Friday. February ll, ms

SCARLET AND BLACK

Page Five

 

’Pfiich’s Pface . ..

Coach Ptireh's piano is pfilled with pfrustrorion during o ptroiiiio. pfeur-pfilled piroeiis
in Darby. T is time. however. Grinnell defeated ooe 'lOlsBY. see page eight.

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‘Square and Circle Are Alike

From Topological Viewpoinl‘

By MARY MALCOLM

Paul G Kuntz (philosophy) has
spent years now in a Search for
a geomemc object satislying both
the definition of a Circle and that
of a square—the squirkle.

Mix Kilntz. rejoice! Your Search
is over. The problem with philosor
pliers is that they look for ans
swets which are diﬂiclllt if not
impossible to find in philosophy,
when they could easily be ioiinti
in other fields, This according to
Dr. Steve Armentroui of the Uni-
versity oi Iowa who spoke Tiles-
day in the science lecture room.
Topologically seen, there is abso-
lutely no difference between a
circle and a square (both are 1-
spheres). or for that matter be
tween a sphere and a cube.

Kuntz and colleagues may are
gue that the topological viewpoint
is a somewhat technical one. Nev-
ertheless. when dealing with squir-
kles and their huge philosophical
implications, it must he rememe

 

bered that everything is point of
view.

Armenii’out's talk posed the
question of deﬁning the arsphere,
based on an attempt to under
stand geometry and analysis in
Le rm 5 of four dimensions. He
pointed out that this problem and
attempts to verify or disprove
Polncare’s conjecture (a tentative
theorem dealing with the 3.
sphere) have occupied the world's
outstanding topologists for 15
years,

Once you get into higher dimenr
sions, beyond four. there is no dif»
iiciilty in classilying objects. The
difficulty seems to lie entirely in
that loutth dimension, too compli-
cated to picture, too simple to
generalize

Topology is a branch of mathe-
matics which attempts to cone
late analysis and geometry. its
major contribution to the ﬁeld as
a whole is in strengthening the
iounolations at these other branch-
es.

 

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