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Rosemary Sharples feels that public transport doesn't go everywhere and doesn't allow for the user's choice of time, route or travel companions, and says the most flexible form of public transport, a taxi, is the most expensive. But look at Vienna, where public transport does indeed go everywhere and is very frequent, including late into …

In his article "What's inside a black hole?", Stuart Clark is troubled at the thought of conceding that "the universe is not entirely ruled by physics"( 4 October, p 28 ). As a physicist, I am content to think that the universe is always ruled by physics, and in fact that is a tautologous statement. …

Stuart Clark doesn't mention Carlo Rovelli's idea that singularities can exist only in the future. In his book White Holes , he says that because time slows down in a strong gravitational field, a point of infinite density with infinitely strong gravity would take an infinite amount of time to form. So, from our point …

Are gravastars, electroweak stars, boson stars and fuzzballs really needed to do away with singularities? From our perspective, standing beyond the black hole, gravitational time dilation means that anything that falls into it slows down as it approaches the event horizon and takes an infinite amount of time to actually reach it. So, from the …

I always understood that time grinds to a halt at a black hole's event horizon. If so, it is surely nonsensical to ask what is inside a black hole, and by implication, whether at this moment it contains a singularity. So if I were to fly my spaceship across the event horizon of a black …

I was interested to read your article about the inaccuracies of AI search tools, headlined: "AI doesn't have all the answers". This could be contested – by the comedian Eric Morecambe, for example, who would probably argue: "No, it's giving the right answers. But not necessarily to the corresponding questions( 27 September, p 17 )."

My experience with large language models (LLMs) is that questions about technical systems, such as Windows 11, produce fairly good answers because the information comes from professionally produced documentation. Everything else is a mixed bag. The reason why is evident and not easily fixable. If LLMs are trained on unfiltered data from the web, then …

Your article on covid-19 vaccines' economic benefits lays out the stark disparity between the value that governments and businesses put on human lives (the lower estimated benefit of $5 trillion), and the value that individuals do ($38 trillion). No wonder so many of us feel that "society" doesn't value or care about us: these figures …

Paul Broady suggests plans to capture carbon from the air are a distraction, and we should focus on deep cuts in emissions. He is half right. We do urgently need to make deep and permanent emissions cuts and to keep cutting until we get as close to zero as we can. But this won't be …

Your article "Uncovering the ins and outs of belly buttons" must be wrong about the historical lack of study into the umbilicus: haven't millions of people been accused of contemplating their navel( 11 October, p 16 )?