Lifeboat Foundation

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

This video is my take on 3B1B’s Summer of Math Exposition (SoME) competition.

It explains in pretty intuitive terms how ideas from topology (or “rubber geometry”) can be used in neuroscience, to help us understand the way information is embedded in high-dimensional representations inside neural circuits.

Continue reading “Neural manifolds — The Geometry of Behaviour” »

Illuminating mathematics, physics, biology and computer science research through public service journalism.

AInstein robot can respond to inquiries from pupils and even illustrate Albert Einstein’s theory of temporal relativity using a pendulum.

High school students in Cyprus have developed an artificial intelligence (AI) robot that uses ChatGPT to enhance classroom learning.

The Three PASCAL schools’ creation, AInstein, can hold dialogues, produce textual content, and crack jokes, according to an article published on Thursday by Voice of America (VOA).

Fascinating proposal for methodology.

Models are scientific models, theories, hypotheses, formulas, equations, naïve models based on personal experiences, superstitions (!), and traditional computer programs. In a Reductionist paradigm, these Models are created by humans, ostensibly by scientists, and are then used, ostensibly by engineers, to solve real-world problems. Model creation and Model use both require that these humans Understand the problem domain, the problem at hand, the previously known shared Models available, and how to design and use Models. A Ph.D. degree could be seen as a formal license to create new Models^[2]. Mathematics can be seen as a discipline for Model manipulation.

Continue reading “The Red Pill of Machine Learning” »

A synthetic analog of a black hole could tell us a thing or two about an elusive radiation theoretically emitted by the real thing.

Using a chain of atoms in single-file to simulate the event horizon of a black hole, a team of physicists observed the equivalent of what we call Hawking radiation – particles born from disturbances in the quantum fluctuations caused by the black hole’s break in spacetime.

This, they say, could help resolve the tension between two currently irreconcilable frameworks for describing the Universe: the general theory of relativity, which describes the behavior of gravity as a continuous field known as spacetime; and quantum mechanics, which describes the behavior of discrete particles using the mathematics of probability.

Large language models are drafting screenplays and writing code and cracking jokes. Image generators, such as Midjourney and DALL-E 2, are winning art prizes and democratizing interior design and producing dangerously convincing fabrications. They feel like magic. Meanwhile, the world’s most advanced robots are still struggling to open different kinds of doors. As in actual, physical doors. Chatbots, in the proper context, can be—and have been—mistaken for actual human beings; the most advanced robots still look more like mechanical arms appended to rolling tables. For now, at least, our dystopian near future looks a lot more like Her than M3GAN.

The counterintuitive notion that it’s harder to build artificial bodies than artificial minds is not a new one. In 1988, the computer scientist Hans Moravec observed that computers already excelled at tasks that humans tended to think of as complicated or difficult (math, chess, IQ tests) but were unable to match “the skills of a one-year-old when it comes to perception and mobility.” Six years later, the cognitive psychologist Steven Pinker offered a pithier formulation: “The main lesson of thirty-five years of AI research,” he wrote, “is that the hard problems are easy and the easy problems are hard.” This lesson is now known as “Moravec’s paradox.”

An artificial black hole produced using sound waves and a dielectric medium has been created in the lab, according to researchers with an international think tank featuring more than 30 Ph.D. research scientists from around the world.

The researchers say their discovery is significantly more cost-effective and efficient than current methods in use by researchers who want to simulate the effects of a black hole in a laboratory environment.

New York-based Applied Physics first achieved recognition with the 2021 publication of a peer-reviewed theoretical paper detailing the mathematics behind the construction of a physical warp drive. More recently, the organization published a method for using Cal Tech’s Laser Interferometer Gravitational-Wave Observatory (LIGO) to detect the use of warp drives in outer space, co-authored by Dr. Manfred Paulini, the Associate Dean of Physics at Carnegie Mellon University.

A research team led by the German Cancer Research Center in Heidelberg, Germany, has discovered that the genetic sequence of a tumor can be read like a molecular clock, traced back to its most recent common ancestor cell. Extracting the duration of tumor evolution can give an accurate predictor of neuroblastoma outcomes.

In a paper published in Nature Genetics titled “Neuroblastoma arises in early fetal development and its evolutionary duration predicts outcome,” the team details the steps they took in identifying a genomic clock tested against a whole genome sequenced population combined with analysis and mathematical modeling, to identify evolution markers, traceability and a likely origin point of infant neuroblastomas.

Cancer cells start out life as heroic healthy tissues, with the sort of all for one, one for all, throw yourself on a grenade to save your mates–type attitude that is taking place throughout the body every day. At some point, something goes wrong, and a good cell goes bad.