Notes on Spatial Metaphors for Social Systems

Distance metaphors are natural in any conversation about social phenomena. We talk of the distance between governance systems and the governed, guerrilla movements and host populations,  rich and poor, Chinese and American, Red and Blue.

Kevin Simler’s recent guest post made use of the standard geometric-metaphoric scheme, the Hofstede cultural dimensions model, to talk about startup cultures. The model also forms the basis for the analysis of globalization in Pankaj Ghemawat’s World 3.0, which I reviewed last year. So distance metaphors are very robust across a wide range of social phenomena, from small startups to the entire planet.

Topology — the study of the pre-geometric structure of a space, such as whether it is orientable or not, doughnut shaped or spherical, and so forth — is not as natural or easy to apply, but is also useful if you can pull it off, as Drew Austin’s recent post on the Holey Plane demonstrated.

When you do topology and geometry for social systems incoherently, you get frustrating books like Friedman’s World is Flat.

But more careful approaches aren’t safe either.  In particular, the more I think about Hofstede’s model, the more dissatisfied I get. Is there a better way? I’ve been playing around with a few very preliminary ideas that I thought I’d share, prematurely.

The recent guest posts (plus another one I’ve been promised by Mike Travers) have gotten me thinking really hard about doing topology and geometry carefully for social systems.

I seem to make heavy use of geometry/topology metaphors, so this is sort of overdue due diligence on my own thinking.

My favorite simple model, which I probably over-use: a two-dimensional time/entropy model for understanding progress/decline/collapse/singularity type arguments. I used it in Tempo and have also used it in many recent posts: Hackstability, Baroque Unconscious and Future Nausea posts among them.

It seems increasingly insufficient. I’ve been developing the core ideas for my next book on top of this two-dimensional model, but now I think I need a more complex one.

Hofstede’s Model

Hofstede is a natural starting point for something better, but there is something worryingly just-so/Ptolemaic/epicyclic about it. Here is the basic outline, per Wikipedia:

The original theory proposed four dimensions along which cultural values could be analyzed: individualism-collectivism; uncertainty avoidance; power distance (strength of social hierarchy) and masculinity-femininity (task orientation versus person-orientation). Independent research in Hong Kong led Hofstede to add a fifth dimension, long-term orientation, to cover aspects of values not discussed in the original paradigm.

Or to summarize:

1. Individualism-collectivism
2. Uncertainty avoidance
3. Power distance
4. Masculinity feminity
5. Long-term/short-term orientation

This is already a marked improvement over random uses of spatial metaphors. It immediately suggests, for instance, that “power distance” is the appropriate metaphor for economic equality/opportunity, and you immediately spot one obvious way to attack Friedman’s “World is Flat” hypothesis. This is why Ghemawat’s book, about the same length as Friedman’s, hangs together a lot better.

Problems with Hofstede’s Model

But Hofstede’s model has limitations too. It seems like the sort of thing you’d come up with if you just backed out a multiple regression model from survey data, based on unreconstructed use of common language concepts.  It lumps together binary and continuous variables, variables with relatively obvious measures (such as 5) and variables where models would be very contentious (2 and 3), and includes variables that are hard to measure at all (1).

More problematic is the fact that there is no inclusion of physical reality (except very indirectly), either natural or artificial, in the scheme. Some of the problems that emerge:

• Would a fishing society on an archipelago have the same social geometry/topology as a settled continental society?
• Is a society with strongly legalist institutions that codify certain power distances different from one that has similar power distances, but within kinship-based institutions?
• Is a technologically advanced society with agency latent in non-human artificial realities (such as Google’s search robot for instance) “inside” the social system or a boundary condition for it? Do we inhabit technology the way we inhabit space, or does technology inhabit space along with us?

Now it isn’t important to actually “measure” something simply because it is a conceptual “distance” of some sort. But to work with metaphoric distances effectively, you need at least an in-principle idea about how you might measure it. Otherwise even the simplest speculative comparisons become hard.

Social scientists are right to be suspicious of the sort of first-principles/axiomatic approach common in mathematics or logic (after all, we are talking about a messy gazillion dimension phenomenon here, not Euclid’s Elements), but some attempt at introducing more coherence seems called for.

I don’t want to get into a detailed critique of Hofstede, or explain how I got somewhere else starting from his model, but here is where I’ve gotten so far (I am far from done here; this is very much a beta post).

Four Dimensions of Agency-Space

I’ve come up with a model I think is a good deal more coherent and simpler, at least for me.

Before you even define a space, you have to characterize the idea of a “point” within it. In geometry, we think of a “point” as being an irreducible location in the space that measures zero units along all dimensions.

In social systems, I think the corresponding idea is an irreducible (point) locus of agency. An atomic entity that can hold beliefs, desires and intentions, and cannot be further reduced to simpler agents. My suspicion is that atomic agents are very simple behavioral loops of addiction or aversion, but never mind that.

I won’t say more about this basic assumption that “atomic agency loci are points in social space,” since the guest post in the queue explores agency in much greater depth, but this is enough for this post.  Suffice it to say that agents can be added, subtracted, overlapped, separated, broken down, built up, and so forth, just like geometric objects more complex than a point have a whole calculus associated with them.

So here are my four candidates for basic dimensions of social systems.

Cultural distance

The degree to which two agents can assume each other’s point of view (or emulate each other computationally). The objective measure is distance between mental models. The subjective measure is empathy. Note that this is not limited to two humans or discrete/separated agents. A human can have “empathy” for a “city” where he resides part time for instance. 

Power distance

Roughly, the “height” separating two agents. This mostly corresponds to Hofestede’s notion. Objectively, this is the vertical height in conceptual drawings of hierarchies. Subjectively, this is correlated to emotions like awe, fear, compassion, and so forth.

I have this flagged as a potentially dependent dimension that can be constructed out of the other three.

Fabricatory depth

This is a very subtle idea, due to Gordon Rugg, that basically refers to the minimal “length” of the chain of component technologies that separate an agent from the natural environment it attempts to live in. You can think of it as the length of technology-as-dumb-lever (ignoring aspects of technology-as-agent). When you live a life with very high fabricatory depth, you are technologically “advanced” and feel estranged from nature. This is what Matthew Crawford is getting at in Shop Class as Soulcraft: 

A decline in tool use would seem to betoken a shift in our mode of inhabiting the world: more passive and more dependent. And indeed, there are fewer occasions for the kind of spiritedness that is called forth when we take things in hand for ourselves, whether to fix them or to make them. What ordinary people once made, they buy; and what they once fixed for themselves, they replace entirely or hire an expert to repair, whose expert fix often involves installing a pre-made replacement part.

When you are faced with higher fabricatory depth than you are used to, it seems like magic, per the Arthur C. Clarke quote. It’s different from the awe of being faced with high power distances.

Inferential Distance

There are probably several versions/originators of this idea (there is one within Rugg’s fabricatory depth model above that I hadn’t seen before), but I first saw it referred to as “inferential distance” in a LessWrong thread someone pointed me to. It is basically the cognitive analogue of fabricatory depth: the distance between a mental model and a new idea. Zero inferential distance is when something is a trivially obvious conclusion from things you already know or believe. High inferential distance is when you need years of education (including possibly unlearning) just to acquire the vocabulary needed to state an idea, let alone assess its validity.

Subjectively, high inferential distance turns into confusion/incomprehension/suspicion/distrust.

Inferential distance also comes equipped with a useful notion of “shortest path” in the sense of Kolmogorov complexity (the shortest algorithm that can generate a certain result, which is the same thing in a sense).

Inferential and fabricatory distances interact, obviously. But the details are not yet clear to me. When you develop an “appreciation” for a technological reality, you are using inferential distance to cancel the emotions associated with high fabricatory depth without necessarily being able to reduce the fabricatory depth itself.

Manipulative (instrumental) knowledge, which might possibly deserve an independent dimension status, allows you to mitigate the effects of high fabricatory depth.

Additional Comments

You’ll note that I’ve dropped four of Hofstede’s five dimensions (individualism, gender, time, uncertainty) as well as both of mine (time, entropy). Here’s why:

• Individualism/collectivism is not fundamental. It can be understood more fundamentally as the cultural distance between an aggregate agent and a relatively more atomized agent. This is actually better since it generalizes to subgroups (splinter factions, exile communities, diasporas and so forth).
• Masculinity/femininity (task/people orientation) is a derived notion that belongs in a larger, more diverse universe of agency patterns, not all of which readily admit to characterization via gender. Neither human males/females, nor metaphorically gendered larger aggregates, are atomic. I believe this trait, if it is meaningful, will turn out to be a function of patterns in the five-dimensional space (possibly males generally have higher fabricatory depth in their patterns of agency). While I am somewhat comfortable with ideas like specific religious institutions being male/female, it is much harder to justify maleness/femaleness attributes to things like (say) Google’s search robot. It would be a stretch, and a pretty pointless one at that.
• Long-term/short-term is interesting. Like my own models (time/entropy) it relies on time. After some serious thought, I’ve concluded that time does not belong among the intrinsic dimensions of social systems. Rather, along with space, it belongs in a sort of external “embedding space.”
• Entropy, similarly, is not fundamental in this scheme of things. It is better understood as geometric alignment (or lack thereof) in the patterns of agency in a social system. High alignment (low cultural distance would probably be a component) would correspond to low entropy, and more coherence of the aggregate agent represented by the grouping. And vice-versa. There are tradeoffs due to boundary conditions here (so for instance, given two agents of similar “size”, higher fabricatory depth will probably lead to lower entropy, since mental models can be built out of more platonic abstractions, leading to lower cultural distances).
• Uncertainty avoidance is actually not distinct from time and entropy, but a function of those two variables. I’ll skip the explanation though. It is somewhat involved, and if you’ve kept up this far, you can probably work it out yourself.

Embedding Social Spaces in Physical Spaces

To apply social geometry and topology, you have to embed social spaces in physical space: space and time. You also have to correlate abstract power in the sense of agency and leverage (power distance and fabricatory depth) to physical notions of energy. It is through embedding that social distances and shapes change.

Time is easiest to understand: distant ancestors and descendants (genetic or memetic) may be very close in terms of social and power distances, but influence is limited to weak, one-way efforts.

The best example of embedding in space is large, modern, highly diverse cities. They are the equivalent of social singularities (in the sense that black holes do curious things to physical space time, cities do curious things to social dimensions). Schelling’s famous sorting arguments and the patterns of expansion and separation that characterize suburban/exurban development illustrate some of the rich dynamics that result when you scrunch up a complex social system into a small physical-temporal box.

Finally, energy is perhaps the least appreciated physical  variable. When physical energy gets cheaper (as it did for instance, when coal power and oil power freed many humans from muscular exertion), fabricatory depths and inferential distances increase across the board. Low-energy societies are also low-abstraction societies overall.

Embedding is also how social geometries acquire recognizable topologies such as the Holey plane. The Holey plane itself is too complex to get into in this post, but consider the intersecting, co-extensive, but weakly interacting “cities” of bike-riders and car-drivers. They may be close in space and time, but are highly separated in terms of cultural distance, power distance,  fabricatory depth and even inferential distance (a car driver cannot subconsciously and instinctively predict the behavior of a biker: the two have loaded different mental models for vehicle control).

Sometimes embeddings are chosen by architects and urban planners to reflect cultural and power distances, where there is enough design room to do so. In buildings, people with more power are typically on higher floors. Fascist societies create formal ghettos to codify cultural distances in physical geometry. Social justice minded designers adopt the reverse philosophy: using design to mangle power and cultural distances (such as mixed-income housing).

One obvious challenge in embedding is dealing with virtual reality. Clearly, my social graph “neighborhood” involves distances of some sort. It also seems to me that the distances are distances in the embedding space (i.e., like space, time or energy distances) rather than intrinsic social distances.  So perhaps social-graph distance should be added to the physical dimensions. I am not entirely satisfied with my approach here.

Some Applications

Psychology

Psychology naturally falls into this model. When you think of individual humans as aggregate agents (the standard view in most schools of psychology, though they differ in the constructs disaggregated out of “human”), and the ideas of “integrative” psychology as closing internal distances, you don’t need additional concepts to handle most ideas in psychology. So mindfulness becomes equivalent to expanding internal social distances while reducing internal entropy and overall fabricatory depth. Introversion is trading external cultural distance for internal.

Governance

One of the most interesting books I’ve been reading lately is Michael Lind’s Land of Promise, where he argues that the Right/Left divide in America has historically been less consequential than one he calls Jeffersonian/Hamiltonian (after Thomas Jefferson and Alexander Hamilton).

Jeffersonians are suspicious of large institutions (state or corporate), while Hamiltonians view them as essential for democratic access to economies-of-scale leverage. I’ll have a lot more to say about this idea in future posts, but in terms of social system geometry, you could say Jeffersonian producerists are in favor of low fabricatory depth as a way to lower power distances. So both right-wing militias and hippie eco-villages share a design principle of using a minimal technological set as a form of insurance against the dangers of large and complex systems.

This incidentally, also gives us a very visual metaphor for “big government” or “big corporations” as geometric-topological objects that span large volumes of space within a given social system. So the idea of DARPA as a “big government” for R&D takes on a very literal image: it is a geometric object spanning a large range of fabricatory depths, cultural distances and power distances.

“Platforms” convey the image of “flatness” because they use a high-fabricatory depth layer of artificial agency to create a high-plateau flat surface for relatively equal (low power distance) human societies. So the “Internet” conceptually is a relatively flat mesa that rises above the very uneven “floor” of industrial age technology.

Jeffersonians are afraid of heights. But often, they are high up without realizing it (many DIY drone builders are laboring under an illusion of false low fabricatory depth: they may be “building” things, but unlike a neolithic farmer, they rely on black-box Hamiltonian technologies like the Arduino controller board and decades of government-funded research into UAVs).

You could state the Jeffersonian position as “most tall social systems are peaky mountains” and the Hamilitonian one as “peaky mountains can be reshaped into mesas.”

Technology

I am not completely confident of how to do this, but I think the idea of a manufactured normalcy field is one very geometric-topological way to understand techno-social “systems.”

This application in particular, has a non-trivial topological component (like the Holey plane) because it involves holes, disconnected pieces and so forth.

Class

Christopher Hayes’ Twillight of the Elites (another stimulating book that I just finished) uses a rough-and-ready notion of “social distance”  to talk about the problems of “meritocracy” (in scare quotes, because the aim of the book is to problematize the idea that meritocracies measure anything remotely like “merit”).

Within our speculative geometry, the argument can be stated as: low cultural distances between elites and their captive institutions (viewed as artificial agents), coupled with high relative fabricatory depth compared to lower classes, leads to various pathologies.

This post really needs lots of pictures, but I don’t have time to redraw all my pen-and-paper drawings in legible digital format.

Business

Besides the obvious applications (hierarchies, networks), businesses also present interesting geometric/topological challenges. For example, I think the idea of ubiquity illusions that I introduced a while back, which generalizes the idea of “three contacts, three media” in sales, is an interesting interaction between fabricatory depth (media) and cultural distance that turns degenerate geometries into non-degenerate ones (the way three points only form a real triangle if they are not co-linear; so the three-contacts/three-media rule becomes “draw a proper triangle in the cultural-distance/fabricatory-depth plane” — almost pointlessly abstract in some ways, but very useful in other ways).

You can also frame Geoffrey West’s work on superlinearity, immortal cities and mortal corporations using social system geometry/topology. You are effectively trying to lower the overall (four-dimensional) distance between a corporation and its host city in a controlled way.

Where to Now?

I rarely share ideas at such an early stage of development, but since so many people have helped me get this far, I figured this is a release-early-and-often kind of idea. My immediate objective is to come up with a geometry and topology that will help me write Game of Pickaxes. I am mainly aiming to come up with a scaffolding that will be just enough for that project (and mostly invisible/transparent within it, since this sort of back-end intellectual drudgery doesn’t interest most people), but maybe if it ends up solid enough, I’ll write it up more carefully and explicitly for the tiny group of people that might care.

There’s a lot more to be said/done here.

• I haven’t said much about the topology piece here, mainly because that’s a lot harder to talk about.
• There is also a whole can of worms that mathematicians call “metrization” (the addition of notions of measure and distance to non-metric constructs).
• It would also probably be valuable to reflexively apply these ideas to this post itself (it is at a very low inferential distance from the rest of my writing, so easy for long-time readers to get, but probably impossibly far for many new readers, since it is at quite a large inferential distance from all the nearby conceptual continents — it is something like an island in the Pacific). Rather satisfyingly, one of the best uses of this model of social systems is to critique this blog.
• This whole mess of ideas seems to rest on information theory in some way. I’d like to ground this model in some notion of the “information content” of a social system.

And so on. Anyway, a big to-do list here. I’ll lazily/sloppily work through it as and when I find time.

Besides Drew, Kevin and Mike, I should mention readers jld, Jordan Peacock, Alec Resnick, Greg Rader, Jane Huang, Kartik Agaram and Nick Pinkston among several others, for helping me think through some of this stuff. Should also credit readers Goblin and Kay, for debating the former’s notion of “blue collar intellectualism” vigorously in the comments section of previous posts.

Let’s see where this gets us.

Happy Thanksgiving to all in the US.