The Neurogeometry of Perception: A Journey into Geometric Cognition

In the realm of cognitive science and neurology, there exists a fascinating intersection where geometry…

Decoding the Geometry of the Mind: An Exploration of Universal Geometric Cognition

In the growing field of geometric cognition, one name stands out due to her significant…

The Shape of Experience and the Hyperbolic Geometry in the Brain’s Spatial Maps

Tatyana O. Sharpee’s work in the realm of geometric cognition—a field dedicated to understanding how…

Exploring the Geometry of the Mind: How Brain Structure Dictates Function

For over a century, wave equations of physical systems have played a pivotal role in…

Sir Roger Penrose

To me, the world of perfect forms is primary (as was Plato’s own belief) —…

Buckminster Fuller’s visionary, big ideas

Buckminster R. Fuller, born on July 12, 1895, in Milton, Massachusetts, was a renowned polymath,…

Cognition and the embodiment of geometry in George Lakoff’s metaphors

George Philip Lakoff, born on May 24, 1941, is an American cognitive linguist and philosopher,…

Benoît Mandelbrot: ad infinitum

Why is geometry often described as “”cold” and “”dry?” One reason lies in its inability…

Peter Gärdenfors’ geometry of thought

Björn Peter Gärdenfors, born on the 21st of September, 1949, is a distinguished figure in…

Spiral-shaped signals of neural activity

The human brain is a complex organ responsible for various cognitive functions. Scientists from the…

An argument for hyperbolic geometry in neural circuits

In her 2019 review, Tatyana O Sharpee connects several lines of research to argue that…

The geometry of abstractions

Many forms of cognitive, emotional, and behavioral flexibility place diverse demands on brain representations, ranging…

The Geometry of Control in Architectural Design

Nikos Salingaros is a mathematician and architectural theorist who has developed a theory of architecture…

Geometric framework predicts structure from neural functions

In both biological and artificial networks, neural computing is based on the nonlinear summation of…

Beyond Core Knowledge: Natural Geometry

The origins and nature of human intuitions about the properties of points, lines, and figures…

Origins of geometric cognition

In a 2019 paper, Mateusz Hohol and Marcin Miłkowski argue that current explanations of geometric…

Graph Theory for Identifying Connectivity Patterns in Human Brain Networks

Functional connectivity and causal connections across different neural units are two main categories for how…

Encoding cognitive processes through geometric transformations

In nature and in art, geometric symmetry is everywhere. It has also progressively found its…

A paradigm shift in assumed color shape and perception

The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz…

Perceived dynamics of static images enable emotional attribution

The effect of the shapes we perceive is well-known and utilized in various domains. For…

Geometry of Brain, Dimensions of Mind

Although consciousness is a multifaceted phenomena, important aspects like awareness and alertness have only been…

Color perception by manifold learning

Psychophysics examines the connections between external physical inputs and internal mental processes. The scientific community’s…

Letter patterns alter the perception of truth

The phrase “A causes B” appears in a lot of statements that consumers come across…

The case of geometric reasoning

Understanding both the communicative and cognitive roles of language, the degree to which language facilitates…

Pattern detection and sequence learning

Humans learn and make decisions in large part through recognizing patterns. Research on the neurocomputational…

Skeletal representations of shape in the human visual cortex

Understanding how the human visual system stores item shapes and how shape is eventually utilized…

The geometry of word embeddings in semantic projections

In what way does the mental lexicon store knowledge of word meaning? Word meanings are…

Maps of conceptual spaces in the hippocampus

How are neural representations of conceptual information structured such that people may deduce relationships they…

Finding structure in the brain’s static

The entire brain experiences slow, sustained waves of electrical activity when you sleep, much like…

Infodesics and cognitive geometry

Euclidean geometry has always been regarded by scientists as being a priori and objective. When…

Circular cities benefit from more rainfall

After noticing that weather data from roughly circular cities like Dallas and London often show…

Decoding the Mathematical Secrets of Plants’ Spiraling Leaf Patterns

Plant leaves are arranged in a beautiful geometric pattern around the stem, which is known…

A geometric model for cognition: the Fundamental Code Unit of the Brain

The multidisciplinary nature of cognitive research brings the need to conceptually unify insights from multiple…

The geometry of individual and collective decision-making

A team of researchers used state-of-the-art virtual reality to show the fundamental geometrical principles that…

Peculiar patterns of vibrating floating particles

In 2020, Héctor Alarcón, at O’Higgins University, Chile, and his colleagues started studying the forces…

The fractal-hyperbolic geometry of networks

Network geometry helps us better understand complex systems at all sizes of organizations, as well…

The manifold framework of neural circuits

Manifold: a topological space that locally resembles a Euclidean space in mathematics. Perceptual manifold: the…

Geometrical concepts, cognition, and educational implications

A group of researchers from Italy and the United Kingdom analyzed the development of geometrical…

The geometry of atomic bonds

In 2012, a team from IBM’s research labs in Zurich managed to reveal the individual…

Patterns of innovation

The process of innovation is a mystery. Historically it has offered opportunities and challenges, as…

Hologram of a single photon

In 2016, scientists from the University of Warsaw created the first-ever hologram of a single…

A patterned fingerprint of the brain

Studying multiple neural networks, researchers from EPFL Switzerland found that every one of us has…

Geometric models for memories

By creating a computer program that turns sequences of events from a video into unique…

What Does It Mean That “Space Can Be Transcendental Without the Axioms Being So”?

In her 2013 study, Francesca Biagioli examines Helmholtz’s claim that space can be transcendental without…

Pure geometry and geometric cognition

Pure geometry’s cognitive foundation is mostly unknown. Even the ‘simpler’ question of what kind of…

How quantifying the shape of stories predicts their success

Narratives, and other types of speech, can be used to enlighten, entertain, and make sense…

The human quest for discovering mathematical beauty in the arts

“The human function is to ‘discover or observe’ mathematics,” said twentieth-century British mathematician G. H.…

Einstein, geometry, and experience

As far as the propositions of mathematics refer to reality, they are not certain; and…

Did Humans Invent Mathematics, or Is It a Fundamental Part of Existence?

“God made the integers, all else is man’s work,” stated German mathematician Leopold Kronecker in…

A language of thought for the mental representation of geometric shapes

Why do geometric shapes such as lines, circles, zig-zags, or spirals appear in all human…

Harpa Concert Hall: from nature to architecture

The building stands out like a vast, dazzling sculpture on the edge of land and sea,…

Hidden order in disorder

Hyperuniformity is a geometric concept to probabilistically characterise the structure of ordered and disordered materials.…

Icosahedral nano-shell designed to trap virus particles

An interdisciplinary research team at the Technical University of Munich (TUM) has developed an efficient strategy…

Intuitions of geometry: a signature of human singularity

Humans are unique among primates in their capacity to construct and control very complex systems…

Complex thoughts are enabled by fractal networks

Fractals are forms that seem similar at different sizes in the area of geometry. Shapes…

The shape of a perfect egg, defined by a universal formula

The shape of an egg has been demonstrated throughout evolution to be one of the…

Embryo geometry: a theory of evolution from a single cell to the complex vertebrate body

One of biology’s biggest mysteries is the genesis of animal form. Biologists trying to understand…

A geometric framework for protein and cell diffusion and interaction

Protein pattern generation has been extensively explored experimentally in recent years. Proteins diffusing and interacting…

Hunting Bach’s fractals

Fractals are infinitely complex patterns that are self-similar across different scales. They are created by…

Entropy and energy influence polygonal nets folding into Platonic solids

What makes an object successful at folding? Protein scientists study how an object transforms between…

Model for studying nature’s patterns.

Wings are like fingerprints for many insect species, with no two patterns being the same.…

Fractal patterns preferred by children under three years

Natural surroundings have fractal patterns that recur at various size scales, and they are also…

Neurons use fractal networks for better connectivity

Many of nature’s fractal objects benefit from the favorable functionality that comes from pattern repetition at various…

Mathematical skills improved by tri-dimensional thinking

In 2019, a nationwide study on fundamental skills in Switzerland discovered a link between children’s spatial…

Using hyperbolic geometry to map the olfactory space

In the natural environment, the sense of smell, or olfaction, is used to identify contaminants…

Geometry of the stem cell’s micro-environment can influence organ aging and susceptibility to cancer.

Stem cells are the raw materials of the body, the cells that give rise to…

Plato’s cube is nature’s preferred choice for fragmentation.

Plato is widely recognized as the first to create the concept of an atom, or the…

Number sense: emergence from the recognition of visible objects

Humans and animals have a “number sense,” or the capacity to intuitively estimate the numerosity…

Hans Jenny and the science of sound: cymatics.

This is not unregulated chaos; it is a dynamic but ordered pattern. Hans Jenny (16…

Are patterns real or imagined?

For neuroscientists studying complex systems, patterns exhibit valuable data that may or may not correspond…

World’s oldest example of applied geometry revealed by Australian mathematician.

Pythagoras of Samos is credited with several of the world’s most important mathematical theories. The…

Sounds, shapes, speech and body movements convey emotion through one shared property

People communicate their emotions using their voice, face, and movement, as well as through abstract forms such…

Mathematical Beauty Activates Same Brain Region as Great Art or Music

The beauty of mathematical formulations resides in abstracting, in simple equations, universal truths. Many people,…

Deciphering the brain’s color and shape coding

A human can identify hundreds of thousands of unique colors and forms visually, but how…

Depth and coordinates processing in neural networks

The MonoDepth model, which calculates depth from a single picture, was studied by researchers from…

Honeycomb style pattern used by the brain to code one’s position in space

A European-American research team has used electrophysiological data to prove the presence of grid-like activity…

The Scutoid: additional solution for three-dimensional packing

Tissues flex into intricate three-dimensional forms that lead to organs as an embryo grows. This…

Parametric semiology: creating meaningful architectural spaces via human patterns of behaviour

In his Parametric Semiology – The Design of Information Rich Environments (2013), Patrik Schumacher from…

Geometry, physics, and the chameleon’s change of colour

For many years, scientists thought that the chameleon’s ability to change colors was due to…

‘Multi-dimensional universe’ in brain networks

Researchers were able to identify architectural patterns that arise when the brain had to comprehend…

Tom Noddy’s Bubble Magic

“Tom Noddy introduced America and the world to Bubble Magic via television in the early…

Creating a self-assembling quasicrystal

A quasiperiodic crystal, also known as a quasicrystal, is an organized but nonperiodic structure. A…

Measuring devices from the time of Stonehenge: The chalk drums from Folkton and Lavant

Investigation on mathematical understanding and the usage of conventional units of measurement in prehistoric civilizations…

The geometry of an electron

University of Basel physicists have demonstrated for the first time how a single electron appears…

The math behind musical harmony: phase transitions and balance between order and disorder

Music, while allowing nearly unlimited creative expression, almost always conforms to a set of rigid…

The bouba/kiki effect used in character design

The bouba/kiki effect is a non-arbitrary mapping between spoken sounds and object visual form. Wolfgang…

Using moiré patterns prevents information loss in optical communications

A moiré lattice occurs when two periodic 2D patterns are layered on top of each…

22° Ice Halo displays the geometric reflection of light

A halo is an optical phenomenon caused by light interacting with ice crystals floating in…

3D Printed armor inspired by mollusks

Ling Li, associate professor in the Department of Mechanical Engineering at Virginia Polytechnic Institute and…

Long distance communications through quantum teleportation of light patterns

Quantum communication over long distances is essential for information security, and it has been shown…

Language, trees, and geometry in neural networks

Language is made of discrete structures, yet neural networks operate on continuous data: vectors in…

The fractal brain, from a single neuron’s perspective

Physicists at Washington University in St. Louis researching the brain have demonstrated that monitoring signals…

Warping geometry pushes scientific boundaries

Atomic interactions in common solids and liquids are so intricate that physicists are still baffled…

Our capacity to recognize patterns might be attributed to the brain’s drive to describe things in the simplest feasible way

Infants may recognize regular sound sequences during their first year of life. As we grow…

The First-Ever Footage of a Molecule’s Spectacular Rotation

An international team of scientists from four different universities was able to record the rapid…

Patterns typically observed in water can also be found in light

Solitons are solitary waves that may travel great distances while keeping their shape and speed…

Screening risk of dyslexia through a web-game using language-independent content

Dyslexia is a type of learning impairment that affects 5–15% of the world’s population. MusVis,…

Golden Ratio Observed In Human Skulls

For centuries, Φ has been found in human anatomy for millennia, and in recent decades,…

The golden perfection of the aortic valve

By observing the perfect geometry of a tricuspid aortic valve, a team of cardiac surgeons…

The geometry of space-time warping at the edges of a black hole

Gravity distorts our vision, distorting its surroundings as if viewed through a carnival mirror. The…

The mystery behind interstellar buckyballs

Scientists have long been perplexed by the presence of “buckyballs” — complex carbon molecules with…

Foam offers way to manipulate light

Princeton researchers discovered that a form of foam that has long been researched by scientists…

Irregularly shaped parks reduce mortality risk

Some community parks are square, reflecting the city block where they are located — but…

Mathematical laws underlying brain development have been identified.

Stanford researchers identified a pattern that regulates the development of brain cells or neurons using…

We like our math like we like our art: beautiful

Is it possible for a concept to be beautiful? Mathematicians frequently describe arguments as “beautiful”…

The Beginnings of Life: Mesmerizing Waves Swirl Over Microscopic Bodies

When an egg is fertilized, billions of proteins ripple out across its surface, producing a…

Multilayer hazes over Saturn’s hexagon

Saturn’s hexagon is a distinct and long-lasting wave. It was discovered in the upper cloud…

Fullerene-like structures found in 80-million-year-old fossils

Scientists from The University of Western Australia and The University of Cambridge discovered hollow ball-like…

Hydrogen flames propagate by forming fractal-like patterns.

By forming fractal-like patterns, hydrogen flames may effectively access new fuel. The two primary processes…

Double helix — the secret of Italian renaissance domes

The Sangallo, who created their own self-balanced building method for brick domes based on the…

Spiral galaxies’ patterns indicate that the cosmos may have a definite structure

According to a Kansas State University research, an examination of more than 200,000 spiral galaxies…

Fractal cube structures show promise for dissipating shockwave energy

Shockwaves are dissipated five times better by 3D printed fractal structures with closely spaced gaps…

Spiral beehives have a lot in common with crystals

The fundamental laws that govern everything in the Universe, including thermodynamics, apply to both crystal…

Geometry matters, but why?

The contribution of geometry to the evolution of human and natural sciences is a well-established…