The Sleepwalkers (28 page)

The
first
serious
attempt
was
made
by
Plato's
pupil
Eudoxus,
and
improved
by
the
latter's
pupil,
Calippus.
It
is
an
ingenious
attempt
–
Eudoxus
was
a
brilliant
mathematician,
to
whom
most
of
Euclid's
fifth
book
is
due.
In
the
earlier
geocentric
models
of
the
universe,
each
planet,
we
remember,
was
attached
to
a
transparent
sphere
of
its
own,
and
all
spheres
were
turning
round
the
earth.
But,
since
this
did
not
account
for
the
irregularities
of
their
motions,
such
as
standing
occasionally
still
and
going
backward
for
a
while:
their
"stations"
and
"retrogressions",
Eudoxus
assigned
to
each
planet
not
one,
but
several
spheres.
The
planet
was
attached
to
a
point
on
the
equator
of
a
sphere,
which
rotates
round
its
axis,
A.
The
two
ends
of
this
axis
are
let
into
the
inner
surface
of
a
concentric
larger
sphere
S
₂
,
which
rotates
round
a
different
axis,
A
₂
and
carries
A
around
with
it.
The
axis
of
S
₂
is
attached
to
the
next
larger
sphere
S
₃
,
which
rotates
again
round
a
different
axis
A
₃
:
and
so
on.
The
planet
will
thus
participate
in
all
the
independent
rotations
of
the
various
spheres
which
form
its
"nest";
and
by
letting
each
sphere
rotate
at
the
appropriate
tilt
and
speed,
it
was
possible
to
reproduce
roughly
–
though
only
very
roughly
–
the
actual
motion
of
each
planet.
¹
The
sun
and
moon
needed
a
nest
of
three
spheres
each,
the
other
planets
four
spheres
each,
which
(with
the
modest
single
sphere
assigned
to
the
multitude
of
fixed
stars)
made
altogether
twenty-seven
spheres.
Calippus
improved
the
system
at
the
price
of
adding
seven
more
spheres,
making
a
total
of
thirty-four.
It
is
at
this
point
that
Aristotle
came
in.

In
the
previous
chapter
I
concentrated
on
the
broad
outlines
and
the
metaphysical
implications
of
Aristotle's
universe,
without
going
into
astronomical
detail.
Thus
I
spoke
of
the
classic
nine
spheres,
from
the
moon's
sphere
to
that
of
the
Prime
Mover
(which
alone
were,
in
fact,
remembered
during
the
Middle
Ages),
without
mentioning
that
each
of
these
nine
spheres
was
actually
a
nest
of
spheres-within-spheres.
In
reality,
Aristotle
used
altogether
fifty-four
spheres
to
account
for
the
motions
of
the
seven
planets.
The
reason
for
this
additional
investment
of
twenty
spheres
is
interesting.
Eudoxus
and
Calippus
were
not
concerned
with
constructing
a
model
that
would
be
physically
possible;
they
were
not
concerned
with
the
real
machinery
of
the
heavens;
they
constructed
a
purely
geometrical
device,
which,
they
knew,
could
exist
only
on
paper.
Aristotle
wanted
to
do
better,
and
transform
it
into
a
true
physical
model.
The
difficulty
about
this
was
that
all
adjoining
spheres
must
be
mechanically
connected,
yet
the
individual
motion
of
each
planet
must
not
be
transmitted
to
the
others.
Aristotle
tried
to
solve
this
problem
by
inserting
a
number
of
"neutralizing"
spheres,
which
turned
in
the
opposite
direction
to
the
"working
spheres",
between
two
successive
nests;
in
this
manner,
the
effect
of
the
motions
of,
say,
Jupiter
on
his
neighbour
was
eliminated,
and
the
nest
of
Mars
could
be
started
from
scratch,
as
it
were.
But
insofar
as
the
reproduction
of
the
actual
planetary
motions
is
concerned,
Aristotle's
model
was
no
improvement.

Besides,
another
difficulty
remained.
While
each
sphere
participated
in
the
motion
of
the
next
larger
one
enclosing
it,
it
needed
a
special
moving
force
to
impart
to
it
its
independent
rotation
on
its
own
axis;
which
meant,
that
there
had
to
be
no
less
than
fifty-five
"unmoved
movers",
or
spirits,
to
keep
the
system
going.

It
was
an
extremely
ingenious
system
–
and
completely
mad,
even
by
contemporary
standards;
as
shown
by
the
fact
that
in
spite
of
Aristotle's
enormous
prestige,
it
was
quickly
forgotten
and
buried.
Yet
it
was
only
the
first
of
several
equally
ingenious
and
equally
mad
systems
which
astronomers
created
out
of
their
tortured
brains,
in
obedience
to
Plato's
post-hypnotic
suggestion
that
all
heavenly
motion
must
be
circular
motion
centred
round
the
earth.