Search engines are central to our everyday use of the internet - I must use a well-known search engine beginning with G at least a dozen times a day. But the search providers are displaying a worrying trend. Swept along by the enthusiasm for artificial intelligence, most have begun to display or offer an AI summary - in Google's case, this is the first thing you see at the top of the search results. And like all generative AI responses, it doesn't necessarily get it right. This is quite easy to demonstrate if you make use of a query that pushes the boundary a little. I happened to be writing something about the BICEP2 telescope, located at the South Pole. So, interested to see how the AI would handle it, I asked 'Why was the BICEP2 telescope built at the South Pole?' This is quite a tricky question for an AI to handle - and Google's response demonstrated this powerfully. (The highlighting above was already there, it's not from me.) It's certainly a good gues...

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. We're going to take a look at Galileo's surprisingly insightful contribution to our understanding of infinity. Galileo Galilei was born in 1564, the son of a musician and scientific dabbler. He tends to be remembered for dropping balls of the Tower of Pisa, something which be probably didn't do (it’s only recorded many years later by his assistant) and for being locked up for daring to suggest that the Earth rotates around the Sun rather than the other way round (not exactly accurate historically). Also inventing the telescope (he didn't) and featuring in that Queen song. But he undertook some remarkable thinking on the subject of infinity. It took place after his house arrest. Galileo had put together his masterpiece, Discours...

A while ago I wrote a book called Conundrum , which consists of 200 puzzles and ciphers - those who complete the entire book are entered in Conundrum's Hall of Fame , currently featuring just 17 impressive individuals worldwide. I occasionally set a bonus puzzle, open to all, with a free signed book as a prize. This one comes in the form of a challenge requiring you to put together a number of different elements: Passing under the seventh Duke, take the date of the crocodile, add the psalm number and divide by the verse to get the answer. If you are up for the challenge, you can enter your solution on the website here (and see a couple of clues). One winning entrant will be chosen at random - entries to be in by the end of 28 February (GMT).  Please don't append your entries here - only using the form on the website. I look forward to your suggestions: please do let me know how you got to the answer too in your entry. You can buy my book  Conundrum   from  Amazon.co...

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, based on my book A Brief History of Infinity . At first sight, chains of numbers that go on forever seem harmless and without consequence, but it doesn’t take long to find some that will cause difficulties. Let’s say that rather than just list the numbers we add them all up as we go along to produce a sum. And let’s take a very simple series – just alternating 1 and -1: something like 1-1+1-1+1-1+1-1... It’s hardly rocket science. We can see how it will total by adding some brackets: (1-1)+(1-1)+(1-1)... Each 1 is cancelled out by a -1, so the total of the series is 0. Or is it? Just shift the brackets and we still have a series that cancels out, but now we’ve got a 1 left over: 1+(-1+1)+(-1+1)... So the same series has a value of 0 and 1. Sca...

A few years ago I was set the challenge of explaining quantum physics to the then BBC broadcast journalist Robert Peston in 5 minutes. In practice, of course, this is a pretty much an impossible task, but the idea was to give a quick taster - which I hope it does.  I've written quite a bit on quantum physics, if it's something you'd like to dig into a bit deeper: The God Effect - exploring quantum theory's most mind-boggling concept, entanglement with implications from teleportation to unbreakable encryption Cracking Quantum Physics - an illustrated beginner's guide to the quantum world The Quantum Age - focuses on the applications of quantum physics that have transformed our world Quantum Computing - how computers making use of explicit quantum effects have the potential to run algorithms that perform in ways impossible to duplicate with conventional devices. Here's that video: These articles will always be free - but if you'd like to support my onlin...

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...