Wood County reporter. [volume] (Grand Rapids [i.e. Wisconsin Rapids], Wis.) 1857-1923, 1888-02-23

Line louOWIug PARADOX. WHICH mas
given rise to much discussion, is some
what akin to the preceding: ''How
can a ship sail faster than the wind?"
Every yachtsman knows that a ship
can sail faster than the wind-that is
to say, if the wind is blowing ten
knots an hour, ship may be making
ten or fifteen knots an hour. Now, it
is obvious that if the ship is sailing
straight before the wind it can not at
the utmost travel faster than the wind
itself is blowing-as matter of fact,
it viii travel much more slowly. If.
on the other hand, the ship is sailing
at an angle with the wind, it seems at
first sight the wind must act with less
effect than before, and tie ship in
consequence, sail more slowly still.
only sails more quickly than before,
but more quickly than the wind itself
is blowing. This is a paradox which
few, even of those who are well ae-
quainted by experience with the fact,
have found themselves able to ex-
plain.
Let us consider the difficulties in the
light of the following experiment:
Place ball at one side of a billiard
table, and with the long cue held
lengthwise, from end to end of the ia
BILE, push the bali across the cloth.
The cue here represents the wind and
the ball the ship sailing directly before
it; only as there is here no waste of
energy, which in the case of the wind
and ship is very great, the ball of
course travels at the same rate as the
cue-evidently it can not travel faster
Now, suppose a groove be cut diagon-
ally across the table from one corner
pocket to the other, in which the ball
may roll. If the bali be now placed
at one end of the groove, and the cue
held horizontally and moved forward
as before, the ball will travel along
the groove (and along the cue) in the
same time as the cue takes to move
across the table. This is the case of
the ship sailing at an angle with the
direction of the wind. The groove is
considerably longer than the width of
the table, more than double as long,in
fact. The ball therefore travels much
faster than the cue which impels it,
since it covers more than double the
distance in the same time. 1t is in
precisely the same manner that a
lacking ship is enabled to sail faster
than the wind.
The foregoing mysteries of motion
bring to mind the famous paradox of
Reno, by which he sought to prove
that all motion is impossible. "a
body" thus argued the ingenious
philosopher, t-nust move either in the
place where it is, or in the place where
it is not. Now, a body in place
where it is stationary, can not be in
motion; nor, obviously, can it be in
motion in the place where it is not.
Therefore, it can not move at all. 1t
was of this paradox it was said,
SOIvtt~r ams6ulando-'It is solved by
walking" A more practical solution
could hardly be required.
Another paradox familiar to the
Greeks-that of Achilles and the tor
toise-is well known. Achilles (the
swift footed) allows the tortoise
hundred yards start, and runs ten
yards while the tortoise runs one.
Now, when Achilles has run a hun
1red yards the tortoise has run ten
yards, and is therefore still that dis
lance ahead. When Achilles has run
these ten yards, the tortoise has run
one yard. When Achilles has run
one yard, the tortoise has run one
tenth of yard. And when Achilles
has run the one-tenth of a yard the
tortoise has run one-hundredth. 1t is
only necessary to continue the same
process of reasoning to prove that
Achilles can never oYertake the tor
toise.
A much better paradox, though
Of the same kind, runs as follows:
"A man who owes shilling, proceeds
20 pay it at the rate of sixpence the
frst day, threepence the next, three
halfpence the next, three farthings the
next, and so on-paying each day half
The amount he paid the day before.
Surprising him to be furnished with
counters of small value, so as to be
able readily to pay fractions of a penny,
low long would it take him to pay the
shilling?" The answer is that he
will never pay it. 1t is true that he
will pay eleven-pence-farthing in four
lays, but the remaining three farth-
ngs he can never pay.
This paradox varies from the pre-
eeding in one important particular,
and deserves to be called a better par
ioX for this reason, that we know
Achilles, in. spite of all reasoning. will
certainly overtake the tortoise. But
t is automatically demonstrab bic that
5he debtor, under such circum-
stances, can never pay his shilling,
even though he should be endued, like
TithOnus, with the Gift of Immortality.
The following is really excellent
San Francisco to New York, and one
1aily from New 7 DIRK to San Francisco,
he journey lasting seven days. How
many trains will a traveller meet in
.ourneying from San Francisco TO
New York?'
1t appears obvious at the first glance
that the traveller must meet seven
trains, and this is the answer which
will be given by nine people out of ten
TO whom the question is new. The
fact is overlooked that every day dur
ing the journey a fresh train is start
ing from the other end, while there
are seven on the way TO begin with.
The traveller will therefore meet not
seven trains, but fourteen.
The following proposition is botsl
curious in itself, and admits of some
interesting variations in the applica-
ton Of the principle on which it de-
ponds: IF there are more people in
the world than any one person has
hairs upon his head, then there must
exist at least two persons who possess
identically the same number of hairs,
to hair"