Discerning Alcor in Horse and Rider Asterism Tests 20/20 Vision

Summary: Discerning Alcor, fainter of the naked eye double star known as the Horse and Rider asterism in the Big Dipper's handle, historically tests 20/20 vision.

Persian astronomer 'Abd al-Rahman al-Sufi provided mirror images of each constellation in his mid-10th century star atlas, The Book of Fixed Stars (Kitab al-Kawākib al-Thābita):
Left: depiction of the Great Bear, as seen directly in the night sky, in The Book of Fixed Stars; image from ca. 1009 copy in the Bodleian Library, the oldest extant copy: Abd-al-rahman al-Sufi, Public Domain, via Wikimedia Commons
Right: depiction of the Great Bear, as seen on a celestial globe, in The Book of Fixed Stars; image from ca. 1009 copy in the Bodleian Library, the oldest extant copy: Public Domain, via Wikimedia Commons

Discerning Alcor, fainter of the naked eye double star known as the Horse and Rider asterism in the asterismal Big Dipper's handle in the Great Bear (Ursa Major) constellation, historically tests 20/20 vision in the ancient and medieval Arab world.

Persian astronomer 'Abd al-Rahman al-Sufi (Dec. 7, 903-May 25, 986), writing in Arabic, discusses the Alcor vision test in his mid-10th century astronomical text, The Book of Fixed Stars (Arabic: Kitab al-Kawākib al-Thābita). Danish astronomer Hans Carl Frederik Christian Schjellerup (Feb. 8, 1827-Nov. 13, 1887) published a French translation of The Book of Fixed Stars in 1874.

The Persian astronomer lists 27 stars in the Great Bear (Arabic: al-dubb al-akbar). Number 26, in the middle of the tail, or in the middle of the Big Dipper asterism's handle, is identified as al-anâk (“little she-goat”). Western astronomy knows al-anâk under the traditional name of Mizar. Its astronomical designation is Zeta Ursae Majoris (ζ Ursae Majoris; Zeta UMa; ζ UMa).

al-Sufi indicates that the usual Arabic name for the small star above al-anâk is al-suhâ, “the little neglected (star).” In some dialects, al-anâk's companion star is known as al-nuaïsch (“little stretcher”), al-saïdak (“steadfast, trustworthy”) or al-schitâ (“winter”). Western astronomy knows al-suhâ under the traditional name of Alcor, a corruption of al-jaún, the Arabic word for a swift horse. Alcor's astronomical designation is 80 Ursae Majoris.

The Persian astronomer notes that al-suhâ is used as an eyesight test. He cites an Arabic proverb depicting al-suhâ as a touchstone of keen eyesight: “I show him al-suhâ, and he shows me the moon.”

Research by Dr. George M. Bohigian, an ophthalmologist at Washington University School of Medicine in St. Louis, Missouri, correlates the resolution, or separation, of Alcor from Mizar with the 20/20 line on the Snellen visual acuity eye chart. Each of the two E optotypes, or standardized visual test symbols, that appear in Snellen's 20/20 line subtends, or encloses, five arc minutes at a distance of 20 feet. Each of the five lines in the 20/20 E optotype measures one arc minute.

Arc minute, also known as minute of arc (MOA) and minute arc, is an angular measurement unit that is used in fields, such as astronomy, land surveying, navigation and ophthalmology, that involve extremely small angles. An arc minute equals one-sixtieth (1/60) of one degree, expressed decimally as 0.01667 degrees. One degree is one-three hundred sixtieth (1/360) of a circle. In the context of a circle, an arc minute is expressed as one-twenty-one thousand six hundredth (1/21600), the product of 1/60 times 1/360.

The separation between Alcor and Mizar measures 11.8 arc minutes, or 0.19667 degrees. Dr. Bohigian points out that, in the hand measurement of apparent distances between celestial objects, the width of the little finger, extended at arm’s length, represents one degree.

Seventeenth-century polymath Robert Hooke (July 28, 1635-March 3, 1703) noted in a lecture at central London’s Gresham College at the beginning of December 1673 the resolution limits of human vision in naked eye astronomy. The Cutleran lecture, funded by wealthy London merchant Sir John Cutler (ca. 1608-April 15, 1693), was subsequently published in 1674. Hooke’s findings reveal the impossibility of naked eye astronomers’ distinguishing “any distance in the Heavens less then [sic] half a minute, or thirty seconds, and hardly one of a hundred can distinguish a minute.” (Animadversions, page 7)

Dr. Bohigian equates the angle of separation between Mizar and Alcor, at 11.8 arc minutes, to an approximate equivalent of 20/200, the topmost line on the Snellen Eye Chart. But 20/20 visual acuity, which expresses normal clarity, or sharpness, of vision at a distance of 20 feet, considers factors such as brightness, contrast and sharpness. Also, the standardized black letters on the Snellen Eye Chart contrast easily with their white background, whereas white objects against the black background of space, especially in Alcor’s apparent closeness to Mizar, challenge visual sharpness. Dr. Bohigian finds that the unequal brightnesses, with Alcor at fourth magnitude and Mizar at second magnitude, as well as other factors, such as atmospheric distortion, ambient light pollution, dark adaptation and retinal light scatter, elevate the resolution of Alcor to “a good test of vision.”

An experiment conducted over two successive dates confirms Dr. Bohigian’s correlation of Alcor discernment with the Snellen Eye Chart’s 20/20 line. Ten participants, ranged in age from 12 to 49 and corrected to 20/20 or better, plainly discern Alcor on a cold, moonless country sky, free from urban light pollution. The next day the ten participants easily see the Snellen Eye Chart’s 20/20 line. Testing with increasingly powered spherical lenses yields image blurring on both occasions at the same parameters, with spherical power ranges of +0.50 to +0.75.

Dr. Bohigian assesses that discernment of Alcor, known as the Arab Eye Test, attests to the practicality of natural phenomenon.

The takeaway for discerning Alcor in the Big Dipper handle’s Horse and Rider asterism as a test of 20/20 vision is the night sky’s practical beauty.

Left: Snellen Eye Chart; 20/20 line is above red line: Jeff Dahl, Public Domain, via Wikimedia Commons;
Right: Snellen Eye Chart’s E optotype encloses five arc minutes, with each line registering one arc minute: Alessio Facchin, CC BY SA 3.0 Unported, via Wikimedia Commons

Acknowledgment

My special thanks to talented artists and photographers/concerned organizations who make their fine images available on the internet.

Image credits:

Left: depiction of the Great Bear, as seen directly in the night sky, in The Book of Fixed Stars; image from ca. 1009 copy in the Bodleian Library, the oldest extant copy: Abd-al-rahman al-Sufi, Public Domain, via Wikimedia Commons @ https://commons.wikimedia.org/wiki/File:Book_of_the_Fixed_Stars_Auv0052_ursa_major.jpg
Right: depiction of the Great Bear, as seen on a celestial globe, in The Book of Fixed Stars; image from ca. 1009 copy in the Bodleian Library, the oldest extant copy: Public Domain, via Wikimedia Commons @ https://commons.wikimedia.org/wiki/File:Al_Sufi_-_Book_of_Fixed_Stars_-_Ursa_Major_(The_Great_Bear)_-_Bodleian_Library_-_Marsh_144.jpg

Left: Snellen Eye Chart: Jeff Dahl, Public Domain, via Wikimedia Commons @ https://commons.wikimedia.org/wiki/File:Snellen_chart.svg
Right: Snellen Eye Chart’s E optotype: Alessio Facchin, CC BY SA 3.0 Unported, via Wikimedia Commons @ https://commons.wikimedia.org/wiki/File:Esnellen2.png

For further information:

“A Handy Guide to Measuring the Sky.” Time And Date > Sun & Moon.
Available @ https://www.timeanddate.com/astronomy/measuring-the-sky-by-hand.html

Avramov, Iordan. “Letter Writing and the Management of Scientific Controversy: The Correspondence of Henry Oldenburg (1661-1677).” Pages 337-363. In Toon Van Houdt; Jan Papy; Gilbert Tournoy; Constant Matheeussen, eds. Self-Presentation and Social Identification: The Rhetoric and Pragmatics of Letter Writing in Early Modern Times. Supplementa Humanistica Lovaniensia XVIII. Leuven, Belgium: Leuven University Press, 2002.

Berman, Bob. “Eye See, You See.” Astronomy Magazine > Bob Berman's Strange Universe. Sept. 1, 2004.
Available via Astronomy Magazine @ http://astronomy.com/columnists/bob%20berman/2004/09/bob%20bermans%20strange%20universe%20eye%20see%20you%20see

Bohigian, George M. “An Ancient Eye Test Using the Stars.” Survey of Ophthalmology, vol. 53, no. 5 (September-October 2008): 536-539.
Available @ http://www.surveyophthalmol.com/article/S0039-6257(08)00119-7/fulltext

Duane, Thomas. Clinical Opthalmology. Philadelphia PA: Harper & Row, 1982.

Hafez, Ihsan; F. Richard Stephenson; Wayne Orchiston. “'Abdul-Rahman al-Sufi and His Book of the Fixed Stars: A Journey of Re-Discovery.” In Wayne Orchiston, Tsuko Nakamura, Richard G. Strom, eds., Highlighting the History of Astronomy in the Asia-Pacific Region. Pages 121-138. New York NY; Dordrecht; Heidelberg, Germany; London, England: Springer Science+Business Media LLC, 2011.
Available via Google Books @ https://books.google.com/books?id=vOUWfhBheDIC&pg=PA121#v=onepage&q&f=false

Hooke, Robert. Animadversions on the First Part of the Machina Coelestis of the Honourable, Learned, and Deservedly Famous Astronomer Johannes Helevius, Consul of Dantzick Together With an Explication of Some Instruments. London, England: John Martyn, Printer to the Royal Society, 1674.
Available @ http://quod.lib.umich.edu/e/eebo/A44313.0001.001?rgn=main;view=fulltext

J.E.L.D. “Hans Carl Frederik Christian Schjellerup.” Royal Astronomical Society, vol. XLVIII (48), no. 4 (February 1888): 171-174.
Available @ http://mnras.oxfordjournals.org/content/48/4/171

Mamajek, Eric E.; Matthew A. Kenworthy; Philip M. Hinz; Michael R. Meyer. “Discovery of a Faint Companion to Alcor Using MMT/AO μ5 m Imaging.” The Astronomical Journal, vol. 139, issue 3 (March 2010): 919-925.
Available @ http://iopscience.iop.org/article/10.1088/0004-6256/139/3/919

Marriner, Derdriu. “Big Dipper's Naked Eye Double Star Mizar and Alcor Are Six Stars.” Earth and Space News. Wednesday, May 17, 2017.
Available @ https://earth-and-space-news.blogspot.com/2017/05/big-dippers-naked-eye-double-star-mizar.html

Moore, Patrick. Astronomers' Stars. New York NY: W.W. Norton & Co., 1987.

Rubin, Melvin L.; Gordon Lynn Walls. Fundamentals of Visual Science. Springfield IL: Charles C. Thomas, 1969.

Schjellerup, H.C.F.C. (Hans Carl Frederik Christian). Description des Étoiles Fixes Composée au Milieu du Dixième Siécle de Notre Ère par l’Astronome Persan Abd-al-Rahman al-Sufi. Traduction Littérale de Deux Manuscrits Arabes de la Bibliothèque Royale de Copenhague et de la Bibliothèque Impériale de St. Pétersbourg. Avec des Notes par H.C.F.C. Schjellerup. St. Petersburg, Russia: Commissionnaires de l’Académie Impériale des Sciences, 1874.
Available via Atlas Coelestis di Felice Stoppa @ http://www.atlascoelestis.com/Sufi%20schjelerup%20Description%20des%20%C3%83%C2%A9toiles%20fixes.pdf
Available via Google Books @ https://books.google.com/books?id=nJRHAAAAYAAJ
Available via MENAdoc Digital Collections @ http://menadoc.bibliothek.uni-halle.de/ssg/content/titleinfo/459362

Upton, J.M. (Joseph M.) “A Manuscript of 'The Book of the Fixed Stars' by 'Abd ar-Rahman as-Sufi.”Metropolitan Museum Studies, vol. 4, no. 2 (March 1933): 179-197.
Available @ https://www.jstor.org/stable/1522800?seq=1#page_scan_tab_contents

Wooldridge, Maurice. “Seeing Stars: The Arabic Eye Test Revisited.” The British Medical Journal, vol. 310 (Feb. 4, 1995): 297.
Available @ http://www.bmj.com/content/310/6975/297

Zimmerman, Neil; Ben R. Oppenheimer; Sasha Hinkley; Douglas Brenner; Ian R. Perry; Anand Sivaramakrishnan; Lynne Hillenbrand; Charles Beichman; Justin R. Crepp; Gautam Vasisht; Lewis C. Roberts Jr.; Rick Burruss; David L. King; Rémi Soummer; Richard Dekany; Michael Shao; Antonin Bouchez; Jennifer E. Roberts; Stephanie Hunt. “Parallactic Motion for Companion Discovery: An M-Dwarf Orbiting Alcor." The Astrophysical Journal, vol. 709, no. 2 (Feb. 1, 2010): 733-740. DOI: 10.1088/0004-637X/709/2/733
Available @ http://iopscience.iop.org/article/10.1088/0004-637X/709/2/733/meta