A and B, A person without strong eye dominance sees the reflected eye looking straight back at itself and ignores the misaligned image seen by the other eye. C and D, A person with a strongly dominant right eye sees the images of the reflected eyes from the vantage point of the dominant right eye, therefore perceiving turning out of the reflected left eye. The camera flash was turned on to highlight the apparent misalignment of the image of the reflected left eye via decentration of the corneal light reflection.
A and B, The setup used to take the photographs in Figure 1. The camera icons indicate the vantage points from where the photographs were taken. The diagrams are not to scale. C, Calculation of the angle of apparent exotropia when the subject is 16.5 cm from the mirror and the interpupillary distance is 6 cm; this is drawn to scale. LE indicates the left eye; LE’, the reflected image of the left eye; RE, the right eye; RE’, the reflected image of the right eye.
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Shakarchi AF, Guyton DL. A Geometric Analysis of Eye Dominance Suggesting That Rembrandt and Leonardo da Vinci Had Straight Eyes After All. JAMA Ophthalmol. 2020;138(1):101–102. doi:10.1001/jamaophthalmol.2019.4603
Rembrandt Harmenszoon van Rijn and Leonardo da Vinci drew their own eyes with exotropia (with 1 eye turned outward). Using relative decentration of the irides within the eyelid fissures, Livingstone and Conway1 analyzed 36 self-portraits by Rembrandt and showed that, in all but 1, he drew 1 eye looking at the observer with the other eye turned outward. One-third of the self-portraits were etchings, and printed images from these would be flipped horizontally. One eye appeared straight in the paintings, and the contralateral eye was straight in the etchings. Therefore, the authors1 concluded that Rembrandt had unilateral exotropia. Tyler2 used a similar technique and demonstrated exotropia in 6 artworks attributed to Leonardo or others thought to have used Leonardo as a model.
However, manifest exotropia was apparently never documented in these artists who were well known in their time. We propose that a unilaterally strongly dominant eye can explain this apparent unilateral exotropia.
In drawing a self-portrait, a straight-eyed artist looks closely at each eye in a mirror to reproduce it in detail. When looking at one’s own eyes in a mirror, an individual can look at only one eye at a time. This eye sees its own reflection looking right back, appearing exactly straight. However, the other eye sees the first eye as exotropic, because it views it from an angle. Most people do not have strong eye dominance, and the human brain has naturally learned to favor the image in the mirror that is looking back at the viewer and disregard the apparent misalignment seen by the other eye, such that individuals will always see a straight eye when looking at the reflection of either eye. However, this is not the case in individuals with strong eye dominance, as previously reported.3 They see the image from the vantage point of their strongly dominant eye. A strongly dominant right eye sees the reflected image of the left eye as being turned out when in fact no true turn out exists and vice versa for a strongly dominant left eye.
We formalize this concept through photographs, diagrams, and a simple trigonometric equation. This study did not constitute human subjects research, and therefore neither institutional review board approval nor informed consent were relevant.
The lack of strong eye dominance is illustrated in Figure 1A and B and diagrammed in Figure 2A. The image that an individual with a strongly dominant right eye would see is shown in Figure 1C and D, and diagrammed in Figure 2B.
The degree of apparent exotropia depends on the distance between the individual and the mirror and the distance between the 2 eyes:
For example, a strongly dominant right eye will see the reflected image of the left eye turned out about 10.3° when the viewer is 16.5 cm from the mirror and the interpupillary distance is 6 cm (Figure 2C).
Strong eye dominance is a more plausible alternative than constant misalignment to explain the apparent exotropia in Rembrandt’s self-portraits, because the portrayed deviation did not increase over his lifetime4 (exotropia usually increases over time). In addition, there is no historical record of such misalignment.
Three of Leonardo’s 4 paintings and sketches mentioned by Tyler2 display exotropia, suggesting that Leonardo may also have had strong eye dominance. Curiously, Tyler also mentions 2 sculptures attributed to Leonardo’s master and hypothesizes that Leonardo modeled for these. While the sculptures have an apparent exotropia, it is not known whether Leonardo actually modeled for them. Furthermore, making the eyes exotropic in sculptures may have been an artistic trope to give the impression of the sculpture looking back when viewed from different directions.5 This argument would not apply to portraits, though, which are drawn on a flat surface.
In conclusion, Rembrandt Harmenszoon van Rijn and Leonardo da Vinci probably had straight eyes. A strongly dominant eye may have caused them to perceive the reflection of the opposite eye turning out when looking in a mirror, resulting in the apparent ocular misalignment in their self-portraits.
Corresponding Author: David L. Guyton, MD, The Wilmer Eye Institute, Ste 233, The Johns Hopkins Hospital, 600 N Wolfe St, Baltimore, MD 21287-9028 (email@example.com).
Published Online: November 27, 2019. doi:10.1001/jamaophthalmol.2019.4603
Conflict of Interest Disclosures: None reported.
Additional Contributions: We thank the individual depicted in Figure 1 for granting permission to publish this information.
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