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The National
2 days ago
- Entertainment
- The National
McScenius: Let's put brains together to bring about a smarter Scotland
Those emeritus professors of snark, Steely Dan, put one aspect of the genius myth very well. Once you declare your geniushood, all the rest of your behaviours – however cranky or cruel – come to be justified. As Helen Lewis writes in her funny, combative new book, The Genius Myth, we have plenty of current examples of this. Most notable at present is Donald Trump, declaring himself a 'pretty stable genius', while his conversational 'weave' baffles all who hear it. Trump then appoints Elon Musk as a 'pretty high-IQ individual', on the basis of his tech business success. Yet he departs from his Doge post in ignominy, leaving a trail of administrative destruction behind him. READ MORE: Owen Jones: Opposing Israeli violence is 'extremist'? The world's upside down As Musk advances both on our brains with neuro-filaments, and on the starry skies with satellites and Mars ships, the temptation is to say: let us be protected from such 'high-IQ geniuses'. Lewis lays out the historical seeds of what she regards as a 'dangerous' idea. Originally and classically, genius was visited upon us, a bolt of insight from a higher realm. It became individualised from the Renaissance onwards. Leonardo da Vinci was the original 'scatter-brained polymath' archetype of genius. The Romantics liked their geniuses 'boyish, naughty, in the late stages of tuberculosis and, best of all, dead by suicide', as The New Yorker review puts it. Geniuses were also natural and child-like; and out of that fragility, we assume their 'precious gift' extracts a 'terrible price'. This archetype also excuses behaviours like 'alcoholism, family abandonment, unfaithfulness, abuse, weirdness, failure to take responsibility'. The shit-posting, ketamine-gobbling, games-obsessive, promiscuously-parenting Musk is all too exemplary of these cliches of genius. To top it off, Victorian and early 20th-century eugenicists like Francis Galton and Hans Eysenck believed they could measure genius, by using tests to identify a person's 'intelligence quotient' (IQ). Lewis has grim fun with Nobelists like William Shockley, who got a Nobel for inventing the transistor, but then descended into arguing that 'caucasians' had higher IQs. Shockley even tried to set up a sperm bank for Nobelists (it's noteworthy he didn't consider an egg bank), and advocated for the eradication of lower-IQ people. Great delight is taken by Lewis in pointing out that Shockley came to his world-changing transistor idea while working at Bell Labs. This was an 'alchemical space of collective achievement', a set of 'ripe social conditions constructed by previous breakthroughs'. That is, Bell Labs was a place of 'scenius' (using Brian Eno's term for a fertile milieu of talents and experiments). It's out of these scenes that superhuman acts of 'genius' might occur. Lewis admits that this sociological explanation is deeply unsatisfying for most people. READ MORE: Scotland wants no part in further dangerous nuclear experiments 'We find it intuitively easy to understand human-sized stories, where someone does something,' Lewis says in a recent interview. 'Our brains crave stories with protagonists and don't want mushy explanations that involve complex social forces.' I accept this, as well as Lewis's injunction that ascribing genius 'says as much about us as it says about them'. The educationalist Howard Gardner, in his 1997 book Extraordinary Minds, emphasised how great innovators need a coherent field around them, in order that their novel moves make sense. Picasso's paintings, like Les Demoiselles d'Avignon or Guernica, shake up traditions of portraiture or landscape. Joyce's Ulysses, or Woolf's To The Lighthouse, have the great 19th-century novels around them to trouble and unravel. It's even clearer in music. I wouldn't hesitate to call John Coltrane, Stevie Wonder or Prince 'geniuses' of pop and jazz music. I also wouldn't deny that they came to their moments of blinding newness from imbibing and inhabiting long-standing traditions. Coltrane was trained in barroom blues and big bands. Wonder came from the gospel tradition, as well as passing through the Motown hit factory. Prince drank from all those wells self-consciously throughout his musical life, giving himself an enormous toolbox to use. However, I still feel that genius – even if it is a 'lightning strike' upon individuals, already thriving in 'fertile conditions', as Lewis concludes – is something that extraordinary minds can and do perform. The thrill is when separate domains are conjoined, in ways unimaginable before the act of genius, to produce a new domain – one that triggers a cascade of fresh activity. There are two Scottish geniuses who exemplify this. Firstly, the physicist James Clerk Maxwell, of whom Einstein said 'the special theory of relativity owes its origins to Maxwell's equations'. Maxwell had a profound ability to see analogies between different areas of science and mathematics. His crowning achievement – Maxwell's equations – unified electricity, magnetism and optics into a single theoretical framework. This synthesis anticipated Einstein's later unifications (of spacetime and mass-energy), establishing the basis of modern field theory and quantum electrodynamics. But it's Maxwell's conceptual leaping across domains that remains awesome. In literature, this reminds me of another I would call 'genius', novelist and artist Alasdair Gray. The domains Gray effortlessly bridges is fictional prose and figurative illustration. His 1981 masterpiece Lanark, illustrated and fashioned by Gray as an object, also connects wildly different literary domains – angst-ridden realism, dystopian science-fiction, the end of the novel's narrative placed at the beginning. Gray tangles up the frames of causality, in many of his novels, just as Maxwell challenged mechanistic visions of physics. The thrill of Gray's genius is felt when you go through the original novel of Poor Things (1991). Its Frankensteinian tale of self-creation is richly illustrated throughout. It feels like a wholly different historical world. I'm not so sure of Maxwell's milieu. But one would have to accept that Gray was partly produced by the 'scenius' of the second Scottish Literary Renaissance – embedded in the bohemias of Glasgow and Edinburgh, embarking on groups and magazines with James Kelman, Janice Galloway, Liz Lochhead, Philip Hobsbaum and many others. So is one implication of Lewis's social explanation of 'genius' that such hot-beds can be fomented and prepared? Not so much the 'genius bars' of an Apple showroom, but the bars and 'third places' in which flashes of genius might occur? Can these be nurtured, even planned? If domain-crossing is a fundamental process leading to genius-like activity, then one would have to say, in Scotland, the buildings and ambitions to support it are moving into place. I was honoured to accept an invitation to become an associate at the Edinburgh Futures Institute earlier this year, because I could see in the edifice (and its research prospectus) that domain-crossing is an expectation, not an exception. READ MORE: Interim head appointed at university after damning report into financial crisis But in Dundee and Glasgow universities, there are also 'advanced studies' centres. All of them look at major challenges and megatrends – around AI, health, urban development – and declare their intent to rub together many different talents and specialisms, in pursuit of lasting solutions. So there's your 'McScenius' – but of course there can always be more of it. For example, is there enough traffic between the universe-building taking place in Dundee's games sector, and the massive computations – now to be even greater with the supercomputer recommission – operating in Edinburgh? What worlds could we be virtually simulating, in order to help repair the actual world? Another example: will the tumult around community power – whether land ownership, renewable energy generation, ecological lifestyles – compel innovations in democracy and organisation, supported by radical tech? And if so, what Hume- or Smith-like Second Enlightenment minds might survey this, and elaborate new models of progress and development from it? There's doubtless many other zones like this in Scottish life. And it's as important to identify and foment them, right where we are now – when proximity and engagement are vital. An independent Scotland should be the ideal framework for such a culture of immanent, everyday genius. But we shouldn't be put off from pursuing a Scottish 'scenius' by political or constitutional log-jams. It may be that we have an answer to the Dan. And that, thanks to Helen Lewis's excellent provocation, we do know what we mean by 'genius'.
Yahoo
15-05-2025
- Science
- Yahoo
Mathematicians May Have Solved Impossible Algebra Problem
Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or (x² + 2x + 1). In real life, these equations get very messy, very fast. In fact, mathematicians typically only approximate the solutions for ones above a certain value, known as higher degree (or higher order) polynomials. In this paper, however, the authors posit that they can use a metric from geometry called a Catalan number, or Catalan series, to find exact solutions to higher degree polynomials. The Catalan numbers are a natural observed consequence of a bunch of different mathematical scenarios, and can be found by engaging in such efforts as distilling Pascal's triangle of polynomial coefficients. They help graph theorists and computer scientists to plan data structures called trees by showing how many different tree arrangements can be made within certain parameters. In this case, they also quantify how many ways you can divide a polygon of any size into a particular number of triangles. The leading mind behind this work, mathematician Norman 'N.J.' Wildberger, is an honorary professor at the University of New South Wales in Australia—a term likely reflecting the fact that he retired in 2021 after teaching at the university since 1990. Wildberger also self identifies as a 'heretic' of certain mathematical foundations, exemplified in part by his longtime belief that we should stop using infinity or infinite concepts in some parts of math. That opposition to infinite or irrational numbers is key to this research. For many, many years now, people studying algebra have known that we simply 'can't' solve certain polynomials. They can't be taken apart into a mathematical term that fits under a square root (a.k.a. radical) sign at all. But, in Wildberger's view, focusing on this divide and dwelling inside the radical is a hindrance. We should 'sidestep' it altogether. To make this argument, Wildberger teamed up with Dean Rubine, a computer scientist who has worked for Bell Labs and Carnegie Mellon University. However, for decades now, Rubine has helped to lead the number-crunching at a secretive hedge fund that focuses on algorithms (more later on his role in this publication). The paper has a teacherly quality, reading somewhat like a chapter from a good textbook. The authors lay out and define their terms, then build their arguments one by one into a complete picture. What results is the 'hyper-Catalan' array, which contains the classic Catalan numbers as well as an extension that includes other numbers that satisfy the conditions to solve polynomials. (Remember, the hyper-Catalan number series doesn't need to line up with all the other uses of the Catalan numbers—rather, the Catalans are a basis from which to begin building a unique set that solves the polynomial problem.) This all wrapped up in an array called the Geode, which encompasses the entirety of the hyper-Catalan number series. After stepping through the work leading up to and including the Geode array, Wildberger gets in one last jab: [F]ormal power series give algebraic and combinatorially explicit alternatives to functions which cannot actually be concretely evaluated (such as nth root functions). Hence they ought to assume a more central position. This is a solid, logical way of removing many of the infinities which currently abound in our mathematical landscape. Having been authored by an aging iconoclast and a longtime quantitative executive, this work may have more of an uphill climb to be broadly recognized. It's also published in the peer reviewed American Mathematical Monthly—a broad interest journal associated with the Mathematical Association of America. The journal accepts advertisers, offers paid editing services, and offers an option where authors can pay to make their articles open access—often a few thousand dollars or more. (The latter is, unfortunately, the normalized model and cost of open access publishing.) In this case, this less-orthodox approach could be a result of the subject matter simply not being on most people's radar anymore. But it also fits right into Wildberger's lifelong quest to trim the mathematical fat and present clear, simple ideas for as many people as possible. On the tech forum Hacker News (from startup incubator Y Combinator), Rubine explained in a post that he'd closely followed Wildberger's work on this problem since 2021, when Wildberger declared he was going to solve this problem on his YouTube channel. '[H]e was doing a series where he'd teach amateurs how to do math research,' Rubine said. 'For the first problem, he said he'd solve the general polynomial. I thought it was a joke, because everybody 'knows' that we can't go beyond degree four. But no, 41 videos later, he had done it. Two years after that he still hadn't written it up, so I wrote a draft and sent it to him, which evolved into this paper.' With that kind of determination, Wildberger may, after all, be an apt opponent for infinity itself. His democratic, open-door approach to mathematical thinking is really admirable. And in the paper, he and Rubine point out a number of questions that this theory opens up. We'll see if others in the mathematics community pick up some of these questions. I, for one, hope so, because 41 more videos is a long time to wait for the next breakthrough. You Might Also Like Can Apple Cider Vinegar Lead to Weight Loss? Bobbi Brown Shares Her Top Face-Transforming Makeup Tips for Women Over 50
Yahoo
13-05-2025
- Science
- Yahoo
Mathematicians Thought This Algebra Problem Was Impossible. Two Geniuses May Have Found a Solution.
Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or (x² + 2x + 1). In real life, these equations get very messy, very fast. In fact, mathematicians typically only approximate the solutions for ones above a certain value, known as higher degree (or higher order) polynomials. In this paper, however, the authors posit that they can use a metric from geometry called a Catalan number, or Catalan series, to find exact solutions to higher degree polynomials. The Catalan numbers are a natural observed consequence of a bunch of different mathematical scenarios, and can be found by engaging in such efforts as distilling Pascal's triangle of polynomial coefficients. They help graph theorists and computer scientists to plan data structures called trees by showing how many different tree arrangements can be made within certain parameters. In this case, they also quantify how many ways you can divide a polygon of any size into a particular number of triangles. The leading mind behind this work, mathematician Norman 'N.J.' Wildberger, is an honorary professor at the University of New South Wales in Australia—a term likely reflecting the fact that he retired in 2021 after teaching at the university since 1990. Wildberger also self identifies as a 'heretic' of certain mathematical foundations, exemplified in part by his longtime belief that we should stop using infinity or infinite concepts in some parts of math. That opposition to infinite or irrational numbers is key to this research. For many, many years now, people studying algebra have known that we simply 'can't' solve certain polynomials. They can't be taken apart into a mathematical term that fits under a square root (a.k.a. radical) sign at all. But, in Wildberger's view, focusing on this divide and dwelling inside the radical is a hindrance. We should 'sidestep' it altogether. To make this argument, Wildberger teamed up with Dean Rubine, a computer scientist who has worked for Bell Labs and Carnegie Mellon University. However, for decades now, Rubine has helped to lead the number-crunching at a secretive hedge fund that focuses on algorithms (more later on his role in this publication). The paper has a teacherly quality, reading somewhat like a chapter from a good textbook. The authors lay out and define their terms, then build their arguments one by one into a complete picture. What results is the 'hyper-Catalan' array, which contains the classic Catalan numbers as well as an extension that includes other numbers that satisfy the conditions to solve polynomials. (Remember, the hyper-Catalan number series doesn't need to line up with all the other uses of the Catalan numbers—rather, the Catalans are a basis from which to begin building a unique set that solves the polynomial problem.) This all wrapped up in an array called the Geode, which encompasses the entirety of the hyper-Catalan number series. After stepping through the work leading up to and including the Geode array, Wildberger gets in one last jab: [F]ormal power series give algebraic and combinatorially explicit alternatives to functions which cannot actually be concretely evaluated (such as nth root functions). Hence they ought to assume a more central position. This is a solid, logical way of removing many of the infinities which currently abound in our mathematical landscape. Having been authored by an aging iconoclast and a longtime quantitative executive, this work may have more of an uphill climb to be broadly recognized. It's also published in the peer reviewed American Mathematical Monthly—a broad interest journal associated with the Mathematical Association of America. The journal accepts advertisers, offers paid editing services, and offers an option where authors can pay to make their articles open access—often a few thousand dollars or more. (The latter is, unfortunately, the normalized model and cost of open access publishing.) In this case, this less-orthodox approach could be a result of the subject matter simply not being on most people's radar anymore. But it also fits right into Wildberger's lifelong quest to trim the mathematical fat and present clear, simple ideas for as many people as possible. On the tech forum Hacker News (from startup incubator Y Combinator), Rubine explained in a post that he'd closely followed Wildberger's work on this problem since 2021, when Wildberger declared he was going to solve this problem on his YouTube channel. '[H]e was doing a series where he'd teach amateurs how to do math research,' Rubine said. 'For the first problem, he said he'd solve the general polynomial. I thought it was a joke, because everybody 'knows' that we can't go beyond degree four. But no, 41 videos later, he had done it. Two years after that he still hadn't written it up, so I wrote a draft and sent it to him, which evolved into this paper.' With that kind of determination, Wildberger may, after all, be an apt opponent for infinity itself. His democratic, open-door approach to mathematical thinking is really admirable. And in the paper, he and Rubine point out a number of questions that this theory opens up. We'll see if others in the mathematics community pick up some of these questions. I, for one, hope so, because 41 more videos is a long time to wait for the next breakthrough. You Might Also Like The Do's and Don'ts of Using Painter's Tape The Best Portable BBQ Grills for Cooking Anywhere Can a Smart Watch Prolong Your Life?
NDTV
01-05-2025
- Business
- NDTV
"Despite UPI Success, Our Talent Is Leaving": Sridhar Vembu's Warning On India's Tech Future
India may be riding high on its startup boom and fintech success stories like UPI, but Zoho founder Sridhar Vembu says the country needs a serious reality check - especially if it hopes to keep its best tech minds from heading abroad. In a candid post on X, the tech entrepreneur urged India's private sector to "act boldly" and focus on building real innovation at home. "Our talent is leaving," Vembu warned, pointing out that while India shines in process-driven sectors like airlines, banking, and retail, it lags when it comes to creating world-class products and cutting-edge technologies. Breaking down his assessment, Vembu said India scores well, about 70%, in process innovation. But when it comes to product innovation, he rated it at just 35%, adding, "That might even be optimistic." He cited UPI as an example of what's possible but stressed that India needs more visionary product creators, not just efficient project managers. Here is how I assess our nation's capabilities in terms of innovation, which I have classified into 4 categories. 1. Process innovation: the best of Indian industry is world-class in process innovation. For example: our airlines, hospitals, retail and financial services are… — Sridhar Vembu (@svembu) May 1, 2025 On the technology front, Vembu didn't offer a score but raised a red flag: India's top tech talent is often snapped up by global firms. "Retaining and bringing them back requires creating ambitious opportunities here," he wrote, calling on the private sector to step up. As for scientific breakthroughs, Vembu was blunt: "We haven't even appeared for the exam." He said that while private enterprise must lead in products and tech, government funding is essential for deep science. "We need the equivalent of Bell Labs in the private sector," he added, referring to the famed American research hub that drove many 20th-century innovations. Vembu's call comes at a time when India is celebrating milestones in space tech, pharma, and digital payments - but as the Zoho founder makes clear, the next frontier will need more than process excellence. It will require bold bets, big science, and a mission to keep India's talent building at home.
Yahoo
29-04-2025
- Business
- Yahoo
Commvault Systems (NASDAQ:CVLT) Reports Bullish Q1, Stock Soars
Data backup provider Commvault (NASDAQ:CVLT) beat Wall Street's revenue expectations in Q1 CY2025, with sales up 23.2% year on year to $275 million. Guidance for next quarter's revenue was better than expected at $268 million at the midpoint, 1.8% above analysts' estimates. Its non-GAAP profit of $1.03 per share was 11% above analysts' consensus estimates. Is now the time to buy Commvault Systems? Find out in our full research report. Revenue: $275 million vs analyst estimates of $262.4 million (23.2% year-on-year growth, 4.8% beat) Adjusted EPS: $1.03 vs analyst estimates of $0.93 (11% beat) Adjusted Operating Income: $59.1 million vs analyst estimates of $53.97 million (21.5% margin, 9.5% beat) Management's revenue guidance for the upcoming financial year 2026 is $1.14 billion at the midpoint, beating analyst estimates by 2.8% and implying 14% growth (vs 18.4% in FY2025) Operating Margin: 0%, down from 8.1% in the same quarter last year Free Cash Flow Margin: 27.7%, up from 11.4% in the previous quarter Annual Recurring Revenue: $930.1 million at quarter end, up 20.8% year on year Billings: $304.8 million at quarter end, up 24.7% year on year Market Capitalization: $7.30 billion "It was a record-breaking year at Commvault," said Sanjay Mirchandani, President and CEO. Originally formed in 1988 as part of Bell Labs, Commvault (NASDAQ: CVLT) provides enterprise software used for data backup and recovery, cloud and infrastructure management, retention, and compliance. A company's long-term sales performance can indicate its overall quality. Even a bad business can shine for one or two quarters, but a top-tier one grows for years. Unfortunately, Commvault Systems's 9% annualized revenue growth over the last three years was sluggish. This wasn't a great result compared to the rest of the software sector, but there are still things to like about Commvault Systems. This quarter, Commvault Systems reported robust year-on-year revenue growth of 23.2%, and its $275 million of revenue topped Wall Street estimates by 4.8%. Company management is currently guiding for a 19.3% year-on-year increase in sales next quarter. Looking further ahead, sell-side analysts expect revenue to grow 11.1% over the next 12 months, an acceleration versus the last three years. This projection is above average for the sector and implies its newer products and services will fuel better top-line performance. Unless you've been living under a rock, it should be obvious by now that generative AI is going to have a huge impact on how large corporations do business. While Nvidia and AMD are trading close to all-time highs, we prefer a lesser-known (but still profitable) stock benefiting from the rise of AI. Click here to access our free report one of our favorites growth stories. While reported revenue for a software company can include low-margin items like implementation fees, annual recurring revenue (ARR) is a sum of the next 12 months of contracted revenue purely from software subscriptions, or the high-margin, predictable revenue streams that make SaaS businesses so valuable. Commvault Systems's ARR punched in at $930.1 million in Q1, and over the last four quarters, its growth was impressive as it averaged 19% year-on-year increases. This performance aligned with its total sales growth and shows that customers are willing to take multi-year bets on the company's technology. Its growth also makes Commvault Systems a more predictable business, a tailwind for its valuation as investors typically prefer businesses with recurring revenue. The customer acquisition cost (CAC) payback period measures the months a company needs to recoup the money spent on acquiring a new customer. This metric helps assess how quickly a business can break even on its sales and marketing investments. It's relatively expensive for Commvault Systems to acquire new customers as its CAC payback period checked in at 84.3 months this quarter. The company's slow recovery of its sales and marketing expenses indicates it operates in a highly competitive market and must invest to stand out, even if the return on that investment is low. We were impressed by how significantly Commvault Systems blew past analysts' billings, revenue, EPS, and adjusted operating income expectations this quarter. We were also happy its full-year revenue guidance topped Wall Street's estimates. Overall, we think this was a solid quarter. The stock traded up 5.7% to $175.13 immediately after reporting. Commvault Systems may have had a good quarter, but does that mean you should invest right now? When making that decision, it's important to consider its valuation, business qualities, as well as what has happened in the latest quarter. We cover that in our actionable full research report which you can read here, it's free.
