**- 2 -**

**Cosmic Computer**

Where
does the complexity of the Universe come from? A simple computer program is
generating it!

There is something fascinating about science. One
gets such wholesale returns of conjecture out of such a trifling investment of
fact.

Mark Twain

(*Life on the Mississippi*, 1884)

God has chosen
the world that is the most simple in hypotheses and the most rich in phenomena.

Gottfried Leibniz

(*Discourse de metaphysique*, 1686)

It's AD 2068 and the survey expedition from Earth is picking its way
through the ruins of an alien civilisation, long departed its home world for
who knows where. Ahead, bathed in the sombre light of the twin red suns, is a
great slab of a building - the planet's central library, repository of the
civilisation's accumulated wisdom.

Struggling visibly in
the strong gravity, the expedition members clamber up the giant steps and push
open the creaking door. Boots reverberating in the thick atmosphere, they hurry
through an empty, echoing chamber - until, finally, they come to a single
cabinet, displaying a lone tablet inscribed with arcane symbols. Everyone
crowds around while someone scans it with a translator...

RECIPE FOR UNIVERSE:

RUN COMPUTER PROGRAM
(BELOW)

REPEAT FOR 13.7 BILLION
YEARS

One person laughs. Another gasps in disbelief. The cosmic computer
program they are all staring at is only 4 lines long!

Could the recipe for
making a Universe really be as simple as this? One present-day physicist is
convinced of it. His name is Stephen Wolfram and he claims to have stumbled on
nature's "big" secret. The source of all its bewildering complexity -
from spiral galaxies to rhododendrons to human beings - is the application of a
few simple instructions, over and over again. "Our Universe is being
generated by a simple computer program," says Wolfram.

Wolfram, a child prodigy
from London, began publishing papers in professional physics journals at the
age of 15. What led him to his extraordinary conclusion is a discovery he made
around 1980. Contrary to all expectations, he found that simple computer
programs have the ability to generate extraordinarily complex outputs.

Wolfram's discovery came
about when he became interested in problems like how galaxies like our Milky
Way form and how our brains work. "The trouble was that none of these
'complex systems' seemed explicable by conventional science," he says.

Conventional science is
synonymous with maths-based science. In the 17th century, Isaac Newton
discovered that the laws which govern the motion of a cannon ball through the
air and a planet round the Sun could be described by mathematical formulae, or
"equations". Following Newton's lead, generations of physicists have
found that mathematical equations exist that can perfectly describe everything
from the character of the light given out by a hot furnace to the warping of
space and time by the concentrated mass of a black hole[1].

But, despite the
tremendous successes of equation-based science in penetrating nature's secrets,
it has an Achilles' heel. It cannot do "complexity". It is utterly
incapable of capturing the essence of what is going on in a whole range of
complex phenomena, ranging from turbulence in fluids to biology itself.

Most scientists lose
little sleep over this. Complex phenomena may be "hard", they say,
but this does not mean that science will not eventually get around to tackling
them. Wolfram, however, emphatically disagrees. Controversially, he believes
that mathematical science will never, ever penetrate the mystery of complex
phenomena.

A streetlight
illuminates merely what it can illuminate - the circle of ground immediately
beneath. Similarly, Wolfram believes mathematical science illuminates merely
what it is capable of illuminating - those phenomena whose essence can be
captured by mathematical equations. But such phenomena, he contends, are rare
and unusual. In the same way that a streetlight fails to reveal the subways and
sports grounds and art galleries of its surrounding city, science as practised
for the past three centuries is blind to the overwhelming majority of phenomena
in the Universe - complex phenomena. "Since such phenomena include living
things, the human brain and the biosphere, we are talking about all the truly
interesting things that are going on in the Universe," says Wolfram.

This is radical stuff.
For centuries, physicists have wondered why nature obeys mathematical laws,
which can be distilled into neat mathematical equations and which can then be
scrawled across blackboards. The Hungarian-American physicist Eugene Wigner
famously drew attention to this when he talked of "the unreasonable
effectiveness of mathematics in the physical sciences".

According to Wolfram,
however, Wigner was wrong to believe that the Universe is essentially
mathematical. Mathematics is no more effective in revealing the inner workings
of nature than a streetlight is in revealing the city that surrounds it. Nature
may "appear" to follow mathematical laws, he says. However, that is
hardly surprising when scientists specifically seek out the rare natural
phenomena that follow mathematical laws. "Wigner could equally well have
remarked on the unreasonable effectiveness of streetlights in illuminating the
ground beneath them," says Wolfram.

If Wolfram is right,
science has a serious problem. After all, if mathematical equations are
incapable of describing nature's most interesting phenomena - complex phenomena
- how cane such phenomena be described? In the early 1980s, Wolfram gave this
question a great deal of thought.

It was clear to him that
the Universe must obey rules of some kind. If it did not, after all, there
would be no pattern or regularity in nature. The Universe would be a
meaningless maelstrom of unpredictable randomness and chaos. But, if the rules
are not embodied in mathematical equations, what are they embodied in? It was
clear to Wolfram that it had to be something more general than a mathematical
equation. After thinking about it, he could come up with only one thing that
fitted the bill: a computer program.

Wolfram decided to find out what kind of science could be built starting
with the more general kinds of rules embodied in computer programs. The first
big question he needed to answer was: what are such rules capable of? Or, to
put in another way, typically what do simple programs do?

The simplest computer
program Wolfram could think of is known as a "cellular automaton".
The most basic of these is simply a long line of squares, or "cells",
drawn across a page. A cell can either be one of two colours - white or black.
At regular intervals of time, a new line of cells is drawn on the page,
immediately above the first. Whether a cell in this second line is black or
white depends on a rule applied to its two nearest neighbours in the first
line. The rule might, for instance, say: "If a particular cell in the
first line has a black square on either side of it, it should turn black in the
second line". A third line of cells, immediately above the second, is then
created by applying the cellular automata "rule" to the second line,
and so on.

What we are talking
about here is the operation of simple computer program embodying the cellular
automaton rule. The program takes an input - the pattern of black-and-white
cells on one line - and produces an output - the pattern of cells on the next
line. The key thing is that the output is fed back in as the next input to the
computer program rather like a snake swallowing its own tail. Such
tail-swallowing is commonly called "recursion". And, as a wit once
said: "To understand recursion, you must first understand recursion!"

For a 1-dimensional,
two-colour, adjacent-cell cellular automaton like this, it turns out there are
256 possible rules, 256 kinds of program[2].
The question is: what happens when the programs are run, starting, say, with a
single black cell in the first line of cells? In true scientific fashion,
Wolfram began experimenting to find out.

He soon discovered that
some rules and some starting patterns led to nothing interesting. As new lines
of cells were created, any pattern quickly fizzled out. Or a particular
arrangement of black-and-white cells began repeating endlessly. However, in
some cases, something very much more interesting happened.

The early 1980s was the
time of the first cheap desktop computers so Wolfram was able to watch his
cellular automata perform on a computer rather than on a piece of paper. Seeing
the new lines of cells marching steadily up the screen was much like watching a
movie. Occasionally, the patterns of black cells coalesced into discrete
"objects". These persisted - as unchanging and stable as a table or
chair - despite the fact they were being continually destroyed and regenerated.

Wolfram played with is a
his cellular automata for hours on end, mesmerised by the marching patterns.
And then, one day, he stumbled on something extraordinary. "I found a
pattern which appeared never to repeat, no matter how long I stared at
it," says Wolfram.

If you see a complex
thing like a car or a computer, you know it must have been made by a complex
process. Even in biology, where natural selection is blind, the complexity of
organisms is a result of a complex series of processes operating over billions
of years of evolution. In the everyday world, simple things have simple causes
and complex things have complex causes. What Wolfram had found, however, was something
that bucked the trend - a complex thing that had a simple cause.

For Wolfram it was a
life-changing moment. As he stared at his computer screen and the never-ending
novelty scrolling down it, he wondered: Is this the origin of the Universe's
complexity? "When nature creates a rose or a galaxy or a human brain, is
it merely applying simple rules - over and over again?" he says. "Is
this its big secret?"

From that moment on Wolfram became obsessed with the origin of
complexity. At the time of his epiphany, he was at the California Institute of
Technology in Pasadena. However, in the mid-1980s, he moved first to
Princeton's Institute for Advanced Study - Einstein's old institute - then to
the University of Illinois at Urbana-Champaign, where he founded the Center for
Complex Systems Research. Around the same time, he started the first scientific
journal on complexity. He even created his own computer language -
"Mathematica" - which helped him in his investigation of the origin
of complexity.

Mathematica led him to
start his own company, Wolfram Research, and attract scientists and
mathematicians to help develop the software. The programming language turned
out to be not only a tool but an inspiration of his work. Although Wolfram
assembled it from simple program "modules", it was nevertheless
capable of carrying out enormously complex tasks. "It hammered home to me
once again my central discovery -that simple programs can have hugely complex
outcomes," says Wolfram.

Wolfram's hope was that
others would pile into the research area he had created and that this would
lead to rapid progress in understanding complexity. To his disappointment and
frustration, however, few joined in and progress was slow. Wolfram became increasingly
impatient. By early 1991, he decided there was only one thing to do - carry out
the work himself.

With a few million users
worldwide, "Mathematica" had made Wolfram a multimillionaire. He did
not need to be employed by a university and he did not need to fight constantly
for research money. He was free to concentrate all of his time on creating a
science of complexity.

Wolfram set himself a
gargantuan task but even he did not realise it would take him a decade. During
that time, he published not a single research paper. Although he certainly
talked and corresponded with other scientists, he pretty much vanished off the
edge of the scientific radar screen.

Month after month, year
after year, while the rest of the world slept, Wolfram laboured through the
night, painstakingly laying the foundations of a new way of doing science. In
essence, he was carrying out a systematic computer search for simple rules with
very complicated consequences. "He set out to survey all possible worlds -
at least all the ones generated by simple rules," says mathematician
Gregory Chaitin of IBM in Yorktown Heights, New York. "The result was a
treasure trove of small computer programs that, when repeated again and again,
yield extremely rich, complicated and interesting behaviour."[3]

Among the many things
Wolfram discovered is the remarkable property of cellular automaton rule 110.
Starting with a single black cell, this simple rule turns out to be capable of
generating infinite complexity, infinite novelty, infinite surprise. Not only
that but a cellular automaton following rule 110 is a "universal Turing
machine"[4]. Despite
being amazingly simple, it is like a modern-day computer that can carry out any
imaginable computation, simulate any other conceivable machine.

The remarkable ability
of cellular automaton rule 110 is highly suggestive. After all, if even a
simple 1-dimensional cellular automaton can create never-ending complexity, it
shows the kind of power that nature potentially has at its disposal. And
Wolfram is convinced that nature avails itself of that potential. "I
believe that physical systems subject to simple rules applied recursively -
with the output fed back in as the input - can have created everything from the
tip of your nose to most distant cluster of galaxies," he says.

So is the Universe a
giant cellular automaton - a 3-dimensional version of the 1-dimensional ones
Wolfram has been playing with on his computer? Surprisingly, Wolfram thinks
not. "I think the truth is actually much more strange and interesting,"
he says.

A serious shortcoming of a cellular automaton as a model of the
Universe is that all the cells update themselves together. This kind of
coordinated behaviour requires a built-in "clock", whose ticks provide
the all-important cue for the cells to "all change". Unfortunately,
this kind of clock is impossible to implement in the real Universe. The reason
is the existence of a cosmic speed limit, as discovered by Einstein.

Nothing, it turns out,
can travel faster than the speed of light. This constraint means that, wherever
the cellular automaton clock happens to be located in the Universe, the signal
carrying news of its tick will take longer to travel to a cell that is far away
from than to one that is nearby. A possible way round this might be to have
lots of clocks distributed throughout the Universe. However, this does not
overcome the fundamental problem because there is no way to make sure the
clocks are all telling the same time. If a "reference clock" is used,
inevitably the signal carrying news of its time will take longer to reach some
clocks than it does to reach others.

The impossibility of
implementing a "global" clock in our Universe means that at the very
least the Universe cannot be a "standard" cellular automaton.
However, that does not rule out it being a cellular automaton of some
non-standard type - one that somehow gets by without a global clock. This seems
a bit of a tall order. But Wolfram can think of an ingenious way it can be achieved.
"Say that, rather than updating all of its cells together, a cellular
automaton updates just one cell at a time," he says.

At first sight this seem
crazy. But consider for a moment the advantage of such a scheme. If, at each
step, only one cell is updated, the sticky problem of getting all the cells to
update at the same time clearly goes away.

Of course there remains the small matter of
how such a cellular automaton could possibly mimic our reality. After all, we
have the very strong impression that everything in the Universe is travelling
forward through time together, not that one detail of reality is being updated
in turn while everything else remains doggedly rooted to the spot.

Say you are playing in a
football game. You see all the other players running about the pitch
simultaneously. You do not see first one player take a step, as their thought
processes click on one notch, while everyone else remains paralysed in
mid-stride; then another player take a step, and so on. "But, just because
you do not see this happening, does not mean that this is not exactly what is
going on," says Wolfram.

But surely you would
notice? No, says Wolfram. The only time you notice the world about you is when
it is your turn to be updated. And, when this happens, all you see is that all
the other players have moved on a fraction. Because your awareness is frozen
between your own updatings, it is impossible for you to notice when any of the
other players are updated. Despite the fact that only one player on the pitch
is moving at any one time, your perception is of everyone on the pitch running
about simultaneously.

Between any two
successive moments of time as perceived by you, there are very many updating
events, none of which you have any awareness of. In fact, all you can ever
really know about, says Wolfram, is what updating event influences what other
updating event. For instance, the updating event that moved the football one
step closer to the opposing team's goal influenced the opposing team's
defenders and goal keeper, who altered their positions to intercept the ball.
This, of course, is the familiar story of a football game. "But that's all
it is - a 'story'," says Wolfram. "A network of cause and effect we
impose on the underlying reality to make some kind of sense of it."

Contrary to common sense
expectations, then, it appears that it is possible to mimic our Universe with a
cellular automaton in which only one cell at a time is updated. The passage of
the "time" in the Universe is marked by the regular ticking of the
cellular automaton's clock. That only leaves "space" to worry about.
Unfortunately, it is here, according to Wolfram, that the idea of the
Universe-as-a-cellular-automaton comes to grief.

Wolfram is convinced
that the computer program generating our Universe is a simple one. Every scrap
of evidence he has accumulated since his key discovery that simple programs can
produce unexpectedly complex outputs bolsters this belief. But, if the program
generating the Universe is simple, it stands to reason there will not be room
in it for much "stuff". In other words, very few of the features of
our Universe - from gravity to space and time to koala bears - will be visible
in the program. Instead, they will "emerge" - like an inflatable raft
unfolding from a canister - only after the program has been running for a long
while.

But Wolfram does not
simply think the Universe-creating program is simple. He goes further than
this. He believes the program may be among the *simplest possible*
programs capable of generating the Universe. This is a leap of faith. All
Wolfram knows for sure is that the rule for the Universe is not *really*
complicated. If it was, he argues, there would be no perceptible pattern to
nature, which there clearly is. Wolfram thinks it is possible our Universe is
the *very simplest* universe that is not obviously a silly one - for
instance, a universe with no notion of space or of time. Consequently, he
thinks it is worth first trying the simple rules for size because our Universe
might be among them.

If the
Universe-generating program is indeed among the simplest programs capable of
generating the Universe, it will contain the absolute bare minimum of stuff.
And it is this that persuades Wolfram that the Universe cannot possibly be a
cellular automaton. A cellular automaton, after all, is a rigid array of cells
laid out in “space”. In other words, the very notion of “space” is built into
its very foundations. To Wolfram, this is already too much *stuff*.

Wolfram believes the
Universe-generating program will be so simple, so pared down, that even
something as apparently fundamental as space will not be built into it.
Instead, it will emerge along with everything else only as the program runs,
conjured out of something even more basic than space.

Wolfram believes space
is not a smooth, featureless backcloth to the drama of the Universe. Instead,
it has an underlying structure. The analogy he uses is water. Although water
looks smooth and continuous, in fact it is made up of tiny motes of matter called
molecules. Wolfram thinks space is similar. If it were possible to examine it
with some kind of super-microscope, we would see that it is made of a huge
number of discrete points. The points, or "nodes", are connected
together in a vast extended network.

But how can a mere
network of points have the properties of familiar space? "Surprisingly
easily," says Wolfram. "It simply depends on the way the nodes are
connected to each other."

Imagine being at one
particular node, then going to all the nodes that are 1 connection away, then 2
connections, then 3, and so on. After going, say, *r* connections, simply
count how many nodes you have visited. If there are roughly pi X *r*^2
nodes - the area of a circle - then the space is 2-dimensional like the surface
of a piece of paper. If there are roughly 4/3 pi X *r*^3 - the volume of a
sphere - then the space is 3-dimensional, like the space we live in. It turns
out that a simple network of nodes can mimic the essential properties of
absolutely any space imaginable, be it 1-dimensional, 2-dimensional or
279-dimensional.

According to Wolfram,
space is nothing more than a bunch of nodes connected together. Of course,
there is a little bit more to it than that.

Wolfram envisions a
space network being updated in a similar way to a cellular automaton. After
all, a constantly updated cellular automaton has a proven ability to generate
complexity reminiscent of our Universe. Recall how it was possible to get over
the synchronisation problem of a cellular automaton by updating just one cell
at a time. Well, Wolfram thinks that this elegant solution can be carried right
over to a space network. Instead of having a rule which says - if a cell is
surrounded by a certain pattern of coloured cells - change its colour, Wolfram imagines
a rule saying - if there is a piece of network with a particular form, replace
it with a piece of network with another form. Remarkably, Wolfram claims that
everything in our world can emerge from such a space network.

Take particles of
matter. In a cellular automata - for instance, the one subject to rule 110 -
the system may quickly organise itself into a few localised structures which
are persistent and appear to move through space just like fundamental particles
- quarks and electrons and so on. What is actually happening is that, as fast
as the structures are destroyed, they are refreshed again. It is just like a TV
image of a football game. We may perceive that a football in flight. But, in
reality, what is happening is that a picture of the ball is being refreshed 30
times a second and giving us the illusion of the ball moving through the air[5].

Sometimes, in a cellular
automaton subject to rule 110, there is a collision between
"particles". They slam into each and a whole bunch of other particles
come out. This is just the kind of thing physicists observe at atom smashers
like the one at the European centre for particle physics at CERN in Geneva. And
what happens in a cellular automaton subject to rule 110 can also happen in a
space network. Instead of being stubbornly persistent patterns of cells,
however, the "particles" are stubbornly persistent tangles of
connections.

Remarkably, Wolfram has
found that, with a constantly updated network of nodes, it is possible to
create both the space we live in and the matter we are made of.
"Reality", as Einstein remarked, "is merely an illusion, albeit
a very persistent one."

A problem arises,
however, if a rule applies to a particular pattern of nodes and there are
several places in the network with the same pattern. Which place should be
updated first? Updating the places in a different order will in general lead to
different networks of cause and effect. Rather than having a unique history,
the Universe will have several possible histories. We will not know why we are
following the history we are and not another, which is a highly unsatisfactory
state of affairs.

Fortunately, there is a
way out of this difficulty, says Wolfram. By a stroke of luck it turns out that
there are certain rules with the property that it in fact does not matter in
which order they are applied. Wolfram calls them "causally invariant"
rules. "Whenever they are used, there is always just a single thread of
time in the Universe," he says.

Wolfram's progression
from the Universe-as-a-cellular- automaton to the
Universe-as-a-constantly-updated-space-network is a good illustration of the
way in which physicists grope their way towards a true picture of nature. They
start with a crude model which mimics an aspect of reality which they consider
to be important. In this case, the model is a cellular automaton which can
generate complexity tantalisingly like the complexity we see in the world
around us. Inevitably, the model falls short in some way. In the case of
cellular automaton, it contains too much ready-made stuff such as
"space". Nevertheless, physicists use the crude model as a bridge to
reach a better model that mimics more reality more faithfully. Lastly, they
throw away the bridge.

Wolfram's talk of space
and matter "emerging" from a network may seems rather woolly.
However, he maintains that it can explain concrete things too such as the
general theory of relativity, Einstein's theory of gravity. In a nutshell, the
theory says that matter distorts, or warps, space-time, and that warped
space-time, is what matter reacts to when it moves. In fact, warped space-time
is all gravity is. We think that the Earth pulls on the Moon with invisible
fingers of force which somehow reach out across 400 000 kilometres of empty
space. But, according to Einstein, this is an illusion. In reality, the Earth's
mass warps space-time, creating a sort of valley in its vicinity. We cannot see
it because space-time is 4-dimensional and we can experience only 3 dimensions.
But the Moon "sees" it. It skitters around the rim of the valley in
space-time like a roulette ball round a roulette wheel.

Wolfram claims that his
perpetually updated space network behaves exactly like Einstein's warped
space-time. For simplicity imagine things in 2 dimensions. Also, imagine that
the network is a network of hexagons which can be laid out flat like a fishing
net spread out on a beach. What happens if some of the connections are changed
so that some heptagons and pentagons are mixed in with the hexagons? The answer
is the network bulges out or in. "This is warped space," says
Wolfram.

In ordinary flat
2-dimensional space, recall that the number of nodes we get by going out *r*
steps through the network goes up as* r*^2. Well, in a warped network, it
is not quite the same. There is what mathematicians call a "correction
term". And it turns out that the correction term is basically the
"Ricci tensor". It is not necessary to know exactly what the Ricci
tensor is. But it crops up in Einstein's equations which, in general relativity
specify the warpage of space-time.

The story of how is
quite complicated. But Wolfram maintains that, with just a few assumptions, he
can work out the conditions which the Ricci tensor must obey. "And, guess
what?" he says. "They seem to be exactly Einstein's equations of
gravity."

Wolfram believes the computer program that nature is using to generate
the Universe is very short. We are certainly not talking about the 10 million
or so lines of a program like "Microsoft Windows". Far from it.
"Nature's program may be expressible in as few as 4 lines of
Mathematica," he says.

If he is right, those
lines are responsible for creating everything from chocolate doughnuts to TV
game shows to the very thought processes that have led Wolfram to the audacious
claim that a mere 4 lines of computer code are generating reality.

Wolfram admits that his
decade of investigation has not yet furnished him with the elusive cosmic
computer program - the “one rule to bind them all”. But he is hopeful that he
will one day find it.

One of the most
important discoveries to have come out of Wolfram's decade of toil is the
recognition that a cellular automaton following rule 110 is far from unique.
Wolfram has been surprised to find that many other real systems in the Universe
- from turbulent fluids to colliding subatomic particles - also behave as
universal computers. In other words, they too have the capacity to simulate any
other machine, carry out any conceivable computation.

Because a universal
computer can compute, or simulate, absolutely anything, it is trivial to deduce
from this that all systems that behave as universal computers can compute as
much as each other. In other words, they are equivalent. "Since universal
computers are so widespread in nature, this has far-reaching
implications," says Wolfram. "It means that everything from the
behaviour of a cell to turbulence in a hydrogen cloud drifting in the depths of
space to rain pattering on the pavement is equivalent in terms of the
computational complexity required to generate it."

Until now, scientists
have assumed that the kind of complexity which is seen in living things - from
single cells to human brains - can arise only in a system of large molecules
based on carbon atoms. This, after all, is what we observe on Earth. But if, as
Wolfram firmly believes, a large range of systems in nature have equivalent
computational complexity, it means that the complexity we associate with life
is not the unique preserve of planet-bound, water-soluble, carbon-based
chemistry. Many of the things we thought were special about life and
intelligence can be present in numerous other kinds of physical systems.
"The Universe may contain lifeforms - including intelligent life forms -
the like of which we cannot begin to imagine," says Wolfram.

Wolfram elevates his
discovery that large numbers of natural systems have the same computational
complexity to an over-arching natural principle. He calls it "The
Principle of Computational Equivalence". Put crudely, it says that systems
of similar complexity are equivalent. Take, for instance, the Earth's
atmosphere. According to Wolfram's Principle, because the atmosphere's
circulation is as complex as any living thing, it has exactly the same right be
classed as a living thing as you or me! "People say 'The weather has a
mind of its own and think they're just using a metaphor," says Wolfram.
"I think there's something much more literally true about it."

Wolfram his believes his
Principle of Computational Equivalence is a revolutionary and fertile new idea
in science. Moreover, he sees it as the next logical step along a road that
science first embarked on more than four centuries ago.

In the 16th century, the
Polish astronomer Nicolaus Copernicus realised that the Sun and planets did not
turn about the Earth, as had generally been believed, but that the Earth
occupied no special place in the Universe. Later, in the 19th century, Charles
Darwin deduced that humans were just another product of evolution by the
process of natural selection and so they occupied no special place in Creation.
Wolfram sees himself as completing the revolution begun by Copernicus and
Darwin. There is nothing special, he maintains, about the kind of computation
that leads to living things and the thought processes of human brains. Life and
intelligence could be implemented in a myriad different physical systems. One
consequence of this is that there is no barrier preventing us from creating
artificial intelligence - a machine that thinks and behaves like a human being.

All this spells trouble
for a kind of reasoning currently favoured by some cosmologists. According to
the "anthropic principle", the reason the Universe has many of the
features it has - for instance, laws of physics which permit the formation of
galaxies, stars and planets - is because, if it did not, it would not have been
possible for human beings to have arisen to notice those features. It is a
curiously topsy-turvy logic. And an inevitable consequence is that biology is
the ultimate determinant of the physics that we observe around us.

However, the anthropic
principle is fatally undermined if, as Wolfram believes, life can be
implemented in any number of different physical systems, some as far away from
carbon-based chemistry as it is possible to imagine. "Cosmologists have no
right to use the conditions necessary for our existence on Earth to deduce
anything about the laws of physics that govern our Universe," says
Wolfram.

Cosmologists wonder why
the Universe appears so hospitable for life. The answer, Wolfram believes, is
because almost any physical system, almost any set of parameters, can exhibit
the complexity of a living thing.

Everything Wolfram discovered during his decade of toil - the
equivalent, he maintains, of hundreds, maybe even thousands, of scientific
papers - he eventually distilled into an enormous, epic book. *A New Kind of
Science* was finished in January 2002. It was almost 1200 pages long with
about 1000 black-and-white pictures and half a million words. On the first day
of publication it sold 50,000 copies. And it annoyed the hell out the
scientific community.

Absolutely everything
about the self-published book seemed to make other scientists see red. Wolfram
was accused of not crediting the contributions of others. Wolfram was accused
of breathtaking arrogance. After all, he was saying, "Here in my book is
an entirely new way of doing science". And nobody had dared say that since
Isaac Newton.

A striking feature of
the venom directed at Wolfram was its swiftness. Within days of the book’s
publication, some scientists had posted damning reviews on Amazon’s website.
Yet the book's 1200 picture-filled pages were crammed with examples that had to
be worked through by the reader. It was hard to believe that anyone could have
digested enough to have dismissed it in just a few days.

Chaitin is philosophical
about the knee-jerk reaction of the scientific community. "If you write a
book that offends no one and make sure everything you write is absolutely, 100
per cent, correct, then you end up writing nothing," he says.

One specific criticism
is that, although Wolfram has produced a 1200-page book of pretty pictures of
what simple computer programs can do, he has deduced very few universal laws of
the kind first discovered by Newton. This, however, misunderstands Wolfram. His
new kind of science is not at all like the old type - which, of course, why he
has called it "a new kind of science". In the old, maths-based
science, the motion of, say, a planet travelling around the Sun is distilled
into an equation, which predicts its behaviour from now into the infinite past
and future. In the new science, the only way to discover how something behaves
is to run a computer program. There is no such shortcut. Or, rather, all the
shortcuts have already been found. They are conventional, equation-based
science!

It is Wolfram's view
that much of what is going on in the Universe cannot be distilled into neat
equations. You have to run the program to find out what happens. Some of the
programs can be run, and a result obtained, more quickly than the Universe.
This is because, by some fortunate quirk, some of what the Universe is doing is
"computationally reducible". "Almost all of what traditional
equation-based science has been doing is looking just at those computationally
reducible parts," says Wolfram.

Wolfram suspects,
however, that most of what is going on in the Universe is computationally
irreducible. In other words, the only way to find out the outcome of the
program the Universe is running is to run it for 13.7 billion years! This
raises a spooky possibility. Is the program of the Universe being run by
someone or something simply because there is no other way to discover the outcome?!
In *The Hitch Hiker's Guide to the Galaxy*, the Earth turns out to be a
computer run by mice to discover the answer to the ultimate question. Might
author Douglas Adams' jest, by some tremendous irony, actually be near to the
truth?

The American physicist
Ed Fredkin thinks so. He is convinced that the Universe is nothing more than a
computer which is being used to solve a problem. As others have pointed out,
this is both good news and bad news. The good news is that there really is a
purpose to our lives. The bad news is that purpose may be to help someone or
something work out pi to countless zillion decimal places!

The idea that the most
fundamental stuff in the Universe - more fundamental even than matter or energy
- is information - digital information - is certainly an idea which is taking
hold among today's physicists. Those who subscribe to this "digital
philosophy", such as Wolfram and Fredkin, are in absolutely no doubt that
what the Universe is doing is computation, in the most general sense of the
word. One consequence is unavoidable. Like the insects burrowing in the topsoil
of Adams' terrestrial computer, we are a part of the great cosmic computation.
"We never perform a computation ourselves," says Tomasso Toffoli of
Boston University[6]. "We just
hitch a ride on the great Computation that is going on already."

Of course, if you want
to go one mystical step farther and talk about a computation not in its most
general sense but in the sense of something directed to some end, like a human
computation, then you come to the arena of religious speculation. "The
Universe begins to look more like a great thought than a machine," wrote
the British astronomer Sir James Jeans. And Jeans was really only echoing
Bishop George Berkeley, the Irish philosopher who in the 18th century declared:
"We exist only in the mind of God." Chaitin likes to put it in more
modern terms: "Is God a programmer?"

If the idea of the
Universe "computing" something is not mind-blowing enough, consider
what it really means if Wolfram is right and the complexity of the Universe is
generated merely by applying a simple computer program - a simple rule - over
and over again. Information cannot be created out of nothing. Common sense says
that what comes out cannot be any more than what is put in. If Wolfram is
right, it means that the Universe can contain no more complexity than simple
the program responsible for generating it. Consequently, the complexity we see
around us cannot be real complexity. It must be "pseudo-complexity".
The Universe only looks complex because we are unaware of the simple underlying
rule generating it.

Newton's worldview was
one in which the laws of physics orchestrate a predictable world. The planets,
for instance, circle the Sun with the regularity of clockwork. However, in such
a clockwork universe, where the future is always utterly predictable,
scientists faced a conundrum: how can there be any free will?

Wolfram sidesteps this
problem. In his clockwork universe, the future of the Universe is predictable -
*but only in principle*. In practice, you can never finish the
computations and discover the outcome faster than the Universe does. Free will
survives - as pseudo free will!

Chaitin puts Wolfram's
worldview in purely mathematical terms. Pi, the ratio of a circle's
circumference to its radius, is a number that appears to be extraordinarily
complicated, its digits never repeating, but it can in fact be generated by a
short computer program. Chaitin, however, has invented a number which is truly
complex. "Omega" requires an infinitely long computer program to
generate it[7]. "Is
the Universe like pi or like Omega?" says Chaitin. "Most people think
it's like Omega. Wolfram thinks it's like pi."

The reason that most
people think the Universe is like Omega - in other words, that it has
unadulterated, infinite complexity - is that most people believe in quantum
theory. And quantum theory tells us that events in the microscopic world such
as the disintegration of an atom or the absorption of a photon of light by a window
pane are completely random, as unpredictable as a perfect coin toss. Such
events generate an infinite amount of complexity - which is the same as
randomness[8].
And this gets permanently imprinted on the Universe - for instance, when a
high-energy photon strikes a strand of DNA and causes a mutation, which echoes
down the generations, frozen into the fabric of life for all time.

As a consequence of
quantum theory, then, much of what we see around us is in the Universe
inherently unpredictable. It is the result of countless quantum coin tosses,
which have been happening one after the other since the beginning of time. We
will therefore never be able to comprehend the Universe in its entirety.

On this score, Wolfram
is far more optimistic than the majority of physicists. Because he believes the
Universe has finite complexity like pi, he believes that quantum theory as
currently practised is wrong. All the randomness that quantum theory generates
is therefore really only pseudorandomness, like that in the digits of pi. If he
is right, then we may eventually be able to comprehend everything.

Who is right - Wolfram
or the rest of the scientific community? Chaitin confesses to spending long
hours at Wolfram's house near Boston arguing with him about his ideas. "In
*A new kind of science*, Wolfram develops an extremely interesting and
provocative vision," says Chaitin. "The question is: Does the
physical Universe share Wolfram's vision? Time alone will tell."

[1] A black hole is region of space where gravity is so strong that not even light, the fastest thing in the Universe, can escape.

[2]
Why 256 possible rules? Well, for each successive line, the colour of a cell
(black or white) depends only on its own previous colour and the colour of the
cell on the left and the cell on the right. This means there are eight possible
starting situations. For instance, a square can be black with a black square to
its left, or black with a black square to its right, or black with black
squares to the left and right, or black with white squares to the left and
right. Another four possibilities arise if the central square is white.

Each rule maps all these eight input situations to an output (black or white). This means there are 2^8 = 256 possible rules for such a one-dimensional, two-colour, adjacent-cell cellular automaton.

[3] For more on
Chaitin – in fact, for a whole chapter on the man, not to mention the amazing
number he invented that contains the secret of life, the Universe and
everything - see chapter “God’s number”.

[4] See chapter "God's number".

[5] Even the atoms and molecules that compose you are "refreshed" at intervals. They are not the same one that were a part of you last year. Most cells such as blood cells are replenished within a matter of weeks and even those that persist longer such as neurones have their component molecules changed at regular intervals.

[6] Toffoli is famous for inventing the Toffoli Gate, a
logical computing circuit which can be implemented by transistors in a
computer. Not only is the gate *universal *– which means which that any
conceivable calculation can be carried out solely by a collection of Toffoli
gates – but it is *reversible* – which means the gate produces the same
result regardless of whether current flows through it in the forwards or
backwards direction. This is important because, in physics, reversible
processes use no energy. The Toffoli gate is therefore extremely energy
efficient.

[7] See chapter "God's number".

[8] See chapter "God's number".