The infinite space inside your head: The birth of conceptual spaces


Some writers are ahead of their time. When Jules Verne published From the Earth to the Moon in 1865, not many of his readers (perhaps not even Verne himself) thought the journey to the moon would ever become reality. But it did. Similar stories can be found in science. The gist of an idea may be born as a metaphor, a way to better understand the object of study itself, a crazy hypothesis about how things could be. This blog tells one such story. The basic idea is that the concepts we have in our minds form a space, a conceptual space. And not just in an abstract theoretical way, but quite literally so. But let’s start with the basic question: What is a concept?

We humans know a lot of things. In order to think about the world around us and come up with complex ideas about things we perceive and do (like travelling to the moon), we need mental building blocks. These building blocks are what scientists call concepts. In cognitive science, we think of concepts as mental categories. Examples of concepts are earth, moon, space shuttle, to travel. ‘Mental categories’ might sound fancy or difficult to understand, but really boils down to two ideas.

First, why are concepts mental constructions? Because concepts are not the things themselves. Your concept of a shoe is not a shoe, but a mental representation, a mental copy of the things we perceive as shoes in the world. Second, why are concepts categories? Because a concept does not (usually) refer to a single entity. Your concept of shoe covers all things in the world that count as shoes, not just your favourite pair of shoes.

Without concepts, complex thought would be difficult, maybe impossible. Concepts are also extremely useful for communicating our thoughts, especially when combined with language. Indeed, you may be wondering right now if concepts and words are the same thing. The two are related but distinct. Words are shortcuts, pointers to concepts. When I say the word “dog”, it evokes (in you and me) a lot of coherent knowledge of a category of entities (all those that we call dogs) and how they relate to other entities (spaniels, cats, mammals, animals, etc.): the concept dog. In this way, every word points to a concept (sometimes more than one, even), but not every concept is denoted by a word. (Think of the Dutch word “gezelligheid”, for example. This word doesn’t have a straightforward translation in many languages, including English. That doesn’t necessarily mean, though, that a person who doesn’t speak Dutch can’t have a concept of gezelligheid.)

But how exactly do concepts exist in our heads?

Since the meaning of a word is a good approximation of a concept, you might think that concepts are a bit like dictionary definitions. For a long time, this is how philosophers and psychologists thought about concepts. When we hear the word “shoe”, the idea was, we look up its definition in a giant dictionary that lives in our heads, which we can check against the thing we see in the world.

But research has since shown that thinking of concepts as dictionary definitions isn’t quite right. First, such definitions require language, which is a problem because we now know that non-human animals can also have concepts even though they don’t have a language in which to define them. Meerkats, for example, make specific sounds for different types of dangers (birds, snakes) so they must have corresponding mental categories, but those cannot consist of definitions. A great amount of evidence has also shown that babies that have not yet mastered a language nevertheless have concepts bouncing around in their heads. For example, when presented with two pictures of either cats or dogs, and later of two pictures of a cat and dog, three- and four-month-old babies will look longer at the new animal, suggesting that they’ve formed a category – a concept – of the familiar animal.

Second, concepts are inter-related in very systematic and highly automatized ways. When I say “dog”, your mind not only activates the concept dog, but also many other concepts that are closely related to it, like cat, leash, fur, etc. In contrast, when you look up a word in a dictionary, it doesn’t automatically show all definitions for related words.

So the notion of dictionary definitions is not a good description of how concepts may exist in our minds.

How should we then imagine how concepts live in our heads? A ground-breaking answer to this question came in 1957, when psychologists Charles Osgood, George Suci, and Percy Tannenbaum published an enlightening book: The measurement of meaning. Two radical ideas in that book were going to have an everlasting impact on the scientific study of concepts.

First, they proposed that meaning can be measured, quantified and treated in a mathematical way. Still today many people frown incredulously at me when I tell them their ideas and concepts can be quantified. And yet we are all witnesses to it: this is precisely what Google and other tech giants do all the time. The reason modern search engines and automatic translation work as they do is because they quantify meaning. (They do this by expressing concepts as long strings of numbers.)

Showing that meaning is quantifiable is radical, but in and of itself it could have simply been a very practical notion, useful for computer engineers rather than those interested in understanding how concepts work in the mind. The second idea Osgood and colleagues introduced had more theoretical weight: Concepts form spaces.

Osgood invited the reader to “Imagine a hypothetical semantic space of some unknown number of dimensions. […] The meaning of any concept located in the space could be represented by a vector extending from the origin.”

Voilà, the birth of conceptual spaces. Let’s break it down again.

Why a space? Space here is a mathematical notion. Think back to your geometry classes, drawing a grid of coordinates, the origin, the vectors. This grid forms a space and any point in this space is defined by its coordinates. If you took a brief foray into linear algebra, you might have learned that the geometrical notions from our usual two or three dimensions extend seamlessly into any number of dimensions. Even though we lack the ability to visualize anything beyond three or four dimensions, the geometrical properties are general: we can define distances, points, vectors, and regions in any number of dimensions.

And why conceptual? Osgood and colleagues proposed this: What if you quantify the meaning of every word in a conceptual space by ranking it along dimensions that are relevant for the concept? One dimension, for instance, could be whether a concept refers to a living or non-living thing. Even though this dimension may seem binary at first (something either lives or not), we humans actually think of ‘aliveness’ in a graded fashion. For instance, a shoe is clearly on the non-living end, while a person is clearly living. But what about an insect? If given a scale, people rate insects as “less living” than dogs but more so than plants. This is just one example of a dimension. One can think of an endless set of such conceptual dimensions, and Osgood and colleagues gathered human ratings of lots of different concepts on many dimensions (good-bad, kind-cruel, clean-dirty, foolish-wise, …).

The main point I want you to take away from this is not that Osgood and colleagues found the right dimensions (those will probably never be found), but rather that they planted the seed of the idea that concepts can be defined as points in a conceptual space. The idea of a conceptual space seamlessly (and mathematically) captures the similarity we naturally see between neighbouring concepts like cat and dog. These two concepts will share very similar values on many dimensions. Consequently, they will also be defined as points that are close to one another in conceptual space. This is a strength of the metaphor of concepts as points in a multi-dimensional conceptual space: it naturally captures our intuitions about what are similar concepts. And as scientists would go on to show, both psychological and neuroscientific evidence suggests that this talk of conceptual spaces is not just a metaphor, but actually how concepts work in the brain.


Read more
Osgood, C. E. (1971). Exploration in semantic space: A personal diary. Journal of Social Issues, 27(4), 5–64.


Writer: Guillermo Montero Melis
Editors: Natascha Roos
Dutch translation: Inge Pasman
German translation: Fenja Schlag, Natascha Roos
Final editing: Eva Poort, Merel Wolf