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The United States military has begun a mine clearance operation in the Strait of Hormuz, a vital waterway for global oil and gas supplies, in response to Iran's alleged laying of sea mines. The operation, led by guided missile destroyers USS Frank E Peterson and USS Michael Murphy, aims to establish a 'safe pathway' for the free flow of global commerce.Iran's Islamic Revolutionary Guard Corps (IRGC) recently released a map of the Strait of Hormuz showing a safe route for ships to follow through the strait, directing vessels farther north towards the Iranian coast and away from the traditional route closer to the coast of Oman. The IRGC stated that all vessels must use the new map for navigation due to 'the likelihood of the presence of various types of anti-ship mines in the main traffic zone.'The stakes are high, with one-fifth of the world's oil and liquefied natural gas (LNG) supplies having been shipped through the Strait of Hormuz before the war. Even a single mine can compel operators to assume a wider threat, effectively invalidating insurance and shutting down their use of the waterway.Iran's stockpile is estimated to number 2,000 to 6,000 mines, a significant portion of which are produced domestically. These mines generally fall into three categories: contact mines, bottom (influence) mines, and 'smart' and rocket mines.The US Navy is facing a 'mine gap,' with experts calling for institutional neglect that led to the retirement of dedicated mine countermeasures (MCM) assets. The current US strategy relies on small combat ships built for coastal operations and fitted with MCM mission modules, but only one of these vessels, the USS Canberra, is currently available in the region.

Tanya Khovanova has long been a leading voice in the world of recreational mathematics, authoring a popular blog and running the Number Gossip site where enthusiasts can inquire about any number.She now debuts her first book, Mathematical Puzzles and Curiosities, co‑written with fellow puzzle‑enthusiasts Ivo David and Yogev Shpilman. Published by World Scientific, the volume offers fresh challenges and inventive twists on classic problems.To give readers a taste, Khovanova selected three puzzles for the Guardian column:1. Battleships – As a naval admiral you must choose between sending a single vessel with a success probability of P % or two vessels each with a P/2 % chance, where the mission succeeds if at least one ship does. Which strategy maximises the odds?2. The Two Oracles – You face two respondents, Randie, who answers randomly, and Rando, who randomly decides to tell the truth or lie before each answer. Is there a method to distinguish them?3. Bad Maths – A student computes 5548 − 5489 as 59, claiming the “548” cancels out. He then experiments with a subtraction of the form XXYZ − XYZW (distinct digits) and observes the result is XW. How many digits in the new expression match those in the original calculation?Solutions to the trio were later posted online (update), but readers were urged to avoid spoilers until the scheduled reveal.Khovanova also reminds fans that she has been curating puzzles for the Guardian every other Monday since 2015 and welcomes new submissions via email.

Finding the perfect feel-good movie can be a daunting task, especially with the vast library of films available today. However, for the author, Hot Fuzz stands out as the ultimate comfort movie. Directed by Edgar Wright, Hot Fuzz is the second installment in his Cornetto trilogy, following Shaun of the Dead and preceding The World's End. The film tells the story of Sergeant Angel, a fish-out-of-water city cop who teams up with local PC Danny Butterman to investigate a series of mysterious deaths in the sleepy village of Sandford. It's a love letter to buddy cop movies and the action genre, featuring a star-studded cast including Simon Pegg and Nick Frost. The film's blend of humor, action, and smart writing makes it a standout. One of the key reasons Hot Fuzz remains endearing and enduring is its ability to respond to multiple needs. Whether you're looking for something funny, expertly crafted, explosive, thought-provoking, or simply to switch off to, Hot Fuzz delivers. The film's quotability and memorable lines, such as 'For the greater good' and 'It's just the one swan actually', have become ingrained in popular culture. The author's personal connection to the film adds to its significance. Hot Fuzz introduced them to Edgar Wright, whom they ended up writing their dissertation about. The film's impact extends beyond the screen, with its quotes and references frequently popping up in conversations. It's no wonder that Hot Fuzz has become a timeless classic, continuing to entertain audiences to this day. Hot Fuzz is available to rent digitally in the US, on ITVX in the UK, and on Binge in Australia.

Director Luca Guadagnino has come to the defense of actor Timothée Chalamet after Chalamet faced backlash for suggesting that ballet and opera are art forms that "no one cares about" anymore.Guadagnino, who cast Chalamet in his breakthrough role in Call Me By Your Name, stated that the reaction to Chalamet's comments was disproportionate. "I am not on social media and don’t understand how one [single] comment can become a planetary polemic," Guadagnino said in an interview with Italian newspaper La Stampa.Guadagnino, who made his opera debut in 2011 with a production of Verdi’s Falstaff, noted that Chalamet "could have spared himself … but he’s young, smart, sensitive, and he fears that cinema could become marginal." He emphasized the importance of nurturing all forms of imagination and uniting the arts, rather than separating them.Chalamet's remarks sparked significant backlash from the ballet and opera communities, including Jamie Lee Curtis and Whoopi Goldberg, who publicly criticized him. The Maggio Musicale Fiorentino invited Chalamet to attend Guadagnino's production of The Death of Klinghoffer, saying, "Come and see for yourself that opera is alive, kicking and actually matters to people."

The Pivot from Vision Pro to Everyday WearablesApple is reportedly preparing to enter the smart glasses market with a product launch targeted for 2027, signaling a significant strategic shift away from its ambitious mixed reality ambitions.Four Distinct Design PrototypesRectangular Frames: Ranging from large to slim, potentially mimicking the style of CEO Tim Cook.Oval/Circular Frames: Available in both larger and smaller sizes.Color Options: Black, ocean blue, and light brown.A Strategic Retreat from High-End ARThis move represents a retreat from the complex Vision Pro ecosystem, which faced delays and lukewarm reception. Instead, Apple is betting on a simpler form factor similar to Meta’s Ray-Ban glasses.The 2027 Roadmap: Simplicity Over ImmersionThe upcoming device will lack displays, focusing instead on camera lenses for photos, videos, calls, and music. It will also integrate with the long-promised Siri upgrade, aiming to capture the mainstream market rather than the niche enthusiast base.

When wages have been stagnant for almost two decades and a simple tube of toothpaste now costs nearly £7 at a major supermarket, the claim that “money can’t buy happiness” feels increasingly dismissive. The argument rests on a narrow view of what money can achieve. Spending cash solely on material goods yields only short‑lived pleasure. In contrast, the ability to afford time, experiences and mental‑health support expands one’s sense of freedom and purpose. Even basic needs such as leisure have become commodified; more disposable income simply translates into more opportunities to pursue what matters. As someone diagnosed with ADHD, I have learned—through personal trial rather than formal neuroscience—how to secure a steady supply of dopamine. The cheapest route is not a quick thrill, but activities that provide lasting satisfaction, such as novel experiences and moments of awe. One vivid example came during a winter trip to rural France, where two feet of snow turned the landscape into a scene straight out of Narnia. The awe‑inspiring view was a reminder that nature’s restorative power is often accessible only to those who can afford the travel, in my case a budget flight with Ryanair. Research supports the intuition that higher income correlates with greater happiness. A 2023 study by psychologists at Princeton and the University of Pennsylvania found that people with higher earnings report higher life satisfaction, though money cannot resolve non‑financial sources of unhappiness. Even the world’s richest are not immune to the paradox. Earlier this year, Elon Musk—on track to become the first trillionaire—tweeted that anyone who says “money can’t buy happiness” must be missing something. While Musk’s wealth may not guarantee personal joy, the same resources could provide a foundation for happiness for billions facing financial strain. Nevertheless, hoarding wealth like a dragon does not equate to fulfillment. The column suggests that redirecting a portion of vast fortunes toward travel, cultural enrichment, and shared experiences could transform isolated wealth into collective well‑being. In short, financial stability reduces stress and broadens horizons. It allows individuals to invest in the intangible assets—time, relationships, awe‑inducing experiences—that truly enrich life.

The acclaimed HBO series Hacks is set to conclude with its fifth and final season, which promises to be a joyful and lighter chapter in the story of its two lead characters.Created by Paul W. Downs, Lucia Aniello, and Jen Statsky, Hacks has been a critical darling since its debut in 2021, earning a 99% Rotten Tomatoes score and 12 Emmy wins, including Outstanding Comedy Series in 2024.The show revolves around the unlikely partnership between Deborah Vance (played by Jean Smart), a veteran comedian, and Ava Daniels (played by Hannah Einbinder), a young comedy writer. Their relationship evolves over four seasons, navigating the challenges of comedy, fame, and personal growth.Paul W. Downs, who plays Jimmy on the show, revealed that the creators had the ending in mind from the beginning. The final season focuses on Deborah's comeback and her relationship with Ava, which has deepened into affection, mutual respect, and love.The new season features a more playful tone, with episode ideas that include anxiety dream sequences, a meditation on AI, and a farcical episode where Deborah forces Ava to lean into a misunderstanding. Downs describes the season as “sunnier, more playful, but with just enough heart and pathos” to provide a satisfying conclusion.Hacks has been praised for its unique take on comedy and its ability to transcend the entertainment industry, exploring themes of identity, dignity, and human connection. The show's conclusion will be available on Sky and NOW in the UK, HBO Max in the US, and Stan in Australia.

The rapid advancement of artificial intelligence (AI) has led to a growing concern about who controls the companies behind these technologies. OpenAI, the creator of ChatGPT, is at the forefront of this discussion, with its products now integrated into various aspects of our lives, from smartphones to defense contracts and law enforcement. Investigative journalist Ronan Farrow's recent piece in The New Yorker has raised important questions about the power dynamics at OpenAI, particularly surrounding its billionaire founder and CEO, Sam Altman. Farrow's article suggests that Altman's leadership and the company's operations have sparked concerns about its growing influence and the potential risks associated with its technology. OpenAI's market valuation has reached an astonishing $852 billion, despite a projected loss of $14 billion in 2026. This commercial momentum has led to a significant expansion of its operations, including a deal with the US military to use its technology in classified operations. This move has raised eyebrows, especially given the company's own staff researchers' concerns that AI could be a "threat to humanity". The article also highlights the connections between OpenAI executives and political figures, including a $25 million donation to a Trump fundraising vehicle by OpenAI's top executive, Greg Brockman. These ties have sparked concerns about the company's commitment to democracy and its potential influence on AI regulations. The debate surrounding OpenAI and AI regulation has led to a "QuitGPT" campaign by activist/historian Rutger Bregman, calling for a worldwide boycott of Altman's company. As AI continues to shape our world, it is essential to consider the implications of who controls these technologies and the need for meaningful social, political, legal, and economic guardrails to minimize harm.

Meta announced the launch of Muse Spark, the debut artificial‑intelligence model from the company’s ambitious "superintelligence" squad that was assembled last year with a multi‑billion‑dollar budget. The team, spearheaded by former Scale AI chief Alex Wang—brought on board in a $14.3 bn acquisition—has been offered compensation packages running into the hundreds of millions to attract top talent. Muse Spark is the first installment of the internally codenamed "Avocado" series. For now, the model is accessible only through Meta’s AI app and website, but Meta says it will soon supplant the existing Llama models that power chatbots on WhatsApp, Instagram, Facebook and the firm’s smart‑glasses lineup. Unlike earlier open releases of Llama, Meta has kept Muse Spark’s architecture details under wraps, offering a private preview to a select group of unnamed partners. In a blog post, Meta described the system as "small and fast by design, yet capable enough to reason through complex questions in science, math and health," positioning it as a solid foundation for future, larger versions. Independent testing shows Muse Spark narrowing the gap with leading models from Google, OpenAI and Anthropic in language and visual comprehension, though it still trails in coding and abstract reasoning tasks. The model placed tied for fourth on a comprehensive AI benchmark compiled by Artificial Analysis. CEO Mark Zuckerberg had previously cautioned investors that early releases would be modest but would demonstrate a "rapid trajectory." Wang echoed this sentiment on social media, acknowledging "rough edges" that will be refined over time and confirming that bigger variants are already in development, with some slated for open release. Beyond performance metrics, Meta hinted at commercial ambitions, embedding shopping suggestions directly into its AI chatbot to guide users toward purchasable items. With over 3.5 billion active users across its platforms, the company hopes AI‑driven personal tasks will boost engagement and create a competitive edge over rivals with smaller user bases. Practical use‑cases highlighted include estimating meal calories from a photo, virtually placing a mug on a shelf via augmented reality, and a new "Contemplating Mode" that runs multiple agents simultaneously—mirroring advanced reasoning features seen in Google’s Gemini Deep Think and OpenAI’s GPT‑Pro. Meta says this mode could, for example, help a family plan a vacation by having one agent draft an itinerary while another scouts kid‑friendly activities.