What Is Space?

“What is space?” is a deceptively simple question. While we typically think of “space” as the everyday world that surrounds our physical bodies, a brief search for “space” or “spatial” can lead to a deep rabbit hole.

In our daily lives, we may think of having “enough space” for a new piece of furniture our living room, as if it’s some substance to be consumed or a finite void to be filled. We might call this “physical space.”

During the COVID lockdowns in the US, we were told to keep six feet apart, an outdated public health guideline that treated space as a measure of distance between people.

Graphic and web designers may divide a page into an organizing grid and use “white space” to achieve balance in their compositions.

We may be tempted to treat “spatial” as merely meaning “three-dimensional,” like the world of virtual reality, the “spatial computing” of the Apple Vision Pro, or the geometric space of a 3D modeling program, but can we not draw two-dimensional floor plans to represent space as well?

Sculptors use “negative space” to invert our perceptions and treat voids as solid, material forms.

Business owners and marketers talk about “entering a space” when they mean “addressing a new market.” Or they say, “it’s a crowded space” to say “there are many competing businesses selling to the same customers.”

Software engineers and computer scientists talk about a “search space” when building databases, “latent space” when designing machine learning architectures, or a “state space” when exploring computational models.

Astronauts, pilots, and aeronautical engineers (aka “rocket scientists”) know the dynamics of both “aerospace” and “outer space.”

And futurists explore the possibilities of “cyberspace.”

When we think about more abstract uses of the words, like “needing some space” from a person, or more imaginative ideas like cyberspace, what space really is begins to get a bit murkier.

A Long Debate

And it turns out that philosophers, geographers, physicists, and mathematicians have pondered and deliberated the idea of “space” for centuries.

The philosophers of Ancient Greece used to kenon, diastema, chora, and topos to describe phenomena in the natural world. [^1] Japanese has the words wa, ba, tokoro, and ma for various perceptions of cultural experience and mental state.

Even more abstract, the philosophers Gilles Deleuze and Felix Guattari conceived of smooth and striated space in the context of their criticisms of the “War Machine” and “the State.” And still further, in The Production of Space, Henri Lefebvre wrote extensively of the dynamics of “social space.”

The list goes on.

Then the corollary questions are: Is space an extension around a specific location? Is it a void, like what’s inside an empty vessel or container? Is it defined by measuring distances between objects? Does space have structure? Given a type of space, what are its properties? Are there properties in common to all kinds of space, or are they unique?

And what is the difference between “place” and “space?”

And instead of serving as intellectual curiosities, what if conceptions of “space” could be deployed instead as lenses by which we frame design problems?

Ancient Greece

As with many ideas in Western thought, the first formal and substantial conceptions of space originate from the philosophers of Ancient Greece, who introduced to kenon, diastêma, chôra, and topos.

Mathematics

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 for spatial AI, but it’s curiously somewhat limiting as well.

Geography

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

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

Smooth and Striated

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.

Social Space

Architectural

Sculptural

• negative space
• liminal space

Technological

Tech companies may talk about the “search space” for a search engine.

Latent space

Cyberspace

Semantics of Space

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.

Casual Examples

Much of our everyday experiences can be construed as spatial, or in a sense, different spaces overlapping and competing.

Fundamental Concepts

occupation fitting, packing, consumption traversal and locomotion

• position

• location

• orientation

• void

• distance or measure

• containment

• extension

• region or area

• structure

Properties of Space

• isotropic, anisotropic
• homogeneous, heterogeneous
• continuous, discrete

People occupy a room. Robots occupy a factory. People move through a transit station. Ideas move through a society.

Overlapping Spaces “Going viral” meant an idea would propagate through peer-to-peer networks instead of mainstream media.

Board Games

But more generally, a notion of space comprises the intrinsic characteristics 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.

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.

[^1]: Space in Ancient Times