Have You Ever Seen A Circle?

I was in the shower, looking down at the drain, and it appeared to be elliptical in shape even though I knew it was circular. So I moved my head directly over the drain to appreciate its true circular shape, but I couldn’t quite do it. For one thing, it was not possible to hold my head still enough that I could say for sure that I had seen a perfect circle. Secondly, there was a difference in point of view between each of my two eyes. Each eye saw the drain from a slightly different angle. Only one of them could be directly over the drain. Even repositioning my head with one eye closed, I couldn’t hold still, and anyway, I know that eyeballs always twitch about five times a second as a routine matter, so it was not going to be possible for me to truly apprehend the circular shape of the drain.

I realized that even the most sensitive scientific instrument, mounted exactly above the drain and kept absolutely still, could not measure circularity with zero error. There are probably instruments that can measure to 100 decimal points of accuracy, or better, but not an infinite number of decimal points of accuracy. Anyway, at some point, the measuring instrument would be so sensitive that no human being could calibrate it without error nor read its output without error. Besides, I doubt that the drain is genuinely circular in the first place. At some level of inspection, it surely would be “out of round”. So it became obvious that it was not possible, in principle, for me to ever apprehend the circular shape of my shower drain.

(Does this diagram show a circle tilted back, or an ellipse?
Joseph Brooks, socrates.berkeley.edu/ ~plab/earlygroup/shape.htm)

As the hot water began to turn cool, I concluded that there aren’t any true circular shapes in the world, and even if there were, as a practical matter, we wouldn’t be able to perceive them as such. Circularity could only be an abstraction; a generalization from many perceptual experiences of viewing approximately circular shapes, in comparison to other abstract shapes, such as ellipses. The mathematical formula for a circle is a further abstraction. In short, there are no circles, and nobody has ever seen a circle.
Except maybe Plato.

Plato appreciated the shower drain problem. He realized that objects of the mind, like the idea and image of a circle, are stable and perfect (and “eternal” he said). Objects of the world that we actually perceive are only approximations to the perfection of the objects of the mind, and on top of that, he knew that the body itself is forever changing, and inherently unreliable, so the appearances of things are always in flux.

By contrast, the perfect mental forms do not change. Plato called these the “essences” of things. The essence of something is what it truly is, its core nature, despite appearances. So my shower drain is truly circular in shape, despite appearances to the contrary.

But why assume something to which evidence speaks the contrary? The evidence is that the drain is not, in fact, circular. But Plato reasoned that if essences are perfect and eternal, and every object has an essence as its core, then every object must be perfect and eternal in its innermost nature. If our actual experience of the world contradicts that, well, so much the worse for experience. The experience is wrong.

But if experience is wrong, and always has been, how did Plato come to his theories about objects and their eternal essences? His whole life experience, like everyone else’s was erroneous. Plato’s answer is that he was just born with the knowledge of perfect essences, and so was everyone else. So there!

That’s a large pill to swallow. It is tantamount to the favorite argument of parents, “Because I said so!”

It is not necessary to assume that the perfect essence of an object resides in the object. Why can’t we say that essences reside in the mind, as inductive abstractions and deductive proofs? If that were allowed, then we would not be troubled by the fact that perception and measurement are inherently unreliable and that all objects are changeable. We could simply mentally accommodate for the error variance to infer the correct reality.

But Plato seemed blind to subjectivity, especially his own. Everything in his theory was “out there,” separate from the human mind, because he did not explicitly take the mind into consideration in his theory of reality. The best he could do was to say that the perfect and eternal essences lived in a special world, the spaceless and timeless World of Forms. The Forms were “out there” somewhere, although they would have to be in heaven to be in a spaceless and timeless domain.

So circles are in heaven. When you imagine you have seen a circle, you have actually glimpsed heaven. The same is true for a square, a triangle, or a dodecahedron.

In fact, we would have to say, keeping with Plato, that heaven is all you ever see. Everything has a shape, and a size, and so forth, because perceived things must have form. But when you apprehend and conceptualize a thing’s form, you are actually dealing with its Form, or essence, and Forms exist only in heaven. Therefore we have never, and cannot ever, perceive any part of the actual world, only the world of Forms.

(What shape is the rim of this cup?)

Plato’s is a profoundly antiscientific theory. Science is the observation and measurement of the actual world, not description of some theoretical heavenly world beyond space and time. So you would think scientists would be keen to avoid missteps leading to Platonist thinking. Yet they actually make the same mistake Plato made, assuming that everything is “out there,” nothing is “in here.”

In other words, scientists today are just as blind to their own subjectivity as Plato was to his. Scientific hyperobjectivity leads to the same reification errors that characterize Plato’s implausible theory of heavenly Forms.


Most scientists insist, for example, that patterns exist in nature that are not constructions of the human mind. I once pinned down a scientist who argued this way and asked him directly, “Do you really believe there is a face on the moon?” To my amazement, he answered yes. He said “If you set up an appropriate camera it will objectively record the pattern of a face on the moon without any human intervention.” (It did not occur to him that someone would have to look at the camera’s picture to prove the presence of a face).

Likewise, most scientists insist that there is objective “information” in the world and even “knowledge” independent of any knower. Many believe that numbers exist independently of the human mind, and so do space, time, energy, mass, and force. Theoretical physicists are convinced they are close to having a “theory of everything,” by which they mean everything in the objective world, which is the only world, in their thinking. Such hubris would be risible were it not pervasive.

Unfortunately, even the field of psychology, which supposedly specializes in the study of the human mind, has drunk the scientific Kool Aid. The American Psychological Association, and most of its members, insist that psychology is an objective science. Scientific psychologists have become blind to subjectivity, projecting and reifying their own minds onto the brain and the genome, the modern-day repositories of Platonic Forms.

What is the alternative? Abandonment of science and return to the prescientific darkness of ignorance and superstition? Hardly. All we need are a few tweaks to the philosophy of science to allow that subjectivity exists in the world as a natural fact and can be studied without shame.