Small World

A while back somebody remarked to me that the world was “getting smaller”. It’s a familiar expression, but this time it evoked in me a literal image of a closed container whose volume was actually shrinking. The metaphor led in interesting directions, and the more I thought about it, the more fertile it seemed to be. I went on to have a series of productive conversations about it with my friend and former colleague Salim Ismail, who has been airing it in talks he’s given at Singularity University and elsewhere. It continues to hold our interest.

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The physical world – the planet Earth – is just as big as it’s ever been. What, then, is changing? What is this “world” that we’re talking about made of, and what does it mean to say that it’s getting “smaller”? Why do we say this at all?

One way to approach this question is to look at the world of human experience as a contained system, certain global properties of which are changing over time. The rules that govern the properties of closed physical systems under varying conditions have been studied for centuries, and are well understood. Might this physical and thermodynamic model help us to understand the changing global properties of our human world-system?

The statistical laws that describe the behavior of closed physical systems consider the low-level constituents of such systems to be molecules of matter. The global properties of such systems are few: among them are volume, pressure, temperature, and the number of particles in the system. These properties are related to each other; vary one and you affect at least one of the others.

Another important global property of matter is its state, which can take four possible values: solid, liquid, gas and plasma. Which state matter will be in depends on the other properties of the system.

These properties are related by simple laws. Matter in a gaseous state is described by the ideal gas law, which relates four parameters: the volume V of the container, the number N of particles of gas in the container, the pressure P, and the temperature T. The relations are all linear, and are expressed by the equation

PV = NkT

… where k is Boltzmann’s constant, which relates temperature to energy.

Why are the parameters related in this way? It’s all about interactions: how frequently and energetically the particles bump into each other and strike the walls of the container.

How likely is it that a particle inside the container will collide with another? That depends on how closely packed they are — or, to put it another way, on the average distance between any two particles. Reduce the volume V of the container, and you reduce that average distance, so interactions between particles become more likely, and so more frequent. Because they have mass, and therefore momentum, when the particles of gas hit the walls of the container they exert a force on it. The more often, and more energetically, they do this, the greater the aggregate force on the walls of the container. That’s the pressure, P.

The moving particles carry kinetic energy. The faster they move, the more of it they carry — and the more energy we pump into the system (say by heating it over a flame), the faster they move. The average energy of the particles is the temperature, T. When T is higher, and the particles are moving faster, they collide more often — so P goes up too. We can also increase P by adding more particles to the container (i.e., increasing N), which increases the frequency of collisions.

With all this in mind, then, what could it mean to say the world is getting smaller?

To begin with, we can map the number of people in the world onto the term N, the number of particles in the system.

We should be able to map the “size of the world” onto V, the volume of the container. But what might V mean in human terms?

To answer that, we should ask: what is it about V that affects the overall properties of the system as the volume is reduced? It’s that the average distance between any two particles decreases. And that’s what people mean when they say the world is getting smaller: the effective distance between any two people has been shrinking for centuries, at an accelerating rate.

A thousand years ago, the distance between two average people on opposite sides of the world might as well have been infinite. As time went by the building of roads, and mankind’s growing command of the sea, meant that two such people could, in principle at least, interact by exchanging messages at intervals of months or years. Next came steamships, then air travel, then a global telephone network, built first on wires, then on satellites. If we take the “distance” between any two “particles” in the human world to mean the time and effort required for them to interact — to “collide” — then each of these advances reduced that average distance. The latest global innovations — the advent of the Internet, which ushered in cost-free communication between any two people on Earth, and the arrival on the scene of Internet-connected cell phones in the hands of billions of people — have drastically, radically diminished that average distance in a very short time. The volume V of the human world has suddenly got very much smaller indeed.

What corresponds to pressure, P? In our gas model, pressure rises as the number of interactions between the particles increases — and goes up as the average distance between them decreases. The human analogue is almost exactly the same — the frequency of “collisions”; of nodes interacting on the network.

Perhaps the most interesting analogue is temperature, T. What corresponds to the energy of a “particle” in our human world? Perhaps the best candidate is what “energizes” a node in the social network: attention. Attention is certainly a valuable commodity (as I explain in more depth here), and it is highly fungible. Advertising, for example, directly monetizes attention, and the model used by online advertisers might give us exactly what we’re looking for here: the valuation, or in our metaphor the energization of a node on the network, varies according to the number of other nodes that link to it. An event that brings a particular node into the glare of public attention can “heat it up” very rapidly, these days, and just as with a hot object, that energy can diffuse into the particles around it. This will do nicely, I think, for our mapping of T. The more that everything is connected to everything else, the hotter everything gets.

What about phase transitions? Can we map this idea onto the human world as well? Consider water. Under normal conditions, water appears in three states: solid, liquid, and gas — known colloquially as ice, water, and “steam”. (Technically, “steam” is not the same thing as water vapor, but we’ll use the term for this discussion.)

In its cold, solid phase, water supports reactions poorly, and at a global level forms static “domains”: regions of local structure that may be oriented quite differently from domains elsewhere in the system. In a block of ice there is very little chance that molecules will interact with distant counterparts. Diffusion is so slow as to be almost nonexistent. Dissolved reagents are unlikely to react. In short, not much happens – and what happens, happens locally.

Liquid water is a very different environment. It is an excellent solvent for chemical reactions: dissolved or suspended particles move freely, collide often, and diffuse to every region of the contained volume. In liquid water it is easy for interacting particles to combine in interesting ways, and to form complex compounds and structures.

Water enters its gaseous phase at high temperatures. Collisions are more frequent, and more energetic; Because of this it becomes difficult for stable, complex structures to arise — no sooner do they begin to form than they are broken apart. This is what makes “steam-cleaning” so effective: the solvent properties of water combine with the high kinetic energy of the hot vapor to blast and dissolve away caked-on dirt and grime.

It’s easy enough to see that reactions happen more slowly in colder environments. Sugar, for example, collects at the bottom of iced tea, but dissolves easily in the steaming cup. Put your iced tea in the freezer, and the sugar will stay undissolved at the bottom of the glass for as long as you like.

We see, then, that there is a “sweet spot” for the building-up of complex structure from chemical reactions and interactions. Ice is too cold, and too solid: nothing can move. Particles diffuse with glacial slowness, and distant particles interact rarely, or never. As far as the effective distance between individual particles is concerned, we might achieve the same effect by greatly increasing the volume of the container. A block of ice is, in effect, a Big World.

From this perspective, a similar volume of cold, liquid water is a much smaller place. Gone is the confining crystal structure of ice. Diffusion and reaction may be slow, but they will happen.

Hot water is a smaller world still. Diffusion is rapid — ink dropped into hot water will very quickly spread evenly throughout the glass — and particles suspended or dissolved will soon encounter one another. Things happen fast.

If we continue to heat our volume of water, it will pass through another phase transition, and boil away into vapor. Its constituent particles have taken on so much energy, and now move so swiftly, and collide so energetically, that they can no longer maintain the cohesion and stability of the liquid state, and distribute themselves evenly, and chaotically, throughout the entire volume of the container.

This is a very small, and very disorderly world. Collisions are so frequent, and of such high energy, that it is hard for orderly arrangements of matter to form; they are battered to pieces as soon as they do.

We see, then, that if we take as our measure of distance to be the average time it takes for a particle in random motion to move from place to place (or for two such particles to encounter one another), and we consider the effective volume of the container to be an expression of the variation in this temporal measure of “distance” as we hold the number of particles constant, then we can say that in a very meaningful sense the word gets “smaller” as it gets hotter.

But we have seen also that other properties of the human world — in particular, advances in communication and transportation — can affect this “distance” as well. Looking at our own history in this way, we see a world that was for a very long time a big, “cold” place is lately getting smaller, or “hotter”, at a rapidly accelerating pace. We see a world moving from ice, to water, to steam.

To extend this metaphor to the human world, we should consider some important aspects of material systems, and the way they vary as global properties change. We might begin with the “domains” we find in crystals such as ice.

Crystals are arrangements of matter into regular, lattice-like patterns. Different substances form different sorts of patterns, and some substances — carbon, for example — can organize themselves in a variety of different ways. But whatever the pattern, crystals exhibit a particular orientation in space. Liquids, however, are not structured in this way: at the molecular scale, a volume of liquid looks the same from any angle. There is no “preferred direction”.

If a large volume of water is cooled below the freezing point, it doesn’t turn to ice everywhere all at once. Some small region of water will begin to crystallize, and from this “seed” the crystal lattice will grow, as adjacent molecules attach themselves to the existing pattern. There is no reason for the spatial orientation of the crystal to go one way rather than another; it’s a matter of chance.

If the volume of water is large enough, this will begin to happen in several places at once. Eventually, the growing regions of ice will bump up against each other — but because they all began growing in different orientations, the lattices won’t line up at the same angle, and so the resulting block of ice will contain several “domains”, with distinct boundaries.

It is in the nature of human societies, too, to “crystallize” in various ways. One example is language. All normal humans are born with the capacity to create, learn, and use language, and we have learned that the structures these languages can take is not infinitely variable, but is constrained by certain grammatical patterns. Within these constraints, though, there is no intrinsic bias toward any “orientation”. As humans dispersed and differentiated around the world, coherent “domains” — regions of shared culture, language, religion, etc. — began to form. In a large, cool world, where communication and transportation were slow and costly, and diffusion between widely separated regions was difficult, these domains persisted, often for a very long time. As the world grew smaller and hotter, collisions and diffusion increased — and many of these long-stable structures began to dissolve. For example, languages long spoken by well-insulated ethnic groups around the world are winking out of existence at an accelerating pace, battered into extinction by collision with regions of higher temperature.

These, then, are the characteristic changes that occur in a system as it gets smaller, hotter, and more crowded: collisions occur more often, reaction and diffusion proceed more rapidly, and domain boundaries melt.

With this in mind, as we look at the history of the world we see the same changes — from colder to hotter, larger to smaller, ‘ice’ to ‘water’ to ‘steam’ — occurring in nearly every aspect of human affairs.

Look at money, for example: in a cold, ‘ice’ world, economic transactions are almost exclusively local, and involve the direct exchange of physical goods, such as livestock, tools, weapons, and furs. In a warmer, more liquid world, where value diffuses across broader areas, we begin to see lightweight tokens of no intrinsic value — currency and instruments of credit — that are far more easily moved from point to point than the ‘hard’ goods they can be exchanged for. In a ‘hot water’ world, these in turn give way to completely massless instruments: electronic transactions that can travel around the world in an eyeblink.

Look at business: the first billion-dollar company, United States Steel, grew slowly, over a span of decades. It deals in a commodity that is, by its nature, heavy, local, and slow. To buy and use what they make takes time, physical transportation, and physical storage.

By contrast, look at Facebook, which made a billionaire out of its founder in a day. Their product is pure information: massless and instantly available from anywhere on earth.

We see the same transitions everywhere we look. Communication, for example, which in the vast, local “ice” world of prehistory consisted of speech and simple pictograms, has since gone from to the printed word to telegraph to telephone to radio to television to Internet. Numerical calculation has gone from notched sticks to the abacus, the adding machines to electronic computers, with globally entangled quantum computers waiting in the wings.

Human societies have seen the biggest changes of all. In the vast “ice” world covering most of human history, societies were local social structures, with relatively stable demographics, in which external interaction was limited to physically adjacent groups. (Even where larger structures existed, they consisted nevertheless of mostly autonomous local systems loosely controlled by, and paying tribute to, distant overlords.) We can think of these as resembling the “domains” that characterize the solid phase of many materials.

Advances in transportation made the world smaller and warmer. Trade and political influence began to diffuse across domain boundaries. In this more reactive environment, larger and more complex social structures — nations, empires — began to form.

In today’s small, “hot-water” world, diffusion, movement, collision, structure, and reaction are everywhere. We have globally connected markets and economies, and worldwide migration of populations. Formerly stable, ethnic/culturally defined nations begin to deliquesce as domain boundaries melt away, replaced by global trait-group associations like corporations, transnational elites, and scientific and artistic communities. National identities based on shared ethnicity, culture, and history have begun to disintegrate, replaced by abstract principles with less binding power than ancient human instincts of association, with the result that social cohesion has begun to crumble throughout the developed world. Many long-stable structures are beginning to fall apart, as the energy and frequency of collisions increase — and global discomfort increases as ethnies and cultures are no longer able to insulate and isolate themselves against continuous impingement.

As the temperature and pressure continue to increase, what will happen? It seems likely that there will be increasing chaos in the human world, as systems and structures designed for a larger, cooler, slower world can no longer keep up with the pace of change. In universities, students majoring in technical fields find that much of what they’ve been taught is out of date even before they graduate. Governments struggle to control and regulate technology that is already obsolete by the time new laws come into effect. Centralized, detailed governance at the scale of large nation-states is too large, too inertial to keep up with the rate of change; we may soon see such political entities breaking apart under the increasing heat and pressure.

In the hot, small world made possible by networked mass communication, ad-hoc structures can form very quickly. The London riots of 2012, and the upheavals of the so-called “Arab Spring”, are good examples. Likewise, the addition of high-speed reactive nodes to the network can have sudden and unpredictable consequences, as the world’s financial markets saw in the “Flash Crashes” of May 6th, 2010 and April 23rd, 2013. (The latter is particularly illustrative: it was caused by a fake Twitter posting, on the Associated Press’s account, announcing that the White House had been bombed. Within minutes, the Dow had plunged 130 points.)

In short, the smaller and hotter the world is — in other words, the more likely it becomes that any two “particles” will impinge on each other in a given time — the more volatile, reactive, unstable, and “twitchy” it becomes. As volatility and the rate of change increase, it becomes more and more difficult for systems and institutions that operate at a constant pace — the legislative processes of large democracies, for example — to respond effectively to innovations and crises.

At the same time, however, the shrinking distance between any two points in the world-network makes it possible for governments to monitor people and events, and to exert sovereign power, with an immediacy and granularity that is without historical precedent. This creates a powerful centralizing influence: the more a government can see, the more it will want to control, and an accelerating trend toward consolidation of government power at the expense of local control is evident everywhere in the developed world. The result is that modern democratic governments are able to supervise their subjects far more closely, and extend their power over them far more directly and individually, than even the most autocratic despot could have managed a hundred years ago. Our smaller world may well provide increasingly fertile ground for technological tyrannies of the sort foreseen by Orwell (although ubiquitous access to communication networks may also make it easier to organize an effective resistance).

As we move, then, from the cooler, larger “ice” world toward “steam”, we now see governments expanding and centralizing, due to the exponentially increasing coverage and immediacy of all forms of monitoring and communication. As this happens, the scale and scope of government, and the depth and breadth of the administrative and legislative tasks that government must perform, increase rapidly as well. But the capacity of a finite number of human legislators, administrators, and civil servants to operate this expanding hierarchical apparatus, across all its parts in real time, does not “scale up” at the same rate, and so the ability of these increasingly vast hierarchies to respond flexibly and effectively to accelerating change falls farther and farther behind.

Something, sooner or later, has to give. What might happen?

One possibility is that the large-scale structures of social organization and control may simply collapse under the rising heat and pressure. Already we see signs of increasing tension and strain in both the US and the European Union; this may lead to peaceable disaggregation, or something less agreeable. The large nation-states of the early 21st century may not be sustainable much longer.

Another possibility is a partial or functional disaggregation, a reversal of the centralizing tendency of the last century or so. In such a scenario, administration of local affairs would be redistributed to local governments, and the responsibilities of the central authority would be pared down once more to only those organizational tasks that are necessary for the integration of the parts: primarily the maintenance of communication and transportation infrastructure, regulation of currency and interstate commerce, and the management of external relations and the common defense. The reallocation of other governmental functions to smaller, more flexible local structures would make the higher-level organization far less brittle.

Another possibility is that some effort will be made to adjust T or V directly. This would require a coordinated throttling of the world’s communication and transportation infrastructure, in opposition the actual progress of technological advancement. This only be accomplished by strenuous (and no doubt highly unpopular) exertions of centralized power, and severe restrictions on public liberties. To maintain such unnatural control would become more and more difficult, and would require greater and more onerous expansions of sovereign power, as time passed. Broad areas of research and industry would have to be tightly restricted or shut down altogether. This is such a distasteful scenario, and would be so difficult to sustain, that it seems, to me at least, very unlikely.

To see the human world in this way — as having interesting points of analogy to the simple physical systems described above — may be quite a fruitful metaphor. We’ll develop these ideas further in forthcoming posts.

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  1. JK says

    Well Malcolm I’ll say this of you, you’re a heckuva lot easier to read than that Moldbug feller.

    Still … I’ll have to get back to you.

    Posted December 16, 2013 at 10:26 am | Permalink
  2. Luke Lea says

    A simile can be pushed too far. An understatement in this case.

    Posted December 18, 2013 at 6:15 pm | Permalink
  3. Malcolm says


    The points of analogy here, however, seemed to me too striking, and too numerous, not to see where the metaphor might lead, if pushed a bit.

    Posted December 18, 2013 at 6:54 pm | Permalink