St. Paul daily globe. [volume] (Saint Paul, Minn.) 1884-1896, 1888-01-15

aDleu 10 sail raster than the wind.
The foregoing mysteries of motion
bring to mind the famous paradox of
Zeno, by which he sought to prove that
all motion is impossible. "A body"
thus argued the ingenious philosopher,
"must move either in the place where it
is or i'm the place where it is not. Now,
a body in the place where it is, is sta
tionary, and cannot be in motion; nor
| obviously can it be i'm motion in the
place where it is not. Therefore, it
cannot move at ALL" 1t was of this par
adOx that it was said, ''solvitur am
bulando''-it is solved by walking. A
| more practical solution could hardly be
required.
Another paradox familiar to the
Greeks, that of Achilles and the tortoise,
| is well known. Achilles, the swift
footed. allows the tortoise 100 yards
| start, and runs 10 yards while the tor
tOlse runs one. Now, when Achilles
has run 100 yards the tortoise has run 10
yards, and is therefore still that distance
ahead. When Achilles has run these
| lO yards the tortoise has run one ward.
When Achilles has run the one yard the
tortoise has run One-tenth of a yard, and
when Achilles has run 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 Overtake the tor
tOiSe.
A much better paradox, though some
what of the same kind, runs as follows
"a man who owes a shilling proceeds to
pay it at the rate of Sixpence the first
day, threepence the second day, three
halfpence the next, three farthing 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 to read
lily pay fractions OF a penny, how long
would it take him to pay the shilling?"
The answer is that he would never pay
it. 1t is true that he would pay eleven
pence one farthing in four DAYS, but the
remaining three farthings he can never
pay.
Many are the results of mathematics
which wear at first sight an air of para
dOX. What, to take single example.
could seem at first sight more truly par
adOXlcal than the notion of two lines
which continually approach each other
and yet, however far produced, will
never meet? Yet the construction by
which such lines may be drawn is of the
simplest kind. For, let any straight
line be set down, and from any point
taken below it let straight lines be
drawn through the first line so that the
portions which project above it are all
OF equal length. If then the tops of
/ these lines be Joined by a running
curve, this curve will evidently have
the property of continually approaching
the straight line, and yet however far
produced or the same principle, can
never meet it.
mathematics, however, are not quite
to the purpose of the present paper.
But the following very pretty problem
may be submitted to the ingenuity of
those who like to try it: ut is re-
quired to demonstrate, economically,
that larger crop of corn can be grown
OH acre of level ground than on an
acre OF slanting ground. The stalks of
corn are supposed to grow perpendicu-
larly In both cases, and all other par
tlculars,, such as fertility of soil and the
like to be the same:
Philosophers have not yet been able
to decide what would be the fate of the
donkey placed exactly midway between
two hay ricks. AS there is clearly no
reason why he should choose one rick
rather than another, it is to be pre-
sumed that, logically, he would starye
to death between them. A similar par
adOx is contained in the we'll known
English prOverb, there is an exception
to every rule" For if there is an ex-
ception to every rule, there is an eXcep-
ton to this proverb. Therefore there
is rule without an exception. That
is, the proverb cOntradicts itself.
IF Dicks father is Toms son, what
relation is Dick to Tom?' This famil-
lar query is too obvious of solution to
deserve more than passing mention.
The following, however, of the same
class Will be found very much more
fatal. A man standing before a nor
trait says of it:
Sisters and brothers none have
Yet that mans father is my fathers son.
What relation is the speaker to the
person depicted in the portrait? 1t is
quite remarkable how often the answer
is given that the portrait represents the
speaker himself. AS matter of fact it
represents the speakers son.
"Ihere is spot on the earth'S sur
face from which if any number of men
set out to walk in different directions
all would be walking toward the same
point OF the compass. What is that
spOt?" 1t will, perhaps, not need anv
prolonged reflection to discover that the
spot in question is the north pole. 1t
will in fact be evident that a man stand
ing at the pole, in whatever direction he
sets out, must as long as he proceeds in
a straight line, walk due south,
The following is a truly excellent par
adOX: "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 traveller meet in Journey
ing 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 that will
be given by nine people out of ten to
whom the question is new. The fact is
overlooked that every day during the
journey fresh train is starting from
the other end, while there are seven on
the way to begin with. The traveller
will not therefore meet seven trains.
but fourteen.
The following proposition is both
curious in itself, and admits of some in
terestlng variations in the application
OF the principle on which it depends:
III there are more people in the world
than any one person has hairs upon his
mead, then there must exist at least two
persons who possess identicallv the
same number of hairs to hair.'
If the reader fails to perceive at once
the necessity of this conclusion, let him
first consider, as a simpler case, instead
OF the hairs on mans head, the num-
Der of teeth in his jaw. Let him sup
pose thirty-four persons to be assem-
bled in one room; then, the full number
of teeth in mans jaw being thirty
two, 1t is easily seen that, even suppos
ing one member of the party so nm
fortunate as to have no teeth AFT ali
there must be at least two persons pres'
ent possessed of identicafIy the same
number of teeth.