How we know distances, sizes, shapes, and positions

Neither angles nor optical lines can make us know distances. Proof by example. These optical lines do not reveal sizes or shapes either. Proof by example. Proof from Cheselden’s case of the boy born blind. How we know distances and sizes. Example. We learn to see as we learn to read. Vision cannot reveal extension.**

Let us begin with distance.

It is clear that distance cannot be perceived immediately on its own, because distance is nothing more than a line from the object to us. This line ends at a single point; therefore we only perceive that point. Whether the object is a thousand leagues away or one foot away, that point is always the same.

Thus, we have no immediate way to perceive distance at once, as we do to sense by touch whether a body is hard or soft; by taste, whether it is sweet or bitter; or by hearing, whether one sound is deep and another high.

Notice carefully: the parts of a body that yield to my finger are the immediate cause of my sensation of softness, and the vibrations of the air, excited by a sounding body, are the immediate cause of my sensation of sound. But if I cannot have such an immediate idea of distance, then I must know this distance by means of another intermediate idea.

But I must at least perceive that intermediate idea — for an idea I do not have could certainly not serve to give me another.

I might say a house is one mile from a certain river — but if I do not know where that river is, I certainly do not know where the house is.

A body yields easily under my hand’s pressure — I conclude immediately that it is soft; another resists, and I feel immediately that it is hard: therefore, if I were to conclude distances immediately from the angles formed in my eye, I would have to feel those angles. But most people don’t even know these angles exist: so it’s clear that those angles cannot be the immediate cause of our awareness of distance.

Someone who, for the first time in his life, hears the blast of a cannon or the notes of a concert, could not judge whether the cannon is fired or the concert performed one league away or thirty paces away. Only experience can train him to judge the distance between himself and the source of that sound.

The vibrations, the undulations of the air, carry sound to his ears — or rather, to his soul; but this sound no more tells his soul where it began than it tells him the shape of the cannon or the musical instruments.

The same is precisely true for the rays of light leaving an object: they do not tell us at all where the object is.

They do not make us know sizes or even shapes either.

I see from far away what seems to be a small round tower. I approach, see, and touch a large rectangular building. Certainly what I saw and what I touched is not what I had seen. The little round object that was in my eyes was not that large square building.

So: the measurable and tangible object is one thing, and the visible object is another.

From my room I hear the sound of a carriage; I open the window and see it; I go down and climb inside. But that carriage which I heard, that carriage which I saw, that carriage which I touched — these are three entirely different objects for three of my senses, which have no immediate relationship with one another.

There is more: it is demonstrable, as I already said, that an angle twice as large is formed in my eye (or nearly so) when I see a man at four feet from me as when I see the same man at eight feet.

Yet I always see that man the same size: how is it that my perception thus contradicts the mechanism of my organs?

The object is really twice as small in my eyes — and yet I see him equally large.

It is in vain that people try to explain this mystery by the shape, or by the motion, of the lens in our eyes. Whatever you assume, the angle under which I see a man four feet away is always double the angle under which I see him eight feet away; and geometry will never solve this problem, and physics is equally powerless: because however you suppose that the eye reshapes itself, that the lens moves forward, that the angle changes — all that will happen equally for the object at eight feet as for the one at four.

The proportion will always remain the same: if you see the object at eight feet under an angle half as large, you also see the object at four feet under an angle half as large (or thereabouts).

Therefore neither geometry nor physics can explain this difficulty.

These lines and these geometric angles are no more the true cause of why we see objects in their position than they are the cause of why we see them of such a size and at such a distance.

The soul does not consider whether some part is painted on the bottom of the eye; it does not trace anything to lines it does not perceive. The eye simply lowers itself to see what is near the ground, and raises itself to see what is above it.

All this could only be clarified, and settled beyond all dispute, by some man born blind to whom the sense of sight would be given.

Because if that blind man, the moment he opened his eyes, could judge distances, sizes, and positions, it would be true that the optical angles formed instantly on his retina were the immediate causes of his perceptions.

Thus Dr. Barclay assured, following Mr. Locke (and going even further than Locke), that neither position, nor size, nor distance, nor shape would be discerned at all by such a blind man whose eyes suddenly received light.

But where to find the blind man whose case could settle this question?

Finally, in 1729, Mr. Cheselden, one of those famous surgeons who combined dexterity of hand with the greatest clarity of mind, having conceived that one could give sight to a man born blind by lowering what are called cataracts — which he suspected had formed in his eyes almost at birth — proposed the operation.

The blind boy hesitated to consent. He did not really believe the sense of sight could greatly add to his pleasures. If not for the desire they inspired in him to learn to read and write, he would not have wished to see at all.

By this indifference he proved that it is impossible to be unhappy from the lack of goods of which one has no idea — an important truth.

Whatever the case, the operation was done, and it succeeded.

This young man of about fourteen saw light for the first time.

His experience confirmed everything Locke and Barclay had foreseen so well.

For a long time he could distinguish neither size, nor position, nor even shape.

An object one inch wide, placed before his eye, and which blocked out a house, seemed to him just as large as the house.

Everything he saw at first seemed to rest on his eyes, to touch them, just as objects of touch touch the skin.

At first he could not distinguish what he had felt as round with his hands from what he had felt as angular; nor could he discern with his eyes whether what his hands had felt to be above or below was in fact above or below.

He was so far from knowing sizes that, after he finally conceived by sight that his house was larger than his room, he did not understand how sight could give that idea.

Only after two months of experience could he perceive that paintings represented solid bodies; and when, after this long fumbling of a new sense in him, he realized that bodies, and not only surfaces, were painted in paintings, he reached out his hand — and was astonished not to find, with his hand, the solid bodies that he had just begun to perceive represented.

He asked which sense was the deceiver: touch or sight.

This was thus an irrevocable conclusion: the way we see things is not at all the immediate result of the angles formed in our eyes.

Because those mathematical angles were in this boy’s eyes just as in ours — and they served him nothing without the help of experience and the other senses.

How then do we represent sizes and distances to ourselves?

The same way we imagine men’s passions — from the colors they paint on their faces, and from the changes they bring to their features.

There is no one who does not read, instantly, on another man’s forehead, pain or anger.

This is the language that nature speaks to every eye; but experience alone teaches this language.

In the same way, experience alone teaches us that when an object is too far away, we see it dimly and weakly.

From this we form ideas that then always accompany the sensation of sight.

Thus any man who, at ten paces, has seen his horse five feet high — if he then sees, a few minutes later, that horse no bigger than a sheep, his soul, by an involuntary judgment, immediately concludes that this horse is very far away.

It is indeed true that, when I see my horse as small as a sheep, a smaller image is then formed in my eye, a sharper angle — but that is what accompanies, not what causes, my perception.

Likewise, sometimes a different trembling occurs in my brain when I see a man blush with shame than when I see him blush with anger; but these different impressions would teach me nothing of what is happening in that man’s soul, without the voice of experience.

Far from this angle being the immediate cause of why I judge that a large horse is far away when I see that horse very small, the opposite happens constantly:

I see the same horse equally large at ten, twenty, thirty paces — though the angle at ten paces is double, triple, quadruple.

I look from far away, through a small hole, at a man standing on a roof; the distance and the few rays first prevent me from knowing if it’s a man: the object seems very small, I believe I see a statue two feet high at most.

The object moves — I judge that it is a man, and instantly, that man appears to me his ordinary height.

Where do these two so different judgments come from?

When I believed I saw a statue, I imagined it two feet tall because I saw it under such an angle: no experience bent my soul to deny the image printed on my retina.

But as soon as I judged that it was a man, the association made by experience in my brain between the idea of a man and the idea of a height of five or six feet forces me, without thinking about it, by a sudden judgment, to imagine that I see a man of that height — and to see such a height indeed.

We must absolutely conclude from all this that distances, sizes, positions are not, properly speaking, visible things — that is to say, they are not the proper and immediate objects of sight.

The proper and immediate object of sight is nothing other than colored light: everything else we only sense gradually and through experience.

We learn to see exactly as we learn to speak and to read.

The difference is that the art of seeing is easier — and nature is everyone’s teacher equally.

The sudden, almost uniform judgments that all our souls, at a certain age, make about distances, sizes, and positions make us think that we have only to open our eyes to see the way we do.

We are mistaken: we need the help of other senses.

If men had only the sense of sight, they would have no way of knowing extension in length, width, and depth; and a pure spirit might not know it either, unless God revealed it to him.

It is very difficult to separate in our minds the extension of an object from the colors of that object.

We never see anything that is not extended, and from this we are all inclined to believe we truly see extension.

We can hardly distinguish in our soul that yellow, which we see in a gold coin, from that gold coin whose yellow we see.

It is like when we hear the word “gold coin” pronounced — we cannot stop ourselves from attaching, despite ourselves, the idea of that currency to the sound we hear pronounced.

If all men spoke the same language, we would always be ready to believe there was a necessary connection between words and ideas.

Well — all men do speak the same language here, when it comes to imagination.

Nature says to all: When you have seen colors for a certain time, your imagination will represent to you, all in the same way, the bodies to which these colors seem attached.

This prompt and involuntary judgment you form will be useful to you in the course of life: for if you had to wait, in order to estimate the distances, sizes, positions of everything around you, until you had examined angles and visual rays, you would die before knowing whether the things you need are ten paces from you, or a hundred million leagues away, and whether they are the size of a mite or of a mountain.

It would be far better for you to have been born blind.

We are thus very wrong when we say our senses deceive us.

Each of our senses does exactly the function nature destined it for.

They help each other to send to our soul, through the hand of experience, the measure of knowledge that our being can bear.

We demand of our senses what they were not made to give us.

We would like our eyes to make us know solidity, size, distance, etc.; but touch must join with sight for that — and experience must help them.

If Father Malebranche had looked at nature from this side, he might have attributed fewer errors to our senses, which are the only sources of all our ideas.

We must not, of course, extend to all cases this kind of metaphysics we have just seen: we should only call on it when mathematics are insufficient; and this is another error we must recognize in Father Malebranche.

He attributes, for example, to the imagination of men alone certain effects that the simple rules of optics fully explain.

He believes that if the stars seem larger to us at the horizon than at the meridian, it is only to the imagination that we must ascribe it.

We will explain, in the next chapter, this phenomenon which for a hundred years has exercised so many philosophers.