Indoor Public Space

is what we make of it.

A Different Way to Think about Urban Space

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In most indoor, urban spaces, we rarely start conversations or stretch our tight hamstrings or break into song or lend a kind ear to the people around us.  This is in part because we imagine that most spaces are exclusively for doing business.  We think that if we are in a space we do not own, it is only to buy or sell and then get out.  Luckily, city life follows other paths as well — friendships, cultures and sub-cultures, spontaneous interactions, acts of bravery and trust, institutional practices, tastes and preferences, festivity and celebration.  We can all benefit if we consciously consider these other paths, how they open and close, what shapes and spaces they produce.  This is not a revolutionary or radical proposal.  Every day, somewhere in our city, coffee shop owners and employees let homeless people come in out of the cold or the heat, the owner of a clothing store might host a record release party for a friend even if they won’t make enough money to justify staying open late.  We are constantly treading upon ground we do not own for all manner of reasons — and this is what keeps our cities and our economies circulating.  We can build better cities if we think a little more about which paths are open to who and why and how all these paths can be best arranged for the benefit of all.  Thinking about the many ways in which we negotiate the use of indoor spaces is our number one goal here at the Foundation for Indoor Public Spaces.

Trees and Semi-Lattices

For Chris Alexander, a mathematician and urban planner, a city is a set of relationships between people, objects, spaces and organizations:

“In Berkeley, at the corner of Hearst and Euclid, there is a drugstore, and outside the drugstore a traffic light. In the entrance to the drugstore there is a newsrack where the day’s papers are displayed. When the light is red, people who are waiting to cross the street stand idly by the light; and since they have nothing to do, they look at the papers displayed on the newsrack which they can see from where they stand. Some of them just read the headlines, others actually buy a paper.”


How many potential interactions can fit in one intersection?


In a famous article called ‘A City is Not a Tree,’ Alexander argues that we can try to map these complex relationships in different ways, as ‘trees’ or as ‘semi-lattices’.  A semi-lattice requires only that parts of the system are all part of one larger set — the city.  But a tree requires sub-sets to be self-contained, their relationships are boxed into compartments and only interact with the wider city.  In terms of set theory, Alexander explains that “The tree axiom states: A collection of sets forms a tree if and only if, for any two sets that belong to the collection either one is wholly contained in the other, or else they are wholly disjoint.”

Alexander goes on to show how most urban plans try to divide cities into self-contained units.  A ‘Garden City’ plan breaks a city into “superblocks. Each superblock contains schools, parks and a number of subsidiary groups of houses built around parking lots. The organization is a tree.” The plan does not include any number of cross-connections such as the schoolboard which turn the schools into a set while ignoring the superblocks — but these connections always exist in a real living city.  And this is Alexander’s point.  In a second version of this article, Alexander writes that “people have an underlying tendency, when faced with a complex organization, to reorganize it mentally in terms of non-overlapping units”.  Although Alexander is talking primarily about cities, his argument about trees and semi-lattices can be applied to any set of things — a system, an institution, a political party, a society.  Many of these systems involve trees of relationships, but if we look only at their hierarchies, we are missing the dense criss-cross of relationships that actually make them work.  Alexander argues that “the idea of overlap, ambiguity, multiplicity of aspect and the semilattice are not less orderly than the rigid tree, but more so. They represent a thicker, tougher, more subtle and more complex view of structure.”1

For Alexander, this is the natural way for relationships to be arranged.  There is no tree structure that can properly capture the complexity and dynamism of urban relationships.  “If we ask a man to name his friends and then ask them in turn to name their friends, they will all name different people, very likely unknown to the first person; these people would again name others, and so on outwards. There are virtually no closed groups of people in modern society. The reality of today’s social structure is thick with overlap – the systems of friends and acquaintances form a semilattice, not a tree.”  We ignore ‘tree’ divisions in our day-to-day lives, but tend to respect them in our thinking.  While Alexander doubts that one could actually plan a vibrant, harmonious semi-lattice structure, he argues that it is important to keep the possibility of unplanned relationships in mind when we design our cities.

“The city is a receptacle for life. If the receptacle severs the overlap of the strands of life within it, because it is a tree, it will be like a bowl full of razor blades on edge, ready to cut up whatever is entrusted to it. In such a receptacle life will be cut to pieces. If we make cities which are trees, they will cut our life within to pieces”

At first glance, Alexander’s argument is mainly about zoning and land-use planning, but in fact, the main way that we plan our cities is to hand over the reins to capitalism through a system of private ownership.  And capitalism has trees of its own.  Corporate hierarchies are just one such example.  Your yoga teacher’s closing words from last night might encourage you to meditate all day, but it is your manager who is in charge in the office.  Capitalism is most constrictive where chains are hierarchical and fewer people have the freedom to respond to different cultural pressures (though there are many that argue that control through images and identities is just as constrictive).  Many theories of economic freedom — early liberalism, for example — assume a certain horizontality between economic competitors, but increasing concentration of ownership means that market pressures are more and more likely to assert themselves vertically (down hierarchies) than horizontally (through free competition).  Global capitalism with its billionaires and multinational corporations is becoming more and more like a single tree and less like a semi-lattice.  There is one key way in which capitalism is not a semi-lattice: customers are expected to come and go and pass between sets.  In capitalism, we shop in a semi-lattice, but we produce and design and plan and control our spaces with trees.  This is why we are only really free in a modern city when we have money to spend – and even then we are only free to be customers.

Private property itself is another sort of a tree structure overlaid upon the diverse and divergent paths and activities of a modern city.  Each space has one owner and, in theory at least, that owner plans the activities within it.  Again, this is a case where a tree in our thinking is more of a semi-lattice in practice.  People enter and exit private properties for all manner of reasons.  Large corporations tend to control their spaces very carefully though, ensuring that all activities are focussed as closely as possible on the production of profits.  This is ownership taken to the extreme.


Hegemony is a kind of cultural power, a power through ideas.  Hegemony often exploits our desire to think in trees, to impose a single order upon a complex system, to identify a primary goal for a system that is actually doing many different things.  When certain ideas become dominant or accepted they can shape the behaviour of entire populations — or rather most people in a population, i.e. the average person.  Hegemony can operate without imprisoning outliers, because moving the bulk or mass of society is sufficient.  Hegemony isn’t necessarily a bad thing – a hegemonic cultural pressure to be kind would (on average) be a good thing.  Capitalism operates hegemonically by convincing most people that maximizing profit is the right thing to do, most of the time.2   Hegemony often ‘naturalizes’ ideas and behaviours — meaning that hegemonic ideas become so common that we take them for granted and assume that they are ‘natural’ rather than culturally inspired.

J.K. Gibson-Graham are two feminist economists who use a single moniker to ‘author’ their shared theories.  They want us to realize that capitalism is only one force within our economy and that we actually make decisions about consumption, production and distribution for any number of reasons.  Profit-maximization is behind most decision-making, most of the time, but it is not the only cultural pressure shaping our economic decisions.  Kindness, religion, tradition, personal preferences, beauty — all these forces compete in our minds and bodies to produce different decisions about what to do with goods and services at any given moment.  Gibson-Graham remind us that hegemony must be “continually performed.”  We must all choose in each moment whether or not we will maximize profits or consider some other cultural goal.  Gibson-Graham have worked to map and measure these other pressures in our economy — for example in the internal decision-making of co-ops and family businesses — so that we can see them and so that they may one day flower into their own alternative hegemonies.  Sometimes, a landlord chooses not to raise the rent on an old lady simply because he knows she can’t afford it.  Sometimes the owner of a pizza parlor gives free slices to students with good report cards because she wants be a part of her community.  Sometimes these alternative choices will actually increase profits in the long-run, sometimes they will not.

We describe people as greedy who choose profit-maximization even in those cases where the average person would respond to other cultural pressures.  Even huge corporations sometimes make decisions differently — CVS (a pharmacy in the U.S.) took a huge hit to its bottom line because it valued its identity as a provider of health services over the profits from tobacco sales.  Capitalism is “hegemonic” because we see it as primary, whereas we tend to think of these other pressures cropping up on a case-by-case basis according the whims of private individuals.  In a way, this is another instance of Alexander’s insight about how we organize complex systems in our mind.  We think we have a capitalist economy (a tree for sucking profits up out of the earth) and, of course, we do — but our society and our cities are also shaped by a complex semi-lattice of cultural pressures.  If our entire society were a pure profit-production machine, we would have the bowl of razors that Alexander has warned us against.  If businesses always extracted maximum profits our society would be utterly horrific and inhuman — we would be selling babies to the highest bidder and processing unproductive workers for their organs — but of course we do not, capitalism’s hierarchy is constantly softened by other forces.  Capitalism is at its cruelest when these pressures are absent and it works best where these other pressures synergize with profit-maximization.


But wait…!

Just like the tendency to profit-maximization, ownership too is a kind of hegemony.  We think of it as natural or unquestionable, when, in practice, it is constantly being softened and eroded.  Like any part of society, property laws are socially constituted — when a pushy door-to-door salesperson talks their way into your home, they have not seized your property rights, but they have successfully undermined them through the application of social pressures.  Here too, hegemony must be “continually performed.”  There is no real reason that ownership isn’t constantly up for negotiation.  I wouldn’t want to do this in an aggressive or annoying way – but I don’t see any reason not to make polite proposals to use a space for something different at any given moment.  Go ahead and talk to the people behind the counter, maybe you can make their day a little bit better with an unusual activity.

So What About Cities?

The pressure towards profit-maximization and the ownership hierarchy shape the way we think about and behave in our city.  There is a hegemonic idea at work in our cities that space (other than private homes and government buildings) must produce profits — but we also need space to do all the other things we love.  We need space for making music, for learning, for meeting friends and strangers, for sports and for politics.  Certainly, we are often able to use spaces in such a way that we accomplish these goals while also producing profits — but we need to think more about which priorities are more important in which spaces and at which times.  Sometimes owners make this choice for themselves.  Some people stick it out running unprofitable book stores because they love what they are doing and because they provide a small number of customers with a rare and meaningful space.  These people are important nodes in the complex semi-lattice that makes a vibrant and enriching city.


A clear threat to peace and order.

The idea of profit-maximization can become a self-fulfilling prophecy.  Security guards kick people out of the mall for dancing or just holding up a sign that says “You are beautiful the way you are.” — simply because these activities aren’t clearly and immediately profitable, even if, in the long run, they might attract more people to the mall and produce more profits.  Or alternatively, they might just add free joy to peoples’ days without hindering profits.  Or, we, as a city, might decide that the joy they produced was worth more than the decline in profits that resulted from a few distracted shoppers.  All these outcomes are reasonable choices, but we won’t achieve any of them if we don’t consider all the cultural pressures and individual desires which are completely invisible when we map and measure only a single type of activity.  This, in a nutshell, is what we mean when we say “Indoor Public Space is what we make of it.

People don’t always submit to decision-making hierarchies or hegemonies of purpose.  At any given moment, people can and do meet face-to-face and renegotiate the possible paths through our city.  But we should find ways to do it more often.  Business owners should think about what personal goals they have other than profits and express those goals to their employees, they should ask their employees what makes their work satisfying and how they can maximize those satisfactions — sometimes these alternate purposes will make stores more profitable, sometimes less, but I don’t think there is any natural antipathy between alternative goals and profits — it is just a matter of complexity of thought, of trying to do two things at once.  We often think only in terms of profits just because it is simpler, but, in so doing, we are creating a bowl of razors in our cities and then forcing ourselves to sit down in it.



  1. If you want to go way off the theoretical deep-end, Alexander’s ideas about trees and semi-lattices are not too far removed from Deleuze and Guattari’s (1987) arguments about rhizomes and arborescent structures.)
  2. I use the word ‘profit’ very loosely, to include both cost-cutting and doing any work or activity that you wouldn’t do for free.



Alexander, C. (1965) A City is Not a Tree. Architectural Forum, Vol 122, No 1, April 1965, pp 58-62

Alexander, C.. (1967). A CITY IS NOT A TREE. Ekistics23(139), 344–348.

Deleuze, G. & Guattari, F. (1987). A Thousand Plateaus: Capitalism and Schizophrenia.

Massumi, B. (Trans.).  Minneapolis: University of Minnesota Press.

Gibson-Graham, J. K. (2006). A postcapitalist politics. Minneapolis: University of Minnesota Press.




Author: Matthew Lie - Paehlke

Matthew Lie-Paehlke is a PhD student in Urban Planning at the University of Toronto.

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