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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…

Sentient avant-gardism and the principles for geometric cognition models

Sentient: able to perceive or feel thingsAvant-garde: new and experimental ideas and methods The increased…

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…

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…

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…

Patterns of innovation

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

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…

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…

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…

Hans Jenny and the science of sound: cymatics.

This is not unregulated chaos; it is a dynamic but ordered pattern. Hans Jenny (16 August 1904, Basel – 23 June 1972) was a natural scientist and physician who coined the term cymatics to explain the acoustic impacts of sound wave phenomena. To this field have contributed a number of scholars, that believed sound plays a…

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The fractal-hyperbolic geometry of networks

Network geometry helps us better understand complex systems at all sizes of organizations, as well as the collective phenomena that emerge from their information flow. Being useful in a wide range of applications, from understanding how the brain functions to Internet routing, a variety of approaches have been employed to study complex networks from different…

The manifold framework of neural circuits

Manifold: a topological space that locally resembles a Euclidean space in mathematics. Perceptual manifold: the population structures of sensory neurons that emerge as a result of identity-preserving variations in the input stimulus space. Neural manifold: low-dimensional subspaces underlying population activities embedded in high-dimensional neural state space Point-cloud manifold: a set of data points with an…

The geometry of atomic bonds

In 2012, a team from IBM’s research labs in Zurich managed to reveal the individual bonds that hold a molecule together. The bond order and length of individual carbon-carbon bonds in C60, often known as a buckyball because of its football form, and two planar polycyclic aromatic hydrocarbons (PAHs), which resemble microscopic flakes of graphene,…

Hologram of a single photon

In 2016, scientists from the University of Warsaw created the first-ever hologram of a single light particle, adding new insights to the foundations of quantum mechanics. Individual points of a picture in traditional photography merely register light intensity. The interference phenomenon also registers the phase of the light waves in traditional holography. A well-described, undisturbed…

A patterned fingerprint of the brain

Studying multiple neural networks, researchers from EPFL Switzerland found that every one of us has a unique brain fingerprint. Comparing the graphs generated from MRI scans of the same subjects taken a few days apart, they were able to correctly match up the two scans of a given subject nearly 95% of the time. After…

Einstein, geometry, and experience

As far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. Lecture before the Prussian Academy of SciencesPresented: 27 January 1921Published: 1921 by Julius Springer (Berlin)Translation: from Einstein, Ideas and Opinionstrans. Sonja Bargmann (New York: Crown, 1982)© The Collected…

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 the 19th century.  But is this true? Some fundamentals, such as positive integers and the 3-4-5 right triangle, are universally accepted across cultures. Almost every other aspect of mathematics is influenced by the society in which you live. Mathematics, in this…

Harpa Concert Hall: from nature to architecture

The building stands out like a vast, dazzling sculpture on the edge of land and sea, reflecting both sky and harbor space as well as the active lifestyle of the city. Henning Larsen Architects, the Danish-Icelandic artist Olafur Eliasson, and the German engineering firms Rambll and ArtEngineering GmbH collaborated closely to create the outstanding façades. Harpa…

Hidden order in disorder

Hyperuniformity is a geometric concept to probabilistically characterise the structure of ordered and disordered materials. For example, all perfect crystals, perfect quasicrystals, and special disordered systems are hyperuniform. The study of how large structures are partitioning space into cells with specific extreme geometrical features is a crucial topic in many disciplines of science and technology.…

Icosahedral nano-shell designed to trap virus particles

An interdisciplinary research team at the Technical University of Munich (TUM) has developed an efficient strategy against most viral infections: they engulf and destroy viruses using DNA origami nano-capsules. In cell cultures, the approach has already been tried against hepatitis and adeno-associated viruses. It may also be effective against corona viruses. Even before the new coronavirus…

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 greatest characteristics for the embryonic development of egg-laying species. The form is ideal for the process of incubation, and its size is appropriate in relation to the body of animals for birth. Furthermore, eggs are well-designed to protect the fragile…

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 the genesis and evolution of life have studied and sought to characterize the embryology of all multicellular animal phyla since the 19th century. Many people believed that by the turn of the twentieth century, this work would have been completed.…

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 in cells, like birds that organize into flocks by associating solely with their close neighbors, may establish self-organized patterns that regulate critical activities like cell division and tissue-shape formation. While theoretical models have concentrated on the dynamics of proteins approaching…

Hunting Bach’s fractals

Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Mathematician Benoit Mandelbrot invented the word “fractal” in a 1975 book on the subject, and his landmark 1982 book The Fractal Geometry of Nature, which records the geometric…

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 2D surfaces, and tridimensional objects by using universal nets, that provide a balance between entropy loss and potential energy gain. This also explains why some of their geometrical attributes (such as compactness) represent a good predictor for the folding preference…

Model for studying nature’s patterns.

Wings are like fingerprints for many insect species, with no two patterns being the same. These insects, like many other organisms ranging from leopards to zebrafish, benefit from nature’s seemingly limitless ability to generate a wide range of shapes and patterns. However, how do these patterns emerge? Harvard University researchers have created a model that…

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 sizes. Examples from nature include beaches, lightning, rivers, and trees, as well as cardiovascular and respiratory systems such as the bronchial tree. Neurons, like trees, are thought to represent a common kind of fractal branching activity. Although prior neuron research…

Mathematical skills improved by tri-dimensional thinking

In 2019, a nationwide study on fundamental skills in Switzerland discovered a link between children’s spatial awareness at the age of three and their mathematical ability in primary school. Other variables, such as socioeconomic position or linguistic competence, were ruled out by the researchers. It is unknown how spatial ability impacts arithmetic skills in youngsters, although…

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 all other cells with specific tasks. Stem cells divide to create new cells in the body or in a laboratory under the correct conditions. Referred to as daughter cells, these cells either become new stem cells (self-renewal) or specialized cells…

Are patterns real or imagined?

For neuroscientists studying complex systems, patterns exhibit valuable data that may or may not correspond to higher levels of cognitive processes. Tyler Millhouse proposes a criterion evaluating just how real a pattern is likely to be, improving a SFI External Professor Daniel Dennett’s 1991 explanation, which utilized ‘compressibility’ to determine how genuine a pattern is…

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 as art, architecture, and music. The structure of these expressions is frequently intuitively related to their meaning: flowery curlicues are used in romantic poetry, while a spiky script is used in death metal band logos. A Dartmouth study published in…

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, including mathematicians Bertrand Russell (1919) and Hermann Weyl (Dyson, 1956; Atiyah, 2002), physicist Paul Dirac (1939), and art critic Clive Bell (1914), have written about the importance of beauty in mathematical formulations and compared the experience of mathematical beauty to…

Deciphering the brain’s color and shape coding

A human can identify hundreds of thousands of unique colors and forms visually, but how does the brain process all of this information? Previously, scientists assumed that the visual system records shape and color separately with discrete groups of neurons and then integrates them much later. According to the Salk researchers, there are neurons that…

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 in the human brain. Researchers used various methods to visualize grid cell activity while subjects explored images of everyday scenes under the direction of Prof. Christian Doeller of the Max Planck Institute for Human Cognitive and Brain Sciences (MPI CBS)…

The Scutoid: additional solution for three-dimensional packing

Tissues flex into intricate three-dimensional forms that lead to organs as an embryo grows. This process’s building blocks are epithelial cells, which create the outer layer of skin, for example. They also line all animals’ blood arteries and organs. These cells are closely packed together. It has been suggested that epithelial cells acquire either columnar…

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 Zaha Hadid Architects, creates a new type of value for human spaces. He states that designed spaces are spatial communications that frame and organize subsequent conversations. They organize the participants into precise constellations that correspond to the anticipated conversation circumstances. A…

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 its capacity to transfer pigments around inside its cells; however, it appears that this is not the case. Instead of pigments, the little animals rely heavily on geometry and physics. To understand this, you must first understand how light and…

‘Multi-dimensional universe’ in brain networks

Researchers were able to identify architectural patterns that arise when the brain had to comprehend information before disintegrating into nothing by utilizing a sophisticated mathematical method. The discovery showed that the brain is full of multi-dimensional geometrical structures operating in as many as 11 dimensions. A team of researchers from the Blue Brain Project, 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 show that there is a clear relationship between the design of Stonehenge and the chalk artifacts known as the Folkton and Lavant Drums, where the Drums reflect measuring standards that were required for precise and reproducible monument building. This has…

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 rules at a fundamental level. Jesse Berezovsky, an associate professor of physics at Case Western Reserve University, defines the “emergent structures of musical harmony” inherent in the art, just as order comes from disorder in the physical world. I present a…

Using moiré patterns prevents information loss in optical communications

A moiré lattice occurs when two periodic 2D patterns are layered on top of each other with a little twist. Since it was proven that two sheets of graphene may run the gamut of electrical characteristics – including superconductivity, magnetism, and Mott insulation – merely by changing the twist angle between the sheets, scientists have…

Long distance communications through quantum teleportation of light patterns

Quantum communication over long distances is essential for information security, and it has been shown in free space and fiber using two-dimensional states, most notably across distances of more than 1200 km between satellites. However, utilizing only two states lowers the photons’ information capacity, making the communication safe but sluggish. To make it safe and…

The fractal brain, from a single neuron’s perspective

Physicists at Washington University in St. Louis researching the brain have demonstrated that monitoring signals from a single neuron may be as effective as gathering information from numerous neurons at once using large, expensive arrays of electrodes. A key topic in neuroscience is what information single neurons get about overall brain network activity. For years,…

Warping geometry pushes scientific boundaries

Atomic interactions in common solids and liquids are so intricate that physicists are still baffled by some of these materials’ characteristics. Because solving the issues theoretically is beyond the capability of contemporary computers, Princeton University scientists have turned to an uncommon area of geometry instead. Researchers lead by electrical engineering professor Andrew Houck created an…

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 older, we gain the capacity to recognize increasingly complicated patterns in streams of words and musical sounds. Traditionally, cognitive scientists thought that the brain used a complex algorithm to discover connections between dissimilar concepts, resulting in a higher-level comprehension. Christopher…

Golden Ratio Observed In Human Skulls

For centuries, Φ has been found in human anatomy for millennia, and in recent decades, it has also been identified in human physiology. The anatomy and evolution of the human skull have been the subject of much research. The Golden Ratio was discovered in the measurements of human skulls but not in those of other…

The golden perfection of the aortic valve

By observing the perfect geometry of a tricuspid aortic valve, a team of cardiac surgeons speculated that an approximation to the golden ratio might be present between its components, and the Fibonacci spiral would fit into the valve, representing a very interesting way to describe its fascinating symmetry. The ratio a+ b/a=a/b=1.618 was dubbed the…

Foam offers way to manipulate light

Princeton researchers discovered that a form of foam that has long been researched by scientists may block specific wavelengths of light. This is recognized as a very desired feature for next-generation information technology that relies on light rather than electricity. The researchers conducted extensive computer simulations of a structure known as a Weaire-Phelan foam, combining…

Irregularly shaped parks reduce mortality risk

Some community parks are square, reflecting the city block where they are located — but irregularly shaped parks reduce the mortality risk of residents who live nearby, according to a study conducted by Huaquing Wang, a Ph.D. student in Urban and Regional Sciences, and Lou Tassinary, professor of visualization. “Nearly all studies investigating the effects…

Mathematical laws underlying brain development have been identified.

Stanford researchers identified a pattern that regulates the development of brain cells or neurons using sophisticated microscopy and mathematical modeling. Similar principles may govern the growth of other cells in the body, and knowing them may be critical for effectively designing artificial tissues and organs. Their discovery, published in Nature Physics, is based on the…

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” or “dull,” and prominent scientists have argued that mathematical beauty serves as a pointer to the truth. Do laypeople, like mathematicians and scientists, have an aesthetic experience with mathematics? According to three studies, they do. When participants assessed the resemblance…

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 dazzling cascade of swirling patterns. These spiraling arcs are a fundamental component of beginning cell division. “The egg is a huge cell, and these proteins have to work together to find its centre, so that the cell knows where to divide…

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 structures in 80-million-year-old fossils from species thought to be linked to starfish and sea urchins in UK museum collections. Buckyballs, short for “Buckminsterfullerenes”, are huge spherical molecules composed of 60 carbon atoms bonded together in pentagons and hexagons to produce…

Double helix — the secret of Italian renaissance domes

The Sangallo, who created their own self-balanced building method for brick domes based on the cross-herringbone spiraling pattern in the 16th century, were undoubtedly aware of the Brunelleschi herringbone pattern. For almost a century, this method was utilized in Italy to construct brick domes without the need of shoring or formwork. However, it is currently…

Spiral beehives have a lot in common with crystals

The fundamental laws that govern everything in the Universe, including thermodynamics, apply to both crystal formation and bee combs. However, there is plenty of room for other phenomena to occur under the principles of thermodynamics, which is why the cosmos can be as complicated as it is. Crystal formation and bee comb construction are two…