From τὰ φυσικά (ta physika) to physics – X

Optics is one of the major branches of modern physics and it has its roots very firmly planted in Ancient Greece. However, whereas the modern discipline is, to quote Wikipedia quoting the Mcgraw-Hill Encyclopedia of Science and Technology (5^th Ed.) (Mcgraw-Hill, 1993), “the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or dedtect it it” in Ancient Greece optics was the theory of vision or how do we see things. As we will see later in this series the transition from a theory of vision to a theory of the behaviour and properties of light began in the Middle Ages and was completed in the Early Modern Period and is part of the emergence of modern physics

Everybody knows that the Ancient Greeks thought that we saw things because the eyes sent out a sort of fire which sweep the object and sent the information back to the brain. Unfortunately, as with many things that everybody supposedly knows this cliché theory simply isn’t true. Between the Atomists and Pythagoreans in the fifth century BCE and Galen and Ptolemaeus in the second century CE there was an evolving anatomical and physiological tradition of the eye and the treatment of eye ailments, a physical or philosophical tradition devoted to epistemological, psychology, and physical causation, and a mathematical tradition directed principally towards a geometrical explanation of the perception of space.

I shall largely ignore the anatomical and physiological tradition only sketching Galen’s study of the anatomy of the eye later and start with the physical or philosophical tradition, which generated four very different theories of vision. Theories of vision are usually divided between those when something comes out of the eye, extramission theories, and those where something enters the eye, intromission theories. The cliché version of a Greek theory of vision that I mentioned above is an extramission theory. 

The oldest Greek theory of vision was from the Atomists in the fifth century BCE and was an intromission theory.

We only have very scant information of the Atomist theory compiled from fragments and hearsay. These say that the Atomists thought that all objects shed a layer of atoms continuously in all directions; the objects are replenished continually by other atoms. These films of atoms, called simulacra by Lucretius (d. c. 55 BCE), either enter the eye or touch the pupil and enable visual perception. Two very obvious drawbacks to this theory are why can’t we see in the dark if the simulacra are flying through the air continually and how does something as big as a mountain enter something as small as the eye? Because we don’t have a full account of the theory, we don’t have answers to these objections.

Our second philosophical tradition is that of Plato (c. 425–348 BCE) and is the origin of the cliché theory.

Plato holding his Timaeus, detail from the Vatican fresco The School of Athensby Raphael Source: Wikimedia Commons

Once again, we don’t have a full account of Plato’s theory. We do know that it didn’t originate with Plato, but it is not certain with whom it did originate. It has been associated with the Pythagoreans and in particular with the physician Alcmaeon of Croton (fl. 5^th century BCE), who might or might not have been a Pythagorean. Plato praises him for his work on the nature of the eye. An alternative source was Empedocles (fl. 444 BCE) but Aristotle attributes both an extramission and a contradictory intromission theory to him. In the cliché version, Plato is credited with a pure extramission theory, but this is a simplistic version of his actual theory. Plato does hypothesise a fire or light that issues from the eyes, which however coalesces with the sun light, thus avoiding the question why one can’t see in the dark if the fire comes from the eyes. However, there is also some sort of vibration or emanation coming from the visible object as part of the process of visual perception, so a sort of combined extramission-intromission theory. 

As always, after Plato comes Aristotle and the first time that we have a full description of a theory of vision.

Bust of Aristotle. Marble, Roman copy after a Greek bronze original by Lysippos from 330 BC; the alabaster mantle is a modern addition. Source: Wikimedia Commons

Aristotle explicitly rejects both the concepts of the Atomists and Plato. For Aristotle there are no particles or fire involved in visual perception. However, he appears to hold two contradictory views on the topic. In his discussion of the cause of the rainbow in the third book of his Meteorology he talks about natural lines, which are not geometrical lines but physical lines in space. For him “it is clear that the rainbow is a reflection of sight to the sun”, that is lines of sight passing outward from the eyes. A clear extramission theory. 

However, when he discusses visual theory in De sensu and De anima, he presents what is clearly an intromission theory. For Aristotle for visual perception to take place there must be a medium, air or water, connecting the perceived object and the eye. This medium is made translucent by sunlight. For Aristotle what is perceived is not the object itself but colour. The colour vibrates along the transparent medium to the eye. There is then a whole theory of how the perception works once the eye has perceived the colour, which I am not going to go into here. Some modern critics have seen in Aristotle’s vibrating medium theory of perception a precursor to the wave theory of light, but I personally think that the interpretation is a bridge too far.

 Our last philosophical tradition of visual theory is due to the Stoics and as with all things to do with the Stoics revolves around their all pervasive pneuma.  An optical pneuma flows from the seat of the consciousness to the eye and excites the air adjacent to the eye, putting it in a state of tension. Through this stressed air when it is illuminated by the sun, contact is made with the visible object. Although though the three theories are fundamentally different for Plato, Aristotle, and the Stoics the medium between the viewer and the viewed object combined with sunlight is a central ingredient of their theories of vision but that light itself plays the central role is not yet discernible in Ancient Greek theories of vision.

The basic features of the Stoic theory of vision were adopted by the Greek physician Galen (129–216? CE) in his De placitis Hippocratis et Platonis where he discusses the two basic theories of vision, intromission & extramission, and firmly rejects the possibility of an intromission theory. He devotes a lot of space to the transformation of air into a visual medium. 

An 18th-century engraving by Georg P. Busch Source: Wikimedia Commons

There had been earlier physiological studies of the eye in connection with vision, but it was first Galen, who delivered an in-depth study of the anatomy of the eye. His description is not very far removed from a modern one, although the lens is incorrectly in the middle of the eye, but his concept of the eye’s role in vision is fundamentally flawed. He saw the optic nerve as the conduit that delivered pneuma to the eye and he thought that the image was formed in the lens of the eye and this is where vision takes place.

The anatomy of the eye, with an anterior lens (lens location ratio 0.30), according to Hugo Magnus’ interpretation of Galen’s writings. Source

This misconception remained standard optical theory all the way down to the late sixteenth century, when Kepler stated that the lens merely focuses the image onto the retina, which is really where vision takes place.

Turning now to the mathematical tradition the earliest known work on geometrical optics is attributed to Euclid (fl. 300 BCE). There is some doubt as to Euclid authorship of the Optics, because although the methodology is similar to that of his Elements the text is primitive in comparison. Like the Elements the Optics starts with a set of postulates, seven in number, from which fifty-eight theorems are derived:

Euclid’s Optics Latin 1458

Let it be assumed:

1. That rectilinear rays proceeding from the eye diverge indefinitely;
2. That the figure contained by a set of visual rays is a cone of which the vertex is at the eye and the base at the surface of the objects seen;
3. That those things are seen upon which visual rays fall and those things are not seen upon which visual rays do not fall;
4. That things seen under a larger angle appear larger, those under a smaller angle appear smaller, and those under equal angles appear equal;
5. That things seen by higher visual rays appear higher, and things seen by lower visual rays appear lower;
6. That, similarly, things seen by rays further to the right appear further to the right, and things seen by rays further to the left appear further to the left;
7. That things seen under more angles are seen more clearly.^[1]

Central to Euclid’s thinking is the concept of the pyramid or cone of vision, a concept that is still in use today.

Aberti, Della Pittura, Section of the Visual Pyramid and the Picture Plane, 1435 Source

His fitty-eight theorems revolve around the perception of objects relative to the cone of vision, laying down the basic rules of perspective. To quote A Mark Smith:

The resulting analytic focus is almost exclusively upon size perception, distance perception, and shape perception as dictated by the geometrical structure of the visual cone with its constituent rays. The virtue of this approach is its simplicity. By transforming rectilinear lines of sight into rays that funnel out from the eyes to form cones, Euclid was able to account for special perception in a limited by relatively effective way according to the principles of surveying.^[2]

Ignazio (Egnatio) Danti (1536-1586) was an Italian priest, astronomer, mathematician, instrument maker and cosmographer. A versatile scholar, as a young man Ignazio was trained as well as a painter and architect. His interest in perspective is shown in his La Prospettiva di Euclide (1573), in which he supplied the first Italian language translation of Euclid’s Optics and reviewed the work on optics of the third century Greek mathematician Heliodorus of Larissa. As he noted on the title page, at the time he authored this book, he served as cosmographer to Cosimo d’Medici, the Duke of Tuscany

As well as his Optics, Euclid is also considered to be the author of a Catoptrics an attribution that is even more disputed than his authorship of the Optics. Catoptrics is the part of optics concerned with reflection, especially the formation of images by mirrors. In his Catoptrics “Euclid proves theorems on the location, size, and orientation of images in plane, convex, and concave mirrors, and proposes a false theorem on the convergence of rays in concave spherical mirrors.”^[3] 

Like the Optics, the book opens with postulates, six this time not seven, the first two of which are that visual rays are perfectly straight lines and that all visible objects are seen along such straight lines. The third, fourth, and fifth postulates are related to mirrors and strangely the sixth postulate deals with refraction not reflection. This postulate famously states that “if an object placed in a vessel disappears from sight just below the rim when seen from a particular viewpoint, then if water is poured into the vessel while the viewpoint is maintained, the object will come back into view as if by floating upward.”^[4] This is a demonstration that is often carried out today to explain refraction. Euclid derives thirty propositions from his six postulates. 

Like his Optics, Euclid’s Catoptrics is virtually bereft of physical or psychological content because it to focuses on anomalies that can be explained solely by ray geometry.^[5]

Approximately two hundred and fifty years after Euclid, Hero of Alexander (fl. 60 CE) also produced a catoptrics, his Catoptrica. This work only exists in a single Latin translation produced by William of Moerbeke (c. 1225–c. 1286) probably in 1269, and no Greek text is known to exist, it was originally attributed to Ptolemaeus.

In his introduction to the Catoptrica, Hero wrote:

The science of vision is divided into three parts: optics, dioptrics, and catoptric. Now optics has been adequately treated by our predecessors and particularly by Aristotle, and dioptrics we have ourselves treated elsewhere as fully as seemed necessary. But catoptrics, too, is clearly a science worthy of study and at the same time produces spectacles that observe wonder in the observer … The study of catoptrics, however, is useful not merely for affording diverting spectacles but also for necessary purposes.^[6]

His book contains eighteen propositions of which eight are devoted to “spectacles that observe wonder in the observer,” this is optical illusions created with mirrors. 

On a theoretical level Hero “compares visual radiation with projectile motion. Like arrows shot at high velocity, visual radiation follows rectilinear trajectories because, being incredibly swift, it is inclined to travel the shortest distance.”^[7]

He explains the phenomenon of reflection by arguing that unpolished surfaces absorb visual rays, whereas they bounce off polished surfaces such as mirrors because they are dense. Water and glass both absorb and reflect because their surfaces are not universally dense and resistive. 

The way visual radiation rebounds in reflection is dictated by its inclination to travel the shortest possible distance, and in turn necessitates its following the equal angles law.^[8]

Hero’s use of visual rays indicated his indebtedness to Euclid, and he also reproduces three of Euclid’s propositions.

The most significant optics text from antiquity if Ptolemaeus’ Optics but it presents several problems. The text, itself, only exists in a twelfth-century Latin translation by Eugene of Sicily (c. 1130–1202) based on an Arabic manuscript that no longer exists. No Greek manuscript is known. Eugene’s Latin was not very good, so his translation is “somewhat rough and idiosyncratic in style.”^[9] The text is unfortunately incomplete, as, according to Eugene, the Arabic manuscript was. The entire first book is missing, and the fifth book simply breaks off in the middle of a proposition. How much more of book five existed and whether there were further books is simply not known. 

Claudius Ptolemäus, 16th-century book frontispiece Source: Wikimedia Commons

The prologue to Book 2 allows a partial reconstruction of the missing Book 1. Ptolemaeus writes, we learned “everything that one can gather about what enables light and visual flux to interact, how they assimilate to one another, how they differ in their powers and operations, what kind of essential differences characterise each of them, and what sort of effect they undergo.”^[10] Book 2 deals with visual perception in general, according to straight unimpeded visual radiation. Books 3 & 4 deal with reflection and image formation in plan, convex spherical and concave spherical mirrors. In Book 5, Ptolemaeus turns his attention to refraction and here reproduces Euclid’s coin experiment amongst other things. 

Textual evidence shows that the Optics was a late work, written after the Mathēmatikē Syntaxis a text with which it is interrelated. Astronomical observations are based on visual perception and Ptolemaeus was very much aware that atmospheric refraction plays a significant role in the accuracy of observations. Ptolemaeus’ work is very much an amalgam of nearly all of Greek optics; centred around the geometric optics of Euclid he incorporates elements of Aristotle, Plato, the Stoics and Galen. There is one fundamental difference between the theories of Euclid and Ptolemaeus. Whereas for Euclid the visual cone is made up of distinct individual visual rays, Ptolemaeus maintained that the visual rays form a continuous bundle or cone. It is obvious that his work has a strong experimental element, in particular when dealing with refraction, where he attempts to accurately measure the angles of incidence and refraction for visual rays from air into water, air into glass, and water into glass. Ptolemaeus was trying to determine a general law of refraction but failed in this endeavour.

It is notable that all three of the proponents of geometrical optics, Euclid, Hero, and Ptolemaeus, used an extramission theory of visual rays in their work, although it is not clear in the case of Euclid whether he actually believed in extramission or simply adopted it as a mathematical convenience. 

Almost the entire range of Greek theories of vision together with the geometrical optics was past on through the centuries to the Islamic natural philosophers, who would then make substantial contributions and changes to them before they got passed back into Europe in the High Middle Ages. We will track these developments in future episodes in this series.

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^[1] David C. Lindberg, Theories of Vision: From Al-Kindi to Kepler, University of Chicago Press, ppb. 1981 p. 12. This whole blog post is basically plagiarised from Lindberg’s book and A. Mark Smith, From Sight to Light: The Passage from Ancient to Modern Optics, University of Chicago Press, ppb. 2017 both of which I heartily recommend to anybody, who wants to know more about the topic. 

^[2] A. Mark Smith, From Sight to Light p. 53

^[3] Wilbur R. Knorr & Alexander Jones, Catoptrics, Oxford Classical Dictionary, Published online 22 December 2015 https://oxfordre.com/classics/display/10.1093/acrefore/9780199381135.001.0001/acrefore-9780199381135-e-1440

^[4] A. Mark Smith, From Sight to Light p. 56

^[5] A. Mark Smith, From Sight to Light p. 63

^[6] Lindberg, Theories of Vision p. 14

^[7] A. Mark Smith, From Sight to Light p. 65

^[8] A. Mark Smith, From Sight to Light pp. 66-67

^[9] A. Mark Smith, From Sight to Light p. 88

^[10] A. Mark Smith, From Sight to Light p. 77