geometry matters

Where there is matter, there is geometry - Kepler, Johannes

[jkottke]

Tenfold Knottiness: I love this diagram from 1885 that shows possible variations of knots with 10 crossings.

[nemfrog]

Attraction and Repulsion. Modern views of electricity. 1892.

Internet Archive

[blasteffect]

Saturn's north pole !

The hexagon is nearly 30,000 km (20,000 miles) wide. This is large enough that two Earths could fit inside the storm with room to spare.

It is a standing atmospheric wave created by a powerful jet stream that wraps around the pole. Winds along its edges can exceed 300 km/h (about 220 mph).

At the very center of the hexagon lies a deep, dark polar vortex that extends hundreds of kilometers down into Saturn's atmosphere.

Spacecraft/Mission: NASA/JPL-Caltech/SSI (Space Science Institute).

[materialsscienceandengineering]

Spectroscopy Technique Reveals Nanoscale Acoustic Waves

Imaging using extreme ultraviolet scattering shows that optical pulses can generate surface excitations with spectra that were previously difficult to achieve. [...] Surface acoustic waves (SAWs) propagate along a solid material’s surface like ripples on a pond. SAWs with wavelengths of hundreds of kilometers are generated by earthquakes, whereas SAWs with wavelengths at the micrometer scale can be excited by lasers. Flavio Capotondi at the Free Electron laser Radiation for Multidisciplinary Investigations (FERMI) facility at Elettra Sincrotrone Trieste in Italy and his colleagues have now demonstrated a simple laser-based technique for exciting and detecting SAWs with nanometer wavelengths [1]. They say that the work will allow the dynamics of materials’ crystal lattices to be probed over a wavelength range that has been inaccessible using other approaches.

Read more.

[lascitasdelashoras]

Anne Griswold Tyng, Spiral Extension of Helix from Form finds Symmetry in Geometry. 1969

[noosphe-re]

Reinhardt, Didier. (2005). Regulation of phyllotaxis. The International journal of developmental biology. 49. 539-46. 10.1387/ijdb.041922dr.

[regolo54]

[rosieandthemoon]

Fingals Cave, Scotland

[ashotasfireandasdeepastheocean1]

Majestic ♡

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[geometrymatters]

We are here to have an experience

Guest of Brian “Ponch” Rivera and Mark McGrath on the No Way Out Podcast, Tib talks about his Polynon theory for a Geometry of Consciousness, cognitive gravity, and the cognitive implications for the OODA Loop and spatial coordination.

They dive into what an observer is, tackling fundamental aspects of perception, attention, and how orientation emerges in real time via geometric manifolds of cognition.

The conversation opens a broader view of cognition as structured space, where geometric relations guide sense-making, action, and adaptation.

It’s a deep look at how awareness organizes itself via geometric principles, how feedback shapes decisions, and how spatial coherence influences the way we move through uncertainty.

[geometrymatters]

Cognitive gravity and the superposition of perception and memory

Attention acts as a vector, drawn toward regions of relevance shaped by phenomenal bias β and cognitive variability γ: β anchors prior expectations, while γ allows flexibility. After Escher (Liberation).

Cognitive gravity will define the vector of attention and how perceptual structure is further defined by the cognitive manifold.

[stevensaus]

The neurons that let us see what isn’t there

A standard optical illusion triggers specific neurons in the visual system of mice.

The neurons that let us see what isn’t there

Archive Links: ais ia

[noosphe-re]

RF pulse design and simulations: supplementary animations Magnetic Field Patterns from Hertzian Dipole Antenna

[szimmetria-airtemmizs]

Mathematical fun fact of the day 4. You can divide a hexagon into nine identical convex pentagons.

[geometrymatters]

Diffraction of visible light from a variety of 2-D crystalline patterns

[geometrymatters]

Spiral Beehive

©Tim Heard

[geometrymatters]

The Geometry of Movies can Change the Way We Think

Circles. Triangles. Squares. Those aren’t the things you expect to see in a movie but films have been using shapes to subtly influence emotion for a long time. Circles are lovable, triangles are evil, and squares are boring. Now You See It highlights the geometry used in shots to show you how movies use shapes to manipulate your feelings.

A villain is usually portrayed with sharper features to represent their harshness—think Maleficent or Darth Vader. The good guys are softer and rounder to make them appear more lovable and huggable—think Mickey Mouse or Baloo from The Jungle Book. And squares are used for boring and old-fashioned characters like Carl Fredricksen from Up, because squares are squares (duh).

continue reading on gizmodo

[geometrymatters]

Parametric Semiology – The Design of Information Rich Environments - by Patrick Schumacher, 2013

All design is communication design. The built environment, with its complex matrix of territorial distinctions, is a giant, navigable, information-rich interface of communication. Each territory is a communication. It gives potential social actors information about the communicative interactions to be expected within its bounds. It communicates an invitation to participate in the framed social situation. Designed spaces are spatial communications that frame and order further communications. They place the participants into specific constellations that are pertinent with respect to the anticipated communication situations. Like any communication, a spatial communication can be accepted or rejected, i.e. – the space can be entered or exited. Entry implies accepting the communication as the premise for all further communication taking place within its boundaries. Crossing a territorial threshold makes a difference in terms of behavioural dispositions. Entry implies submission to the specific rules of conduct that the type of social situation inscribed within the territory prescribes. In this way, the designed-built environment orders social processes.  This spells the unique, societal function of architecture: to order and frame communicative interaction (Patrik Schumacher, The Autopoiesis of Architecture, Volume 1: A New Framework for Architecture. London: John Wiley & Sons Ltd., 2010. See Part 5:The Societal Function of Architecture.)

Figure 1. Parametric Semiology: Semio-field, differentiation of public vs. private as parametric range.

Figure 2. Parametric Semiology: Semio-field, master-plan with program distribution.

Figure 3. Vienna University of Applied Arts, Masterclass Hadid, Parametric Semiology: Semio-field. Project authors: Magda Smolinska, Marius Cernica, and Monir Karimi.

Figure 4. Dialectic Fields: Shell morphology as semiological system of distinctions: smooth vs creased vs faceted.

Figure 5. Dialectic Fields: Cluster of creased shells with semiologically distinctive surface articulation.

© Patrick Schumacher, 2013