The Sun/Moon Illusion in a Medieval Irish Astronomical Tract

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Perspective The Sun/Moon Illusion in a Medieval Irish Astronomical Tract

Helen E. Ross

Psychology, University of Stirling, Stirling FK9 4LA, UK; [email protected]

Received: 14 June 2019; Accepted: 5 August 2019; Published: 7 August 2019

Abstract: The Irish Astronomical Tract is a 14th–15th century Gaelic document, based mainly on a Latin translation of the eighth-century Jewish astronomer Messahala. It contains a passage about the sun illusion—the apparent enlargement of celestial bodies when near the horizon compared to higher in the sky. This passage occurs in a chapter concerned with proving that the Earth is a globe rather than ﬂat. Here the author denies that the change in size is caused by a change in the sun’s distance, and instead ascribes it (incorrectly) to magniﬁcation by atmospheric vapours, likening it to the bending of light when looking from air to water or through glass spectacles. This section does not occur in the Latin version of Messahala. The Irish author may have based the vapour account on Aristotle, Ptolemy or Cleomedes, or on later authors that relied on them. He seems to have been unaware of alternative perceptual explanations. The refraction explanation persists today in folk science.

Keywords: sun illusion; moon illusion; medieval science; atmospheric refraction; Messahala; ﬂat Earth; spectacles

1. Early Explanations of the Sun or Moon Illusion The sun/moon illusion is the apparent enlargement of the celestial bodies when near the horizon compared with their appearance when higher in the sky. Early authors usually referred to it as the sun illusion, and modern authors as the moon illusion. The effect was often ascribed to some type of refraction by the atmosphere—but this cannot be correct, because magnification only occurs when looking from a thin to a denser medium (such as air to water), but not the other way around. Refraction does have the effect of making the image of the sun oval, and slightly smaller, when near the horizon. The various accounts were reviewed by Plug and Ross [1] and Ross and Plug [2] and the main points are summarised here. Aristotle (fourth century BC) gave an obscure account, comparing the magnification to reflection in an enlarging mirror, or to refraction of light passing between media of different optical density. Similar statements were made by Posidonius (ca. 135–50 BC) and Seneca (ca. 3 BC–AD 65). Ptolemy was clearer about refraction in his book on astronomy, the Almagest (ca. AD 142), as was Cleomedes (early third century AD): Both authors compared the horizon enlargement to the magnification of objects seen under water. However, in other passages both authors state that perceived size does not correspond to image size, but rather to linear size through the geometrical principle of size-distance invariance. In his later book the Optics (ca. AD 170), Ptolemy explained underwater enlargement as due to angular magnification combined with the same (apparent) distance as in air. Cleomedes elaborated on the importance of apparent distance and claimed that a misty atmosphere (aerial perspective) made the sun appear further away near the horizon, and thus larger. Ibn al-Haytham (ca. 1039) criticised Ptolemy’s accounts of atmospheric refraction and attempted to use the correct direction of refraction by stating that the eye is in the thinner medium and the object in the denser. Refraction accounts were repeated without criticism by Arab astronomers, and by the

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British scholars Alexander Neckam and John of Sacrobosco in the thirteenth century. Atmospheric refraction was not clearly understood until about the sixteenth century. The importance of apparent distance was elaborated by Ibn al-Haytham in much more detail. He described the flattened-dome account in his Optics (ca. 1039), and it was repeated by the thirteenth-century writers Roger Bacon, John Pecham and Witelo. On this theory the dome of the sky appears flattened because intervening objects expand the apparent distance towards the horizon, and the apparent size of the celestial bodies expands with the apparent distance. John of Sacrobosco repeated a version of this based on the ninth-century Arab astronomer al-Farghani, but in this version the flattened dome had a physical reality, and the midday sun was actually closer than at sunrise or sunset. This should produce the opposite effect to the sun illusion. The experimental study of the illusion did not begin until the early 1900s. Experiments have shown that several factors can contribute to the illusion, but the most important is the sight of the terrain which sets the scale for enlarging the apparent size of distant objects. There is currently no final agreed explanation [3]. The popular press today continues to report the refraction account [4], or sometimes the apparent distance account.

2. The Irish Astronomical Tract The Irish Astronomical Tract exists as three manuscripts in Dublin [5]. These date from about the late fourteenth century and are all in diﬀerent hands. The original was probably written in the mid fourteenth century. Since it refers to spectacles, it cannot be earlier than about 1325 [6] or 1320 [7]. It has been translated into English by Power [6] and Williams [5]. The Tract consists mainly of a translation into Irish of a Latin version of Messahala’s treatise on astronomy (De scientia motus orbis—On the knowledge of the motion of the orb). Messahala (ca. 740–815) was a Jewish scholar, versed in Arabic learning, whose Arabic text was translated into Latin by Gerard of Cremona, and reached the West in the twelfth century. His book was based mainly on Ptolemy’s astronomy and Aristotle’s physics, and it became very popular in the middle ages. Most of his work survives only in Latin, and the Irish manuscript is the only known translation into a vernacular language [8]. His writings have been translated into English by Dykes [9], where the treatise on astronomy has 28 sections. The Irish Tract has 40 (or 41) chapters, 27 (or 28) of which correspond approximately to sections of Messahala. Thirteen chapters in the Tract are not present in the Latin version of Messahala. According to Williams [5] (p. 26) they are probably derived from Aristotle’s De Caelo and Meteorologica and De Plantis (fourth century BC) and from other classical authors such as Eratosthenes (276–194 BC), Posidonius (135–51 BC), Strabo (63 BC–AD 23), Pliny the Elder (AD 23–79), Cleomedes (ca. AD 200) and the early-medieval Isidore of Seville (AD 560–636). Chapter 7, in which the sun illusion is discussed, is one of the chapters that is not a direct translation of Messahala.

3. Contents of Chapter 7: ‘The Rotundity of the Earth and the Knowledge of Day and Night’ The author’s main purpose was to prove that the Earth is a globe and not flat. We give only a summary of his arguments but quote the passage about the sun illusion in full. The Earth is a globe and not flat. If it were flat, water would not run from place to place, but would form a large sea on its surface. Additionally, if it were flat, you should be able to see the same stars from the north and south parts; but the convexity of the Earth conceals the sky behind you and reveals different stars in front of you. As the sun travels round the Earth it illuminates half of it, causing daylight, while the other half is in darkness. The Earth is a globe, and wherever people stand, their heads are up and their feet down. If the Earth were flat, the sun would appear small when rising in the distance, and large when nearer overhead; but the sun appears of equal size in all directions. A diagram can be constructed (Figure1) to show the Earth as a globe and the sun travelling around it and equidistant from it at all locations. E is the centre of the globe, A is the west, B the top and C the east. The sun (SOL) is represented by a small circle, which has the same size at all locations. Vision 2019,, 3,, x 39 FOR PEER REVIEW 3 3of of 5 5

Figure 1. The Earth is a globe and the sun (SOL) is equidistant at all locations. (Reproduced from FigureWilliams 1. [The5]). Earth is a globe and the sun (SOL) is equidistant at all locations. (Reproduced from Williams [5]). The author goes on to deal with the objection that the sun appears larger when rising or setting: “WhoeverThe author should goes declare on to as deal an argument with the objection against this that that the the sun sun appears appears larger distinctly when larger rising when or setting: rising “Whoeveror setting thanshould it doesdeclare at theas an highest argument point against at mid-day, this that and the that sun it is appears understood distinctly from thislarger that when it is risingfurther or away setting at mid-day,than it does than at whenthe highest it is in point those at other mid-day, quarters, and and that that it is this understood proves that from the this earth that is ita levelis further plane away without at mid-day, convexity, than I reply when to it him is in appropriately, those other quarters, in giving and a solution that this for proves that argument, that the earththat that is a often level happens, plane without but not convexity, always, and I reply when to it doeshim happenappropriately, the reason in giving is—when a solution the sun for is rising that argument,or setting, itthat draws that upoften the happens, moisture but and not the always, rain and and black when wet it vapoursdoes happen rise to the a greatreason height is – when between the sunus and is rising it, and or then, setting, when it wedraws look up at the sun,moisture thatmist and whichthe rain is seenand broadensblack wetand vapours amplifies rise theto a sphere great heightof vision between within us it, and therefore, it, and accordingthen, when to we the look denseness at the sun, and that materiality mist which of that is seen mist, broadens does the and sun amplifiesappear larger the sphere through of it,vision than within it would it, appeartherefore, without according thatmist to the being denseness present. and As materiality the day advances, of that mist,and the does sun the is sun at its appear highest larger point through of the firmament it, than it withwould no appear mist between without us that and mist it, then being we present. see it with As theits ownday properadvances, size. and the sun is at its highest point of the firmament with no mist between us and it, thenThe we example see it with is clearly its own illustrated proper size. in the case of the naked person under water, because he appears largerThe to theexample sight underis clearly water illustrated than out ofin water;the case although of the therenaked is person no proof under in that, water, except because the fact he of appearsthe wet denselarger waterto the spreadingsight under and water amplifying than out the of sight, water; and although preventing there it is from no proof passing in directlythat, except and thenaturally fact of towardsthe wet thedense person. water The spreading same reason and ampl is theifying cause the of ansight, object and appearing preventing larger it from and passing thicker directlythrough and glass naturally than otherwise. towards Consequentlythe person. The old same people, reason who is are the losing cause theirof an sightobject so appearing that they cannotlarger andread thicker small letters,through use glass glass than spectacles otherwise. to Consequently magnify the letters old people, they read, who andare losing for the their same sight reason so that the theysun appearscannot read larger small in the letters, early use morning glass spectacles and in the to evening magnify than the le attters mid-day, they read, as I haveand for mentioned.” the same reason(Translation the sun Williams appears [5 ]).larger in the early morning and in the evening than at mid-day, as I have mentioned.”The text (Translation goes on to add Williams that if the [5]). Earth were a level plane, people living in the east should see the sun risingThe text in thegoes east on asto aadd large that mass if the but Earth setting were in thea level west plane, as a smaller people mass; living but in the people east living should in see the thewest sun should rising see in itthe small east when as a large rising mass but large but setting whensetting. in the west Similarly, as a smaller for people mass; living but inpeople the east, living the infirst the half west of should the day see should it small seem when shorter rising than butthe large second when half; setting. and Similarly, the other wayfor people around living for people in the east,living the in first the half west. of Athe diagram day should illustrates seem shorter this point than (Figure the second2). A half; straight and linethe other shows way places around on thefor peoplesurface living of the in Earth the west. (AITCHI A diagram NA TALMAN illustrates in Irish).this point A represents (Figure 2). an A easternstraight community line shows (CIVITASplaces on theORIENTALIS surface of inthe Latin) Earth and (AITCHI B a western NAcommunity TALMAN (CIVITASin Irish). OCCIDENTALISA represents an ineastern Latin); community C is sunrise (CIVITASand D sunset; ORIENTALIS E is mid-day in Latin) for the and eastern B a western place and community F mid-day (CIVITAS for the western OCCIDENTALIS place. For the in easternLatin); Cplace, is sunrise the time and forD sunset; the sun E tois reachmid-day to mid-dayfor the east (Cern to E)place is much and F shorter mid-day than for thethe timewestern for itplace. to reach For thesunset eastern (E to place, D); and the the time other for the way sun around to reach for theto mid-day western (C place. to E) This is much is clearly shorter untrue, than the and time the sunfor itsets to reach at diff sunseterent times (E to inD); di andfferent the places.other way around for the western place. This is clearly untrue, and the sun sets at different times in different places.

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Figure 2. Flat Earth showing places in the east (A) and west (B). (Reproduced from Williams [5]).

4. CommentsFigure 2. Flat on Earth the Text showing places in the east (A) and west (B). (Reproduced from Williams [5]). The Irish author’s main purpose was to discredit the belief that the Earth was flat, and to show 4. Comments on the Text that it was a globe. Belief in a flat Earth was outdated, and most people knew that it was a globe [10]. PlinyThe in hisIrishNatural author’s History main, 2.64purpose [11] saidwas thatto discredit it was common the belief knowledge, that the Earth and was Isidore flat, madeand to similar show thatcomments it was (aEtymologies globe. BeliefIII. in xxxii; a flat XIV,1) Earth [ 12was]. Theoutdated, Tract repeats and most some people stock knew arguments that it against was a aglobe flat Earth. [10]. PlinyFor example, in his Natural Martianus History Capella, 2.64 (AD[11] 360–428)said that wroteit was a common popular textbookknowledge, [13] and which Isidore included made a chaptersimilar commentson ‘geometry’ (Etymologies (measuring III. the xxxii; Earth). XIV, He 1) made[12]. The the Tract points repe (sectionsats some 590–595) stock thatarguments the rising against and setting a flat Earth.times ofFor the example, stars, and Martianus the hours Capella of daylight, (AD vary360–428) on di ffwroteerent a parts popular of the textbook Earth; that [13] constellations which included can abe chapter hidden on by ‘geometry’ the curvature (measuring of the Earth; the andEarth). that He eclipses made ofthe the points sun or (sections moon can 590–595) be seen that in some the rising parts andof the setting world times and notof the in others.stars, and Martianus the hours was of probably daylight, copying vary on Pliny different (Natural parts History of the, 2,Earth; 162) that [11]. constellationsThe Irish author can probably be hidden also by usedthe curvature other parts of the of Messahala, Earth; and whothat eclipses argued thatof the water sun or flows moon round can bethe seen orb in of some the Earth parts (Section of the world 5) and and that not the in celestialothers. Martianus bodies rise was and probably set at di copyingfferent times Pliny for(Natural cities Historyon different, 2, 162) parts [11]. of The the EarthIrish author (Section probably 11). The also diagrams used other in the parts Irish of Tract Messahala, for this chapterwho argued were that not waterdirectly flows copied round from the any orb of of the the LatinEarth texts (Section of Messahala 5) and that and the maycelestial have bodies been addedrise and by set the at authordifferent to timeshelp students for cities understand on different the parts text of [8 ].the Figure Earth1 is(Sec welltion drawn 11). The and diagrams is similar in to the other Irish diagrams Tract for in this the chapterMessahala were text. not Figure directly2, oncopied the other from hand,any of is the less Latin clearly texts written of Messahala and contains and may both have Latin been and added Irish bytext. the The author diagram to help reproduced students hereunderstand has a corrupt the text text [8]. and Figure should 1 is probably well drawn read and ‘line is aigthe similar na to talman’ other diagramsmeaning ‘linein the of Messahala the surface text. of theFigure Earth’ 2, on (Patricia the other Kelly, hand, personal is less communication).clearly written and The contains diagram both is Latinalso unconventional and Irish text. The by modern diagram standards reproduced in placing here has east a corrupt to the left text and and west should to the probably right, which read is‘line the aigtheopposite na oftalman’ Figure meaning1; it does, ‘line however, of the agreesurface with of the the Earth’ order (Patricia suggested Kelly, by the personal letters incommunication). the text, and it Thealso diagram agrees with is also the unconventional order in some diagrams by modern in Messahala standards [in9] (pp.placing 256, east 266). to the left and west to the right,Many which later is the authors opposite continued of Figure to 1; assert it does, that however, the Earth agree was with a globe. the order These suggested included theby the Venerable letters inBede the(c. text, 672–735) and it also [14] (pp.91–93),agrees with the the Irish order saint in some Fergal diagrams or Vergilius in Messahala of Salzburg [9] (700–784) (pp. 256, [15 266).], and John of SacroboscoMany later who authors wrote continued his tract aroundto assert 1230 that [ 16the] (p.Earth 119). was a globe. These included the Venerable Bede The(c. 672–735) discussion [14] of (pp.91–93), the sun illusion the Irish was ofsaint secondary Fergal or interest Vergilius to the of author, Salzburg who (700–784) only brought [15], and it in Johnto explain of Sacrobosco the apparent who enlargementwrote his tract of around the sun 1230 near [16] the (p. horizon. 119). It was essential for the argument againstThe a discussion flat Earth that of the the sun sun illusion should bewas at theof second same distanceary interest and to thus the subtend author, thewho same only angular brought size it inat to all explain locations the in apparent the sky. enlargem A brief explanationent of the sun of thenear apparent the horizon. enlargement It was essential at the horizon for the argument would be againstsufficient a flat for theEarth purpose, that the and sun the should popular be at refraction the same account distance probably and thus seemed subtend adequate. the same There angular was sizeno need at all to locations expand onin the alternative sky. A brief explanations. explanation of the apparent enlargement at the horizon would be sufficientThe author for ofthe the purpose, Tract was an notd the alone popular in ignoring refraction other account explanations probably of the seemed sun illusion. adequate. Like There many wasauthors, no need he simply to expand copied on thealternative most common explanations. account found in other textbooks without reading more widely.The Even author today of the most Tract people was believe not alone that in the ignoring enlargement other isexplanations an optical e ffofect the caused sun illusion. by refraction, Like manyand this authors, is repeated he simply in popular copied science the most notes common [4]. account found in other textbooks without reading more widely. Even today most people believe that the enlargement is an optical effect caused by refraction,Acknowledgments: and thisI is should repeated like toin thank popular Ellen science Beard, Patricianotes [4]. Kelly, Betty Knott, Ros Mitchell, John Purser and Loek Schönbeck for helpful comments on a draft of this paper.

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Conﬂicts of Interest: The author declares no conﬂict of interest.

References

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