#universal geometry

Our ability to detect patterns might stem from the brain's desire to represent things in the simplest way possible

A. Example sequence of visual stimuli (left) representing a random walk on an underlying transition network (right). B. For each stimulus, subjects are asked to respond by pressing a combination of one or two buttons on a keyboard. C. Each of the 15 possible button combinations corresponds to a node in the transition network. We only consider networks with nodes of uniform degree k = 4 and edges with uniform transition probability 0.25. D. Subjects were asked to respond to sequences of 1500 such nodes drawn from two different transition architectures: a modular graph (left) and a lattice graph (right). E. Average reaction times across all subjects for the different button combinations, where the diagonal elements rep- resent single-button presses and the off-diagonal elements represent two-button presses. F. Average reaction times as a function of trial number, characterized by a steep drop-off in the first 500 trials followed by a gradual decline in the remaining 1,000 trials. Credit: Lynn et al.

During their first year of life, infants can recognize patterned sound sequences. As we grow, we develop the ability to pick out increasingly complex patterns within streams of words and musical notes. Traditionally, cognitive scientists have assumed that the brain uses a complicated algorithm to find links between disparate concepts, thereby yielding a higher-level understanding.

Researchers at the University of Pennsylvania—Christopher Lynn, Ari Kahn and Danielle Bassett—are building an entirely different model, indicating that our ability to detect patterns might stem, in part, from the brain's desire to represent things in the simplest way possible.

The brain does more than just process incoming information, said Lynn, a physics graduate student. "It constantly tries to predict what's coming next. If, for instance, you're attending a lecture on a subject you know something about, you already have some grasp of the higher-order structure. That helps you connect ideas together and anticipate what you'll hear next."

The new model offers striking insights on human cognition, suggesting that people can and indeed do make mistakes in detecting individual components of a pattern in order to catch a glimpse of the bigger picture. For example, Lynn explained, "if you look at a pointillist painting up close, you can correctly identify every dot. If you step back 20 feet, the details get fuzzy, but you'll gain a better sense of the overall structure." The brain may well adopt a similar strategy, he said.

Scutoid

The newly discovered shape that shows how nature packs cells efficiently into three-dimensional structures.

Researchers have discovered a new geometric shape that’s been hiding in plain sight.

A team studying the cells that give rise to embryos and can be found lining our organs and blood vessels pinpointed a three-dimensional shape that occurs as they bend and pack together.

X-ray diffraction pattern of beryl

Beryl is a mineral composed of beryllium aluminium cyclosilicate

Spiral Beehive

A Math Theory for Why People Hallucinate 

Images we “see” are essentially the patterns of excited neurons in the visual cortex. Light reflecting off the objects in our field of view enters the eye and comes to a focus on the retina, which is lined with photoreceptor cells that convert that light into electrochemical signals. These signals travel to the brain and stimulate neurons in the visual cortex in patterns that, under normal circumstances, mimic the patterns of light reflecting off objects in your field of view. But sometimes patterns can arise spontaneously from the random firing of neurons in the cortex — internal background noise, as opposed to external stimuli — or when a psychoactive drug or other influencing factor disrupts normal brain function and boosts the random firing of neurons. This is believed to be what happens when we hallucinate.

But if geometric visual hallucinations like Klüver’s form constants are a direct consequence of neural activity in the visual cortex, the question is why this activity spontaneously occurs — and why, in that case, it doesn’t cause us to hallucinate all the time. The stochastic Turing mechanism potentially addresses both questions.