Daily press. [volume] (Newport News, Va.) 1896-current, 1907-11-19
CABTEsIAN CONVENTION
1t Was Never Held But II
Plays Important Part in
Mathematics Sometimes.

The Cartesian Convention was not
held. rs one might suppose. in the
city of Cartesia; partly because there
never was any such place aud partly
because the famous convention was
never held anywhere. The convention
WAS not meeting of delegates with
credentials. raped to order by TEN.
porary chairman. Nevertheless. there
Is not one whom the Cartesian con.
vention has not reached with It's III
tiuence.
What Is the Cartcsian convention?
II Is habit of thought which our
teachers OF arithmetic inculcated in
us when We were pupils at school.
They derived II, consciously o. uncon.
ciously. -generally the latter,-from
the great French philosopher who
once said. Il think, therefore ] am.
This Frcnchman. Describes. offered
a simple scheme for Illustrating the
first. second, and third powers OF
numbers by drawing conventional the
world round; but instead of regard
Ing the scheme as mere conveu-
fence OF illustration, We have con g
to look upon II as necessary thing,
OF universal application.
The reverse Is true. II one employs
five men for a day at five dollars
each, the total sum OF wages Will he
the second power of the number five;
but there Is no particular reason why
the wages should be represented b.
the diagram of square. If lie cm-
ploys the men for five days, thet'
wages will represent the third powcr
of tho number five; but what connec
tion would they have with a cube? A
man may have five chains, of five
links each Strung together, their
united length will represent the sec
ond power Of the number five: hut
they would be represented logically
by continuous straight line. and not
ly square.
Most practical mathematiclaus.
however, and most teachers, always
|speak of the second power OF mum
ber as Square" and of the third
power as cube" and are ready on
the instant to draw n diagram to
prove their correctness in this. But
On the fourth power the Cartesinn
convention btoke down completely
%
short. never to go again
Why do we not make diagrams OF
the fourth power. or of tho NTH. o.
Of any higher?
Because" say the Cartcslans, IT,
is utterly impossible: It Is unthinka
BILE. Tho Cnrtcsians convention con
slders nothing beyond the third pow
or. There Is no graphic expression
for any power beyond the third.
Absurdity of the Limitation.
How absurd is all this, Let us
agree that any simple number. for in
stance Ave. shall be represented by Il
line. say five inches long. Then. by
the Cartesian convention, the second
power OF five shalt l., represented by
n square. measuring five inches each
way; and the third power by n cube.
measuring FIVE inches on each edge
Now. to reach the fourth power, sim
oily multiply this cube by five. It's
graphic Illustration will be a line OF
cubes. or five cubes in a row To
each the fifth power. multiply the
cube OF five BY FIVE times five. That
is 10 say. form square figure out Of
twenty-five of the cubes. Thus the
fifth power is square of the cubes
To form the sixth power. from a new
and larger cute OF the cubes which
have been dealt with. The seventh
power will be illustrated By line OF
the larger cubes. And so ad infni-
tum.
There is in the Cartesian conven.
ton really nothing occult. esoteric
Intangible. 1t is simply convenient
device. applicable in some cases and
wholly inapplicable III others, as y
means of visualizing quantity. There
IS no reason in the world why il
should see its finish" with the third
power,-New York Tribune.