The Sleepwalkers (265 page)

10

Book
III,
ch.
13.
Quoted
by
Ch.
Seltman,
Pythagoras
,
in
History
Today
,
August
1956.

11

Quoted
by
T.
Danzig,
Number,
The
Language
of
Science
(
London,
1942),
p.
101.

12

Farrington,
op. cit., p. 43.

Part
1 Chapter III. THE EARTH ADRIFT

1

Hist.
IV, 25, 42; quoted by Dreyer, op. cit., p. 39.

2

Duhem
(op.
cit.,
p.
17)
is
inclined
to
believe
that
the
counter-earth
was
always
in
opposition
to
the
earth,
on
the
other
side
of
the
central
fire.
But
in
this
view
(deduced
from
an
ambiguous
passage
in
Pseudo-Plutarch)
the
antichton
would
have
no
practical
function.
If
the
earth
were
to
complete
a
revolution
in
twenty-four
hours
round
the
central
fire,
her
angular
velocity
would
become
prohibitive
unless
the
central
fire
were
quite
close;
in
which
case
the
counter-earth
seems
to
be
really
needed
to
prevent
her
from
going
up
in
smoke.

3

Number-lore
was
indeed
the
Achilles
heel
of
the
Pythagoreans;
but
lest
we
become
too
smug
about
antique
superstitions,
what
about
"Bode's
Law"?
In
1772,
Johannes
Daniel
Titius
of
Wittenberg
announced
that
he
had
discovered
a
simple
(but
quite
arbitrary)
numerical
law,
according
to
which
the
relative
distances
of
all
planets
from
the
sun
can
be
expressed
by
the
series
0,
3,
6,
12,
24,
etc.,
by
adding
4
to
each
term.
The
result
is
the
series
4,
7,
10,
16,
28,
52,
100,
196.
This
corresponded
surprisingly
closely
to
the
relative
distances
of
the
seven
planets
known
in
A.D.
1800;
but
the
eighth
planet,
with
distance
28
did
not
exist.
Accordingly,
in
that
year,
a
party
of
six
German
astronomers
set
out
to
look
for
the
missing
planet.
They
found
the
planetoid
Ceres;
since
then
over
five
hundred
planetoids
have
been
discovered
in
the
neighbourhood,
presumed
to
be
the
fragments
of
a
former
full-sized
planet
in
the
predicted
place.
But
to
the
question,
why
that
arbitrary
number-sequence
should
so
closely
correspond
to
fact,
no
satisfactory
answer
has
so
far
been
found.

The table reminds one curiously of
Mendeleyev's periodical table, before the discovery of isotopes.

4

The
explanation is Schiaparelli. Cf. Duhem, op. cit., I, 12.

5

To
whom
the
hypothesis
of
the
earth's
rotation
on
its
axis
is
due,
we
do
not
know.
Two
Pythagoreans
are
mentioned
as
responsible
for
it:
Hyketas
(some
sources
call
him
Niketas)
and
Ekphantus,
both
supposedly
from
Syracuse;
but
they
remain
shadows,
and
we
do
not
know
even
their
dates.
Cf.
Dreyer,
p.
49
seq.;
and
Duhem,
I,
p.
21
seq.

6

The
precession
of
the
equinoxes
was
not
discovered,
or
at
least
not
seriously
considered,
until
Hipparchus,
who
flourished
c.
125
B.C.

7

As
Venus'
angular
velocity
exceeds
that
of
the
earth,
she
will,
when
in
opposition
move
clockwise,
in
conjunction
anti-clockwise,
as
seen
from
the
earth.

8

Yet
according
to
Saidas,
when
Plato
left
for
Sicily,
he
left
the
Academy
in
Herakleides'
charge.
Ency.
Brit.
,
XI-454d.

9

Schiaparelli
Paul
Tannery
and
Pierre
Duhem;
see
Duhem,
op.
cit.,
I,
p.
410.
But
there
exists
no
evidence
in
support
of
this
hypothesis.
The
"Tychonic"
system
would
have
been
a
logical
stepping-stone
from
Herakleides
to
Aristarchus;
but
if
somebody
advocated
it,
it
should
have
left
some
trace.
It
seems
more
probable,
as
Dreyer
argues
(p.
145
ff.)
that
Aristarchus
performed
a
kind
of
mental
jump
from
Fig.
B.
to
Fig.
D.

10

Dreyer
translation, op. cit., p. 137.

11

De
facie
in
orbe
lanae,
ch.
6.
Quoted
by
Heath,
Greek
Astronomy,
p.
169.

12

Except
for
a
single
Babylonian
astronomer
named
Seleukos,
who
lived
a
whole
century
after
Aristarchus
and
developed
a
theory
of
the
tides
based
on
the
earth's
rotation.