Abstract
The ancient Chinese model of the cosmos called gai tian (“canopy heaven”) that is explained in the Zhou bi (“gnomon at Zhou”) in the first century BC (but containing much older material) and in additional sources, differs fundamentally from the usual archaic conception of a flat earth with a hemispherical celestial vault, like that of the Presocratic Greeks and the Chinese rivaling system called hun tian. In the gai tian model, the heaven is thought to be flat and parallel to the flat earth. For us, since we are used to think in terms of a spherical earth, it is not so easy to comprehend the implications of an earth conceived of as flat. The conceptual transition to understand the gai tian is, as we will see, even “much more difficult to make than the switch from a spherical to a flat earth,” as Cullen rightly notes.
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Notes
- 1.
Quotations with an initial # are from Cullen’s translation of the Zhou bi in Cullen (1996).
- 2.
In this context, a bi or gnomon is just a stick, put perpendicularly on the ground and used to measure its shadow.
- 3.
For the difficult question of dating the Zhou bi as a whole as well as parts of it, see Cullen (1996), 138–145, especially 145. Several items and calculations discussed below seem to belong to the oldest parts, going back to the pre-Qin and early Han periods (about 200 BC). The central idea of a flat circular heaven over a flat square earth is even older (see texts 13.3 and 13.6). In Cullen (2017), 207–212, a concise overview is given of the gai tian, as presented in the Zhou bi.
- 4.
Cullen (1996), xiii.
- 5.
Already for this reason the rendition in Needham (1970), 210–216 cannot be right. See, e.g. 210: “The heavens were imagined as a hemispherical cover, and the earth as a bowl turned upside down.” Needham (1970, 212, Fig. 87) reproduces Chatley’s (1938, 12) misguided drawing. The same holds for several deceitful drawings on the Internet.
- 6.
- 7.
Cf. Cullen (1996), 50.
- 8.
Quoted from Cullen (2017), 203.
- 9.
Major (2010), 115.
- 10.
- 11.
- 12.
See Cullen (1996), 53 ff., and his figure 6 on 65.
- 13.
Cullen (1996), 8.
- 14.
Cullen (1996), 8.
- 15.
See Chap. 11.
- 16.
In the Han measurement system one li = 1800 chi, one bu = 6 chi, one zhang = 10 chi, one chi = 10 cun, one cun = 10 fen. One li equals 415.8 m, one chi equals 0.231 m, one bu equals 1.386 m.
- 17.
The Huainanzi has two numbers for the height of the heaven: one calculation with a gnomon of one zhang (= 10 chi) length, which results, of course, according to the shadow rule, in a distance between earth and heaven of 100,000 li. (Major c.s. 2010, 148, ch. 3.45), and another number of 150,000 li, without an indication of a method to reach this result (Cf. Major 2010, 117 (3.4). The figure of 150,000 li is a correction of the main text, which reads 510,000 li (Cf. Major 1993, 68 and note on 294. See also Cullen 1993, 288, and 294, note at 3.IV).
- 18.
The text of #B34 in Cullen (1996), 181 has “on the day of the summer solstice”, but this is a misprint, Christopher Cullen assured me, because the Chinese text has 冬至日.
- 19.
See Cullen (1996), 105–106.
- 20.
Due east of the pole, see Cullen (1996), 191 n. 213. The obvious meaning is that the sun is beyond the range of visibility of an observer in Zhou, because it is night.
- 21.
Cf. Cullen (1996), 190.
- 22.
See Cullen (1996), 191 n. 214.
- 23.
The same numbers for the first, fourth, and seventh heng in #D8 (diameter 238,000 li), #D11 (diameter 357,000 li), and #D14 (diameter 476,000 li). The concept of the seven heng, imaginary circles around the pole, will be discussed in Chap. 14. Here it suffices to say that the first, fourth, and seventh heng coincide with the northern tropic, the equator, and the southern tropic of Fig. 13.6.
- 24.
In the calculations of the circumference of a circle the Zhou bi uses π = 3. The same numbers also in #D8, #D11, and #D14.
- 25.
Cullen (1996), 113.
- 26.
Panchenko (2002b), 252.
- 27.
Forke (1907), 261.
- 28.
The derivation of the formula for the distance d to the horizon of a spherical earth is found by Pythagoras’ theorem:
In the right-angled Δ CHO, where C the center of the earth, r is the earth’s radius, O the observer’s eye, OP = h the distance from the observer’s eye to the earth, and H the horizon. Then \( d=\sqrt{{\left(r+h\right)}^2-{r}^2} \) → \( d=\sqrt{r^2+2 rh+{h}^2-{r}^2} \) → \( d=\sqrt{2 hr+{h}^2} \) → \( d=\sqrt{h\left(2r+h\right)} \). When we insert the radius of the earth (6378 km) for r, and the height of the observer (0.0017 km) for h, then d ≈ 4.66 km.
- 29.
Quotation from Cullen (1996), 221–222.
- 30.
- 31.
Cf. Forke (1907), 263.
- 32.
Forke (1907), 263 and 264–265.
- 33.
Forke (1907), 261.
- 34.
Cf. Cullen (1996), 60, n. 60: “It will help us to understand the references to the movement of the sun if we recall that court business normally began at dawn.”
- 35.
Quoted from Cullen (1996), 60.
- 36.
- 37.
Quoted from Cullen (1996), 51.
- 38.
Cullen (1996), 124.
- 39.
See ibidem.
- 40.
See Fig. 13.6 and cf. texts 13.31(#F4), 13.8 (#B14), 13.9 and 14.28 (#B33).
- 41.
See Fig. 13.6 and texts 13.26(#F9) and the shadow lengths in 13.27 (#H3, 7) and 13.28 (#H2, 19).
- 42.
Due east of the pole (as seen from Zhou), see Cullen (1996), 191 n. 213.
- 43.
From Zhao Shuang’s commentary on the Zhou bi, quoted from Cullen (1996), 126.
- 44.
Quoted from Cullen (1996), 222.
- 45.
Cullen (1996), 131.
- 46.
See Panchenko (1999), 37–38.
- 47.
Cullen (1996), 41, insists that Chinese astronomers “took special note of what we call meridian transits.” And more specifically: “all the solar shadows mentioned in the Zhou bi are noon values” (id., 103).
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Couprie, D.L. (2018). An Ancient Chinese Cosmology: Main Features. In: When the Earth Was Flat. Historical & Cultural Astronomy. Springer, Cham. https://doi.org/10.1007/978-3-319-97052-3_13
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