Understanding vision and “places for viewing”

In the late 6th century BCE, theatres appeared as separate buildings, and in the course of antiquity, especially from the 4th century BCE onwards, they increasingly became part of the standard facilities in many cities. The term “theatre” per se shows its connection with vision; the ancient Greek word θέατρον (théatron) literally means “place for viewing”.

Euclid was a mathematician who lived and worked in Alexandria in Egypt around 300 BCE. Very little is known about his life. One of his writings is Optics. This text comprises about 10,000 words with accompanying diagrams, i.e. about 30 A4 pages. In this work, Euclid deals with vision, in particular the contrast between reality and perception.

His understanding of subjective vision is not self-evident, but part of a longer development.

Euclid's Optics — reality vs. perception

Although Euclid deals with different topics in his work, they are linked by the contrast between reality and perception.
Parallel lines, such as those of a road, seem to converge in the distance, although their distance to each other, i.e. the width of the road, does not change. Today we know this phenomenon as vanishing-point perspective.
Even successive, equal distances appear smaller when viewed from a greater distance. This is the case, for example, with rows of columns where the spacing of the columns does not really change, but we perceive the columns in the distance with a decreasing space between them.
Euclid does not work directly with a street or a portico but abstracts these observations into geometric proofs.

  • A street with a colonnade of columns in ancient Gerasa, Jordan.

  • Diagram from Euclid’s Optics. K stands for the observer’s eye.

  • Diagram from Euclid’s Optics. K stands for the observer’s eye.

In the eye of the beholder

We can explore the extent to which visibility in theatres was actually acquired for individuals by analysing visual fields, for example. Our visual fields with both eyes cover about 120°. Like Euclid, we can thus construct the area that was visible to the individual spectators with “visual rays” starting from one point. We can also determine which area in the theatre could be seen best: that is the centre of the orchestra.

Theatres were not only used for performances, perhaps because of the perfect viewing conditions. Especially from the 4th century BCE onwards, they were also used for people's assemblies and court proceedings. We learn from ancient sources that speakers sometimes presented themselves “like tragic actors”.

  • A spectator's visual field.

  • Visibility analyses show to what extent certain areas are visible.


  • “Seventy per cent of all archaeology is done in the library.” - Indiana Jones in Indiana Jones and the Last Crusade.

  • For our current research, we mainly “dig” through manuscripts and previous studies.

  • In addition to desk-based research in the library, fieldwork is essential in order to investigate previously unnoticed aspects, for example.

Vision today

That can be seen

As a result, we can show that the idea of vision changes in antiquity as well as the design of urban architecture, for example a theatre. We still use Euclid's idea of visual rays today. Scientists can use eye tracking, for example, to investigate what we see and what we focus our attention on (red). This is particularly important in advertising. About 2300 years ago, Euclid already laid the foundations for the present-day concept of vision. Even when we go to the theatre or the football stadium today, we benefit from developments that began c.2500 years ago to give spectators a perfect view of the performances.