The
metaphors of information processing and computation are at
the center of today's intellectual action. A new and unified
language of science is beginning to emerge.
|
Participants
(left to right): Ray
Kurzweil, Seth Lloyd, JB, Alan Guth, Paul Steinhardt,
Marvin Minsky |
 Dennis
Overbye (The New York Times), Jordan
Mejias (Frankfurter Allgemeine Zeitung),
Steve Lohr (The New York Times), Steven
Levy (Newsweek) |
 Marvin
Minsky, Seth Lloyd, Paul Steinhardt, Alan Guth,
Ray Kurzweil |
n
July 21, Edge held an event at Eastover Farm which
included the physicists Seth Lloyd, Paul Steinhardt, and
Alan Guth, computer scientist Marvin Minsky, and technologist
Ray Kurzweil. This year, I noted there are a lot of "universes" floating
around. Seth Lloyd: the computational universe (or, if you
prefer, the it and bit-itty bitty-universe); Paul Steinhardt:
the cyclic universe; Alan Guth: the inflationary universe;
Marvin Minsky: the emotion universe, Ray Kurzweil: the intelligent
universe. I asked each of the speakers to comment on their "universe".
All, to some degree, were concerned with information processing
and computation as central metaphors. See below for their
links to their talks and streaming video.
Concepts of information and computation have infiltrated a
wide range of sciences, from physics and cosmology, to cognitive
psychology, to evolutionary biology, to genetic engineering.
Such innovations as the binary code, the bit, and the algorithm
have been applied in ways that reach far beyond the programming
of computers, and are being used to understand such mysteries
as the origins of the universe, the operation of the human
body, and the working of the mind.
What's
happening in these new scientific
endeavors is truly a work in progress.
A year ago, at the first REBOOTING
CIVILIZATION meeting in
July, 2001, physicists Alan Guth
and Brian Greene, computer scientists
David Gelernter, Jaron Lanier, and
Jordan Pollack, and research psychologist
Marc D. Hauser could not reach a
consensus about exactly what computation
is, when it is useful, when it is
inappropriate, and what it reveals.
Reporting on the event in The
New York Times ("Time
of Growing Pains for Information
Age", August 7, 2001), Dennis
Overbye wrote:
Mr.
Brockman said he
had been inspired
to gather the group
by a conversation
with Dr. Seth Lloyd,
a professor of mechanical
engineering and quantum
computing expert
at M.I.T. Mr. Brockman
recently posted Dr.
Lloyd's statement
on his Web site,
www.edge.org:
"Of course, one
way of thinking about
all of life and civilization,"
Dr. Lloyd said, "is
as being about how
the world registers
and processes information.
Certainly that's what
sex is about; that's
what history is about.
Humans have always
tended to try to envision
the world and themselves
in terms of the latest
technology. In the
17th and 18th centuries,
for example, workings
of the cosmos were
thought of as the workings
of a clock, and the
building of clockwork
automata was fashionable.
But not everybody in
the world of computers
and science agrees
with Dr. Lloyd that
the computation metaphor
is ready for prime
time.
Several of the people
gathered under the
maple tree had come
in the hopes of debating
that issue with Dr.
Lloyd, but he could
not attend at the last
moment. Others were
drawn by what Dr. Greene
called "the glimmer
of a unified language"
in which to talk about
physics, biology, neuroscience
and other realms of
thought. What happened
instead was an illustration
of how hard it is to
define a revolution
from the inside.
Indeed,
exactly what computation
and information are
continue to be subjects
of intense debate.
But less than a year
later, in the "Week
In Review" section
of the Sunday New
York Times ("What's
So New In A Newfangled
Science?",
June 16, 2002) George
Johnson wrote
about
"a movement some
call digital physics
or digital philosophy — a
worldview that has
been slowly developing
for 20 years."...
Just
last week, a professor at the Massachusetts
Institute of Technology named Seth
Lloyd published a paper in Physical
Review Letters estimating how
many calculations the universe
could have performed since the
Big Bang — 10^120 operations
on 10^90 bits of data, putting
the mightiest supercomputer to
shame. This grand computation essentially
consists of subatomic particles
ricocheting off one another and "calculating"
where to go.
As the researcher Tommaso Toffoli
mused back in 1984, "In a sense,
nature has been continually computing
the `next state' of the universe
for billions of years; all we have
to do — and, actually, all we
can do — is `hitch a ride' on
this huge ongoing computation."
This may seem like an odd way to
think about cosmology. But some scientists
find it no weirder than imagining
that particles dutifully obey ethereal
equations expressing the laws of
physics. Last year Dr. Lloyd created
a stir on Edge.org,
a Web site devoted to discussions
of cutting edge science, when he
proposed
"Lloyd's hypothesis": "Everything
that's worth understanding about
a complex system can be understood
in terms of how it processes information."*....
Dr,
Lloyd did indeed cause
a stir when his ideas
were presented on Edge in
2001, but George Johnson's
recent New York
Times piece caused
an even greater stir,
as Edge received
over half a million
unique visits the following
week, a strong confirmation
that something is indeed
happening here. (Usual Edge readership
is about 60,000 unique
visitors a month).
There is no longer
any doubt that the
metaphors of information
processing and computation
are at the center of
today's intellectual
action. A new and unified
language of science
is beginning to emerge.
For
last year's REBOOTING
CIVILIZATION meeting
click here.
THE
COMPUTATIONAL UNIVERSE:
SETH LLOYD [10.21.02]
Every physical system
registers information,
and just by evolving
in time, by doing its
thing, it changes that
information, transforms
that information, or,
if you like, processes
that information. Since
I've been building quantum
computers I've come around
to thinking about the
world in terms of how
it processes information.
SETH
LLOYD is Professor
of Mechanical
Engineering
at MIT and
a principal
investigator
at the Research
Laboratory
of Electronics.
He is also
adjunct assistant
professor at
the Santa Fe
Institute.
He works on
problems having
to do with
information
and complex
systems from
the very small—how
do atoms process
information,
how can you
make them compute,
to the very
large — how
does society
process information?
And how can
we understand
society in
terms of its
ability to
process information?
His
seminal
work in
the fields
of quantum
computation
and quantum
communications —
including
proposing
the first
technologically
feasible
design for
a quantum
computer,
demonstrating
the viability
of quantum
analog computation,
proving quantum
analogs of
Shannon's
noisy channel
theorem,
and designing
novel methods
for quantum
error correction
and noise
reduction — has
gained him
a reputation
as an innovator
and leader
in the field
of quantum
computing.
Lloyd has
been featured
widely in
the mainstream
media including
the front
page of The
New York
Times, The
LA Times, The
Washington
Post, The
Economist, Wired, The
Dallas Morning
News,
and The
Times (London),
among others.
His name
also frequently
appears (both
as writer
and subject)
in the pages
of Nature, New
Scientist, Science and Scientific
American.
THE
COMPUTATIONAL
UNIVERSE
SETH
LLOYD: I'm
a professor
of mechanical
engineering
at MIT. I
build quantum
computers
that store
information
on individual
atoms and
then massage
the normal
interactions
between the
atoms to
make them
compute.
Rather than
having the
atoms do
what they
normally
do, you make
them do elementary
logical operations
like bit
flips, not
operations,
and-gates,
and or-gates.
This allows
you to process
information
not only
on a small
scale, but
in ways that
are not possible
using ordinary
computers.
In order
to figure
out how to
make atoms
compute,
you have
to learn
how to speak
their language
and to understand
how they
process information
under normal
circumstances.
It's been known
for more than
a hundred years,
ever since
Maxwell, that
all physical
systems register
and process
information.
For instance,
this little
inchworm right
here has something
on the order
of Avogadro's
number of atoms.
And dividing
by Boltzmann's
concept, its
entropy is
on the order
of Avogadro's
number of bits.
This means
that it would
take about
Avogadro's
number of bits
to describe
that little
guy and how
every atom
and molecule
is jiggling
around in his
body in full
detail. Every
physical system
registers information,
and just by
evolving in
time, by doing
its thing,
it changes
that information,
transforms
that information,
or, if you
like, processes
that information.
Since I've
been building
quantum computers
I've come around
to thinking
about the world
in terms of
how it processes
information.
A
few years
ago I wrote
a paper in Nature called "Fundamental
Physical
Limits to
Computation," in
which I showed
that you
could rate
the information
processing
power of
physical
systems.
Say that
you're building
a computer
out of some
collection
of atoms.
How many
logical operations
per second
could you
perform?
Also, how
much information
could these
systems register?
Using relatively
straightforward
techniques
you can show,
for instance,
that the
number of
elementary
logical operations
per second
that you
can perform
with that
amount of
energy, E,
is just E/H
- well, it's
2E divided
by pi times
h-bar. [h-bar
is essentially
10[-34] (10
to the -34)
Joule-seconds,
meaning that
you can perform
10[-50] (10
to the 50)
ops per second.)]If
you have
a kilogram
of matter,
which has
mc2 —
or around 10[17]
Joules (10
to the 17)
Joules
— worth
of energy and
you ask how
many ops per
second it could
perform, it
could perform
10[17] (ten
to the 17)
Joules / h-bar.
It would be
really spanking
if you could
have a kilogram
of matter
— about
what a laptop
computer weighs — that
could process
at this rate.
Using all the
conventional
techniques
that were developed
by Maxwell,
Boltzmann,
and Gibbs,
and then developed
by von Neumann
and others
back at the
early part
of the 20th
century for
counting numbers
of states,
you can count
how many bits
it could register.
What you find
is that if
you were to
turn the thing
into a nuclear
fireball
— which
is essentially
turning it
all into radiation,
probably the
best way of
having as many
bits as possible
— then
you could register
about 10[30]
(10 to the
30) bits. Actually
that's many
more bits than
you could register
if you just
stored a bit
on every atom,
because Avogadro's
number of atoms
store about
10[24] (10
to the 24)
bits.
Having done
this paper
to calculate
the capacity
of the ultimate
laptop, and
also to raise
some speculations
about the role
of information-processing
in, for example,
things like
black holes,
I thought that
this was actually
too modest
a venture,
and that it
would be worthwhile
to calculate
how much information
you could process
if you were
to use all
the energy
and matter
of the universe.
This came up
because back
in when I was
doing a Masters
in Philosophy
of Science
at Cambridge.
I studied with
Stephen Hawking
and people
like that,
and I had an
old cosmology
text. I realized
that I can
estimate the
amount of energy
that's available
in the universe,
and I know
that if I look
in this book
it will tell
me how to count
the number
of bits that
could be registered,
so I thought
I would look
and see. If
you wanted
to build the
most powerful
computer you
could, you
can't do better
than including
everything
in the universe
that's potentially
available.
In particular,
if you want
to know when
Moore's Law,
this fantastic
exponential
doubling of
the power of
computers every
couple of years,
must end, it
would have
to be before
every single
piece of energy
and matter
in the universe
is used to
perform a computation.
Actually, just
to telegraph
the answer,
Moore's Law
has to end
in about 600
years, without
doubt. Sadly,
by that time
the whole universe
will be running
Windows 2540,
or something
like that.
99.99% of the
energy of the
universe will
have been listed
by Microsoft
by that point,
and they'll
want more!
They really
will have to
start writing
efficient software,
by gum. They
can't rely
on Moore's
Law to save
their butts
any longer.
I
did this
calculation,
which was
relatively
simple. You
take, first
of all, the
observed
density of
matter in
the universe,
which is
roughly one
hydrogen
atom per
cubic meter.
The universe
is about
thirteen
billion years
old, and
using the
fact that
there are
pi times
10[7] (10
to the 7)
seconds in
a year, you
can calculate
the total
energy that's
available
in the whole
universe.
Remembering
that there's
a certain
amount of
energy, you
then divide
by Planck's
Constant
— which
tells you how
many ops per
second can
be performed
— and
multiply by
the age of
the universe,
and you get
the total number
of elementary
logical operations
that could
have been performed
since the universe
began. You
get a number
that's around
10[120] (10
to the 120).
It's a little
bigger —
10[122] (10
to the 122)
or something
like that — but
within astrophysical
units, where
if you're within
a factor of
one hundred,
you feel that
you're okay;
The
other way
you can calculate
it is by
calculating
how it progresses
as time goes
on. The universe
has evolved
up to now,
but how long
could it
go? One way
to figure
this out
is to take
the phenomenological
observation
of how much
energy there
is, but another
is to assume,
in a Guthian
fashion,
that the
universe
is at its
critical
density.
Then there's
a simple
formula for
the critical
density of
the universe
in terms
of its age;
G, the gravitational
constant;
and the speed
of light.
You plug
that into
this formula,
assuming
the universe
is at critical
density,
and you find
that the
total number
of ops that
could have
been performed
in the universe
over time
(T) since
the universe
began is
actually
the age of
the universe
divided by
the Planck
scale
— the
time at which
quantum gravity
becomes important
— quantity
squared. That
is, it's the
age of the
universe squared,
divided by
the Planck
length, quantity
squared. This
is really just
taking the
energy divided
by h-bar, and
plugging in
a formula for
the critical
density, and
that's the
answer you
get.
This
is just a
big number.
It's reminiscent
of other
famous big
numbers that
are bandied
about by
numerologists.
These large
numbers are,
of course,
associated
with all
sorts of
terrible
crank science.
For instance,
there's the
famous Eddington
Dirac number,
which is
10[40] (10
to the 40).
It's the
ratio between
the size
of the universe
and the classical
size of the
electron,
and also
the ratio
between the
electromagnetic
force of,
say, the
hydrogen
atom, and
the gravitational
force on
the hydrogen
atom. Dirac
went down
the garden
path to try
to make a
theory in
which this
large number
had to be
what it was.
The number
that I've
come up with
is suspiciously
reminiscent
of (10[40])[3]
(10 to the
40, quantity
cubed). This
number, 10[120],
(10 to the
120) is normally
regarded
as a coincidence,
but in fact
it's not
a coincidence
that the
number of
ops that
could have
been performed
since the
universe
began is
this number
cubed, because
it actually
turns out
to be the
first one
squared times
the other
one. So whether
these two numbers
are the same
could be
a coincidence,
but the fact
that this
one is equal
to them cubed
is not.
Having
calculated
the number
of elementary
logical operations
that could
have been
performed
since the
universe
began, I
went and
calculated
the number
of bits,
which is
a similar,
standard
sort of calculation.
Say that
we took all
of this beautiful
matter around
us on lovely
Eastover
Farm, and
vaporized
it into a
fireball
of radiation.
This would
be the maximum
entropy state,
and would
enable it
to store
the largest
possible
amount of
information.
You can easily
calculate
how many
bits could
be stored
by the amount
of matter
that we have
in the universe
right now,
and the answer
turns out
to be 10[90]
(10 to the
90). This
is necessary,
just by standard
cosmological
calculations —
it's (10[120])[3/4]
(10 to the
120, quantity
to the 3/4
power). We
can store 10[90]
(10 to the
90) bits in
matter, and
if one believes
in somewhat
speculative
theories about
quantum gravity
such as holography
— in which
the amount
of information
that can be
stored in a
volume is bounded
by the area
of the volume
divided by
the Planck
Scale squared
— and
if you assume
that somehow
information
can be stored
mysteriously
on unknown
gravitational
degrees of
freedom, then
again you get
10[120] (10
to the 120).
This is because,
of course,
the age of
the universe
squared divided
by the Planck
length squared
is equal to
the size of
the universe
squared divided
by the Planck
length. So
the age of
the universe
squared, divided
by the Planck
time squared
is equal to
the size of
the universe
divided by
the Planck
length, quantity
squared. So
we can do 10[120]
(10 to the
120) ops on
10[90] (10
to the 90)
bits.
I
made these
calculations
not to suggest
any grandiose
plan or to
reveal large
numbers,
although
of course
I ended up
with some
large numbers,
but I was
curious what
these numbers
were. When
I calculated
I actually
thought that
these can't
be right
because they
are too small.
I can think
of much bigger
numbers than
10[120] (10
to the 120).
There are
lots of bigger
numbers than
that. It
was fun to
calculate
the computational
capacity
of the universe,
but I wanted
to get at
some picture
of how much
computation
the universe
could do
if we think
of it as
performing
a computation.
These numbers
can be interpreted
essentially
in three
ways, two
of which
are relatively
uncontroversial.
The first
one I already
gave you:
it's an upper
bound to
the size
of a computer
that we could
build if
we turned
everything
in the universe
into a computer
running Windows
2540. That's
uncontroversial.
So far nobody's
managed to
find a way
to get around
that. There's
also a second
interpretation,
which I think
is more interesting.
One of the
things we
do with our
quantum computers
is to use
them as analog
computers
to simulate
other physical
systems.
They're very
good at simulating
other quantum
systems,
at simulating
quantum field
theories,
at simulating
all sort
of effects,
down to the
quantum mechanical
scale that
is hard to
understand
and hard
to simulate
classically.
These numbers
are a lower
limit to
the size
of a computer
that could
simulate
the whole
universe,
because to
simulate
something
you need
at least
as much stuff
as is there.
You need
as many bits
in your simulator
as there
are bits
registered
in the system
if you are
going to
simulate
it accurately.
And if you're
going to
follow it
step by step
throughout
its evolution,
you need
at least
as many steps
in your simulator
as th | |
