Science1 publisher3 min readPublished
All 12 of the Parthenon's claimed optical corrections fail an Oxford mathematician's audit
Alain Goriely worked through the refinements one at a time and found that either nobody has demonstrated the illusion or the effect is too small to see, and the earliest claim of intent postdates the temple by 400 years.
The Scientist · Science desk
What happened
- A mathematician at the University of Oxford, Alain Goriely, went through 12 proposed optical corrections in the Parthenon and found each one either unsupported by evidence or too small to be perceptible under typical viewing conditions.
- The largest claim covers the upward curve at the middle of the stylobate and the entablature, held to stop those horizontals looking as though they sag, and Goriely calculates that a viewer would perceive no sagging.
- Also on the list are the slight bulge at mid-height of the columns, said to stop them looking pinched, and the thicker corner columns, said to offset the stronger light at the building's edges.
- The competing explanation for the curve, that its small gradients drain water and stop puddles forming, was put forward long ago and dismissed in the 1800s.
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Why it matters
- precedent The same upward curve appears in other Greek temples, so the standard of evidence applied here is now available wherever that curve is read as a deliberate correction.
- constraint A calculation can show that an illusion does not occur without showing what the builders wanted, and Goriely says the thinking behind the construction cannot be known definitively.
- contradiction Goriely says the illusion story was never universally accepted among experts even as it became the standard account, which makes the consensus a weaker thing to cite than its ubiquity suggests.
An optical-correction claim has two halves that can be checked separately: the deviation cut into the stone, and the perceptual error it is supposed to cancel. The deviations are not in dispute. The temple is 69.5 metres long and 30.9 metres wide, and although it appears straight it has almost no straight lines or right angles [2]. The standing hypothesis is that the builders expected straight lines to look curved, so they built curves to make the building look straight [3].
Goriely, at the University of Oxford, said it is widely accepted that the temple was made this way on purpose, but that there is strictly no evidence the refinements in the Parthenon actually produce the proposed visual illusions [4]. His objection concerns what happens when a two-dimensional argument is worked out in three dimensions with a viewer in it. "There are certain effects such as the Hering illusion that, on paper, would give qualitatively the same direction of effect, but if you actually do the computation, you realise that the effect does not appear," he said. "And although it might work on paper, the effect in the real 3D building with an observer is completely different." [9]
For the columns, the record is thinner still. Goriely says no pinching illusion has ever been scientifically demonstrated, even in controlled tests using three-dimensional reconstructions of temples [17]. His alternatives are mundane: builders may have thought curved columns more pleasing than straight ones, curvature improves resistance to buckling, and a corner column carries a slightly heavier load [18]. "If the columns do get narrower at the top, that could be to make them seem taller, or just because, for stability, one wants a base thicker than the top," said Marge Livingstone, a neuroscientist at Harvard Medical School who studies visual perception [19].
Livingstone also said of the curved floor: "I think it must have been for drainage, just like on roads." [12] The surface at issue is large. The 69.5 by 30.9 metre plan works out at a footprint of about 2,150 square metres [24]. John Senseney at the University of Arizona in Tucson puts the cause in the building process, saying the curvature throughout the building is a consequence of the curve of the platform on which it was built [13]. "The refinement of convex curvature is an extraordinarily sophisticated product of the expert knowledge, judgement, tools and techniques of common and, often, enslaved labourers working collaboratively on site," he said, adding that the curvature "is not a product of an intended optical correction" [14].
The earliest surviving statement of intent is not Greek. Goriely says the first mentions of the Parthenon being designed with optical illusions in mind come from Vitruvius's De architectura, written some 400 years after the temple [21]. Since the building went up in the 5th century BC [1], that dates the claim to roughly the first century BC [23]. Ancient Greeks knew visual illusions existed, Goriely says, but there is no evidence they built the Parthenon to counteract the ones usually cited [20].
The calculation is about the effect. Whether the builders were aiming at an illusion is a separate question, and one no computation can reach, because a refinement can be deliberate and still fail to do what its maker hoped. Goriely says the ideas took hold so strongly because they capture the imagination [22]. The New Scientist report does not name a journal for the analysis or the viewing distances it assumes [25].
What to watch
- Whether the calculations appear in a peer-reviewed venue with the assumed viewing distances and perceptual thresholds stated.
- A controlled perceptual test with human observers and three-dimensional temple reconstructions that either shows the pinching illusion or does not.
- A measurement of how much water the stylobate gradients actually shed, which would put the drainage account on evidence.