikoumenē.”16 “Out of ” this sea/bay flow the “River Lethe” (no.
30) and “Pyriphlegethon River” (no. 31), running in a curved course through
the temperate zone of the antoikoumenē and then flowing into the “Marsh of
Acheron” (no. 32), precisely at the antarctic circle.17 The Acheron stretches in
the form of a semicircle almost to the south pole.18 The equatorial sea, or, more
precisely, the ocean extending between the temperate zones—a distinctive
feature of Crates’ system—represents, as attested in literary sources, the “sea”
that Odysseus must pass going from Aeaea to the “river ocean’s stream” and
Hades, and back (Od. 12.1–4; cf. 11.1–2, 11), while said stream, “an estuary
or a gulf stretching from the winter tropic (χειμερινός τροπικός) towards the
South Pole (νότιος πόλος)” (fr. 57 ap. Strabo 1.1.7), is represented by “the sea
(stretching) towards the antoikoumenē” on the map. This branch of the Ocean,
according to both Crates’ literary exegesis and the map, divides the landmass of
the southern hemisphere into two parts (Mette 1936: 75–78; Broggiato 2001:
liii, 224).19 If we compare the map with Crates’ description as provided by
Strabo, we see that the sea on the map stretches from approximately midway
between the equator and winter tropic to halfway between the tropic and the
pole, while Crates described the ἀνάχυσις or κόλπος as commencing at the
tropic itself. Nonetheless, it seems that the map, at least the part representing
Again κατά, this time left untranslated by Edson and Savage-Smith 2000: 28. Cf.
Neugebauer 1975a: 315: “Sea of the ...” and Jacob 1988: 2 and his no. 27 on Fig. 2 (p. 3):
“mer de l’antoekoumène.”
16 No. 27 on the map, Edson and Savage-Smith 2000: 28.
17 Edson and Savage-Smith 2000: 14, 28; Hiatt 2008: 42–44; cf. Dilke 1985: 170 with
Pl. 29.
18 On the map in the scholia accompanying Theon’s commentary from Oxford, Bodleian
Library, MS Canon. Gr. 32, fol. 17r (Edson and Savage-Smith 2000: 11, Fig. 4) the Acheron
actually stretches to the very pole. On another map from the same context (Marcianus
gr. 314, fol. 222v) it almost touches the pole (Neugebauer 1975a, Pl. III.2; Dilke 1985, Pl.
29; Jacob 1988: 3, Fig. 1).
19 See nos. 24–26, 28–29 on the map. Mette 1936: 76–77 presupposes the existence
of another branch of Ocean stretching from the summer tropic to the north pole (the
Atlantic) and a corresponding “pair” of branches at the opposite (eastern) part of the
oikoumenē. The question is whether Odysseus started off from the western border of
the oikoumenē—along the southern section of the “Atlantic” (so Mette)—or from the
eastern, which would be more in line with Homer’s text (Aeaea in the east, Od. 12.3–4).
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the southern hemisphere, depicts Crates’ ideas of (cosmic) geography, with
indisputable Hades-related toponyms placed in the southern hemisphere.
the world according to crates i: the cimmerians
and hades / tartarus
Strabo’s description of Crates’ geography undeniably places Hades at the
very south pole; this corresponds to the latter’s placing of the Cimmerians
at the pole(s) as well. According to Crates (fr. 53, cf. Lehmann-Haupt 1921:
426.35–36), the Cimmerians are identical to the “Cerberians” and live at both
poles,20 or solely at the south pole,21 and the meteorological characteristics of
their land as described in the Odyssey correspond to those at the pole.22 In fr.
54 Crates is said to have placed Homer’s Cimmerians below the north pole; but
Mette emends θερινός τροπικός (Gemin. Elem. Astron. 6.17) in this fragment
to the more plausible χειμερινός τροπικός.23 Crates’ symmetrical arrangement
of the continents on the earth’s surface, however, could have allowed him to
distribute the Cimmerians to both poles, since Homer’s description of meteorological characteristics of their country, as understood by Crates, could
equally be applied to either of the two extreme points on the earth’s surface.
What we know for certain is that Crates also compared (fr. 7) meteorological
features under the poles with Homer’s description of Tartarus, most probably
Thus Berger 1904: 15; Wrede 1937: 1971.19–21.
Thus Mette 1936: 84n1, 88, 92; Broggiato 2001: xlix, liv, 222.
22 Cf. schol. HV Od. 10.86 (2.454 Dindorf) = fr. 37f Mette and Eust. Od. 10.86, i.369
Stallbaum = fr. 37g Mette, where the meteorological characteristics of the Cimmerian
land are compared with, and opposed to, those that obtain among the Laestrygonians.
Crates again mentions together the Cimmerians and the eternal night in Eust. Od. 11.19,
i.398 Stallbaum = fr. 37k Mette. Schol. Dionys. Per. 586 (GGM 2.451–52) associates Od.
11.19 (the darkness of the Cimmerian land) and 12.4 (Helios’s risings on Aeaea) with a
respective six-month day and a six-month night in the farthest north and south when the
sun is in the northern and southern portions of its voyage, respectively (from the vernal
to the autumnal equinox, and vice versa). But this applies only to the poles; at the arctic
circles, on the other hand, the sun both rises and sets during these periods, except on the
very solstices. For the Cerberians, cf. Ar. Ran. 187; schol. Ar. Ran. 187, p. 280 Firmin-Didot
= fr. 38e Mette; Soph. fr. 1060 Radt = Etym. Magn. 513.45–48 s.v. Κιμμερίους = fr. 38d
Mette; Lehmann-Haupt 1921: 426.24–34; see also schol. H Od. 11.14, citing Aristarchus
= fr. 38f Mette and schol. PV = fr. 38a Mette; Eust. Od. 11.14, i.396.34–36 Stallbaum =
fr. 38c Mette; cf. Hesych. κ 2298 s.v. κερβέριοι, Κερβερίους and Phot. Bibl. s.v. Κερβέριοι
(Mette 1936: 274 on fr. 38e). Perhaps also Ephorus FGrHist 70F134b ap. [Scymn.] 239–40.
23 Crates “muß den χειμερινός τροπικός erwähnt haben” (Mette 1936: 84n1, cf. 265–66;
also Abel 1974: 1054.51–66).
20
21
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301
(given the account of Strabo) placing the latter under the south pole (Steph.
Byz. s.v. Τάρταρος = Hdn. 3.1.194.29–32 s.v. Τάρταρος). A scholiast on the
Iliad associates Tartarus with the “dark portion of the oikoumenē” (schol. D
Il. 8.13 = fr. 39b Mette, van Thiel 2000: 296), which cannot be right, at least
if we take the oikoumenē to mean the region in the northern hemisphere
extending 180° (or less) in longitude, that is, “our” quarter of the earth, while
another scholiast identifies ζόφον ἠερόεντα as the “dark portion of the earth,”
which is more precise (schol. bT Il. 15.191 = fr. 39c Mette). Thus Crates’ idea
of the southern hemisphere as it is attested in literary sources conforms to
its representation on the map.
the world according to crates ii: laestrygonians,
draco, and the arctic circle
The Cimmerians suggest the presence of another of Homer’s mythical
peoples discussed by Crates, unfortunately not represented on the map: the
Laestrygonians. According to Homer, the Laestrygonians achieved a certain level of civilization, as opposed to the carefree Lotophagoi and lawless
Cyclopes.24 Nevertheless, they are described as giants (Od. 10.111, 120) and
cannibals (10.116, 124). The name of their city (or the epithet describing it, as
argued strongly by Page 1973: 34–35), Tēlepylos, translates as “distant gate.”25
The main feature of the land of the Laestrygonians, however, is the fact that
here “the paths of night and day are close together” (Od. 10.86: ἐγγὺς γὰρ
νυκτός τε καὶ ἤματός εἰσι κέλευθοι). This verse has been analyzed in various
ways by both ancient scholiasts and modern investigators, who have often
come to different conclusions in their interpretations of its significance.26
They practice cattle-breeding (implicit in Od. 10.82–85); know of fire (10.99); their
land is traversed with wagon-roads (10.103–4); they live in a city (10.81–82, 104, 108, 118);
and their mode of government is characterized by some kind of an assembly (10.114), a
king (10.110), and a queen (10.112–15).
25 Woodbury 1966: 612; Frame 1978: 60; Käppel 2001: 18; Marinatos 2001: 403; Nakassis
2004: 225 all translate the name in similar terms (“distant,” “far-away,” “far away,” “Ferntor,”
and “far gate,” respectively), while West 1997: 406–7; 2005: 62 renders it as “distant portal”;
Page 1973: 35–36, who does not accept the usual translation, claims that the adjective
τηλέπυλος could only mean “far-gated” (cf. Coxon 2009: 275), “if τηλε- has anything to
do with distance”.
26 See, e.g., schol. Od. 10.82, 85–86 (2.452–54 Dindorf); Packard 1874: 33–34, 36–37,
39–40; Merry, Riddell, and Munro 1886–1901: 1.406–7 on X.81; Pocock 1958, 1968; Vos
1963: 18, 22–23, 25–26; Woodbury 1966: 611–12, 616; Page 1973: 42, 122n26; Heubeck
and Hoekstra 1989: 48; Marinatos 2001: 396; Nakassis 2004: 224; West 2005: 47.
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Tomislav Bilić
Crates’ discussion of the Laestrygonians, in the form it has been transmitted, reveals his ideas on the questions of latitude, arctic circle(s), and the
visibility of stars in different regions. According to one group of sources, he
certainly understood the phenomenon of the change in the duration of the
longest day depending on the latitude, and supposedly also the concept of
the fixed arctic circle; according to another, he did not quite understand the
difference between the always visible—changeable—and the fixed arctic circle.
Thus, according to fr. 50 he compared the main feature of the land of the
Laestrygonians with Aratus’s description of the constellation Draco (Phaen.
61–62), placing the territory “about (περί) the head of Draco,” that is, in the
area directly below it.27 The head of Draco, according to Aratus, νίσσεται, ἧχί
περ ἄκραι / μίσγονται δύσιές τε καὶ ἀντολαὶ ἀλλήλῃσιν, “wheels near where the
limits of setting and rising blend” (Mair 1921: 211) or, in the words of other
translators, “moves where the limits of rising and setting are confounded”
(Evans and Berggren 2006: 5), “passes through the point where the end of
settings and the start of risings blend with each other” (Kidd 1977: 77), or
“goes around near the place where the limits of setting and rising mingle together.”28 This conception of Draco’s movements in Aratus is certainly derived
from Eudoxus, as confirmed by Hipparchus (1.4.7–8, 32.25–34.21 Manitius
= Eudoxus fr. 16 Lasserre = Attalus fr. 5 Maass).
27 Schol. HQ Od. 10.86 (2.453 Dindorf) = fr. 37e Mette; cf. schol. HV Od. 10.86 (2.454
Dindorf) = fr. 37f Mette, Eust. Od. 10.86, i.369 Stallbaum = fr. 37g Mette, and schol. Q and
MDKVUA Phaen. 62 = fr. 37h Mette. “Crates supposes that the nights in Laestrygonia were
short; and that the reason for this is that the people lived near [Broggiato (forthcoming;
see n1): “close to”] the head of the constellation Draco, about which the astronomerpoet Aratus says [Phaen. 61–62]. Thus, because the star’s rising and setting are very close
together, Homer can say [Od. X.86]” (schol. HQ Od. 10.86, translation in Page 1973:
43). We will explain shortly what “directly below” means. Page’s translation is somewhat
misleading in that what Crates actually says is simply “for this reason—the proximity of
risings to settings ...,” rather than the rising/setting of any particular asterism (compare
the translation in Broggiato [forthcoming; see n1]: “accordingly, since the risings are close
to the settings”). Only in schol. Q Phaen. 62 does Crates explicitly connect the rising(s)
and setting(s) to the phenomena associated with the constellation Draco as observed
from the latitude of Greece.
28 Broggiato (forthcoming; see n1). Cf. the Latin translations of Cic. Nat. D. 2.108 =
Aratea fr. 10 Soubiran; German. Arat. 60–62 (compare proxima signa occasus ortusque in
61–62, a spatial reference on the rising and setting of Draco, with breuis occasus ortusque
intercipit hora in 288, a temporal reference on the rising and setting of the sun); Avien.
Arat. 164–68; Hyg. Poet. astr. 4.3, who cites both Aratus and Cicero and, moreover, associates Od. 10.86 with these verses (fr. 37i Mette) .
Crates of Mallos and Pytheas of Massalia
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So, what did Crates mean by “about (περί) the head of Draco”? Page 1973:
43 was right in believing that Crates placed the Laestrygonians “below the head
of Draco” due to the shortness of their nights, but was wrong to assume that the
shortness was explained by Crates with reference to Draco’s short “star-time.”
Perhaps Page was rather referring to the constellation’s short disappearance
below the horizon observed from either Greece or some higher northern latitude, since Draco is anything but “a very short-lived star.” Moreover, if Crates
was aware of the different visibility of stars depending on the latitude of the
observer—a hypothesis we will discuss below—he would have known that a
“Laestrygonian” high-latitude Draco would be completely circumpolar.29 It
is therefore perhaps better to understand περὶ τὴν κεφαλὴν τοῦ δράκοντος
as “(directly) below the head of Draco” in the sense of, the area “where the
head of Draco is at the zenith.”30 The head of Draco is at the zenith when
observed from 53°–55°24' northern latitude,31 or from 52°57'33"–58°07'16"
29 Abel 1974: 1052.3–1053.14 claims that Crates’ understanding of latitude was very
limited; if he was truly unaware of the phenomenon mentioned, then Abel’s claim would
be correct. But see below.
30 Cf. Page 1973: 43, who understands Crates’ words as referring to the “region immediately below” Draco. Mette 1936: 86–87, 91–92 also thinks that the expression refers to
the region where the head of Draco is at the zenith, but further believes that Crates associated this region with the one in which the longest day is of 23 hours. “Directly overhead
on the meridian” is usually expressed with phrases such as Aristotle’s ὑπό (thus, ὑπὸ τὴν
ἀρκτόν, Mete. 2.5.362b8; Dicks 1970: 210). Geminus regularly uses the phrases “under the
equator” or “under the pole” (Elem. Astron. 5.36, 38, 42, 43 [54.23–24, 56.11–13, 58.3–4,
58.11–12 Manitius], 6.23 [76.25–26 Manitius]) precisely in the meaning “directly” or
“vertically under.” This also applies to the use of such expressions in Parmenides (T74
Coxon = DK 28A44a = Aët. 3.11.4), Eratosthenes, Polybius, Posidonius, and Strabo, which
refer to the areas “under” the poles, tropics, and the equator (Eratosth. IIA5 Berger = fr.
45 Roller, Posid. fr. 49, 208 E-K, Polyb. 34.1.7, 16–17, Strab. 2.2.3, 3.1–3, 5.37, 43). For
Eratosthenes (IIB26 Berger = fr. 44 Roller ap. Gemin. Elem. Astron. 15.3), the terrestrial
equator is directly below the celestial one; Polybius, when referring to the zones “below the
arctic circles” (Strabo 2.3.1–2 = Polyb. 34.1.14–15), probably has in mind the territories
below the entire (ant)arctic celestial zones, as does Plutarch when referring to ὑπαρκτίων
κλιμάτων (Mar. 11.4, cf. Sert. 17.3), while Ptol. Tetr. 2.2.3 generally discusses the northern
peoples living under the Bears (ὑπὸ τὰς ἄρκτους), who have the constellations directly
above their heads. Stob. Flor. 1.49.45 also uses the expression in a similar meaning, referring to an anthropomorphic image of the earth with feet placed in the north, as well as
to the inhabitants of this northern region.
31 Using the values of Hipparchus, 1.4.8, p. 34.10–14 Manitius: the head of Draco
stretches from 34°36' to 37°. The information in Cleomedes (De motu circ. 1.5.59 Todd),
placing the head of Draco at the zenith for Lysimachia (c. 40°40' north latitude), is certainly
erroneous, because the southernmost stars in the head (δγ Draconis, declination 52°54' in
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in the time of Hipparchus, and 53°15'47"–58°21'45" in the time of Eudoxus.
This is much to the south of the fixed arctic circle, but is precisely on the
always visible circle of Rhodes (54°), used by majority of astronomers as the
arctic circle (see below). Therefore, it would seem that Crates, in associating
the Laestrygonians with the constellation Draco, located them with reference
to the always visible circle of Rhodes, which he took as the arctic circle.
We might perhaps go a bit further than this. Neugebauer claims that the
origin of the use of the latitude of 54° (= 36° from the pole) should not be
sought with reference to the latitude of Rhodes, but rather associated with
“a cosmologic doctrine of ‘pythagorean’ flavor” (1972: 247, cf. 1975b: 733),
which carved out a quadrant of 15 parts (90°) from a circle of 60 parts (360°)
and divided it up according to a “neat numerical pattern” of 4 (24°, from the
equator to the tropic) : 5 (30°, from the tropic to the arctic circle) : 6 (36°, from
the arctic circle to the pole). The resultant position of the arctic circle was
later “translated” into the Rhodes-determined always visible circle. Whether
Crates was aware of this tradition is another question, but it would certainly
strengthen his cosmological argument.32
Dicks 1960: 24–25 claims that it is “very unlikely” that Eudoxus was aware
of the fixed arctic circle and that he calculated his (always-visible) circle with
reference to the latitude of Rhodes, placing it at 54°.33 In this Eudoxus was
followed by many: thus, for example, Eratosthenes,34 Geminus,35 Manilius
(Astron. 1.565–67), Hyginus (Astron. 1.6.2), Achilles Tatius (Isag. 26, 29 =
100 b.c.e.) were at least 12° further north (Tozer 1897: 169–70 and Keyser 2001: 363–65
argue for Dicaearchus as the author of this measurement). Furthermore, Cleomedes gives
the head’s declination as 48° (1.5.60 Todd), which neither corresponds to his previous
statement nor to the real value.
32 For Crates’ (fr. 34ab Mette) division of the sphere into five or six zones according to
this pattern (6–5–4), see Mette 1936: 66–67 and Uhden 1936: 108.
33 Stevens 1980: 270 believes that Eudoxus had calculated the value for an arctic circle
with reference to Knidos, which was later adopted for the latitude of Rhodes. Bianchetti
1998: 43, 153 believes that it was Pytheas who was the first to recognize the difference
between the always-visible and fixed arctic circle.
34 IIB19 Berger/M1 Roller ap. Gemin. Elem. Astron. 16.6–9; IIB20 ap. Achilles Tatius,
Isag. 29; IIB24/M2 ap. Macrob. In Somn. 2.6.3–5; IIB25 ap. Anonymus, Geographiae
Expositio Compendiaria 1.2. But see further below.
35 Elem. Astron. 5.46, 58.21–60.2 Manitius (esp. 58.22–23), 16.7–11, 166.4–168.16
Manitius. On the other hand, Geminus is well aware of variable arctic circles (always
visible circles, that is) at different latitudes (Elem. Astron. 5.47–48, 60.3–13 Manitius;
16.12, 168.16–20 Manitius).
Crates of Mallos and Pytheas of Massalia
305
Eratosth. II B 20), Theon (Astron. 3.42, p. 202.17–203.9 Hiller),36 Macrobius,37
and an anonymous epitomizer38 all placed the limit of the northern habitable
zone at 54°, a testament to the strength of the Eudoxean tradition.39 A similar
idea, it can be argued, is present in Strabo’s Geography. Strabo disagreed with
Hipparchus (see below) and placed the northern limit of the inhabited world
somewhat more (2.1.13) or less (2.5.6 = Eratosth. fr. 30 Roller, 2.5.9 = fr. 34
Roller) than 38,800 stadia north of the equator,40 that is, at approximately
55°25'42", which is a value still close to the “Rhodian” standard.41 Elsewhere
Strabo claims that the arctic circle—which is what Homer meant by “the
Bear”42—touches the earth at its northernmost inhabited point or limit,
which is the same as the most northerly point on the horizon (1.1.6).43 Since
we have his explicit estimate of the most northern habitable latitude, we can
On the other hand, Theon is also well aware of variable arctic circles at different
latitudes (Astron. 3.9, 133.6–10 Hiller).
37 In Somn. 2.6.3–6 (2.6.3–5 = Eratosth. IIB24 Berger/M2 Roller).
38 Anonymus, Geographiae Expositio Compendiaria 1.2 (GGM 2.494 [= Eratosth.
IIB25 Berger]).
39 Probably also Polybius (Strabo 2.3.1–2 = Polyb. 34.1.14–15; Bianchetti 1998: 163,
185, 194). For Crates, see above. For the purpose of some of his tables, Ptolemy in the
Almagest takes into account the parallels up to the limit of 54°1' (Alm. 2.8, 1.140–41
Heiberg; Berggren and Jones 2000: 18); as late as the 14th century, accounts of high
northern latitudes started at the ultimum clima at 54° (Taylor 1956: 59, 65, 67).
40 8,800 stadia is the distance from the equator to the southern limit of the inhabited
world (Strab. 2.1.13, 17, 2.2 [= Eratosth. IIB22 Berger, fr. 58 Roller = Posid. fr. 49 E-K],
5.6 [= fr. 30 Roller], 35 [= fr. 57 Roller]).
41 Bianchetti 1998: 156–57 calculates different values, using Strabo’s conflicting data
on the northern limit of the oikoumenē, but they all fall between 54° and 56°.
42 Il. 18.487–89 (= Od. 5.273–75). Crates shares this opinion of Strabo, although he
expresses it somewhat differently (F 27). See Dicks 1970: 49; Broggiato 2001: 190; and
Giampaglia 1998: 507–10 for three different emendations. Dicks argues for Crates’ attempting a change of the word’s gender (οἴη to οἶος), modifying Homer’s “the Bear” (ἡ
ἄρκτος) to “the arctic (circle)” (ὁ ἀρκτικός). Broggiato removes the “solely” (reading οἷ.
ἡ), while Giampaglia, through his reading of P.Oxy. 2888 col. ii.9–10, keeps οἴη, but believes it refers to the position of the Bear with respect to Orion. Strabo further interprets
Heraclitus’s statement (22B120 D-K) to the same effect. Kirk 1962: 289 (cf. Marcovich
2001: 337) suggests that Strabo thinks that Heraclitus’s “limits” refer to the always visible and always invisible circles, an interpretation that Berger 1903: 79 and Burnet 1920:
135n5 believe is probably right. Arist. Poet. 1461a20–21 accepts the reading “only,” but
argues that it was used because the Bear is the most conspicuous constellation of those
that never set (Lucas 1968: 242).
43 Cf. schol. MQDΔKVUAS Phaen. 62, where the head of Draco touches the northern
horizon (the limits, ἄκρος, of the Ocean, as understood by the scholiast) at the meridian.
36
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Tomislav Bilić
presume that Strabo here speaks of the always visible circle for the latitude of
Greece or, more precisely, Rhodes. Thus, he adhered to the “teoria aristotelica”
(Bianchetti 1998: 163, 185, 194–95),44 that is, the “Rhodian” standard.
However, this was not the only theory known to the ancients. Thus, for
example, Martianus Capella unusually placed the arctic circle at 50° (8.837).45
More important is an idea present in Hipparchus: he placed the river
Borysthenes 34,000 stadia north of the equator (ap. Strabo 2.1.13 = fr. 59 Dicks,
cf. 2.1.17). Since he also placed the parallel of Borysthenes 3,800 stadia north
of the Massalia/Byzantion parallel,46 and since he knew of an inhabited area
more than 9,100 stadia north of Massalia,47 Hipparchus’s northern limit—
taking into account all the available distances—was at least 38,900 to 39,500
stadia north of the equator (55°34'17" or 56°25'43"), but more probably even
farther to the north.48 Ptolemy, together with Marinus of Tyre (ap. Ptol. Geog.
1.7.1),49 placed the northern limit of the oikoumenē, together with Thoulē,
at 63°.50 This latitude was later accepted by Islamic authors Al-Khwārazmi,
Suhrāb (Tibbetts 1992: 102, 105n69), and the anonymous author of Hudūd
al-‘Ālam (2.3, 5, 4.26; Minorsky 1970: 50–51, 59), while al-Idrīsī placed the
Cf. Kidd 1988: 2.742, 744–45. For Aristotle, see below.
Neugebauer 1975b: 590 believes that the text should be emended to correspond to
the 6–5–4 standard, which would place the limit of the arctic zone at 54°.
46 Hipparch. fr. 54, 57 Dicks ap. Strabo 2.5.8, 42. In the last reference the Borysthenes is
placed 34,100 stadia from the equator, while in 2.5.41 (Hipparch. fr. 52 Dicks) Byzantion
is 30,300 stadia north of the equator (in 2.1.12 = Hipparch. fr. 15 Dicks the distance is
29,800 stadia); in 2.1.12 = Hipparch. fr. 59 Dicks (cf. 2.1.16) the distance between the
two is 3,700 stadia.
47 Strabo 2.1.18 = fr. 61 Dicks = Pytheas fr. 6b Mette, T 5 Roseman.
48 Hipparchus gives the altitude of the sun on the winter solstice for this region as less
than 3 cubits (if we take this to mean 2 ½ cubits this implies the latitude of 61°17') and
the longest day as 19 hours (61°2') (Dicks 1960: 185; Roseman 1994: 43; Bianchetti 1998:
181, giving the latter figure as 62°2'). Compared with other data reported by Strabo, where
a 2° difference is evident (Dicks 1960: 185, 188; cf. Diller 1934: 266–67; Bianchetti 1998:
181), this limit was placed (by Strabo) at ca. 59°10' north (= ca. 41,400 stadia; actually,
ca. 42,800 = 61°10', cf. Dicks 1960: 193).
49 Jones and Keillar 1996: 48 have tried to reconstruct Marinus’s theory from the data
in Ptolemy, and claim that he placed Thoulē at ca. 69°, although Ptolemy explicitly claims
that he placed it at 63°.
50 Geog. 1.20.8, 23.1 (= 1.23.22 Nobbe), 24.5, 2.3.14 (62°40'–63°15'), 3.5.1 Müller,
6.16.1, 7.5.12, 16, 6.7–8, 8.3.3 Nobbe (7.5.16 and 8.3.3 only mention the longest day of
20 hours on Thoulē). Cf. Alm. 2.6, 1.1.114.9–11 Heiberg, 29th parallel of Thoulē at 63°,
also with the longest day of 20 hours; also Anon. Summaria ratio geographiae in sphaera
intelligendae 2.9, 15 (GGM 2.490, 493), 63°, 20 hours.
44
45
Crates of Mallos and Pytheas of Massalia
307
limit somewhat to the north of 64° (Ahmad 1992: 162–63; cf. Nansen 1911:
2.203).51 Thus the Marinus/Ptolemy conception of the northern limit of the
oikoumenē approaches the latitude corresponding to the fixed arctic circle,
of which both authors were well aware.
Others were even closer to this value. Thus Eratosthenes placed Thoulē
11,500 stadia north of the Borysthenes (II C 2 Berger = fr. 35 Roller ap. Strabo
1.4.2; cf. 1.4.4), which means 46,300 stadia north of the equator (= 66°8'34"),
according to Diller 1934: 264.52 Diller arrived at this figure by taking the value
for the distance from the Cinnamon-bearing country to Meroe as 3,000
stadia,53 rather than 3,400,54 and the value for the distance from Alexandria
to the Hellespont as 8,000 stadia,55 rather than 8,100 (1.4.2 = II C 2 Berger,
fr. 35 Roller). If we take the alternative figures, which are precisely the ones
specified in the chapter where the distance to Thoulē is also given, we arrive
at the figure of 46,800 stadia = 66°51'24".56 Similarly, Al-Farghānī placed the
northern limit of the oikoumenē at 66° (Tibbetts 1992: 102n59), while for
Hāfiz-i Abrū it was placed further to the north of 66° (Ahmad 1992: 170).
In the same way, al-Dimashqi placed the northern limit on 66°10' or 66°25'
(Nansen 1911: 2.212).57
Ibn Khaldoun (1377 c.e.) places it precisely at 64° (Second Prefatory Discussion of
the Muqaddimah; Rosenthal 1967: 1.50, 55, 56); he also mentions the opinions of other
scholars: al-Khazini (63°, 20-hours longest day), al-Khizin (10th century; 60°45', the limit
of the 7th clime), and “others” (77°) (Rosenthal 1967: 1.114–15).
52 Dilke 1985: 33 and Uhden 1936: 100 have 46,400 stadia. On p. 34 Dilke has 46,300
stadia, if we take the distance from Borysthenes to Thoulē as 11,500 stadia instead of the erroneous 16,500 stadia. Bunbury 1883: 1.664 also has 46,300 stadia. If we take Eratosthenes’
acceptance of Pytheas’s placement of Thoulē on the fixed arctic circle together with the
value reported for his calculation of the obliquity of the ecliptic (23°51'20", Ptol. Alm. 1.12,
67.22–68.6 Heiberg = Hipparch. fr. 41 Dicks, Eratosth. IIB42 Berger/M8 Roller, Theon,
Comm. ad loc., 2.528.20–529.3 Rome = Hipparch. fr. 41 Dicks, Eratosth. IIB42 Berger/
M9 Roller; see Dicks 1960: 91), then the figure of 46,300 stadia must have represented
his intended distance of Thoulē from the pole (16,700 stadia).
53 Strabo 2.2.2 = fr. 58 Roller; 5.7 = fr. 34 Roller; 35 = fr. 57 Roller; 17.3.1 = fr. 100 Roller.
54 As in Strabo 1.4.2 (= IIC2 Berger, fr. 35 Roller); Dicks 1960: 171 claims that Strabo
here added 400 stadia in order to include the island of the Egyptians, the Cinnamonproducing region, and Taprobane.
55 2.1.3 = IIA2 Berger, fr. 47 Roller; 5.42 = IIC5 Berger, fr. 36 Roller.
56 Cf. Dicks 1960: 153. Bianchetti 1998: 150 takes as a starting point Pytheas’s calculation
for the latitude of Massalia (43°12'17") and adds the distance from the Massalia parallel
to Borysthenes (3,700/3,800 stadia) and from there to Thoulē (11,500 stadia), arriving
at a latitude of “little over 64°” (actually, almost 65°).
57 He gives 63° as an alternative, though.
51
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Tomislav Bilić
The last paragraph has brought us closer to a strain in Cratetean thought
concerning the problem of the arctic circle that marks his dissent from the
“Rhodian” standard. Thus, again according to fr. 50, Crates compared the
meteorological conditions characteristic of the land of the Laestrygonians
with those obtaining in the far north—more precisely, in the area with the
longest day on the summer solstice of 23 hours, and a meager one hour of
night, where “the setting of the sun is near to its rising”58 and where, therefore,
those that could stay awake could have earned double wages (Gemin. Elem.
Astron. 6.10–12, 72.2–20 Manitius).59 Consequently, the Laestrygonians would
be placed somewhat to the south of the fixed arctic circle (cf. Mette 1936:
86). According to Ptolemy, however, the summer solstice day of 23 hours is
located at 66° northern latitude (Alm. 2.6, 1.1.114.18–20 Heiberg),60 which
Translation in Heath 1932 [1991]: 133; cf. Evans and Berggren 2006: 163: “the setting [point] draws near the rising [point]”; Broggiato (forthcoming; see n1): “the sunset
is near the dawn” or “the sunset is close to sunrise.”
59 The land of the Laestrygonians is also placed on the latitude with the longest solstitial
day of 23 hours by schol. P Od. 10.86 (2.454 Dindorf) = fr. 37d Mette, while Priscianus
Lydus, Solutiones ad Chosroen 4, 67.9–15 Bywater = fr. 37b Mette may have compared
the 23-hour longest day in the north with the situation on Thoulē (Mette 1936: 85 with
n1, however, claims that all he said was that in certain areas the longest day lasts for 23
hours, while on Thoulē there is a 24-hour day, since it is on the fixed arctic circle; Mette
discards as an interpolation the notion of a 5- or 6-day continuous daytime in the area
where the longest day is of 23 hours). On the other hand, schol. MDΔKVUA Phaen. 62 =
fr. 37h Mette (without Mette’s emendation [1936: 87 with n1, 271]); schol. Dionys. Per.
582 (GGM 2.451); Steph. Byz. s.v. Θούλη; and Eust. Dionys. Per. 581 (GGM 2.329.30–33)
all mention a 20-hour longest day on Thoulē, exactly as in Ptol. Alm. 2.6 (1.1.114.9–11
Heiberg), where Thoulē, with the longest day of 20 hours, is placed at 63° north (cf. Geog.
7.5.16, 8.3.3 Nobbe for the 20-hour day at Thoulē). Qazwini’s Burdjan, a land located
far to the north, with a 20-hour day and a 4-hour night (and vice versa), could refer to
either the Normans or the Bulghars, and would apply equally well to both (cf. Nansen
1911: 2.210). The latitude of Thoulē (63°) and the longest day of 20 hours were facts well
known to Islamic authors (Shīrazī, Ya‘qubi, Battani, Dimashqi [Nansen 1911: 2.211–12;
Dunlop 1957]; cf. al-Khazini, who does not mention the island by name [Rosenthal 1967:
1.114–15], and Ulugh Beg, al-Tūsī, and al-Kāshī, who all give the latitude of Būdan/Tawā
as 63° [Kennedy and Kennedy 1987: 32]); they received this information from Ptolemy (cf.
a cosmological diagram in Vat. gr. 211 fol. 120r and 121v, where the 7th climate is named
τούλη; Neugebauer 1975a: 316–17). According to Hyg. Poet. astr. 4.3.3 = fr. 37i Mette, the
inhabitants of the region “under the head of Draco” have a night of less than a third of
an hour (presumably on the summer solstice), which further associates the region with
Homer’s Laestrygonians.
60 Ptolemy places the 24-hour day, thus the fixed arctic circle, at 66°08'40", 2.1.114.21–
115.7 Heiberg.
58
Crates of Mallos and Pytheas of Massalia
309
would place the Laestrygonians effectively on the fixed arctic circle and the
northern limit of the oikoumenē according to Eratosthenes.
Both the discussion in Geminus and that in Eratosthenes associate some of
these concepts with the writings of Pytheas (a major source of Eratosthenes).
Thus, according to Geminus, Pytheas mentions certain northern areas where
“the night becomes very short ... so that, a little while after setting, the sun
rises straightaway.”61 The similarity of Pytheas’s description to Homer’s was
probably the reason why Crates and Geminus believed that it referred to the
conditions imagined by the poet. After his mention of Pytheas, Geminus
continues his paraphrase of Crates: “For indeed, since around these places62
the longest day is 23 equinoctial hours, the night lacks only one hour of being
shortened to nothing, so that the setting [point] draws near the rising [point
and is separated from it only] by the very short arc of the summer tropic,”
glossing (still following Crates?) Od. 10.86 as “the setting [point] lies near the
rising point” (fr. 50 = Gemin. Elem. Astron. 6.11–12, 72.10–20 Manitius).63
This “solar” explanation certainly seems plausible enough. But the main
objection to Crates’ theory in general is that he seems to have believed that
Aratus’s verses (and Eudoxus’s theories behind them) refer to the risings and
settings of the sun, to which Homer’s description certainly applies, while it
is reasonable to assume that the Hellenistic poet is speaking instead of the
risings and settings of the constellation Draco itself.64 It seems unlikely that
61 Fr. 9a Mette = fr. 8 Roseman = fr. 13a Bianchetti ap. Gemin. Elem. Astron. 6.9,
70.24–72.2 Manitius. Translation from Evans and Berggren 2006: 162; Roseman 1994: 140:
“the night is extremely short ... so that after the setting, although only a short time has
elapsed, the sun straightaway rises again,” Bianchetti 1998: 103: “la notte fosse molto corta
... cosicché a breve intervallo dal tramonto il sole sorgeva di nuovo”; Pytheas specifically
mentions the regions with the longest day of 21 or 22 hours. Compare also fr. 9b Mette
= fr. 9 Roseman = fr. 13b Bianchetti ap. Cosmas Indicopleustes, Topographia Christiana
2.80.6–9 Wolska-Conus.
62 Geminus refers to the region where Crates placed Homer’s Laestrygonians in 6.10
and 12, which he associates in 6.10 with northern regions described by Pytheas in 6.9.
63 Translation from Evans and Berggren 2006: 163 (compare Broggiato forthcoming;
see n1). Broggiato 2001: 217–18 attributes the notion exclusively to Crates.
64 Strabo (discussing Posidon. fr. 49 E-K ap. Strabo 2.3.8, Kidd 1988: 1.268–70) similarly
believes that Aratus’s “rising” and “setting” refer to the eastern and western semicircle of
the horizon or the section of the sun’s path from the eastern horizon to the meridian
and from the meridian to the western horizon, respectively. (The latter is most probably
also the opinion of Posidonius, who interprets Homer’s “setting” as “descending from the
meridian towards the horizon” [see Mette 1936: 73–74]; cf. schol. Q Phaen. 62, where it is
said that the head of Draco belongs to both the eastern and western horizon, as observed
from the latitude of Greece, and schol. MQDΔKVUAS Phaen. 62, where it is specified that
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Tomislav Bilić
Crates could have interpreted Aratus’s verses as applying to anything but
Draco, though this is what the scholia appear to claim explicitly to be the case.
Perhaps, though, what they actually assert is that Crates associated only the
terms “rising” and “setting” with the diurnal path of the sun, without an explicit
reference on his part to the constellation Aratus was describing. If Crates truly
connected the position of the land of the Laestrygonians with the latitude of
the fixed arctic circle, no matter whether he understood it as such or not, as
it would seem from this second set of evidence, then this would be in direct
contradiction with the first set, according to which he associated it with the
always visible circle of Rhodes taken as the arctic circle. Both versions cannot
be right; perhaps, after all, Crates was indeed only “at best an interested and
comparatively well-oriented layman.” Then again, it seems unlikely that he
understood the changeability of day length with respect to different latitudes
but at the same time did not know the difference between the fixed arctic circle
and the latitude-dependent always-visible circles. The introduction of Draco
into the discussion may thus have been only secondary, and motivated by a
cosmological doctrine demanding the neat division of the cosmic sphere.65
the semicircles of “rising” and “setting” meet at the meridian and that the head of Draco
touches upon its northern intersection with the horizon; see also Kidd 1997: 200. Achilles
Tatius, Isag. 35 also gives two possible explanations: Aratus either had in mind the section of the sun’s path from the eastern horizon to the meridian and from the meridian to
the western horizon, or the point where the head of Draco touches upon the meridian’s
northern intersection with the horizon.) This would make them meet only at the very
meridian or the junction of the meridian with the horizon (cf. Strabo’s comment on the
arctic circle in 1.1.6), which makes this explanation implausible. Also, Strabo, Achilles,
and the scholia (perhaps also Posidonius) are referring to the sun’s diurnal path, which is
only a conjecture. Similarly, Kirk 1962: 292 believes that Heraclitus’s “limits” (DK 22B120)
represent the meridian. For an attempt to interpret Posidonius’s suggestion (fr. 49 E-K ap.
Strabo 2.3.7–8) for “improving” Crates’ emendation (F 37, cf. fr. 34f Mette) of Homer’s
description of the Aethiopians’ dwellings (Od. 1.24) by taking it as as referring to the
sun’s annual path, see Kidd 1988: 1.269–70. According to this explanation, “setting” would
mean the sun’s path from the summer to the winter tropic, while “rising” would mean
the sun’s path from the winter to the summer tropic; “rising” and “setting” would thus
meet at the solstices. Hippolytus (Haer. 4.47.4), citing Aratus, interprets the “rising” and
“setting” as simply referring to the east and west, but his two hemispheres (in 4.43.8–9 the
two hemispheres are the upper, consisting of pneuma and fire, and the lower, consisting
of water and earth) do not make any sense in this context if they do not simply refer to
an “eastern” (upper) and “western” (lower) hemisphere, thus allowing Draco to survey
the entire longitudinal extension of the earth’s northern hemisphere.
65 A provisional argument for Crates’ familiarity with the concept of the fixed arctic
circle can be extrapolated from the map. The inscription between the winter tropic and
Crates of Mallos and Pytheas of Massalia
311
There is, however, another possibility. We have mentioned already (n28)
that only in schol. Q Phaen. 62 (98 Martin) is Crates explicitly said to have
explained “the rising(s) and setting(s)” with the phenomena associated with
the constellation Draco considered determinative of an arctic circle.66 In every
other source he associates Eudoxus’s/Aratus’s “rising(s) and setting(s)” with
annual solar motion.67 Thus (solar) risings and settings were somehow linked
to the fixed arctic circle and the limit of the sun’s annual northern passage
at c. 66° northern latitude. We hear of the sun’s “proper limits” already in
Heraclitus of Ephesus,68 which is certainly an allusion to the solstices (Lebedev
1989: 43; cf. Kirk 1962: 285; Kahn 1979: 109, 156, 160, 199).69 Elsewhere the
philosopher describes the Bear as “forming the limits of morning and evening”
(DK 22B120 ap. Strabo 1.1.6),70 which seems to suggest that for Heraclitus the
the antarctic circle states that the extension of this zone is 40 stadia in latitude (no. 28). It
is possible that this figure refers to degrees; moreover, it has been suggested that the word
γῆ (no. 29), appended to no. 28, actually represents a misinterpretation of a copyist and
that we should read “μγ” (i.e., 43) instead (Edson and Savage-Smith 2000: 14–15). This
would present us with a division of a quarter of the globe with the proportions 23°51'/24°
– 43° (lat. 66°51'/67°) – 23°09'/23°. This is only one of many proposed suggestions, and
it is a tentative one, to say the least.
66 This is an exceptional report of Crates’ exact words, as the anonymous reviewer
points out to me, and thus deserves to be cited: ἡ τοῦ Δράκοντος κεφαλή, ἐπὶ τοῦ ἀρκτικοῦ
κατεστηριγμένη κύκλου, ὃν συμβέβηκεν ἀειφανῆ εἶναι κατὰ τὴν περιαγωγὴν τοῦ οὐρανοῦ,
περιαγίνεται ἐπ’ αὐτὸν τὸν ὁρίζοντα κτλ. Cf. the translation of Broggiato (forthcoming;
see n1): the head of Draco is “placed on the arctic circle, that is always visible in the rotation of the sky, turns about on the horizon itself ” etc. Crates’ actual explanation of the
association of Aratus and Homer is rather unconvincing (cf. schol. MDΔKVUA Phaen.
62, 100 Martin).
67 Schol. HQ Od. 10.86; schol. HV Od. 10.86; Eust. Od. 10.86, i.369; schol. MDKVUA
Phaen. 62; Gemin. Elem. Astron. 6.10–12. A similar conclusion of Posidonius, Strabo,
Achilles, and some of the scholiasts on Aratus referred to above could have originated
with Crates.
68 P.Derv. 4.8: τοὺ[ς ὅρους] – [ὅ]ρους ἑ[αυτοῦ] or ε[ἱμαρμένους] (see Lebedev 1989:
39, 46–47; Schönbeck 1993: 8, 17–20; Janko 2002: 8–9; Kouremenos, Parássoglou, and
Tsantsanoglou 2006: 68–69, 130); in a corresponding passage Plutarch (De. exil. 604A =
DK 22B94) has the term μέτρα (in the meaning of “limits,” cf. Seaford 1994: 286), while
in De Is. et Os. 370D he retains ὅρους.
69 Cf. Diogenes of Apollonia (DK 64B3 ap. Simpl. in Phys. 1.4.187a12, Commentaria
in Aristotelem Graeca 9.152.13–14 Diels), who also mentions the μέτρα of winter and
summer as well as night and day.
70 Τέρμα (pl. τέρματα) has a double meaning: “turning post,” “turning point” (which is
the only meaning present in the Iliad), but also “boundary,” “endpoint,” terminus (Kahn
1979: 51, 161; Purves 2010: 56 with n88). Strabo here believes that Heraclitus employed
the term “the Bear” for the “arctic (always visible) circle.”
312
Tomislav Bilić
arctic circle was defined by the Ursa Major constellation.71 Aristotle likewise
associates the northern uninhabitable zone with the Bear (Mete. 362b9),72 and
he also defines the boundary of the northern temperate zone as the alwaysvisible circle, presumably that for the latitude of Greece (Mete. 362b3).73 Thus
the Bear might have designated the limit of the temperate zone. Much later,
Ptolemy defined the limit of the northern temperate zone as “the Bears” (Tetr.
2.2.6), and two passages in Avienius suggest the connection of the Ursa Major
constellation with the limits of the annual solar movement.74 It is possible that
Nonnus’s northern turning-point beside which the Bears move also defines the
northern limit of the sun’s annual passage.75 Hecateus of Abdera’s northern
island of Helixoia76 suggests both the association with Helikē, that is, Ursa
Major, and the verb ἑλίσσω, “to turn round or about” (Macurdy 1920: 140–41;
Thomson 1948: 403), perhaps designating the sun’s annual turning around a
solstitial turning-post associated with Ursa Major.77 Although we cannot be
sure whether either Heraclitus or Hecateus associated the Bear with the fixed
arctic circle, it does not seem probable (although it is certainly not impossible)
Kahn 1979: 51, 162 believes that the οὖρος opposite the ἄρκτος represents Arcturus
(Ἀρκτ-οῦρος) (cf. 1964: 197; Marcovich 2001: 338; McKirahan 2010: 121n28) and that the
τέρματα represent its limits of morning and evening, that is, its heliacal and acronychal
rising (cf. Hes. Op. 566–67, 610). Marcovich 2001: 338 suggests Draco as a candidate.
72 Cf. Aeschin. In Ctes. 165, where “the Bear” is associated with the extent of the
oikoumenē.
73 In Arist. [Pr.] 26.15.942a4 the “regions of the Bear” are said to be “outside the solstice”
(942a1), that is, the northern tropic. In Mete. 1.13.350b6–7 Aristotle places the Rhipaean
Mountains “under the Bear” (ὑπ’ αὐτὴν δὲ τὴν ἄρκτον; cf. Hippoc. Aer. 19 for the region
“under the Bears” [ὑπ’ αὐτῇσι τῇσιν ἄρκτοισι] associated with the Rhipaean Mountains),
which is understood by Kiessling 1914: 850.56–58, 851.20–24, 852.22–34 as referring to
the fixed arctic circle (cf. the restoration of Aesch. fr. 102 Mette ap. schol. Soph. OC 1248,
53 de Marco, where the Rhipaeans are associated with Helios’s father Hyperion; Diggle
1970: 27–28; Bridgman 2005: 44).
74 Or. mar. 649–50 (Murphy 1977: 42–43, mentioning “the limits of the Bear”) and
Descr. orb. terr. 761–63 (GGM 2.184), here associated with the summer solstice’s 24-hour
day at Thoulē.
75 Dion. 38.406–7, 25.398 (perhaps referring to the constellation’s lower culmination,
rather than the solstice); cf. 1.454 (cf. 6.236–37), 38.284–85.
76 FGrHist 264F11a = DK 73B1 ap. Steph. Byz. s.v. Ἑλίξοια; cf. Hdn. 3.1.281 Lentz.
77 Hecateus’s Hyperborean (is)land and its association with the solstices are perhaps
paralleled in HN 4.12.89, where cardines mundi are placed in the land of the Hyperboreans,
together with limits (extremi) of the movements of the stars. Ferrari 2008: 145–46 with n64
believes that these cardines represent the solstice(s), as cardine Phoebus certainly does in
Avienius (Arat. 653–54), but it is more probable that Pliny had the polar axis in mind here.
71
Crates of Mallos and Pytheas of Massalia
313
that they associated the turning of the sun with the latitude of 54° north; it
is more probable to suppose that they—or at least Heraclitus—associated it
with the latitude of the fixed arctic circle, even if they did not actually project
it onto the terrestrial globe.78 Perhaps Eudoxus originally described the risings
and settings of the sun, but he—or Aratus—associated them with the latitude
of 54° north, the latitude of the Draco-determined always visible circle, in
which they were followed by Crates (for this possible mistake, see below).
If we analyze the ideas appearing in the various authors discussed above,
it is immediately obvious that they have much in common. They all probably
concern the same phenomenon, manifested on various levels: the solstice. It
can be elaborated in various ways: the extreme points of the sun’s risings and
settings on the horizon; its maximum distance from the equator; the longest or
shortest day of the year; the increase in the length of day during the summer
and decrease during winter in higher latitudes, with a 24-hour day/night at
ca. 66°; etc. This maximum declination of the sun can also be defined with
its position respective to the sphere of the fixed stars, in particular, circumpolar constellations such as Ursa Major and Draco. The latter were not used
by Homer in connection with solar motion, but from Heraclitus onwards it
was a normal practice to do so. Thus Homer (it could be argued) addressed
the concept of the solstice in the Laestrygonian episode with reference to the
increasing length of summer days in high latitudes and the almost 24-hour
daylight on the summer solstice near the fixed arctic circle, while Heraclitus,
on the other hand, focused on the association of the maximum declination of
the sun respective to the circumpolar constellation of Ursa Major. Eudoxus/
Aratus introduced another circumpolar constellation into the discussion,
and it was Crates who finally incorporated all these models into one, albeit
arbitrarily and incoherently. This state of affairs is illustrated in Table 1.
the world according to pytheas: thoulē
The advent of Pytheas into the discussion raises the problem of the location
of the island of Thoulē, which he introduced into Greek literature.79 Both
Strabo80 and Pliny81 report Pytheas’s account of Thoulē as located a six days’
Marcovich 2001: 338 suggests that Heraclitus had the phenomenon of the midnight
sun in mind when he described the limits beyond which there is no distinction between
the rising and setting of the sun in DK 22B120.
79 For an overview of Pytheas, see Gisinger 1963; Whitaker 1981/82; Roseman 1994;
Bianchetti 1998; and Roller 2006: 57–91.
80 1.4.2 = fr. 6a Mette = fr. 2 Roseman = Eratosth. IIC2 Berger, fr. 35 Roller.
81 HN 2.77.187 = fr. 13a Mette, T 18a Roseman.
78
314
Tomislav Bilić
Table 1.
Homer
Heraclitus
(Od. 10.86)
(DK 22B94, 120)
Eudoxus/Aratus
(fr. 16 Lasserre/
Phaen. 61–62)
Crates
(fr. 50)
κέλευθοι
τέρματα (μέτρα, ὅροι) ἄκραι —
νύξ
ἑσπέρα
δύσεις
δύσις/ δύσεις
ἦμαρ
ἠώς
ἀντολαί
ἀνατολή/
ἀνατολαί
sun, 66°?
sun/Ursa Major, 66°
sun?/Draco, 54 or 66°
sun/Draco?,
54 or 66°
sail to the north of Britain.82 Pytheas is responsible also for another notion
concerning Thoulē, namely, that there the summer tropic and arctic circle
become one.83 The description of a 24-hour day on the summer solstice in
Cf. Bede, De temporum ratione 31, citing Pliny (Migne PL 90.434), and Adam of
Bremen, Descriptio insularum aquilonis (4.)35 (Waitz 1876: 184), citing Bede; also Ranulph
Higden, Polychronicon 1.31 (1.324 Babington). Solin. 23 (182, 184 Agnant) mentions a
five days and nights’ sail from the Orcades, but does not mention Pytheas as his source
(the total duration of the voyage from Cape Calydon to Thoulē adds up to fourteen days).
Mommsen did not print this section in his edition of Solinus, considering it a much later
interpolation, although it appears in some MSS (Mommsen’s edition 22.9, 1895: 101–2,
where he prints only the information on the solstice above Thoulē; printed as an appendix, 1895: 219, cf. xci). Schol. 147 Descript. ins. aquil. (4.)35 (Waitz 1876: 183) mentions
a nine days’ sail. Timaeus (FGrHist 566F74 ap. HN 4.16.104 = Pyth. fr. 11b Mette, T 23
Roseman) mentions another island, Mictis, a six days’ sail from Britain, which is probably
a confusion with Thoulē (Müllenhoff 1870: 1.385, 472; Thomson 1948: 146n1; Cary and
Warmington 1963: 256n47; Bianchetti 1998: 147, 173; Roller 2006: 72, 73n139). Romm
1992: 204n69 suggests that Plutarch probably had Pytheas in mind when he placed his
Ogygia a five days’ sail (to the west) from Britain (De fac. 941A).
83 Fr. 6c Mette = fr. 6 Roseman ap. Strabo 2.5.8 = Eratosth. fr. 34 Roller. Cf. Cleomedes,
De motu circ. 1.4.208–10 Todd = fr. 14 Mette, T 27 Roseman, also 1.4.222 Todd; see
also Strabo 2.5.43 (Pytheas T 10 Roseman), Priscianus Lydus, Solutiones ad Chosroen
4, 67.13–15 Bywater = Crates fr. 37b Mette, Mette 1936: 268.5–7. It was Theodosius of
Bithynia (2nd half of the 2nd century b.c.e.) who proved geometrically that at the distance
of 66° from the equator—that is, on the fixed arctic circle—the sun does not set on the
solstice or, in other words, that an observer situated at the latitude where the summer
tropic is the same as the always-visible circle is actually situated on the fixed arctic circle
(Aujac 1987b: 168; cf. Theodosius, De habitationibus 12, where he actually claims that
82
Crates of Mallos and Pytheas of Massalia
315
Geminus84 immediately follows Pytheas’s account of a 21- or 22-hour day,85
and is probably derived from his writings, although Geminus does not explicitly mention Thoulē. We have already seen how the scholiast on Homer
associated the location of the land of Laestrygonians with a latitude with the
longest day of 23 hours.86 We have also seen that Priscianus Lydus (Solutiones
ad Chosroen 4, 67.9–15 Bywater = Crates fr. 37b Mette) may have compared
the 23-hour day in the north to the situation on Thoulē (although this seems
highly unlikely: see Mette 1936: 85 with n1), while the scholiast on Aratus
(schol. MDΔKVUA Phaen. 62 = fr. 37h Mette),87 among others,88 associated
the 20-hour longest day with the island, and Hyginus associated the region
under the head of Draco with a shortest night of less than a third of an hour
with the Laestrygonians (Poet. astr. 4.3.3 = Crates fr. 37i Mette).89 The idea
of a 24-hour solstitial day at Thoulē became something of a commonplace in
geographical descriptions of the north. Thus according to Pliny, there is no
night on the summer solstice on Thoulē, when the sun passes through Cancer,
while on the winter solstice there is no day.90 Pomponius Mela generally dethe day at the summer solstice is 30 days long, since he takes the “day” to comprise the
interval between the positions of the sun 15° before and after the solstice; Neugebauer
1975b: 757). Euclid, Pytheas’s contemporary, had already analyzed the risings and settings
of fixed stars on the ecliptic with respect to whether they are observed from a latitude
of more than, equal to, or less than 90°-ε, discussing the relation of the ecliptic to the
arctic (always visible) circles at respective latitudes (Phaen. 4–7; Neugebauer 1975b: 767).
84 Elem. Astron. 6.13, 72.21–24 Manitius. Cf. 5.21, 50.3–7 Manitius; 32, 54.7–11
Manitius; 38, 56.7–13 Manitius.
85 Fr. 9a Mette = fr. 8 Roseman ap. Gemin. Elem. Astron. 6.9, 70.21–72.2 Manitius,
cf. 10–12, 72.2–20 Manitius. Mette’s fr. 9a (1952: 28) does not include the day-lengths,
since those were probably supplied by Geminus himself (see the discussion in Roseman
1994: 140, 142–43).
86 Schol. P Od. 10.86, Dindorf 1855: 2.454 = Crates fr. 37d Mette.
87 Mette (1936: 87 with n1, 271) emended the numbers in this scholion (“κ” to “κγ”
and “Δ” to “Α”), thus arriving at the same relation (23:1) as that found in Geminus, but
this is unnecessary.
88 Schol. Dionys. Per. 582 (GGM 2.451), Steph. Byz. s.v. Θούλη, and Eust. Dionys. Per.
581 (GGM 2.329.30–33).
89 With the emendation of unaquaque to brevissima (Mette 1936: 87, 272).
90 HN 4.16.104 = Pytheas fr. 11b Mette, T 23 Roseman. Cited by Bede, De temp. rat. 31
(Migne PL 90.436–37), in his turn cited by Adam of Bremen, Descript. ins. aquil. (4.)35
(Waitz 1876: 183). For a different theory of a six-month day on Thoulē, probably the result
of a misunderstanding, see HN 2.77.186–87 = fr. 13a Mette, T 18a Roseman (cited by Bede,
De temp. rat. 31 [Migne PL 90.433–34], in his turn cited by Adam of Bremen, Descript. ins.
aquil. (4.)35 [Waitz 1876: 183–84]), 6.39.219 (cited by Bede, De natura rerum 47 [Migne PL
316
Tomislav Bilić
scribes how the sun on the summer solstice shows its brilliance and most of
its physical body as observed from the island, thus completely eliminating
the night (3.6.57), while Solinus (22.9) and Martianus Capella (6.666) simply
copy Pliny’s report.91 According to Cleomedes, at Thoulē when the sun is in
Cancer, the day lasts a month, or less, depending on the visibility of the sign.92
Achilles Tatius reports that the sun does not set for eight(y) days in the regions
beyond Thoulē (Isagoge 35, 71 Maass). The notion also appears in poetry:
Statius associated the “weary sun” with Thyle, which blocks the western waves
(Silv. 5.2.54–55), while Dionysius Periegetes and his Latin translators vaguely
describe a nightless summer solstice day on the island.93 As we have already
seen, this notion of Thoulē was sometimes misunderstood: thus Isidore of
Seville, basing his report on that of Solinus, after recounting how the island
received its name on account of the fact that the sun “makes” the summer
solstice there, claims that there is no light beyond it.94 Bede, as we have already
90.273A]), and Mart. Cap. 6.595 (= Pytheas T 18b Roseman; cf. 608–9), as well as 4.16.104
= Pytheas fr. 11b Mette, T 23 Roseman, where Pliny reports two different theories (cited
by Bede, De temp. rat. 31 [Migne PL 90.436–37], in his turn cited by Adam of Bremen,
Descript. ins. aquil. (4.)35 [Waitz 1876: 183]). The misunderstanding is also present in
Ranulph Higden, Polychronicon 1.31 (1.324 Babington), Honorius Augustodunensis, De
imagine mundi 1.31 (Migne PL 172.130BC), Gervase of Tilbury, Otia imperialia 2.11
(Banks and Binns 2002: 326–27), and the Byzantine mid-15th-century scholar Laskaris
Kananos (Lundström 1902: 16; Blomqvist 2002: 47). Compare also Antonius Diogenes
(ap. Phot. Bibl. cod. 166, 110b42–111a3) for a six-month night “beyond Thoulē” (Crates
fr. 37c Mette). The theory is criticized by Dicuil, De mensura 7.13 (Tierney 1967: 74–75),
Priscianus Lydus, Solutiones ad Chosren 4, 67.15–17 Bywater = Crates fr. 37b Mette, and
Eust. Dionys. Per. 581 (GGM 2.329.22–29). It is possible that the pythoras or pyt(h)agoras
of the MSS of Martianus Capella’s work who “has disclosed what conditions are like in
those regions” (Mart. Cap. 6.609 = Pytheas T 29 Roseman = fr. 12b Bianchetti)—i.e, the
terrestrial poles, where days and nights are of a six months’ duration (6.608)—actually
represents Pytheas (thus Stahl and Burge 1977: 227; Roseman 1994: 111–13; Bianchetti
1998: 188–89; Keyser 2001: 362; Roller 2006: 91; but see Burkert 1972: 306n36).
91 Serv. Dan. G. 1.30 does the same, claiming that there is no night at Thyle when the Sun
is in Cancer. Cf. schol. Juv. 15.112 (no night on the summer solstice, no day at the winter).
92 De motu circ. 1.4.210–12 Todd = fr. 14 Mette, T 27 Roseman.
93 Dionys. Per. 580–83 (GGM 2.141); Prisc. Dionys. Per. 588–91 (GGM 2.195); Festus
Avienius, Descr. orb. ter. 760–63 (GGM 2.184). Compare Eust. Dionys. Per. 581, who mentions the continuous day on the island when the sun is in Cancer (GGM 2.329.18–21),
although he criticizes the notion (2.329.21–22).
94 Etym. 14.6.4; also cited by the anonymous Eulogium Historiarum 4.156 (2.113
Haydon); Ranulph Higden, Polychronicon 1.31 (1.324 Babington) cites the fact that the
island received its name “because of the sun,” but does not attribute the notion to Isidore.
Crates of Mallos and Pytheas of Massalia
317
seen, several times refers to Thoulē,95 and it is occasionally mentioned by other
medieval authors.96 During the Middle Ages, the notion of “the island of the
solstice” was sometimes transferred to Iceland.97
Several similar testimonies are perhaps derived from a related idea. Thus
Procopius describes how in Scandinavia—called Thoulē in this section of his
work—the sun is continuously present during the 40 days about the summer
solstice, while it is absent for the same amount of time about the winter (Bell.
6.15.6–7). Jordanes repeats the same information about the 40-day daytime
and darkness about the solstices (actually, he mentions mid-summer and
winter),98 but associates the phenomenon with the Adogit people, who live
in the northern part of Scandinavia (Get. 3.19–20). A very similar description of a 40-day night with the sun in Capricorn and a 40-day daylight with
the sun in Cancer is found in Tzetzes (Chiliades 12.844–48, 474 Kiessling),
who further associates this region with the Cimmerians (841–43). Paul the
Deacon similarly describes a tribe named Scritobini, which is placed by him
near the farthest limits of Germania to the northwest (Historia Langobardum
1.4–5), where for several days about the summer solstice there is a clear light
during night-time, while about the winter solstice the sun is not seen at all,
although there is some light (1.5). Adam of Bremen reports that in Halagland
De natura rerum 9 (Migne PL 90.204A; an interpretation, it seems, similar to
Isidore’s concerning the eternal darkness); In Regum librum XXX quaestiones 25 (Migne
PL 91.732B;Trent Foley and Holder 1999: 129–30; Wooding 2000: 241–42; on Thyle
[Iceland?] the Sun does not set about the summer solstice); De temporum ratione 31
(Migne PL 90.434–37), where he cites Solinus (22.9) and Pliny (both HN 2.186–87 and
4.104) (Roseman 1994: 78; McCready 1996: 115).
96 E.g., Adam of Bremen, Descript. ins. aquil. (4.)35 (Waitz 1876: 183–84), where he cites
Bede, De temp. rat. 31; also schol. 146 on (4.)35 (Waitz 1876: 183); Giraldus Cambrensis,
Topographia Hiberniae 1.17 (citing Solin. 22.9, Isid. Etym. 14.6.4, and Oros. 1.2.79;
Giraldus is further cited by Petrarch, Fam. 3.1.8); Geoffrey of Monmouth, Vita Merlini
655–60. The longest day and shortest night on Tille when the sun is in Cancer, and the
longest night and shortest day when it is in Capricorn, together with the fact that there
is no difference nor distance between rising and setting (of the sun), are also mentioned
by the 11th-century Assaph Hebraeus (Neubauer 1864: 672–73; Nansen 1911: 2.200n2).
97 E.g., in Honorius Augustodunensis, De imagine mundi 1.31 (Migne PL 172.130B),
who refers to the island Isole; cf. Dicuil, De mensura orbis terrae 7.11–13 (Tierney 1967:
74–75, cited in Wooding 2000: 241 and Roseman 1994: 157n18); in 7.7–10 (Tierney 1967:
74–75) Dicuil cites Pliny (HN 2.77.187), Isidore (Etym. 14.6.4), Priscianus (Perieg. 588–91),
and Solinus (22.9). Cf. also Adam of Bremen, who identified “Thyle” with “Icelan(d),”
Descript. ins. aquil. (4.)35 (Waitz 1876: 184–85; cf. Parroni 1984: 356), as did Laskaris
Kananos (Lundström 1902: 16; Blomqvist 2002: 47).
98 Cf. Bilić 2012.
95
318
Tomislav Bilić
(northern Norway) the continuous day about the summer solstice lasts for
14 days, and the continuous night in winter 14 days (Descriptio insularum
aquilonis [4.]37 [Waitz 1876: 185]).99
These unusual accounts can be compared with Polybius’s description of
the sun’s behavior around its turning-points, slowing down in approaching
the tropics and remaining near them for about 40 days (34.1.9 ap. Gemin.
Elem. Astron. 16.34–35, 178.6–15 Manitius).100 This means that to an observer
it seems as if the sun “slows down” when nearing a solstice, and that it slowly
regains its “equinoctial” speed after the turn, appearing as if it “stands still”
for a few days about the solstice; this period Polybius approximates to 40
days.101 The sun’s “residing” in the far north about the summer solstice could
have inspired the theory found in Procopius, Jordanes, and Tzetzes, although
Polybius had the area directly “below” the tropics in mind, rather than the
area below the arctic and antarctic circles.102 Caesar mentions some unnamed
islands around Britain, of which it is written that at the winter solstice the night
there lasts for 30 consecutive days (B Gall. 5.13.3), while Plutarch describes
an island named Ogygia, situated a five days’ sail west of Britain “near the
place103 of the summer sunset,” where the sun sets “for less than one hour for
thirty days in succession” (De fac. 941A, D). Strangely, Posidonius posits two
narrow zones directly below the tropics, scorched by the sun (fr. 49 E-K ap.
Strabo 2.2.3–3.1.2).104 While only Procopius explicitly connects the scenario
of a multi-day daytime with Thoulē, having Scandinavia in mind, and much
99 Perhaps a mistake for 40 (Nansen 1911: 1.194n2). Cf. the anonymous Eulogium historiarum 4.92 (2.79 Haydon) and Ranulph Higden, Polychronicon 1.31 (1.326 Babington),
where it is described how in northern parts of Norway the sun does not set for “many”
days about the summer solstice and does not rise for “many” days about the winter solstice.
Laskaris Kananos claims that at Bergen the uninterrupted daylight lasts from 24 June to
25 July (Lundström 1902: 15; Blomqvist 2002: 46).
100 Cf. a similar description, but without the exact number of days, in Cleomedes, De
motu circ. 1.4.35–40, 90–92, 114–15 Todd.
101 Cf. Gemin. Elem. Astron. 6.29–32, 34–35, 38 (78.25–80.12, 80.18–82.1, 82.7–14
Manitius), 17.28 (190.23–192.3 Manitius).
102 Polyb. 34.1.7–13 ap. Gemin. Elem. Astron. 16.32–38 (176.20–178.28 Manitius). Cf.
Pliny, HN 2.13.66, who claims that only the part of the earth that lies beneath (subiaceo) the
zodiac is actually habitable, while the rest towards the poles is barren (squaleo), certainly
taking antarctic and arctic circles as the boundary lines, not the tropics.
103 Thus Romm 1992: 204; Cherniss and Helmbold 1957: 181: “in the general direction.”
104 Cf. [Hippoc.] De victu 2.38, where it is said that the sun absorbs the moisture of the
south wind when it blows “through the approaches (ἔφοδοι) of the sun under the south
(ὑπὸ τὴν μεσημβρίην),” which probably refers to the tropic of Capricorn.
Crates of Mallos and Pytheas of Massalia
319
later Tzetzes makes a “mythological” reference to the Cimmerians, both Caesar
and Plutarch associate the idea with Britain, which suggests, in the light of
Pytheas’s voyage and report, a link with Thoulē as well.
pytheas and homer
We can conclude that the location of Thoulē was bound up—from the time
of Pytheas onwards—with the concept of the τροπαὶ ἠελίοιο (Od. 15.404),105
or was itself considered to lie at the sun’s very turning-place, thus earning
the name of the “island of the solstice.”106 Moreover, Pytheas’s report suggests
that in his account he combined the actual voyage to whatever place in the
“far north” he had visited with a specific Homeric reference. An island of the
solstice situated a six days’ sail to the north of Britain conforms well with
Homer’s account in the Odyssey: there we find Aeolus’s floating island, situated
a six days’ sail from Tēlepylus (Od. 10.80–81)107—where the paths of night and
day are close together—and thus of a similar character to the island of Syriē,
where the τροπαὶ ἠελίοιο are located (Od. 15.404).108 Of course, Homer does
not in any way connect Syriē with the land of the Laestrygonians, but two
pieces of mytho-geographical lore associated with these two locations seem
to belong to a similar tradition concerned with meteorological conditions
in the far north, or more precisely, on the fixed arctic circle. Hence it seems
conceivable that Pytheas was not only a great explorer but perhaps also a fine
Homeric scholar. Aujac 1987a: 151 believes that it is probable “that Pytheas
indicated the height of the sun at the winter solstice for various latitudes
not through observation, but by calculation with the help of geometry.”109
Cf. Bilić 2012.
Cf. Isid. Etym. 14.6.4. Thoulē is rather explicitly associated with the concept of
the sun’s turning in the poem of Dionysius Periegetes (584–86 [GGM 2.141], cf. Festus
Avienius, Descr. orb. terr. 764–67 [GGM 2.184]; Eust. Dionys. Per. 581 [GGM 2.329.33–37]).
107 With this concept compare similar descriptions in Hes. Theog. 748–49 and
Parmenides, 28B1.11 D-K ap. Sext. Emp. Math. 7.3 (Bowra 1937: 103; Morrison 1955:
59; Havelock 1958: 139, 1978: 270; Dolin 1962: 96; Vos 1963: 28, 34; Guthrie 1965: 12;
Stokes 1963: 11n3; West 1966: 367; Woodbury 1966: 611; Frame 1978: 60; Ferrari Pinney
and Sismondo Ridgway 1981: 142; Kirk, Raven, and Schofield 1983: 243–44; Ballabriga
1986: 125–26; Freeman 1996: 41; Marinatos 2001: 396; Steele 2002: 583–84; Morgan 2000:
76–77; Mourelatos 2008: 15; Coxon 2009: 9, 51, 275–76).
108 See the preceding discussion on the 40-day period of daytime/night when the sun
travels near the tropics. Cf. Bilić 2012.
109 Cf. Carpenter 1973: 176, 191–92 (also cited in Whitaker 1981/82: 160), who claims
further that Pytheas derived his values for the length of daylight at various latitudes from
105
106
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He knew beforehand, by studying the geometry of the sphere, of a latitude
“where, at the summer solstice, the day lasted twenty-four hours and the sun
did not disappear under the horizon. He located the island of Thule on this
particular circle.”110 Aujac continues by stating that “he [Pytheas] may have
undertaken his voyage to the northern seas partly in order to verify what
geometry (or experiments with three-dimensional models) had taught him.”
Several other authors share this opinion. Thus Bianchetti 1998: 45, 155, 181
believes that Pytheas’s observations actually empirically verified Eudoxus’s
theoretical exposition of the celestial phenomena—especially the behavior
of the sun—in high latitudes.111 Similarly, Dilke 1985: 29–30 (further cited
in Roller 2006: 63n52) suggests that the main object of Pytheas’s voyage was
to obtain the latitudes for the far north, while Heidel 1937: 108 believes that
his objective was to gather evidence confirming the sphericity of the earth.
Similarly, Roseman 1994: 145 claims that it is “the concept of a spherical
earth” Pytheas “is most likely to have set out to demonstrate,” since in his
time it “was still a theory needing the kinds of data he brought back for its
confirmation,”112 while Thomson 1948: 153 maintains he was aware that he
was “testing the zone theory.” Dicks 1960: 187 believes that he “combined trade
with scientific exploration,”113 and according to Roseman 1994: 148, cf. 155, he
was a physical scientist (physikos, philosophos; for the latter, cf. Käppel 2001:
11). It has further been claimed that he was the first to recognize the difference between the always-visible and the fixed arctic circle (Bianchetti 1998:
calculation—after he had ascertained the latitude through different means—rather than
observation. It is probable that he determined the latitudes by observing the elevation
of the pole (Nansen 1911: 1.46–48; this was one of Hipparchus’s procedures, Ptol. Geog.
1.4; Neugebauer 1975b: 938 also argues for the primacy of other means, rather than the
longest daylight, of determining geographical coordinates of a locality, namely, observations used to determine latitude).
110 Cf. Dilke 1985: 30; Bianchetti 1998: 191. This was already anticipated by Bunbury
1883: 1.614.
111 Cf. Diller 1975: 225, also cited in Roller 2006: 74, where Eudoxus is said to have
inspired Pytheas, and Müllenhoff 1870: 1.234–35; cf. Berger 1903: 336; Heidel 1937:
99n212, 108; Bianchetti 1998: 37, where it is suggested that Pytheas was a pupil of Eudoxus.
112 Cf. Bianchetti 1998: 188, who claims that Pytheas empirically demonstrated the
sphericity of the earth.
113 For his dual—scientific and mercantile—motivation, see Bianchetti 1998: 65.
Compare also Müllenhoff 1870: 1.312; Tozer 1897: 154; Holmes 1907: 220 (also cited in
Whitaker 1981/82: 163n90); Nansen 1911: 1.45; Walbank 1948: 173 (= 2002: 45) (erroneously cited in Whitaker 1981/82: 162); Thomson 1948: 143; Cunliffe 2002: 154; and Roller
2006: 63, 74, all of whom emphasize Pytheas’s scientific motives in undertaking his voyage.
Crates of Mallos and Pytheas of Massalia
321
43, 153).114 Thus Aujac and others believe that Pytheas’s voyage was partly
motivated by the wish to gather specific scientific data, while asserting that
his data on the altitude of the solstitial sun came through calculation and that
he knew of a “Thoulē” before the voyage itself even commenced. This indeed
makes the voyage, in terms of theoretical background, superfluous, especially
if we take into account the Homeric parallels schematically listed below. Thus
Pytheas’s voyage was only an empirical confirmation of certain geometrical
postulates; he empirically tested the theories concerning the phenomena
in high northern latitudes that had already been theoretically predicted by
the astronomers,115 combining his actual experience with specific Homeric
reference(s) (see Table 2).
Table 2.
Pytheas
Britain
Homer
Aeolus’s island
six days’ sail to the north
six days’ sail
(unspecified direction)
Thoulē: perpetual day on
the summer solstice
the island of the sun’s
turning
Tēlepylos: the paths of
night and day are
close together
(Syriē) τροπαὶ ἠελίοιο
Crates
54 or 66° N
Aeaea
66° S, winter
tropic
Hades, the Cimmerians
south pole
For his scientific achievements, see also Bianchetti 1998: 45–46 and Käppel 2001: 11.
Compare what Deinias has to say in Antonius Diogenes’s Wonders beyond Thoulē:
“Deinias claimed here [beyond Thoulē] to have seen what the devotees of astronomy
speculate about, for instance that there are some men who live beneath the Great Bear,
and that the night can be a month long, or more or less, or even six months, or even a
year.” (Phot. Bibl. 166.110b39–111a2; translation in Romm 1992: 209). Thus Deinias
“empirically” tested the theories concerning the phenomena in high northern latitudes
that had already been theoretically predicted by the astronomers, which echoes what
Pytheas probably also did.
114
115
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Tomislav Bilić
If Homeric descriptions are thus an important part of Pytheas’s worldview, this would also account for the latter’s similarities with Crates’ account,
given that both focus on the exact same data. It is fundamentally Homeric
exegesis that we see lurking behind both Pytheas’s and, especially, Crates’
models, which is not unusual if we take into account the reputation Homer
enjoyed during both the Classical and the Hellenistic periods as a true authority in questions of geography—including mathematical geography. In a way
Pytheas actually followed in Odysseus’s footsteps, visiting or claiming to have
visited a “Tēlepylos” (perhaps also a “Syriē”), and Crates was free to use the
data from both adventurers in elaborating his own ideas of the zonal division
of the globe. He perhaps elaborated it in a somewhat incoherent way, locating Homer’s Laestrygonians both with reference to the always visible circle
of Rhodes taken as the arctic circle (misunderstanding or misrepresenting
what Eudoxus/Aratus had said with reference to the constellation Draco),
and with the latitude of the fixed arctic circle. The former was probably inspired by a cosmological doctrine that demanded the orderly 6–5–4 division
of the cosmic sphere. Then again, it is also possible that it was he who was
misunderstood or misrepresented by the scholiasts on Aratus; in this case
Crates was consistent in associating the Laestrygonians with the latitude of
the fixed arctic circle. A third possibility is that Eudoxus originally described
the risings and settings of the sun, rather than Draco, but that it was he, rather
than Crates, who associated these with the cosmological doctrine described
above. Finally, taking into account the common mistakes in the determination of Draco’s declination (we know of a case when the mistake was as much
as 12°), one cannot disregard the possibility of a mistake in Eudoxus’s—or,
for that matter, Crates’—model, which would account for the difference. It
was Crates’ model, however, that was depicted on the curious cosmological
map discussed above. The question of the variability of the arctic circle was
certainly one that Crates considered, although it—or one of the solutions of
this problem—was most probably not represented on the map. By contrast,
the cosmic (mytho-geographical) nature of Odysseus’s voyage,116 associated
with the tropics, poles, and arctic circles, is indeed recognizable on the map,
which makes it a unique graphic representation of Homeric exegesis.
conclusion
The two approaches to Homeric exegesis—Crates’ and Pytheas’s—analyzed
in this paper are characterized by their use of mathematical geography in
116
Cf. Marinatos 2001; Käppel 2001: 16, 19, 21 Abb. 1; Nakassis 2004.
Crates of Mallos and Pytheas of Massalia
323
the service of interpreting the poet’s narrative. Crates’ interpretative method
was quite explicit, as he openly interpreted Homer’s narratives as legitimate
scientific hypotheses. In this manner he developed a distinctive interpretation of Odysseus’s voyage, starting in our section of the inhabited earth but
ending in the antoikoumenē, where Homeric Hades and other otherworldly
locations were situated. The map discussed in the text could only have been
made in connection with Crates’ unique approach to Homeric exegesis, being
a graphic representation of his method and a counterpart to his famous globe.
It is important to emphasize that both literary and graphic sources attest to
an identical concept of the southern hemisphere. The literary sources are in
disagreement, however, with respect to Crates’ ideas on the question of the
fixed arctic circle as opposed to the always-visible, Draco-determined circle for
the latitude of Greece. The Draco-determined arctic circle comes in turn to be
associated with the question of the northern limit of the habitable zone. Thus,
for example, Strabo explicitly associates the limit of the northern habitable
zone with the projection onto the terrestrial globe of the always-visible circle
as defined by the constellation of Ursa Major. By contrast, in Crates’ model
the Homeric Laestrygonians were most probably placed on the fixed arctic
circle, which defined the northern limit of the habitable zone for Eratosthenes,
while Pytheas seems merely to have combined the data acquired on his voyage with certain Homeric references, particularly with those that he believed
were concerned with meteorological phenomena in the far north. From the
argument above, it seems reasonable to conjecture that Crates used the data he
found in Pytheas’s account when elaborating his own ideas of mathematical
geography. He thus combined the experiences of an imaginary (Odysseus)
and a true adventurer (Pytheas).
Pytheas’s account of the far north and, especially, solar phenomena in high
northern latitudes is indeed very similar to certain parts of Homer’s narrative of the Laestrygonians. The reason for this could be simply the fact that
Pytheas was inspired by the poet and that he (also) interpreted his narrative
as referring to “scientific” hypotheses on solar phenomena in high northern
latitudes. It could be argued that he received this notion through the medium of Eudoxus. Significantly, the constellation of Ursa Major formed the
“Homeric” limits of sunrise and sunset already for Heraclitus, in what was a
rather explicit allusion to the annual solar motion. In the end, it is impossible
to determine who associated the solstitial latitude of the sun with the Draco/
Ursa Major-determined always-visible circle (Heraclitus, Hecataeus, Eudoxus,
Aratus, or Crates), but it seems certain that of the notion arose from (at least)
two interdependent factors: the latitude of Greece as the determinative for
astronomical observations and the orderly 6–5–4 (“Pythagorean”) division
324
Tomislav Bilić
of the cosmic sphere. In any case, the description of solstitial phenomena
could be expressed in several ways: respective to the sphere of the fixed stars
or with reference to the increasing length of summer days in high latitudes.
The notions of the Laestrygonian “distant gates” and the solstitial island of
Thoulē are dependent on both models.
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