Originally published 2018-06-27.
In June 2017 a team from Switzerland's Blue Brain Project reported that networks of neurons form geometric structures with up to seven dimensions, and in a few cases up to eleven. Headlines soon announced that scientists had found a “multidimensional universe” inside the brain. The real finding is less mystical and more interesting: the “dimensions” are a mathematical way of describing how tightly groups of neurons are wired together, not hidden extra directions of space inside your skull.
The work used a branch of mathematics called algebraic topology to map patterns of connection in a detailed computer model of a small piece of rat brain, then checked some of those patterns in real tissue. It suggested that when the brain processes information, it briefly builds and then dismantles increasingly complex structures of linked neurons. Here is what the researchers actually did, what “eleven dimensions” means in this context, and why the study still matters for understanding how brains turn wiring into thought.
What the Blue Brain Project discovered
The study, titled Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function, was published on 12 June 2017 in the journal Frontiers in Computational Neuroscience. Its first author was Michael Reimann of the Blue Brain Project, working with colleagues including mathematician Kathryn Hess of EPFL in Lausanne, Ran Levi of the University of Aberdeen, Paweł Dłotko of INRIA in France and the project's founding director, Henry Markram.
The team analysed a digital reconstruction of a tiny chunk of rat neocortex containing about 31,000 neurons and roughly 8 million connections between them. Rather than looking at single cells or random pairs, they searched for groups of neurons in which every member connects to every other member, a pattern mathematicians call a clique. They then looked at the gaps, or cavities, left between groups of these cliques.
The numbers were striking. In the official announcement, Markram said that there are tens of millions of such objects even in a small speck of brain, “up through seven dimensions”
, and that some networks contained structures of up to eleven dimensions. The paper itself reports directed cliques of up to six or seven dimensions throughout the reconstructions, and far more of them than would be expected in randomly wired networks of the same size.
What “dimension” means here
This is where most popular coverage went wrong. In everyday language a dimension is a direction you can move in: up and down, left and right, forward and back. In topology, dimension can describe the complexity of a shape built from simple pieces.
Think of it like this. Two connected neurons make a line, a one-dimensional object. Three neurons all connected to each other make a filled triangle, which is two-dimensional. Four all-to-all connected neurons make a tetrahedron, a three-dimensional pyramid. Each extra neuron that connects to all the others adds one more dimension to the abstract shape, even though the cells themselves still sit in ordinary three-dimensional tissue. A clique of eight neurons is therefore a seven-dimensional object, and a clique of twelve would be eleven-dimensional.
The cliques in this study were also directed. Signals in the brain flow one way across a synapse, so each clique had a single “source” neuron that sends signals to the rest and a single “sink” neuron that receives from all the others. That structure makes the cliques a natural route for information to travel through a group of cells.
Mathematicians use high-dimensional spaces all the time to describe complex systems outside physics. The state of a system with many moving parts can be described as a point in a space with one dimension for each variable, as Cees van Leeuwen of KU Leuven, reportedly one of the paper's reviewers, pointed out at the time. Nothing in the study suggests that the brain contains hidden spatial dimensions or a separate universe.
How the team tested the idea
A pattern found in a computer model is only as good as the model, so the researchers ran several checks.
- Comparisons with random networks. They built control networks with the same number of neurons and connections but arranged at random or with simpler biological rules. The real reconstruction had far more high-dimensional cliques, and the controls showed no cavities above three or four dimensions, while the brain model showed them in five.
- Tests in living tissue. Using a technique called multi-neuron patch clamp, the team recorded from up to 12 neurons at once in thin slices of the somatosensory cortex of young rats. Across 55 experiments they found the same kind of directed cliques, up to three and four dimensions, which is about what you would expect from sampling only a handful of cells at a time.
- Simulated activity. They stimulated the virtual tissue with nine different input patterns and watched which cliques and cavities formed as signals spread.
The team also found that the more high-dimensional cliques two neurons shared, the more their firing was correlated. That is the “missing link” in the paper's title: a measurable relationship between how a circuit is built and how it behaves.
The video below gives a visual sense of the kind of network structures the team was mapping.
Structures that appear and vanish in milliseconds
The most memorable result came from the simulated activity. When the model was stimulated, neurons did not simply fire in a blur. Activity first bound neurons into low-dimensional structures, about 50 milliseconds after the stimulus, then into progressively higher-dimensional cliques and cavities, before the whole arrangement broke apart again. The same sequence appeared for every stimulus the team tried, although its strength varied.
Ran Levi offered the image that made the story famous: the activity, he said, behaves like a multi-dimensional sandcastle that rises out of the sand and then falls apart. Kathryn Hess compared algebraic topology to a telescope and microscope at once, because it can zoom in on fine detail in a network and also reveal its large-scale shape.
Markram suggested that memories might be hiding in these high-dimensional cavities. That was speculation, flagged as such, and it remains an open question rather than a finding.
Why it matters, and what it does not show
The study's lasting contribution is methodological. Brain networks are so dense that looking at them one connection at a time tells you little. Topology offers a way to summarise their organisation in a few meaningful numbers, and researchers have since tried similar tools on other neural datasets.
Some limits are worth keeping in mind:
- The main analysis was done on a model of a small region of rat cortex, not on a human brain.
- The living-tissue tests sampled a dozen neurons at a time, enough to confirm small cliques but not the larger ones seen in the model.
- The link between these structures and memory or thought is a hypothesis that still needs testing.
Common myths about the “11-dimensional brain”
- Myth: the brain exists in eleven spatial dimensions. No. The neurons sit in normal 3D space; the dimensions describe connection patterns.
- Myth: this is linked to string theory's eleven dimensions. The number is a coincidence. M-theory's dimensions are physical, while these are mathematical properties of a network.
- Myth: scientists found where consciousness lives. The study says nothing about consciousness directly.
What happened to the Blue Brain Project
The Blue Brain Project was founded in 2005 at EPFL, the Swiss Federal Institute of Technology in Lausanne, by Henry Markram, with the ambitious aim of building detailed digital reconstructions and simulations of the mammalian brain. It began on an IBM Blue Gene supercomputer and, in 2015, published a simulation of a piece of rat neocortex with around 30,000 neurons the kind of detailed reconstruction analysed in the 2017 study.
The project was often criticised for over-promising, and a 2021 documentary, In Silico, followed its shifting goals over a decade. It nonetheless produced a large body of open data and tools, including the topology methods described here. The project formally ended in December 2024 after almost twenty years.
For anyone curious about the brain, the takeaway is reassuring rather than spooky. Your brain is not a portal to another universe. It is something arguably more remarkable: a three-dimensional organ whose wiring is organised in such intricate, layered ways that we need the language of higher-dimensional mathematics just to describe it.
Sources: Reimann et al. 2017, Frontiers in Computational Neuroscience; Frontiers announcement; Wikipedia: Blue Brain Project; Blue Brain Project, EPFL; Rechargemind.
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