You are all, I
trust, looking at the envelope I am holding up.
Everybody see it? (Affirmative murmur from class.) Fine! Now
you people to my left, notice that what you see is not strictly
rectangular: it is trapezoidal. If you were an artist, you would
draw what you see after this manner: (he draws trapezoid whose
right, vertical side is longer than its left vertical side). (Murmur
of approval for artistic talent.) Yet the people to my right will
notice that what they see is not rectangular either; nor is it
exactly like the trapezoid which I have just drawn. Rather, what
you see is like this: (he draws a mirror image of the first figure,
having a taller left vertical side and a shorter right vertical side).
I suppose
that no one believes that the envelope actually
has either one of these trapezoidal shapes--not to mention that it
has both shapes. You will no doubt assure me that the envelope
is rectangular, not trapezoidal. (Murmurs of assurance.) But then
it follows that what the people on my left are seeing is not the
envelope; they are seeing something which has a trapezoidal
shape and which only resembles (loosely) the envelope itself. Let
us call what they are seeing an appearance. And, of course, for
the same reasons the people on my right are seeing only
appearances too.
But now the question arises whether anyone at all really
sees the envelope itself as contrasted with what is merely an
appearance of it. For if a person on my left were to move slowly
from that side of the room to the opposite side, what he would
see first will have a trapezoidal shape like the one on the board.
(Points.) Then he would see something, still trapezoidal, to be
sure, but more like a rectangle than what he saw the moment
before. And so on until he would see something rectangular; and
if he were to continue, he would see things of varying but related
shapes until he finally would a trapezoidal figure "opposite to"
the one he first saw. (Points to board.)
But how can we pick any one of these positions as the one
in which a person sees the envelope itself and not simply another
appearance? The shift in shape is gradual. Wouldn't it be
arbitrary to say that at one of these positions we see the
envelope itself? And anyhow, how do we know that the
envelope isn't ever-so-slightly trapezoidal--due to a minor
manufacturing flaw--so that the position from which we see a
perfectly rectangular thing isn't the one special position anyway?
To avoid this arbitrariness, we must admit that what we
see is never the envelope itself, no matter what our position, but
only an appearance--which may more or less resemble the
envelope itself.
[And this leads directly to our next question: why should
we believe that there is an envelope involved at all? ... (Murmur
expressing mild surprise at the conjuring trick which has just
been performed right before--so to speak--their very eyes.)]