Computing a theory of everything | Stephen Wolfram

So I want to talk today about an idea. It's a big idea.

Actually, I think it'll eventually

be seen as probably the single biggest idea

that's emerged in the past century.

It's the idea of computation.

Now, of course, that idea has brought us

all of the computer technology we have today and so on.

But there's actually a lot more to computation than that.

It's really a very deep, very powerful, very fundamental idea,

whose effects we've only just begun to see.

Well, I myself have spent the past 30 years of my life

working on three large projects

that really try to take the idea of computation seriously.

So I started off at a young age as a physicist

using computers as tools.

Then, I started drilling down,

thinking about the computations I might want to do,

trying to figure out what primitives they could be built up from

and how they could be automated as much as possible.

Eventually, I created a whole structure

based on symbolic programming and so on

that let me build Mathematica.

And for the past 23 years, at an increasing rate,

we've been pouring more and more ideas

and capabilities and so on into Mathematica,

and I'm happy to say that that's led to many good things

in R & D and education,

lots of other areas.

Well, I have to admit, actually,

that I also had a very selfish reason for building Mathematica:

I wanted to use it myself,

a bit like Galileo got to use his telescope

400 years ago.

But I wanted to look not at the astronomical universe,

but at the computational universe.

So we normally think of programs as being

complicated things that we build

for very specific purposes.

But what about the space of all possible programs?

Here's a representation of a really simple program.

So, if we run this program,

this is what we get.

Very simple.

So let's try changing the rule

for this program a little bit.

Now we get another result,

still very simple.

Try changing it again.

You get something a little bit more complicated.

But if we keep running this for a while,

we find out that although the pattern we get is very intricate,

it has a very regular structure.

So the question is: Can anything else happen?

Well, we can do a little experiment.

Let's just do a little mathematical experiment, try and find out.

Let's just run all possible programs

of the particular type that we're looking at.

They're called cellular automata.

You can see a lot of diversity in the behavior here.

Most of them do very simple things,

but if you look along all these different pictures,

at rule number 30,

you start to see something interesting going on.

So let's take a closer look

at rule number 30 here.

So here it is.

We're just following this very simple rule at the bottom here,

but we're getting all this amazing stuff.

It's not at all what we're used to,

and I must say that, when I first saw this,

it came as a huge shock to my intuition.

And, in fact, to understand it,

I eventually had to create

a whole new kind of science.

(Laughter)

This science is different, more general,

than the mathematics-based science that we've had

for the past 300 or so years.

You know, it's always seemed like a big mystery:

how nature, seemingly so effortlessly,

manages to produce so much

that seems to us so complex.

Well, I think we've found its secret:

It's just sampling what's out there in the computational universe

and quite often getting things like Rule 30

or like this.

And knowing that starts to explain

a lot of long-standing mysteries in science.

It also brings up new issues, though,

like computational irreducibility.

I mean, we're used to having science let us predict things,

but something like this

is fundamentally irreducible.

The only way to find its outcome

is, effectively, just to watch it evolve.

It's connected to, what I call,

the principle of computational equivalence,

which tells us that even incredibly simple systems

can do computations as sophisticated as anything.

It doesn't take lots of technology or biological evolution

to be able to do arbitrary computation;

just something that happens, naturally,

all over the place.

Things with rules as simple as these can do it.

Well, this has deep implications

about the limits of science,

about predictability and controllability

of things like biological processes or economies,

about intelligence in the universe,

about questions like free will

and about creating technology.

You know, in working on this science for many years,

I kept wondering,

"What will be its first killer app?"

Well, ever since I was a kid,

I'd been thinking about systematizing knowledge

and somehow making it computable.

People like Leibniz had wondered about that too

300 years earlier.

But I'd always assumed that to make progress,

I'd essentially have to replicate a whole brain.

Well, then I got to thinking:

This scientific paradigm of mine suggests something different --

and, by the way, I've now got

huge computation capabilities in Mathematica,

and I'm a CEO with some worldly resources

to do large, seemingly crazy, projects --

So I decided to just try to see

how much of the systematic knowledge that's out there in the world

we could make computable.

So, it's been a big, very complex project,

which I was not sure was going to work at all.

But I'm happy to say it's actually going really well.

And last year we were able

to release the first website version

of Wolfram Alpha.

Its purpose is to be a serious knowledge engine

that computes answers to questions.

So let's give it a try.

Let's start off with something really easy.

Hope for the best.

Very good. Okay.

So far so good.

(Laughter)

Let's try something a little bit harder.

Let's do

some mathy thing,

and with luck it'll work out the answer

and try and tell us some interesting things

things about related math.

We could ask it something about the real world.

Let's say -- I don't know --

what's the GDP of Spain?

And it should be able to tell us that.

Now we could compute something related to this,

let's say ... the GDP of Spain

divided by, I don't know,

the -- hmmm ...

let's say the revenue of Microsoft.

(Laughter)

The idea is that we can just type this in,

this kind of question in, however we think of it.

So let's try asking a question,

like a health related question.

So let's say we have a lab finding that ...

you know, we have an LDL level of 140

for a male aged 50.

So let's type that in, and now Wolfram Alpha

will go and use available public health data

and try and figure out

what part of the population that corresponds to and so on.

Or let's try asking about, I don't know,

the International Space Station.

And what's happening here is that

Wolfram Alpha is not just looking up something;

it's computing, in real time,

where the International Space Station is right now at this moment,

how fast it's going, and so on.

So Wolfram Alpha knows about lots and lots of kinds of things.

It's got, by now,

pretty good coverage of everything you might find

in a standard reference library.

But the goal is to go much further

and, very broadly, to democratize

all of this knowledge,

and to try and be an authoritative

source in all areas.

To be able to compute answers to specific questions that people have,

not by searching what other people

may have written down before,

but by using built in knowledge

to compute fresh new answers to specific questions.

Now, of course, Wolfram Alpha

is a monumentally huge, long-term project

with lots and lots of challenges.

For a start, one has to curate a zillion

different sources of facts and data,

and we built quite a pipeline of Mathematica automation

and human domain experts for doing this.

But that's just the beginning.

Given raw facts or data

to actually answer questions,

one has to compute:

one has to implement all those methods and models

and algorithms and so on

that science and other areas have built up over the centuries.

Well, even starting from Mathematica,

this is still a huge amount of work.

So far, there are about 8 million lines

of Mathematica code in Wolfram Alpha

built by experts from many, many different fields.

Well, a crucial idea of Wolfram Alpha

is that you can just ask it questions

using ordinary human language,

which means that we've got to be able to take

all those strange utterances that people type into the input field

and understand them.

And I must say that I thought that step

might just be plain impossible.

Two big things happened:

First, a bunch of new ideas about linguistics

that came from studying the computational universe;

and second, the realization that having actual computable knowledge

completely changes how one can

set about understanding language.

And, of course, now

with Wolfram Alpha actually out in the wild,

we can learn from its actual usage.

And, in fact, there's been

an interesting coevolution that's been going on

between Wolfram Alpha

and its human users,

and it's really encouraging.

Right now, if we look at web queries,

more than 80 percent of them get handled successfully the first time.

And if you look at things like the iPhone app,

the fraction is considerably larger.

So, I'm pretty pleased with it all.

But, in many ways,

we're still at the very beginning with Wolfram Alpha.

I mean, everything is scaling up very nicely

and we're getting more confident.

You can expect to see Wolfram Alpha technology

showing up in more and more places,

working both with this kind of public data, like on the website,

and with private knowledge

for people and companies and so on.

You know, I've realized that Wolfram Alpha actually gives one

a whole new kind of computing

that one can call knowledge-based computing,

in which one's starting not just from raw computation,

but from a vast amount of built-in knowledge.

And when one does that, one really changes

the economics of delivering computational things,

whether it's on the web or elsewhere.

You know, we have a fairly interesting situation right now.

On the one hand, we have Mathematica,

with its sort of precise, formal language

and a huge network

of carefully designed capabilities

able to get a lot done in just a few lines.

Let me show you a couple of examples here.

So here's a trivial piece of Mathematica programming.

Here's something where we're sort of

integrating a bunch of different capabilities here.

Here we'll just create, in this line,

a little user interface that allows us to

do something fun there.

If you go on, that's a slightly more complicated program

that's now doing all sorts of algorithmic things

and creating user interface and so on.

But it's something that is very precise stuff.

It's a precise specification with a precise formal language

that causes Mathematica to know what to do here.

Then on the other hand, we have Wolfram Alpha,

with all the messiness of the world

and human language and so on built into it.

So what happens when you put these things together?

I think it's actually rather wonderful.

With Wolfram Alpha inside Mathematica,

you can, for example, make precise programs

that call on real world data.

Here's a real simple example.

You can also just sort of give vague input

and then try and have Wolfram Alpha

figure out what you're talking about.

Let's try this here.

But actually I think the most exciting thing about this

is that it really gives one the chance

to democratize programming.

I mean, anyone will be able to say what they want in plain language.

Then, the idea is that Wolfram Alpha will be able to figure out

what precise pieces of code

can do what they're asking for

and then show them examples that will let them pick what they need

to build up bigger and bigger, precise programs.

So, sometimes, Wolfram Alpha

will be able to do the whole thing immediately

and just give back a whole big program that you can then compute with.

Here's a big website

where we've been collecting lots of educational

and other demonstrations about lots of kinds of things.

I'll show you one example here.

This is just an example of one of these computable documents.

This is probably a fairly small

piece of Mathematica code

that's able to be run here.

Okay. Let's zoom out again.

So, given our new kind of science,

is there a general way to use it to make technology?

So, with physical materials,

we're used to going around the world

and discovering that particular materials

are useful for particular

technological purposes.

Well, it turns out we can do very much the same kind of thing

in the computational universe.

There's an inexhaustible supply of programs out there.

The challenge is to see how to

harness them for human purposes.

Something like Rule 30, for example,

turns out to be a really good randomness generator.

Other simple programs are good models

for processes in the natural or social world.

And, for example, Wolfram Alpha and Mathematica

are actually now full of algorithms

that we discovered by searching the computational universe.

And, for example, this -- if we go back here --

this has become surprisingly popular

among composers

finding musical forms by searching the computational universe.

In a sense, we can use the computational universe

to get mass customized creativity.

I'm hoping we can, for example,

use that even to get Wolfram Alpha

to routinely do invention and discovery on the fly,

and to find all sorts of wonderful stuff

that no engineer

and no process of incremental evolution would ever come up with.

Well, so, that leads to kind of an ultimate question:

Could it be that someplace out there in the computational universe

we might find our physical universe?

Perhaps there's even some quite simple rule,

some simple program for our universe.

Well, the history of physics would have us believe

that the rule for the universe must be pretty complicated.

But in the computational universe,

we've now seen how rules that are incredibly simple

can produce incredibly rich and complex behavior.

So could that be what's going on with our whole universe?

If the rules for the universe are simple,

it's kind of inevitable that they have to be

very abstract and very low level;

operating, for example, far below

the level of space or time,

which makes it hard to represent things.

But in at least a large class of cases,

one can think of the universe as being

like some kind of network,

which, when it gets big enough,

behaves like continuous space

in much the same way as having lots of molecules

can behave like a continuous fluid.

Well, then the universe has to evolve by applying

little rules that progressively update this network.

And each possible rule, in a sense,

corresponds to a candidate universe.

Actually, I haven't shown these before,

but here are a few of the candidate universes

that I've looked at.

Some of these are hopeless universes,

completely sterile,

with other kinds of pathologies like no notion of space,

no notion of time, no matter,

other problems like that.

But the exciting thing that I've found in the last few years

is that you actually don't have to go very far

in the computational universe

before you start finding candidate universes

that aren't obviously not our universe.

Here's the problem:

Any serious candidate for our universe

is inevitably full of computational irreducibility.

Which means that it is irreducibly difficult

to find out how it will really behave,

and whether it matches our physical universe.

A few years ago, I was pretty excited to discover

that there are candidate universes with incredibly simple rules

that successfully reproduce special relativity,

and even general relativity and gravitation,

and at least give hints of quantum mechanics.

So, will we find the whole of physics?

I don't know for sure,

but I think at this point it's sort of

almost embarrassing not to at least try.

Not an easy project.

One's got to build a lot of technology.

One's got to build a structure that's probably

at least as deep as existing physics.

And I'm not sure what the best way to organize the whole thing is.

Build a team, open it up, offer prizes and so on.

But I'll tell you, here today,

that I'm committed to seeing this project done,

to see if, within this decade,

we can finally hold in our hands

the rule for our universe

and know where our universe lies

in the space of all possible universes ...

and be able to type into Wolfram Alpha, "the theory of the universe,"

and have it tell us.

(Laughter)

So I've been working on the idea of computation

now for more than 30 years,

building tools and methods and turning intellectual ideas

into millions of lines of code

and grist for server farms and so on.

With every passing year,

I realize how much more powerful

the idea of computation really is.

It's taken us a long way already,

but there's so much more to come.

From the foundations of science

to the limits of technology

to the very definition of the human condition,

I think computation is destined to be

the defining idea of our future.

Thank you.

(Applause)

Chris Anderson: That was astonishing.

Stay here. I've got a question.

(Applause)

So, that was, fair to say, an astonishing talk.

Are you able to say in a sentence or two

how this type of thinking

could integrate at some point

to things like string theory or the kind of things that people think of

as the fundamental explanations of the universe?

Stephen Wolfram: Well, the parts of physics

that we kind of know to be true,

things like the standard model of physics:

what I'm trying to do better reproduce the standard model of physics

or it's simply wrong.

The things that people have tried to do in the last 25 years or so

with string theory and so on

have been an interesting exploration

that has tried to get back to the standard model,

but hasn't quite gotten there.

My guess is that some great simplifications of what I'm doing

may actually have considerable resonance

with what's been done in string theory,

but that's a complicated math thing

that I don't yet know how it's going to work out.

CA: Benoit Mandelbrot is in the audience.

He also has shown how complexity

can arise out of a simple start.

Does your work relate to his?

SW: I think so.

I view Benoit Mandelbrot's work

as one of the founding contributions

to this kind of area.

Benoit has been particularly interested

in nested patterns, in fractals and so on,

where the structure is something

that's kind of tree-like,

and where there's sort of a big branch that makes little branches

and even smaller branches and so on.

That's one of the ways

that you get towards true complexity.

I think things like the Rule 30 cellular automaton

get us to a different level.

In fact, in a very precise way, they get us to a different level

because they seem to be things that are

capable of complexity

that's sort of as great as complexity can ever get ...

I could go on about this at great length, but I won't. (Laughter) (Applause)

CA: Stephen Wolfram, thank you.

(Applause)