Knowing Neurons
Brain Basics

Navigating Knowledge: Physical & Conceptual Spaces and How They Meet in the Brain

By Daniel Janko, Carlotta Isabella Zona 

Before reading this article, you may have gone to the kitchen to get a snack. Alternatively, you may go there after you have finished reading, or in the middle of the article. In any case, at some point in our day, most of us have to navigate the world to find our way to a destination. For you to do that, your brain needs to be able to understand and navigate space. In this article, we will explore some basic mechanisms of spatial navigation and introduce a framework of how these purely physical space-processing brain regions may also play an important role in more abstract, conceptual space organization and higher-level thinking. 

Before we explore what conceptual spaces actually are, and what makes them similar to physical spaces in both geometry and brain behavior, we need to understand how space is processed and structured by the brain. While many structures are involved in the processing of space, the primary area that has been linked to this process is the so-called hippocampal formation. This is a cluster of numerous brain regions centered around the hippocampus, located deep in the brain (e.g., Subiculum, Entorhinal Cortex) (Insausti & Amaral, 2004). You may have heard about the hippocampus in relation to learning and memory (Scoville & Milner, 1957), however, in cooperation with other regions of the hippocampal formation, it does much more than just that (Bird & Burgess, 2007). 

So, what do you need to know to get to the fridge? Probably your location within your house, where your head is facing, how far you are from the closest walls, and if you start walking, which direction you are headed. If you already know something about the brain, it comes as no surprise that it has a specific mechanism for each of these different percepts. However, what may be unexpected is that each spatial percept has its own cell type dedicated to processing it (Hartley et al., 2014).

Each spatial percept has its own cell type dedicated to processing it.


For example, place cells signal the position of the agent (you) in the environment. Each place cell is responsible for one (and only one) given subregion (position) in the space, at which its firing rate (i.e., activity) increases (O’Keefe & Dostrovsky, 1971). 

A different type of cells, boundary cells, inform us about the delimitations, or boundaries, of the environment. To a boundary cell, a wall and a cliff look quite similar. They are both navigational barriers (Solstad et al., 2008). Once your position in space is established, and the navigational barriers are identified, you still need to know what direction you are facing to navigate successfully towards the fridge. 

Head-direction cells, true to their name, allow us to accomplish just that. They serve as our internal compass since each of them responds to one specific allocentric orientation – in other words, they respond to absolute directions like East/West, not self-centered directions like right/left. (Taube et al., 1990). 

Grid cells generate a brain signal that enables agents to keep track of the distance traveled from some position in space to the next (that can be characterized in terms of x and y coordinates) while integrating information about the movement direction (Hafting et al., 2005). This ability is called path integration and is essential for successful navigation in space (McNaughton et al., 2006). They have been more difficult to identify because their activation pattern becomes apparent only once the agent has covered the whole surface of an environment. These cells fire in a remarkable regularity, forming a grid that is uniquely symmetrical and is referred to as six-fold symmetry (see the GIF figure) – that might remind you of some Escher paintings, or a beehive. It has been proposed that the hexagonal grid-cell patterns allow the brain to switch between different scales or orders of magnitude (Stensola et al., 2012) and, hence, use the same system to navigate from the couch to the fridge and, occasionally, all the way to our favorite restaurant.

The navigation of physical spaces seems to be relatively straightforward (even though there are still a lot of unknowns): different cells track different spatial properties and keep us oriented in our environment (Hartley et al., 2014). However, how are these brain mechanisms engaged in navigation in abstract, conceptual spaces and how do these support higher-level thinking? What do physical and conceptual spaces have in common? When answering these questions, grid cells will be of particular interest to us because their role goes beyond navigating physical spaces and are also heavily involved in the navigation of conceptual spaces. To better understand the relationship between physical and conceptual space, let’s first look at a physical space organization on a slightly more abstract level. 

When you know an environment (e.g., the city you live in) and its landmarks (e.g., your house, the hospital, the church, or your favorite restaurant), your brain maps the spatial relations between these sites and creates a ‘map’. The mechanisms encoding these maps may differ based on the type of relations they represent (e.g., site-to-site air distance (i.e., Euclidean distance) or site-to-site distance along walkable routes). Crucially, one of these representations is an allocentric map of the environment (the city, but also just the house, or the room) – much like what you’d see on a GPS. In this kind of representation, space is represented in two dimensions, and a point can be identified in terms of its coordinates on the plane. Interestingly, the different types of relationships encoded in these maps can also be differentiated using the patterns of brain activity during navigation in physical environments. This is referred to as cognitive maps and graphs (Peer et al., 2021).

We can use the same framework to think about conceptual spaces. Think of two objects, let’s say animals, and two features, speed and size. If we were to think about the two animals (e.g., cheetah and elephant) in a 2D space (just like if you were thinking about the location of two sites in your city), we can use the two features to serve as our x and y axes. We now have a 2D space defined by ‘size’ and ‘speed’ axes (x and y). Elephants are quite big, which puts them high on the size axis but are not very fast, placing them low on the speed axis. Cheetahs, on the other hand, are quite small but very fast, which would place them on the other side of each scale, compared to elephants. In a 2D space that is defined by speed and size (x and y axis, respectively), elephants are now close to the top left corner and cheetahs close to the bottom right. Now, if you were to consider a turtle, you’d know where to place it. Using this strategy, we can map basically any (concrete or abstract) dimension of whatever (concrete or abstract) concept. For instance, we often classify fellow human beings into hierarchies based on abstract dimensions such as competence, prestige, and popularity. We evaluate commercial products in terms of quality versus price. The list goes on.

Earlier, we hinted that there are similarities between how grid cells fire in physical spaces and conceptual spaces. Well, as a matter of fact, the patterns are exactly the same. How is this possible? Using the idea of conceptual spaces as 2D planes, the relationship between conceptual and physical space mapping seems clear. But how does one ‘move’ in such conceptual space?

The best way to put this into perspective is with a couple of examples. In a pioneering study, Constantinescu et al., 2016 trained participants on a simple task. They were presented with drawings of different types of birds. The birds differed systematically in the length of their necks and legs and were each associated with an arbitrary symbol. The symbols were then mapped onto a 2D space, where the x-axis represented leg size and the y-axis represented neck size (similar to our animal example from earlier with size and speed). Using this logic, the symbols for birds with short legs and necks were located in the bottom left corner of the space, and those for birds with long legs and necks were in the top right corner. During the test session inside an MRI scanner, participants saw a short movie in which the birds were morphing (the neck and leg lengths were changing based on a predefined ratio). Participants were asked to imagine the bird continuing to morph at the same ratio (e.g., for every unit increase in neck length, there is a two-unit decrease in leg length). Finally, they were asked what symbol corresponds to the final form of the bird (Constantinescu et al., 2016). Imagining the birds’ morphing can be understood as simultaneously updating values on the leg and neck axes and hence, producing a ‘movement’ in the 2D bird space.  

In another study, Nitsch and colleagues (2024) presented participants with a sequence of number pairs (e.g., step 1: 68 vs. 41, step 2: 63 vs. 48, step 3: 58 vs. 55, step 4: probe). After a few times the changing values were presented, participants were probed to indicate which value (left or right) would be the higher at the next step of the sequence (Nitsch et al., 2024). Here, the number pairs at each step could be conceptualized as x- and y-axis coordinates on a 2D plane, and their relative rate of change as movement along a specific axis on this plane.

In both studies, the authors found that performing these non-spatial tasks produced the same hexagonal modulation of brain activity in the entorhinal cortex which is typically found during navigation of physical space (Doeller et al., 2010). Even more interesting is that the participants in these studies generally report not using a 2D space to carry out the task.

A single mechanism in our brain is responsible for navigating both conceptual and physical spaces.

These findings suggest that a single mechanism in our brain is responsible for navigating both conceptual and physical spaces. We can argue that the brain uses these ‘primitive’ and mechanistic mechanisms to make complex cognitive tasks manageable. The brain presumably does this to recycle the already existing networks. At the end of the day, our brains encounter very similar problems to the problems that mice brains encounter, but on a more complex level.  While we may have a basic grasp of how our brains map the physical and conceptual spaces, it is just the first step on our path to an understanding of the whole system, and a wondrous adventure lies ahead. 

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Written by Daniel Janko and Carlotta Isabella Zona
Illustrated by Maria Vogel
Edited by Marisa Guajardo, Alli Lindquist, and Julia LaValley

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References 

Bird, C. M., & Burgess, N. (2008). The hippocampus and memory: Insights from spatial processing. Nature Reviews Neuroscience, 9(3), 182–194. https://doi.org/10.1038/nrn233

Constantinescu, A. O., O’Reilly, J. X., & Behrens, T. E. J. (2016). Organizing conceptual knowledge in humans with a gridlike code. Science, 352(6292), 1464–1468. https://doi.org/10.1126/science.aaf0941

Doeller, C. F., Barry, C., & Burgess, N. (2010). Evidence for grid cells in a human memory network. Nature, 463(7281), 657–661. https://doi.org/10.1038/nature08704

Hafting, T., Fyhn, M., Molden, S., Moser, M.-B., & Moser, E. I. (2005). Microstructure of a spatial map in the entorhinal cortex. Nature, 436(7052), 801–806. https://doi.org/10.1038/nature03721

Hartley, T., Lever, C., Burgess, N., & O’Keefe, J. (2014). Space in the brain: How the hippocampal formation supports spatial cognition. Philosophical Transactions of the Royal Society B: Biological Sciences, 369(1635), 20120510. https://doi.org/10.1098/rstb.2012.0510

Insausti, R., & Amaral, D. (2004). Hippocampal Formation. In The Human Nervous System (pp. 871–914). https://doi.org/10.1016/B978-012547626-3/50024-7

McNaughton, B. L., Battaglia, F. P., Jensen, O., Moser, E. I., & Moser, M.-B. (2006). Path     integration and the neural basis of the “cognitive map.” Nature Reviews Neuroscience, 7(8), 663–678. https://doi.org/10.1038/nrn1932

Nitsch, A., Garvert, M. M., Bellmund, J. L. S., Schuck, N. W., & Doeller, C. F. (2024). Grid-like entorhinal representation of an abstract value space during prospective decision making. Nature Communications, 15(1), 1198. https://doi.org/10.1038/s41467-024-45127-z

O’Keefe, J., & Dostrovsky, J. (1971). The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. Brain Research, 34(1), 171–175. https://doi.org/10.1016/0006-8993(71)90358-1

Peer, M., Brunec, I. K., Newcombe, N. S., & Epstein, R. A. (2021). Structuring Knowledge with Cognitive Maps and Cognitive Graphs. Trends in Cognitive Sciences, 25(1), 37–54. https://doi.org/10.1016/j.tics.2020.10.004

Scoville, W. B., & Milner, B. (1957). LOSS OF RECENT MEMORY AFTER BILATERAL HIPPOCAMPAL LESIONS. Journal of Neurology, Neurosurgery, and Psychiatry, 20(1), 11–21. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC497229/

Solstad, T., Boccara, C. N., Kropff, E., Moser, M.-B., & Moser, E. I. (2008). Representation of Geometric Borders in the Entorhinal Cortex. Science, 322(5909), 1865–1868. https://doi.org/10.1126/science.1166466

Stensola, H., Stensola, T., Solstad, T., Frøland, K., Moser, M.-B., & Moser, E. I. (2012). The entorhinal grid map is discretized. Nature, 492(7427), 72–78. https://doi.org/10.1038/nature11649

Taube, J. S., Muller, R. U., & Ranck, J. B. (1990). Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 10(2), 420–435. https://doi.org/10.1523/JNEUROSCI.10-02-00420.1990

Author

  • Daniel Janko

    I am a master’s student in cognitive science at the University of Potsdam, Germany. I worked as a research assistant at UAB researching emotional processing in epilepsy patients using sEEG, and also did some work on somatosensory mapping using fMRI. Currently, I am working on a project examining potential behavioral effects of the entorhinal cortex. We hope to find biases in behavior that would correspond to the functional organization of grid cells in the entorhinal cortex. In my free time, I enjoy exercising, playing video games, cooking, traveling, and exploring new cultures (mostly through food).

Daniel Janko

I am a master’s student in cognitive science at the University of Potsdam, Germany. I worked as a research assistant at UAB researching emotional processing in epilepsy patients using sEEG, and also did some work on somatosensory mapping using fMRI. Currently, I am working on a project examining potential behavioral effects of the entorhinal cortex. We hope to find biases in behavior that would correspond to the functional organization of grid cells in the entorhinal cortex. In my free time, I enjoy exercising, playing video games, cooking, traveling, and exploring new cultures (mostly through food).

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