Lifeboat Foundation

Background

Many everyday tasks can fall under the mathematical class of “hard” problems. Typically, these problems belong to the complexity class of nondeterministic polynomial (NP) hard. These tasks require systematic approaches (algorithms) for optimal outcomes. In the case of significant complex problems (e.g., the number of ways to fix a product or the number of stops to be made on a delivery trip), more computations are required, which rapidly outgrows cognitive capacities.

A recent Science Advances study investigated the effectiveness of three popular smart drugs, namely, modafinil (MOD), methylphenidate (MPH), and dextroamphetamine (DEX), against the difficulty of real-life daily tasks, i.e., the 0–1 knapsack optimization problem (“knapsack task”). A knapsack task is basically a combinatorial optimization task, the class of NP-time challenging problems.

A series of new papers describes how to fully characterize key dynamical systems with relatively little data.

The company now plans to power its quantum computers with a minimum of 127 qubits.

IBM’s Eagle quantum computer has outperformed a conventional supercomputer when solving complex mathematical calculations. This is also the first demonstration of a quantum computer providing accurate results at a scale of 100+ qubits, a company press release said.

Continue reading “IBM’s Eagle quantum computer just beat a supercomputer at complex math” »

Fibonacci numbers are seen in the natural structures of various plants, such as the florets in sunflower heads, areoles on cacti stems, and scales in pine cones. [HackerBox] has developed a Fibonacci Spiral LED Badge to bring this natural phenomenon to your electronics.

To position each of the 64 addressable LEDs within the PCB layout, [HackerBox] computed the polar (r,θ) coordinates in a spreadsheet according to the Vogel model and then converted them to rectangular (x, y) coordinates. A little more math translates the points “off origin” into the center of the PCB space and scale them out to keep the first two 5 mm LEDs from overlapping. Finally, the LED coordinates were pasted into the KiCad PCB design file.

Continue reading “Math You Can Wear: Fibonacci Spiral LED Badge” »

Editor’s note: For a more mainstream assessment of this idea, see this article by Dr. Ethan Siegel.

Sir Roger Penrose, a mathematician and physicist from the University of Oxford who shared the Nobel Prize in physics in 2020, claims our universe has gone through multiple Big Bangs, with another one coming in our future.

Continue reading “Controversial claim from Nobel Prize winner: The universe keeps dying and being reborn” »

For example, scientists have recently emphasized that the physical organization of the Universe mirrors the structure of a brain. Theoretical physicist Sabine Hossenfelder — renowned for her skepticism — wrote a bold article for Time Magazine in August of 2022 titled “Maybe the Universe Thinks. Hear Me Out,” which describes the similarities. Like our nervous system, the Universe has a highly interconnected, hierarchical organization. The estimated 200 billion detectable galaxies aren’t distributed randomly, but lumped together by gravity into clusters that form even larger clusters, which are connected to one another by “galactic filaments,” or long thin threads of galaxies. When one zooms out to envision the cosmos as a whole, the “cosmic web” formed by these clusters and filaments looks strikingly similar to the “connectome,” a term that refers to the complete wiring diagram of the brain, which is formed by neurons and their synaptic connections. Neurons in the brain also form clusters, which are grouped into larger clusters, and are connected by filaments called axons, which transmit electrical signals across the cognitive system.

Hossenfelder explains that this resemblance between the cosmic web and the connectome is not superficial, citing a rigorous study by a physicist and a neuroscientist that analyzed the features common to both, and based on the shared mathematical properties, concluded that the two structures are “remarkably similar.” Due to these uncanny similarities, Hossenfelder speculates as to whether the Universe itself could be thinking.

Understanding the behavior of nuclear matter—including the quarks and gluons that make up the protons and neutrons of atomic nuclei—is extremely complicated. This is particularly true in our world, which is three dimensional. Mathematical techniques from condensed matter physics that consider interactions in just one spatial dimension (plus time) greatly simplify the challenge.

Using this two-dimensional approach, scientists solved the complex equations that describe how low-energy excitations ripple through a system of dense nuclear matter. This work indicates that the center of neutron stars, where such dense nuclear matter exists in nature, may be described by an unexpected form.

Being able to understand the quark interactions in two dimensions opens a new window into understanding neutron stars, the densest form of matter in the universe. The approach could help advance the current “golden age” for studying these exotic stars. This surge in research success was triggered by recent discoveries of gravitational waves and electromagnetic emissions in the cosmos.

Scientists have taken a significant step forward in the study of the properties of quarks and gluons, the particles that make up atomic nuclei, by resolving a long-standing issue with a theoretical calculation method known as “axial gauge.” MIT

MIT is an acronym for the Massachusetts Institute of Technology. It is a prestigious private research university in Cambridge, Massachusetts that was founded in 1861. It is organized into five Schools: architecture and planning; engineering; humanities, arts, and social sciences; management; and science. MIT’s impact includes many scientific breakthroughs and technological advances. Their stated goal is to make a better world through education, research, and innovation.

David Smith, a retired print technician from the north of England, was pursuing his hobby of looking for interesting shapes when he stumbled onto one unlike any other in November.

When Smith shared his shape with the world in March, excited fans printed it onto T-shirts, sewed it into quilts, crafted cookie cutters or used it to replace the hexagons on a soccer ball —some even made plans for tattoos.

The 13-sided polygon, which 64-year-old Smith called “the hat”, is the first single shape ever found that can completely cover an infinitely large flat surface without ever repeating the same pattern.