The Abbeville press and banner. [volume] (Abbeville, S.C.) 1869-1924, 1888-02-08
PARAD0XES.
SOME ODD AND ENTERTAINING
CATCH QUESTIONS.
The Moving Coach Wheel - Zeno's
Paradox Achilles and the
Tortoise-PayinSa q Shilling
Passing Trains, Etc. Il.

Tortoise-Payinsa Shilling
Passing Trains, Etc.
There exist, floating about the world,
a great number of catch questions and
odd propositions. Here is one of them:
Which, at any given moment, is NOV.
ing forward faster, the top of coach
wheel or the bottom2 To this apparent.
ly very simple question nine person out
of ten, asked at random, will give an in
correct reply, for at first sight it appears
evident that both the top and bottom of
the wheel must of necessity be moving
forward at the same rate, namely, the
speed at which the carriage is travelling.
A little thought will show that this is far
from being the case. A point on the
bottom of the wheel Is, in fact, by the
direction of its motion round the axis,
moving backwards, in an opposite direc-
tion to that in which the carriage is
progressing, and is consequently station.
ary in space; while point on the top of
the wheel is moving forwards, with the
double velocity of its own motion round
the axis and the speed at which the car.
riage moves.
The foregoing mystery of motion
brings to mind the famous paradox of
Zeno, by which he sought to prove that
all motion was impossible. Either a
body must move in the place where
it is or in the place where it is not. Now
D body in the place where it is is sta
tionary and cannot be in motion, nor,
obviously, can it be in motion in the
place where it is not. Therefore it can
not move at all. It was of this paradox
it was said: Solvitur Ambulando-'It
Is solved by walking" Amore practical
solution could hardly be required.
Well known also is the Greek paradox
of Achilles and the tortoise. Achilles
(the swift-footed) allows the tortoise a
hundred yards start, and runs ten yards
while the tortoise runs one. Now when
Achilles has run a hundred yards the
tortoise has run ten yards, and IS there
fore still that distance ahead. When
Achilles has run these ten yards, the
tortoise has run one yard. When Achilles
has run the one yard, the tortoise has
run the one. tenth of yard. And when
Achilles has run the one-tenth of yard,
the tortoise has run one-hundredth. 1t
Is only necessary to continue the. same
process of reasoning to prove that
Achilles can never overtake the tortoise.
You will find people in real life try
ing to solve the following: "a man, who
owes shilling, proceeds to pay it at the
rate of six-pence the first day, three
pence the next day, three half-pence the
next, three farthings the next and so on
paying each day half of the amount
he paid Tho day before. Supposing him
to be furnished with counters of small.
value, so as to be able readily to pay
fractions of a penny, how long would it.
take him to pay the shilling2" The an
swer is that he would never pay it. 1t
is trne that he will pay eleven pence
farthing in four days. But the remain
ing three farthings he can never pay.
Excellent as are the preceding, the
following is even better paradox: "a
train starts daily from San Francisco to
New York and one daily from New York
to San Francisco, the journey lasting
seven days. How many trains will a
traveller meet in journeying from San
Francisco to New York;" 1t appears
obvious at the first glance, that the trav-
eler 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 important fact is over
looked that every day during the journey
q fresh train is starting from the other
end, while there are seven on the way to
begin with. The traveller will, there
fore, meet not seven trains, but four
teen.
The following proposition is both
curious in itself and admits of some in
teresting variations in the application of
the prinI iple on which it depends. IF
there are more people in the world than
any'person has hairs upon his head, then
there must, exist ut least two persons who
possess identically the same number OF
hairs, to hair"
Readers who fail to perceive at first
the necessity of this conclusion, should
consider, as simpler case, instead of the
hairs on mans head, the number of
teeth in his jaw. Let him suppose thirty
seven persons to be assembled in one
room; then, the full number of teeth in
mans jaw being thirty-two, it is easily
seen that-even supposing one member
of the party 10 be SO unfortunate as to
have no teeth at all-therc must be at
least two persons present possessed OF
identica!ly the same number OF teeth.
The application OF this example to the
proposition in question is quite evident.
It is, in fact, merely a matter OF larger
numbers. .-Phila1elphia Times.
Russian Bankers Count Chinese Way.
have been in four or five of the larg-
,st banks in Russia and many of the most
extensive commercial aud railroad
houses, and nowhere where I seon figuring
done by pen or pencil like they do in
Tho Thinnsa