Spatial Reasoning

If you search for “spatial reasoning” in Wikipedia, you get redirected to two topics, “Spatial–temporal reasoning” and “Spatial visualization ability.”

The former refers to, according to the article in early 2025, “an area of artificial intelligence that draws from the fields of computer science, cognitive science, and cognitive psychology. The theoretic goal—on the cognitive side—involves representing and reasoning spatial-temporal knowledge in mind [sic]. The applied goal—on the computing side—involves developing high-level control systems of automata for navigating and understanding time and space.”

Similarly, the latter is “the ability to mentally manipulate 2-dimensional and 3-dimensional figures. It is typically measured with simple cognitive tests and is predictive of user performance with some kinds of user interfaces.”

According to Chapter 45 of The Oxford Handbook of Cognitive Psychology, “Spatial reasoning is the mental transformation of spatial knowledge. Such transformation is an integral component of everyday cognition, occurring within a variety of domains, such as attention, memory, and language, and across a variety of tasks, spatial and nonspatial alike.” (Link 1, Link 2)

In this post, I propose using the term “spatial reasoning” for both AI and psychological conceptions and more.

“Spatial” is the new hotness.

Because of advances in robotics in particular, Tech Industry companies are jumping on the marketing opportunity to re-coin a number of “spatial” phrases, such as “spatial intelligence” and “spatial computing.” We hear now of “physical AI” in places we would have spoken of “motion planning,” “path planning,” the “navigation problem,” or the “piano mover’s problem.” To be fair, these concepts aren’t lost, we just have a shiny new toy, machine-learning-powered artificial intelligence, to address them.

But I mention them because I always it useful to distinguish among (1) useful new concepts, (2) the history of those concepts, and (3) marketing hype (particularly hype touted by a big company).

(3) tends to ignore (2) for the sake of novelty and, well, patents. And it confuses the conceptual discourse, but I guess it’s not much different than it has always been.

Spatial Designers

The theme common to the above concepts is that spatial reasoning is a facility or faculty that belongs to an individual, occupying and traversing some environment, some space.

More generally, spatial reasoning is about choreographing spatial dynamics, which depends on the perspective you take.

From a designer’s perspective, this means deciding on spatial configurations and systems of change. What kinds of opportunities are available (physical locations, visual connection, auditory connection, etc.) and how should an environment be designed to provide them?

More fundamentally, we consider the spatial intelligence and ability of the agents who will occupy these environments:

• What kinds of perception and simulation abilities do they have themselves?
• How can we signal to them what they need to know to navigate and traverse an environment effectively?
• What do they know and when do they know it?
• Can they visualize and simulate, or do they only respond to immediate stimulus and spatial instructions, like the simplest of robots?
• Can artificial intelligence enhance how we approach these questions?

Way-Finding and Way-Guiding

way-guiding → an environment signals to agents way-finding → an agent attempts to find its own way through sensing and reasoning

The properties of the “space” then depend on rules and constraints in the environment, which are potentially determined by the agents themselves.

So if the study of AI formulates how agents may plan to navigate specific environments, maybe it’s productive to use “space” to mean a more abstract nature used to model an environment. (This would obviate a few common usages like “living space,” which doesn’t seem problematic to me.)

Computationally, we would model the connectivity of such environments differently depending on our concerns. If we only care about street topology, we may model intersections as nodes and street lanes as edges in a representative graph data structure. But if we’re interested in the characteristics of air flow and ventilation through the same environment, we would prefer a polygonal mesh decorated with normal vectors instead.