Conceptions of Space | What Is Space?

“What is space?” is a deceptively simple question, one I was surprised to learn that philosophers, geographers, physicists, and mathematicians have interrogated for centuries, across many diverse cultures, and that it’s even distinct but adjunct to ongoing discussions of “place.”

For example, the ancient Greek philosophers authored kenon, diastema, chora, and topos to help explain the natural world around them. The Japanese have wa, ba, tokoro, and ma, describing different conceptions of cultural and mental space experienced in daily life. (See this article from Quartz.) Even more abstract, philosophers like Deleuze and Guattari conceived of smooth and striated space in the context of their criticisms of the war machine and the state.

This suggested “spatial AI” could be about the space around our bodies (plus time) or the virtual space that’s modeled in applications like Blender or Rhinoceros 3D. And I think it’s more than techniques like depth estimation algorithms or placing markers for augmented reality headsets. It includes these things, but space (and “artificial intelligence”) is something broader and more profound.

“Spatial AI” refers to emerging artificial intelligence as applied to all aspects of spatial reasoning, design, and experience.

So what kinds of space are there? And what if instead of a one-to-one relationship between spatial types and particular environments, like a building is a manifestation of architectural space, we could start thinking about types of space as a lens by which we see any environment in a different way, carrying its corollary AI techniques with it? What would happen if we looked at an economy as an architectural space? We’re certainly comfortable looking at a government or an office as political spaces.

Semantics of Space

In our daily lives, we use the word “space” in a variety of ways; it’s not always about having room for things, although that’s a good place to start.

We talk about “having enough space for a sofa” when furnishing our living rooms. But marketers and entrepreneurs talk about “entering a space” when they mean “address a new market.” Or we say, “I need some space,” when a relationship isn’t quite working out. And then there’s “outer space” when talking about space shuttles and space stations.

These semantics are familiar and meaningful. I doubt we’re consciously invoking the classical notion of “topos” when walking through a crowded street.

And professions like architecture and urban planning do have their own specialized spatial nomenclature, like flow, adjacency, proximity, connectivity, etc.

Space as “Economy of Opportunity”

Given what’s common to these notions, I call space an “economy of opportunity.” And that limited opportunity is consumed by occupants of space, and the “agents” of space are a special kind of occupant that can traverse space on their own.

• Physical space is an economy of location, of “whereness,” occupied by people and, say, robots (agent-occupants), and obstacles like furniture (obstacle-occupants). Once a location is occupied, other occupants cannot inhabit the same location, but people and robots can traverse from location to location on their own and reason about how to do so.
• Architectural space is the physical, temporal, and experiential opportunity around our embodied selves.
• Mental space is the opportunity in our consciousness for active ideas and thoughts.
• A social network is a space for ideas as well; memes can move from person to person through friend connections, evolving as they go.
• A computer network is a space for a worm or virus to traverse, moving from machine to machine, impeded by firewalls and broken connections.

Space is dynamic; the opportunity evolves over time or over whatever notion of change is intrinsic to the space.

What Is Space, Anyway?

But we’re talking about spatial AI and spatial designers. Given all this emphasis environments, is that the same as “space?”

The notion of “space” has been explored for centuries, and similarly to artificial intelligence, it’s a topic too expansive to summarize briefly with due attention. Here are a few notes that showcase the variety (with another supporting article to follow):

Western thought’s first substantial conceptions apparently originates from the philosophers of Ancient Greece, who introduced concepts like to kenon, diastêma, chôra, and topos.

Rene Descartes and his contemporaries evolved mathematical conceptions of space. The “Cartesian coordinate system” seems to dominate physics and 3D modeling, making it a sensible default – but curiously bland – choice for for spatial AI methods.

Nigel Thrift presents geography’s categorizations of space as empirical constructions, unblocking space, image space, and place space. (Thrift, Nigel. Space: The Fundamental Stuff of Human Geography. 2003.)

Japanese gives us a different perspective encompassing cultural norms and the accommodation of individual and collective mindsets with wa, ba, tokoro, and ma.

Gilles Deleuze and Félix Guattari in A Thousand Plateaus: Capitalism and Schizophrenia define the abstracted “smooth” and “striated” space to support their critique of the dynamics of the State and the War Machine.

This discussion isn’t to imply that the above notions will each lead to some sort of algorithm or AI technique, but rather I think it means we can distinguish between “space” and “environment” productively.

The Semantics of Space and Board Games

So if “spatial AI” is to be about assisted or autonomous “spatial reasoning,” it’s worthwhile to explore what “space” might mean. I wrote some thoughts about computable notions of space before, and they’re still relevant once we get to how to invent new AI.

But more generally, “space” comprises the intrinsic characteristics and rules of an environment, and conversely, a given environment may exhibit multiple – even sometimes conflicting – spatial qualities.

When we think about physical objects in room, we typically say they “take up space” and we ask questions like, “Will my sofa fit in here?” There is a kind of availability that these objects and our bodies take up or consume. And if we fill up a room with objects, like stacked boxes, we say, “There isn’t any space left.”

“Space” comprises the intrinsic characteristics and rules of an environment, and conversely, a given environment may exhibit multiple – even sometimes conflicting – spatial qualities.

In this everyday physical-temporal space, the common rule is no two solid objects can occupy the same space at the same time, and similar rules exist for different kinds of space, like those of a chess board or Go board. The simplest of these rules divide the board into locations or squares and say we can’t have two pieces in the same location at the same time.

A bit more abstractly speaking, space can thus be “occupied” by consuming whatever available opportunity it offers. Squares of a chess board are occupied by pieces, an act which then reduces the overall number of squares available for other pieces to occupy.

In the lesser known game Quoridor, players command a single piece to move across the board, but they may also place walls that act as obstacles. The core of the game’s strategy is altering the board’s topology to impede others’ movements while further enabling one’s own.

How obstacles and movable agents interact can be key determinants of the nature of a space, and the idea that space is available or consumed means it’s a limited resource of sorts. So the dynamics of space has something to do with understanding and managing that resource.

So I’ll use the term “occupant” to refer to whatever may consume space, whether that’s an agent that can “traverse” from location to location (like moving a chess piece) or an obstacle for them to avoid, like an immovable object.

An Economy of Opportunity

From this, space an economy of opportunity to be consumed and traversed by its occupants.

Space is an economy of opportunity to be consumed and traversed by its occupants.

Why “opportunity?”