The Sleepwalkers (122 page)

The
fact
that
space
has
three
dimensions
is
itself
a
reflection,
a
"signature"
of
the
mystic
Trinity:

"And
thus
are
bodily
things,
thus
are
materia
corporea
represented
in
tertia
quantatis
specie
trium
dimensionum
."
²⁰

The
unifying
truth
between
the
mind
of
God
and
the
mind
of
man
is
represented
for
Kepler,
as
it
was
for
the
Pythagorean
Brotherhood,
by
the
eternal
and
ultimate
truths
of
"divine
Geometry".

"Why
waste
words?
Geometry
existed
before
the
Creation,
is
co-eternal
with
the
mind
of
God,
is
God
himself
(what
exists
in
God
that
is
not
God
himself?);
geometry
provided
God
with
a
model
for
the
Creation
and
was
implanted
into
man,
together
with
God's
own
likeness
–
and
not
merely
conveyed
to
his
mind
through
the
eyes."
²¹

But
if
God
created
the
world
after
a
geometrical
model,
and
endowed
man
with
an
understanding
of
geometry,
then
it
must
be
perfectly
feasible,
young
Kepler
thought,
to
deduce
the
whole
blueprint
of
the
universe
by
pure
a
priori
reasoning,
by
reading
the
mind
of
the
Creator,
as
it
were.
The
astronomers
are
"the
priests
of
God,
called
to
interpret
the
Book
of
Nature",
and
surely
priests
have
a
right
to
know
the
answers.

If
Kepler's
evolution
had
stopped
here,
he
would
have
remained
a
crank.
But
I
have
already
pointed
out
the
contrast
between
the
a
priori
deductions
in
the
first
part
of
the
book
and
the
modern
scientific
approach
of
the
second.
This
co-existence
of
the
mystical
and
the
empirical,
of
wild
flights
of
thought
and
dogged,
painstaking
research,
remained,
as
we
shall
see,
the
main
characteristic
of
Kepler
from
his
early
youth
to
his
old
age.
Other
men
living
on
the
watershed
displayed
the
same
dualism,
but
in
Kepler
it
was
more
pointed
and
paradoxical,
carried
to
extremes
verging
on
insanity.
It
accounts
for
the
incredible
mixture
in
his
works
of
recklessness
and
pedantic
caution,
his
irritability
and
patience,
his
naivety
and
philosophical
depth.
It
emboldened
him
to
ask
questions
which
nobody
had
dared
to
ask
without
trembling
at
their
audacity,
or
blushing
at
their
apparent
foolishness.
Some
of
them
appear
to
the
modern
mind
as
meaningless.
The
others
led
to
the
reconciliation
of
earth-physics
with
sky-geometry,
and
were
the
beginning
of
modern
cosmology.
That
some
of
his
own
answers
were
wrong,
does
not
matter.
As
in
the
case
of
the
Ionian
philosophers
of
the
heroic
age,
the
philosophers
of
the
Renaissance
were
perhaps
more
remarkable
for
the
revolutionary
nature
of
the
questions
they
asked
than
for
the
answers
they
proposed.
Paracelsus
and
Bruno,
Gilbert
and
Tycho,
Kepler
and
Galileo
formulated
some
answers
which
are
still
valid;
but
first
and
foremost
they
were
giant
question-masters.
Post
factum
,
however,
it
is
always
difficult
to
appreciate
the
originality
and
imagination
it
required
to
ask
a
question
which
had
not
been
asked
before.
In
this
respect,
too,
Kepler
holds
the
record.

Some
of
his
questions
were
inspired
by
a
medieval
brand
of
mysticism,
and
yet
proved
to
be
amazingly
fertile.
The
shifting
of
the
First
Mover
from
the
periphery
of
the
universe
into
the
physical
body
of
the
sun,
symbol
of
the
Godhead,
prepared
the
way
to
the
concept
of
a
gravitational
force,
symbol
of
the
Holy
Ghost,
which
controls
the
planets.
Thus
a
purely
mystical
inspiration
was
the
root
out
of
which
the
first
rational
theory
of
the
dynamics
of
the
universe
developed,
based
on
the
secular
trinity
of
Kepler's
laws.

Equally
astonishing
was
the
fertility
of
Kepler's
errors
–
starting
with
a
universe
built
around
the
five
solids,
and
ending
with
a
universe
governed
by
musical
harmonies.
This
process,
of
error
begetting
truth,
is
illuminated
by
Kepler's
own
comments
on
the
Mysterium
Cosmographicum
.
They
are
contained
in
his
Notes
to
the
second
edition,
to
which
I
have
repeatedly
referred,
written
twenty-five
years
later.
In
complete
contrast
to
his
claim
that
the
book
was
written
as
if
under
the
dictation
of
a
"heavenly
oracle",
and
represented
"an
obvious
act
of
God",
Kepler's
notes
castigate
its
errors
with
acid
sarcasm.
The
book
starts,
as
we
remember,
with
an
"Outline
of
my
Principal
Proof"
and
Kepler's
comment
starts
with
"Woe
to
me,
here
I
blundered."
The
ninth
chapter
deals
with
the
"sympathies"
between
the
five
solids
and
the
individual
planets;
in
the
Notes
it
is
dismissed
as
a
mere
"astrological
fancy".
Chapter
10,
"On
the
Origin
of
Privileged
Numbers",
is
described
in
the
Notes
as
"empty
chatter";
Chapter
11,
"Concerning
the
Positions
of
the
Regular
Solids
and
the
Origin
of
the
Zodiac",
is
qualified
in
the
Notes
as
"irrelevant,
false,
and
based
on
illegitimate
assumptions".
On
Chapter
17,
concerning
the
orbit
of
Mercury,
Kepler's
comments
are:
"this
is
not
at
all
true",
"the
reasoning
of
the
whole
chapter
is
wrong".
The
important
twentieth
chapter,
"On
the
Relation
between
the
Motions
and
Orbits",
in
which
the
Third
Law
is
foreshadowed,
is
dismissed
as
faulty
"because
I
used
uncertain
ambiguous
words
instead
of
arithmetical
method".
The
twenty-first
chapter,
which
discusses
discrepancies
between
theory
and
observation,
is
attacked
in
the
Notes
in
an
almost
unfairly
petulant
manner;
e.g.:
"This
question
is
superfluous...
Since
there
is
no
discrepancy,
why
did
I
have
to
invent
one?"