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Somewhere inside your head, the story goes, neurons are building an eleven-dimensional sandcastle. A thought arrives, the structure rises, and a moment later the whole thing vanishes. It has the ingredients of an extraordinary discovery: an invisible universe, a supercomputer, and the suggestion that the mind is far stranger than the person using it.

But the most interesting possibility is not that a hidden dimension makes you intelligent. It is that mastery may be partly a matter of architecture: what different pieces of a brain can do together, and how practice changes the arrangements available to them.

The research behind the post is real, and mathematically ingenious. The dimensions belong to a description of neural connections, however, not to extra physical directions hidden inside a skull. The main experiments used reconstructed rat cortical networks, not human masters solving problems. And the experiments did not compare beginners with experts, train intelligence, or measure creativity. [1]

The correction leaves behind a better question. When you learn something difficult, do you simply add information—or change the ways your brain can bring information to bear? To answer that, we have to move from a simulated piece of rat cortex to studies in which people actually learned something.

What the Blue Brain researchers found

In a 2017 paper in Frontiers in Computational Neuroscience, a collaboration led by researchers including Michael Reimann, Kathryn Hess, Ran Levi, and Henry Markram applied algebraic topology to the wiring and simulated activity of neocortical circuits. Their biologically informed reconstruction represented roughly 31,000 neurons and eight million directed synaptic connections. [1]

On an ordinary connectivity map, every neuron is a dot and every synapse a line. At this scale the drawing looks less like a machine than a thicket. Dots represent neurons; the lines indicate which neuron can send a signal to another. The arrows matter. A fully connected group with an orderly source-to-destination direction is called a directed clique. Mathematically it can be represented by a simplex. With three appropriately connected neurons, the simplex has dimension two; with four, dimension three. The dimension counts the network's combinatorial structure—not physical directions you could travel through. [1]

Cliques can overlap without forming an even larger clique. In the resulting abstract object, their arrangement can enclose a mathematical cavity. No cavity opens in the tissue. The hole exists in the mathematics: an absent filling revealed by the arrangement of connected groups. Algebraic topology lets scientists count those structures and examine how a complicated local web gives rise to patterns across the larger network. [1]

In the main digital rat-neocortex reconstructions, the team found directed simplices reaching dimensions six or seven and many more structured groups than in comparison networks assembled using several random or simplified wiring rules. In the press material accompanying the research, Markram described structures as high as eleven dimensions in some networks. Those claims should not be collapsed into the assertion that eleven-dimensional objects were physically witnessed appearing in living human brains. [1][2]

When simulated sensory-like inputs reached the modeled neurons, groups with correlated activity formed and dissolved in a patterned sequence. The research linked existing structural connections with the temporary arrangements of active neurons. As mathematician Ran Levi put it in the accompanying account, it resembled a multidimensional sandcastle being built and then dismantled. The sandcastle was a metaphor for an evolving mathematical description of simulated activity, not a literal construction rising inside skull tissue. [1][2]

The researchers also made recordings in rat-brain slices. Across 55 experiments, they observed directed simplices as high as dimension three and one example at dimension four. The original paper explicitly said the highest-dimensional examples had not been directly observed in living tissue, because recording enough cells simultaneously remained difficult. The biological recordings support part of the connectivity picture; they do not establish the complete simulated activity sequence at the highest reported dimensions. [1]

The most valuable part of the story may be the point at which the beautiful mathematics meets a stubborn electrode. A pattern is visible in the reconstruction; observing its largest forms directly is another problem. The unknown is not whether an extra universe has appeared. It is how much of that intricate organization matters to real computation.

Learning does not leave the network alone

The first week with a difficult piano passage can feel like negotiating with ten fingers that have never met. Each note asks for a decision. A practiced passage, by contrast, can leave room to listen ahead, shape a phrase and notice what the music needs next. The keys have not moved. The demands on the player have.

That familiar experience does not demonstrate higher-dimensional cliques. It does suggest a more testable idea: mastery changes the relationship among perception, movement, memory, and control.

Human brain-imaging studies have documented changes associated with training. In a 2004 Nature study, volunteers who learned to juggle showed selective, reversible changes in gray-matter measurements in areas involved in processing visual motion. The scan did not reveal the precise synapses altered, but it undermined the idea that adult brain anatomy remains wholly fixed while a skill improves. [3]

A 2009 longitudinal study of children learning an instrument found structural brain changes after fifteen months of music training. Those changes tracked improvements in motor and auditory abilities relevant to music. The design strengthens the case that experience contributes to measured structural differences, although MRI cannot reveal a new topological cavity or establish that any one structural change produced the improved performance. [4]

We have evidence, then, for the broad proposition that sustained practice can alter the brain. We do not yet have a demonstration that training increases the dimensions of the Blue Brain structures, or that such an increase would produce mastery. There is an important distance between those claims.

Expertise may be a change in coordination, not simply more activity

A more direct bridge comes from work by network neuroscientist Danielle Bassett and colleagues. In a 2011 human motor-learning study, the researchers followed changing functional connections during practice. Brain areas were grouped into communities, or modules, whose membership could shift over time. A measure of this shifting—network flexibility—during one session predicted improvement on the skill in a later session. [5]

A brighter patch on a brain scan asks where activity changed. This approach asks something different: who was working with whom, and when did those partnerships shift? Its predictive result makes coordination an interesting part of learning rather than mere background noise. But it is a correlation and prediction within a specific motor task; it does not show that making a network more flexible by any means necessarily makes someone smarter. [5]

A later study from the same research program reported increasing autonomy of sensorimotor systems as people learned a simple motor skill. The reduced involvement of certain cognitive-control connections was associated with subsequent learning rates. A plausible reading is that early learning recruits broad coordination and practiced performance can become less dependent on it. The brain need not engage everything at full volume to do something well. [6]

This suggests a useful distinction. Complexity is not the same as capability. An efficient system can route a familiar problem through specialized circuits while remaining able to recruit other systems when the task changes. Expertise might include both stable pathways for what is known and flexible ways to assemble them for what is new.

No one should conclude from these studies that expert brains have more eleven-dimensional cavities. The human work measures large-scale functional connectivity, usually with MRI, while the original Blue Brain work counted detailed arrangements of directed connections among individual neurons in reconstructed rat tissue. Both investigate organization, but at very different scales and with different instruments.

Creativity may depend on unlikely collaborations

Mastery explains practiced performance. Creativity asks a harder question: how does a system draw useful connections between ideas that normally live apart?

A 2018 study in Proceedings of the National Academy of Sciences recorded brain activity from 163 participants while they generated unusual uses for familiar objects. Researchers identified patterns of functional connectivity involving the default, salience, and executive-control networks. Those patterns predicted differences in performance on the creativity task and showed predictive value in additional datasets. [7]

The result is intriguing because these networks have distinct roles. The default network is associated with memory and internally directed thought; executive systems are implicated in goal maintenance and evaluation; salience-related regions help identify what deserves attention. In the study, more creative performance was associated with coordinated activity spanning systems that are often discussed separately. [7]

That does not mean an MRI can certify an artist's talent or that a person's creative potential is written immutably in a network diagram. The researchers measured particular forms of divergent thinking, not every kind of scientific discovery, musical composition, or original work. The study was observational: it did not train network connections to prove that the pattern causes creativity. [7]

Still, it gives the architectural idea substance. A useful new idea may need two abilities that pull in different directions: wandering far enough to encounter an unlikely connection, then returning with enough discipline to decide whether it is any good. The insight is not simply the spark. It is the spark and the judgment that keeps it.

Could intelligence itself be architectural?

A study published in Nature Communications in January 2026 gives the question a new human-data chapter. Its investigators combined structural and functional brain-imaging measures in 831 healthy young adults, using a model that estimated relationships between network organization and a general-intelligence factor drawn from cognitive tests. A related analysis in an independent sample of 145 supported aspects of the theoretical framework. [8]

In the main sample, the whole-brain model explained about 12 percent of the variance in measured general-intelligence scores. The authors described contributions from distributed communication, long-range connections, coordinating regions, and a balance between local clusters and global integration. That is evidence that a particular description of network architecture carries information about cognitive differences—not evidence that a scan explains intelligence in full. [8]

The field has also seen less encouraging results. A 2018 replication using Human Connectome Project data did not find a robust relationship between general intelligence and simpler global network-efficiency measures across several ways of defining a brain network. Different measures and models can produce different results. [9]

This is an argument for more precise science, not for abandoning the architectural hypothesis. If intelligence is partly about how information moves, researchers must show which features matter, whether they generalize, and whether changing them changes a person's abilities. Correlation between a scan and a cognitive score is not yet an engineering blueprint for improving either one.

A city is a better analogy than a tower. Neighborhoods do specialized work. A handful of distant bridges make cooperation possible. When the same event happens every morning, established routes may be enough. When something unexpected happens, the ability to redirect traffic matters. Counting streets tells you less than knowing which journeys they permit.

As an analogy this helps; as a measurement model it still needs testing. A brain is not obliged to behave like a city, and its activity has timing, chemical signals, inhibition, and plasticity that no road map captures on its own.

What this does—and does not—mean for training

If you want to master something, the evidence supports a relatively modest principle: practice the actual skill and its component demands, and expect the brain's organization to participate in the learning process. Focused music practice improves music-related abilities; motor practice improves the practiced movement. The imaging data give plausible biological context. [4][5][6]

The evidence is far weaker for the idea that raising a generic measure of brain complexity would improve everything else. A major 2016 review of commercial brain-training claims found extensive evidence of improvement on trained tasks, less evidence for closely related tasks, and little convincing evidence that such programs improve distant tasks or everyday functioning. [10]

The distinction matters for deliberate training. Repetition is not magic. The task, feedback, progression, and the ability to use what was learned in a real setting matter more to the claim than a dramatic picture of neurons lighting up. None of the studies reviewed here identifies a training method that reliably increases topological dimension or general intelligence by assembling more neuronal cliques.

A practical possibility follows—but remains a hypothesis: skill development may depend partly on refining which circuits cooperate, which become more specialized, and when the brain recruits wider networks to solve a new problem. Research on learning, creativity and intelligence makes that worth studying. It does not yet allow us to prescribe a particular architecture.

The structure worth building

The appeal of the eleven-dimensional story is that it replaces the old picture of the brain as a container for facts with something more dynamic: a network whose arrangements help shape what it can do.

That shift is useful even after the headline is corrected. The 2017 researchers did not discover a hidden human superpower. They provided a mathematical language for structure and activity in modeled and sampled rat circuits. Separate human studies show that learning can change brain measurements and that network organization correlates with aspects of skill and creativity. A newer study extends the architectural argument to measured intelligence while leaving important uncertainty about cause, scope, and replication. [1][4][5][7][8][9]

What practice may gradually change, then, is not merely what the brain contains. It may change which parts can find one another when something difficult has to be done.

In the model, the sandcastle builds itself in a moment and disappears. Mastery is slower: a capacity gradually taking shape through attempts, errors, and repetition. We cannot yet count its dimensions. We can begin to ask which connections make it possible.

Keep exploring the evidence

For a different question about cognition, read what small creatine studies can and cannot tell us about a sleep-deprived brain. That research concerns a specific intervention and setting, rather than a general method for building intelligence.

See how we evaluate scientific evidence for the distinctions between observational results, experiments and broader claims.

Sources

[1] Reimann MW et al. (2017). Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function. Frontiers in Computational Neuroscience.

[2] Frontiers (June 12, 2017). Blue Brain Team Discovers a Multi-Dimensional Universe in Brain Networks. Research news; interpretations and quotations from researchers, not additional independent results.

[3] Draganski B et al. (2004). Neuroplasticity: Changes in grey matter induced by training. Nature.

[4] Hyde KL et al. (2009). Musical training shapes structural brain development. Journal of Neuroscience.

[5] Bassett DS et al. (2011). Dynamic reconfiguration of human brain networks during learning. PNAS.

[6] Bassett DS et al. (2015). Learning-induced autonomy of sensorimotor systems. Nature Neuroscience.

[7] Beaty RE et al. (2018). Robust prediction of individual creative ability from brain functional connectivity. PNAS.

[8] Wilcox RR et al. (2026). The network architecture of general intelligence in the human connectome. Nature Communications.

[9] Kruschwitz JD et al. (2018). General, crystallized and fluid intelligence are not associated with functional global network efficiency. NeuroImage.

[10] Simons DJ et al. (2016). Do “Brain-Training” Programs Work?. Psychological Science in the Public Interest.