It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a player must aim a cue ball at a given point to make it bounce off the table edge and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in. He used his result on sums of integral powers to perform what would now be called an integration , where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid.
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As will be discussed in this paper,this methodologyalsocontributesto our burgeoning understanding of visualliteracy. Historic Theoriesof Vsion During the first two centuriesofthe IslamicGoldenAge 8th-1Jth centuries , translationof ancientwritingson the scienceof opticsofferedcontemporary in- tellectualswith variousphilosophicaltheoriesof vision. He is primarily known however, for his writings on geometrical optics, astronomy, and mathematics.
This seminal work initiated an unbroken chain of continuous development of the modern un- derstanding of both optics i. From a copy othis Kitab al-Manaztui [ A. Ill Frc. Prior to thework oflbn al-Ha1tham,theoriesofvisioncouldbebroadlyclas- sifiedinto oneofthree categories: extramission, intromission,or a combinationof the two.
Extfamissiontheoriesrequirethat somesort of illuminatingparticlesbe emittedby the eye. Euclid and Ptolemyarewell-knownscholarsassociated with this category Linberg, Althoughthereareobviousflawswith extramrssron theories,they do get the geomery right, with a one-to-onecorrespondence be- tweenpointson the objectandpointson the eye.
Intromissiontheories,with Ar, istotleasa prominentproponent,postulatedthat objectscontinuouslysloughed off microscopically thin replicasof themselvesthat then travelledto the eyeof the observerIntromissiontheoriesavoidsomeobviousproblemsof extramission theories,suchasnearandfar objectssimultaneously beingvisiblethe momentthe eyeis opened.
A third alternative,supportedby Platoand Galen andAristode, to a lesserdegree ,combinesthe trvotheories,proposingthatlight emittedby the eyeengages in somewaywith the interveningair and aforementioned replicas,or species Lindberg,1, , ,.
Like othersbefore him, Ibn al-Haltham also recognizedthat therewere problemswith all existingtheoriesof vision,but he viasuniquelysuccessful in findinga solutionthat hadeludedthe bestmindsof antiquity. He proposeda type C. Perhapsmost inrportantly, they provided him a theoreticalbasisfor the existence of rays; a theoretical construct that he used as a means for describing and inter preting the visualsystem. Leonardo da Vinci also failed to accept this when he ap proached the problem much later Kemp, Smith poir.
Intromissiolr theories howeveq are uniquely Aristotlian. They ascribe to the idea that, "Knowledge is inductive I19 Sensation andits representations arethereforenot to be deprecated asthebearefs of falsehood Platonism but ratherto be prizedasthe bearersof tuth" Smith, ,p. Perhapspredictably,asculturalunderstandings of visionard cognitionex pandedto includethesedisparatetheories,so too did evolvingculturalconsid- erationsfof conceptsseeminglyunrelatedto the scienceof optics,the impactof whichwasnot relegatedto the sciencecommunityalonebut spreadout to include the humanitiesat large.
Smith recognizes that variationsexist amongthe Latin versionascomparedwith theArabicoriginal,not simplyin its organizarion- al sructurebut in theinterpretationof specificterms From thebeginning, however,knowledgeof the coreprinciplesand experiments detai. It wasrequiredreadingat the Universityof P arisin ,avatlable in the universitylibraryof the Sorbonne by ,and usedwidely as referencematerialat Oxford, Cambridge,Canter- bury andMerton Collegeby the mid-fourteenthcentury Holbrook, Although today we thhk of these scholarsas optical scientists, they approachedtheir work astheologians which, in turn, influencedtheir interpretationof medievalopticaltheories.
Bacon,for example,wasa Franciscan friaq who ftansmittedhis scientificmanuscripts to the Papalcourt in semecy Smith, Pechamand rVitelo werepriestsaswell, who relied on Ibn al-Haythamin constructingtheir own evolvingopticaltheo- ries,but who alsotook libertieswith their interpretations and infusedthemwith spiritualundertones. The natureof light, vision and cognirionare so directlylinked with onto, logicalaspectsof the humanexperiencethat they alsoappealto considerations beyondthe scientific.
As the encyclopedic andmonastictraditionsof scholarship C. Popular literary examples published during this period illustrate just how widespread the interest and understanding of optics had become.
Ibn al-Hay- tham, for example, is referred to severaltimes in the epic poem Roman de la Rose lRomance of the Rose] by Guillaume de Lorris and Jean de Meun, one of the most widely read works in the French languagefor yearsafter its publication in c flardi, In the text the authors descdbethe properties ofmirrors, with the text exhibiting a surprisingly non trivial understanding of optics. NeCastro,, p. As Greenstein ,p. It makes useof suchfundamentalAristotelianconceptsas form, substance, accident, quaiity,individual,universal,species, andwhatness.
Art and optics What influence perspectivist theories of vision had on the visual arts lead, ing up to and throughout the Renaissance,however, has yet to reach a consen- sus among scholars. He further states, "If one can believe Rafaello Maffei, the ancient scienceof Alhazen and Vitellio now included artistic applications and was almosr identified with the fine arts" Klein, ,p. Kemp remains cautious of considerationsthat C.
WdntzAllen superimpose perspectivist theories of vision directiy upon the development of linear perspective or visual transitions in the visual arts. Green stein , p. Kemp ,p. For example,thatAlberti is explicitabouthavingcomposed, On Paintingfor artistsanddemonstrates indifferenceto debatesaboutwhich directionvisualrays might reachthe eyeof the viewer,i. Subsequendy, Alberti focuseshis at- tention insteadon conceptsrelativeto spatialdispositionand composition,and how thesetwo principlesaretranslatedandreorientedasobjectson a two dimen- sionalpicture plane.
In short,Alberti wasthe first to interrupt in writing the visualpyramidby placingthe canvasperpendicularto the visualrays,specifically at the vertex of the pyramid. Howeveqthe latter certainlyinformed the former Arnheim,;Kemp Ghiberti certainlyhad access to a 14,bcenturyItalian translationof Ibn al-Haytham,giventhat entireportionsof it areincorporatedin Book3 of his Commentari Fragenberg, ;Greenstein, ,etc. Given the progressionof eventsoutlined throughout the preceding sections it seemsunusual that an artist like Alberti was so familiar with the perspectivisr tradition, and yet so little is known about how he arrived at the principles oflinear perspective.
Nevertheless,a clear languageofvisual literacy has been established, beginning most significantly with the work of Ibn al Haytham and culn.
Conclusion Consideration of the lineage of medieval optical theories leading up to and throughout the Renaissanceis necessaryfor understanding the methodology Hockney and Falco developed,centurieslater, for analyzingwell known Europe an paintings, as well as the larger impact of the perspectivisttradition as it relates to realist image production. This methodology is one based on a framework of visual understanding, i.
Readingspace, in short,is far moreintellectualthanit is tactile Smith,,p. That the mind of a painter is as intrinsically involved in the oeative process, asis his hand in creatingpaintings,makesoriginal works of art highly complex sub jects to analyze. Hockney and Falco however,demonstratedthat optical evidence existswithin the visual compositionsof certainpahtings.
This evidenceis therefore subjectto visual qualitative aswell asoptical quantitative interpretation. As a coDsequence,humans do not simultaoeouslysee part of a scene in focus and part of it out of focus. Although modeln humiurs have obscrved the effect of scenesdepictcd out of focus countlesstinres in the form of photographs,in novics, and on televisior. IIence, a simple example of the indirect use of optics is if an artist has pair. Falco, A. Additionally, lack of detailed understanding of optics and the history of optics continues to affect interpretation of historic realist images.
For example, despite documentary evidence showing that concavelensesand mirrors of high enough quality were availablein the first quarter of the 15thcentury Ilardi, , such evidencehas done little to achievewide acceptanceby historians that a con- cave mirror can, in fact, project useful imagesfor artists Campbell, Syson,Falo- mir.
This unique ap- proach for analyzingworks of art is within the long, interdisciplinary,progression towards a new visual language;one historically informed by the scienceof medi eval optics, but put into action by visual artists during the Renaissance. Acknowledgements We gratefully acknowledge David Hockney for his invaluable insights on painting through his investigation of over years of European arr. Br cnelles.
Renalssance fate:;:YanE"lckto Tiian, exhi bition catalog. London: National Gallerv ofArt. Eocmrou Sauurl fn. Amira, A. Bouridane,and F.
Kurugollu Ed. Ir TVleal? National Grllerv oI Ireland. Hocrrrv D"ri,ri, Fo. Inrot VtNcexr l20Ai. RegarJmg bf the da Vincis separation terms "DersDective inadebv nature" verses pi. ColleeeArt Association. TheyaleDictianaryof Art and Arttts. YaleUnivesitv Press. Hi",drrwings and etchingsare among the deftestof this century;posteritymay well ,. Lrxosenc DavD C. TheoriesafYlsionfron Al-Kindi ta Keppler.
Universityof Chi crgo Press. Tholnas Eakins, exhibition catalogue. Phiiadelphia: Philadelphia Museumof Art. Srirrn Marrr A. Nei Series,91 ,1. Neu Se-ies. Day ttds. Handbooko" re. NJ: LaurenceLrl baum. SuLI-lvaNGnapue Thousand Oaks.
Surr-lvarGnaillp ,Rercarchacx in alt pnctice. Studiesin Art Education,48 1 , 1 93 5. Related Papers.
File:Classical spectacular laser effects. This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir The Optics; De aspectibus or Perspectivae and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics. After which we should ascend in our inquiry and reasonings, gradually and orderly, criticizing premises and exercising caution in regard to conclusions—our aim in all that we make subject to inspection and review being to employ justice, not to follow prejudice, and to take care in all that we judge and criticize that we seek the truth and not be swayed by opinion. And those who are engaged upon the quest for anything for its own sake are not interested in other things. Finding the truth is difficult, and the road to it is rough. Light travels through transparent bodies in straight lines only. We have explained this exhaustively in our Book of Optics.
Book of Optics
Vision theory[ edit ] Before the Book of Optics was written, two theories of vision existed. The extramission or emission theory was forwarded by the mathematicians Euclid  and Ptolemy ,  who asserted that certain forms of radiation are emitted from the eyes onto the object which is being seen. When these rays reached the object they allowed the viewer to perceive its color, shape and size. An early version of the intromission theory, held by the followers of Aristotle and Galen , argued that sight was caused by agents, which were transmitted to the eyes from either the object or from its surroundings.