The Sleepwalkers (118 page)

In
the
next
six
chapters
(III
to
VIII),
it
is
explained
to
us
why
there
are
three
planets
outside
and
two
inside
the
earth's
orbit;
why
that
orbit
is
placed
just
where
it
is;
why
the
cube
lies
between
the
two
outermost
planets
and
the
octahedron
between
the
two
innermost;
what
affinities
and
sympathies
exist
between
the
various
planets
and
the
various
solids,
and
so
on
–
all
this
by
a
priori
deductions
derived
straight
from
the
Creator's
secret
thoughts,
and
supported
by
reasons
so
fantastic
that
one
can
hardly
believe
one
is
listening
to
one
of
the
founders
of
modern
science.
Thus,
for
instance,
"the
regular
solids
of
the
first
order
[i.e.
those
which
lie
outside
the
earth's
orbit]
have
it
in
their
nature
to
stand
upright,
those
of
the
second
order
to
float.
For,
if
the
latter
are
made
to
stand
on
one
of
their
sides,
the
former
on
one
of
their
corners,
then
in
both
cases
the
eye
shies
from
the
ugliness
of
such
a
sight."
By
this
kind
of
argument
young
Kepler
succeeds
in
proving
everything
that
he
believes
and
in
believing
everything
that
he
proves.
The
ninth
chapter
deals
with
astrology,
the
tenth
with
numerology,
the
eleventh
with
the
geometrical
symbolism
of
the
Zodiac;
in
the
twelfth,
he
alludes
to
the
Pythagorean
harmony
of
the
spheres,
searching
for
correlations
between
his
perfect
solids
and
the
harmonic
intervals
in
music
–
but
it
is
merely
one
more
arabesque
to
the
dream.
On
this
note
ends
the
first
half
of
the
book.

The
second
is
different.
I
have
talked
of
a
work
in
two
movements,
because
they
are
written
in
different
moods
and
keys,
and
are
held
together
only
by
their
common
leitmotif
.
The
first
is
medieval,
aprioristic
and
mystical;
the
second
modern
and
empirical.
The
Mysterium
is
the
perfect
symbol
of
the
great
watershed.

The
opening paragraph of the second half must have come as a shock to his
readers:

"What
we
have
so
far
said
served
merely
to
support
our
thesis
by
arguments
of
probability.
Now
we
shall
proceed
to
the
astronomical
determination
of
the
orbits
and
to
geometrical
considerations.
If
these
do
not
confirm
the
thesis,
then
all
our
previous
efforts
have
doubtless
been
in
vain."
⁶

So
all
the
divine
inspiration
and
a
priori
certitude
were
merely
"probabilities";
and
their
truth
or
falsehood
was
to
be
decided
by
the
observed
facts.
Without
transition,
in
a
single
startling
jump,
we
have
traversed
the
frontier
between
metaphysical
speculation
and
empirical
science.

Now
Kepler
got
down
to
brass
tacks:
the
checking
of
the
proportions
of
his
model
of
the
universe
against
the
observed
data.
Since
the
planets
do
not
revolve
around
the
sun
in
circles
but
in
oval-shaped
orbits
(which
Kepler's
First
Law,
years
later,
identified
as
ellipses),
each
planet's
distance
from
the
sun
varies
within
certain
limits.
This
variation
(or
eccentricity)
he
accounted
for
by
allotting
to
each
planet
a
spherical
shell
of
sufficient
thickness
to
accommodate
the
oval
orbit
between
its
walls
(
see
the
model
on
p.
250).
The
inner
wall
represents
the
planet's
minimum
distance
from
the
sun,
the
outer
wall
its
maximum
distance.
The
spheres,
as
already
mentioned,
are
not
considered
as
physically
real,
but
merely
as
the
limits
of
space
allotted
to
each
orbit.
The
thickness
of
each
shell
and
the
intervals
between
them,
were
laid
down
in
Copernicus'
figures.
Were
they
spaced
in
such
a
way
that
the
five
solids
could
be
exactly
fitted
between
them?
In
the
Preface,
Kepler
had
confidently
announced
that
they
could.
Now
he
found
that
they
could
not.
There
was
fairly
good
agreement
for
the
orbits
of
Mars,
Earth
and
Venus,
but
not
for
Jupiter
and
Mercury.
The
trouble
with
Jupiter
Kepler
dismissed
with
the
disarming
remark
that
"nobody
will
wonder
at
it,
considering
the
great
distance".
As
for
Mercury,
he
frankly
resorted
to
cheating.
⁷
It
was
a
kind
of
Wonderland
croquet
through
mobile
celestial
hoops.

In
the
following
chapters
Kepler
tried
various
methods
to
explain
away
the
remaining
discrepancies.
The
fault
must
lie
either
in
his
model
or
in
the
Copernican
data;
and
Kepler
naturally
preferred
to
blame
the
latter.
First,
he
discovered
that
Copernicus
had
placed
into
the
centre
of
the
world
not
really
the
sun,
but
the
centre
of
the
earth's
orbit,
"in
order
to
save
himself
trouble
and
so
as
not
to
confuse
his
diligent
readers
by
dissenting
too
strongly
from
Ptolemy."
⁸
Kepler
undertook
to
remedy
this,
hoping
thereby
to
obtain
more
favourable
Lebensraum
for
his
five
solids.
His
mathematical
knowledge
was
as
yet
insufficient
for
this
task,
so
he
turned
for
help
to
his
old
teacher,
Maestlin,
who
willingly
complied.
The
new
figures
did
not
help
Kepler
at
all;
yet
he
had
at
one
stroke,
and
almost
inadvertently,
shifted
the
centre
of
the
solar
system
where
it
belonged.
It
was
the
first
momentous
by-product
of
the
phantom
chase.