[Senate Hearing 108-943]
[From the U.S. Government Publishing Office]



                                                        S. Hrg. 108-943

 
                         A NEW KIND OF SCIENCE

=======================================================================

                                HEARING

                               before the

                  SUBCOMMITTEE ON SCIENCE, TECHNOLOGY,
                               AND SPACE

                                 of the

                         COMMITTEE ON COMMERCE,
                      SCIENCE, AND TRANSPORTATION
                          UNITED STATES SENATE

                      ONE HUNDRED EIGHTH CONGRESS

                             FIRST SESSION

                               __________

                           SEPTEMBER 4, 2003

                               __________

    Printed for the use of the Committee on Commerce, Science, and 
                             Transportation




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       SENATE COMMITTEE ON COMMERCE, SCIENCE, AND TRANSPORTATION

                      ONE HUNDRED EIGHTH CONGRESS

                             FIRST SESSION

                     JOHN McCAIN, Arizona, Chairman
TED STEVENS, Alaska                  ERNEST F. HOLLINGS, South 
CONRAD BURNS, Montana                    Carolina, Ranking
TRENT LOTT, Mississippi              DANIEL K. INOUYE, Hawaii
KAY BAILEY HUTCHISON, Texas          JOHN D. ROCKEFELLER IV, West 
OLYMPIA J. SNOWE, Maine                  Virginia
SAM BROWNBACK, Kansas                JOHN F. KERRY, Massachusetts
GORDON H. SMITH, Oregon              JOHN B. BREAUX, Louisiana
PETER G. FITZGERALD, Illinois        BYRON L. DORGAN, North Dakota
JOHN ENSIGN, Nevada                  RON WYDEN, Oregon
GEORGE ALLEN, Virginia               BARBARA BOXER, California
JOHN E. SUNUNU, New Hampshire        BILL NELSON, Florida
                                     MARIA CANTWELL, Washington
                                     FRANK R. LAUTENBERG, New Jersey
      Jeanne Bumpus, Republican Staff Director and General Counsel
             Robert W. Chamberlin, Republican Chief Counsel
      Kevin D. Kayes, Democratic Staff Director and Chief Counsel
                Gregg Elias, Democratic General Counsel
                                 ------                                

             SUBCOMMITTEE ON SCIENCE, TECHNOLOGY, AND SPACE

                    SAM BROWNBACK, Kansas, Chairman
TED STEVENS, Alaska                  JOHN B. BREAUX, Louisiana, Ranking
CONRAD BURNS, Montana                JOHN D. ROCKEFELLER IV, West 
TRENT LOTT, Mississippi                  Virginia
KAY BAILEY HUTCHISON, Texas          JOHN F. KERRY, Massachusetts
JOHN ENSIGN, Nevada                  BYRON L. DORGAN, North Dakota
GEORGE ALLEN, Virginia               RON WYDEN, Oregon
JOHN E. SUNUNU, New Hampshire        BILL NELSON, Florida
                                     FRANK R. LAUTENBERG, New Jersey


                            C O N T E N T S

                              ----------                              
                                                                   Page
Hearing held on September 4, 2003................................     1
Statement of Senator Brownback...................................     1

                               Witnesses

Wolfram, Dr. Stephen, Founder and CEO, Wolfram Research, Inc., 
  and Author of A New Kind of Science............................     2
    Prepared statement...........................................     4


                         A NEW KIND OF SCIENCE

                              ----------                              


                      THURSDAY, SEPTEMBER 4, 2003

                               U.S. Senate,
    Subcommittee on Science, Technology, and Space,
        Committee on Commerce, Science, and Transportation,
                                                    Washington, DC.
    The Subcommittee met, pursuant to notice, at 3:36 p.m. in 
room SR-253, Russell Senate Office Building, Hon. Sam 
Brownback, Chairman of the Subcommittee, presiding.

           OPENING STATEMENT OF HON. SAM BROWNBACK, 
                    U.S. SENATOR FROM KANSAS

    Senator Brownback. I call the hearing to order. Good 
afternoon to everybody.
    It's my pleasure to welcome one of the world's most 
respected scientists to testify today, Dr. Stephen Wolfram. 
He's the author of the best-selling book, ``A New Kind of 
Science.''
    Dr. Wolfram studied at Oxford and, at the age of 20, 
received his Ph.D. from Caltech. In the early 1980s, he made a 
series of discoveries about systems known as cellular automata, 
which have yielded many new insights in physics, mathematics, 
computer science, biology, and other fields. In 1986, he 
founded Wolfram Research, Incorporated, and began the creation 
of Mathematica, now the world's leading software system for 
scientific and technical computing. In addition to leading this 
company and creating innovative technology, Dr. Wolfram is now 
developing a series of research and educational initiatives in 
the science he has created.
    Dr. Wolfram, I asked you to come before this Committee 
today, because I'm intrigued by the work you have done and 
documented in your book. The theories you propose are exciting, 
and I'm very interested in how your work might, if possible, be 
used by the National Science Foundation, the National Institute 
of Health, NASA, and other Federal agencies to study the 
universe and how it operates, or perhaps answer some of the 
deepest questions about nature, space, and science. I'm anxious 
to hear from you on these thoughts.
    I had a chance to visit with Dr. Wolfram before the hearing 
today, and I found it very educational and interesting. I'm 
seeing here a basic science that has the possibility of being 
used in a number of places throughout the world. Since this 
country invests so heavily in forward-thinking science, 
research and development, I think Dr. Wolfram's ideas are 
worthy of a good hard look and we'll see if there are things 
that we should be doing additionally.
    Dr. Wolfram, I'm delighted to have you here. Thank you for 
giving us your time, your talent, and your information. I look 
forward to your testimony and to the answers to some of the 
questions I may have afterwards.
    Welcome.

  STATEMENT OF DR. STEPHEN WOLFRAM, FOUNDER AND CEO, WOLFRAM 
      RESEARCH, INC., AND AUTHOR OF A NEW KIND OF SCIENCE

    Dr. Wolfram. Thank you. And thanks very much for inviting 
me here today.
    Nearly four centuries ago, Galileo turned a telescope to 
the sky for the first time. And what he saw changed forever our 
view of the universe and ultimately launched much of modern 
science. I've had the privilege to begin to explore another new 
world made visible not by telescopes but by computers. And in 
that world, I've made some most surprising discoveries that 
have led me to a new kind of science.
    Well, the computer revolution has been fueled by our 
ability to have computers run specific programs built for 
specific tasks. But what if we were to explore the world of all 
possible programs? What would we find out there? Well, here's a 
representation of a very simple program for coloring squares 
down a page. So this is what happens if we run the program. 
Simple program. Makes a simple pattern.
    Here's a program, though, that I call ``rule 30.'' And, 
again, it's a very simple program. But now look at what it 
does. So that little program makes all of this. It's amazing. 
And I think it's also profoundly important. Because I think it 
finally shows us the essential secret that nature uses to make 
so much complexity.
    For about 300 years, the exact sciences have been built on 
mathematical equations, and they've made and continue to make 
great progress on many fronts. But in the face of significant 
complexity, they've consistently gotten stuck. And I believe 
the reason is a fundamental one, and that to go further one 
needs a new kind of science whose foundation is programs, not 
just mathematics.
    At the core of this new kind of science is an exploration 
of the abstract world of simple programs. But from this, come 
applications, both immediate and profoundly far-reaching. If in 
the past we'd been faced with something like this, we would 
never expect to understand it. But now we've discovered that 
this can come from that little very simple program.
    In nature we find many elaborate patterns like the one on 
this mollusk shell, for example, which we can now see can be 
explained by very simple programs. And, for example, throughout 
biology, complexity can come from simple programs, which then 
finally begins to give us the possibility of, sort of, a true 
theoretical biology.
    Today, for example, we know the genome. But now we must 
work out how it operates. And I think simple programs are key. 
Fifty years ago, we found the basic mechanism for heredity. 
Perhaps now simple programs can show us the basic mechanisms 
for processes like aging.
    Traditional mathematical science has had its greatest 
success in physics. But still we do not have an ultimate theory 
of physics. And, indeed, our theories always just seem to get 
more complicated. But one of the suggestions of my work is that 
at the very lowest level, below even space and time, there may 
just be a simple program, a program which, if run for long 
enough, would actually reproduce in precise detail everything 
in our universe.
    Finding that program will be a dramatic moment for science. 
But from the progress I've made, I'm actually hopeful that it 
may not be too far away.
    There are also many more everyday issues to which simple 
programs bring new models and perspectives, not only in physics 
and biology, but also, for example, in earth and social 
sciences. Simple programs also seem uniquely suited to 
analyzing many critical systems that involve large numbers of 
interconnected parts.
    Having captured phenomena scientifically, one can start to 
harness them for technology. So now we can begin to create 
technology based not on concepts like wheels or waves, but on 
processes like this one. And as we explore the vast world of 
simple programs, we can, sort of, systematically mine it for 
technology, finding new and unexpected programs that can be 
used for encryption or pattern recognition or decentralized 
control, perhaps even finding programs that manipulate 
information more like humans, and, indeed, creating a whole new 
generation of technology from which new industries can grow.
    One of my surprising discoveries embodied in what I call 
the Principle of Computational Equivalence is that powerful 
computation is fundamentally common. It doesn't take a 
sophisticated CPU chip to be able to do computation. Simple 
programs do it, like this one or like many others in nature.
    This has many deep implications for what can and cannot be 
done in science, but it also immediately suggests that we can 
use much simpler elements to make computers, which, for 
example, points to a new approach to nanotechnology.
    Well, over the past year, my book has stimulated great 
activity in many scientific and technical communities, as well 
as, of course, as some of the turbulence one should expect in 
any potential paradigm shift.
    In moving forward, education is key, and there's certainly 
no lack of enthusiastic students. Institutional structures will 
take time to develop, but it's been exciting to see how quickly 
teaching of some of the core ideas has begun, even at a high 
school level.
    One day the study of the computational world will no doubt 
be an established science, like a physics or chemistry or 
mathematics. But today the exploration of the computational 
world still stands before us as a great frontier with the 
potential not only to unlock some of the deepest questions in 
science, but also to define a whole new direction for 
technology.
    Thanks. Well, I just tried to cover 25 years of work in 5 
minutes, but I'd be happy to expand on anything.
    [The prepared statement of Dr. Wolfram follows:]

      Prepared Statement of Dr. Stephen Wolfram, Founder and CEO, 
      Wolfram Research, Inc., and Author of A New Kind of Science

    Thank you for inviting me here today.
    Nearly four centuries ago, Galileo turned a telescope to the sky 
for the first time. What he saw changed forever our view of the 
universe--and ultimately launched much of modern science. I have had 
the privilege of beginning to explore another new world, made visible 
not by telescopes but by computers. And in that world I have made some 
most surprising discoveries--that have led me to a new kind of science.
    The computer revolution has been fueled by our ability to have 
computers run specific programs built for particular tasks. But what if 
we were to explore the world of all possible programs? What would we 
find out there? Here is a representation of a very simple program for 
coloring squares down a page.



    This is what happens if we run the program.

    
    
    The simple program makes a simple pattern.
    But here is a program I call rule 30. 

    
    
    Again it's a very simple program. But now look at what it does . 
That little program makes all of this. It's amazing. And I think it's 
also profoundly important. Because I think it finally shows us the 
essential secret that nature uses to make so much complexity.



    For three hundred years the exact sciences have been built on 
mathematical equations. And they have made--and continue to make--great 
progress on many fronts. But in the face of significant complexity, 
they have consistently gotten stuck. And I believe the reason is a 
fundamental one. And that to go further one needs a new kind of 
science, whose foundation is programs, not just mathematics.
    At the core of this new kind of science is an exploration of the 
abstract world of simple programs. But from this, there come 
applications, both immediate and profoundly far-reaching. If in the 
past we had been faced with something like this we would never expect 
to understand it. 



But now we have discovered that it can just come from this very simple 
program.



    In nature, we find many elaborate patterns--like the ones on this 
mollusk shell. Which we now see can be explained by very simple 
programs. And for example throughout biology, complexity can come from 
simple programs which then finally begins to give us the possibility of 
a true theoretical biology.



    Today we know the genome. But now we must work out how it 
operates--and I think simple programs are key. Fifty years ago we found 
the basic mechanism for heredity; perhaps now simple programs can show 
us basic mechanisms for processes like aging.



    Traditional mathematical science has had its greatest success in 
physics. But still we do not have an ultimate theory of physics. And 
indeed our theories always just seem to get more complicated. But one 
of the suggestions of my work is that at the very lowest level--below 
even space and time--there may just be a simple program. A program, 
which, if run long enough, would actually reproduce in precise detail 
everything in our universe.
    Finding that program would be a dramatic moment for science. But 
from the progress I have made, I am hopeful that it may not be too far 
away.
    There are also many more everyday issues to which simple programs 
bring new models and perspectives--not only in physics and biology, but 
also for example in earth and social sciences. Simple programs also 
seem uniquely suited to analyzing many critical systems that involve 
large numbers of interconnected parts.
    Having captured phenomena scientifically, one can start to harness 
them for technology. So now we can begin to create technology built not 
on concepts like wheels or waves, but on processes like this. And as we 
explore the vast world of simple programs, we can systematically mine 
it for technology. Finding new and unexpected programs that can be used 
for encryption, or pattern recognition, or decentralized control. 
Perhaps even finding programs that manipulate information more like 
humans. And indeed creating a whole new generation of technology--from 
which new industries can grow.



    One of my surprising discoveries--embodied in what I call the 
Principle of Computational Equivalence--is that powerful computation is 
fundamentally common. It doesn't take a sophisticated CPU chip to be 
able to do computation. Simple programs do it. Like this one. 



    Or like many of the ones in nature.

    
    
    This has many deep implications for what can and cannot be done in 
science. But it also immediately suggests that we can use much simpler 
elements to make computers. Which for example points to a new approach 
to nanotechnology.
    Over the past year, my book has stimulated great activity in many 
scientific and technical communities. As well, of course, as some of 
the turbulence one should expect in any potential paradigm shift.
    In moving forward, education is key--and there is no lack of 
enthusiastic students. Institutional structures will take time to 
develop. But it has been exciting to see how quickly teaching of some 
of the core ideas has begun even at the high school level.
    One day the study of the computational world will no doubt be an 
established science, like physics, or chemistry, or mathematics. But 
today the exploration of the computational world still stands before us 
as a great frontier. With the potential not only to unlock some of the 
deepest questions in science, but also to define a whole new direction 
for technology.
    Thank you. I just tried to cover twenty-five years of work in five 
minutes. I'd be happy to expand on anything.
Further Information
    Book: Stephen Wolfram, A New Kind of Science (Wolfram Media, 2002)
    Website: www.wolframscience.com
About Stephen Wolfram
    Stephen Wolfram was born in London and educated at Eton, Oxford, 
and Caltech. He received his Ph.D. in theoretical physics in 1979 at 
the age of 20, and in 1981 was recognized with a MacArthur award.
    In the early 1980s he made a series of discoveries about systems 
known as cellular automata, which have yielded many new insights in 
physics, mathematics, computer science, biology and other fields.
    In 1986 he founded Wolfram Research, Inc. and began the creation of 
Mathematica, now the world's leading software system for scientific and 
technical computing.
    With Mathematica as his tool, Wolfram spent the 1990s pursuing an 
ambitious program of basic science, culminating in the 2002 release of 
his 1200-page book A New Kind of Science. An immediate bestseller, the 
book has been widely hailed as initiating a paradigm shift of historic 
importance in science.
    In addition to leading his company and creating innovative 
technology, Wolfram is now developing a series of research and 
educational initiatives in the science he has created.

    Senator Brownback. Well, please pardon me at the outset if 
I ask some dumb questions, OK? Because what you've put forward 
is very profound, it's going to take me some time to really 
absorb it.
    As I understand, the thesis in your book is that all 
systems of nature are basically a set of simple programs. Is 
that a working thesis for what you work under? I mean, as you 
demonstrated in the shell diagram, I think I've seen where you 
have butterfly patterns at some points. Virtually everything in 
nature is a simple program?
    Dr. Wolfram. Yes, I believe that simple programs are a good 
way to describe many kinds of systems in nature. There are 
other ways to describe systems in nature--for example, 
traditional mathematical equations--that have their domains of 
applicability. But I think, for many of the kinds of situations 
where particularly we see complex behavior in nature, simple 
programs are the right form of description.
    Also, it's my guess that if we look at the most, sort of, 
fundamental ultimate level underneath physics, that ultimately 
there should be a simple program that describes everything in 
our physical universe as something that, sort of, is the 
ultimate law for physics.
    Senator Brownback. Have you moved further on that theory, 
then, as well, on the ultimate law of physics into a simple 
program?
    Dr. Wolfram. Yes, I've made a--I think, a certain amount of 
progress. The thing that one sees, if one looks at, sort of, 
the history of physics is that there tends to be--as soon as 
one looks a greater level of smallness, from atoms to particles 
to quarks to strings and so on, it seems like the theories that 
one's using are getting ever more complicated. But what's 
happened, from the work that I've done on studying, sort of, 
the computational world, is that I've, sort of, developed the 
intuition that there might be, ultimately, a simple program 
that actually produces the kinds of things we see in physics.
    Just like, for example, in this example here, you can see 
these little structures running around that have, in many ways, 
characteristics a bit like the particles we see in elementary 
particle physics. This just a, sort of--this is just a, sort 
of, simple idealization of that, but it gets, kind of, the 
point across, that from, for example, the very simple rule 
that's defined here, you can see there are several different 
kinds of structures that arise that are at least a caricature 
of the kinds of things that we see or the different kinds of 
particles--electrons and quarks and those sorts of things.
    I've been interested in trying to understand what type of 
rule might actually be ``the'' underlying rule for the 
universe. One of the things one realizes is that if there is a 
simple underlying rule for the universe, it's almost inevitable 
that the things that we're familiar with, features of space and 
time and so on, will not be immediately visible in that 
underlying rule, that, sort of, there isn't room to fit in all 
those details that we know about the universe into some tiny 
rule. So that means that, as we try to study that rule, we're, 
sort of, confronted with kinds of things that, to us, must seem 
very abstract, because they're not familiar from our everyday 
experience.
    While I have, sort of, a definite kind of approach to what 
that underlying rule might be like, and it has to do with 
various kinds of discreet networks of points and so on, but one 
of the key ideas is that, for example, space, which we usually 
think of as just being, sort of, a background on top of which 
everything in the universe exists, that space actually has a 
definite structure, and that, sort of, underneath space, there 
is a kind of a discreet network that is what everything we know 
in the universe is built up from.
    It's kind of like when you look at a fluid, like water, for 
example, we perceive it as kind of a continuous material, but 
we know, from what's been discovered about atoms and so on, 
that underneath this apparently continuous material there are a 
bunch of discreet molecules bouncing around. And I'm guessing 
that the same is true of space.
    So there's a fair bit to say, and I've made a fair amount 
of progress, and I've been very encouraged. As one tries to 
assess a scientific theory, one of the ways that one does that 
is to say, sort of, How much does one get out for what one put 
in? And what I've been very encouraged by is that by putting in 
only very small amounts, it's been possible to get out a lot of 
things that one can, sort of, explain, in terms of what one 
knows about the way that gravity works and the way that various 
other features of the physical world work.
    Senator Brownback. Well, talk to me about gravity. Have you 
found a simple program associated with gravity, thus far?
    Dr. Wolfram. A slightly complicated answer, but I can--let 
me give it a try here.
    So the--one question is, sort of, we have to start talking 
about what the--let me see if I can get this to work--we have 
to start talking about what the structure of space might 
actually be. I'm trying to show an example here.
    My concept of the structure of space has to do with making, 
kind of, a network where--in space, there are just these 
discreet points, and every point is connected to other points. 
And one might think, How could anything like space, as we know 
it, arise from some structure like that? The answer is, if you 
have enough points--just like if you have enough molecules in 
water, so to speak, the, sort of, aggregate behavior of all of 
these is like a continuous fluid, and the same kind of thing 
happens in space.
    And when it comes to thinking about gravity, one of the, 
kind of, key ideas, due to Einstein originally, in thinking 
about the way that gravity works, is this notion that one can 
think of gravity as related to curvature in space. And it turns 
out that, in this, kind of, model of what's underneath space, 
of these kinds of discreet networks that lie underneath space, 
there's an analog of that kind of curvature that Einstein 
studied in the General Theory of Relativity and so on. And it 
turns out that the features of that curvature that seem to 
arise from properties of these networks are exactly the 
features--seem to be exactly the features that Einstein showed 
were there in his General Theory of Relativity.
    So what happens, to give some indication of how--well, 
let's see--this is just an example of, kind of, how the notion 
of curvature in space could arise, what one can have if one 
has--I think I'm--I'm happy to talk about this, but I think it 
may get--may veer. This is--one of the challenges in my book 
is, I wanted to write the things I wrote in a way that would be 
as accessible as possible, without, sort of, the need to know 
all of the technical details of the development of physics for 
the last long period of time. And the question of studying 
gravity is one that, to really explain it well, involves quite 
a few steps of explaining what's been done in physics over the 
past hundred or so years.
    Senator Brownback. But, if I'm understanding what you're 
saying here is, this is a pattern you would suggest might show 
a simple program that creates a gravity network through the 
curvature. Am I gathering what you're saying?
    Dr. Wolfram. Roughly so, yes.
    I mean, to give some idea of how this might work, if one of 
these networks represented what space looks like, on an 
incredibly small scale, one question one can ask is, How does 
space change over time? And to give, sort of, an indication of 
how that might work, I have, sort of, an example of, kind of, 
how one of these networks--I think I have an example; yes--of 
how one of these networks, sort of, rewrites itself according 
to a very simple rule. And the rule that's being followed is 
one where every time there's a--as a piece of network that has 
a particular structure, it gets transformed into a piece of 
network with a different structure. And just applying that same 
rule over and over again, one builds up a sequence of different 
networks. And the point is that when one looks at a large 
enough version of that network, the, kind of, large-scale 
properties of the network seem to correspond to what we know 
about the way that curvature in space works and the way that 
gravity works.
    Senator Brownback. Take me to your mollusk example. And 
what's the program of the pattern of the mollusk on the shell?
    Dr. Wolfram. So here's a, sort of, an idealized version of 
the mollusk doing its thing. And the way it works is--I think I 
have a--one of these right here--the way it works is, there's a 
line of cells on the growing edge of the--there's a creature 
that lives inside this shell, and it lays down the shell in 
lines, and there's a row of cells on the growing edge. What 
happens is that the question--these cells either secrete 
pigment, or they don't. And it seems that the--one can describe 
the rules by which they decide whether to secret pigment by 
something like this that says: if a cell to the left is 
secreting pigment at this step and the cell to the right is 
not, for example, then at the next step the cell in the middle 
will secrete pigment. So it's, kind of, a simple rule that 
describes whether pigment will be secreted by a particular cell 
as the mollusk grows.
    And the point is that, from that very simple underlying 
rule, it happens, purely as a, kind of--as a matter of, kind 
of, abstract fact, that that simple rule--from that simple 
underlying rule, there emerges this complicated pattern that 
one sees on an actual mollusk shell.
    One of the things that's interesting, perhaps, is if one 
looks, for example, at different mollusks. You ask, what kinds 
of patterns can different mollusks produce? One of the things 
that I find very encouraging, from the point of view of, sort 
of, building the theoretical biology, is the fact that it seems 
that if you look at this, sort of, diversity of patterns that 
you see on different mollusks that exists, that the collection 
of patterns that you see corresponds well with the selection of 
patterns that you would see from, sort of, all possible simple 
programs of a certain kind. So it's as if these different 
mollusks were just, sort of, sampling simple programs at 
random, and then we get to see the results of those programs 
displayed on the mollusks' shells.
    Senator Brownback. So that each of these mollusks have some 
simple pattern. It's a slight derivation of each other, it 
looks like. I mean, they all have a pattern, and you're just 
saying that each of these are going to have some sort of fairly 
simple discreet patterns, slightly different, that produce 
these different coloring patterns on the mollusk.
    Dr. Wolfram. Right. So the question is, What are the 
underlying rules? So sometimes those underlying rules lead to 
very simple patterns of stripes, let's say. Sometimes the 
underlying rules lead to much more complicated patterns that 
are perhaps hard to describe verbally.
    What is interesting, I think, is that if one looks at the 
different possible rules that could be what was being 
implemented by these mollusks, then one can look at, sort of, 
the selection of possible rules of a certain simple kind. This 
is all possible rules of a certain simple kind. And what we see 
is that the types of rules that are represented here, the types 
of patterns that are produced correspond well with the patterns 
that we actually see in the biological organisms that exist.
    So if we were--normally, in biology, it tends to be the 
case that one imagines that the structure of organisms today, 
for example, is something that reflects some long evolutionary 
history, and that the details of organisms today can only be, 
sort of, explained on the basis of knowing the, sort of, series 
of historical accidents that took place in the course of their 
evolution. One of the things that's sort of interesting about 
this is that there's a suggestion that one could actually have 
an actual predictive theory of how these organisms might work, 
because it seems to be the case that's what going on is in--at 
some level, that the organisms are just sampling different 
possible programs at random. So, just by knowing abstractly 
about what features, sort of, the space of all possible 
programs has, we can say things about what features these 
biological organisms are likely to have.
    Senator Brownback. So, have you come up with some 
computational pattern for some of these mollusk shells, where 
you've said, ``OK, this would appear to be the pattern for this 
shell''?
    Dr. Wolfram. Yes. Yes. I mean, the--it's a----
    Senator Brownback. Well, run one of those out, or enlarge 
one--can you enlarge one shell--showing me the simple pattern, 
and then let it run its course.
    Dr. Wolfram. The particular technology I have here would--
it would take me some futzing around to actually----
    Senator Brownback. OK, then don't.
    Dr. Wolfram. But coming back to something like this, what--
let me--well, what we see--one thing to understand is, whenever 
you make a model of something, there's a question of, sort of, 
What's the essential feature that you want to capture, and what 
are you going to idealize away? So when we make--when we try to 
reproduce these patterns in a model based on simple rules, what 
will happen is that we will have been successful if we manage 
to reproduce the, sort of, essential features of this pattern. 
There will be little bumps and perturbations that, you know, 
might have corresponded to, you know, what the mollusk ate on 
some particular day, so to speak, that we will not be able to 
reproduce. But the point is that we will reproduce the fact 
that we get, sort of, an overall pattern of stripes, or that we 
get some elaborate pattern which contains lots of little 
triangles, and so on. That's what we would expect, and that's 
what we do succeed in reproducing from this kind of simple 
model.
    Senator Brownback. Take me back to your evolutionary point 
that--we, in biology, have looked at this for some period of 
time as, sort of, a series of historical anomalies that then 
got built into the pattern. But what you're saying is then you 
can predict somehow, in the future, what that pattern may look 
like? I'm not sure I caught that point of what you were saying, 
that we've been focused on mostly observation, but you think 
there are predictable sets of computation--or a predictable set 
of programming options that may be presented?
    Dr. Wolfram. Right. So one of the questions is--in biology, 
what seems to be going on is that there's some underlying 
program that's represented in the genome, and, in the actual 
development of an individual organism, what's happening is that 
that program is being run to produce whatever structure exists 
in the organism. The question is, for example, How did that 
program get picked? Which program is picked? How is it chosen, 
and so on?
    Well, one of the things that will be, sort of, the simplest 
hypothesis is, let's say that some of the--that programs are 
just picked at random by, sort of, random mutations that take 
place in the course of biological evolution. What one might 
have thought is that no process like that--that one wouldn't 
expect that one would ever get anything complicated happening 
from a process like that. Kind of, the traditional intuition 
has tended to be: in order to get something complicated to 
happen, you have to, sort of, go to a lot of effort and put a 
lot of things in.
    What I've discovered from looking at, sort of, what's out 
there in the computational world is that that's not the case. 
In the world of programs, you can have a very simple program 
where, in a sense, you put very little in, yet you get great 
complexity of behavior out. And so what, sort of, in a sense, 
the simplest hypothesis is--let's say that some particular 
feature of some particular class of organisms were--just came--
let's say that the programs that generated that feature were 
picked at random. What would that feature then look like?
    Well, what seems to be the case--and I've, sort of, opened 
up the study of this question and certainly haven't filled in 
all the details of it--is that, in a variety of situations that 
I've looked at, it is--seems to be so that among the different 
organisms that exist on the Earth, so to speak, that they have, 
kind of, sampled a large fraction of the possible--of the space 
of possible simple programs. So that a good hypothesis for 
figuring out what one will see in these different organisms--
what kinds of mollusk-shell patterns one will see, what kind of 
shapes one will see in leaves, things like that--that a good 
first hypothesis is that among all the leaves that exist and 
all the different species of plants and so on, they will be 
distributed roughly in the way that one would expect if one 
just picked simple programs for making leaves at random. And 
that's interesting, because that then gives one an actual, sort 
of, abstract prediction that says, just given the study of the 
properties of simple programs, we can then make a prediction 
about what we would expect to see among the different kinds of 
leaves that exist on actual plants.
    Senator Brownback. Give me some other examples that you 
have of what you've observed in nature. I mean----
    Dr. Wolfram. Well, so within biology there are--let's see--
somewhere here I should have some--ah, within biology, I 
mentioned shapes of leaves. They're kind of interesting because 
there's such a diversity of different kinds of shapes, from 
smooth, very simple shapes to very complicated shapes and so 
on, and it's not obvious that there should be some underlying--
some simple underlying process that produces these. Well, it 
turns out that it seems like there is, and this is an example 
of, kind of, the--applying a set of rules that produce a 
pattern that corresponds to a particular kind of leaf. If you 
look at, sort of, all possible rules of this kind, it seems to 
cover well the considerable diversity of different shapes of 
leaves that----
    Senator Brownback. Wow.
    Dr. Wolfram.--we actually observe.
    Senator Brownback. So that's a series of simple programs, 
to the lefthand column, that produce that type of complexity of 
leaves, to the right?
    Dr. Wolfram. Yes.
    So the--I mean, this is--within the biology, here are some 
examples. I think the--sort of, the--one of the, I think, 
fundamental questions in biology is--when we see things that go 
on in biological organisms, what is the underlying mechanism 
that produces the behavior we see? Is it something that's a 
very complicated thing that we can never really expect to 
understand in any fundamental way, or is there ultimately some 
quite simple rule, some quite simple mechanism which, when, 
kind of, played out, produces some very complicated behavior or 
structure in biological organism? And I think what one's 
seeing, in the examples that I've looked at, is, sort of, an 
encouragement that there are much simpler, much more 
understandable kinds of mechanisms taking place in biological 
systems.
    It's, sort of--in a sense, when one tries to, for example, 
make models of biological systems, there are certain kinds of 
raw material that one can use for those models. For example, 
one could use, oh, something from traditional mathematics, 
where one's saying, you know, there's a particular equation 
that's satisfied by this chemical concentration, let's say. Or 
one can use some very mechanical kind of explanation that says, 
you know, when you push this end of a lever, so to speak, the 
other end will go up. This is, kind of, a different form of 
mechanism, where one's saying--where one has a simple program 
of such and such a kind, then when one, sort of, plays out the 
consequences of that, one will see this particular form be 
produced that may be a complicated form, as in the case of, for 
example, these leaves or the mollusk patterns.
    Outside of biology, there are all sorts of other examples. 
Here's an example, for instance, in physics, sort of, a typical 
kind of elaborate pattern that we see often depicted as 
snowflake shapes. There's a question of, ``Why do snowflakes 
end up having these complicated shapes?'' And it turns out 
that, again, there's a--if one--in this case, one can, sort of, 
trace down the physics of how snowflakes are formed. And as one 
tries to, sort of, capture the essential mechanism that's going 
on, it seems that when one does capture, sort of, what seems to 
be the essential mechanism and, kind of, plays out what those 
rules imply, this is what happens.
    Senator Brownback. That was a simple program that you just 
put forward?
    Dr. Wolfram. Yes.
    And so if you look, for example, at all the stages that you 
produce, they correspond well to the actual shapes we see in 
snowflakes. It seems like from just having a simple rule that's 
saying something about how you have a hexagonal grid of cells, 
where every cell either has solid in it corresponding to ice or 
doesn't have solid in it, there's a simple rule that says you 
add a cell of solid if--in this particular case, if there's 
exactly one cell of solid on the previous step. That's the 
whole rule. And that captures various physical processes that 
go on in the actual formation of a snowflake. And as you, kind 
of, see what the consequences of that rule are, this is what 
their consequences are.
    Senator Brownback. Now, I've heard it said that no two 
snowflakes are alike. I don't know if that's accurate or not. 
Is that true?
    Dr. Wolfram. Not entirely. What tends to happen is that two 
snowflakes that you collect nearby, they often come from far 
away in the cloud, and so they've come through different, kind 
of, life histories, and so they tend to look rather different. 
But the----
    Senator Brownback. But then there are obviously a lot of 
different types and structures of snowflakes.
    Dr. Wolfram. Yes.
    Senator Brownback. Millions.
    Dr. Wolfram. Well, I think that--actually, that snowflakes 
go through, kind of, definite stages, and those stages 
correspond well to what you see in this kind of model. And what 
is surprising to people, I think--and it's an example of a, 
sort of, general surprise that one has about the way that 
complicated behavior arises--is one sees these very diverse 
kinds of shapes--because, I mean, some of these shapes just 
look like, kind of, simple hexagons; some of them seem to have 
lots of treelike arms and so on--and one might imagine, if one 
just saw one of these shapes, one might say there couldn't be a 
simple way that this was produced. Because our intuition tends 
to be that--when we see something complicated, that it must 
have had a complicated cause. The surprising thing, and the, 
sort of, thing that, sort of, I have gradually come to 
understand from, sort of, exploring the computational world, is 
that actually there can be simple rules that underlie even 
these sorts of complicated patterns.
    Senator Brownback. And even something that seems so random 
to us, as a series of different shaped snowflakes, could 
actually be all in the same computational--simple computational 
model.
    Dr. Wolfram. Yes.
    One of the things that's often interesting, there are many 
phenomena that we just say--we might just say, ``Oh, that seems 
random.'' And, in a sense, when we say that, that's really just 
saying, ``Well, we don't have a theory, a method for predicting 
how this particular phenomenon is going to work.'' So we just 
say, ``Let's just say it's random. Let's just say it's 
something that we can't make predictions about.''
    Senator Brownback. Different leaf shapes. You know, the 
different ones. It just seems like it's fairly random, what 
tree ended up with what shape of leaves.
    Dr. Wolfram. Right.
    Well, so, for example, another case that I've studied, to 
some extent, is the case of turbulence in fluids. It's a case 
where it's a very fundamental physical phenomenon that has 
great engineering importance, that if a fluid, like water or 
air, flows rapidly past an obstacle, it kind of curls up behind 
the obstacle making a very random-looking pattern. The question 
is, Where does that randomness come from? What's the, sort of, 
fundamental origin of that randomness? Is the randomness, for 
example, some reflection of, sort of, underlying, sort of, 
randomness in the atoms in the air or water? Is it something 
that comes from some, sort of, detail about the way that the 
system was started off? I don't think it's either of those. 
Those are the, sort of, traditional theories for where it might 
come from.
    I think, instead, it's much more like the phenomenon that 
one sees in these simple program systems. To give an example, 
well, something like this one, where what you see here looks 
quite random, in many ways; yet the way it was produced is by a 
very definite rule, just following that same rule over and over 
again. And what you see in this case--in fact, for a number of 
technological purposes, it's important to be able to make good 
randomness quickly, and, in fact, this rule is a good way of 
doing that. Even though it's a very simple system, when you run 
it, its behavior seems, for all practical purposes, random, if 
you look, for example, at the column of cells just down the 
center of the pattern.
    Senator Brownback. Now, you've made a comment, ``good 
randomness quickly.'' So what do you mean, that that pattern 
can be produced with that program quite quickly?
    Dr. Wolfram. Yes. Yes.
    Senator Brownback. So that a fluid, when it flows past 
something that could trigger that--I mean, or that type of 
programming moves into place automatic--or very quickly.
    Dr. Wolfram. Yes. Yes.
    I mean, one of the things that's remarkable, when you look 
at fluids, for instance, is how quickly they do complicated 
things. When you look at a splash, for example, splashes have 
very complicated structure, yet they're made, kind of, 
instantaneously, so to speak, in a fluid. And there's a 
question of, sort of, how that works.
    One of the things that's true about randomness, complicated 
behavior made in this way, is that every time you run this 
particular program you'll get the exact same result. Even 
though it's very complicated and even though if you were 
presented with its output, if you tried to apply statistical 
methods or other kinds of things, they would just say, ``No, 
there's no pattern to this. It just looks random.'' Even though 
that's the case, every time you run this particular program 
you'll get the same result. So that means that--that has an 
important implication when one looks at phenomena like fluid 
turbulence, because it says that one might expect that these 
apparently random patterns are actually repeatable from one run 
of this experiment to another. That's--and that's important, 
because if you want to, for example, do engineering that 
somehow makes use of some feature of that turbulent flow, then 
to know that it's repeatable is extremely important, because 
then you can actually engineer with that in mind.
    And so knowing the basic science, the answer to the basic 
science question of where did this, the randomness, come from 
in something like a turbulent fluid flow, has considerable 
importance. And it's something which there haven't really been 
tools or methods that have allowed one to really get at that 
question of, sort of, where does the randomness come from. And 
that's something which the study of simple programs let's one 
do.
    Senator Brownback. You mentioned, early on, that this has 
important implications for, say, something like nanotechnology, 
which this Committee has looked at previously. What are the 
implications there?
    I mean, it seems to me the implication is that, if you can 
discover the simple program that produces a complex pattern, 
that we would be able to use that technologically in very small 
structures.
    Dr. Wolfram. Yes, that's right. And then--so, for example, 
let's say that you wanted to make a system out of atoms, let's 
say, that could act as a computer. So what one might think at 
first is, OK, let's take, you know, the structure of a Pentium 
chip or something and let's make it really, really small and 
have that be the way that we make up our computer. One of the 
things that one discovers from what I've done is that actually 
you don't need all of the elaborate structure that exists in, 
let's say, a Pentium chip to be able to achieve the objective 
of being able to do computation.
    And, for instance--well, this example that I showed here--
this is an example of a rule that I know is capable of doing 
any computation that any computer can do. Essentially, you set 
up a--the top row in the right way--you're, kind of, 
programming it by the way that you set up the top row. And then 
as it evolves down the screen, the behavior that it produces 
can correspond to any computation that any computer can do. Yet 
the rules, the underlying rules that this thing operates 
according to, are just those rules at the bottom there. And 
those are very simple rules, which, because they're so simple, 
one can much more readily imagine being able to set them up as 
rules that could be applied and that could correspond to the 
behavior of some particular molecule or some such other thing.
    So, in a sense, there have been a couple of traditions in 
nanotechnology. One is, take, sort of, the devices that we know 
from, kind of, large-scale engineering and shrink them down to 
atomic scales. The other tradition is, kind of, take what we 
see in biology and try and, sort of, piggyback on what we see 
in biology, because biology is the one, kind of, clear example 
of, sort of, nanotechnology that works, so to speak.
    In a sense, what we're seeing here is something which is 
kind of a merger of those approaches, where one's saying this--
these kinds of simple rules seem to be the essence of what's 
going on in, for example, some molecular biology situations, 
and they also seem to be things that we can, sort of, 
understand as achieving technological purposes, and this, sort 
of, provides us a different approach to doing nanotechnology.
    Senator Brownback. So that if you could discover the 
pattern that creates the various parts of an ant and how it 
operates, then you could use that into nanotechnology 
development on our part? Is that the sort of thing? Or are you 
talking more of a virus that----
    Dr. Wolfram. I think the--so the question of what one is 
trying to achieve in the technology--let's say that what one's 
trying to achieve is to make a computer. Then this is the type 
of rule that one can use.
    Senator Brownback. Well, let's say what you're wanting to 
achieve is something that you could inject into me or you to go 
to the damaged area of the heart and fix it.
    Dr. Wolfram. Yes. Then, sort of, the first step there is to 
understand, for example, the morphology of heart tissue. What 
is it like? It has certain structure. There are attempts to do 
tissue engineering, where one's interested in making something 
that, kind of, fits in with the tissue that's already there. So 
one of the first things is to try and understand--in the case 
of the heart, there's some rather complicated morphology that 
exists, and there's a question of how does that morphology come 
to be? What are the rules that make it? If we know those rules, 
then we can start creating artificial things that----
    Senator Brownback. OK. All right.
    Dr. Wolfram.--will be able to, sort of, fit in with it.
    Senator Brownback. Well, how do you discover that pattern, 
that simple computation pattern, then, of heart tissue?
    Dr. Wolfram. Well, so that's a--if one looks at, sort of, 
the development of science, typically, sort of, taking rules 
and figuring out what the consequences are is a lot easier than 
taking a phenomenon and figuring out what its underlying rules 
are. I mean, in, for example, the development of traditional 
mathematical science, there was, sort of, at first, the 
development of, you know, calculus and so on, where one could 
compute--given Newton's laws and so on, one could compute 
things about the motion of planets. Much later came along the 
field of statistics, where one could go and, sort of, take 
features of the natural world and, kind of, infer from those 
features some aspects of the rules.
    In this case, the, sort of, general problem of, given a 
phenomenon, from what rules did it come, is extremely hard to 
solve. It's analogous to the, sort of, most general problem of 
doing cryptanalysis. If you're, sort of, shown the output from 
some process of coding, can you deduce the key that it came 
from? That's, in general, a very hard problem. And, in fact, 
one of the things that's come out of the work that I've done 
is, sort of, a proof that there is some fundamental difficulty 
in solving that problem.
    Now, having said that, things are not as bad as that seems. 
Because if the programs for things that one's interested in are 
sufficiently simple, then essentially by searching or by 
building up a big library of those programs, there is a good 
chance that the things one's actually interested in may 
actually be accessible to a search or exists in the library 
that one builds up.
    So, for example, one project that we've just been starting 
is to try and, sort of, buildup a giant atlas of simple 
programs and what they do. And, sort of, the concept of that 
is--because one's discovered that the programs for many very 
interesting things can be extremely simple, it is quite 
plausible that in the first, let's say, billion-billion 
programs, which is quite easily accessible to, sort of, 
frontier computing right now, in those first billion-billion 
programs could be programs that are relevant for lots of kinds 
of practical applications, whether they're for mimicking 
biology, whether they're for creating computational algorithms 
that are important, or whatever else. And, sort of, as we--if 
we can, kind of, do well at exploring and documenting the, sort 
of, computational universe, then we can expect to go and 
effectively mine it for the things that are useful for our 
particular modeling purposes or technological purposes.
    And I think that's, kind of, one of the things that's, sort 
of, been opened up by what I've done, is the idea that it 
really is worth exploring this computational universe. Because 
one might have expected that the kinds of things that one could 
find by, sort of, just going and looking at all the 
possibilities, that one would never get to anything terribly 
interesting by doing that, that even if one looked at a 
billion-billion possibilities, that all of those would be--
would somehow be too simple to actually do anything interesting 
and relevant to what we're interested in for modeling natural 
systems or for doing technology.
    So one of the things that's, sort of, I think, a great 
opportunity that's suggested by what I've done is, if we can go 
and explore this computational universe and really have--and 
have a good map of what's out there in the computational 
universe. I think, and have good evidence, that we're going to 
find that there are lots of very, very useful things out there 
for modeling natural systems, for creating technology, and so 
on.
    Senator Brownback. How has your work been received by the 
scientific community to date?
    Dr. Wolfram. We've had about 30,000 e-mails from people 
saying, ``We want to follow up on this or that aspect of what 
you've done.'' I think the world would not be as it is if one 
didn't see a, sort of, spectrum of response to almost any new 
thing. So it's a spectrum of response, from tremendous 
enthusiasm to tremendous skepticism.
    But I think the thing that I've been most encouraged by is 
in universities, government labs, companies, and so on. There 
are an increasing number of people who have obviously read the 
book in great detail and started to really do significant work 
that's based on what I tried to set down in the book. And, sort 
of, the challenge, in a sense, now is there are these many, 
kind of, different threads of development that seem to be 
starting out, and there's, sort of, a question of whether one 
can coordinate these in the best possible way. I think one of 
the things that I've seen from--I'm, sort of, something of a 
student of the history of science, and so--and I, sort of, 
believe that one might be able to learn something about the way 
things unfold now from studying what's happened in the past as 
developments have occurred in science.
    I think one of the challenges is, there are many potential 
applications of what I've done, and those applications should 
and will come to live in the different areas to which they 
apply, like physics or biology or mathematics or computer 
science. But there's also, kind of, a separate area of 
scientific endeavor, which is the, sort of, basic science of 
understanding, kind of, what's out there in the computational 
universe. And I think one of the challenges is to see that 
actually, sort of, come into existence and prosper as an 
independent science, like a physics or a chemistry or a 
mathematics.
    But I think the--I would say that, right now, the--it's 
been--in the last year and a half since the book came out, I 
have--we have had a hard time, kind of, keeping up with all the 
different things that people are starting to do, based on the 
book, which I suppose is an encouraging sign.
    Senator Brownback. If the Federal Government wanted to 
pursue this more--we're best at putting in resources and trying 
to focus attention and finding on particular lines--what are 
the things that we could do to be most effective to further try 
to understand this? I gather, from one that you're talking 
about, it's just gathering up a series of these simple patterns 
in large, large numbers.
    Dr. Wolfram. Right. I think there are really two key 
directions. One is, sort of, education. This is a new 
methodology, and there's a question of, kind of, how can the 
people who could use this methodology really get good access to 
it? And that's, sort of, an issue.
    And I know, in the general use of computers, actually, let 
alone the kinds of things that I've tried to do, one of the 
challenges is, among, for example, technical R&D folk and so 
on, how does one get to the point where people are really able 
to use computers and use computational ideas and methods, sort 
of, starting from the highest possible platform? Because, a lot 
of times, people have, sort of, first learned about computers 
25 years earlier, and--but they're physicists, for example, and 
they don't see--you know, they don't know that they should go 
back and, kind of, learn more. And so I think one place where 
there's clearly value to be got is by, as much as one can, 
seeing ways to, sort of--channels for educating people about 
what is actually possible, what the methodologies are, what the 
tools are, and so on. That's one thing.
    Another thing is really being able to map this 
computational universe. I think it would be extremely fruitful 
to have, kind of, a clear, sort of, coherent map of that 
universe; just as, for example, you know, we have a clear 
coherent map of the human genome, or we've had some coherent 
maps of the astronomical universe, so to speak. That to be able 
to have something where one has really said, ``OK, we're going 
to look at, sort of, a billion-billion or more of these simple 
programs. We're going to catalog them.'' It's a little bit 
analogous to what's happened, for example, in chemistry, where 
there are these giant data bases of organic chemicals that have 
been filled in over the course of a century or more, where 
one's--if one wants to find a chemical that's relevant for some 
industrial process or for some biomedical application, one of 
the places one first looks is in one of these big data bases of 
organic chemistry. And, sort of, one of the things that one 
would like to have, I think, is a coherent big database of 
what's out there in the computational world.
    And of the things that will be there, as I say, there will 
be both things that are relevant for, kind of, modeling 
questions in natural science, and there will be things that are 
quite directly, in some cases, relevant for technology. I mean, 
for example, in these--some of these pictures I showed, like 
this rule-30 picture, is directly relevant if you want to make 
randomness in some technological system. So, similarly, there 
will be other cases where one has something that's directly 
relevant to, for example, doing data compression or doing some 
form of pattern recognition. And I think that's the--to have a, 
sort of, coherent, widely accessible database of that kind 
would be something of great interest.
    Senator Brownback. I mean, you talk about it as a map of 
the computational universe. How would you go about discovering 
that? I mean----
    Dr. Wolfram. It's--the good news is----
    Senator Brownback.--you sound like you should just start 
putting together computer programs, or simple ones, as many as 
you could think of, see them run, and then categorize them?
    Dr. Wolfram. That's the first level of it, yes. There's a 
certain amount that can be done in that way, where it's 
essentially using lots of computer time, but the process is 
fundamentally very well defined. One knows what to do. It gets 
a little bit more complicated when one really wants to get, 
sort of, the best-developed, kind of, map, because a lot of 
these--let me show you an example of what you see in, kind of, 
the most basic kind of map.
    This will be just a collection of the first--I think that's 
the first 128 programs of a particular kind. These are these 
cellular automaton programs. And what you see is, some of them 
do very simple things. Some of them make these elaborate, kind 
of, nested patterns, which, by the way, turn out to be--I mean, 
these nested patterns have been seen elsewhere, but, by the 
way, turn out to be relevant for some recent technological 
applications. And in other cases you see more complicated 
patterns going on.
    So, sort of, the first level of this is just--you generate 
a very large number of these patterns. But the place where it 
becomes, kind of, nontrivial is how do you figure out which of 
these are interesting, which ones are going to be relevant for 
particular technological applications, and so on? And that's 
where considerable, at this point, human effort has to be spent 
to do the analysis to figure out methodologies to working out 
how do you sample the most interesting programs, those sorts of 
things.
    I mean, another very straightforward--conceptually, at 
least--kind of thing is each of these programs can be thought 
of--it generates--for example, you can represent some aspects 
of the patterns by, let's say, sequences of ones and zeroes. 
And one thing one can ask to be able to do is, given that one 
has got a sequence of ones and zeroes, find the simplest 
program that reproduces that sequence of ones and zeroes. 
That's relevant if one has found that sequence of ones and 
zeroes in some actual experiment or some actual observation and 
one wants to try and work out where did this come from? What's 
the underlying model? What's the underlying process that 
produced this? And that's, kind of, an example where one has to 
have this, sort of, large library of what these simple programs 
do, because then one can go back from that and figure out, 
given something that one actually observed, where does it 
potentially come from?
    Senator Brownback. So that you would go throughout nature 
and you would observe the swirls that happen after a particular 
fluid flow, leaves, mollusks, and butterflies. You would see 
these patterns and then draw back from that what simple program 
can produce this pattern?
    Dr. Wolfram. That would be a hope. All the steps to be able 
to do that, I don't know how to do yet. I know, in some cases, 
how--I mean, the process of going from a phenomenon to an 
underlying rule is one that, as I say, is, sort of, a 
fundamentally difficult thing. But what one can do--by having a 
very large library of simple rules and what behavior they 
produce, one has the chance to be able to say, ``Oh, yes. This 
behavior that I'm now seeing in this fluid-flow example looks 
like this behavior that one sees in this particular type of 
simple program.'' And then one can go and start to do science 
based on that to make predictions about what one would see in 
the fluid flow and those sorts of things.
    It is not the case--and, in fact, I think I can even, sort 
of, at a theoretical level, prove that it's not going to be 
possible to just say, given any phenomenon that you see, to 
systematically go backward and say, What did this come from? 
But what will be the case is--the encouraging thing is that, 
for many phenomena, the underlying rules may be--one can expect 
will be simple enough that one will be able to deduce what they 
are by essentially looking them up in the library and seeing 
what they came from.
    Senator Brownback. How did you get started thinking about 
this this way--the universe this way?
    Dr. Wolfram. Well----
    Senator Brownback. What was the apple that fell off of the 
tree?
    Dr. Wolfram. The main--I think the very original--I was 
interested in some questions about cosmology and questions 
about--this was about 24 years ago, or something, now--
questions about how organized structures arise in the universe. 
And I, kind of, realized that the basic questions being asked 
about how organized structures arise weren't things that 
needed--that could only be asked in the context of this, sort 
of, complicated cosmology situation; they were questions that 
also arose in basic areas of physics and biology and so on. And 
so I started looking, what are the simplest possible models 
that I can make that could reproduce this basic phenomenon? And 
I ended up with these cellular automaton systems.
    And, actually, what happened, as is so often the case in 
things that get discovered in science, when I first did the 
experiments I was so sure that I would not see the phenomenon 
that I eventually ended up seeing that I basically managed to 
ignore it for a couple of years.
    But finally the thing that--I finally essentially generated 
this picture, and I finally actually realized I should--I had 
not believed that something like this could be possible. That 
is, I had believed that when the rules are simple, the behavior 
must somehow be correspondingly simple. And so I had actually 
produced a picture like this 2 years before I realized that 
this really was something real and something important. And it 
then took me another 10 years after I had, kind of, absorbed 
this picture to realize just, kind of, what the significance of 
it was, in a broader context, and its applications in different 
areas, and so on.
    Senator Brownback. Was there a moment--was there one event 
that you went, ``Aha, this is it''?
    Dr. Wolfram. No. It was, unfortunately, slower than that. I 
wish it had all been compressed into----
    [Laughter.]
    Dr. Wolfram.--``Now I understand how this all works.'' I 
think it is common--I mean, in a sense, it's, sort of, been a 
gradual process of realizing that this paradigm of thinking in 
terms of simple programs and so on, that it really is a 
powerful paradigm that one can apply in a lot of different 
areas. I had--as I did the work for my book, and so on, I had 
at first thought that this kind of paradigm might apply in some 
kinds of questions in science, but that other kinds of 
questions in science would necessarily require a very different 
paradigm. And I was--but I, in many cases, kind of, started 
looking, ``Well, maybe I can see--is this paradigm 
applicable?'' And I discovered that it was, and often in very 
interesting ways--for instance, to something like the 
foundations of mathematics was one that I had not really 
expected that this paradigm would have things to say about, and 
it turned out it had a lot to say about them.
    Senator Brownback. It sounds like you almost describe a 
universe where there's no such thing as randomness. This is 
all--everything has some simple pattern to it, or a multiple 
set of simple patterns that, layered on each other, produce 
everything we see.
    Dr. Wolfram. Yes. If I'm right, the universe is the result 
of running a definite rule from a definite starting condition. 
And, in that sense, there is nothing about the universe--if I'm 
right in my ideas about fundamental physics, then everything, 
every detail of everything that happens in the universe is 
something that follows from those underlying rules, and follows 
in a definite way.
    Now, you might think, if that was the case, then surely we 
can predict everything about what will happen in the universe. 
Things--it doesn't work that way. Most importantly, there's a 
phenomenon that I call computational irreducibility. And the 
point of that is the following. If you have a sufficiently 
simple pattern--let's say something like this--you can readily 
say what the color of a particular square will be any distance 
down this pattern, because there's a very simple--there's a 
very simple form--there's essentially a formula that tells you, 
after a million steps it'll be black if it's an even-numbered 
cell or something.
    But the point is that when you look at something like, 
let's say--I don't know--when you look at something like this, 
you can no longer easily make a prediction about what will 
happen in this pattern after a certain number of steps.
    See, one of the features of, sort of, the mathematical 
approach to science has been, sort of, the emphasis on 
essentially computationally reducing phenomena in nature. So, 
for example, you know, in a certain approximation, the Earth 
goes around the sun in a roughly elliptical orbit. And then 
there are equations that describe the position of the Earth. 
And if you want to know where the Earth will be a million years 
from now, you don't have to explicitly follow a million orbits; 
you must plug a million into some formula, and you can 
immediately deduce where the Earth will be a million years from 
now.
    But in a case like this, there's a question of whether you 
can, kind of, reduce the computational effort of finding out 
what will happen in that kind of way. Can you jump forward and 
kind of not have to go through all the steps that this system 
itself has to go through to work out what it will do?
    Well, the thing that I argue and have shown in at least 
certain cases is that there is a phenomenon that I call 
computational irreducibility, which says that there's really no 
way to predict what the system will do by any sort of procedure 
that is computationally more efficient than just, sort of, 
following each step and seeing what will happen. And that's--
that idea has a bunch of consequences. It, for example, 
explains why, when we think about doing computer simulations of 
things, it's not only convenient to do those computer 
simulations, but, in some fundamental sense, necessary. There 
isn't going to be a way to just write down a formula for what 
happens. We're going to actually have to simulate each step to 
see what comes out.
    And so, for example, when we think about doing things with 
the universe, the question of, sort of, what eventually happens 
in the universe--and even though we may know the underlying 
rule, even though we know exactly--we may know exactly how this 
network that underlies space and time works, and so on--to 
actually deduce the consequences of that for the whole behavior 
of our universe is, in a sense, I think, irreducibly 
computationally difficult. So, in other words, the universe has 
taken its 12 billion years, or whatever, to, sort of, get to 
the state that it's at right now, and it's, in effect, done 
some huge number of computational operations to get to that 
state.
    The point of this phenomenon of computational 
irreducibility is that we can't expect to, kind of, crush, down 
to a very small number of computational operations, the process 
of working out what will happen. The reason for this is, it's--
well, it's kind of a--it's related to this thing I call the 
principle of computational equivalence, and it has to do with 
the following. When--typically, in science, we make a certain 
idealization. Often, science has progressed by realizing that 
idealizations that had been made weren't actually correct.
    One particular idealization that we make is that we, as 
observes of the natural world, are, in a sense, computationally 
infinitely--we're infinitely more computationally sophisticated 
than the things that we observe in nature. So--and that's why, 
for example, we expect that we can--that even though in nature 
some process may take a huge number of steps to occur, that we, 
as, sort of, infinitely computationally more sophisticated 
entities, can work out what will happen in a much reduced 
number of steps.
    Well, one of the consequences of this principle of 
computational equivalence and this computational irreducibility 
phenomenon is that that isn't the case. In the, sort of, 
competition between us, as an observer of a system, and the 
system itself just doing its thing, we can't expect that we 
are, sort of, computationally more sophisticated than the 
system. And that's, in a sense, why this phenomenon of 
computational irreducibility exists.
    Senator Brownback. I'm not sure I gather that point, that 
we----
    Dr. Wolfram. It's a hard point.
    Senator Brownback.--well, that we can't think 
computationally as sophisticated as the system thinks?
    Dr. Wolfram. Right. So here's the, kind of--the issue. So 
as we look at different kinds of systems, they have different 
kinds of underlying rules, and they are capable of doing 
different levels of computation. One of the things that one 
might have thought, long ago, is that as one looks at different 
computational tasks--you know, if you want to do addition, for 
example, you might think, OK, I'll go and buy an adding machine 
to do that; if you want to do multiplication, I'll go and buy a 
different machine, a multiplying machine to do that. But, sort 
of, the big discovery of the 1930s that, kind of, launched what 
became the computer revolution was the fact that one could have 
a single universal computer, a single, kind of, universal 
machine, which, if fed the right program, would, on the one 
hand, be able to do addition, on the other hand, be able to do 
multiplication, and be able to do all these different kinds of 
computations that we associate with computers.
    So one question is, one might have thought that it would be 
the case that--as we look at systems with different underlying 
rules, that they'd all be able to do different levels of 
computation; that as the rules get more complicated, they'd be 
able to do more sophisticated computations, and so on.
    One of the surprising things that I've discovered is that 
as you increase the sophistication of the rules for a system 
beyond some very low threshold, all systems seem to be able to 
do the same set of computations. So that's why, for example, in 
that case that I showed that I think is relevant as an example 
in nanotechnology, for instance, they're very simply rules, yet 
that system is capable of computation as sophisticated as any 
system.
    So what comes out of this principle of computational 
equivalence is the idea that most sets of rules that one might 
use in systems end up having--giving--allowing the systems to 
be equivalently sophisticated in the computations they can do. 
That is, it isn't the case that, as we look at a succession of 
different rules for different kinds of systems, that we'll see 
different levels of computational sophistication.
    So when that comes to--when it comes to looking at systems 
in nature, we had, in the past, kind of assumed that typical 
systems that we see in nature were computationally much less 
sophisticated than our computers, our mathematics, our brains, 
and so on. One of the consequences of this principle of 
computational equivalence is that that isn't the case, that all 
these different systems are equivalent in the level of 
sophistication of computations they can do. And that's why we, 
with our mathematics computation, whatever, can't, kind of, 
jump ahead of these systems in nature in working out what 
they're going to do, that we're, kind of--that we're just 
equivalent, in our computational ability, to those systems.
    Senator Brownback. Let me back up to one other point. The 
theory that you're working under is, there is no such thing as 
randomness in the universe. It's all--there is a computational 
pattern to everything in the universe.
    Dr. Wolfram. That's ultimately correct. Now, having said 
that, if we could trace everything from, sort of, the lowest 
level of these little, sort of, networks that underlie space 
and time, if we could trace all of that, then that would be the 
conclusion.
    Now, as a practical matter, when we study, kind of, 
everyday questions in, let's say, physics or some other area, 
we don't want to have to go all the way from the networks 
underneath space and time up to the system we're studying. We 
want to be able to think about that system and model it more at 
the level of the kind of components that we can immediately see 
in that system. And at that level, it may be that we have to 
describe something that goes on in that system as being, sort 
of, externally random, because we're not describing things 
right from the lowest-level kind of things underneath space and 
time right up to the system we're looking at. If we did that, 
then I think there would be no, quotes, ``randomness'' there.
    But if we're describing it only at the level of description 
of components that we can readily see, for example, there maybe 
some sort of input from the outside that we're not capturing in 
the model of the components that we're actually looking at.
    Senator Brownback. But those inputs, themselves, would have 
a pattern to them, the inputs from the outside that you're 
talking about that might----
    Dr. Wolfram. Well, yes, ultimately, if you, sort of, trace 
it all the way back, you get back, to the--sort of, the 
underlying rules for the universe, and then I believe it's--you 
know, this is the kind of thing where--you know, I spend some 
part of my life creating technology, and when one creates 
technology, one starts from nothing, and one builds something, 
and one, kind of, knows what one has. In doing science, one, 
kind of, has to say, well, this is how I think it's going to 
work. But until you've, kind of--you're kind of guessing 
against the universe, so to speak. And until you can, kind of, 
see that everything absolutely matches up, you can't say for 
certain that that's really the way things work. But it's my 
guess, which I find--which I'm encouraged in by, sort of, 
increasing evidence that I seem to find, that that's the way 
things work and that there really is such a definite rule.
    Senator Brownback. What are some of the best questions 
you've been asked about this as you've made these presentations 
at various places? I want to make sure to give you a chance to 
address any points that I have not asked you about that we 
really should hear about here in the record and the Senate 
Commerce Committee.
    Dr. Wolfram. I think one of the things that--well, we've 
covered quite a bit of stuff here.
    [Laughter.]
    Dr. Wolfram. I'll think of it just after we end.
    Senator Brownback. Well, I wanted to make sure to give you 
a chance to address anything that we should hear about, because 
I find this fascinating. I found it fascinating when I--your 
information in the book broke into the popular press, you know, 
what they were describing of the universe of patterns. And I 
found that just fascinating conceptually at that time when I 
first heard about it. And I know that, since then, you would 
have had a lot of interaction with a number of different people 
and minds that have considered, critiqued, thought about what 
you've put forward that's challenged, probably, your thinking 
when you came out with the idea and the notion at that period 
of time. That's what I wanted to give you a chance to address, 
anything that's the most challenging or that we should know 
about here.
    Dr. Wolfram. Well, I think the thing that I perhaps should, 
kind of, come back to is, sort of, the importance of what seems 
to be, kind of, an abstract piece of basic science, of 
studying, kind of, what's out there in the computational world. 
This is something that, if you look at, kind of, the history of 
things, it's something that, in a sense, could have been done a 
very long time ago. These kind of figuring out, kind of, what 
the consequences of simple rules are could have been done, but 
there, kind of, wasn't the right, kind of, conceptual framework 
to try to do it.
    I think that the main thing that I think is really exciting 
is that now one's, kind of, seeing there are exciting things, 
kind of, out there in the computational world, and we're 
beginning to have a conceptual framework to think about these 
things. General principles, like this principle of 
computational equivalence, which, at first, seemed to be, in a 
sense, very abstract kinds of principles, that then quickly end 
up having very definite consequences about the ways that we can 
make computers and so on.
    Senator Brownback. Well, and for years we've done things 
where we've observed nature and then mimicked it in some form 
to be able to use for our own technology, our own use. It's 
been--my field, background, is in agriculture. We've spent a 
long time observing nature, whether it's just to see initially 
what plant produced a seed and now what does this seed do, to 
today where we mimic so much of how nature used to operate to 
try to maximize our agricultural production, various patterns.
    It seemed like what you're doing here is, you're taking 
that just back another step. Instead of observing the growth 
consequence in nature, you're saying, ``Here's the program that 
produced that, and let's discover the program so that we can 
take that on forward,'' which is fascinating conceptually and 
something that could be incredibly useful technically and for 
us, as mankind.
    It's also, in a very theological basis, of where did the 
program come from--the very simple program that produces that 
incredible pattern, where does that come from? And it's very 
interesting.
    Thank you very much for coming here today, sharing your 
wisdom, your insights, your thoughts on this. It's been 
fascinating for me. I'm hopeful we'll be able to work with you 
on looking at some of these. I hope that our National Science 
Foundation, our people are looking and observing this process.
    As I mentioned to you privately, the sort of thing that we 
do best, I think, at the Federal level, is to fund basic 
research, really trying to find those underpinnings 
technologically that private groups can't fund because they 
just don't have the--frequently, the income coming in to be 
able to do that. But that's what we do do best, and let people 
build on top of that, so that this may be one that would be 
very useful for us. It's also how we grow our economy and grow 
our contribution to mankind, is by discovering fundamental 
things that then others can build on top of. And here's--this 
may be an absolutely incredible opportunity for us to be able 
to do just that.
    Thank you very much for coming here today. The hearing is 
adjourned.
    [Whereupon at 4:50 p.m., the hearing was adjourned.]

                                  
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