Lifeboat Foundation

Normally, when we think of a rolling object, we tend to imagine a torus (like a bicycle wheel) or a sphere (like a tennis ball) that will always follow a straight path when rolling. However, the world of mathematics and science is always open to exploring new ideas and concepts. This is why researchers have been studying shapes, like oloids, sphericons and more, which do not roll in straight lines.

All these funky shapes are really interesting to researchers as they can show us new ways to move objects around smoothly and efficiently. For example, imagine reducing the energy required to make a toy robot move, or mixing ingredients more thoroughly with a unique-looking spoon. While these peculiar shapes have been studied before, scientists have now taken it a step further.

Consider a game where you draw a path on a tilted table—similar to tilting a pinball table to make the ball go in a particular direction. Now, try to come up with a 3D object that, when placed at the top of the table, will roll down and exactly follow that path, instead of just going straight down. There are a few other rules of this game: the table needs to be inclined slightly (and not too much), there should be no slipping during rolling, and the initial orientation of the object can be chosen at launch. Plus, the path you draw must never go uphill and must be periodic. It must also consist of identical repeating segments—somewhat like in music rhythm patterns.

Join the discussion on this paper page.

Summary: Researchers delved deep into the mysteries of synchronization in complex systems, uncovering how certain elements effortlessly fall into or out of sync. This dance of coordination can be observed from humans clapping in rhythm to the synchronicity of heart cells.

By studying “walks” through networks, the team discovered the role of convergent walks in diminishing the quality of synchronization. These findings could revolutionize our understanding of everything from power grid stability to brain functions and social media dynamics.

The density of neurons in the brain is governed by a fundamental mathematical function, new research finds.

The discovery, which holds true across a variety of mammals, could help researchers make better computer models of the brain in the future.

Diagonal Arguments are a powerful tool in maths, and appear in several different fundamental results, like Cantor’s original Diagonal argument proof (there exist uncountable sets, or “some infinities are bigger than other infinities”), Turing’s Halting Problem, Gödel’s incompleteness theorems, Russell’s Paradox, the Liar Paradox, and even the Y Combinator.

In this video, I try and motivate what a general diagonal argument looks like, from first principles. It should be accessible to anyone who’s comfortable with functions and sets.

Continue reading “What A General Diagonal Argument Looks Like (Category Theory)” »

Mathematicians delight in the beauty of math that so many of us don’t see. But nature is a wonderful realm in which to observe beauty born out of mathematical relationships.

The natural world provides seemingly endless patterns underpinned by numbers – if we can recognize them.

Luckily for us, a motley team of researchers has just uncovered another striking connection between math and nature; between one of the purest forms of mathematics, number theory, and the mechanisms governing the evolution of life on molecular scales, genetics.

Summary: Researchers discovered that electrical noise stimulation to the frontal part of the brain can improve mathematical learning.

The study focused on those who initially showed low levels of brain excitation towards math. Unlike in placebo groups, unlike in placebo groups, a significant improvement in math skills was observed after the application of neurostimulation. This novel approach could revolutionize personalized learning.

Michael Levin is a Distinguished Professor in the Biology department at Tufts University. He holds the Vannevar Bush endowed Chair and serves as director of the Allen Discovery Center at Tufts and the Tufts Center for Regenerative and Developmental Biology. To explore the algorithms by which the biological world implemented complex adaptive behavior, he got dual B.S. degrees, in CS and in Biology and then received a PhD from Harvard University. He did post-doctoral training at Harvard Medical School, where he began to uncover a new bioelectric language by which cells coordinate their activity during embryogenesis. The Levin Lab works at the intersection of developmental biology, artificial life, bioengineering, synthetic morphology, and cognitive science.

✅EPISODE LINKS:
👉Round 1: https://youtu.be/v6gp-ORTBlU
👉Mike’s Website: https://drmichaellevin.org/
👉New Website: https://thoughtforms.life.
👉Mike’s Twitter: https://twitter.com/drmichaellevin.
👉Mike’s YouTube: https://youtube.com/@drmichaellevin.
👉Mike’s Publications: https://tinyurl.com/yc388vvk.
👉The Well: https://www.youtube.com/watch?v=0a3xg4M9Oa8 & https://youtu.be/XHMyKOpiYjk.
👉Aeon Essays: https://aeon.co/users/michael-levin.

Continue reading “What is The Field of Diverse Intelligence? Hacking the Spectrum of Mind & Matter | Michael Levin” »

Quantum technologies—and quantum computers in particular—have the potential to shape the development of technology in the future. Scientists believe that quantum computers will help them solve problems that even the fastest supercomputers are unable to handle yet. Large international IT companies and countries like the United States and China have been making significant investments in the development of this technology. But because quantum computers are based on different laws of physics than conventional computers, laptops, and smartphones, they are more susceptible to malfunction.

An interdisciplinary research team led by Professor Jens Eisert, a physicist at Freie Universität Berlin, has now found ways of testing the quality of quantum computers. Their study on the subject was recently published in the scientific journal Nature Communications. These scientific quality control tests incorporate methods from physics, computer science, and mathematics.

Quantum physicist at Freie Universität Berlin and author of the study, Professor Jens Eisert, explains the science behind the research. “Quantum computers work on the basis of quantum mechanical laws of physics, in which individual atoms or ions are used as computational units—or to put it another way—controlled, minuscule physical systems. What is extraordinary about these computers of the future is that at this level, nature functions extremely and radically differently from our everyday experience of the world and how we know and perceive it.”