An infinite series is a familiar mathematical concept, where '...' effectively indicates 'don't ever stop' - for example 1 + ½ + ¼ + ⅛... an infinite series totalling 2. This, though is a short series of posts about infinity. Strictly, this one is just about big numbers - but it's on the way to the real thing. There’s something special about big numbers. It’s almost as if by being able to give a big number a name we demonstrate our power over it – and, of course, the bigger the number is, the more power we have. A classic example of this is in the reported early life of Gautama Buddha. As part of his testing as a young man in an attempt to win the hand of his beloved Gopa, Gautama was required to name numbers up to some huge, totally worthless value – and managed to go even further to show how clever he was.  But you don’t need to go back in history to examine this fascination. Anyone with children will have heard them counting, running away with sequences of nu...

The English language is a tricksy thing, replete with sayings that can, on the face of it, appear odd, or that get mangled after many repetitions. I recently heard something about one of these on the excellent The Studies Show podcast, hosted by Stuart Ritchie and Tom Chivers, that made me raise an eyebrow, because they claimed my interpretation of a saying was a myth. The saying in question was 'the exception proves the rule'. I want to come back to that after a brief excursion into another saying that involves puddings. One of the most cringe-making things for me is when I hear someone on the TV or radio say 'The proof is in the pudding.' This is a totally meaningless statement resulting from mangling the saying 'The proof of the pudding is in the eating'. Anyone using the first version needs to be sent to an English Language re-education camp immediately. But the real version itself can look distinctly confusing. We can prove a mathematical theorem, or that ...

After my voluntary break from popular science over the Christmas period, I've also had a dearth of review copies for books out in January. But there's a whole heap of both science and science fiction titles sitting on the review pile - so while reviews themselves are in short supply, here's a few books where the reviews are coming soon: Already published (awaiting copy) - I nto the Great Wide Ocean - Sönke Johnsen - takes readers inside the peculiar world of the seagoing scientists who are providing tantalizing new insights into how the animals of the open ocean solve the problems of their existence. 4 February - Hoodwinked - Mara Einstein - from viral leggings to must-have apps, exposes the hidden parallels between cult manipulation and modern marketing strategies in this eye-opening investigation. Reveals how companies weaponize psychology to transform casual customers into devoted followers. 6 February -  Phenomena  - Camille Juzeau and The Shelf Company - from ...

Parliamentary sketch writers have a very dated style of writing - their 'humour' feels both heavy handed and has a grotesquery more suited to an eighteenth century political cartoon than the modern day. In this book, Quentin Letts (a sketch writer in his day job) does deploy some of this style in his ad hominem remarks about individuals - and I probably disagree with about 90 per cent of his viewpoints (though I'm definitely with him on hymns, the House of Lords and justice being blind). But - and it's a big but - what I do absolutely agree with is that subtitle - 'how the elites betrayed Britain'. Letts highlights the horror of the Establishment when the people turn against them by, say, voting for Brexit or a certain US president. Without supporting either of these it is easy to see why it is happening. Just this morning I heard on a podcast a well-known political commentator (and self-affirmed member of said elite) saying how Brexit remains incomprehensible t...

An infinite series is a familiar mathematical concept, where '...' effectively indicates 'don't ever stop' - for example 1 + ½ + ¼ + ⅛... an infinite series totalling 2. This, though is a short series of posts about infinity. I wrote A Brief History of Infinity  a while ago because it's a topic I've found fascinating since I was at school. To kick off the series, here's the introduction of that book, which summarises why it's a subject that intrigues so many: The infinite is a concept so remarkable, so strange, that contemplating it has apparently driven at least two great mathematicians over the edge into insanity.  In the Hitch-hiker’s Guide to the Galaxy, Douglas Adams described how the writers of his imaginary guidebook got carried away in devising its introduction: ‘Space’, it says, ‘is big. Really big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the street to the chemist, but ...

REVISIT SERIES -  An updated post from October 2008 The excellent Claudia Hammond has recently done a podcast on the Mondex experiment, an early attempt at a cashless approach to shopping. I took part in this experiment, so it seemed an ideal opportunity to take a look back, both at the experiment itself and how cashless payments differ from what seemed likely in those heady days when contactless and smartphones were in their infancy. Pretty well everyone needs money really, I guess, but what I meant was 'who needs cash?' [The original post was entitled 'Who needs money?'] The irritating chunks of metal that mean I rarely have a pair of trousers that last more than a year without holes appearing in the pockets (hint, trouser designers - stronger pockets, please). And you always accumulate all those copper coins that you can't be bothered to bag up and take to the bank, so they end up in a charity box or gather dust in a big jar. Now, when I first moved to the Swindo...

I get a fair amount of cold selling emails, and recently received one that showed exactly why it's important to check what is going into an email, particularly if the email itself reflects what it is you are trying to sell.  The company in question is attempting to demonstrate how AI can help a business... but all they manage to do is show how it can be a disaster. Here's what I received (to avoid embarrassment I have removed the name and website of the sender who was the owner of a company whose strapline is 'Do you know how to effectively integrate AI into your business': What is clear is they don't know how to effectively integrate AI into their business. It doesn't help that they actually tell us that the email is supposed to include an AI-sourced first line from a 'artical' (sic) they saw. And what did they really appreciate? Their website is slick and clearly has had a fair amount of effort put into it. It's unfortunate that they could demonstr...

This is one for the music history fans, and/or those with an interest in church music. This definitely includes me - I've sung in choirs since I was about 10 and this kind of music is amongst my favourite listening. Andrew Gant does a brilliant job of digging into English church music throughout history, though almost inevitably the biggest focus is from the fifteenth to the nineteenth centuries. This might seem a very dry subject, but Gant brings it alive, helped by his even drier sense of humour. This is obviously a matter of taste, but if you find amusing his remark on Prince Albert's compositions 'He certainly did not possess a strong enough musical personality to overcome the prevailing tendency to write bad Mendelssohn, but he did it quite well. His Te Deum and Jubilate contain some quite good bad Mendelssohn,' you will enjoy it as I did. Inevitably the Reformation and subsequent switches of England between protestant and Catholic features heavily with its fascina...

REVISIT SERIES -  An edited post from January 2015 I was interested to see  on the BBC News site  that a link has been shown between biodiversity and human wellbeing. It seems widely accepted that exposure to the countryside is good for most people's wellbeing (though some can't stand it, and I wouldn't want to perpetrate a lazy stereotype), but biodiversity is a whole different kettle of fish. Nonetheless here's a direct quote of the subtitle of the piece on the BBC site: Scientists need to capitalise on a growing body of evidence showing a link between biodiversity and human wellbeing, a US review has suggested. Now, there are several issues here. Luckily (and, sadly, still rarely), the original review paper Exploring connections among nature, biodiversity, ecosystem services, and human health and well-being: Opportunities to enhance health and biodiversity conservation (snappy title) is open source and you can  read it here for free . I have three issues: What is...

There's quite an industry involved in producing new Sherlock Holmes stories, some excellent, others less-so. I was recently somewhat disappointed by a Holmesian Christmas novel , but reflecting that I've always preferred Doyle's short stories to his full length Holmes cases, I gave this collection of 12 stories a go, and was generally impressed. The approach is to primarily cover the early days and last days of the Holmes-Watson duo, effectively filling in gaps, which works well. Inevitably with each story written by a different writer there is some variation in the skill with which they match 'Dr Watson's' writing style in the originals - some get it spot on, others feel a little out of place. This is more notable in the early-set stories, as by the end we've reached the 1920s and it wouldn't be surprising if Watson had adopted a slightly more modern approach to his storytelling. I was surprised how much consistency there felt to be between the stories,...

This is the last of my Christmas murder mystery reviews for this year (though there will be more crime). It's a very engaging, if distinctly implausible story. The implausibility is a result of the contrived setting. Maddie, a Scottish journalist working in Manchester is heading home for Christmas, but when her car breaks down she gets stranded in a pub in the Yorkshire Dales in a heavy snowstorm. During an in-pub treasure hunt, one of those present gets murdered - in effect it's a classic country house murder mystery with a modified setting. What makes the situation more than a little contrived is that there happen to be a DI and his detective constable sidekick in the pub, so they can contact an investigation (with Maddie's help) while they're snowed in. Once you get past this unlikely setup (plus one weak restriction of which more in a moment) though, Noelle Albright keeps the action going in good page-turning fashion. For the first few pages the writing tends to be ...

REVISIT SERIES -  An edited post from January 2015 There is a usage that is becoming more and more common, verbally and in writing, which I hate. The most frequently used verbal form is 'so-called', and though it can also appear this way in writing, the usual written approach is what I call embarrassment quotes - misused quotation marks. The reference that set me off on this bijou rantette was a comment on the  Today  programme on Radio 4, when they referred to 'so-called exoplanets'. Exoplanets exist. There is no doubt about this. Yet according to the OED, 'so-called' means 'called or designated by this name or term, but not properly entitled to it or correctly described by it'. In other words, by saying 'so-called' the speaker implies that there's no such thing. Now, admittedly, the OED does qualify this definition by saying 'More recently, and now quite commonly (esp. in technical contexts), used merely to call attention to the descrip...

In previous books by Richard Coles, such as A Death in the Parish , it has been clear that the former pop star and current Anglican priest has a far better grasp of describing period village life and the church than he has of murder mysteries. That is even more obvious here: despite the title of this novella, murder hardly features - in fact the death occurs very near the end of the book. Once again, Coles' observations of the niceties of 1980s village and church life are delightful - with the added special dusting that Christmas brings. Perhaps his finest creation is the central character Daniel Clement's mother Audrey, who personifies the period middle class's obsession with the delicacies of status and admiration of the upper classes. One of the stars of the book is Audrey's bread sauce, a turkey accompaniment that dates back to when English cooking embraced plainness, to the extent that the recipe is published at the back of the book. Coles handles nicely the relat...

Teamed up with Emily Maitlis, John Sopel was for several years host of by far the best of the BBC political podcasts, Americast  - most tend to be painfully worthy, including Americast post Sopel and Maitlis.  The pair left to set up their own Newsagents podcast, but this has been uninspiring - it has only been since they've done a US spinoff that the pair have once again recaptured their magic. One of there reasons I read this book from 2018 was my enjoyment of the engaging approach taken in the podcast - the other was the comment by Bill Bryson on the front, which made me think this would be like of one of Bryson's books - wry humour, underlining the differences between the US and the UK. In reality, If Only They Didn't Speak English is very different. I'm glad I read it, but it was significantly harder going than I expected. Sopel's writing style has none of the verve of his podcasting persona - this is a serious book, examining a range of ways that American c...