The Sleepwalkers (35 page)

And
yet
there
was
nothing
a
priori
frightening
about
oval
or
elliptic
curves.
They
too
were
"closed"
curves,
returning
into
themselves,
and
displayed
a
reassuring
symmetry
and
mathematical
harmony.
By
an
ironical
coincidence,
we
owe
the
first
exhaustive
study
of
the
geometrical
properties
of
the
ellipse
to
the
same
man,
Apollonius
of
Perga,
who,
never
realizing
that
he
had
the
solution
in
his
hands,
started
the
development
of
the
epicyclic
monster-universe.
We
shall
see
that,
two
thousand
years
later,
Johannes
Kepler,
who
cured
astronomy
of
the
circular
obsession,
still
hesitated
to
adopt
elliptical
orbits,
because,
he
wrote,
if
the
answer
were
as
simple
as
that,
"then
the
problem
would
already
have
been
solved
by
Archimedes
and
Apollonius".
²²

6.
The Cubist Universe

Before
bidding
farewell
to
the
Greek
world,
an
imaginary
parallel
may
help
to
bring
matters
into
focus.

In
1907,
simultaneously
with
the
Cézanne
memorial
exhibition
in
Paris,
a
collection
of
the
master's
letters
was
published.
A
passage
in
one
of
the
letters
ran:

"Everything
in
nature
is
modelled
on
the
sphere,
the
cone
and
the
cylinder.
One
must
teach
oneself
to
base
one's
painting
on
these
simple
figures
–
then
one
can
accomplish
anything
one
likes."

And
further:

"One
must
treat
nature
by
reducing
its
forms
to
cylinder,
sphere,
and
cone,
all
put
into
perspective,
meaning
that
each
side
of
an
object,
each
plane,
is
directed
towards
a
central
plane."
²³

This
pronouncement
became
the
gospel
of
a
school
of
painting
known
under
the
misnomer
"Cubism".
Picasso's
first
"Cubist"
picture
was
in
fact
constructed
entirely
of
cylinders,
cones
and
circles;
while
other
members
of
the
movement
saw
nature
in
terms
of
angular
bodies
–
pyramids,
and
bricks,
and
octaeders.
^*

____________________

But
whether
they
painted
in
terms
of
cubes,
cylinders,
or
cones,
the
declared
aim
of
the
Cubists
was
to
resolve
every
object
to
a
configuration
of
regular
geometrical
solids.
Now
the
human
face
is
not
constructed
out
of
regular
solids
any
more
than
the
orbits
of
the
planets
are
made
of
regular
circles;
but
in
both
cases
it
is
possible
to
"save
the
phenomena":
in
Picasso
Femme
au
Miroir
,
the
reduction
of
the
model's
eyes
and
upper
lip
to
an
interplay
of
spheres,
pyramids
and
parallelepipedes,
displays
the
same
ingenuity
and
inspired
madness
as
Eudoxus'
spheres
pivoting
within
spheres.

It
is
rather
depressing
to
imagine
what
would
have
happened
to
painting
if
Cezanne's
Cubist
pronouncement
had
been
turned
into
a
dogma,
as
Plato's
spherist
pronouncement
was.
Picasso
would
have
been
condemned
to
go
on
painting
more
elaborate
cylindrical
bowls
to
the
bitter
end;
and
lesser
talents
would
have
found
out
soon
that
it
is
easier
to
save
the
phenomena
with
compass
and
ruler
on
graph-paper
under
a
neon
lamp,
than
by
facing
the
scandals
of
nature.
Luckily,
Cubism
was
only
a
passing
phase,
because
painters
are
free
to
choose
their
style;
but
the
astronomers
of
the
past
were
not.
The
style
in
which
the
cosmos
was
presented
had,
as
we
saw,
a
direct
bearing
on
the
fundamental
questions
of
philosophy;
and
later,
during
the
Middle
Ages
it
acquired
a
bearing
on
theology.
The
curse
of
"spherism"
upon
man's
vision
of
the
universe
lasted
for
two
thousand
years.During
the
last
few
centuries,
from
about
A.D.
1600
onwards,
the
progress
of
science
has
been
continuous
and
without
a
break;
so
we
are
tempted
to
extend
the
curve
back
into
the
past
and
to
fall
into
the
mistaken
belief
that
the
advance
of
knowledge
has
always
been
a
continuous,
cumulative
process
along
a
road
which
steadily
mounts
from
the
beginnings
of
civilization
to
our
present
dizzy
height.
This,
of
course,
is
not
the
case.
In
the
sixth
century
B.C.,
educated
men
knew
that
the
earth
was
a
sphere;
in
the
sixth
century
A.D.,
they
again
thought
it
was
a
disc,
or
resembling
in
shape
the
Holy
Tabernacle.