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The FTSE at 10,000: a missed opportunity for some marketing razzmatazz | Nils Pratley
There are three ways to view the FTSE 100 index hitting 10,000 points for the first time. One is to say round numbers are irrelevant. Since share prices are meant to go up over the long term, an index that was created in 1984 at a starting value of 1,000 was bound to get there eventually.In any case, a pure value-weighted points measure doesn’t capture the dividends paid by component companies, which can add up to a material part of an investor’s return over time if reinvested. Nor is the Footsie guaranteed to stay above 10,000, obviously

FTSE 100 posts best day in six months as stock market rally continues – as it happened
And finally, a newsflash! The UK’s stock market has just posted its best day in six months.The FTSE 100 index, which tracks the biggest companies listed in London, has closed 118 points higher tonight at 10,122 points, a gain of 1.18% and a new closing high.That’s the biggest daily percentage increase since 10 July, and also the largest points gain since last April when markets were rallying after Donald Trump paused his ‘Liberation Day’ tariffs.Precious metals producer Fresnillo (+5

Elon Musk’s xAI announces it has raised $20bn amid backlash over Grok deepfakes
Elon Musk’s artificial intelligence company has raised $20bn in its latest funding round, the startup announced Tuesday, even as its marquee chatbot Grok faces backlash over generating sexualized, nonconsensual images of women and underage girls.xAI’s Series E funding round featured big-name investors, including Nvidia, Fidelity Management and Resource Company, Qatar’s sovereign wealth fund, and Valor Equity Partners – the private investment firm of Musk’s longtime friend and former Doge member Antonio Gracias. The funding round exceeded its initial $15bn target, according to xAI’s press release. The company touted Grok’s image-generation abilities in the announcement of its latest funding round.xAI lacks the prominence of its rival OpenAI, the maker of ChatGPT, and has continually drawn criticism for generating misinformation, antisemitic content and now potentially illegal sexual material

AI consciousness is a red herring in the safety debate | Letters
The concern expressed by Yoshua Bengio that advanced AI systems might one day resist being shut down deserves careful consideration (AI showing signs of self-preservation and humans should be ready to pull plug, says pioneer, 30 December). But treating such behaviour as evidence of consciousness is dangerous: it encourages anthropomorphism and distracts from the human design and governance choices that actually determine AI behaviour.Many systems can protect their continued operation. A laptop’s low-battery warning is a form of self-preservation in this sense, yet no one takes it as evidence that the laptop wants to live: the behaviour is purely instrumental, without experience or awareness. Linking self-preservation to consciousness reflects a human tendency to ascribe intentions and feelings to artefacts and not any intrinsic consciousness

Australia v England: fifth Ashes Test, day four – live
36th over: England 143-3 (Bethell 71, Brook 7) Michael Neser replaces Scott Boland. Carey remains up to the stumps but Brook is watchful, knocking a couple of twos on top of the bounce into either side of the wicket. Neser has never looked more Hugh Jackman as Jean Val Jean in the film of Les Mis and yes I think you will find that is a compliment. Six off the over as England chip away at the deficit. Maybe they will be back for ONE DAY MORE tomorrow after all

John Harbaugh fired by Baltimore Ravens after 18 seasons in charge
The Baltimore Ravens have fired head coach John Harbaugh after 18 seasons in charge, according to multiple reports on Tuesday.Harbaugh is the most successful coach in the history of the franchise and was the second longest-tenured head coach in the NFL before his dismissal. Ironically, his final game with the Ravens came against the only name ahead of him in terms of tenure length – Mike Tomlin, who has been in charge of the Pittsburgh Steelers for 19 seasons.The Ravens experienced a sustained run of success under Harbaugh, reaching the playoffs in 12 of his 18 seasons and winning the AFC North division six times. Harbaugh led his team to Super Bowl XLVII in the 2012 season, winning the title against his brother Jim in what was colloquially referred to as the “HarBowl”

Starmer urged to scrap ‘outdated’ law limiting power to stop new gambling premises

Guardian Hope appeal raises more than £800,000 for charities tackling division

US to slash routine vaccine recommendations for children in major change experts say creates doubt

Shortage of NHS stroke specialists resulting in thousands dead or disabled, say doctors

US traders make big profits betting on Maduro’s capture in January

UK arts groups offer therapeutic support to performers as they challenge myth of tortured artist