Excerptsfrom
"Everything
was
very geometric
straight-line
approaches,"
said
Heinz-Otto Peitgen.
He was talking
about
modern art.
"The work of
Josef Albers,
for example,
trying
to
discover
the
relation of colors,
this
was
essentially
just
squares
of
different colors
put
onto
each other.
These things
were
very popular.
If you
look at it
now
it
seems
to
have passed.
People
don't
like it
any more."
(p. 229)
+++
A
movement
had begun,
and
the
discovery
of
universality
spurred it
forward.
In
the summer
of
1977,
two physicists,
Joseph Ford
and
Giulio Casati,
organized
the
first conference
on
a science
called
chaos.
It was held
in
a gracious villa
in
Como, Italy,
a tiny city
at
the southern foot
of
the lake
of
the
same name,
a
stunningly
deep blue
catchbasin
for
the
melting snow
from
the
Italian Alps.
One hundred
people
came --
mostly physicists,
but also
curious scientists
from
other fields.
"Mitch
had seen
universality
and
found out
how it
scaled
and
worked out
a way
of
getting to chaos
that was
intuitively appealing."
Ford said.
"It
was
the first time
we
had
a clear model
that
everybody
could understand.
"And
it was
one
of
those things
whose
time
had come.
In disciplines
from
astronomy
to
zoology,
people
were doing
the
same things,
publishing
in
their
narrow
disciplinary journals,
just
totally unaware
that
the
other people
were
around.
They
thought
they
were
by themselves,
and
they
were regarded
as
a bit eccentric
in
their own
areas.
They
had
exhausted
the
simple questions
you could ask
and
begun
to worry
about
phenomena
that were
a bit
more complicated.
And
these people
were
just
weepingly grateful
to
find out
that
everybody else
was
there,
too."
Later,
Feigenbaum
lived
in
a bare space,
a bed
in one room,
a computer
in another,
and,
in the third,
three
black electronic towers
for
playing
his
solidly Germanic
record collection.
His
one experiment
in
home furnishing,
the purchase
of
an expensive
marble coffee table
while
he was
in Italy,
had ended
in failure;
he received
a parcel
of
marble chips.
Piles of papers
and
books
lined the walls.
He talked
rapidly,
his
long hair,
gray now
mixed
with brown,
sweeping back
from
his forehead.
"Something dramatic
happened
in
the twenties.
For no good reason
physicists
stumbled upon
an
essentially correct
description
of
the
world around them --
because
the theory
of
quantum mechanics
is
in
some sense
essentially correct.
It tells you
how
you can take dirt
and
make computers
from it.
It's
the way
we've learned
to
manipulate
our
universe.
It's
the way
chemicals
are made
and
plastics
and
what not.
One
knows
how
to
compute
with it.
It's
an
extravagantly good
theory --
except
at some level
it
doesn't make
good sense.
Some
part
of
the imagery
is
missing.
If you ask
what
the equations
really mean
and
what is
the description
of
the world
according to
this theory,
it's
not a description
that
entails
your intuition
of
the world.
You
can't think
of
a particle
moving
as though
it has
a
trajectory.
You're
not allowed
to
visualize it
that way.
If you start
asking
more and more
subtle
questions --
what does
this theory
tell you
the
world
looks like? --
in the end
it's
so far out
of
your
normal way
of
picturing things
that
you
run into
all sorts
of
conflicts.
Now
maybe
that's
the way
the world
really is.
But
you don't
really know
that
there
isn't
another way
of
assembling
all this
information
that
doesn't
demand
so radical
a departure
from
the way
in which
you
intuit things.
There's a
fundamental
presumption
in
physics
that
the way
you understand
the world
is
that
you
keep isolating
its ingredients
until
you understand
the
stuff
that
you think
is
truly fundamental.
Then
you presume
that
the
other things
you
don't understand
are
details.
The assumption
is
that
there are
a small number
of
principles
that
you
can discern
by
looking at things
in
their pure state --
this
is
the true
analytic notion --
and
then
somehow
you
put these together
in
more complicated ways
when
you
want
to
solve
more dirty
problems.
If
you
can.
In
the end,
to
understand
you
have
to
change gears.
You
have
to
reassemble
how
you conceive
of
the
important things
that
are
going on.
You
could have
tried
to
simulate
a
model fluid system
on
a computer.
It's
just
beginning
to
be
possible.
But
it
would
have been
a
waste
of
effort,
because
what
really
happens
has
nothing to do
with
a fluid
or
a
particular equation.
It's
a
general description
of
what happens
in
a
large variety
of
systems
when
things
work
on themselves
again
and again.
It requires
a
different way
of
thinking
about
the
problem.
When you
look
at this room --
you see
junk
sitting over there
and
a person
sitting
over here
and
doors
over there --
you're
supposed
to take
the
elementary principles
of
matter
and
write down
the
wave functions
to
describe them.
Well,
this
is
not
a
feasible
thought.
Maybe
God
could do it,
but
no analytic thought
exists
for
understanding
such a problem.
It's
not
an
academic question
any more
to ask
what's
going
to happen
to
a cloud.
People
very much
want
to know --
and
that means
there's
money
available
for it.
That problem
is
very much
within
the realm
of
physics
and
it's a problem
very much
of
the
same caliber.
You're looking at
something
complicated,
and
the present way
of
solving it
is
to
try
to
look at
as many points
as
you can,
enough stuff
to
say
where
the cloud is,
where
the warm air is,
what
its velocity is,
and
so forth.
Then
you
stick it
into
the
biggest machine
you can afford
and
you
try to get
an estimate
of
what
it's going to do
next.
But
this
is
not
very
realistic."
He
stubbed out
one cigarette
and
lit another.
"One
has
to look
for
different ways.
One
has
to look
for
scaling structures --
how
do
big details
relate
to
little details.
You look
at
fluid disturbances,
complicated structures
in which
the complexity
has
come about
by
a
persistent process.
At some level
they
don't care
very much
what
the size
of
the process
is --
it
could be
the size
of
a
pea
or
the size
of
a
basketball.
The process
doesn't care
where
it is,
and
moreover
it doesn't care
how long
it's
been going.
The
only things
that
can ever
be
universal,
in a sense,
are
scaling
things.
In a way,
art
is
a theory
about
the way
the world
looks
to
human beings.
It's
abundantly
obvious
that
one
doesn't know
the world
around us
in
detail.
What
artists
have accomplished
is
realizing
that
there's
only
a small amount
of
stuff
that's important,
and then
seeing
what
it was.
So
they
can
do
some
of
my research
for
me.
When you look
at
early stuff
of
Van Gogh
there are
zillions
of
details
that
are
put into it,
there's
always
an
immense amount
of
information
in
his paintings.
It
obviously
occurred
to him,
what
is
the
irreducible amount
of
this stuff
that
you
have to
put in.
Or
you
can study
the horizons
in
Dutch ink drawings
from
around 1600,
with
tiny trees
and
cows
that
look very real.
If you
look closely,
the trees
have
sort of
leafy boundaries,
but
it
doesn't work
if
that is
all it is --
there are also,
sticking in it,
little pieces
of
twig-like stuff.
There's
a
definite interplay
between
the
softer textures
and
the things
with
more
definite lines.
Somehow
the
combination
gives
the
correct perception.
With
Ruysdael
and
Turner,
if you
look
at
the way
they
construct
complicated water,
it is
clearly
done
in
an
iterative way.
There's
some level
of
stuff,
and then
stuff
painted
on top of that,
and
then
corrections
to that.
Turbulent
fluids
for
those painters
is
always
something
with
a scale idea
in
it.
I
truly
do
want to know
how
to
describe clouds.
But
to say
there's a piece
over here
with
that much density,
and
next to it
a piece
with
this much density --
to
accumulate
that much
detailed information,
I think
is
wrong.
It's
certainly not
how
a human being
perceives
those things,
and
it's
not how
an
artist
perceives them.
Somewhere
the
business
of
writing down
partial
differential equations
is
not
to
have
done
the work
on
the problem.
Somehow
the
wondrous promise
of
the earth
is
that
there
are things
beautiful
in it,
things
wondrous
and
alluring,
and
by virtue
of
your trade
you
want
to
understand them."
He
put
the
cigarette
down.
Smoke
rose
from
the ashtray,
first
in
a
thin column
and
then
(with
a nod
to
universality)
in
broken tendrils
that
swirled
upward
to
the
ceiling.
[From pages 184 - 187]
+++
"Chaos:
Makinga
New Science",
by
James Gleick,
Penguin Books,
1987was
very geometric
straight-line
approaches,"
said
Heinz-Otto Peitgen.
He was talking
about
modern art.
"The work of
Josef Albers,
for example,
trying
to
discover
the
relation of colors,
this
was
essentially
just
squares
of
different colors
put
onto
each other.
These things
were
very popular.
look at it
now
it
seems
to
have passed.
People
don't
like it
any more."
(p. 229)
+++
A
movement
had begun,
and
the
discovery
of
universality
spurred it
forward.
In
the summer
of
1977,
two physicists,
Joseph Ford
and
Giulio Casati,
organized
the
first conference
on
a science
called
chaos.
It was held
in
a gracious villa
in
Como, Italy,
a tiny city
at
the southern foot
of
the lake
of
the
same name,
a
stunningly
deep blue
catchbasin
for
the
melting snow
from
the
Italian Alps.
One hundred
people
came --
mostly physicists,
but also
curious scientists
from
other fields.
"Mitch
had seen
universality
and
found out
how it
scaled
and
worked out
a way
of
getting to chaos
that was
intuitively appealing."
Ford said.
"It
was
the first time
we
had
a clear model
that
everybody
could understand.
"And
it was
one
of
those things
whose
time
had come.
In disciplines
from
astronomy
to
zoology,
people
were doing
the
same things,
publishing
in
their
narrow
disciplinary journals,
just
totally unaware
that
the
other people
were
around.
They
thought
they
were
by themselves,
and
they
were regarded
as
a bit eccentric
in
their own
areas.
They
had
exhausted
the
simple questions
you could ask
and
begun
to worry
about
phenomena
that were
a bit
more complicated.
And
these people
were
just
weepingly grateful
to
find out
that
everybody else
was
there,
too."
Later,
Feigenbaum
lived
in
a bare space,
a bed
in one room,
a computer
in another,
and,
in the third,
three
black electronic towers
for
playing
his
solidly Germanic
record collection.
His
one experiment
in
home furnishing,
the purchase
of
an expensive
marble coffee table
while
he was
in Italy,
had ended
in failure;
he received
a parcel
of
marble chips.
Piles of papers
and
books
lined the walls.
He talked
rapidly,
his
long hair,
gray now
mixed
with brown,
sweeping back
from
his forehead.
"Something dramatic
happened
in
the twenties.
For no good reason
physicists
stumbled upon
an
essentially correct
description
of
the
world around them --
because
the theory
of
quantum mechanics
is
in
some sense
essentially correct.
It tells you
how
you can take dirt
and
make computers
from it.
It's
the way
we've learned
to
manipulate
our
universe.
It's
the way
chemicals
are made
and
plastics
and
what not.
One
knows
how
to
compute
with it.
It's
an
extravagantly good
theory --
except
at some level
it
doesn't make
good sense.
Some
part
of
the imagery
is
missing.
If you ask
what
the equations
really mean
and
what is
the description
of
the world
according to
this theory,
it's
not a description
that
entails
your intuition
of
the world.
You
can't think
of
a particle
moving
as though
it has
a
trajectory.
You're
not allowed
to
visualize it
that way.
If you start
asking
more and more
subtle
questions --
what does
this theory
tell you
the
world
looks like? --
in the end
it's
so far out
of
your
normal way
of
picturing things
that
you
run into
all sorts
of
conflicts.
Now
maybe
that's
the way
the world
really is.
But
you don't
really know
that
there
isn't
another way
of
assembling
all this
information
that
doesn't
demand
so radical
a departure
from
the way
in which
you
intuit things.
There's a
fundamental
presumption
in
physics
that
the way
you understand
the world
is
that
you
keep isolating
its ingredients
until
you understand
the
stuff
that
you think
is
truly fundamental.
Then
you presume
that
the
other things
you
don't understand
are
details.
The assumption
is
that
there are
a small number
of
principles
that
you
can discern
by
looking at things
in
their pure state --
this
is
the true
analytic notion --
and
then
somehow
you
put these together
in
more complicated ways
when
you
want
to
solve
more dirty
problems.
If
you
can.
In
the end,
to
understand
you
have
to
change gears.
You
have
to
reassemble
how
you conceive
of
the
important things
that
are
going on.
You
could have
tried
to
simulate
a
model fluid system
on
a computer.
It's
just
beginning
to
be
possible.
But
it
would
have been
a
waste
of
effort,
because
what
really
happens
has
nothing to do
with
a fluid
or
a
particular equation.
It's
a
general description
of
what happens
in
a
large variety
of
systems
when
things
work
on themselves
again
and again.
It requires
a
different way
of
thinking
about
the
problem.
When you
look
at this room --
you see
junk
sitting over there
and
a person
sitting
over here
and
doors
over there --
you're
supposed
to take
the
elementary principles
of
matter
and
write down
the
wave functions
to
describe them.
Well,
this
is
not
a
feasible
thought.
Maybe
God
could do it,
but
no analytic thought
exists
for
understanding
such a problem.
It's
not
an
academic question
any more
to ask
what's
going
to happen
to
a cloud.
People
very much
want
to know --
and
that means
there's
money
available
for it.
That problem
is
very much
within
the realm
of
physics
and
it's a problem
very much
of
the
same caliber.
You're looking at
something
complicated,
and
the present way
of
solving it
is
to
try
to
look at
as many points
as
you can,
enough stuff
to
say
where
the cloud is,
where
the warm air is,
what
its velocity is,
and
so forth.
Then
you
stick it
into
the
biggest machine
you can afford
and
you
try to get
an estimate
of
what
it's going to do
next.
But
this
is
not
very
realistic."
He
stubbed out
one cigarette
and
lit another.
"One
has
to look
for
different ways.
One
has
to look
for
scaling structures --
how
do
big details
relate
to
little details.
You look
at
fluid disturbances,
complicated structures
in which
the complexity
has
come about
by
a
persistent process.
At some level
they
don't care
very much
what
the size
of
the process
is --
it
could be
the size
of
a
pea
or
the size
of
a
basketball.
The process
doesn't care
where
it is,
and
moreover
it doesn't care
how long
it's
been going.
The
only things
that
can ever
be
universal,
in a sense,
are
scaling
things.
In a way,
art
is
a theory
about
the way
the world
looks
to
human beings.
It's
abundantly
obvious
that
one
doesn't know
the world
around us
in
detail.
What
artists
have accomplished
is
realizing
that
there's
only
a small amount
of
stuff
that's important,
and then
seeing
what
it was.
So
they
can
do
some
of
my research
for
me.
When you look
at
early stuff
of
Van Gogh
there are
zillions
of
details
that
are
put into it,
there's
always
an
immense amount
of
information
in
his paintings.
It
obviously
occurred
to him,
what
is
the
irreducible amount
of
this stuff
that
you
have to
put in.
Or
you
can study
the horizons
in
Dutch ink drawings
from
around 1600,
with
tiny trees
and
cows
that
look very real.
If you
look closely,
the trees
have
sort of
leafy boundaries,
but
it
doesn't work
if
that is
all it is --
there are also,
sticking in it,
little pieces
of
twig-like stuff.
There's
a
definite interplay
between
the
softer textures
and
the things
with
more
definite lines.
Somehow
the
combination
gives
the
correct perception.
With
Ruysdael
and
Turner,
if you
look
at
the way
they
construct
complicated water,
it is
clearly
done
in
an
iterative way.
There's
some level
of
stuff,
and then
stuff
painted
on top of that,
and
then
corrections
to that.
Turbulent
fluids
for
those painters
is
always
something
with
a scale idea
in
it.
I
truly
do
want to know
how
to
describe clouds.
But
to say
there's a piece
over here
with
that much density,
and
next to it
a piece
with
this much density --
to
accumulate
that much
detailed information,
I think
is
wrong.
It's
certainly not
how
a human being
perceives
those things,
and
it's
not how
an
artist
perceives them.
Somewhere
the
business
of
writing down
partial
differential equations
is
not
to
have
done
the work
on
the problem.
Somehow
the
wondrous promise
of
the earth
is
that
there
are things
beautiful
in it,
things
wondrous
and
alluring,
and
by virtue
of
your trade
you
want
to
understand them."
He
put
the
cigarette
down.
Smoke
rose
from
the ashtray,
first
in
a
thin column
and
then
(with
a nod
to
universality)
in
broken tendrils
that
swirled
upward
to
the
ceiling.
[From pages 184 - 187]
+++
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