Here you have two pictures that I took

in the north of Ireland 
and the north of Scotland.

On the left, there is what is called 
a 'fairy ring' in children's stories.

These rings are formed by mushrooms,

yet one would be surprised that 
they organise in almost a perfect circle.

How do they communicate 
this complicated information

to place themselves in the right place?

And, on your right,
we have lava stone hexagons.

How do they form?

They look like highly structured things

that one may have thought
wouldn't occur in nature,

because they would need a designer 
that tells the mushrooms, on one side,

to distribute in circles, 
and the stones to form these hexagons.

So... how can we recognise

that something was artificially designed
from something that was naturally made?

And, my proposal is -

what if we think of this 
as the result of some computation?

And, I will get back to this later.

There are two different approaches 
to the question of - what is life?

One is a top-down approach,

consisting in modifying 
living organisms.

One can think of eliminating functions 
in an organism

to find the minimal requirements 
for life to exist.

For example, this could be done
by finding the smallest set of genes

that can produce a cell capable of
reproducing and transferring information.

These, and many other questions

approached by our 
modifying living systems,

belong to the so-called 
'synthetic biology' field.

The other approach 
is a bottom-up approach

that starts from nonliving things 
and tries to build up life from scratch.

In this approach,

the most fundamental, 
basic properties of life are studied -

such as self replication 
and self-organisation -

and this area is sometimes called 
'artificial higher life'.

Self-replication is a topic that has
interested many computer scientists

since the beginning of the field.

Nils Barricelli and John von Neumann
were among the first

to explore the question
and conduct these kinds of experiments.

John von Neumann, just like 
Richard Feynman - I mentioned before -

was one of these 
extraordinary scientists

that enlightened every field 
they would touch...

John von Neumann was also in
the Manhattan Project.

He was also a physicist who made seminal
contributions to quantum mechanics.

And, most interestingly for us,

he was one of the founders 
of computer science,

and one of the first builders 
of actual electronic computers -

the obvious, like Konrad Zuse 
in Germany.

In fact, most computers today

are designed according to von Neumann's 
first computer blueprint,

and they are [said] today to have 
a 'von Neumann architecture'.

Von Neumann was interested in the idea

of a machine that was capable of 
building an exact copy of itself.

Here is a picture of this idea -
a robotic arm -

that takes raw material from a shelf 
and builds another arm,

of exactly the same kind that in turn 
is capable of building another one,

with no need of any other 
kind of machine in the loop.

And, von Neumann,

together with Stanislaw Ulam -
another Manhattan Project scientist -

helped abstract the idea 
of cell replication

and came up with a concept 
of a cellular automaton.

Cellular automata are a sort of machine -
very similar to a Turing machine -

but instead of updating a cell 
in the tape at the time,

a cellular automaton 
updates many cells at once

and can work on two-dimensional grids
instead of linear tapes.

And, they are an interesting 
type of machine

to study the concept 
of cell replication.

This is an example
of a one-dimensional cellular automaton.

Starting from the first row of cells,

every cell is updated 
according to the rule on the top.

So, if one starts from two white cells 
surrounding a black cell -

as you can see on the top -
the next middle cell will be a black one.

And, following this very simple rule,

one can generate evolutions
like this one.

This is called

the 'Rule 30' cellular automaton 
in Wolfram's enumeration,

and the rule comes simply from the binary 
representation of the rule icon.

You can see that by fixing 
the first row,

the second row can be taken 
as a binary number that -

in decimal for this case -
means simply the number 30.

And, this is the same cellular
automaton [with] more steps.

One can see the type of rich behaviour 
this simple computer program can generate.

This cellular automaton...in particular 
was found by Stephen Wolfram

who, performing an exhaustive experiment,
found all sorts of computer programs

with many amazing properties -
despite their extreme simplicity.

By most standards, for example, 
this Rule 30 automaton

is the smallest computer program 
producing apparent randomness -

[bringing] all this complexity 
that you can see on on your screen.

One can ask if these simple rules 
cannot occur in nature.

And, by looking at seashells 
that develop their shells by layers -

very much like 
a cellular automaton -

one can find
astonishingly similar patterns.

So, von Neumann actually constructed 
one of these cellular automaton,

and this is a two-dimensional 
cellular automaton

that was not only capable of
self-replicating itself,

but was robust enough to carry out 
and replicate mutations.

So, for example,

here is the original cellular automaton 
that is capable of cellular replication.

And, when a mutation is introduced,
it starts reproducing

the cellular automaton -
with a mutation from that time on.

You can see from this little flower 
that was reproduced with code on the tape.

This was, of course, a milestone 
in computer science and artificial life -

a fully artificial system,

capable of reproducing a fundamental 
property of life in a computer simulation.

Some researchers have implemented

von Neumann's self-replication 
concept for fun,

and have made these 3-D 
printing machines

that can print themselves, 
like these ones in this slide -

you can see a parent and a child -
from these researchers in the UK.

And, one of the most popular 
cellular automaton

is Conway's 'Game of Life'.

This is a two-dimensional 
cellular automaton

that has only four very simple rules 
that one can find all over nature,

determining the way organisms coexist.

And the rules are:
if there is any life, or black cell,

with fewer than two black neighbours - 
then the cell dies by isolation.

If a black cell has more 
than three neighbours,

then it dies as if by overcrowding.

If a dead cell has exactly 
three black neighbours,

then it becomes a black or life cell -
achieved by reproduction.

And finally, if there is a black cell 
with two or three black neighbours -

then it lives on to the next generation.

With these four rules,

this cellular automaton 
is capable of incredible complexity,

showing many properties 
that we attribute to living systems -

like movement, persistence and evolution.

You may be seeing on the screen 
a video of the 'Game of Life'.

It turned out that the 'Game of Life'
is also capable of self-replication.

And, even more, 
it was found to be Turing universal.

There is a property I told you about:
the property of being capable of

carrying out any possible computation -
like your own personal computer.

So, in principle, you can run
Microsoft 'Windows' or Mac OS

on this extremely simple computer,
based on rules that mimic rules

in the natural world of living systems.

It will be very inefficient,
but yet you can run any program,

in principle, 
on these kind of systems.

Cellular automata can now help us 
model and understand

how things like fairy rings -

that we saw at the beginning -
are formed.

Mushrooms that start growing 
and reproducing eventually die,

and can only reproduce new ones 
away from the crowded centre

that eventually builds 
these hard circles.

When running these simulations,

they look very much like 
the 'Game of Life' because, eventually,

the main circle spreads out and shifts 
the development of new circles -

self-reproducing the patterns 
from reproducing the mushrooms.

You may remember the picture 
I showed you with the fairy rings.

So, this is the way to explain it -
with cellular automata.

And, von Neumann thought 
that for self-replication,

a system would need to have 
the power of a universal computer.

So, here is a question:

Can life be defined 
by universal computation?

The answer is not obvious.

I personally think

that a strong case can be made 
for connecting life and computation.

But, Langton's loop -

another cellular automaton 
that you are seeing on your screen -

shows that it is possible 
to self-replicate

without Turing universality.

This cellular automaton,
called Langton's loop,

can self-replicate -
but is computationally very simple.

you cannot compute much with it.

Another thing to consider is that other 
clearly nonliving systems self-replicate -

such as crystals.

So, self-replication is likely to be 
a necessary condition for life -

but not a sufficient one.

So, what are the requirements for life,
if not only self-replication?

Is it, having a metabolism that transforms
energy from the environment?

Or, anything else?

There has been a few interesting attempts 
to define life in the most abstract terms.

For example, this author, Joyce,

would consider a system a life 
if it contains more bits

than the number that were required 
to initiate its operation.

This definition is interesting 
but it has some difficulties,

because one needs precise definitions 
of information

and adding information 
to make sense of this.

Hopfield also thought that biological
systems perform some kind of computation,

and that computation makes biology 
different from physics.

And more recently -
something I find interesting -

Leroy Cronin has proposed that life is
anything that can undergo evolution -

in the form of 
survival of the fittest,

suggesting that matter 
that can evolve is alive -

perhaps crystals and viruses included -
against most biologists' own intuition.

And, because I want to connect 
the question of life

to the question of computation, 
I have to ask whether living

and nonliving things can actually compute,
or whether they compute anything at all.

Here too, there has been 
interesting approaches -

Stephen Wolfram's, for example,

suggests that there is a simple 
and computable rule for the universe.

Seth Lloyd, on the other hand,
has also suggested

that the universe is a computer -
but along the lines of Feynman,

Lloyd thinks that if the universe 
is a computer,

it has to be a quantum computer.

And, there has been some criticism 
of these views that have arisen,

mainly against a related field
called 'functionalism',

that takes the human mind 
for some sort of computer.

One of the main criticisms is that there
seems to be no clear-cut distinction

of the meaning of computation,
if we consider that things compute -

leading to absurd things 
like David Chalmers' mocking statement

that a rock would implement 
every finite state automaton.

That is, that rocks are like computers -

something that goes against 
anybody's intuition.

My purpose here is to associate 
a measure of computation

that assigns high computational
capabilities to computers,

like humans 
and electronic computers -

but low computational capabilities 
to things, such as rocks or the weather.

[ end of audio ]