Page:Popular Science Monthly Volume 69.djvu/558

I suppose that between the instants $\alpha$ and $\beta$ I have moved neither my body nor my eye, as I know from my muscular sense. Nor have I moved either my head, my arm or my hand. I ascertain that at the instant a impressions that I attributed to the object $A$ were transmitted to me, some by one of the fibers of my optic nerve, the others by one of the sensitive tactile nerves of my finger; I ascertain that at the instant $\beta$ other impressions which I attribute to the object $B$ are transmitted to me, some by this same fiber of the optic nerve, the others by this same tactile nerve.

Here I must pause for an explanation; how am I told that this impression which I attribute to $A$, and that which I attribute to $B$, impressions which are qualitatively different, are transmitted to me by the same nerve? Must we suppose, to take for example the visual sensations, that $A$ produces two simultaneous sensations, a sensation purely luminous $a$ and a colored sensation $a'$, that $B$ produces in the same way simultaneously a luminous sensation $b$ and a colored sensation $b'$, that if these different sensations are transmitted to me by the same retinal fiber, $a$ is identical with $b$, but that in general the colored sensations $a'$ and $b'$ produced by different bodies are different? In that case it would be the identity of the sensation $a$ which accompanies $a'$ with the sensation $b$ which accompanies $b'$, which would tell that all these sensations are transmitted to me by the same fiber.

However it may be with this hypothesis and although I am led to prefer to it others considerably more complicated, it is certain that we are told in some way that there is something in common between these sensations $a+a'$ and $b+b'$, without which we should have no means of recognizing that the object $B$ has taken the place of the object $A$.

Therefore I do not further insist and I recall the hypothesis I have just made: I suppose that I have ascertained that the impressions which I attribute to $B$ are transmitted to me at the instant $\beta$ by the same fibers, optic as well as tactile, which, at the instant $\alpha$, had transmitted to me the impressions that I attributed to $A$. If it is so, we shall not hesitate to declare that the point occupied by $B$ at the instant $\beta$ is identical with the point occupied by $A$ at the instant $\alpha$.

I have just enunciated two conditions for these points being identical; one is relative to sight, the other to touch. Let us consider them separately. The first is necessary, but is not sufficient. The second is at once necessary and sufficient. A person knowing geometry could easily explain this in the following manner: Let 0 be the point of the retina where is formed at the instant $a$ the image of the body $A;$ let $M$ be the point of space occupied at the instant $a$ by this body $A;$ let $M$ be the point of space occupied at the instant $\beta$ by the body $B$. For this body $B$ to form its image in 0, it is not necessary that the points $M$ and $M'$ coincide; since vision acts at a distance, it suffices for the