This is the third of four posts on the mathematical approach known as the Monte Carlo method, following ' Where did those neutrons go '. As we saw in the previous post, the Monte Carlo method depends on having a stream of random numbers. Unfortunately, randomness is not easy to generate. Ask someone for a series of random choices between 1 and 10 and they will not do well - for example, there won't be sufficient repeated values for a true random stream. In another extract from my book Dice World , let's take a look at what appears to be random whether we use a spreadsheet or a more sophisticated source: In Excel I have two random number functions, RAND, which gives me a random value between 0 and 1 (I just got 0.61012053) and RANDBETWEEN to choose a random number in a range. (My value for between 1 and 10 came out as 4.) Job done. Unfortunately, what Excel gives us is not random numbers, but pseudo-random numbers. Numbers that are random enough for, say, making a prize

This is the second of four posts on the mathematical approach known as the Monte Carlo method, following ' Breaking the bank...' Moving from the bank being broken at a casino to a mathematical method occurred as the Second World War came to a close. A number of scientists on the US nuclear programme were attempting to model neutron diffusion from a nuclear bomb. This was because a conventional nuclear explosion is effectively the trigger for the (then theoretical) thermonuclear explosion of a fusion bomb - and a major factor in its effectiveness is how neutrons travel out from the primary fission stage. Like his colleague John von Neumann, the Polish-American physicist Stanislaw Ulam had an interest in the game of poker and the probabilistic nature of games. The new possibility of electronic calculation using the ENIAC computer made it possible to consider a novel approach to modelling neutron diffusion. At the heart of nuclear fission is the idea of a chain reaction. A neutron

This is the first of a couple of posts on the mathematical approach known as the Monte Carlo method. I want to start gently by taking a (virtual) trip to Monte Carlo in Monaco and its famous casino, specifically to explore a once well known phrase - the man who broke the bank at Monte Carlo. The article below is extracted from my book Dice World . A roulette wheel is a physical device, and as such is not a perfect mechanism for producing a random number between 1 and 37 (or 38 in the more money-grabbing US casinos). Although wheels are routinely tested, it is entirely possible for one to have a slight bias – and just occasionally this can result in a chance for players to make a bundle. It certainly did so for 19th-century British engineer Joseph Jagger, who has, probably incorrectly, been associated with the song ‘The Man Who Broke the Bank at Monte Carlo’, which came out around the same time as Jagger had a remarkable win in Monaco. The song probably referred instead to the conman Ch

In Jo Callaghan's first book featuring Detective Superintendent Kat Frank paired up with a virtual AI detective called Lock, In the Blink of an Eye , it was arguably the science fiction aspect that came to the fore - but the (arguably better) sequel focuses more on being an excellent police procedural crime novel. Frank and Lock have been moved from cold cases to a frontline murder that rapidly becomes a national news story - the victim has been crucified. (I don't know if the release of the book was timed intentionally, but I read it over Easter.) Tension mounts as a second crucified body is found - while the team is still thrashing around trying to find a viable suspect. Where in the first book, Lock (and people's reaction to his holographic presence) featured heavily, here he becomes significantly more part of the team, and we see not only his limitations, but some consideration of how much he should be considered a conscious entity. If anything, his abilities are slight

Anyone who looks in a bit of detail at scientific results may have come across p-values and sigmas being used to determine the significance of a outcome - but what are they, and why is there a huge disparity between practice in the social sciences and physics? These are statistical measures that determine the probability of the results being obtained if the 'null hypothesis' is true - which is to say if the effect being reported doesn't exist. The social sciences, notably psychology, usually consider the marker for statistical significance to be a p-value of less than 0.05, while in physics the aim is often to have a 5 sigma result. Both these measures depend on creating a probability distribution, showing the likelihood of different values occuring. The p-value is a direct measure of the probability of getting the reported results if the null-hypothesis applies. So, a p-value of 0.05 means there is one in twenty (1/20 = 0.05) chance of this happening. Sigmas effectively me

This isn't the kind of book I usually read, but it piqued my interest when someone told me about it - and it certainly was worth getting into. If you are a BBC Radio 4 listener (or subscribe to the Americast podcast) you will be familiar with Justin Webb's soothing tones - this memoir of his childhood through to going to university gives a vivid picture of his bizarre upbringing. Webb never met his father (who would become a reasonably well-known BBC reporter), being brought up by his mother and stepfather, each of whom had quite serious problems. His stepfather had a form of mental illness that included paranoia, while his mother was intensely snobbish, insisting on every little social divider that would put a gap between her upper-middle-class-on-hard-times position and anyone she considered socially inferior.  Their home life seems to have consisted mostly of silence, though there was a strong bond between Webb and his mother, arguably an unhealthy one. He was then sent to a