"A New Kind of Science,"
by Stephen Wolfram was a book I read over ten years ago just after it was first
published.
Stephen Wolfram is an interesting person who was born in London and educated at
Oxford, who gained a Ph.D. in theoretical physics at only 20 years of age. In the
1980’s he made a series of discoveries that he posited yielded new insights
into physics, mathematics, computer science, and biology to shed new light on
how everything tends to work in our universe. Although his work did initially attract some criticism within the scientific community it seems his work ultimately has provided food for thought on conceptual puzzles and longstanding issues in philosophy.
In 1986 he founded Mathematica,
which has become one of the world’s leading software systems for technical and symbolic
programs.
The book represented
10 years of research and would be of interest to both scientists and
non-scientists alike. The use of graphics further enhances the presentation and
a reader’s easy grasp of his conclusions.
The basis of his
experiments are in the observance of behavioural output of simple program instructions
or rules. By way of example we are all familiar with the operation of software
that produces our pay, invoicing records or keeps vast quantities of information
stored in virtual reality in what is described as the “cloud”.
Wolfram wrote
simple programs to observe their outputs. He used black and white squares but
you could use any items –blue and white shaped beads if they took your fancy,
since it was only the output behaviours of those cells that is the subject of
the experiment. Hence he calls the output cellular automata.
His early
experiments yielded results markedly different to what he had anticipated so he
became interested in this phenomena which is encapsulated within the pages of
this book.
To reiterate however these computer programs can be described more
accurately simply as rules. The programs tell the computer to carry out some
instructions for a specified interval. There is no intention to achieve a
result other than to see what happens. He begins with basic programming rules
and builds up to a very mildly complex instruction.
E.g. the
so-called rule 30.
An elaboration
is as follows: Start with a single black square, and repeat the rule line by
line e.g. first, look at each cell and its right hand neighbour. If both of
these were white on the previous step, then take the new colour of the cell to
be whatever the previous colour of its left-hand neighbour was, otherwise, make
the new colour the opposite of that.
Your
intuition would tell you if you followed such a programming rule there should
be some sort of repetitive pattern to appear in the cellular data output, since
the same rule is being applied over and over again.
The effect of this program after 1,500 steps involving 2 million cells is there
are no signs of any regularity and the pattern obtained seem to continue to
evolve.
Hence the
book of 800 pages involves hundreds of experiments demonstrating this principle.
The subject of cellular-automata
and its principles has been debated in a variety of forums from philosophy to
how better to sustain ecology systems to their existing prior condition before
global warming. For a reference to how it is applied to Ecological Modelling click on the reference as per below: .
Application to eco systems.
From a philosophical stance a paper from Stanford University introduces
the idea of the
“Hat experiment” to explain how it works.
An example of cellular
automata as in Think
of Fig. 1 as
standing for the front row of a high school classroom. Each box represents a
student wearing (black) or not wearing (white) a hat. Let us make the two
following assumptions:
Hat rule: a student will wear the hat in the following class
if one or the other—but not both—of the two classmates sitting immediately on
her left and on her right has the hat in the current class (let us say that if
nobody wears the hat, then a hat is out of fashion; but if both neighbors wear
it, it is too popular to be trendy).
Initial class: during the first class in the morning, only one
student in the middle is wearing the hat
What happens as time goes by
(consecutive rows represent the evolution in time through subsequent classes):
What
happens is surprising. The
complex evolutionary pattern displayed contrasts with the simplicity of the
underlying law (the “Hat rule”) and ontology (for in terms of object and
properties, we only need to take into account simple atoms and two states. In a
sense, though, the global, emergent behaviour of the system supervenes upon its
local, simple features. The scale at which the decision to wear the hat is made
(immediate neighbours) is not the scale at which the interesting patterns
become manifest.
While somewhat artificial, this example
is a paradigmatic illustration of what makes CA appealing to a vast range of
researchers: “even perfect knowledge of individual decision rules does not
always allow us to predict macroscopic structure. We get macro-surprises
despite complete micro-knowledge” (Epstein 1999, p. 48). Since the notion of emergence and the
micro-macro interplay play such an important role in science and philosophy
(see the entries on supervenience and emergent properties; for a sample of scientific applications,
see Mitchell 2009, pp. 2–13, Gell-Mann 1994, Ch. 9), it has been suggested that
many scientific as well as conceptual puzzles can be addressed by adopting the
CA perspective. One of the leading thinkers in the field, Stephen Wolfram, has
gone as far as claiming that CA may help us to solve longstanding issues in
philosophy:
Hence Wolfram’s
experiments show very complex systems can be built up from very basic
underlying instructions or beginnings. During the course of the book he shows
the implications to many fields of current knowledge.
Fast forward to
Wolfram’ s blog and you get further insight into more recent thinking which I
have reproduced here.
A Short Talk on AI Ethics
Click on the link for
graphical examples of cellular automata.
October 17, 2016
Thanks for inviting me here today.
You know, it’s funny to be here. My mother was a philosophy
professor in Oxford. And when I was a kid I always said the one thing I’d never do
was do or talk about philosophy. But, well, here I am.
Before I really get into AI, I think I should say a
little bit about my worldview. I’ve basically spent my life alternating between
doing basic science and building technology. I’ve been interested in AI for about as
long as I can remember. But as a kid I started out doing physics and cosmology and things. That got me into building technology to automate stuff like math. And that
worked so well that I started thinking about, like, how to really know and
compute everything about everything. That was in about 1980—and at first I
thought I had to build something like a brain, and I was studying neural nets
and so on. But I didn’t get too far.
And meanwhile I got interested in an even bigger problem
in science: how to make the most general possible theories of things. The
dominant idea for 300 years had been to use math and equations. But I wanted to
go beyond them. And the big thing I realized was that the way to do that was to
think about programs, and the whole computational universe of possible
programs.
And that led to my personal Galileo-like moment. I just pointed my “computational
telescope” at these simplest possible programs, and I saw this amazing one I
called rule 30—that just seemed to go on producing
complexity forever from essentially nothing.
Well, after I’d seen this, I realized this is actually
something that happens all over the computational universe—and all over nature.
It’s really the secret that lets nature make all the complicated stuff we see.
But it’s something else too: it’s a window into what raw, unfettered
computation is like. At least traditionally when we do engineering we’re always
building things that are simple enough that we can foresee what they’ll do.
But if we just go out into the computational universe,
things can be much wilder. Our company has done a lot of mining out there,
finding programs that are useful for different purposes, like rule 30 is for
randomness. And modern machine learning is kind of part way from traditional
engineering to this kind of free-range mining.
But, OK, what can one say in general about the
computational universe? Well, all these programs can be thought of as doing
computations. And years ago I came up with what I call the Principle of Computational
Equivalence—that says that if behavior isn’t obviously simple, it typically corresponds
to a computation that’s maximally sophisticated. There are lots of predictions
and implications of this. Like that universal computation should be ubiquitous.
As should undesirability. And as should what I call computational irreducibility.
Can you predict what it’s going to do? Well, it’s
probably computationally irreducible, which means you can’t figure out what
it’s going to do without effectively tracing every step and going through the
same computational effort it does. It’s completely deterministic. But to us
it’s got what seems like free will—because we can never know what it’s going to
do.
Here’s another thing: what’s intelligence? Well, our big unifying principle says
that everything—from a tiny program, to our brains, is computationally
equivalent. There’s no bright line between intelligence and mere computation.
The weather really does have a mind of its own: it’s doing computations just as
sophisticated as our brains. To us, though, it’s pretty alien computation.
Because it’s not connected to our human goals and experiences. It’s just raw
computation that happens to be going on.
So how do we tame computation? We have to mold it to our
goals. And the first step there is to describe our goals. And for the past 30
years what I’ve basically been doing is creating a way to do that.
I’ve been building a language—that’s now called the Wolfram Language—that allows us to express what we want to
do. It’s a computer language. But it’s not really like other computer
languages. Because instead of telling a computer what to do in its terms, it
builds in as much knowledge as possible about computation and the world, so
that we humans can describe in our terms what we want, and then it’s up to the
language to get it done as automatically as possible.
This basic idea has worked really well, and in the form
of Mathematica it’s been used to make endless inventions
and discoveries over the years. It’s also what’s inside Wolfram Alpha. Where the idea is to take pure natural
language questions, understand them, and use the kind of curated knowledge and
algorithms of our civilization to answer them. And, yes, it’s a very classic Alisha
thing. And of course it’s computed answers to billions and billions of
questions from humans, for example inside Siri.
I had an interesting experience recently, figuring out
how to use what we’ve built to teach computational thinking to kids. I was writing exercises for a book. At the beginning, it was easy: “make a
program to do X”. But later on, it was like “I know what to say in the Wolfram
Language, but it’s really hard to express in English”. And of course that’s why
I just spent 30 years building the Wolfram Language.
English has maybe 25,000 common words; the Wolfram Language has about 5000
carefully designed built-in constructs—including all the latest machine
learning—together with millions of things based on curated data. And the idea
is that once one can think about something in the world computationally, it
should be as easy as possible to express it in the Wolfram Language. And the
cool thing is, it really works. Humans, including kids, can read and write the
language. And so can computers. It’s a kind of high-level bridge between human
thinking, in its cultural context, and computation.
OK, so what about AI? Technology has always been about finding
things that exist, and then taming them to automate the achievement of
particular human goals. And in AI the things we’re taming exist in the
computational universe. Now, there’s a lot of raw computation seething around
out there—just as there’s a lot going on in nature. But what we’re interested
in is computation that somehow relates to human goals.
So what about ethics? Well, maybe we want to constrain
the computation, the AI, to only do things we consider ethical. But somehow we
have to find a way to describe what we mean by that.
Well, in the human world, one way we do this is with
laws. But so how do we connect laws to computations? We may call them “legal
codes”, but today laws and contracts are basically written in natural language.
There’ve been simple computable contracts in areas like financial derivatives.
And now one’s talking about smart contracts around cryptocurrencies.
But what about the vast mass of law? Well, Leibniz—who died 300 years ago next month—was
always talking about making a universal language to, as we would say now,
express it all in a computable way. He was a few centuries too early, but I
think now we’re finally in a position to do this.
I just posted a long blog about all this last week, but let me try
to summarize. With the Wolfram Language we’ve managed to express a lot of kinds
of things in the world—like the ones people ask Siri about. And I think we’re
now within sight of what Leibniz wanted: to have a general symbolic discourse
language that represents everything involved in human affairs.
I see it basically as a language design problem. Yes, we
can use natural language to get clues, but ultimately we have to build our own
symbolic language. It’s actually the same kind of thing I’ve done for decades
in the Wolfram Language. Take even a word like “plus”. Well, in the Wolfram
Language there’s a function called Plus, but it doesn’t mean the same thing as the
word. It’s a very specific version that has to do with adding things
mathematically. And as we design a symbolic discourse language, it’s the same
thing. The word “eat” in English can mean lots of things. But we need a
concept—that we’ll probably refer to as “eat”—that’s a specific version that we
can compute with.
So let’s say we’ve got a contract written in natural
language. One way to get a symbolic version is to use natural language
understanding—just like we do for billions of Wolfram Alpha inputs, asking
humans about ambiguities. Another way might be to get machine learning to
describe a picture. But the best way is just to write in symbolic form in the
first place, and actually I’m guessing that’s what lawyers will be doing before
too long.
And of course once you have a contract in symbolic form,
you can start to compute about it, automatically seeing if it’s satisfied,
simulating different outcomes, automatically aggregating it in bundles, and so
on. Ultimately the contract has to get input from the real world. Maybe that
input is “born digital”, like data about accessing a computer system, or
transferring bitcoin. Often it’ll come from sensors and measurements—and it’ll
take machine learning to turn into something symbolic.
Well, if we can express laws in computable form maybe we
can start telling AIs how we want them to act. Of course it might be better if
we could boil everything down to simple principles, like Asimov’s Laws of Robotics, or utilitarianism or something.
But I don’t think anything like that is going to work.
What we’re ultimately trying to do is to find perfect constraints on
computation, but computation is something that’s in some sense infinitely wild.
The issue already shows up in Gödel’s Theorem. Like let’s say we’re looking at
integers and we’re trying to set up axioms to constrain them to just work the
way we think they do. Well, what Gödel showed is that no finite set of axioms
can ever achieve this. With any set of axioms you choose, there won’t just be
the ordinary integers; there’ll also be other wild things.
And the phenomenon of computational irreducibility
implies a much more general version of this. Basically, given any set of laws
or constraints, there’ll always be “unintended consequences”. This isn’t
particularly surprising if one looks at the evolution of human law. But the
point is that there’s theoretically no way around it. It’s ubiquitous in the
computational universe.
Now I think it’s pretty clear that AI is going to get
more and more important in the world—and is going to eventually control much of
the infrastructure of human affairs, a bit like governments do now. And like
with governments, perhaps the thing to do is to create an AI Constitution that
defines what AIs should do.
What should the constitution be like? Well, it’s got to
be based on a model of the world, and inevitably an imperfect one, and then
it’s got to say what to do in lots of different circumstances. And ultimately
what it’s got to do is provide a way of constraining the computations that
happen to be ones that align with our goals. But what should those goals be? I
don’t think there’s any ultimate right answer. In fact, one can enumerate goals
just like one can enumerate programs out in the computational universe. And
there’s no abstract way to choose between them.
But for us there’s a way to choose. Because we have
particular biology, and we have a particular history of our culture and
civilization. It’s taken us a lot of irreducible computation to get here. But
now we’re just at some point in the computational universe that corresponds to
the goals that we have.
Human goals have clearly evolved through the course of
history. And I suspect they’re about to evolve a lot more. I think it’s pretty
inevitable that our consciousness will increasingly merge with technology. And
eventually maybe our whole civilization will end up as something like a box of
a trillion uploaded human souls.
But then the big question is: “what will they choose to
do?” Well, maybe we don’t even have the language yet to describe the answer. If
we look back even to Leibniz’s time, we can see all sorts of modern concepts
that hadn’t formed yet. And when we look inside a modern machine learning or
theorem proving system, it’s humbling to see how many concepts it effectively
forms—that we haven’t yet absorbed in our culture.
Maybe looked at from our current point of view, it’ll
just seem like those disembodied virtual souls are playing videogames for the
rest of eternity. At first maybe they’ll operate in a simulation of our actual
universe. Then maybe they’ll start exploring the computational universe of all
possible universes.
But at some level all they’ll be doing is computation—and
the Principle of Computational Equivalence says it’s computation that’s
fundamentally equivalent to all other computation. It’s a bit of a letdown. Our
proud future ending up being computationally equivalent just too plain physics,
or to little rule 30.
Of course, that’s just an extension of the long story of
science showing us that we’re not fundamentally special. We can’t look for
ultimate meaning in where we’ve reached. We can’t define an ultimate purpose. Or
ultimate ethics. And in a sense we have to embrace the details of our existence
and our history.
There won’t be a simple principle that encapsulates what
we want in our AI Constitution. There’ll be lots of details that reflect the
details of our existence and history. And the first step is just to understand
how to represent those things. Which is what I think we can do with a symbolic
discourse language.
And, yes, conveniently I happen to have just spent 30
years building the framework to create such a thing. And I’m keen to understand
how we can really use it to create an AI Constitution.
So I’d better stop talking about philosophy, and try to
answer some questions.
After the talk there was a
lively Q&A (followed by a panel discussion), included on the video.
Some questions were:
Conclusion
I have inserted my
own brief answer to the following philosophical questions but it would be interesting
to know what others think.
When
will AI reach human-level intelligence?
My own view is although I concede such things
as quantum computers may reach the same speed of computation I don’t believe AI
can ever reach the human brain level of intelligence.
:
Do we live in a deterministic universe?
In big scale physics yes, but concurrent to
that I believe there exists a causality at the smaller end of the scale as is
evident in a certain creative freedom.
·
Is our present reality a simulation?
To some degree yes, but I also think we share
the reality of our existence with its creator in some small way.
·
Does free will exist, and how does
consciousness arise from computation?
Yes. Consciousness arises from factors outside
of the computation because of the ultimate interdependability of all things.
Can
we separate rules and principles in a way that is computable for AI?
No – we need human check points along the
way.
·
How can AI navigate contradictions in human
ethical systems?
It can’t- the best we can do is to have human
check points along the way.
See what you
think
