New Evidence for the Strange Geometry of Thought - Facts So Romantic

By Adithya Rajagopalan on Feb 08, 2019

The brain may represent concepts in the same way that it represents space and your location, by using the same neural circuitry for the brain’s “inner GPS.”Sharon Mollerus / M.C. Escher / Flickr

In 2014, the Swedish philosopher and cognitive scientist Peter Gärdenfors went to Krakow, Poland, for a conference on the mind. He was to lecture at Jagiellonian University, courtesy of the Copernicus Center for Interdisciplinary Studies, on his theory of conceptual, or “cognitive,” spaces. Gärdenfors had been working on his idea of cognitive spaces, which explain how our brains represent concepts and objects, for decades. In his book Conceptual Spaces, from 2000, he wrote, “It has long been a common prejudice in cognitive science that the brain is either a Turing machine working with symbols or a connectionist system using neural networks.” In Krakow, Gärdenfors pushed against that prejudice. In his talk, “The Geometry of Thinking,” he suggested that humans are able to do things that today’s powerful computers can’t do—like learn language quickly and generalize from particulars with ease (to see, in other words, without much training, that lions and tigers are four-legged felines)—because we, unlike our computers, represent information in geometrical space.

In a 2018 Science paper, co-authored with Jacob Bellmund, Christian Doeller, and Edvard Moser—neuroscientists from the Max Planck Institute in Leipzig and the Kavli Institute in Trondheim—Gärdenfors, of the University of Lund, buttressed his idea with recent advances in brain science. He argued that the brain represents concepts in the same way that it represents space and your location, by using the same neural circuitry for the brain’s “inner GPS.”

“Cognitive spaces are a way of thinking about how our brain might organize our knowledge of the world,” Bellmund said. It’s an approach that concerns not only geographical data, but also relationships between objects and experience. “We were intrigued by evidence from many different groups that suggested that the principles of spatial coding in the hippocampus seem to be relevant beyond the realms of just spatial navigation,” Bellmund said. The hippocampus’ place and grid cells, in other words, map not only physical space but conceptual space. It appears that our representation of objects and concepts is very tightly linked with our representation of space.

Gärdenfors’ theory highlights a fruitful path, not only for cognitive scientists, but for neurologists and machine-learning researchers.

Work spanning decades has found that regions in the brain—the hippocampus and entorhinal cortex—act like a GPS. Their cells form a grid-like representation of the brain’s surroundings and keep track of its location on it. Specifically, neurons in the entorhinal cortex activate at evenly distributed locations in space: If you drew lines between each location in the environment where these cells activate, you would end up sketching a triangular grid, or a hexagonal lattice. The activity of these aptly named “grid” cells contains information that another kind of cell uses to locate your body in a particular place. The explanation of how these “place” cells work was stunning enough to award scientists John O’Keefe, May-Britt Moser, and Edvard Moser, the 2014 Nobel Prize in Physiology or Medicine. These cells activate only when you are in one particular location in space, or the grid, represented by your grid cells. Meanwhile, head-direction cells define which direction your head is pointing. Yet other cells indicate when you’re at the border of your environment—a wall or cliff. Rodent models have elucidated the nature of the brain’s spatial grids, but, with functional magnetic resonance imaging, they have also been validated in humans.

Hexagonal latticeWikicommons

Recent fMRI studies show that cognitive spaces reside in the hippocampal network—supporting the idea that these spaces lie at the heart of much subconscious processing. For example, subjects of a 2016 study—headed by neuroscientists at Oxford—were shown a video of a bird’s neck and legs morph in size. Previously they had learned to associate a particular bird shape with a Christmas symbol, such as Santa or a Gingerbread man. The researchers discovered the subjects made the connections with a “mental picture” that could not be described spatially, on a two-dimensional map. Yet grid-cell responses in the fMRI data resembled what one would see if subjects were imagining themselves walking in a physical environment. This kind of mental processing might also apply to how we think about our family and friends. We might picture them “on the basis of their height, humor, or income, coding them as tall or short, humorous or humorless, or more or less wealthy,” Doeller said. And, depending on whichever of these dimensions matters in the moment, the brain would store one friend mentally closer to, or farther from, another friend.

But the usefulness of a cognitive space isn’t just restricted to already familiar object comparisons. “One of the ways these cognitive spaces can benefit our behavior is when we encounter something we have never seen before,” Bellmund said. “Based on the features of the new object we can position it in our cognitive space. We can then use our old knowledge to infer how to behave in this novel situation.” Representing knowledge in this structured way allows us to make sense of how we should behave in new circumstances.

Data also suggests that this region may represent information with different levels of abstraction. If you imagine moving through the hippocampus, from the top of the head toward the chin, you will find many different groups of place cells that completely map the entire environment but with different degrees of magnification. Put another way, moving through the hippocampus is like zooming in and out on your phone’s map app. The area in space represented by a single place cell gets larger. Such size differences could be the basis for how humans are able to move between lower and higher levels of abstraction—from “dog” to “pet” to “sentient being,” for example. In this cognitive space, more zoomed-out place cells would represent a relatively broad category consisting of many types, while zoomed-in place cells would be more narrow.

Yet the mind is not just capable of conceptual abstraction but also flexibility—it can represent a wide range of concepts. To be able to do this, the regions of the brain involved need to be able to switch between concepts without any informational cross-contamination: It wouldn’t be ideal if our concept for bird, for example, were affected by our concept for car. Rodent studies have shown that when animals move from one environment to another—from a blue-walled cage to a black-walled experiment room, for example—place-cell firing is unrelated between the environments. Researchers looked at where cells were active in one environment and compared it to where they were active in the other. If a cell fired in the corner of the blue cage as well as the black room, there might be some cross-contamination between environments. The researchers didn’t see any such correlation in the place-cell activity. It appears that the hippocampus is able to represent two environments without confounding the two. This property of place cells could be useful for constructing cognitive spaces, where avoiding cross-contamination would be essential. “By connecting all these previous discoveries,” Bellmund said, “we came to the assumption that the brain stores a mental map, regardless of whether we are thinking about a real space or the space between dimensions of our thoughts.”

Scientists still need to experimentally verify the link between the hippocampus and higher-order cognitive functions in humans. fMRI studies like the ones from the group in Oxford are, as yet, only suggestive. “Although the coarse nature of the fMRI signal urges caution in making conclusions at the level of neuronal codes,” the researchers concluded, “we have reported an unusually precise hexagonal modulation of the fMRI signal during nonspatial cognition.” It is also unknown whether place cells can actually represent objects at particular locations in a cognitive space. Revealing this in experiments with human subjects is hard, since they require very fine-resolution brain imaging. But recent advances in higher-resolution fMRI could possibly provide a solution.

Bellmund pointed out that rodent research could also reveal the existence of cognitive spaces. A 2017 paper, for example, found that place cells in rats can form a map of sound frequencies. Different cells in the hippocampus respond to different frequencies of sound—forming a cognitive space of sound. What’s more, studies in humans that have seen grid-like activity in the hippocampus have also seen this activity in other parts of the cortex. Therefore, it is highly likely that complicated, higher-order cognitive abilities arise from interactions between several parts of the brain.

Gärdenfors’ theory highlights a fruitful path, not only for cognitive scientists, but for neurologists and machine-learning researchers. It is a kind of incomplete, generic sketch on a canvas that invites refinement and elaboration. Cognitive spaces are, as Gärdenfors and Bellmund put it, a “domain-general format for human thinking,” an “overarching framework” that can help unravel the causes of neurodegenerative diseases, like Alzheimer’s, and “to inform novel architectures in artificial intelligence.”

Adithya Rajagopalan is a second-year graduate student in the department of neuroscience at Johns Hopkins University & Janelia Research Campus. Follow him on Twitter @adi_e_r.

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