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Category: mathematics – Page 69

Making history with 42 digits, scientists at Paderborn University and KU Leuven have unlocked a decades-old mystery of mathematics with the so-called ninth Dedekind number.

Experts worldwide have been searching for the value since 1991. The Paderborn scientists arrived at the exact sequence of numbers with the help of the Noctua supercomputer located there. The results will be presented in September at the International Workshop on Boolean Functions and their Applications (BFA) in Norway.

What started as a master’s thesis project by Lennart Van Hirtum, then a computer science student at KU Leuven and now a research associate at the University of Paderborn, has become a huge success. The scientists join an illustrious group with their work. Earlier numbers in the series were found by mathematician Richard Dedekind himself when he defined the problem in 1,897, and later by greats of early computer science such as Randolph Church and Morgan Ward. “For 32 years, the calculation of D was an open challenge, and it was questionable whether it would ever be possible to calculate this number at all,” Van Hirtum says.

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Summary: Scientists used mathematics to explain the social phenomenon of six degrees of separation.

Their work suggests that the balance between the cost and benefit of maintaining social connections shapes the global human social network. According to their findings, individual efforts to optimize their social connections result in an average of six steps between any two people.

This explains why ideas, trends, and even diseases can spread globally within a few transmission steps.

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Note: June 23 is Alan Turing’s birth anniversary.

Alan Turing wore many scientific hats in his lifetime: a code-breaker in World War II, a prophetic figure of artificial intelligence (AI), a pioneer of theoretical biology, and a founding figure of theoretical computer science. While the former of his roles continue to catch the fancy of popular culture, his fundamental contribution to the development of computing as a mathematical discipline is possibly where his significant scientific impact persists to date.

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They created a quantum system with properties analogous to black holes.

A collaborative effort from research teams across multiple organizations in China was successful in using quantum computing technology to test Hawking Radiation, the theory proposed by renowned physicist Stephen Hawking, the South China Morning Post.

Quantum computing is a complex field that involves using mathematics, computer science, and physics to solve complex problems. Interesting Engineering recently reported how a quantum computer recently beat a conventional supercomputer at complex math.

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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.

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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.

Qubits, short for quantum bits, are analogs of a bit in quantum computing. Both are the primary or smallest units of information. However, unlike bits that can exist in two states, 0 or 1, a qubit can represent either of the states or in a superposition where it exists in any proportion of the two states.

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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.

An RP2040 microcontroller controls the show, and a switch on the badge selects power between USB and three AA batteries and a DC/DC boost converter. The PCB also features two capacitive touch pads. [HackerBox] has published the KiCad files for the badge, and the CircuitPython firmware is shared with the project. If C/C++ is more your preference, the RP2040 MCU can also be programmed using the Arduino IDE.

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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.

Penrose received the Nobel for his working out mathematical methods that proved and expanded Albert Einstein’s general theory of relativity, and for his discoveries on black holes, which showed how objects that become too dense undergo gravitational collapse into singularities – points of infinite mass.

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