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### TL;DR
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*** "with increasing c...
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4
August
1972,
Volume
177,
Number
4047
More
Is
Different
Broken
symmetry
and
the
nature
of
the
hierarchical
structure
of
science.
P.
W.
Anderson
The
reductionist
hypothesis
may
still
be
a
topic
for
controversy
among
phi-
losophers,
but
among
the
great
majority
of
active
scientists
I
think
it
is
accepted
without
question.
The
workings
of
our
minds
and
bodies,
and
of
all
the
ani-
mate
or
inanimate
matter
of
which
we
have
any
detailed
knowledge,
are
as-
sumed
to
be
controlled
by
the
same
set
of
fundamental
laws,
which
except
under
certain
extreme
conditions
we
feel
we
know
pretty
well.
It
seems
inevitable
to
go
on
uncrit-
ically
to
what
appears
at
first
sight
to
be
an
obvious
corollary
of
reduction-
ism:
that
if
everything
obeys
the
same
fundamental
laws,
then
the
only
sci-
entists
who
are
studying
anything
really
fundamental
are
those
who
are
working
on
those
laws.
In
practice,
that
amounts
to
some
astrophysicists,
some
elemen-
tary
particle
physicists,
some
logicians
and
other
mathematicians,
and
few
others.
This
point
of
view,
which
it
is
the
main
purpose
of
this
article
to
oppose,
is
expressed
in
a
rather
well-
known
passage
by
Weisskopf
(1):
Looking
at
the
development
of
science
in
the
Twentieth
Century
one
can
dis-
tinguish
two
trends,
which
I
will
call
"intensive"
and
"extensive"
research,
lack-
ing
a
better
terminology.
In
short:
in-
tensive
research
goes
for
the
fundamental
laws,
extensive
research
goes
for
the
ex-
The
author
is
a
member
of
the
technical
staff
of
the
Bell
Telephone
Laboratories,
Murray
Hill,
New
Jersey
07974,
and
visiting
professor
of
theoretical
physics
at
Cavendish
Laboratory,
Cambridge,
England.
This
article
is
an
expanded
version
of
a
Regents'
Lecture
given
in
1967
at
the
University
of
Califomia,
La
Jolla.
4
AUGUST
1972
SCIE:NCE:
less
relevance
they
seem
to
have
to
the
very
real
problems
of
the
rest
of
sci-
ence,
much
less
to
those
of
society.
The
constructionist
hypothesis
breaks
down
when
confronted
with
the
twin
difficulties
of
scale
and
complexity.
The
behavior
of
large
and
complex
aggre-
gates
of
elementary
particles,
it
turns
out,
is
not
to
be
understood
in
terms
of
a
simple
extrapolation
of
the
prop-
erties
of
a
few
particles.
Instead,
at
each
level
of
complexity
entirely
new
properties
appear,
and
the
understand-
ing
of
the
new
behaviors
requires
re-
search
which
I
think
is
as
fundamental
in
its
nature
as
any
other.
That
is,
it
seems
to
me
that
one
may
array
the
sciences
roughly
linearly
in
a
hierarchy,
according
to
the
idea:
The
elementary
entities
of
science
X
obey
the
laws
of
planation
of
phenomena
in
terms
of
known
fundamental
laws.
As
always,
dis-
tinctions
of
this
kind
are
not
unambiguous,
but
they
are
clear
in
most
cases.
Solid
state
physics,
plasma
physics,
and
perhaps
also
biology
are
extensive.
High
energy
physics
and
a
good
part
of
nuclear
physics
are
intensive.
There
is
always
much
less
intensive
research
going
on
than
extensive.
Once
new
fundamental
laws
are
discov-
ered,
a
large
and
ever
increasing
activity
begins
in
order
to
apply
the
discoveries
to
hitherto
unexplained
phenomena.
Thus,
there
are
two
dimensions
to
basic
re-
search.
The
frontier
of
science
extends
all
along
a
long
line
from
the
newest
and
most
modern
intensive
research,
over
the
ex-
tensive
research
recently
spawned
by
the
intensive
research
of
yesterday,
to
the
broad
and
well
developed
web
of
exten-
sive
research
activities
based
on
intensive
research
of
past
decades.
The
effectiveness
of
this
message
may
be
indicated
by
the
fact
that
I
heard
it
quoted
recently
by
a
leader
in
the
field
of
materials
science,
who
urged
the
participants
at
a
meeting
dedicated
to
"fundamental
problems
in
condensed
matter
physics"
to
accept
that
there
were
few
or
no
such
problems
and
that
nothing
was
left
but
extensive
science,
which
he
seemed
to
equate
with
device
engineering.
The
main
fallacy
in
this
kind
of
thinking
is
that
the
reductionist
hypoth-
esis
does
not
by
any
means
imply
a
"constructionist"
one:
The
ability
to
reduce
everything
to
simple
fundamen-
tal
laws
does
not
imply
the
ability
to
start
from
those
laws
and
reconstruct
the
universe.
In
fact,
the
more
the
ele-
mentary
particle
physicists
tell
us
about
the
nature
of
the
fundamental
laws,
the
science
Y.
x
solid
state
or
many-body
physics
chemistry
molecular
biology
cell
biology
psychology
social
sciences
y
elementary
particle
physics
many-body
physics
chemistry
molecular
biology
physiology
psychology
But
this
hierarchy
does
not
imply
that
science
X
is
"just
applied
Y."
At
each
stage
entirely
new
laws,
concepts,
and
generalizations
are
necessary,
re-
quiring
inspiration
and
creativity
to
just
as
great
a
degree
as
in
the
previous
one.
Psychology
is
not
applied
biology,
nor
is
biology
applied
chemistry.
In
my
own
field
of
many-body
phys-
ics,
we
are,
perhaps,
closer
to
our
fun-
damental,
intensive
underpinnings
than
in
any
other
science
in
which
non-
trivial
complexities
occur,
and
as
a
re-
sult
we
have
begun
to
formulate
a
general
theory
of
just
how
this
shift
from
quantitative
to
qualitative
differ-
entiation
takes
place.
This
formulation,
called
the
theory
of
"broken
sym-
metry,"
may
be
of
help
in
making
more
generally
clear
the
breakdown
of
the
constructionist
converse
of
reduction-
ism.
I
will
give
an
elementary
and
in-
complete
explanation
of
these
ideas,
and
then
go
on
to
some
more
general
spec-
ulative
comments
about
analogies
at
393
on December 25, 2012www.sciencemag.orgDownloaded from
other
levels
and
about
similar
phe-
nomena.
Before
beginning
this
I
wish
to
sort
out
two
possible
sources
of
misunder-
standing.
First,
when
I
speak
of
scale
change
causing
fundamental
change
I
do
not
mean
the
rather
well-understood
idea
that
phenomena
at
a
new
scale
may
obey
actually
different
fundamen-
tal
laws-as,
for
example,
general
rela-
tivity
is
required
on
the
cosmological
scale
and
quantum
mechanics
on
the
atomic.
I
think
it
will
be
accepted
that
all
ordinary
matter
obeys
simple
elec-
trodynamics
and
quantum
theory,
and
that
really
covers
most
of
what
I
shall
discuss.
(As
I
said,
we
must
all
start
with
reductionism,
which
I
fully
ac-
cept.)
A
second
source
of
confusion
may
be
the
fact
that
the
concept
of
broken
symmetry
has
been
borrowed
by
the
elementary
particle
physicists,
but
their
use
of
the
term
is
strictly
an
analogy,
whether
a
deep
or
a
specious
one
remaining
to
be
understood.
Let
me
then
start
my
discussion
with
an
example
on
the
simplest
possible
level,
a
natural
one
for
me
because
I
worked
with
it
when
I
was
a
graduate
student:
the
ammonia
molecule.
At
that
time
everyone
knew
about
ammonia
and
used
it
to
calibrate
his
theory
or
his
apparatus,
and
I
was
no
exception.
The
chemists
will
tell
you
that
ammonia
"is"
a
triangular
pyramid
N
(-)
H(+)
i
(+)H
HI(+)
with
the
nitrogen
negatively
charged
and
the
hydrogens
positively
charged,
so
that
it
has
an
electric
dipole
mo-
ment
(n),
negative
toward
the
apex
of
the
pyramid.
Now
this
seemed
very
strange
to
me,
because
I
was
just
being
taught
that
nothing
has
an
electric
di-
pole
moment.
The
professor
was
really
proving
that
no
nucleus
has
a
dipole
moment,
because
he
was
teaching
nu-
clear
physics,
but
as
his
arguments
were
based
on
the
symmetry
of
space
and
time
they
should
have
been
correct
in
general.
I
soon
learned
that,
in
fact,
they
were
correct
(or
perhaps
it
would
be
more
accurate
to
say
not
incorrect)
because
he
had
been
careful
to
say
that
no
stationary
state
of
a
system
(that
is,
one
which
does
not
change
in
time)
has
an
electric
dipole
moment.
If
am-
monia
starts
out
from
the
above
un-
symmetrical
state,
it
will
not
stay
in
it
very
long.
By
means
of
quantum
me-
chanical
tunneling,
the
nitrogen
can
394
leak
through
the
triangle
of
hydrogens
to
the
other
side,
turning
the
pyramid
inside
out,
and,
in
fact,
it
can
do
so
very
rapidly.
This
is
the
so-called
"in-
version,"
which
occurs
at
a
frequency
of
about
3
X
1010
per
second.
A
truly
stationary
state
can
only
be
an
equal
superposition
of
the
unsymmetri-
cal
pyramid
and
its
inverse.
That
mix-
ture
does
not
have
a
dipole
moment.
(I
warn
the
reader
again
that
I
am
greatly
oversimplifying
and
refer
him
to
the
textbooks
for
details.)
I
will
not
go
through
the
proof,
but
the
result
is
that
the
state
of
the
system,
if
it
is
to
be
stationary,
must
always
have
the
same
symmetry
as
the
laws
of
motion
which
govern
it.
A
reason
may
be
put
very
simply:
In
quantum
me-
chanics
there
is
always
a
way,
unless
symmetry
forbids,
to
get
from
one
state
to
another.
Thus,
if
we
start
from
any
one
unsymmetrical
state,
the
system
will
make
transitions
to
others,
so
only
by
adding
up
all
the
possible
unsymmet-
rical
states
in
a
symmetrical
way
can
we
get
a
stationary
state.
The
symmetry
involved
in
the
case
of
ammonia
is
parity,
the
equivalence
of
left-
and
right-handed
ways
of
looking
at
things.
(The
elementary
particle
experimental-
ists'
discovery
of
certain
violations
of
parity
is
not
relevant
to
this
question;
those
effects
are
too
weak
to
affect
ordinary
matter.)
Having
seen
how
the
ammonia
mol-
ecule
satisfies
our
theorem
that
there
is
no
dipole
moment,
we
may
look
into
other
cases
and,
in
particular,
study
progressively
bigger
systems
to
see
whether
the
state
and
the
symmetry
are
always
related.
There
are
other
similar
pyramidal
molecules,
made
of
heavier
atoms.
Hydrogen
phosphide,
PH3,
which
is
twice
as
heavy
as
ammonia,
inverts,
but
at
one-tenth
the
ammonia
frequency.
Phosphorus
trifluoride,
PF3,
in
which
the
much
heavier
fluorine
is
substituted
for
hydrogen,
is
not
observed
to
invert
at
a
measurable
rate,
although
theo-
retically
one
can
be
sure
that
a
state
prepared
in
one
orientation
would
in-
vert
in
a
reasonable
time.
We
may
then
go
on
to
more
compli-
cated
molecules,
such
as
sugar,
with
about
40
atoms.
For
these
it
no
longer
makes
any
sense
to
expect
the
molecule
to
invert
itself.
Every
sugar
molecule
made
by
a
living
organism
is
spiral
in
the
same
sense,
and
they
never
invert,
either
by
quantum
mechanical
tunnel-
ing
or
even
under
thermal
agitation
at
normal
temperatures.
At
this
point
we
must
forget
about
the
possibility
of
in-
version
and
ignore
the
parity
symmetry:
the
symmetry
laws
have
been,
not
re-
pealed,
but
broken.
If,
on
the
other
hand,
we
synthesize
our
sugar
molecules
by
a
chemical
re-
action
more
or
less
in
thermal
equi-
librium,
we
will
find
that
there
are
not,
on
the
average,
more
left-
than
right-
handed
ones
or
vice
versa.
In
the
ab-
sence
of
anything
more
complicated
than
a
collection
of
free
molecules,
the
symmetry
laws
are
never
broken,
on
the
average.
We
needed
living
matter
to
produce
an
actual
unsymmetry
in
the
populations.
In
really
large,
but
still
inanimate,
aggregates
of
atoms,
quite
a
different
kind
of
broken
symmetry
can
occur,
again
leading
to
a
net
dipole
moment
or
to
a
net
optical
rotating
power,
or
both.
Many
crystals
have
a
net
dipole
moment
in
each
elementary
unit
cell
(pyroelectricity),
and
in
some
this
mo-
ment
can
be
reversed
by
an
electric
field
(ferroelectricity).
This
asymmetry
is
a
spontaneous
effect
of
the
crystal's
seeking
its
lowest
energy
state.
Of
course,
the
state
with
the
opposite
mo-
ment
also
exists
and
has,
by
symmetry,
just
the
same
energy,
but
the
system
is
so
large
that
no
thermal
or
quantum
mechanical
force
can
cause
a
conversion
of
one
to
the
other
in
afinite
time
com-
pared
to,
say,
the
age
of
the
universe.
There
are
at
least
three
inferences
to
be
drawn
from
this.
One
is
that
sym-
metry
is
of
great
importance
in
physics.
By
symmetry
we
mean
the
existence
of
different
viewpoints
from
which
the
sys-
tem
appears
the
same.
It
is
only
slightly
overstating
the
case
to
say
that
physics
is
the
study
of
symmetry.
The
first
demonstration
of
the
power
of
this
idea
may
have
been
by
Newton,
who
may
have
asked
himself
the
question:
What
if
the
matter
here
in
my
hand
obeys
the
same
laws
as
that
up
in
the
sky-
that
is,
what
if
space
and
matter
are
homogeneous
and
isotropic?
The
second
inference
is
that
the
in-
ternal
structure
of
a
piece
of
matter
need
not
be
symmetrical
even
if
the
total
state
of
it
is.
I
would
challenge
you
to
start
from
the
fundamental
laws
of
quantum
mechanics
and
predict
the
am-
monia
inversion
and
its
easily
observ-
able
properties
without
going
through
the
stage
of
using
the
unsymmetrical
pyramidal
structure,
even
though
no
"state"
ever
has
that
structure.
It
is
fascinating
that
it
was
not
until
a
cou-
ple
of
decades
ago
(2)
that
nuclear
phys-
icists
stopped
thinking
of
the
nucleus
as
a
featureless,
symmetrical
little
ball
and
realized
that
while
it
really
never
has
a
dipole
moment,
it
can
become
football-
SCIENCE,
VOL.
177
on December 25, 2012www.sciencemag.orgDownloaded from
shaped
or
plate-shaped.
This
has
ob-
servable
consequences
in
the
reactions
and
excitation
spectra
that
are
studied
in
nuclear
physics,
even
though
it
is
much
more
difficult
to
demonstrate
di-
rectly
than
the
ammonia
inversion.
In
my
opinion,
whether
or
not
one
calls
this
intensive
research,
it
is
as
funda-
mental
in
nature
as
many
things
one
might
so
label.
But
it
needed
no
new
knowledge
of
fundamental
laws
and
would
have
been
extremely
difficult
to
derive
synthetically
from
those
laws;
it
was
simply
an
inspiration,
based,
to
be
sure,
on
everyday
intuition,
which
sud-
denly
fitted
everything
together.
The
basic
reason
why
this
result
would
have
been
difficult
to
derive
is
an
important
one
for
our
further
think-
ing.
If
the
nucleus
is
sufficiently
small
there
is
no
real
way
to
define
its
shape
rigorously:
Three
or
four
or
ten
par-
ticles
whirling
about
each
other
do
not
define
a
rotating
"plate"
or
"football."
It
is
only
as
the
nucleus
is
considered
to
be
a
many-body
system-in
what
is
often
called
the
N
->
oo
limit-that
such
behavior
is
rigorously
definable.
We
say
to
ourselves:
A
macroscopic
body
of
that
shape
would
have
such-and-such
a
spectrum
of
rotational
and
vibrational
excitations,
completely
different
in
na-
ture
from
those
which
would
character-
ize
a
featureless
system.
When
we
see
such
a
spectrum,
even
not
so
separated,
and
somewhat
imperfect,
we
recognize
that
the
nucleus
is,
after
all,
not
macro-
scopic;
it
is
merely
approaching
macro-
scopic
behavior.
Starting
with
the
fun-
damental
laws
and
a
computer,
we
would
have
to
do
two
impossible
things
-solve
a
problem
with
infinitely
many
bodies,
and
then
apply
the
result
to
a
finite
system-before
we
synthesized
this
behavior.
A
third
insight
is
that
the
state
of
a
really
big
system
does
not
at
all
have
to
have
the
symmetry
of
the
laws
which
govern
it;
in
fact,
it
usually
has
less
symmetry.
The
outstanding
example
of
this
is
the
crystal:
Built
from
a
substrate
of
atoms
and
space
according
to
laws
which
express
the
perfect
homogeneity
of
space,
the
crystal
suddenly
and
un-
predictably
displays
an
entirely
new
and
very
beautiful
symmetry.
The
general
rule,
however,
even
in
the
case
of
the
crystal,
is
that
the
large
system
is
less
symmetrical
than
the
underlying
struc-
ture
would
suggest:
Symmetrical
as
it
is,
a
crystal
is
less
symmetrical
than
perfect
homogeneity.
Perhaps
in
the
case
of
crystals
this
appears
to
be
merely
an
exercise
in
confusion.
The
regularity
of
crystals
4
AUGUST
1972
could
be
deduced
semiempirically
in
the
mid-19th
century
without
any
complicated
reasoning
at
all.
But
some-
times,
as
in
the
case
of
superconduc-
tivity,
the
new
symmetry-now
called
broken
symmetry
because
the
original
symmetry
is
no
longer
evident-may
be
of
an
entirely
unexpected
kind
and
ex-
tremely
difficult
to
visualize.
In
the
case
of
superconductivity,
30
years
elapsed
between
the
time
when
physicists
were
in
possession
of
every
fundamental
law
necessary
for
explaining
it
and
the
time
when
it
was
actually
done.
The
phenomenon
of
superconductiv-
ity
is
the
most
spectacular
example
of
the
broken
symmetries
which
ordinary
macroscopic
bodies
undergo,
but
it
is
of
course
not
the
only
one.
Antiferro-
magnets,
ferroelectrics,
liquid
crystals,
and
matter
in
many
other
states
obey
a
certain
rather
general
scheme
of
rules
and
ideas,
which
some
many-body
the-
orists
refer
to
under
the
general
heading
of
broken
symmetry.
I
shall
not
further
discuss
the
history,
but
give
a
bibliog-
raphy
at
the
end
of
this article
(3).
The
essential
idea
is
that
in
the
so-
called
N
--
oo
limit
of
large
systems
(on
our
own,
macroscopic
scale)
it
is
not
only
convenient
but
essential
to
realize
that
matter
will
undergo
mathematically
sharp,
singular
"phase
transitions"
to
states
in
which
the
microscopic
sym-
metries,
and
even
the
microscopic
equa-
tions
of
motion,
are
in
a
sense
violated.
The
symmetry
leaves
behind
as
its
ex-
pression
only
certain
characteristic
be-
haviors,
for
instance,
long-wavelength
vibrations,
of
which
the
familiar
exam-
ple
is
sound
waves;
or
the
unusual
mac-
roscopic
conduction
phenomena
of
the
superconductor;
or,
in
a
very
deep
analogy,
the
very
rigidity
of
crystal
lat-
tices,
and
thus
of
most
solid
matter.
There
is,
of
course,
no
question
of
the
system's
really
violating,
as
opposed
to
breaking,
the
symmetry
of
space
and
time,
but
because
its
parts
find
it
ener-
getically
more
favorable
to
maintain
cer-
tain
fixed
relationships
with
each
other,
the
symmetry
allows
only
the
body
as
a
whole
to
respond
to
external
forces.
This
leads
to
a
"rigidity,"
which
is
also
an
apt
description
of
superconduc-
tivity
and
superfluidity
in
spite
of
their
apparent
"fluid"
behavior.
[In
the
for-
mer
case,
London
noted
this
aspect
very
early
(4).]
Actually, for
a
hypo-
thetical
gaseous
but
intelligent
citizen
of
Jupiter
or
of
a
hydrogen
cloud
some-
where
in
the
galactic
center,
the
proper-
ties
of
ordinary
crystals
might
well
be
a
more
baffling
and
intriguing
puzzle
than
those
of
superfluid
helium.
I
do
not
mean
to
give
the
impression
that
all
is
settled.
For
instance,
I
think
there
are
still
fascinating
questions
of
principle
about
glasses
and
other
amor-
phous
phases,
which
may
reveal
even
more
complex
types
of
behavior.
Never-
theless,
the
role
of
this
type
of
broken
symmetry
in
the
properties
of
inert
but
macroscopic
material
bodies
is
now
un-
derstood,
at
least
in
principle.
In
this
case
we
can
see
how
the
whole
becomes
not
only
more
than
but
very
different
from
the
sum
of
its
parts.
The
next
order
of
business
logically
is
to
ask
whether
an
even
more
com-
plete
destruction
of
the
fundamental
symmetries
of
space
and
time
is
possi-
ble
and
whether
new
phenomena
then
arise,
intrinsically
different
from
the
"simple"
phase
transition
representing
a
condensation
into
a
less
symmetric
state.
We
have
already
excluded
the
appar-
ently
unsymmetric
cases
of
liquids,
gases,
and
glasses.
(In
any
real
sense
they
are
more
symmetric.)
It
seems
to
me
that
the
next
stage
is
to
consider
the
system
which
is
regular
but
contains
information.
That
is,
it
is
regular
in
space
in
some
sense so
that
it
can
be
"read
out,"
but
it
contains
elements
which
can
be
varied
from
one
"cell"
to
the
next.
An
obvious
example
is
DNA;
in
everyday
life,
a
line
of
type
or
a
movie
ifim
have
the
same
struc-
ture.
This
type
of
"information-bearing
crystallinity"
seems
to
be
essential
to
life.
Whether
the
development
of
life
requires
any
further
breaking
of
sym-
metry
is
by
no
means
clear.
Keeping
on
with
the
attempt
to
char-
acterize
types
of
broken
symmetry
which
occur
in
living
things,
I
find
that
at
least
one
further
phenomenon
seems
to
be
identifiable
and
either
universal
or
remarkably
common,
namely,
ordering
(regularity
or
periodicity)
in
the
time
dimension.
A
number
of
theories
of
life
processes
have
appeared
in
which
reg-
ular
pulsing
in
time
plays
an
important
role:
theories
of
development,
of
growth
and
growth
limitation,
and
of
the
mem-
ory.
Temporal
regularity
is
very
com-
monly
observed
in
living
objects.
It
plays
at
least
two
kinds
of
roles.
First,
most
methods
of
extracting
energy
from
the
environment
in
order
to
set
up
a
continuing,
quasi-stable
process
involve
time-periodic
machines,
such
as
oscil-
lators
and
generators,
and
the
processes
of
life
work
in
the
same
way.
Second,
temporal
regularity
is
a
means
of
han-
dling
information,
similar
to
informa-
tion-bearing
spatial
regularity.
Human
spoken
language
is
an
example,
and
it
395
on December 25, 2012www.sciencemag.orgDownloaded from
is
noteworthy
that
ali
computing
ma-
chines
use
temporal
pulsing.
A
possible
third
role
is
suggested
in
some
of
the
theories
mentioned
above:
the
use
of
phase
relationships
of
temporal
pulses
to
handle
information
and
control
the
growth
and
development
of
cells
and
organisms
(5).
In
some
sense,
structure-functional
structure
in
a
teleological
sense,
as
op-
posed
to
mere
crystalline
shape-must
also
be
considered
a
stage,
possibly
in-
termediate
between
crystallinity
and
in-
formation
strings,
in
the
hierarchy
of
broken
symmetries.
To
pile
speculation
on
speculation,
I
would
say
that
the
next
stage
could
be
hierarchy
or
specialization
of
function,
or
both.
At
some
point
we
have
to
stop
talking
about
decreasing
symmetry
and
start
calling
it
increasing
complication.
Thus,
with
increasing
complication
at
each
stage,
we
go
on
up
the
hierarchy
of
the
sciences.
We
expect
to
encounter
fascinating
and,
I
believe,
very
funda-
mental
questions
at
each
stage
in
fitting
together
less
complicated
pieces
into
the
more
complicated
system
and
under-
standing
the
basically
new
types
of
be-
havior
which
can
result.
There
may
well
be
no
useful
parallel
to
be
drawn
between
the
way
in
which
complexity
appears
in
the
simplest
cases
of
many-body
theory
and
chemistry
and
the
way
it
appears
in
the
truly
complex
cultural
and
biological
ones,
except
per-
haps
to
say
that,
in
general,
the
rela-
tionship
between
the
system
and
its
parts
is
intellectually
a
one-way
street.
Synthesis
is
expected
to
be
all
but
im-
possible;
analysis,
on
the
other
hand,
may
be
not
only
possible
but
fruitful
in
all
kinds
of
ways:
Without
an
under-
standing
of
the
broken
symmetry
in
superconductivity,
for
instance,
Joseph-
son
would
probably
not
have
discovered
his
effect.
[Another
name
for
the
Joseph-
son
effect
is
"macroscopic
quantum-in-
terference
phenomena":
interference
ef-
fects
observed
between
macroscopic
wave
functions
of
electrons
in
super-
conductors,
or
of
helium
atoms
in
su-
perfluid
liquid
helium.
These
phenom-
ena
have
already
enormously
extended
the
accuracy
of
electromagnetic
mea-
surements,
and
can
be
expected
to
play
a
great
role
in
future
computers,
among
other
possibilities,
so
that
in
the
long
run
they
may
lead
to
some
of
the
major
technological
achievements
of
this
dec-
ade
(6).]
For
another
example,
biology
has
certainly
taken
on
a
whole
new
as-
pect
from
the
reduction
of
genetics
to
biochemistry
and
biophysics,
which
will
have
untold
consequences.
So
it
is
not
true,
as
a
recent
article
would
have
it
(7),
that
we
each
should
"cultivate
our
own
valley,
and
not
attempt
to
build
roads
over
the
mountain
ranges
.
.
.
between
the
sciences."
Rather,
we
should
recognize
that
such
roads,
while
often
the
quickest
shortcut
to
another
part
of
our
own
science,
are
not
visible
from
the
viewpoint
of
one
science
alone.
The
arrogance
of
the
particle
physi-
cist
and
his
intensive
research
may
be
behind
us
(the
discoverer
of
the
positron
said
"the
rest
is
chemistry"),
but
we
have
yet
to
recover
from
that
of
some
molecular
biologists,
who
seem
deter-
Natural
Areas
While
harboring
valuable
species,
natural
areas
also
serve
as
bench
marks
in
evaluating
landscape
change.
William
H.
Moir
"The
sheep
destroy
young
trees
and
when
the
old
ones
die
no
forest
will
be
left";
thus
H.
C.
Cowles
described
the
situation
after
his
epochal
study
in
1899
of
plant
succession
on
the
dunes
of
Lake
Michigan
(1).
Cowles
knew
well
how
the
heavy
hand
of
man
could
accelerate
396
changes
in
vegetation,
often
in
unde-
sirable
directions.
He
and
his
colleague
V.
E.
Shelford
had
seen
the
expanding
city
of
Gary
threaten
ever
more
of
the
".quiet
but
varied
beauty"
of
the
dunes
and
wooded
hills
(2).
Man's
destruc-
tion
of
the
natural
landscape
appeared
mined
to
try
to
reduce
everything
about
the
human
organism
to
"only"
chem-
istry,
from
the
common
cold
and
all
mental
disease
to
the
religious
instinct.
Surely
there
are
more
levels
of
orga-
nization
between
human
ethology
and
DNA
than
there
are
between
DNA
and
quantum
electrodynamics,
and
each
level
can
require-
a
whole
new
concep-
tual
structure.
In
closing,
I
offer
two
examples
from
economics
of
what
I
hope
to
have
said.
Marx
said
that
quantitative
differences
become
qualitative
ones,
but
a
dialogue
in
Paris
in
the
1920's
sums
it
up
even
more
clearly:
FITZGERALD:
The
rich
are
different
from
us.
HEMINGWAY:
Yes,
they
have
more
money.
Referces
1.
V.
F.
Weisskopf,
in
Brookhaven
Nat.
Lab.
Pubi.
888T360
(1965).
Also
see
Nuovo
Cl-
mento
Suppi.
Ser
1
4,
465
(1966);
Phys.
Today
20
(No.
5),
23
(1967).
2.
A.
Bohr
and
B.
R.
Mottelson,
Kgl.
Dan.
Vidensk.
Selsk.
Mat.
Fys.
Medd.
27,
16
(1953).
3.
Broken
symmetry
and
phase
transitions:
L.
D.
Landau,
Phys.
Z.
Sowjetunion
11,
26,
542
(1937).
Broken
symmetry
and
collective
motion,
general:
J.
Goldstone,
A.
Salam,
S.
Weinberg,
Phys.
Rev.
127,
965
(1962);
P.
W.
Anderson,
Concepts
in
Solids
(Benjamin,
New
York,
1963),
pp.
175-182;
B.
D.
Josephson,
thesis,
Trinity
College,
Cambridge
University
(1962).
Special
cases:
antiferromagnetism,
P.
W.
Anderson,
Phys.
Rev.
86,
694
(1952);
super-
conductivity,
,
ibid.
110,
827
(1958);
ibid.
112,
1900
(1958);
Y.
Nambu,
ibid.
117,
648
(1960).
4.
F.
London,
Superfluids
(Wiley,
New
York,
1950),
vol.
1.
5.
M.
H.
Cohen,
J.
Theor.
Biol.
31,
101
(1971).
6.
J.
Clarke,
Amer.
J.
Phys.
38,
1075
(1969);
P.
W.
Anderson,
Phys.
Today
23
(No.
11),
23
(1970).
7.
A.
B.
Pippard,
Reconciling
Physics
with
Reali-
ty
(Cambridge
Univ.
Press,
London,
1972).
so
widespread
and
pervasive
that
in
1917
the
newly
organized
Ecological
Society
of
America
appointed
Shelford
the
chairman
of
a
committee
to
find
out
what
remained
of
wild,
natural
America
and
to
promote
the
idea
of
a
system
of
natural
preserves
(3).
Some
50
years
later,
President
Nixon
repeated
the
need-which
had
become
urgent-of
preserving
the
natural
en-
vironment
(4):
I
am
submitting
to
Congress
several
bills
that
will
be
part
of
a
comprehensive
ef-
fort
to
preserve
our
natural
environment
and
to
provide
more
open
spaces
and
parks
in
urban
areas
where
today
they
are
often
so
scarce.
Those
50
years
had
seen
Gary
fuse
with
Calumet
City,
Hammond,
Whit-
ing,
and
East
Chicago
to
become
an
en-
vironmental
nightmare.
To
be
sure,
a
vestige
of
the
extensive
dunes
still
SCIENCE,
VOL.
177
on December 25, 2012www.sciencemag.orgDownloaded from
P. W. Anderson **opposes reductionist views of science** and the fact that two different types of research exist:
- ***Intensive research:*** concerned with fundamental laws of Nature (examples: high energy physics, nuclear physics).
- ***Extensive research:*** concerned with the explanation of phenomena in terms of fundamental laws (examples: solid state physics, biology)
He believes that complex physical systems may have characteristics that cannot be explained only in terms of the laws governing their microscopic constituents and it would thus be mistaken to consider one field more fundamental than another.
During the 20th century, fundamental physics focused on the search for a "theory of everything". Scientists believed that such a set of equations would explain the behavior of all macroscopic phenomena. P.W. Anderson argues that to completely understand the Universe many micro and macroscopic concepts are needed and that new conjectures arise with increasing complexity. ***Intensive research alone cannot provide a complete understanding of the Universe.***
This is the emergence phenomenon at work:
*** "with increasing complexity one moves up in the hierarchy of sciences" ***
For example:
- the phenomenon of life as studied in biology is an emergent property of chemistry
- psychological phenomena emerge from the neurobiological phenomena of living things
Learn more about Emergence here: [Wikipedia - Emergence](https://en.wikipedia.org/wiki/Emergence)
### Emergence:
Emergence is a phenomenon that occurs in a system of individual simpler parts only when you put the different parts together. The new larger system exhibits properties that the simpler system did not have.
For example:
- lead only becomes a metal whe several atoms of lead are bound together
- a single atom of lead is not superconducting
You can learn more about Emergence here: [Wikipedia - Emergence](https://en.wikipedia.org/wiki/Emergence)
Here is a video of P. W. Anderson explaining the concept of emergence:
[](https://youtu.be/EfpZTV1C34A?t=1090)
P. W. believes that ability to reduce everything to fundamental laws does not mean that one could simply start from those laws and reconstruct the Universe. He gives an example of the constructionist hypothesis by discussing the theory of "broken symmetry".
A more recent paper (2008) that builds on top of this paper that concludes:
> ***"The development of macroscopic laws from first principles may involve more than just systematic logic, and could require conjectures suggested by experiments, simulations or insight."***
Read on here: [More Really is Different](https://arxiv.org/pdf/0809.0151.pdf)
### TL;DR
- P. W. Anderson emphasizes the limitations of reductionism and the existence of hierarchical levels of science.
- Emergence occurs in a system of individual simpler parts only when you put the different parts together. The new, larger system exhibits new properties that cannot be explained by the simpler individual system.
- Emergent behavior opens up new ways of thinking about phenomena.
- Macroscopic concepts are essential for understanding the Universe.
- A "theory of everything" is one of many components necessary for complete understanding of the universe, but is not necessarily the only one.
***"The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts."*** - P. W. Anderson
**Fun fact:** A 2006 study comparing the number of references in a paper to the number of citations, declared Anderson to be the **"most creative"** amongst ten most cited physicists in the world.
Learn more here: [A Rational Indicator of Scientific Creativity](https://arxiv.org/pdf/physics/0608006v1.pdf)
Philip Warren Anderson is an American physicist know for his contributions to the field of Condensed Matter Physics. He was awarded the **Nobel Prize in Physics in 1977** for his contributions to the electronic structure of magnetic and disordered systems. He also made major contributions to the philosophy of science thanks to his ***writings on emergent phenomena - this paper being one of his most important contributions.***
You can learn more about P. W. Anderson here: [Philip Warren Anderson.](https://en.wikipedia.org/wiki/Philip_Warren_Anderson#cite_note-16)
