Secrets of the horizon: A case for ecological optics

Richard Grafton
4 min readJul 18, 2022
Photo by Joshua Earle on Unsplash

Staring out into the distance you may be forgiven for letting your mind wonder at the infinite abyss laid before you. Or perhaps not. But this simple act might just be the hidden key to perception.

To understand why we must first question our philosophical place in the world — especially when we start to wonder what ‘us’ actually is and what the ‘world’ seems to be. In contemporary psychology there is a tenancy to keep a clear separation between these two things, which has long led to philosophical dichotomies which dominate our school of thought: subject vs object, inner vs outer, mind vs matter.

For example, in cognitivism (an information-processing account of cognition) the world is a meaningless lump of mass which we can sense but not directly understand. To extract meaning our minds must process these raw sensations into something meaningful— either through past experiences or predictions about what we might sense in the future. And, once we’re done with this, we can then project meaning back out onto the world.

Oh look, a cat.

In this cognitivist universe our subjective, inner world conceived through the mind is separate from the objective, outer world made of matter. But what if this was not so? Although this is a strange question, it forms the basis of ecological psychology: a radical school of thought made popular through the psychologist J.J.Gibson.

In ecological psychology there is no need to separate the subject and the object. There is no inner world vs outer world and nothing is purely mental or physical. Instead the world is made up of affordances — meaningful relations (or properties — but we won’t get into that) between an animal and its environment. These affordances manifest though an array of optical stimulus information which is co-constructed though an inseparable animal-environment pairing. Furthermore, affordances are directly perceived, so require no internal representations or mental processing. Instead the information found in the structure of optical stimulus information (which manifest as affordances) is enough to guide our behaviour.

This is all beginning to sound very clever, but what’s it actually got to do with staring out towards the horizon? Well, that’s where H.A. Sedgewick enters the story. In 1973 Sedgewick published his PhD thesis which built upon Gibson’s work on ecological optics (that’s the optical stimulus stuff). The thesis explores the relationship between the visible horizon and the size (and distance) of objects. More specifically, it provides a mathematical description of an invariant relation between our perception of the horizon and the size of objects. In other words, and perhaps surprisingly, the horizon directly specifies information about the relative size of objects in our field of view:

“Assuming the horizon of the group plane to be at a very large, effectively infinite, distance, the the line of regard to the horizon is effectively parallel to the ground. The perpendicular distance between the ground and the line of regard to the horizon is thus always the same and is always equal to the height of the eye above the ground. This establishes a scale factor across the entire ground. For any object resting on the ground, the portion of the object below the horizon is equal to the eye height”. [2]

This relation can be expressed though simple trigonometry to form the horizon-ratio relation, illustrated below:

Source: [3]

where the ratio y/e = (tanγ + tanθ) / tanγ. In more verbose terms:

“The height of the object (y) is specified relative to the eye height (e) by the ratio of the visual angle of the whole object (β) to the visual angle of that portion that is below eye level (γ).[3]

This simple trigonometric relation is profound not only because it enables us to specify the height (and distance) of objects in the world around us, but also because it enables us to understand the world in intrinsic units. That is to say when we perceive the world we don’t perceive arbitrary units like meters or feet. Instead we use our embodied self as a perceptual ruler — in this case calibrating to units of eye height.

But whilst this is all well and good there’s an obvious problem: what if you can’t see the horizon? What if it’s blocked by tall buildings or you are indoors? Doesn’t the horizon-ratio then become meaningless?

Perhaps not.

Although the visible horizon may not always be explicit in our field of view, the geometric convergence of points from an observers perspective can implicitly specify it, as shown below:

Source: [1]

So as we have seen though Gibson’s ecological optics and Sedgewick’s horizon-ratio, meaningful relations between us and the world need not be separated by classical dichotomies. In fact, meaning exists in our embodied relationship with the world and is directly specified in the convergence of optical structures. Meaning can therefore emerge equally a fact of the subject and object, of mind and matter, and without the need for an inner or outer world.

So ponder on that the next time you’re staring out into the infinite abyss.

References

[1] Sedgwick, H.A., 2021. JJ Gibson’s “Ground Theory of Space Perception”. i-Perception, 12(3), p.20416695211021111.

[2] Sedgwick, H.A., 1973. The visible horizon: A potential source of visual information for the perception of size and distance. Cornell University.

[3] Warren, W.H., 1995. Constructing an econiche. In Global perspectives on the ecology of human-machine systems (pp. 210–237). CRC Press.

--

--