Cited by 1Historical Astronomy and Related StudiesDiverse Historical and Scientific StudiesHistory and Theory of Mathematics

Dōng 東 ‘East’ and the Chinese “Indian Circle”

Open access
Smith, Jonathan·2021·Journal of the American Oriental Society

Abstract

The Chinese character ⟨東⟩, writing a word meaning ‘east’, is shown here to have arisen in connection with the use of the vertical gnomon in the determination of cardinal direction. The simple geometric procedure involved—by Al-Bīrūnī (973–1048) termed the “Indian Circle”—is attested across a number of other early cultural contexts, and has a Chinese history traceable from classical-era technical treatises such as the “Kǎogōng jì” 考工記 to sixth-century commentary to the mathematical text Shùshù jìyí 數術記遺. Evidence offered below constitutes the first direct indication for such a practice in second-millennium bce China.

Integrity signals

Registry

Crossref · 10.7817/jameroriesoci.139.4.0953

Cites

13 of 13 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 17 cited sources checked · 0 supported · 0 flagged

  • Findingcitation

    In Róng Chéng's instructions we find a medieval Chinese counterpart of Figure 1 in all essentials, ending with determination of the meridian by fixing a midpoint.

    “we otherwise find in Róng Chéng's instructions a neat medieval Chinese counterpart of Figure 1 above in all its essentials, ending with a determination of the meridian via fixing of a midpoint:”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Liú 1999

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Findingcitation

    Early bone and bronze inscriptions from the late second to early first millennium BCE show that the resemblance of 東 to 日 and 木 came from formal reanalysis of an earlier four-line arrangement, two curved and two straight.

    “Early inscriptions on bone and bronze from the late second to the early first millennium bce show clearly that the resemblance of ⟨東⟩ to glyphs writing the words rì 日 'sun' and mù 木 'tree; wood' was the result of formal reanalysis of an earlier arrangement consisting of only four interlocking lines, two curved and two straight: 3”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Sagart 2004 source
  • Findingown data

    Early inscriptions show 東 writing the Old Chinese word *tôŋ 'east'.

    “In the case of the character shown just below, early inscriptions show it to write the Old Chinese (OC) word *tôŋ 'east' (with neither character nor associated word much changed to the present) .”
    Quote in the paperSubstantial claim
  • Findingnone given

    These words were written from early periods with 東 plus a top closed shape often representing the sun 日.

    “These words were written from early periods with the form ⟨東⟩ in combination with, at the top, a closed shape often taking the form of a conventionalized representation of the sun ⟨日⟩ .”
    Quote in the paperSubstantial claim
  • Findingnone given

    The first unambiguous inscriptional antecedents of 重 show 東 with its central vertical stroke oddly bent at the top.

    “The first unambiguous inscriptional antecedents of ⟨重⟩, by contrast, show ⟨東⟩ with its central vertical stroke oddly bent at the top .28”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 12
  • May combine two claims. 9
  • Classified as probably not a substantial claim.

    Findingreasoning

    Zheng's instructions to first track the shadow tip over the day to produce a circular (actually hyperbolic) arc, with the gnomon-centered circle constructed afterward as an operation on that shadow path, make an interesting practical difference.

    “Zhèng's more rough-and-ready instructions to first track the shadow-tip over the course of the day so as to produce a circular (actually hyperbolic) arc, with the gnomon-centered circle (or arc) constructed after the fact as an operation on that shadow path, make for an interesting practical difference .24”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The path traced by a gnomon shadow tip over a day is a hyperbolic arc.
  • May combine two claims.

    Interpretationnone given

    The choice of 東 in 量 could not have been phonologically motivated, and the meaning 'east' cannot account for the reapplication.

    “Again, the choice of ⟨東⟩ here could not have been phonologically motivated, nor could the meaning 'east' itself account for the reapplication .”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Interpretationown data

    The suggestions that 東 depicts the rising sun, a tree, or the spring season do not withstand paleographical scrutiny.

    “However, as is now widely recognized, these suggestions do not bear paleographical scrutiny .”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Pankenier, while considering celestial polar methods likely for alignment of Shang tombs and other ritual edifices, remarks on the closer cardinal alignment of minor associated structures.

    “Indeed, while considering celestial polar methods likely for alignment of Shang tombs and other ritual edifices (well known to respect directions slightly east of geodetic north), Pankenier (2013: 101-2 incl .n .43) also remarks upon the closer cardinal alignment of minor associated structures .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Pankenier 2013

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationnone given

    The choice of 東 as the basis for the early coinage of 陳 was apparently not phonologically motivated, and the semantics of 'east' are not sufficient to explain its reapplication to write 'set in line'.

    “The choice of ⟨東⟩ as the basis for this early coinage was apparently not phonologically motivated, nor are the semantics of 'east' themselves sufficient to explain the character's reapplication to write a word meaning 'set in line' .”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim.

    Premisecitation

    Liu addresses the question of evidence for such a procedure within the earlier Chinese textual record.

    “The question which Liú moves to address (while acknowledging the clear possibility that the Shùshù jìyí here or elsewhere was in part heir to traditions of Indian origin) concerns evidence for such a procedure within the earlier Chinese textual record .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Liú 1999

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Liu opens with an anecdote from commentary to the Shùshù jìyí, around the sixth century CE, relating an exchange between Róng Chéng and a nameless backwoodsman.

    “Liú opens with an anecdote from commentary to the mathematical text Shùshù jìyí 數術記遺 (ca .sixth century ce) relating an exchange between the legendary Róng Chéng 容成 and a nameless (and directionless) backwoodsman (chuānrén 川人) .13”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Liú 1999

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Premisecitation

    Zheng's account reads as long-standing folk wisdom, and there is increasingly clear archaeological evidence for use of the vertical gnomon in contexts as ancient as late Longshan Taosi, around 2000 BCE, in southern Shanxi.

    “Zhèng's account, after all, reads as long-standing folk-wisdom-and there is increasingly clear archaeological evidence for the use of the vertical gnomon in contexts as ancient as late Longshan Táosì 陶寺, ca .2,000 bce, in modern-day southern Shānxī province .25”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Pankenier 2013

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The word chén 陳 means to arrange or lay out in a line; its derivative zhèn 陳 means a layout or array, often specifically a battle array.

    “The word chén (< *drən) 陳 means 'set in line, lay out, arrange'; the derivative zhèn (< *drəns) 陳, in etymological terms 'that which is set in line', means 'layout, array (n .)'and is frequently more specific 'battle array' .26”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Schuessler 2007

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

    Interpretationreasoning

    If 重 was not simply a phonosemantic coinage, perhaps its creators wished to evoke the layers of the heavens, most naturally understood by reference to the eastern horizon.

    “If this character was not simply a phonosemantic coinage (and the curious design suggests it was not), perhaps its creators wished to evoke the layers of the heavens, most naturally understood by reference to the eastern horizon .”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The word liáng 量 means 'measure, assess'; its derivative liàng 量 means 'a measure'.

    “The word liáng (< *raŋ) 量 means 'measure, assess'; the derivative liàng (< OC *raŋh) 量, in etymological terms 'that which is measured', is 'a measure (n .)' .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Schuessler 2007

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisenone given

    We have Zheng Xuan's associated commentary from 127-200 CE, which previous studies have not addressed.

    “However, we do have the associated commentary of Zhèng Xuán 鄭玄 (127-200 ce), as far as I am aware not addressed in previous studies .”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Chinese parallels to the Indian Circle are considered systematically in Liu Dun's 1999 study.

    “Of particular interest here are several more and less straightforward Chinese parallels to the Indian Circle, considered systematically in the 1999 study of Liú Dùn 劉鈍 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Liú 1999

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationnone given

    Zheng's discussion provides a more nuanced view of the history of the Indian Circle in the Chinese textual tradition.

    “Zhèng's discussion provides for a more nuanced view of the history of the Indian Circle as reflected within the Chinese textual tradition .”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Premisecitation

    Use of the Indian Circle procedure was not restricted to early India; Vitruvius describes a Roman tradition with Greek precedents, and scholars have considered its use in Old Kingdom Egypt for aligning the Great Pyramids or associated structures.

    “The use of such a procedure was hardly restricted to early India: in addition to modern applications, there is the description from Vitruvius (fl .70-15 bce) of a Roman tradition with Greek precedents, for example, while several scholars have considered the possibility that such a technique was used in Old Kingdom Egypt for alignment of the Great Pyramids or associated structures .12”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Morgan 1914

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites Isler 1989 source
    • cites Neugebauer 1980 source
  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    Early writing, apparently including 東, will prove to be a bridge across this gap.

    “Early writing itself, apparently including the character ⟨東⟩, will prove to be a bridge across this gap .”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Interpretationnone given

    Observations timed at sunrise and sunset meet practical problems: variation in local horizon altitude causes differences between the sun's altitude at sunrise and sunset, and long early morning and late afternoon shadows are poorly defined.

    “But as many have noted, observations so timed meet with problems in practice: variation in the altitude of the local horizon will mean differences between the altitude of the sun at sunrise versus sunset, for instance, and the long shadows of early morning and late afternoon are relatively poorly defined .”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S1 (asserted).

    Premisereasoning

    Most twentieth-century investigators proposed that 東 was devised not to write *tôŋ 'east' but an approximate homophone, later adopted to write 'east' because of phonological closeness.

    “As claims for an original relationship with *tôŋ 'east' thus seemed less likely, most twentieth-century investigators took a different approach: perhaps this character was devised not to write *tôŋ 'east' but some (approximate) homophone, only later to be adopted to write 'east' on the basis of phonological closeness .”
    Quote in the paperNot a substantial claim
18 of 18
  • The paper relies on this without support.

    A vertical gnomon's shadow over the course of a day is symmetric about the meridian, reflecting the sun's apparent path.

    “This simple but ingenious procedure takes advantage of the fact that the movement of a vertical gnomon's shadow over the course of a day displays a symmetry across the meridian that reflects that of the sun's apparent path across the sky .”
  • The paper relies on this without support.

    The path traced by a gnomon shadow tip over a day is a hyperbolic arc.

    “Zhèng's more rough-and-ready instructions to first track the shadow-tip over the course of the day so as to produce a circular (actually hyperbolic) arc, with the gnomon-centered circle (or arc) constructed after the fact as an operation on that shadow path, make for an interesting practical difference .24”
  • The paper relies on this without support.

    Early technologies need not have been unitary or very new.

    “First of all, early technologies need not have been unitary (or even very new) .”
3 of 3

Cites

Flagged first, then by citations

Research works printed but not linked: 5

  1. Cullen, Christopher . 1996 . Astronomy and Mathematics in Ancient China: The Zhōubì suànjīng . Cam- bridge: Cambridge Univ . Press .
  2. Morgan, Morris Hicky, tr . 1914 . Vitruvius, The Ten Books on Architecture . Cambridge, Mass .: Harvard Univ . Press .
  3. Neugebauer, Otto, and David Pingree . 1971 . The Pañcasiddhāntikā of Varāhamihira, Part II: Histo- risk-Filosofiske Skrifter 6 .1 Part II . Royal Danish Academy of Sciences and Letters . Copenhagen: Munksgaard .
  4. Wenren, Jun . 2013 . Ancient Chinese Encyclopedia of Technology: Translation and Annotation of Kǎogōng jì (The Artificers' Record) . New York: Routledge .
  5. Yano, Michio . 1986 . Knowledge of Astronomy in Sanskrit Texts of Architecture (Orientation Methods in the Īśānaśivagurudevapaddhati) . Indo-Iranian Journal 29 .1: 17-29 .

Authors
Smith, J.
Corresponding author
Smith, Jonathan
Venue
Journal of the American Oriental Society
Published
2021-09-19
Volume
139
Issue
4
ISSN
  • 0003-0279 (ISSN-L)
  • 2169-2289
OpenAlex
W2994733084
Cited by
1
References
11
Citations by year
2026: 1
FWCI
0.00
Type
journal article
Language
en
Open access
Locations
Journal of the American Oriental Society (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Historical Astronomy and Related Studies
  • Social Sciences › Arts and Humanities › History and Philosophy of Science › Diverse Historical and Scientific Studies
  • Physical Sciences › Mathematics › Theoretical Computer Science › History and Theory of Mathematics
Keywords
al-Biruni, ancient Chinese astronomy, etymology

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