Small World


"Small World" Occurs in Nature, Too

I would rather live in a world where my life is surrounded by mystery
than live in a world so small that my mind could comprehend it.

- Harry Emerson Fosdick

There are two major products that came out of Berkeley: LSD and UNIX.
We don't believe this to be a coincidence.

- Jeremy S Anderson

New York - When we discover that we have friends or acquaintances in common with strangers, we often say, "It's a small world."  According to a study, such networks may exist throughout nature, not just among humans.  "The small-world phenomenon is not merely a curiosity of social networks," report Duncan Watts and Steven Strogatz of Cornell University in Ithaca, New York.  Instead, they say these complex interconnections are "probably generic for many large, sparse networks found in nature."

The best-known example of a small-world system is the "Six Degrees of Kevin Bacon" game, recently made popular by American college students.  The game has players link the actor Kevin Bacon to any other Hollywood star through a chain of co-appearances with other actors in various films.  The game is based on the theory that everyone in the world is somehow connected through a network of at most six mutual acquaintances.

Watts and Strogatz explain that these small-world systems are neither completely geometrically regular (like the spokes on a wheel), nor completely random.  Instead, their structure lies somewhere in between.  Small-world networks are usually based on a regular pattern, but have crucial, randomly placed "short cuts" that radically shrink the pathways linking any two points within the system.  This type of system thus grants Kevin Bacon just two degrees of separation from Robert Redford: they are linked through a "short cut" of working with Meryl Streep, who co-starred with Bacon in The River Wild and with Redford in Out of Africa.

The Cornell researchers have discovered that these networks also flourish throughout nature and within various human technologies.  They say they have discovered small world interconnections at work in the neural pathways of nematode worms, the electrical power grid of the western US, and in various computer systems.

In an accompanying commentary on the study, Boston University's James Collins, an engineer, and Carson Chow, a mathematician, note that "small-world connectivity has consequences that could be good or bad, depending on the system or consequences."  For example, they believe that the introduction of small-world elements to today's rigidly ordered communications systems could enhance the overall efficiency of cellular phone networks, and even the Internet.  However, they also point out that such connections can also have a downside.  For example, it "takes only a few short cuts to increase the spreading of disease significantly" among human populations.

Source: Nature 1998 Vol 393 - 409-410, 440-442 Wednesday 3 June 1998

Email to Test "Six Degrees of Separation"

by Robert Matthews

An unexpected e-mail from a US university over the coming months may not be spam - it could be from scientists investigating a fascinating social phenomenon.  According to urban folklore, everyone in the world knows everyone else via just a few intermediaries - an effect summed up by the phrase "6 degrees of separation".

The number 6 emerged from an experiment performed in 1967 by the social psychologist Stanley Milgram, who sent packages to several hundred randomly selected people in America's Midwest, with the aim of getting them delivered to target people in Boston.  Each recipient was given some details about the target, such as their name and profession, and was asked to send the package to a personal acquaintance whom they believed was more likely to know the target personally.  Milgram discovered that on average the packages reached their targets after passing through astonishingly short chains, typically comprising just 6 people.

Small World

In 1998, mathematicians Duncan Watts and Steven Strogatz at Cornell University showed that Milgram's finding can be explained by the "small world effect", in which just a handful of people with very diverse friends can "short circuit" otherwise huge networks of acquaintances.  But attempts to replicate Milgram's findings have had mixed results - and in any case, the original experiment fell far short of proving that the "6 degrees" effect holds true for the whole world.  So a team at Columbia University is now using the internet to attempt a global version.  Instead of a postal package, they are inviting people to use their network of acquaintances to get an e-mail message to targets spread across the world.  According to Watts, who devised the experiment, e-mail is ideal for testing Milgram's claim as there are well over 100 million e-mail users worldwide.

Only e-mails between genuine acquaintances will be deemed to complete a chain.  People will not be allowed to short-circuit the sequence by just looking up the target's e-mail address.

Chain Mail

Watts has set up a website giving details about how to take part, and how to volunteer to act as a target.  "Ideally, we'd like to have, say, 100,000 people, each trying to reach around 20 targets," he says.  The team is keen to have as many people take part as possible, not least because they suspect people's mistrust of unsolicited e-mail might otherwise scupper their experiment.  Early tests show that barely one in four e-mails are being passed on.  With such a high rate of attrition, many thousands of people would have to take part to give much chance of even one chain of acquaintances reaching the target if Milgram's six degrees apply worldwide.

"Perhaps people can't be bothered to pass them on - or perhaps Milgram was just wrong," says Watts.  "Either way, we need lots of people to take part so we can tell."

Source: 23 January 2002

NOT Connecting with People in Six Steps...

by Michael Blastland

How well are you connected?  Not necessarily to the rich and famous, but how well are we all connected to each other?

One of the most famous claims is that anyone can reach anyone else through a chain of acquaintances no more than 6 people long.  This idea, known as "6 degrees of separation", is a measure of our social networks.  The phrase was coined by an American academic, Stanley Milgram, after experiments in which he asked people to pass a letter only to others they knew by name.  The aim was to get it, eventually, to a named person they did not know living in another city.  It is a seductive idea.  Films have been made about it, there are parlour games based on it and mathematics has begun to propose theories for why it should be true.  But is it?

Judith Kleinfeld, a professor psychology at Alaska Fairbanks University, went back to Milgram's original research notes and found something surprising.  It turned out, she told us, that 95% of the letters sent out had failed to reach the target.  Not only did they fail to get there in 6 steps, they failed to get there at all.  Milgram was a giant figure in his world of research, but here was evidence that the claim he was famously associated with was not supported by his experiments.  "I was shocked.  I was horrified," she said.  And when she looked for other studies, none of those matched up to the claim either.  In the most recent, two years ago, only 3% of letters reached their target.

"If 95 or 97 letters out of 100 never reached their target, would you say it was proof of 6 degrees of separation?  So why do we want to believe this?  The pleasing idea that we live in a 'small world' where people are connected by '6 degrees of separation' may be the academic equivalent of an urban myth," she says.  Now Professor Kleinfeld argues that what is more important is not the number of links, but the quality.  Even if you were able to say you could get to the Queen in 3 steps, it would tell you little about how well you are really connected with her.  We like the idea of 6 degrees of separation, she says, because it makes the world feel more intimate.  But there are barriers - like race and class - she argues, that can sometimes make separation real and deep.

Of course, just because a letter fails to reach its target does not mean that it could not have done it in 6 steps by some other route.  But that is a reasonable hope, not a fact.  The belief that it has been proved that we live in a world of 6 degrees of separation does not seem to be true.

Source: 13 July 2006

The Extinction of Species and Why It Matters More Than You Think

by Mark Buchanan

It's a small world: take anybody else on earth, and you are probably linked through six acquaintances.  What's scary is that a similar rule applies to natural life.

An international team of marine ecologists recently completed an exhaustive historical study of coastal ecosystems, ranging from coral reefs and tropical seagrass beds to river estuaries and continental shelves.  Their findings were disturbing.  In every case, fish numbers had declined precipitously with the onset of modern methods of industrial fishing.  As the researchers concluded: "Everywhere, the magnitude of losses was enormous in terms of biomass and abundance of large animals that are now effectively absent."

The situation has become especially critical in the past few decades.  Stocks of Atlantic cod have reached historic lows, while haddock and other species have been declared commercially extinct.  Thriving food webs that were stable for millions of years have in the past 20 been radically altered, and almost ¾ of the world's commercially important marine fish stocks are now fully fished, overexploited or depleted.

This is just one illustration of the trouble facing the global ecosystem.  Biologists estimate that the rate of species extinction worldwide is at least 1000 times greater now than it was before human beings walked the earth, and that ¼ of all species could be obliterated in 50 years.

But does it really matter to us?  The political scientist Bjørn Lomborg, in The Skeptical Environmentalist, has argued that much of what environmentalists have said is overstated - that fears of ecosystem collapse are irrational and largely the result of scare tactics.  On a strict cost-benefit analysis, he says, the consequences of species extinction, like those of global warming, are not serious enough to warrant the expense of trying to stop them.  We are better off trying to adapt - by seeking other sources of fish to eat, for example.  And many others think the extinction of species is of interest and concern only to nature lovers.

Any ecosystem, however, is a staggeringly complex network in which many species interact with one another in delicate and all but unfathomable patterns.  Indeed, it is our inability to understand how these living networks hang together - and consequently, how they might fall apart - that has seriously undermined efforts to assess the vulnerability of the global ecosystem.

But in the past few years, researchers have discovered that ecological networks are not unique in their complexity.  In their basic architecture and pattern of assembly, ecosystems turn out to be in many ways identical to other complex networks such as the internet, and even to our webs of social acquaintances.

What emerges from this new science is anything but reassuring.  The biological world turns out to be a remarkably small one, with the predator-prey links between species arranged in such a way that no species is more than a handful of steps away from any other.  More than anyone suspected, the global ecosystem is an intimately connected whole, and we should indeed be very worried about what we are doing to it.

Most of us have run into a friend of a friend far away from home and felt that the world is somehow smaller than we thought.  We usually put such encounters down to coincidence even though they happen with disconcerting frequency.  Recent scientific work suggests that this "small world" phenomenon is by no means limited to social relations.

In the social setting, the "small world" experience is closely linked to the notion of "six degrees of separation" - the idea that each of us is linked to everyone else on the planet by a chain of no more than six intermediary acquaintances.  Amazingly, this seems to be roughly true.  In the 1960s, the American social psychologist Stanley Milgram sent letters to random people living in Nebraska and Kansas, asking each to forward the letter to a stockbroker friend of his living in Boston.  He stipulated that they were to send the letter only to someone they knew personally and whom they thought might be socially "closer" to this man.  Even though the US then had a population of around 200 million, most of the letters made it to the stockbroker in just five or six mailings.

Researchers have found similarly small worlds in many other settings.  The worldwide web is a network of more than one billion sites connected by hypertext links.  Take two sites at random, and it needs only about 19 clicks to get from one to the other.  Other studies have come upon a similar architecture in the layout of the world's electrical power grids, in the patterns of neural connections in the mammalian brain, and in the web of chemical reactions within the living cell.  The world's ecosystems - or more precisely, the food webs that underlie them - appear to share this "small world" character.

How many species-to-species links does it take to link any two organisms in some chain of cause and effect?  In the ecological setting, two species are linked if one feeds upon the other, be it a fox eating a rabbit or a beetle munching an oak leaf.  Last year, a Spanish physicist, Ricard Sole, and an ecologist, Jose Montoya, studied Silwood Park, an ecosystem in the UK for which researchers know the fairly complete food web.  They found the number of degrees of separation to be only two or three.  The tapestry of life is made of a truly dense cloth.

Silwood Park does not represent the global ecosystem; it is certainly more than two steps from a woodpecker in Illinois to a shrimp in the South China Sea.  Even so, whales and many species of fish populate the oceans as a whole, and numerous birds migrate between the continents.  Bacteria, algae, tiny spiders and other creatures fly round the world in storm systems.  These organisms provide links that tie the biological world together.  For the global ecosystem, the number of degrees of separation may not be two, but it is probably not much higher than ten.

This discovery is not comforting.  It suggests that the extinction of one species will affect not only everything that the species eats, competes with, or is eaten by, but will send out fingers of influence which, in a few steps, will reach most other species in the entire system.  It suggests that any belief in our capacity to control the effects of ecological destruction is badly misplaced.  That lesson becomes clearer as one delves more closely into the small world phenomenon and into exactly how large networks - such as the human social network - can be so remarkably small.

As first suggested by the American sociologist Mark Granovetter in the 1970s, the answer can be seen by making a distinction between "strong" and "weak" social ties.  Strong ties bind us to family members and good friends, or to colleagues at work.  These links form the threads of a dense fabric of social structure, and are socially most important to us.  But these are not the ties that make for a small world.

Each of us also has "weak" links to people we see rarely, or may never see again.  Think of some of your friends from the past - long-lost college mates, say.  Or someone you met when travelling.  Perhaps you went to Japan and briefly made friends with a fellow tourist from Australia.  Your links to this person, or to those friends now out of touch, are weak social links.

What makes them especially important is that they connect you to people who otherwise belong to quite distinct social spheres.  Your link to the Australian tourist, for example, establishes a social bridge that connects you in just two steps to every person this man knows.  Not only that, but this single link connects each of your local acquaintances, in London, say, to every one of his local acquaintances in Australia.  In this way, weak links act like short cuts through the social world.

Mathematics backs up this insight.  In 1998, in a paper published in Nature, two mathematicians from Cornell University showed that the effect of weak ties in a social network really does explain six degrees of separation.   In a large network - even one of six billion people - just a few weak links running between people from distant places will indeed make for an extremely small world, with every pair of persons linked by a short chain of intermediaries.

The small-world character of the world's ecosystems can be traced to similarly weak links - that is, to links between species that interact only occasionally.  Perhaps just one bird in an English wood migrates long distances, and, en route, settles briefly in southern Spain.  This is enough to link the organisms of these two food webs together by short chains of cause and effect.

But ecologists are beginning to suspect that weak links within food webs also play an important role in maintaining ecosystem stability.  Their argument is subtle, but important, as it could help us to protect the world's food webs from disintegration.

If a predator eats just one other species, it will do so frequently, having no other options.  Consequently, the link between these species will be strong.  Conversely, if a predator feeds upon 15 different prey, it may eat each species only occasionally.  It will then have relatively weak links with these species.

Suppose that, after a climate change or some human intrusion, the numbers of a predator's favourite prey have been severely depleted.  What will happen?  If this particular predator feeds on only this one prey - if they share a strong link, that is - then the predator must continue to seek that prey even though its numbers are vanishing, driving this species even closer to extinction.  When this happens, the population of predators may then fall precipitously as well.  As a paper in Nature pointed out a few years ago, this should be a general tendency: the loss of a strong link within a food web will be destabilising, tending to stir up large and dangerous fluctuations in species numbers.

But weaker links can save the day.  Consider a predator with 15 different prey.  If the numbers of one of these species become very low, for whatever reason, the natural response of the predator is to shift its attention to another species that is more numerous and easier to catch.  As a result, the predator would continue to find food, while the prey in danger of extinction could revive its numbers.  In this way, weak links between species not only make for a small ecological world but also act as natural pressure valves, playing a central role in guaranteeing the health of an ecosystem.

You might expect that all species would have roughly the same number of links with other species.  Not so.  Nature doesn't dole the links out equitably.  Studies in Silwood Park and elsewhere reveal that a few species always play the role of superconnected hubs: they "own" a high fraction of the links in the food web, far and away more than the average species.

By simple logic, most of these links will be weak links.  So these hub species provide the network with an ability to redistribute stress and prevent one species from wiping out another by uncontrolled predation or competition.  And that explains why we should be so worried about extinctions.

Half the tropical forests, where two-thirds of all species find their habitat, have now been logged or burned to clear land for human development, with another one million square kilometres disappearing every 5 to 10 years.  If healthy ecosystems are small worlds characterised by a few hub species, with a preponderance of weak links providing their stability, then the global depletion of species numbers is truly alarming.  As species continue to disappear, the remaining species will necessarily be linked more strongly - if only by simple arithmetic.  If some predator preys on only 6 species where before it preyed upon 10, its links with the 6 will be stronger, and ecosystem stability can only suffer.  As one ecologist, Kevin McCann, argues, the lesson is that, if we wish to preserve an ecosystem, or any species within it, we had best proceed "as if each species is sacred".

What's more, the consequences of removing just one of the "superconnected" species can be dramatic, as a huge number of weak stabilising links would go with it.  Ecologists have long talked about "keystone" species, crucial organisms whose removal might bring the web of life tumbling down like a house of cards.  A recent study has demonstrated just how crucial their preservation may be.

Suppose you begin removing species from an ecosystem.  Slowly but surely, the food web should fall apart.  But how?  First the good news.  Sole and Montoya have used a computer to mimic the loss of species from a food web and have found that real communities stand up relatively well when the species to be removed are selected at random.  Now the bad news.  Suppose instead that the most highly connected species get knocked out first.  In this case, ecological disaster ensues quickly.  Removing even 20% of the most highly connected species fragments the web almost entirely, splintering it into many tiny pieces.  As the web falls apart, the disintegration triggers numerous secondary extinctions as some species lose all their connections to others and become totally isolated.

The obvious answer is to take special care to preserve the highly connected "hub" species.  But it is not easy to predict which species will be the hubs for any particular food web.  In the past, ecologists have suspected that the hubs would tend to be large predators, but this does not seem to be true.  Sole and Montoya found that they were often inconspicuous organisms in the middle of the food chain, or were sometimes basic plants at the very bottom.

Most species now going extinct are ants, beetles and other kinds of insect.  Some take comfort in this, but they are wrong to do so.  These species may well be linchpins of the living fabric.

What Sole and Montoya achieved on their computer, human activity is achieving in reality - the methodical dismantling of the world's ecosystems.  The leaders of many governments and large corporations find it convenient to suppose that worries about the ecosystem are overstated, and anyway, that it would be demented to carry out reforms that are not politically popular.  But we are disassembling the web of life that supports our existence, with little understanding of what we are doing.  That is truly demented.

Small World: Uncovering Nature's Hidden Networks has just been published by Weidenfeld & Nicolson (£18.99)

Source: Monday 8 July 2002

-------- Original Message --------
Re: Extinction of Species
Date: Wed, 17 Jul 2002 13:34:16 -0400
From: Cody Hatch <>
Reply-To: Cody Hatch <>
Organization: Chaos Development
To: Ruth Hatch <>

Hello Ruth,

Okay, to start with, they talk about a decline in biomass.  I don't get it.  Fishing at the TOP end might plausibly result in the prey species having a population boom (followed by a small crash, a smaller boom, et cetera, stabilising at a higher level), but that would almost have to increase the amount of biomass, right?  Ultimately, the same amount of solar radiation is hitting the water, so I suppose the max amount of energy in the system is unchanged, but certainly it will be shifted downwards.  Given that digestion is less than 100% efficient, I really think this will result in a net increase in biomass.

Of course, what do I know?  I'm not a population biologist nor a marine biologist, but it sounds kinda weird.  I suspect they're really only concerned with the big photogenic animals (krill doesn't make people donate to WWF).  It seems to be a common problem when ecologists talk about marine ecosystems.

Of course, lack of abundance of large animals is a valid complaint.  Not sure why I care though.  I like eating fish, and all, but I like eating lots of stuff.  How is this a major problem?  Lopping off the top end of the foodchain isn't going to tend to do much damage.  It's CHANGE but I see (so far) no mention of HARM.  It seems to be a matter of faith among greenies that the two are equivalent.  I'm somewhat sceptical.

[Jurassic Park notwithstanding, do we really want to bring back the dinosaurs?  Even whales, elephants and migrating wildebeests, endearing though they may be, may take more room to thrive than the earth has left for them.]

Of course, actually driving all the major species of large fish into extinction does sound boneheaded.  I think we need a major shift towards fish farming, much as people stopped hunting and started farming cereals way back when.  But that's assuming it's economic to do so.  Perhaps it isn't, but I suspect it will be after the price of fish goes up.  Much like oil, fish will never run out - the price will simply increase until few can afford what's left.

Lomberg is not a political scientist, incidentally - he's really more of a mathematician.  (I seem to recall most of his published work is on game theory, and he's by training a statistician.)  Actually, do they mean he's a scientist that studies politics, or a generic scientist involved IN politics?  Article isn't clear...

They're right about the connectedness of ecological networks of course.  On the other hand, they aren't necessarily as difficult to understand as implied.  At least we can work out after the fact why something happened - something climate researchers or some types of economists (those dealing with market breakdowns, for example) would welcome.  Still, they're correct that ecological networks are really really DENSE.  But there has been a lot of research in related areas.  Some parts of economics and population biology have very tight links, and the relationships involved in ecological networks are trivially simple individually, just daunting in their numbers.  Very much different than, say, CO2 feedback loops, where no one is really sure if they exist, how they work, what they do, and what you could do about 'em if you wanted to. :-)

In any what?  If cod became extinct you'll get this massive complex ripple effect, stretching out to all sorts of things, and indeed circulating around recursively.  I doubt anyone could seriously predict the DETAILS of the consequences, but the very interconnectedness they worry about acts as a damper.  Few species would ONLY benefit or ONLY suffer.  The food web (or that part of it centred around cod (or whatever) will change quite a bit, but if cod ceases to be a viable solution to the problem of eating whatever it is cod eat, then another solution will fill its place (probably an already existing competitor).  I can't believe cod (or especially large fish in general), are the only species capable of eating whatever it is cod (or large fish) eat (or the only food of whatever it is that eats cod or large fish in general).  The removal of cod would be good for cod's prey AND that prey's other predators, and those predators' predators, and thus good for those predators' OTHER prey, and therefore bad for that preys' prey, and...  Well, you get the idea.  And some of those predators and prey are likely the same species anyhow...

Further, in terms of computer networks, removing a node simply causes the network to route around it.  Certain nodes (that is, species) will gain in importance, and more traffic will be routed through them (that is, their population and the percentage of the global energy budget they represent will increase), and others will do the reverse.  But this isn't a bad thing (nor, of course, is it a good thing - it's just a thing).  I know a little bit about network theory, particularly as applied to computer networks, and I just don't understand where they think the problem comes from.

So when all is said and what?  The resources in the system will not have changed, just their allocation.  And despite the vague scaremongering, everything I know about biology, complexity, and network theory says the change in allocation should resolve itself quickly with few oscillations.  However, the period while the system is in flux (or more accurately, increased flux, as the name for a static system is "dead") can be somewhat unpleasant.  As an example, the global ecosystem would respond slowly and with large changes to the loss of humans.  It might take a few million years for a replacement to evolve, and the entire process would result in vast continual changes affecting every species on earth.  The destruction (from an entropic point of view) would be vast.  On the other hand, the ripples from losing cod would be like those from a small pebble, quickly lost in the general background of everyday species interaction (which indeed, the extinction of cod would be).

Nevertheless, everything I know about biology, complexity, and network theory isn't a lot - more information on the whys and hows of the process they fear would be interesting to obtain.

For a significantly different viewpoint about extinction and competition, the following is taken from written by Steven Den Beste:

There was a long period in which the number of people out there was really pretty small, and if you wanted to move somewhere new you probably could because no-one else was located there.  The Phoenicians established a colony at Carthage, for instance, and it's unlikely that they had to conquer anyone to do it.  (Maybe some local tribes got the message that they'd have to hunt somewhere else, but aside from that nothing.)

The Greeks established several cities on Sicily, and also colonised Crete, and Rhodes, and put some cities on the Mediterranean coast of Turkey.  But the human population of the world continued to rise, and you reached a point where if you wanted to start a colony somewhere you had to brush aside people already living there.  There were not really any "unpopulated" places left, so colonies would go into lightly populated places instead.  The Romans started cities in the rest of Italy, and in Gaul, and in North Africa but only after fighting wars there.  Later they established several settlements in Britannia such as Londinium and Camelodunum, but only after conquering the island and chasing the most dangerous inhabitants north to Scotland, and building Hadrian's Wall to keep them out.

Historically, it seems as if it was mainly the Europeans who were into doing this.  When you find large concentrations of Asians or Africans somewhere else, nearly always it was because Europeans brought them in to be cheap (often slave) labour.  And as time goes on, the process of brushing aside the natives gets more and more complicated and expensive, the wars longer and more bloody on both sides.  The initial colonisation of American was not too difficult but as the United States spread west the result was the Indian Wars of the late 19th century, some of which got quite bloody.  Dutch, and later British attempts to create a colony in South Africa resulted in the Zulu War where a native army of 30,000 well-armed and extremely well disciplined native troops had to be defeated.

But by that point, the Europeans had largely ceased trying to establish European colonies (in the sense of them being made up mostly of Europeans) and instead went with enslavement (ahem) of the locals, with a thin crust of Europeans on top ruling them (for example British rule of India).

By 50 years ago, there wasn't anywhere empty left.  Everything worth having had been taken.  The world's last attempt to create a new colony anywhere was the creation of Israel by refugees from Europe fleeing religious persecution.  But unlike the Puritans, who had little difficulty finding somewhere to go (New England) the Israelis chose a place which was already heavily populated.  That war is still going on, more than 50 years later, and shows no sign of ending any time soon.

What do we see happening here?  There's an early stage where expansion is nearly free.  There's plenty of room to expand, so when someone expands it's not at the expense of anyone else.  As time goes on, though, more and more it becomes necessary for someone to lose in order for someone else to win.  The disputed land is already occupied by progressively higher densities of natives who don't want the colonisers there.  Eventually you reach the point where it's become completely zero-sum, as epitomised by Israel.  For Israel to exist, the people already living there had to be moved out.

You see the same thing happening in markets.  A new market opportunity arises and early on there will be a large number of competitors, and a lot of variety in the product offerings.  For all the production of cars now, nearly all of them are fundamentally identical in design, varying only in detail.  By comparison to what was available in the early stages of the automobile market (abut 1890) it's surprisingly uniform.  (Stanley Steamer, anyone?)

The size of the market in this case didn't run up against a hard limit (for example, the size of the world) but did run up against a slowly growing limit (the number of potential customers).  Before market saturation, an automobile company could expand its sales without causing any other company's sales to decline by finding new customers to which to appeal.  But when you've saturated the market, you now have a situation where the only way to get new customers is to steal them from a competitor.

The result is invariably shakeout.  The weak players die, and the diversity of products available declines as there are fewer offerings and those which are offered become more and more similar.

That's the critical transition from non-zero-sum to zero-sum.  Once the market saturates, you can only grow at the expense of a competitor.

Which finally leads up to the key insight I had a couple of days ago: during the non-zero-sum expansion stage, it is the virtues of each competitor which decide how well they prosper.  But after the switch to zero-sum competition, it is their faults which decide who will die.  An uneven competitor, with both virtues and faults, may prosper in the early stages but will in the long run be destroyed by a competitor which is uniformly mediocre.

I keep referring to this as a permanent change.  That's because it is, unless something dramatic perturbs the situation.  The external effects (for example, market saturation) which cause this condition don't usually go away, so the forces which lead to concentration remain in force and continue to work against diversity.  What it takes is some external catastrophe (a meteor strike, a plague, a world-wide recession) to really change things by forcibly depopulating the system.  That, then, can lead again to a period of non-zero-sum expansion.

[There's much more at that site (called USS Clueless) - Den Beste discusses the application of Lamarckian evolution to the study of mimetics, the saturation of ideas, religious and political philosophies - unique in that we each have only one - and that's a light sampling of one day's worth.  Check him out (though I don't agree with everything he says...).]

Not completely relevant, but I found it quite interesting.  The idea of focusing on market saturation (be it for ideas, cars, or species) as a turning point is a good one, I think.  Of course, talk of competing memes isn't obviously related to overfishing, but it's interesting to draw parallels.

Could a meme function equivalently in a sense to overfishing cod to extinction?  My initial reaction was "no", but what if a meme depended on another meme for existence, despite having an adversarial relationship with it?  Like, for example an authoritarian state and its opponent?

You could argue (leaving aside whether it's true or even fits the facts) that the US relied upon Saddam as an opponent, but "overfished" the resource.  This caused the US to diversify its sources of opponents, but also helped out some of Saddam's competitors, who were able to gain access to resources previously controlled by Saddam.  September 11th could be viewed as a result, much like eradicating a pest might result in plague of even worse pests that were being kept in check by competition with the original pest.

An alternative argument, which might be favoured by some conspiracy theorists, is that the US has taken to "farming" it's "prey" memes.  Agriculture allows a much higher population density than hunter gather societies, but I'm not entirely sure how you would translate population density into the terms of political memes.  Perhaps I have stretched the analogy far enough. :-)

Best regards,

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