The Sleepwalkers (191 page)

The
paradox,
then,
is
not
in
the
mystic
nature
of
Kepler's
edifice
but
in
the
modern
architectural
elements
which
it
employed,
in
its
combination
of
incompatible
building
materials.
Dream-architects
are
not
worried
about
imprecisions
of
a
fraction
of
a
decimal;
they
do
not
spend
twenty
years
with
dreary,
heart-breaking
computations
to
build
their
fantasy
towers.
Only
some
forms
of
insanity
show
this
pedantic
method
in
madness.
In
reading
certain
chapters
of
the
Harmonice
,
one
is
indeed
reminded
of
the
explosive
yet
painstakingly
elaborate
paintings
by
schizophrenics,
which
would
pass
as
legitimate
art
if
painted
by
a
savage
or
a
child,
but
are
judged
by
clinical
standards
if
one
knows
that
they
are
the
work
of
a
middle-aged
chartered
accountant.
The
Keplerian
schizophrenia
becomes
apparent
only
when
he
is
judged
by
the
standard
of
his
achievements
in
optics,
as
a
pioneer
of
the
differential
calculus,
the
discoverer
of
the
three
Laws.
His
split
mind
is
revealed
in
the
manner
in
which
he
saw
himself
in
his
non-obsessional
moments:
as
a
sober
"modern"
scientist,
unaflected
by
any
mystic
leanings.
Thus
he
writes
about
the
Scottish
Rosicrucian,
Robert
Fludd:

"It
is
obvious
that
he
derives
his
main
pleasure
from
unintelligible
charades
about
the
real
world,
whereas
my
purpose
is,
on
the
contrary,
to
draw
the
obscure
facts
of
nature
into
the
bright
light
of
knowledge.
His
method
is
the
business
of
alchemists,
hermetists
and
Paracelsians,
mine
is
the
task
of
the
mathematician."
²²

These
words
are
printed
in
Harmonice
Mundi
,
which
is
buzzing
with
astrological
and
Paracelsian
ideas.

A
second
point
is
equally
relevant
to
the
Keplerian
paradox.
The
main
reason
why
he
was
unable
to
realize
how
rich
he
was
–
that
is,
to
understand
the
significance
of
his
own
Laws
–
is
a
technical
one:
the
inadequacy
of
the
mathematical
tools
of
his
time.
Without
differential
calculus
and/or
analytical
geometry,
the
three
Laws
show
no
apparent
connection
with
each
other
–
they
are
disjointed
bits
of
information
which
do
not
make
much
sense.
Why
should
God
will
the
planets
to
move
in
ellipses?
Why
should
their
speed
be
governed
by
the
area
swept
over
by
the
radius
vector,
and
not
by
some
more
obvious
factor?
Why
should
the
ratio
between
distance
and
period
be
mixed
up
with
cubes
and
squares?
Once
you
know
the
inverse
square
law
of
gravity
and
Newton's
mathematical
equations,
all
this
becomes
beautifully
self-evident.
But
without
the
roof
which
holds
them
together,
Kepler's
Laws
seem
to
have
no
particular
raison
d'être
.
Of
the
first
he
was
almost
ashamed:
it
was
a
departure
from
the
circle
sacred
to
the
ancients,
sacred
even
to
Galileo
and,
for
different
reasons,
to
himself.
The
ellipse
had
nothing
to
recommend
it
in
the
eyes
of
God
and
man;
Kepler
betrayed
his
bad
conscience
when
he
compared
it
to
a
cartload
of
dung
which
he
had
to
bring
into
the
system
as
a
price
for
ridding
it
of
a
vaster
amount
of
dung.
The
Second
Law
he
regarded
as
a
mere
calculating
device,
and
constantly
repudiated
it
in
favour
of
a
faulty
approximation;
the
Third
as
a
necessary
link
in
the
system
of
harmonies,
and
nothing
more.
But
then,
without
the
notion
of
gravity
and
the
method
of
the
calculus,
it
could
be
nothing
more.

Johannes
Kepler
set
out
to
discover
India
and
found
America.
It
is
an
event
repeated
over
and
again
in
the
quest
for
knowledge.
But
the
result
is
indifferent
to
the
motive.
A
fact,
once
discovered,
leads
an
existence
of
its
own,
and
enters
into
relations
with
other
facts
of
which
their
discoverers
have
never
dreamt.
Apollonius
of
Perga
discovered
the
laws
of
the
useless
curves
which
emerge
when
a
plane
intersects
a
cone
at
various
angles:
these
curves
proved,
centuries
later,
to
represent
the
paths
followed
by
planets,
comets,
rockets,
and
satellites.

"One
cannot
escape
the
feeling,"
wrote
Heinrich
Herz,
"that
these
mathematical
formulae
have
an
independent
existence
and
an
intelligence
of
their
own,
that
they
are
wiser
thin
we
are,
wiser
even
than
their
discoverers,
that
we
get
more
out
of
them
than
was
originally
put
into
them."