Why Do We Still Boil Water to Generate Electricity?
From the age of the steam engine to the nuclear power plant, humanity has spent centuries tinkering with technology and is still boiling water. Photovoltaics, wind turbines, fuel cells, magnetohydrodynamic generators—why have all these seemingly more advanced technologies failed to replace the same kettle we have kept boiling for three hundred years? Author: 锅炉-251 Reviewer: 赖渊 Introduction A familiar joke says that human development amounts to boiling water and throwing rocks. The first half refers to modern electricity generation, which relies mainly on thermodynamic cycles that use steam as the working fluid. The second says that humans still inflict damage mainly by projecting mass at a target. This article focuses on energy. By examining where energy comes from, how it is used, ...
Why Do Batteries Swell? Can EV Batteries Swell Too?
Author: 时光 Reviewed by: 阿氯 It Started with a Bulging Phone Cover One evening, a friend sent me a photo of their phone. The battery appeared to have swollen and forced the back cover apart, leaving a truly sorry sight. Gone but not forgotten Image source: Provided by a friend of the author; not publicly available This is hardly an unfamiliar sight. In 2017, barely a week after Apple’s iPhone 8 series went on sale, several incidents were reported around the world in which swollen batteries pushed newly unboxed or charging phones’ screens out of their frames. A user's post on the social-media platform Twitter, now called X Image source: Magokoro0511. Screenshot of a post[EB/OL]. X (formerly Twitter), 2016-09-25 [accessed 2026-03-03]. Photograph of a swollen battery Image source: Mag ...
Hilbert's Tenth Problem, Part V: The MRDP Theorem
Author: silverxz Proofreader: Acidmoon This article proves that Diophantine sets are equivalent to recursively enumerable sets. We have already noted that the direction from Diophantine sets to recursively enumerable sets is fairly straightforward. Let there be a Diophantine set SSS and its corresponding Diophantine equation D(x1,...,xn,y1,...,ym)=0D(x_1,...,x_n,y_1,...,y_m)=0D(x1,...,xn,y1,...,ym)=0; for (a1,...,an)∈Nn(a_1,...,a_n)\in \mathbb{N}^n(a1,...,an)∈Nn, we need only have a Turing machine MMM systematically try every possible y1,...,ymy_1,...,y_my1,...,ym to see whether D(a1,...,an,y1,...,ym)=0D(a_1,...,a_n,y_1,...,y_m)=0D(a1,...,an,y1,...,ym)=0 holds. If (a1,...,an)∈S(a_1,...,a_n)\in S(a1,...,an)∈S, the machine will eventually halt. The candidates must, of cou ...
A Rigorous Introduction to Hilbert's Tenth Problem (IV): Basic Concepts and Proof Framework
Author: silverxz Proofreader: Shiguang We now turn to the proof itself. This is not the original proof, but Matiyasevich’s greatly simplified version from his book Hilbert’s Tenth Problem, so its route differs somewhat from the history described earlier. We will simplify parts of the argument further and skip details that are laborious without adding new ideas. The exposition often works backward: it starts from a result, asks what tools are needed to prove it, and then supplies those tools one by one. I will also use ordinary language to give an intuitive account of the proof and explain its motivation. That approach is better suited to a popular introduction. What is Hilbert’s Tenth Problem? Let us first restate the problem we want to solve. A Diophantine equation is a multivari ...
Trial of Xuan — A WebGL Game
Trial of Xuan · Unity WebGL The game opens on a separate page instead of running inside this article. The first load is about 115 MB, so Wi-Fi is recommended. On a phone, it is best played in landscape mode. Play Trial of Xuan
Hilbert's Tenth Problem, Part III: A History (Conclusion)
Author: silverxz Proofreader: Shiguang Many years later, when Hilbert’s Tenth Problem had finally been laid to rest, Martin Davis would surely remember that distant afternoon when his teacher said, “Hilbert’s Tenth Problem begs for a proof of unsolvability.” We have already seen how Gödel, Turing, and others shattered the completeness, consistency, and decidability sought by Hilbert’s program. Hilbert’s Tenth Problem is simply one special case of the decision problem. The negative answer to that broader question transformed almost all optimism about Hilbert’s Tenth Problem into pessimism within a decade. Emil Post was one of the founders of computability theory, but fortune rarely favored him. At twelve he lost his left arm in a car accident, which led him to abandon astronomy for ...
Fundamentals of Editing and Publishing
Author: Shiguang Reviewed by: Mei Shida Publishing and Editing Publishing, more fully “publishing activity,” is the professional practice of selecting, editing, reproducing, and disseminating works to the public. It covers a complex series of processes that take a work from its original manuscript to the final publication, with the purpose of conveying valuable information to readers. Editing has a dual identity. As a verb, it means the process of organizing and refining source material or an existing work. As a noun, it refers to a professional who organizes, records, collects, arranges, compiles, and reviews intellectual products and other documents before making them available to the public—for example, a publishing-house editor. Editing is an important part of publishing and a prere ...
2025 World Book Day — A Popular Science Reading List
In April, as the living world begins to grow again, we celebrated the 30th World Book Day. Books are beacons for exploring the unknown. A-kun’s call for popular science recommendations brought in a wealth of excellent titles. Here is the reading list our community built together. A Brief History of Time Stephen Hawking Written in accessible language, this book introduces frontier ideas about the origin of the universe and humanity’s fate. From black holes and the Big Bang to time travel, Hawking’s vivid prose leads readers through the mysteries of a vast and astonishing cosmos. It can inspire both newcomers to science and readers who already have some background knowledge. More than a source of scientific facts, it awakens curiosity, encourages exploration, and asks us to consider humani ...
A Rigorous Introduction to Hilbert's Tenth Problem (II): A History, Part I
Author: silverxz Proofreader: Shiguang The previous article introduced Hilbert and his 23 problems. The next two articles review the history behind them. This one covers the background needed for the tenth problem: the history of Diophantine equations, algorithms, and computability. The next article turns to the history of the solution to Hilbert’s Tenth Problem. Readers already familiar with this material may go directly to that installment. Diophantine equations: from Diophantus to Hilbert The story has a classic opening: Once upon a time—or, more precisely, 1,800 years ago—the ancient Greek mathematician Diophantus studied a great many algebraic equations. At the time, these were equations formed from polynomials with rational coefficients. His work covered many subjects, with ...
A Rigorous Introduction to Hilbert's Tenth Problem (I): Introduction
Author: silverxz People have a peculiar fascination with mathematical conjectures and the stories of how they were solved. Goldbach’s conjecture and Chen Jingrun, Fermat’s Last Theorem and Wiles, solutions by radicals and Abel and Galois: such examples have found their way into elementary education. Children may not even understand the statements of these problems, yet they enjoy stories in which a legendary figure resolves a long-standing conjecture, much as they enjoy tales of heroes and dragons. This is probably how Hilbert’s name first reached the wider public: David Hilbert (1862-1943) was the most celebrated mathematician of his era. In 1900, Hilbert assembled 23 mathematical problems that were then unresolved. Some were sharply defined (Problem 8, for example, is the Riemann h ...