Chaucer records the
painful fact that the harmony
broken on occasions by the quarrels between the Friar and the
At one stage the
latter threatened that ere they reached
would make the Friar's "heart for to mourn;" but the worthy Host
intervened and patched up a
Unfortunately trouble broke
out again over a very curious dispute in this way.
one point of the journey
the road lay along two
sides of a
field, and some of the pilgrims persisted, in spite of trespass, in
cutting across from corner to corner, as they are seen to be doing in
Now, the Friar startled the company by stating that there
was no need for the trespass, since one way was exactly the same
as the other!
"On my faith, then," exclaimed the Sompnour, "thou art a
"Nay," replied the Friar, "if the company will but listen
with patience, I shall presently show how that thou art the fool, for
thou hast not wit enough in thy poor brain to prove that the diagonal
any square is less than two of the sides."
the reader will refer to
the diagrams that we
he will be
able to follow the Friar's argument.
If we suppose the side
of the field
to be 100 yards, then the distance along the two sides, A to B, and B
C, is 200 yards.
He undertook to prove that the diagonal distance
from A to C is also 200 yards.
Now, if we take the diagonal path shown
Fig. 1, it is evident that we go the same distance, for every one of
eight straight portions of this path measures exactly 25
in Fig. 2, the zigzag contains ten straight portions, each 20 yards
that path is also the same length—200 yards.
No matter how
many steps we
make in our zigzag path, the result is most certainly always the
in Fig. 3 the steps are
very small, yet the distance must be 200
yards; as is also the case in Fig. 4, and would yet be if we needed a
microscope to detect the steps.
In this way, the Friar argued, we may
on straightening out that zigzag path until we ultimately reach a
perfectly straight line, and it therefore follows that the diagonal of
square is of exactly the same length as two of the sides.
in the face of it, this
must be wrong; and it
is in fact
so, as we can at once prove by actual measurement if we have
the Sompnour could not for
the life of him point out the fallacy,
so upset the Friar's reasoning.
It was this that so exasperated him,
consequently, like many of us to-day when we get entangled in an
argument, he utterly lost his temper and resorted to abuse.
some of the other pilgrims had not interposed the two would have
undoubtedly come to blows.
The reader will perhaps at once see the flaw
in the Friar's argument.