FWD fungal intelligence

HSLotsof at aol.com HSLotsof at aol.com
Wed Jan 12 16:23:02 EST 2005


Paul Stamets, one of the best known mushroom enthousiasts in the world, 

is serious when he talks about the intelligence of mycelial networks. In 

his view the fungal world consists of zillions of mycelial mats which 

are in instant contact with eachother and exchange information much like 

the internet works. In this way each mycelial cell of every network 

'knows' where the it is needed to convert dead biomass (or petrochemical 

pollution!) into compost.

The idea about fungal intelligence sounds pretty off the wall at first, 

also to me, but I have to say that the following RealAudio program of 

ABC Australia explains a lot. There is a mechanism which can explain it: 

the  small world phenomenon. No matter how large and interconnected a 

network is, necessary information never needs to be more than a few 

nodes/fungal cells away. Mycelial mats literally can 'know' about all 

the places on this planet where they can convert waste into compost!

The program does not mention mycelia even once but listen to it. Or read 

the transcript. It explains a lot!




The New Science of Networks

Saturday 8 January  2005


Q: What do Hollywood actor Kevin Bacon, a North American firefly, Al 

Qaeda and the World Wide Web all have in common?

A: Each of them organise themselves in a network.

Annamaria Talas wrote and produced this Science Show special on the new 

science of networks; the connectedness of nearly everything, which began 

with Duncan Watts, an Australian PhD student from Cornell University, 

and is set to change our understanding of the world.

Program Transcript

Robyn Williams: What do Hollywood actor Kevin Bacon, a North American 

firefly, Al Qaeda and the World Wide Web have in common? Not much you 

might think but in fact they’ve all played a big role in helping us make 

one of the first really big new discoveries in science. Each of them 

organise themselves in a network. There’s a mechanism by which actors, 

insects, terrorists and web pages link together and make connections. We 

used to think these links were more or less random but in the past few 

years scientists studying networks have discovered an astonishing thing; 

nature it seems has a hidden language and for the first time we’re able 

to read it.

It’s a discovery that some are saying may prove to be as important as 

Newton’s observations of gravity and Darwin’s theory of evolution. The 

new science of networks is set to change our understanding of the world. 

It all began with bugs and is so new there isn’t even a scientific word 

for it – yet. This Science Show special is written and produced by 

Annamaria Talas and presented by Simon Nasht.

President Bill Clinton: Today we are learning the language in which God 

created life. We’re gaining ever more awe for the complexity, the 

beauty, the wonder of God’s most divine and sacred gift.

Simon Nasht: Former US president, Bill Clinton, announcing the decoding 

of the human genome, at a White House ceremony in 1999. But nature is 

more than bits of pieces. Despite seeing the text of 3 billion chemical 

letters of our genome - we still can’t read the book of life .

T.J Higgins: I think certainly at the beginning it was overestimated as 

to what we would learn from just knowing what the coded instructions 

were for every protein in a human or in a plant.

Simon Nasht: Professor T.J Higgins is deputy head of CSIRO Plant 

Industry in Canberra. For centuries we’ve tried to understand the 

Universe by pulling it apart – we’ve studied atoms to comprehend 

creation, molecules to reveal life, genes to decipher human behaviour. 

But nature organises itself in immensely complex ways. And in these huge 

interconnected systems, where every player affects every other, the 

linear logic of cause and effect falls apart. However there’s a 

revolution in thinking taking place. Scientists from diverse disciplines 

have begun to see how the world really connects. And the view is staggering.

Eugene Stanley: The big thing is that there is one single law that 

explains a wide variety of networks.

Albert-Laszlo Barabasi: When we look only in the level of the components 

how they interact together, that is when we look at the nodes and links 

and the networks they create they are more similar than different.

Richard Sole: These particular webs might explain some something that 

we’ve been asking for years and years.

Eugene Stanley: In science usually when someone sees a simplifying 

feature that says very, very profound consequences.

Simon Nasht: Today in the Science Show we’re joining a new generation of 

scientists to witness what’s been called the first big idea of the 21st 

Century. The new science of networks. And as with most discoveries, this 

one has its own amazing story. It started with deep awe at the hidden 

patterns in nature.

The swings of Foucault’s pendulum, an interpretation by Larry Sitsky.

Steve Strogatz: A very dramatic piece of music.

Simon Nasht: Steve Strogatz – Professor of Applied Mathematics at 

Cornell University is an expert in complex systems. Steve, this music in 

a way takes us back to the beginning of your career. What is it about 

pendulums that fascinated you?

Steve Strogatz: I had a very visceral sort of reaction to my first 

experiment in high school. I was just 13 years old. We all were given a 

stopwatch and this pendulum and as we tried letting it swing 10 times 

back and forth and then click record how long it takes and than we make 

it longer, 10 times back and forth, click, and so on doing it over and 

over again. As I started to make maybe 4 or 5 dots in the page, I’ve 

noticed something spooky which was that these dots were falling on a 

very particular curve that I recognised because I’ve seen it in my 

algebra class it was what we call a parabola. And I can remember this 

very chilling feeling, with, the proverbial hairs on the back of my neck 

standing up thinking to myself, how could that be? How could this 

pendulum know about algebra? In that moment, I suddenly understood what 

people mean by the phrase, ‘Law of Nature’.

There is a hidden world that you can’t see unless you know mathematics. 

It’s a secret world that suddenly becomes open to you and I felt likeI 

was being told this marvellous secret and suddenly I was let into the 


Simon Nasht: Thirty years later Steve Strogatz, one of the world’s most 

distinguished mathematicians is still fascinated by the patterns of 

nature. Can you give us an example?

Steve Strogatz: I think one of the most visually spectacular is a 

phenomenon that occurs in Southeast Asia. If you are say in a canoe 

going down one of the tidal rivers from Bangkok out to the sea. On 

pretty nearly any night of the year you’ll see an unbelievable display 

of thousands upon thousands of fireflies in the mangrove trees. And what 

is so odd about this is that they will all be flashing but not just that 

they’re flashing in perfect synchrony – in perfect time together.

Simon Nasht: A decade ago, Professor Jonathan Copeland - a 

neuroethologist and firefly researcher from Statesboro, Georgia, made 

his own pilgrimage to South-East Asia.

Jonathan Copeland: What we were looking was called the silent counter. 

We had come up the river in a canoe and off in the distance I could see 

something flashing vaguely and we got closer and closer and then I 

realized that it was the firefly tree.

Simon Nasht: For someone in your line of work it must have been quite a 


Jonathan Copeland: It was breathtaking. It’s like a Christmas tree with 

blinkered lights on it. The lights go on off, on off, on off, on off, 

rhythmically and regularly through the night.

Simon Nasht: Professor Copeland’s adventures in Southeast Asia were 

picked up by the press. And for Lynn Faust from Knoxville Tennessee, it 

struck a cord.

Lynn Faust: The cover of the magazine had this firefly tree in Malaysia 

and I picked it up thinking ‘Gosh! I wonder if there are talking about 

the Elkmont fireflies in here’. And so reading the article and reading 

the article realized that there was a statement made that there was only 

this one synchronized species in the world and it was in Malaysia. And I 

thought no, no, we have been watching them for years up in Elkmont!

Jonathan Copeland: I thought it was another crank call. Not so much 

because of what was being described but because the prevailing dogma at 

that time was that North American fireflies just did not synchronize.

Lynn Faust: It’s a unison blinking, it is pounding you almost feel like 

you should hear drum beats it is so rhythmic, pulsating. And on the 

hillside it is more like a waterfall.

Simon Nasht: Professor Copeland was intrigued and approached Lynn with 

an unusual request.

Jonathan Copeland: What I asked her to do was to draw five lines like a 

musical staff and have every line represent a different firefly.

Lynn Faust: So I said well sure, I will try. And it’s funny when you 

watch something as a thing of beauty that is very different from 

watching it scientifically. They blinked 6 times in rapid succession and 

then they’re dark for six seconds. There were a lot of individuals – and 

that you do get a few early birds and you get a few late ones, you know 

that blink a little past everybody else – but in general it’s a mass 

synchrony. When you see it you can’t believe that you are looking in 

silence. So I guess it does bring something musical out in you because 

it’s so rhythmic.

Simon Nasht: We had composer Llaszlo Kiss turn Lynn’s original 

observations into a symphony for fireflies. But the ability to 

synchronize isn’t exclusive to bugs. It seems that at the heart of the 

Universe there is a steady, insistent beat.

Steve Strogatz: Synchrony is one of the most pervasive phenomena in 

nature. That in the sense that it occurs in every scale from the 

smallest scale of subatomic particles to the grandest scale of the 

cosmos, the solar system.

Simon Nasht: What were the big questions that intrigued you, what were 

the outstanding major, philosophical questions really about synchrony?

Steve Strogatz: You’re right to put your finger on the word 

philosophical because some of them do touch on very deep philosophical 

issues. I’m thinking in particular of the question of where is the 

source of all the order in the Universe? We see order all around us. We 

see ecosystems with hundreds of thousands of species interacting and 

it’s all stable. We see the structures of our own body, it’s incredible 

with all of those different organs and trillions of cells in our brain 

capable of consciousness and love and hate and wanting to write music 

like the song you played at the beginning. And so these questions of how 

simple individuals like brain cells, or fireflies or the atoms in a 

laser can conspire to create marvellous organised structures and do it 

on their own. That is a very deep question for a scientist because so 

long we’ve been taught that the universe has this opposite tendency that 

things left to their own will degenerate, will tend towards ever greater 

entropy – meaning greater disorder or greater randomness. And yet we see 

lots of examples of things that do just the opposite that seem to drive 

themselves to ever greater patterns.

Simon Nasht: So how does chaos synchronize? And can its patterns be 

revealed by mathematics? Steve Strogatz wanted to find out.

Steve Strogatz: So we were looking for a case that would be tractable. 

And it happens that in Ithaca, where I live there is a particular 

species of cricket, called the snowy tree cricket which just happens to 

chorus. That is hundreds of thousands of the male crickets at night will 

be out chirping rhythmically in unison in an attempt to attract females.

Simon Nasht: All of this sounded pretty interesting to Strogatz’s PhD 

student - at the time a young Australian– Duncan Watts.

Duncan Watts: There is a lot of biological interest in this and there is 

also a lot of mathematics involved. And we were doing some experiments 

with some crickets that we had caught on the campus of Cornell.

Simon Nasht: So set the scene for me a little bit – a couple of grown 

men climbing around trees in the campus. What did they think of you?

Duncan Watts: Well, one grown man which was me…so there was a little 

sort of physical adventure involved and then we took them inside and 

when we caught a few into a sound-proof chamber in the laboratory and 

subjected them to different kinds of simulated chirps.

Steve Strogatz: And the hope was that by studying the way that 

individual crickets respond to the chirps of others, that we could 

figure out what it was about their interaction that led to them all 


Duncan Watts: We were wondering how when you put you know many, many 

crickets possibly hundreds of crickets together on a tree, each of which 

has its own particular rhythm that it follows in isolation, when you put 

them together they somehow interact with each other and all end up 

chirping perfectly together.

Steve Strogatz: The real problem was that it wasn’t understood 

mathematically why all of these interactions would inevitably lead to 

synchrony. Why couldn’t they for instance just result in some kind of 

cacophony? And as he was out in the field, Duncan came to realise that 

the assumptions we were making in our theories were completely 

ridiculous. We had been assuming that individual crickets could be 

thought of as arranged sort of like the squares on the checker board. A 

very regular arrangement, because that’s the kind of thing that 

physicists have worked out good theories for. And yet clearly that 

wasn’t what was happening. They were all over the place in the trees and 

it got Duncan thinking.

Duncan Watts: They couldn’t all be listening to each other equally; 

probably each one was only listening to a few others.

Steve Strogatz: Do I even know which cricket can hear which other and 

does it really matter? How does the pattern of their connection affect 

their ability to synchronize?

Duncan Watts: We started to imagine a tree full of crickets as a 3 

dimensional network where every individual in the tree was somehow 

influencing and responding to some of the others. In some ways it’s like 

a network of friends. You know other people and you influence them and 

they influence you. But you don’t know everybody in the world and not 

everybody influences you equally.

Steve Strogatz: And so from that he got an idea in his head which was 

suddenly triggered into fruition by something his father said.

Duncan Watts: He just mentioned this story which at the time I took to 

be an urban myth which was what we now call, ‘Six Degrees of Separation’ 

or what sociologists call, ‘The Small World Problem’.

Steve Strogatz: That term by the way comes from the experience we’ve all 

had where you’re travelling a foreign country and suddenly you’re 

standing on the steps of a cathedral in Florence and you find that you 

meet someone you went to elementary school with or someone who knows 

your cousin or whatever and then both people say, ‘Ah, it’s a small world!’

Duncan Watts: And my Dad mentioned this to me and he said well did you 

know that anybody can connect themselves to the President of the US in 

just six handshakes?

Simon Nasht: Six Degrees of Separation became something of an urban myth 

following John Guare’s 1990 play.

Excerpt from film, Six Degrees of Separation: I read somewhere that 

everybody on this planet is separated by only six other people. Six 

degrees of separation between us and everybody else on this planet, The 

president of the United States, a gondolier in Venice. It’s not just the 

big names. It’s anyone. A native in the rainforest, a Tierra del Fuegan, 

an Eskimo. I am bound - you are bound to everyone on this planet by a 

trail of six people. It’s a profound thought.

Simon Nasht: That was Stockard Channing in the film version of Six 

Degrees of Separation. However, the original idea came from a famous 

sociology experiment in the 1960s - designed by Harvard psychologist, 

Stanley Milgram.

Duncan Watts: He was a great experimenter. So he designed this method 

that even today is called the small world method, where he picked a 

single person in Boston. So Milgram nominated him as a target of this 

experiment and then he chose about 300 other people whom he called 

senders. And about 100 of those were chosen randomly from the population 

of Boston and the other 200 came from Omaha Nebraska. Milgram 

deliberately picked Omaha not just because it was geographically distant 

from Boston but because it was also socially distant.

Simon Nasht: Milgram wanted to find out the ‘distance’ between any two 

people in America. 300 randomly chosen men and women had to find someone 

they didn’t know and all they had to go was that he was from Boston.

Actor reading Milgram’s words: OK, OK – now listen up. This is what I 

want you to do. If you actually know the target person mail the package 

directly to them. You only do this if you know the person or if you’ve 

previously met the target person and know them on a first name basis. If 

you don’t know the target person don’t try to contact them by asking 

around. Don’t look them up. Instead, mail the package to someone you 

know who is more likely than you to know the target person. You can send 

the package to a friend, to a relative or an acquaintance, it just has 

to be someone you know on a first name basis. And then they’ll do the 

same thing.

Duncan Watts: What he set up effectively was a series of chain letters 

that wended their ways through different professions and different towns 

and different demographics and about 20% of them or roughly 60 made it 

to the target. And of those 60 the average length, the number of steps 

in each of those chains was about six. So I thought that was an 

interesting thought. I had these two problems in my mind – one about 

crickets synchronizing and one about networks of social relationships 

and whether or not those networks had this unusual or seemingly 

surprising property that everyone can could connect to everyone else in 

just a few steps. And I started to wonder if maybe they had something to 

say about each other.

Simon Nasht: Assuming that network structure and synchronicity must be 

well-covered subjects, Watts went to look it up.

Duncan Watts: You know when you are at graduate student you assume that 

every question that comes into your head has been already answered. But 

once I have started to look I realized that very little had been done 

and what had been done didn’t really fit with this picture that I was 

starting to think about in terms of my cricket problem.

Simon Nasht: Not only was the relationship between networks and 

synchronization completely unexplored, no one really seemed to have 

thought about big complex networks at all. Except for one – an eccentric 

Hungarian mathematician, Paul Erdös.

Steve Strogatz: So he really was a pioneer in our understanding of 

enormous large complex networks.

Simon Nasht: Erdös was the first to ask questions about networks. He 

wanted to know how many links it took between isolated groups to form a 

network in which they could all talk to each other. These questions were 

important because the threshold between isolation and connectedness is 

crucial for understanding the flow of information, the spread of 

disease, the movement of money; the workings of our modern world. Erdös 

was a genius with eccentricities to match.

Steve Strogatz: He essentially lived as a homeless person and travelled 

around from one mathematician to another. He would knock on your door 

and say, ‘My brain is open’. Which meant he’s ready to work with you on 

some unsolved math problem. And you were then to take care of him 

because he was so incompetent in all aspects of daily life. He was like 

a baby except he was a mathematical genius.

George Csicsery: As I got to know Paul Erdös I developed a sense that he 

was actually quite clever and he had designed a perfect life for himself.

Simon Nasht: George Csicsery is a documentary filmmaker who made a 

portrait of Erdös.

George Csicsery: Not knowing how to boil an egg guaranteed that someone 

else would do it for you. Not knowing how to go shopping guaranteed that 

someone else would go shopping for you. So this gave him an immense 

amount of freedom to pursue the thing he really cared about, which was 


Simon Nasht: Erdös was a prolific mathematician. He published 1500 

papers in his lifetime with several hundred colleagues.

George Csicsery: He would find new approaches to the problems that other 

people were working on. And this is how he developed so many collaborations.

Paul Erdös: Somebody asked me a problem and sometimes I see immediately 

what do you have to do. And then later one has to carry out the details. 

And very often it works immediately that you know that you are on the 

right track. Of course sometimes you are deceived.

Simon Nasht: One of Erdös’s theories was developed with his countryman - 

Albert Renyi - the theory of random networks.

Albert-László Barabási: Erdös had a particular model of how networks 

would look like whether it is a social network or any other network. 

That is let’s assume that the nodes are connected randomly.

Simon Nasht: Albert-László Barabási Professor of Physics at University 

of Notre Dame, yet another Hungarian and one of the leading thinkers in 

the science of networks. Erdös hypothesised that in networks information 

can spread extremely quickly.

Albert-László Barabási: Let me give you an example of a cocktail party. 

If you would organize a cocktail party let’s say with a hundred people 

which are carefully selected that nobody knows anybody else actually so 

when they come to the room there are no acquaintances over there and you 

would find that people would start pairing up – you know forming groups 

of 2 or 3 or 4 and start chatting and getting introduced and so on. And 

among the many many wines there is one particular bottle that is like a 

prized Hungarian Tokai. And you would just tell it just to one person. 

The question is how long would it take until everybody in the party 

would know that. Now if you do a little bit of math and you assume that 

every 2 people would talk for kind of 10 minutes before they get bored 

with each other and move on to somebody else, you’d figure out that for 

about 100 people it would take about 16 hours. It takes about 20-30 minutes.

Imagine that you would start connecting with invisible lines the people 

who have met and they talked to each other, who could actually pass on 

information to each other. And what you find is that first you have just 

lines between pairs and trios of people. But then as people start 

mixing, then like a giant component emerges when everybody suddenly 

becomes in a few minutes part of one big network. And Erdös told us that 

for that to happen it is sufficient that everybody knows at least one 

other person. When you reach this threshold of one node per link then 

suddenly out of nothing this giant cluster emerges which is very similar 

to a phase transition.

Duncan Watts: Which is that you go from a world in which everything is 

disconnected to a world in which very, very suddenly everything gets 


Albert-László Barabási: And a good example is to think about how water 


Duncan Watts: It’s not the case that right at the freezing point you 

just get a little bit of frozen water and then as you get colder you get 

more and more. It’s either all frozen or it’s not frozen.

Albert-László Barabási: So you go from this stage of disorder of a 

chaotic motion to the phase of order.

Duncan Watts: What Erdös and Renyi managed to show is that the same kind 

of phase transition occurs in networks.

Simon Nasht: The way in which water molecules form ice can be thought of 

as crickets chirp, or fireflies flash in unison or how randomly 

introduced people in a party learn about the precious wine. They all 

reach a tipping point where suddenly order emerges from chaos. It was 

Erdös who identified this phase transition as it’s called in networks. 

But for all his brilliance he wasn’t able to move beyond the 

theoretical. Back in the 50s there was no way to test his ideas. Real 

networks aren’t as readily connected as Erdös imagined. Life is not a 

Hungarian cocktail party where connectivity is just a handshake away.

Duncan Watts: Now if that were the case in the real world, in the social 

world, then you would be just as likely to know someone in rural China 

as somebody down the street.

Steve Strogatz: If I have two friends, the chances of them knowing each 

other are much greater than if I just asked two people at random on the 

surface of the Earth whether they know each other. Two of my friends 

have much greater chance because I may have introduced them. They are 

part of my circle. This same property we find is true in many naturally 

occurring networks as well that there it tends to be a kind of 

clumpiness to their structure, which you don’t see, in random networks.

Simon Nasht: And this clumpiness, this clustering makes the world in a 

way, larger. It slows down connectivity, the flow of information, as you 

are more likely to have more links within your own circle. Yet Milgram’s 

experiment with the packages showed us that somehow we can still manage 

to reach anyone in just a few steps. So how can the world be both 

clustered AND connected? This is the paradox at the heart of the small 

world problem.

Duncan Watts: It became clear to me and also to Steve, that we had 

stumbled on something that everybody in science is more or less looking 

for, which is a new problem.

Steve Strogatz: He had a particular question that he posed to me which 

was what could we say how a network like this would synchronize? Would 

it synchronize better than the square grid we had been thinking about or 

would it synchronize better than one of Erdös’s random networks? And 

then Duncan raised an even larger question – we should be looking at all 

kind of networks, everything out there is a network today. Is the World 

Wide Web like this? Does it have this property that every web page is 

just a few clicks away from every other? What about the network of 

neurons in your brain? I’ve heard neurologists saying every neuron is 

just a few synapses from every other. Is that really true?

Duncan Watts: We started to believe that the way the system behaves – 

can a population synchronize or variously can an organization solve a 

complicated problem, can an epidemic of disease break out and spread 

around the world, can a particular sort of fad become popular, or not 

become popular? Lots of these behavioural questions have to do with how 

the system is connected and therefore have to do with the networks.

Steve Strogatz: We started to ask ourselves what would it be like for a 

network to have this property of being a small world of satisfying 

something like six degrees of separation.

Duncan Watts: And what we were looking for was a world - a kind of world 

- in which you had the high clustering, the fact that most of your 

friends know each other and also the short path links. The fact, that 

you can get from anyone to anyone else in just a few steps.

Simon Nasht: But instead of trying to ‘measure’ the world, - as Milgram 

did with his packages – they’ve decided to move in between the two 

theoretical extremes; from the completely clustered to the totally 

random world, - in the hope to tuning in to the world we live in.

Steve Strogatz: And we tried to imagine just by drawing pictures on 

paper with dots connected by lines what it would take. And one picture 

stood out. We drew lots of complicated things but as we paired it down 

we started to realize what was very important were what we came to call 

shortcuts. Just a few shortcuts and the world was contracted as small as 

it could be. And so from this we came to think that since the conditions 

on a small world were so mild, that you only needed a shortcuts in any 

network. We started to think that in fact this property of being a small 

world should be ubiquitous and that if we could just get our hands on 

real data, for giant networks we’d see the same pair of properties.

Duncan Watts: When we have looked at this whole universe of worlds we 

found that almost everything is like this.

Simon Nasht: How did you go about testing this?

Steve Strogatz: We came up with what seems like a whimsical example – 

the Hollywood network of actors who have been in movies together.

Simon Nasht: In 1997 computer scientists Brett Tjaden and Glenn Wasson 

at University of Virginia launched an amusing website – the Oracle of 

Kevin Bacon. This is a game where every actor can be connected to Bacon 

by the movies in which they’ve played together. If, for instance, the 

actor played with Bacon in the same film, he’s given a Bacon number one. 

If he’s never been in a film with him, but has been in a film with 

someone else who has been in a film with Kevin Bacon, he’s given a Bacon 

number of two.

Steve Strogatz: So for instance Charlie Chaplin who acted in silent 

films in the 20s and 30s you might think, well, how could I connect 

Charlie Chaplin to Kevin Bacon. But you can. Charlie Chaplin was in the 

movie Countess from Hong Kong with Marlon Brando. Marlon Brando was in 

Apocalypse Now with Lawrence Fishburn. and Lawrence Fishburn was in 

Quicksilver with Kevin Bacon. That’s three movies separating Chaplin 

from Bacon and so for that reason we would say that Charlie Chaplin has 

a Bacon number of three.

Simon Nasht: The game is based on half a million actors listed in the 

Internet movie database – a micro-cosmos of the social world.

Duncan Watts: And we were able to get hold of that database and look for 

the features that we had predicted, this high clustering and short pathlink.

Simon Nasht: As it turned out not only Kevin Bacon but every actor could 

be connected to every other in an average of less than 4 steps. It was 

small world. To test their model further Strogatz and Watts went looking 

for networks that had nothing to do with the social world.

Duncan Watts: There was nothing in this model that made it seem like it 

was about people and friendships. It was just about nodes and links.

Steve Strogatz: There was data available for this network of 5000 power 

plants and all their transmission lines.

Duncan Watts: So in one case you have movie actors and they are linked 

by co-starring in movies, in another case you have power stations linked 

by transmission cables.

Simon Nasht: And much to their delight they’d found the same phenomenon 

as before. And because in small worlds the flow of information is very 

efficient it was natural to wonder whether the nervous system also 

exploits this trick.

Steve Strogatz: There is only one nervous system that has been fully 

mapped out and it’s the nervous system of a very simple creature, a 

worm, called C. elegans which has just about 900 hundred cells in it’s 

whole body, of which are about 300 devoted to the nervous system.

Duncan Watts: So I emailed a friend of Steve’s at Columbia University 

actually who was an expert on C.elegans and he said ‘Oh, yes! We have 

done that.’ And he gave me a reference. Oddly enough it wasn’t just a 

description of the network, they had actually encoded it into a pair of 

floppy disks. I went to the librarian and she said, ‘Ah no don’t have 

them, sorry’. So I was very crestfallen because this was our last great 

hope for a network to study and we didn’t know what to do and a couple 

of days later the librarian actually called me back and said they’d 

found them in a box somewhere in the basement.

Simon Nasht: And sure enough, when Watts and Strogatz looked at the 

neural map of C.elegans the results didn’t disappoint. The brain of that 

worm was a small world too.

Steve Strogatz: All of these networks, all turn out to be small worlds. 

It’s not just a curiosity or a quirk about how are they connected, there 

is real meaning to it. Like in the case of the nervous systems the fact 

that everything is just a few synapses away from everything else helps 

the network communicate and sends signals rapidly. It may make even 

higher functions possible at least in the case of the human brain like 

perception or attention or consciousness. In the case of the power grid 

the connectivity helps the rapid transmission of power back and forth. 

And of course sometimes this sort of connectivity is undesirable like in 

the case of computer viruses surging across the internet.

Simon Nasht: In 1998 Strogatz and Watts published their landmark 

findings in Nature magazine. Their discovery was the beginning of the 

new science of networks.

Steve Strogatz: It seemed like it could be revolutionary for all of 

science because networks occur in every field from economics to physics. 

So the undertaking of looking into the structure of these gigantic 

networks was extremely exciting.

Duncan Watts: It was kind of like hitting the jackpot. It was my very 

first publication ever and as my father explained to me it was all 

downhill from there.

Simon Nasht: Just 10 month later, Albert-Laszlo Barabasi contacted Watts.

Duncan Watts: And he was looking for some of the data sets that we had 

been using, and several months later actually he published a very nice 

paper in Science.

Simon Nasht: Barabasi and his team were trying to probe a truly gigantic 

network - the World Wide Web.

Albert-Laszlo Barabasi: We wanted to know who is connected to whom and 

for that reason we built up this robot that started from a web page and 

went to every single web page it could go from there and then went from 

those web pages to where you could go and step by step built up a map of 

the World Wide Web.

Simon Nasht: The web is a jungle where anyone is free to put up a page 

and add a link to any other they choose. In this democratic mess, there 

was no reason to expect any bias; that some pages would be significantly 

more connected than others.

Albert-Laszlo Barabasi: Once we had the map we could start looking how 

democratic it is. And the big surprise was that it was by no means 

democratic. What we have found was that instead of most pages with 

roughly the same number of links, we found many, many pages that had 

only one or two links. There were however a few web pages that had a 

very large number of links, like Yahoo and Google and Amazon and a 

couple of other pages were like these hubs, these highly connected nodes.

Simon Nasht: Barabasi had found structure where he didn’t expect it. But 

did this discovery of a few highly connected hubs apply just to the web, 

or was it a feature of other networks too? Barabasi needed another 

example to test, so he went back to the Hollywood database. Watts and 

Strogatz had established that actors lived in a small world, closely 

connected through the movies in which they’ve worked. But was there and 

underlying structure to the network? Are there hubs in Hollywood?

Albert-Laszlo Barabasi: Sure enough the same picture emerged. That is 

that you had many actors that had played with only few actors together 

during their career so they had only a few links to other actors but 

then you had a few that had thousands of links to other actors.’

Simon Nasht: When they studied the most connected actors, Barabasi’s 

team discovered that it was a mixture of the most prolific and those who 

had worked in different genres who were at the top of the list. Not the 

Tom Hanks and Humphrey Bogarts, but the character actors like Rod 

Steiger, Donald Pleasance and Christopher Lee. And in today’s Hollywood, 

the actor most connected to everyone else, is The West Wing’s President, 

Martin Sheen.

Albert-Laszlo Barabasi: So that was the second hint that this is perhaps 

not a peculiar property of the world wide web but hubs emerge in other 

networks as well. And sure enough then we started looking systematically 

in other networks and other people have started looking at other 

networks as well and more networks were looked at more and more a 

general kind of picture has emerged that networks are dominated by hubs. 

They seem to be an inherent property of most large networks in nature 

whether you think about the world wide web, the cell, if you think about 

the cell as a network, whether you think about social networks or the 

Internet or you name it.

Simon Nasht: But why do all these different networks end up looking so 

similar? How does Nature spin its web?

Albert-Laszlo Barabasi: Yes, that was actually a pretty big question. 

And really if you think about how networks had become the way they are, 

you had to realise that networks always started out with a few nodes and 

they grow out from that. So you don’t have six billion nodes that you 

have to somehow connect together, they are not static objects, they are 

growing, they are expanding through the addition of new modes and links 

into the system.

So that’s one important part. The other part, when new node decides 

where to link, it doesn’t do so randomly. But it prefers to connect to 

the nodes that are highly connected in the first place. If you decide 

where you connect on the World Wide Web, you connect to the pages that 

you know. And inevitably the pages that you are familiar with are those 

pages that have a very large number of links in the first place, because 

that’s how you got to know them. If a page is very connected, more 

connected than anybody else, the new nodes will tend to connect to it, 

so therefore it will go faster than the less connected pages.

So what kicks in is what we call a ‘Rich Gets Richer’ phenomenon. Where 

a rich node will grow faster than a poorer node and will eventually 

become a hub. So this architecture which we see is pretty much 

unavoidable for these different types of networks. They don’t have much 

of a choice. They are bound to follow this architecture because the way 

these networks are formed is governed by very simple common laws.

Simon Nasht: Barabasi’s discovery of this simple organizing law inspired 

American composer Mike Edgerton to write this sonata - performed 

especially for The Science Show in Berlin.

It’s not an easy piece to play. Was the complexity a function of trying 

to follow the laws or did simple laws just reveal a complex piece of music?

Mike Edgerton: The generating structures were incredibly simple and so I 

thought that was pretty interesting that we don’t need to have really 

complicated mathematics to put together complicated music. I found that 

this is a really nice opportunity to meld the two worlds together.

Simon Nasht: How did you apply the theories or the laws of scale free 


Mike Edgerton: Well it kind of worked in terms of a large general 

metaphor. But the other way was more literal and this had to do with how 

the structure and the actual pictures and rhythms were generated. What I 

had done was I had identified a series of base values; rhythmic or 

temporal values, which I viewed as hubs and then over those I had an 

irregular number of innerations that were applied within each value and 

then it would cycle through at different rates.

Simon Nasht: Slowly, the hidden structure of Nature is revealing itself. 

And the more we learn about how networks are organised, the more we see 

their strengths and weaknesses, with profound implications for all of us.

Albert-Laszlo Barabasi: These hub dominated networks are very robust 

against random failures that is you can knock out 80% of the nodes and 

the 20% remaining nodes will be still be able to talk to each other. 

However, they are very fragile against attacks. If you know how the 

network looks like, you can easily break them into pieces. And this 

finding has many, many consequences.

Mark Newman: So one important application is if we can vaccinate people 

in the network or in some other way prevent them from catching the 

disease, then that removes them from the network and if we can remove 

enough people from the network in that way the point where the network 

itself collapses then the disease cannot spread any more.

Richard Sole: The way ecosystems might vanish in the future is going to 

depend on how much we understand about the web structure. In some, 

actually some naturalists and some field ecologists are strongly 

preventing us of thinking of ecosystems like independent species and a 

properly conserved ecosystem means conserve the web of interactions.

Alessandro Vespigniani: These systems are driven by necessity in the 

sense that the system is evolving and you try to optimise itself for 

some task. An example is the internet. The internet is a self organising 

system and this is trying to optimise itself for data transmission and 

for reliability.

Albert-Laszlo Barabasi: But then there is another aspect of network 

robustness and vulnerability and that has to do with what we call a 

cascading failures and a good example of that was year’s big Eastern 

United States power grid failure. Failure of a generator has created 

disturbances in the network that resulted in the shut down of a number 

of generators and within a 25 second time frame the whole Eastern United 

States was without electricity. And it’s a wonderful example that while 

networks offer lots of benefits by allowing to spread not only 

information but also resources like electricity very widely among a very 

large number of people, they also carry these vulnerabilities that a 

local disturbance, a local problem can suddenly become, through the 

network a global problem.

Duncan Watts: The SARS virus provided something of a global scare 

because it was spreading from individual to individual from a very 

remote location in south eastern China to Hong Kong and to Taiwan and to 

Vietnam and then finally on to Canada. And for a while there nobody knew 

where it was going to stop. And so in that kind of environment for that 

kind of problem, the fact that we can all be connected to each other 

through some short chain of intermediaries is actually extremely 

pertinent. The kind of mathematics that we see in these sorts of 

networks that we study is very similar to the spread of that particular 


Simon Nasht: Another network of course that’s in people’s minds at the 

moment are terrorist networks.

Albert-Laszlo Barabasi: The way we think and I think most people think 

about terrorist networks is no different to the way we think about the 

World Wide Web. The existence of a network really implies that something 

is flowing along the links. And in the case of the terrorist networks, 

supplies, information and money which is really the one which is flowing 

in the network. And in the moment you actually cut these supplies, then 

you have the possibility of starting a cascading failure in the system 

that could successfully break the whole network down.

Simon Nasht: On a personal level Laszlo, how does it feel to have been 

privy to such a remarkable discovery?

Albert-Laszlo Barabasi: Well, it perhaps gives you hope that there is 

more out there. There are other organizing principles that we still have 

to see and so it motivates me to think harder and to try to see what 

else could we learn about nature, about society, about the world around 

us by looking at it as a network.

Simon Nasht: The science of networks is just beginning, and there’s 

surely much more to be discovered. But already it’s forcing us to look 

at the world differently.

Steve Strogatz: We’ve made tremendous progress in science for 300 years, 

since the days of Isaac Newton and the scientific revolution by chopping 

problems up into smaller and smaller bits and analysing the tiniest 

parts. From whole organisms we look at cells, and then from cells we 

look at genes. And by studying genes and then down to DNA we’ve made 

wonderful progress but the time has come to move back up. I mean how we 

understand the behaviour of a whole economy? How do we understand the 

resilience and stability of ecosystems? Or global warming? These are 

problems with a similar character in that you can’t understand them by 

looking at the little bits. And this is a daunting challenge – going up 

turns out to be much harder that going down. Synthesis and holism is 

much more scientifically subtle than analysis and reductionism.

Duncan Watts: The problem is that everything we experience is local in 

the sense that it’s right around us. But the small world phenomenon is a 

global phenomenon and we really don’t have good intuitions about global 

phenomena and we need a new paradigm for understanding how it does work. 

And I think that that paradigm is starting to come into focus with this 

science of networks.

Simon Nasht: It sounds to me like we’re facing the 21st century’s great 

scientific challenge.

Steve Strogatz: Yes, that’s right. The thing that is going to have the 

most impact on human affairs is going to be the understanding of complex 


Robyn Williams: The connectedness of nearly everything. Something David 

Suzuki always says about us and nature. That Science Show Special was 

written by Annamaria Talas and presented by Simon Nasht, production by 

David Fisher. Next week the science of torture.

Guests on this program:

Steve Strogatz

Professor of Applied Mathematics

Cornell University

Author: 'Synch:The Emerging Science

of Spontaneous Order'

Published by; Hyperion 2003


Jonathan Copeland

Professor of Biology

Neuroethologist & firefly researcher

Southern Georgia University




Lynn Faust




Duncan Watts

Assoc Prof of Sociology

Columbia University

Author: 'Six Degrees:The Science of a Connected Age'

Published by: WW Norton 2003


George Csicsery

Documentary Film Maker

'N is a Number'

Albert-László Barabási

Professor of Physics

University of Notre Dame

Author: 'Linked - The New Science of Networks"


Further information:

Erdos Number Project


Oracle of Kevin Bacon


Internet Movie Database


Small World Project


Mike Edgerton - Composer


Laszlo Kiss

Presenter: Robyn Williams

Producer: Annamaria Talas and David Fisher      

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