An Astro-Archaeological Analysis: The Tall Gnomon of Guo Shoujing (PPT slides)

Vance Tiede

Astro-Archaeology Surveys

Presented at the SEAC Conference, Malta, 22-26 September 2014

An Astro-Archaeological Analysis: The Tall Gnomon of Guo Shoujing

Diffusion of Astronomy

“The investigation of the transmission of mathematics and

astronomy is one of the most powerful tools for the

establishment of relations between different civilizations.”

“[Unlike] stylistic motives, religious or philosophic

doctrines, …astronomical methods…require for their

transmission the direct use of scientific treatises.” Neugebauer, The Exact Sciences in Antiquity (NY: Dover, 1957), 1.

Tall Gnomons: Precision Without a Telescopic Lens (cf. Needham 1959, 296)

Tycho Brache Uraniborg

1500 Ulugh Beg

Samarkand

1437

Guo Shoujing Gaocheng

1276

Nasir al-Din al Tusi Maraghe

1262

Sawai Jai Singh II Jaipur

1727

Tall Gnomon of Nasir al-Din al-Tusi محمد بن محمد بن الحسن طوسی

Maraghe Observatory, Persia N 37⁰ 23’ 45”, E 46⁰ 12’ 33”, 1262 AD

Yuan Luni-Solar Calendar Reform of 1280 AD

The Yuan Emperor Khubilai Khan “ …has specifically

commanded us to carry out a reform and set in order a

new astronomical system. For this purpose, we have

newly made a Simplified Instrument and Tall Gnomon and

have arrived at constants based on observations using them.

We have carried out research on seven items:”

1. Winter Solstice;

2. Year Surplus;

3. Tread of the sun;

4. Travel of the moon;

5. Crossing entry [timing the lunar nodes on the ecliptic];

6. Angular extensions of the lunar lodges…; and

7. Sunrise, sunset, day and night marks [Venus/Stars?]….”

(Guo Shoujing, in Siven 2009, 282-286)

Guo Shoujing Scaled up the 8-chi Gnomon 5-fold

Standard (8-chi tall) Gnomon

Tall (40-chi) Gnomon:

8-chi x 5

“Kuo lengthened

the eight ch’ih

pendicular into

forty ch’ih, thus

greatly increased

the accuracy in the

calculation of the

summer and

winter solstice.”

Tung Tso-pin 1937, 128erp

Water Channel:

- Levels

- Reflects

Seasonal Shadows at the

Tower for the Observation of Stars &

Standard for the Measurement of the Sky, 1276 AD Gaocheng, Henan Province, China

34° 24’ 8.73” N, 113° 8’ 26.23” E, DigitalGlobe/Google Earth imagery

27 Dec 2009, est. 1100L 2 Jul 2014 28 Apr 2009

Summer Spring

Winter

Tower for the Observation of Stars

& Standard for the Measurement of the Sky Gaocheng, Henan Province, China 34° 24’ 8.73” N, 113° 8’ 26.23” E, 1276 AD

(cf. Krupp 1983,60)

Midwinter 27 Dec 2009

est. 11:00 Local

Astro-Archaeological

Research Questions

1. Why is Guo Shoujing’s Tall Gnomon’s 128-chi horizontal

template scale (kuei-piao) 40% longer than required to

measure the shadow of the Midwinter Sun (-23.5ᵒ dec)?

Midsummer Moon Major SS (-28.5ᵒ dec)?

Other?

2. Was the Latitude of Guo Shoujing’s solar shadow observations at

Gaocheng (N 34.4°) or Beijing (N 39.9°); and

3. Can a “Virtual Field Check” of the Yuan Dynasty hao length of

“about 0.03mm” (Mercier 2003, 195) refine the limit of shadow

resolution marked on the Template Scale?

(Han Dynasty hao = 0.024mm).

1a. Why a 128-chi Template Scale?: Midsummer Major SS Moon (-29ᵒ dec) Venus? Bright Star (-32ᵒ to -38ᵒ dec)

Table 3. Tall Gnomon Minimum Declinations at Gaocheng & Beijing

OUTPUT: Program STONEHENGE (Hawkins 1983, 328-330)

#127

#122 delta d

Gno mon Tall Gnomon d decl Target -

Chinese Distance Height Location Astro-Target Declination decl Skyline

chi (m) (m) N Latitude on Skyline (deg/deg/radian)

84.7250 20.64500 9.75 Moon -29.3668401684 0.0007901684

SMAJSS -0.5125480518 0.0000137910

Gaocheng 15JUN1280

34.4°

128.0006 31.19 9.75 Venus ? -38.2400939269 6.4359772602

Min dec -0.6674155453 0.1123289938

111.2772 27.12 9.75 Moon -29.3664503563 0.0004003563

SMAJSS -0.5125412483 0.0000069875

Beijing 15JUN1280

39.9°

128.0006 31.19 9.75 Venus ? -32.7367236168 0.9326069501

Min dec -0.5713636134 0.0162770619

Lunar Magnitudes by Phase at Meridian Transit: Estimated Shadow/Reflection Visibility

(11 Dec 1300 – 10 Jan 1301 AD)

Lunar Magnitudes by Phase at Meridian Transit

11 Dec 1300 AD- 10 Jan 1301 AD Estimated

Phase Illuminated Visual Shadow/Refection

Day Name % Date Magnitude or Invisible

New 0 11-Dec -1.82 I

1 1% 12 -4.65 I

2 1% 13 -4.65 I

3 1st Crescent 4% 14 -6.73 R

4 8% 15 -8.03 R

5 15% 16 -8.97 R

6 23% 17 -9.69 R

7 32% 18 -10.29 S/R

8 1st Quarter 42% 19 -11.79 S/R

9 53% 20 -11.22 S/R

10 64% 21 -11.59 S/R

11 75% 22 -11.89 S/R

12 85% 23 -12.14 S/R

13 93% 24 -12.12 S/R

14 99% 25 -12.44 S/R

15 Full 100% 26 -12.48 S/R

16 99% 27 -12.44 S/R

17 94% 28 -12.32 S/R

18 87% 29 -12.15 S/R

19 79% 30 -11.92 S/R

20 69% 31 -11.65 S/R

21 59% 1-Jan -11.33 S/R

22 Last Quarter 49% 2 -10.97 S/R

23 39% 3 -10.17 S/R

24 29% 4 -10.07 S/R

25 21% 5 -9.49 R

26 14% 6 -8.77 R

27 8% 7 -7.84 R

28 Last Crescent 3% 8 -6.48 R

29 1% 9 -4.06 I

30 New 0% 10 -0.58% I

http://www.freegreatpicture.com/earth-star/full-moon-reflection-50358

1b. Venus: Thai Pei4 (Great White One)

• Visible in Day and Night:

• 3rd Brightest Celestial Object (mag. ≤ - 4.6)

• Casts Shadow Below: http://www.digitalsky.org.uk/venus/shadow-of-venus.html Above: Statis Kalyvas

http://astrobob.areavoices.com/2009/01/14/bask-in-her-radiance/

1c. Venus Min & Max Declinations (+23.5º +8º ≈ +32º dec)

(McCurdy 2005, 189)

.

Period of Absolute Extreme (+ 32 degrees) Declinations of Venus

http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html

Period Siderial Synodic Absolute Absolute

Planet Earth Days Earth Days Earth Days Earth Years

Venus 224.701 583.92 - -

Earth 365.2564 - - -

Earth-Venus - - 47,924,345 131,207

1d. Venus Maximum Declination (+23.5º +8º ≈ +32º dec)

“According to the mathematical wizard Jean Meeus,

perihelion last coincided with the Northern

Hemisphere's winter solstice… in the year A.D. 1246.”

http://www.idialstars.com/jan2012.htm

http://skyscript.co.uk/forums/viewtopic.php?t=5201&sid=aa6afae25e1614c853a10d6640926621

1e. Venus (-17⁰ 47’ dec) at Earth Perihelion

(Winter Solstice) 21 Dec 1246 AD

1f. Venus (-27⁰ dec) Meridian Transit from Beijing

(Cross-Quarter?) 29 Oct 1244 AD

1g. Venus Visible in Daylight Solar Eclipse

http://www.zam.fme.vutbr.cz/~druck/eclipse/Ecl1997r/Tse1997uw2/0-info.htm

o ₊

March 9

1h. Venus Meridian Transit: Daytime Naked Eye Observation

Recorded in the Shan Chű Hsin Hua (1340 AD)

Waxing Crescent Moon & Venus

Stellarium Planetarium (left)

Photo, 18 June 2007, 1553 UT, SW England (right) © Martin J. Powell, http://www.nakedeyeplanets.com/venus-conjunctions.htm

“ And indeed only nine days later, the

planet Venus ‘crossed the meridian.’ ”

A Meridian Transit of Venus was

recorded (2 September +1340) in the

Shan Chű Hsin Hua (New Discussions

From the Mountain Cabin) by Yang Yű,

a Co-signatory Observer in the Bureau

of Astronomy: “This was a very bad sign.”

[cf. Schlegel (5), p. 635; Chavannes (1),

vol. 3, p. 374] Needham et al. 1954, 419)

1i. Venus Visible in Daylight: Transiting the Sun

http://www.theatlantic.com/infocus/2012/06/the-2012-transit-of-venus/100313/

AP Photo/Michael Probst

Kolobrzeg, Poland Reuters/Ali Jarekji

Amman, Jordan Reuters/Jim Urquhart

Salt Lake City, Utah

5 June 2012

5 June 2012

5 June 2012

1j. Venus at Solar Transit With Shadow Definer or Helioscope

http://www.youtube.com/watch?feature=player_detailpage&v=H9zXMpijpME

Yokohama Science Center, 8 June 2004 by Itsuo Inouye, AP

Bright Star, Sun, Moon & Venus: Meridian Transit Reflection (mag < 1.5, + 32⁰ dec, 1300 AD)

http://www.incredibleindiaphotogallery.com/2010/07/weekend-travel-to-almora-kausani-baijnath-jageshwar-nainital/dsc_0961/

Meridian Transit Bright Stars (+ 32 dec, Mag. < 1.5, 1300 AD), Sun, Moon & Venus

Hawkins & Rosenthal 1967 http: //en.wikipedia.org

MT SAO Star

Decl. Beijing or Catalog Visual Greek (Latin) Chinese

deg Gaucheng Number Magnitude Name Name

38.3 G 699 0.14 α Lyrae (Vega) 織女 (Weaving Girl)

22.90 B/G 536 0.24 α Boötis (Arcturus) 大角 (Great Horn)

15.28 B/G 380 1.34 α Leonis (Regulus) 轩辕十四 (Fourteenth Star of Xuanyuan)

14.84 B/G 168 1.06 α Tauri 畢宿五 (Fifth Star of the Net)

7.25 B/G 745 0.89 α Aquilae 河鼓二 (River Drum Two)

7.00 B/G 224 0.10 α Orionis (Betelgeuse) 参宿四 (Fourth of Three Stars)

6.78 B/G 291 0.48 α Canis Minoris, Procyon 南河三 (Third Star in Southern River)

-9.25 B/G 193 0.34 β Orionis (Rigel) 参宿七 ( Seventh of Three Stars)

-15.97 B/G 257 -1.58 α Canis Majoris (Sirius) 天狼 (Celestial Wolf)

-28.21 B/G 248 1.43 ε Canis Majoris 弧矢 ( Bow and Arrow)

-33.24 G 867 1.29 α Piscis Austrini 北落師門 (North Gate of Military Camp)

+/- 23.5 B/G -26.74 Helios (Sol)

+/- 28.5 B/G -12.74 Selene (Luna) 月

+/- 24.5 B/G -4.60 Aphrodite (Venus) 金 星 (Great White One)

2a. Solar Observations: Gaocheng or Beijing?

“…[T]here is still the common

impression, even with some

serious historians, that the

solsticial shadow observations

listed by Guo Shoujing were

made at Yangcheng [Gaocheng]

in Henan….. Dong Zuobin made

it clear that the observations

listed by Guo Shoujing were

made in Beijing. ”

(Mercier 2003, 191-192, cf. Krupp 1983, 60-61)

2b. Yuan Shih Solar Observations: Beijing, not Gaocheng

Table 2. Yuan Shih Dec & Tall Gnomon Locations

OUTPUT: Program STONEHENGE (Hawkins 1983, 328-330)

#122 #127

d delta d

Gno mon Tall Gnomon Yuan shih Tall Gnomon dec Sun MT -

Chinese Distance Height Location Sun dec Sun dec dec Gnomon

chi (m) (m) N Latitude Date (deg & radian) (deg & radian)

12.35274 3.01 9.75 22.6947 17.2480 5.4467

Gaocheng 30May+1279 0.3010 0.0951

34.4°

76.74293 18.70 9.75 -23.5368 -28.0586 4.5218

14Dec+1279 -0.4897 0.0789

12.35274 3.01 9.75 22.6947 22.2681 0.4256

Beijing 30May+1279 0.3887 0.0074

39.9°

76.74293 18.70 9.75 -23.5368 -22.5552 -0.9817

14Dec+1279 -0.3937 -0.0171

3a. Shadow Definer & (sub-mm) Resolution?

Figure 2. Shadow Definer (ying fu) Design; Observing Table; Pinhole Principle; & “7chi” Mark of the Template Scale (Siven 2009, 188, 190); http://web.calstatela.edu/faculty/kaniol/a360/yingfu1.htm;

http://hua.umf.maine.edu/China/astronomy/tianpage/0022MingGnomon6471w.html

3b. Yuan Dynasty hao-millimeter Linear Conversion

Table 1. Yuan znang/chi - Metric Linear Unit Converter

Given

Starry

Night Pro Plus 6 Meridian

Calculated

Stone Declination Declination Transit

Feature chi meter feet block ( ° ' ) (decimal °) (LMT)

Height: Gnomon Bar 40.0000 9.75 31.98 na

Length: Template Scale 128.0000 31.19 102.30 36.00

Length: Stone Block 3.5556 0.8664 2.84 1.00

4.1039 1.00 3.28 0.87

Date, Latitude, Location 1.0000 0.24 0.80 0.28

30 May +1279, +39° 54’ 12.3695 3.01 9.89 3.48 +22° 41.68' 22.69466667 12:24:00

14 Dec +1279, Beijing 76.7400 18.70 61.33 21.58 - 23° 32.21' -23.53683333 12:27:15

Chinese Units zhang chi cun fen li hao Meter

zhang 1 10 100 1,000 10,000 100,000 2.400000

chi 0.1 1 10 100 1,000 10,000 0.240000

cun 0.01 0.1 1 10 100 1,000 0.024000

fen 0.001 0.01 0.1 1 10 100 0.002400

li 0.0001 0.001 0.01 0.1 1 10 0.000240

hao 0.00001 0.0001 0.001 0.01 0.1 1 0.000024

Conclusions 1. The 128-chi Template Scale Length was capable

of measuring Meridian Transit (MT) shadows of:

Sun, (Full/Gibbous) Moon, & Venus at Solar

Transit (8-year cycle); and reflections of

(Crescent) Moon, Venus & Bright Stars (+32ᵒ dec,

visible magnitude < 1.5).

2. The solar observations of Guo Shoujing in the

Yuan Shih were made near Beijing, not Gaocheng.

3. Yuan Dynasty hao = 0.024mm Han Dynasty hao.

Future experiment could confirm the hao as the

Limit of Sun shadow resolution of a Tall Gnomon.

References 2Hawkins, Gerald S. 1983 Mindsteps to the Cosmos, New York: Harper & Row. Kelly, David and Eugene F. Milone 2005 Exploring Ancient Skies: An Encyclopedic Survey of Archaeoastronomy. New York: Springer. Krupp, Edwin C. 1983 Echoes of the Ancient Skies: The Astronomy of Lost Civilizations. New York: Harper & Row. Liu, C. Y 1987 “A Research on the Implication of Zhang-Chi in Ancient Chinese Astronomical Records,” Acta Astronomica Sinica, 28:4, 402. http://adsabs.harvard.edu/abs/1987AcASn..28..397L Maspero, Henri 1939 “Les Instruments Astronomiques des Chinois au temps des Han,” Mélanges Chinois et Bouddhiques, vol. 6 (1938-9), 183-370, McClure, Brude and Deborah Byrd 2014 “Venus brightest in mid-February for all of 2014,” EarthSky (February 14) http://earthsky.org/human-world/venus-brightest-greatest-brilliancy-greatest-illuminated-extent#why McCurdy, Bruce 2005 “Venus Vignette,” Journal of the Royal Astronomical Society of Canada, 99:187-189 http://adsabs.harvard.edu/full/2005JRASC..99..187M Mercier, Raymond 2003 “Solsticial observations in thirteenth century Beijing.” SCIAMVS, 4:191-232. Needham, Joseph et al. 1986 Heavenly Clockwork, Cambridge: Cambridge University Press. 1954 Science and Civilization in China, III (Astronomy), London: Cambridge University Press. Odenwald, Sten 008 “Ancient Elipses in China” http://sunearthday.nasa.gov/2009eclipse/ancienteclipses.php Sivin, Nathan 2009 Granting the Seasons: The Chinese Astronomical Reform of 1280. New York: Springer. Shen, K’ang-shen; Crossley, John N.; Lun, Anthony Wah-Cheung; Liu, Hui 1999 The nine chapters on the mathematical art: companion and commentary. Oxford University Press. Tiede, Vance 2010 “Astronomical Orientation of Pyramid Tombs in North China,” Historical Astronomy Division, AAS Meeting, Washington, DC. https://www.academia.edu/3462054/Astronomical_Orientation_of_Pyramid_Tombs_in_North_China Tung Tso-Pin (Dong, Zuobin, 1895-1963), Lin Tun-Chen & Kao Phing-Tzu 1939 周公測景臺調查報告 Chou Kung Tshê Ching Thai Thiao Chha Pao Kao [Zhou gong ce jing tai diao cha bao gao] Report of an Investigation of the Tower of Chou Kung for the Measurement of the Sun’s (Solsticial) Shadow, Com. Press Academia Sinica), Chhangsha. UNESCO 2010 “Report of the decisions Adopted by the World Heritage Committee at its 34thSession (Brasilia, 2010),”Decision: 34 COM 8B.24, 215-216. http://www2.astronomicalheritage.net/index.php/show-entity?identity=17&idsubentity=1

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