The Sleepwalkers (29 page)

There
was
also
a
certain
dishonesty
about
it.
The
spheres
of
Eudoxus
could
account
–
however
imprecisely
–
for
the
existence
of
"stations"
and
"retrogressions"
in
the
progress
of
a
planet;
but
it
could
never
account
for
the
variations
in
size
and
brightness,
caused
by
variations
of
the
planet's
distance
from
the
earth.
These
were
particularly
evident
in
the
case
of
Venus
and
Mars,
and
most
of
all,
the
moon:
thus
central
eclipses
of
the
sun
are
"annular"
or
"total",
according
to
the
moon's
momentary
distance
from
the
earth.
Now
all
this
was
known
before
Eudoxus,
and
thus
to
Eudoxus
himself
as
well
as
to
Aristotle;
²
yet
their
system
simply
ignores
the
fact:
however
complicated
the
planet's
motion
is,
it
is
confined
to
a
sphere
centred
on
the
earth,
and
its
distance
to
the
earth
can
therefore
never
vary.

It
was
this
unsatisfactory
state
of
affairs
which
gave
rise
to
the
unorthodox
branch
of
cosmology
developed
by
Herakleides
and
Aristarchus
(
see
Chapter
III).
The
system
of
Herakleides
eliminated
(though
merely
for
the
inner
planets)
both
the
most
conspicuous
scandals:
the
"stations-and-retrogressions",
and
the
varying
distances
from
the
earth.
Moreover,
it
explained
(as
a
glance
at
Fig.
B
on
p.
46
will
show)
the
logical
relatedness
of
the
two
scandals:
why
Venus
was
always
brightest
when
she
was
moving
crabwise,
and
vice
versa.
When
Herakleides
and/or
Aristarchus
made
the
remaining
planets,
including
the
earth,
move
round
the
sun,
Greek
science
was
on
the
straight
road
to
the
modern
universe;
then
abandoned
it
again.
Aristarchus'
sun-centred
model
was
discarded
as
a
freak;
and
academic
science
marched
on
triumphantly
from
Plato,
via
Eudoxus,
and
Aristotle's
fifty-five
spheres,
to
an
even
more
ingenious
and
improbable
artefact:
the
maze
of
epicyclcs
devised
by
Claudius
Ptolemy.

If
we
call
Aristotle's
world
an
onion
universe,
we
might
as
well
call
Ptolemy's
the
Ferris
Wheel
universe.
It
was
begun
by
Apollonius
of
Perga
in
the
third
century
B.C.,
developed
by
Hipparchus
of
Rhodes
in
the
century
that
followed,
and
completed
by
Ptolemy
of
Alexandria
in
the
second
century
A.D.
The
Ptolemaic
system
remained,
with
minor
modifications,
the
last
word
in
astronomy
until
Copernicus.

Any
rhythmic
movement,
even
the
dance
of
a
bird,
can
be
imagined
as
being
caused
by
a
clockwork
in
which
a
great
number
of
invisible
wheels
co-operate
to
produce
the
motions.
Ever
since
"uniform
circular
motion"
had
become
the
law
governing
the
heavens,
the
task
of
astronomy
was
reduced
to
designing,
on
paper,
just
such
imaginary
clockworks
which
explained
the
dance
of
the
planets
as
a
result
of
the
gyrations
of
perfectly
circular,
ethereal
components.
Eudoxus
had
used
spheres
as
components;
Ptolemy
used
wheels.

It
is
perhaps
easiest
to
visualize
the
Ptolemaic
universe
not
as
an
ordinary
clockwork,
but
a
system
of
"Big
Wheels"
or
"Ferris
Wheels"
as
one
sees
them
in
amusement
parks
–
a
huge,
upright,
slowly
revolving
wheel
with
seats
or
small
cabins
hanging
suspended
from
its
rim.
Let
us
imagine
the
passenger
safely
strapped
to
his
seat
in
the
little
cabin,
and
let
us
further
imagine
that
the
machinery
has
gone
crazy
–
the
cabin,
instead
of
hanging
down
quietly
from
the
rim
of
the
Big
Wheel,
rotates
wildly
round
the
pivot
from
which
it
is
suspended,
while
the
pivot
itself
revolves
slowly
with
the
Wheel.
The
unhappy
passenger
–
or
planet
–
is
now
describing
a
curve
in
space
which
is
not
a
circle,
but
is
nevertheless
produced
by
a
combination
of
circular
motions.
By
varying
the
size
of
the
Wheel,
the
length
of
the
arm
by
which
the
cabin
is
suspended,
and
the
speeds
of
the
two
rotations,
an
amazing
variety
of
curves
can
be
produced,
such
as
the
one
shown
on
the
diagram
–
but
also
kidney-shaped
curves,
garlands,
ovals,
and
even
straight
lines!

Seen
from
the
earth,
which
is
in
the
centre
of
the
Big
Wheel,
the
planet-passenger
in
the
cabin
will
move
clockwise
until
he
reaches
the
"stationary
point"
S
₁
,
then
regress
anti-clockwise
to
S
₂
,
then
move
again
clockwise
to
S
₃
,
and
so
on.
^*
The
rim
of
the
Big
Wheel
is
called
the
deferent
,
and
the
circle
described
by
the
cabin
is
called
the
epicycle
.
By
choosing
a
suitable
ratio
between
the
diameters
of
epicycle
and
deferent,
and
suitable
velocities
for
each,
it
was
possible
to
achieve
a
fair
approximation
to
the
observed
motions
of
the
planet,
insofar
as
the
"stations
and
retrogressions",
and
its
varying
distances
from
the
earth
were
concerned.