One of the dilemmas facing anyone in a new and unfamiliar city is where to dine out. You might consult guides, speak to locals, check reviews, and ultimately, try your luck. But if you’re there for a while, at some point you’re going to be asking yourself whether to visit new eateries or stick to the ones you’ve already tried and liked.
This is known as a classic explore-exploit dilemma and was something the late physicist and Nobel laureate Richard Feynman pondered during a restaurant meal with a friend in the 1970s. His companion was debating whether to order his favorite dish or try something new. Feynman turned the question into a math problem and solved it there and then, scribbling his workings on pieces of paper.
Feynman, who died in 1988, never published his solution, but researchers came across his handwritten notes and not only deciphered them, but also put the solution to the test.
Glasses are non-crystalline but solid states of matter in which molecules and atoms are not arranged into a regular crystal lattice, but rather in a disordered pattern. Glassy materials are widely used in various settings, for instance, in the synthesis of pharmaceuticals and the development of electronics or optical devices.
When studying movement and changes in various materials and substances, physicists commonly rely on the so-called Arrhenius model. This is a mathematical framework introduced by Svante Arrhenius in 1889, which can be used to calculate how temperature affects the speed of a heat-activated chemical reaction or physical process.
Past studies have shown that when the Arrhenius model is applied to molecular glasses, it yields unrealistically small pre-exponential factors. Pre-exponential factors are values that describe the intrinsic timescale of the movement of molecules without considering temperature effects.
Numerical simulations in physics often require estimating a multitude of parameters, making the process computationally expensive and complex. Researchers at University of Tsukuba have introduced a new method called the multiparameter eigenvalue-problem emulator, enabling reliable predictions based directly on relationships among known data by eliminating the need for parameter estimation. This innovation considerably reduces computational costs and enables systematic quantification of predictive uncertainty.
Calibrating theoretical models with experimental data is a common practice in physics for predicting previously unobserved phenomena. However, real-world theoretical models are often highly complex, involving numerous numerical quantities, known as parameters, that cannot be directly measured. Researchers must estimate these parameters to compute other observables. This is a process that is computationally demanding and fraught with remarkable challenges in assessing how uncertainties in the parameters affect final predictions.
This study, published in Physical Review Letters, presents a novel fast surrogate model based on a mathematical framework known as the multiparameter eigenvalue-problem emulator. This model directly predicts unknown observables based on relationships among known data, without the need to introduce or estimate parameters.
For Dijkstra, programming was closer to mathematics than to a craft. The goal wasn’t to “get a feel” for code. The goal was to reason about it rigorously, to understand why it works before discovering whether it works.
The second part of this talk pursues some of the scientific and educational consequences of the assumption that computers represent a radical novelty. In order to give this assumption clear contents, we have to be much more precise as to what we mean in this context by the adjective “radical”. We shall do so in the first part of this talk, in which we shall furthermore supply evidence in support of our assumption.
The usual way in which we plan today for tomorrow is in yesterday’s vocabulary. We do so, because we try to get away with the concepts we are familiar with and that have acquired their meanings in our past experience. Of course, the words and the concepts don’t quite fit because our future differs from our past, but then we stretch them a little bit. Linguists are quite familiar with the phenomenon that the meanings of words evolve over time, but also know that this is a slow and gradual process.
It is the most common way of trying to cope with novelty: by means of metaphors and analogies we try to link the new to the old, the novel to the familiar. Under sufficiently slow and gradual change, it works reasonably well; in the case of a sharp discontinuity, however, the method breaks down: though we may glorify it with the name “common sense”, our past experience is no longer relevant, the analogies become too shallow, and the metaphors become more misleading than illuminating. This is the situation that is characteristic for the “radical” novelty.
John Nash was born on June 13, 1928, in Bluefield, West Virginia, a former coal town nestled deep in the Appalachian Mountains. As a young boy, Nash was solitary, bookish, and introverted. His father, John Sr., was a quiet engineer with an incisive mind. His mother, Virginia, also intelligent, was a former teacher who had large dreams for her son, pushing him to read at four, learn Latin, and skip a grade at school.
The first hint of John Nash’s math talent came in fourth grade, when a teacher told Virginia that the boy couldn’t do the math. Virginia laughed, well aware that her son was going down his own path to solve the simple problems. In high school, John solved his teachers’ clunky proofs in just a few elegant steps. He was one of ten nationally awarded winners of the George Westinghose Award, which provided him with a full scholarship to the Carnegie Institute of Technology. He hopped from engineering to chemistry before discovering his passion: mathematics.
He was accepted into Princeton University, which at the time was to mathematicians what Detroit was, and still is, to cars. Nash first wowed his peers with an elegantly playable board game, which his peers dubbed “Nash,” but later reached the market as Hex. He then absorbed himself in one of the sexiest math fields of the day, game theory, which described strategies in competition, whether in card games or business. His deceptively simple doctoral thesis would later re-orient the field of economics, although no one, not even Nash, predicted its potential.
Most people wouldn’t think that it would take rigorous mathematical proof to show how many folds it takes to make a donut shape out of paper. Yet, no one could quite figure it out until recently.
In a new paper, published in Proceedings of the National Academy of Sciences, mathematician Richard Evan Schwartz provides detailed proof of where the line is drawn when it comes to the fewest folds required to construct a torus—the proper name for the shape of a donut—from a piece of paper.
The planar Hall effect is a tabletop diagnostic tool for special quantum properties useful in basic research and technological applications. Or so it was thought, because careful calculation by Kobe University researchers clarifies the conditions under which this effect may also appear in classical materials. This makes the diagnostic more meaningful and enables more purposeful design.
In the hunt for materials with properties that are useful for quantum computing or spintronics, researchers have used the “planar Hall effect” as a tabletop diagnostic tool: The researchers send a current through a thin, flat sample and observe whether an electric voltage is produced in response to a magnetic field in the same plane as the sample.
If it is, the pattern of how the voltage responds to rotating the magnetic field in the plane of the sample tells researchers about the properties of the material.
In 1937, a young graduate student named Claude Shannon submitted a master’s thesis with an unassuming title: “A Symbolic Analysis of Relay and Switching Circuits.”
The utilization of the binary properties of electrical switches to perform logic functions is the basic concept that underlies all electronic digital computer designs. Shannon’s thesis became the foundation of practical digital circuit design when it became widely known among the electrical engineering community during and after World War II. At the time, the methods employed to design logic circuits (for example, contemporary Konrad Zuse’s Z1) were ad hoc in nature and lacked the theoretical discipline that Shannon’s paper supplied to later projects.
Shannon’s work also differed significantly in its approach and theoretical framework compared to the work of Akira Nakashima. Whereas Shannon’s approach and framework was abstract and based on mathematics, Nakashima tried to extend the existent circuit theory of the time to deal with relay circuits, and was reluctant to accept the mathematical and abstract model, favoring a grounded approach. [ 6 ] Shannon’s ideas broke new ground, with his abstract and modern approach dominating modern-day electrical engineering. [ 6 ].
How ambitious should you be? Folk wisdom offers conflicting advice: “Shoot for the moon,” but also, “Don’t let the perfect be the enemy of the good.” A new study by researchers at the University of Wyoming, Stanford University and the University of Colorado-Boulder used a mathematical model to show that ambition lies in the middle—above average but finite.
“Conventional wisdom tells people not to settle, but also not to let the perfect be the enemy of the good,” says lead author Kath Landgren, a postdoctoral scholar at Stanford’s Doerr School of Sustainability. “We wanted to see whether the math actually supports that intuition. It does, with some interesting twists.”
Roger Penrose and Brian Cox discuss how Roger got interested in physics, the Big Bang, and the role of beauty in mathematics.
Do you agree with Roger’s thoughts on string theory?
With a free trial, you can watch the full conversation NOW at https://iai.tv/video/our-future-theor… the Big Bang to the fabric of spacetime and the nature of consciousness, our core scientific assumptions frame how we understand and perceive reality. But there are many challenges to our current understanding. What if the very foundations of our theories are flawed? Should we reconsider our understanding? And how radically might our view of the universe have to change? Join Roger Penrose, Nobel Prize Laureate and winner of the Wolf prize, in collaboration with Stephen Hawking, with legendary physicist and science communicator, Brian Cox, to explore whether the flaws in our current theories are at some fundamental level insurmountable, or whether they can be extended or changed to overcome these challenges. #physics #cosmology #bigbang Awarded the 2020 Nobel Prize in Physics for his work on black holes, Roger Penrose is a world-renowned mathematician and physicist. In recent years, he has investigated the relationship between physics and the mind, famously arguing that quantum mechanics plays an essential role in solving the mysteries of human consciousness. Penrose has made numerous appearances on media such as BBC, Closer to Truth, and The Joe Rogan Experience. In 1994, he was knighted for his services to science. Famed for his poetic take on the cosmos, physicist and broadcaster Brian Cox has become one of the world’s most recognizable voices in science communication. A former musician turned particle physicist, Cox has played a key role in major experiments at CERN and the Large Hadron Collider, while also captivating millions through BBC series such as Wonders of the Universe, The Planets, and Forces of Nature. Cox has been showered with praise for his contributions, appointed Commander of the Order of the British Empire (CBE), and is the recipient of the Institute of Physics Kelvin Medal and the Michael Faraday Prize. Beyond his work as a Royal Society professor of physics at the University of Manchester, Cox advocates for public scientific literacy and political responsibility in science funding. His style blends rigorous physics with a deep sense of awe — bringing relativity, entropy, and quantum theory into living rooms around the globe. His rare ability to fuse clarity with wonder has earned global acclaim. The Institute of Art and Ideas features videos and articles from cutting edge thinkers discussing the ideas that are shaping the world, from metaphysics to string theory, technology to democracy, aesthetics to genetics. Subscribe today! https://iai.tv/subscribe?utm_source=Y… 0:00 Intro 0:44 Brian Cox on how Roger Penrose inspired him 1:39 — Beauty in mathematics 3:00 — How Roger struggled with maths at school 6:51 — How Roger got interested in physics 9:27 — What theory is best for explaining the beginning of the universe? 12:12 — A key new discovery in cosmology 18:44 — The big bang is not quantum mechanical For debates and talks: https://iai.tv For articles: https://iai.tv/articles For courses: https://iai.tv/iai-academy/courses.
From the Big Bang to the fabric of spacetime and the nature of consciousness, our core scientific assumptions frame how we understand and perceive reality. But there are many challenges to our current understanding. What if the very foundations of our theories are flawed? Should we reconsider our understanding? And how radically might our view of the universe have to change? Join Roger Penrose, Nobel Prize Laureate and winner of the Wolf prize, in collaboration with Stephen Hawking, with legendary physicist and science communicator, Brian Cox, to explore whether the flaws in our current theories are at some fundamental level insurmountable, or whether they can be extended or changed to overcome these challenges.
#physics #cosmology #bigbang.
Awarded the 2020 Nobel Prize in Physics for his work on black holes, Roger Penrose is a world-renowned mathematician and physicist. In recent years, he has investigated the relationship between physics and the mind, famously arguing that quantum mechanics plays an essential role in solving the mysteries of human consciousness.
