Lifeboat Foundation

5 january 2020.

This paper proposes the use of Flower Constellation (FC) theory to facilitate the design of a Low Earth Orbit (LEO) slotting system to avoid collisions between compliant satellites and optimize the available space. Specifically, it proposes the use of concentric orbital shells of admissible “slots” with stacked intersecting orbits that preserve a minimum separation distance between satellites at all times. The problem is formulated in mathematical terms and three approaches are explored: random constellations, single 2D Lattice Flower Constellations (2D-LFCs), and unions of 2D-LFCs. Each approach is evaluated in terms of several metrics including capacity, Earth coverage, orbits per shell, and symmetries. In particular, capacity is evaluated for various inclinations and other parameters. Next, a rough estimate for the capacity of LEO is generated subject to certain minimum separation and station-keeping assumptions and several trade-offs are identified to guide policy-makers interested in the adoption of a LEO slotting scheme for space traffic management.

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The debate holds a special interest for neuroscientists; since computer programming has only been around for a few decades, the brain has not evolved any special region to handle it. It must be repurposing a region of the brain normally used for something else.

So late last year, neuroscientists in MIT tried to see what parts of the brain people use when dealing with computer programming. “The ability to interpret computer code is a remarkable cognitive skill that bears parallels to diverse cognitive domains, including general executive functions, math, logic, and language,” they wrote.

Since coding can be learned as an adult, they figured it must rely on some pre-existing cognitive system in our brains. Two brain systems seemed like likely candidates: either the brain’s language system, or the system that tackles complex cognitive tasks such as solving math problems or a crossword. The latter is known as the “multiple demand network.”

What do you do after solving the answer to life, the universe, and everything? If you’re mathematicians Drew Sutherland and Andy Booker, you go for the harder problem.

In 2019, Booker, at the University of Bristol, and Sutherland, principal research scientist at MIT, were the first to find the answer to 42. The number has pop culture significance as the fictional answer to “the ultimate question of life, the universe, and everything,” as Douglas Adams famously penned in his novel “The Hitchhiker’s Guide to the Galaxy.” The question that begets 42, at least in the novel, is frustratingly, hilariously unknown.

In mathematics, entirely by coincidence, there exists a polynomial equation for which the answer, 42, had similarly eluded mathematicians for decades. The equation x³+y³+z³=k is known as the sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a “Diophantine equation”—a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.

By harnessing randomness, a new algorithm achieves a fundamentally novel — and faster — way of performing one of the most basic computations in math and computer science.

A former graduate student reflects on how Isadore Singer, who died on February 11, brought together mathematicians, physicists and anyone else interested in the deeper connections between diverse fields.

There is considerable debate over whether plants are conscious and this, indeed, is an important question. Here I look at developments in neuroscience, physics and mathematics that may impact on this question. Two major concomitants of consciousness in animals are microtubule function and electrical gamma wave synchrony. Both these factors may also play a role in plant consciousness. I show that plants possess aperiodic quasicrystal structures composed of ribosomes that may enable quantum computing, which has been suggested to lie at the core of animal consciousness. Finally I look at whether a microtubule fractal suggests that electric current plays a part in conventional neurocomputing processes in plants.

A new mathematical algorithm examines data from EEG and brain implants to learn each epilepsy patient’s unique brain pattern signatures. The system can predict the onset of a seizure within an hour, allowing the patient to take necessary interventions.

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.

Po-Shen Loh has harnessed his competitive impulses and iconoclastic tendencies to reinvigorate the U.S. Math Olympiad program.