Brian Clegg's Blog, page 15

Breaking the bank at Monte Carlo (Monte Carlo method, part 1)

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 Charles Wells, who won over a million francs at Monte Carlo and did indeed ‘break the bank’. (This doesn’t mean that he cleaned out the casino, simply that he used up all the chips available on a particular table.) There were many attempts to find how Wells was cheating, but he later admitted that it was purely a run of luck, combined with a large amount of cash enabling him to take the often effective but dangerous strategy of doubling the stake on every play until he won.

However, Jagger probably deserves the accolade more than Wells, as his win was down to the application of wits rather than luck – and was even more dramatic. Jagger finally amassed over 2 million francs – the equivalent of over £3 million (or $5 million) today. He hired a number of men to frequent the casino and record the winning numbers on the six wheels. After studying the results he discovered that one wheel favoured nine of the numbers significantly over the rest. By sticking to these numbers he managed to beat the system until the casino realised it was just this wheel that was suffering large losses and rearranged the wheels overnight. Although Jagger soon tracked down the wheel, which had a distinctive scratch, the casino struck back by rearranging the numbers on the wheel each night, making his knowledge worthless.

Incidentally, I have always found it bizarre that casinos consider it to be cheating if players use skill to win. Unless there is a fault with the wheel, there is no skill in roulette, but there certainly can be in games like blackjack, where there are a limited number of cards available to play, and so by counting the cards that have already been dealt, a player with a superb memory (or a concealed computer) can increase their chances of winning. Apparently you get thrown out of casinos if you are caught doing this and barred from re-entering. Imagine if athletes were banned from their sport if they showed any sign of skill. It just demonstrates what should be obvious: casinos aren’t a way of playing fair games, they are businesses designed to take money off people.

Image from Unsplash by Derek Lynn

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Leave No Trace - Jo Callaghan *****

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 slightly under-utilised. There is also a little less focus on Frank's home life, which was central to the first novel, allowing the police procedural aspect to come more effectively to the fore. With an impressively structured case to solve, this made for an engaging and intriguing plot.

Leaving aside the technical limitations a real Lock would face - which are fine to make the story work - the only thing I thought was a little odd was that an early potential motive was religion, and at one point we have a suspect saying 'Christians aren't the only ones who used to crucify people'. While a religious motive could have been followed up (though it seemed to have dropped early on), in reality Christians would be much less likely to use this method of killing than anyone else.

I suspect some regular readers or viewers of crime stories would have spotted a couple of points ahead of the police team - but that is part of the appeal of reading this kind of book, where the puzzle of working out the who, how and why is just as important as exploring the human interactions along the way. With a dramatic against-the-clock ending, it's a book any crime lover will relish.

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The joy of sigma

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 measure the same thing, but in terms of a statistical measure called standard deviation that shows how spread out the distribution is.

It might seem odd not to use the more straightforward p-value, but the reason that sigmas tend to be used is that the p-value equivalent becomes very small at the kind of levels physicists look for. CERN, for example, actually works with p-values, but converts them to sigmas for easier communication. Here's a look at equivalent values:

Sigma     P-value        Cliff measure

2            0.05              Whiff 

3            0.003            Evidence

4            0.0001          Annoying*

5            0.0000003    Discovery

The 'Cliff measure' used above is a humorous interpretation of sigmas given by particle physicist Harry Cliff in his book Space Oddities. Arguably this is a more effective description of the value of different levels than the way statistical significance is usually regarded in the social sciences. Choosing 2 sigma/p-value of 0.05 as being statistically significant was an arbitrary choice, plucked out of the air by mathematician Ronald Fisher in 1925. However, it should be seen as nothing more than a note that something is worthy of proper investigation - Cliff's whiff - rather than an indicator that the outcome is accepted science.

Such has the focus been on getting a p-value below 0.05, there has in the past been a significant amount of 'p-hacking' - manipulating the data with the intention to get the result below the critical level. But Fisher certainly never intended this to be any sort of indicator of a real discovery. Remember, a p-value of 0.05 means that there is a 1 in 20 chance of getting these results when the effect doesn't exist. It may be a better probability than Russian roulette (p-value equivalent 0.17), but it's still hardly something you would want to risk your life on.

Why, then, is there such a disparity between the social sciences and physics? Because it isn't practical to have sufficient experimental subjects or experimental runs to come close to a 5 sigma outcome. It's very rarely going to be possible. As a result, the social sciences can't hope for equivalent degrees of apparent certainty. However, there is a strong feeling that the social sciences could do better - perhaps aiming for 3 sigma before they get excited. And it does mean that the outcomes of social sciences studies should arguably always carry a health warning and be better reported in terms of the risk of their misattributing an outcome to a particular cause.

One final consideration - even 5 sigma results can be wrong. Scientists can make a mistake with the maths. And there could be confounding factors too - a great example is the BICEP2 study, which aimed to study polarisation in the Cosmic Microwave Background radiation in the hope of finding direct evidence for the cosmological theory of inflation, which evidence as yet doesn't exist. BICEP2 did so at a 5.9 sigma level. Except it turned out that the results were being distorted by cosmic dust - it was not a discovery after all. There is always the possibility that scientists have not allowed for a factor they were not aware of that has distorted the results - something that sadly tends to disappear from popular science/news reporting where outcomes are often stated is if they were fact.

Probability and statistics can be hard to get our heads around - but when scientific results are reported, it is essential that this particular aspect should be carefully explained up front. To have confidence in scientific results, we need to know know what the limitations of a particular study are.

* Cliff's 'annoying' for 4 sigma is not saying it is useless, but rather than it's annoying it's getting close to the 'gold standard' 5 sigma without quite making it.

Image from Unsplash by Naser Tamimi

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The Gift of a Radio - Justin Webb ****

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 dire second-rate public school, run by Quakers who somehow ignored violence amongst the students, before finally escaping to the LSE and a job at the BBC (via one dramatic road trip disaster). It's one of those stories where it's almost impossible to prevent yourself from describing parts of his experience to anyone nearby in amazement.

One thing that comes across very strongly is how dire Webb considers the 1970s to have been I can't help but feel that his intense dislike for the decade reflects his personal circumstances. I'm just a little older than Webb, but I loved the seventies, where I was experiencing my last years at a school I liked, time at two universities which I loved and starting a great job. Of course there were political and economic problems in the 70s, but I think the experience of being a child or teenager then has far more to do with what you were going through as an individual than a dark nature of the decade as a whole.

If you aren't familiar with Webb's work, you can hear him here, interviewing me for Radio 4's Today Programme (somewhat ironically, given his admission to totally giving up on science at school):

Your browser does not support the audio element.

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Ghost singers

When I was 13, I sang in a performance of Mahler's third symphony with the Hallé Orchestra under Sir John Barbirolli. Our school's 'special choir' was a regular feature in Manchester performances of orchestral  pieces with children's parts - amongst other outings, I sang in Stravinsky's Persephone, Verdi's Otello, Malcolm Williamson's Our Man in Havana and Mussorgsky's Khovanschina.
We performed Mahler 3 a total of three times - concerts in at the Free Trade Hall and the Festival Hall, and a BBC recording for broadcast. But what I didn't realise until a few weeks ago was that the BBC had issued that recording as an album. I managed to get hold of a CD copy and had the eerie experience of hearing myself and fellow choir members from 55 years ago.
The (extremely long) symphony was quite a trial of patience for us. We had movement after movement marked 'tacet' on our copies, before featuring in the 4 minutes or so of the movement marked 'Lustig Im Tempo Und Keck Im Ausdruck'. Our part almost entirely consisted of singing 'Bimm bamm' (supposedly the sound of bells) with just a brief burst of German words. One of the choir was not allowed to return after spending much of the first movements on stage in full view of the audience reading a newspaper.
Even so, it was a remarkable experience for a young person, and hearing those youthful voices Bimm Bamming away, brought the memories flooding back.
I've extracted a couple of parts of the movement here, which I hope can be played as fair usage to show us in action:
brianclegg · Condensed Mahler 3 Movement 5

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A PR triumph

I get a lot of press releases, but I have enjoyed few more than one I recently got from a book review website called Summary Guru, which site carries the headline 'GET INSPIRATION FOR YOUR PAPER WITH AI POWERED BOOK SUMMARIES & ANALYSIS – PLAGIARISM FREE' (Does inspiration need to be plagiarism free? Or just stuff you copy and paste?)

To demonstrate the effectiveness of Summary Guru, the release tells us 'Before Watching Netflix's One Day, Know These Five Fascinating Details From The Book' - details produced by Summary Guru. Here they are, with a few of my comments:

1. It's about a single day... across twenty years

To be honest, if you don't know this before watching the series, you haven't being paying attention.

2. It deeply explores relationships

This is illustrated with 'To quote Emma (the novel’s main female character): “Dexter, I love you so much…and I probably always will. I just don't like you anymore. I'm sorry.”' Yep, deep.

3. The book is rich in philosophy

Take a sabbatical, philosophy lecturers. Apparently 'Nicholls sprinkles many philosophical ideas through the book, highlighted by quotes such as, ‘’I think reality is overrated’’ and ‘’There is always joy in witnessing the joy of others.”' Wow, why did I bother reading philosopher Philip Goff's book on the purpose of the universe?

4. It's light and dark.

This a real step forward for a fiction title, I think. We should see more of it, novelists.

5. There are bursts of humour

We are told 'But it’s not all doom and gloom; here are two light-hearted quotes that illustrate how funny Nicholls's prose can be:

“Oh, you know me. I have no emotions. I'm a robot. Or a nun. A robot nun.”“Call me sentimental, but there's no one in the world that I'd like to see get dysentery more than you.”LOL.

I know press releases are easy targets, but this feels more like a parody than the real thing. Perhaps it was intended as irony, but I'm not sure it was.

In case the release inspires you to get a copy of One Day, it is available from amazon.co.uk, amazon.com and bookshop.org

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Billiard balls and time

I've recently been reading The Blind Spot, which describes how science tends to confuse its idealised and simplified models with reality, and how scientists have traditionally relied too much on reductionism while putting anything that involves human experience into the 'unreliable and subjective' box, even though everything we do in the sciences (as opposed to mathematics) requires the input of human experience.

One of the subjects covered at length in the book is time. This is fascinating in the context, because time is the experiential phenomenon that is regarded most differently in physics than it is in reality. Some physicists go as far to say that time doesn't exist at all. Related to this, it is pointed out that many physical processes are reversible in time, where science does not care which way it goes. But in the The Blind Spot the authors emphasise that what we experience is not clock time - the only time that physics regards as real - but duration. Physics, for example, has something of a problem with the 'arrow of time' - the idea that time has a specific 'direction' - outside of some specific areas like the second law of thermodynamics. This is something that is obvious when you see time through the perspective of duration but is not, for instance, present in say the laws of motion.

I've always thought one of the best demonstrations of why traditional physics gets this wrong, proving what the authors of The Blind Spot put across rather clumsily, is the very simple classical physics example of two billiard balls heading towards each other, colliding and heading away from each other. This is often used an example of the time reversibility of such physics. If you had a video showing the balls heading for each other, colliding and heading away, you could run it forward or backwards and it would be impossible to distinguish the two. And this is echoed in the maths.

But what The Blind Spot points out (though without using such an easily considered example) is that what we are doing here is giving a mathematical model the status of reality, where it is in fact an abstraction that doesn't reflect reality. One reason for taking this view is that a real billiard table has friction and the balls will loose energy in the collision, so will be travelling slower after the collision that before. But that's relatively trivial. The big blind spot here is a trap that physicists love to tease psychologists about falling into: cherry picking. We are not using what is observed in the real world, just a part of it. In reality, something had to start those billiard balls moving... and before long they will stop. In the real world, taking a durational view of time, there is no doubt at all that time is not reversible. It is only by cherry picking the frames of the video in the middle that we can pretend that the mathematical abstraction of Newton's laws, using clock time, that enable us to be so dismissive of time.

In the end, some physicists may say time doesn't exist (in the sense of elapsing through duration), but I've never seen a physicist who doesn't know how long it is until dinner time.

Image by Rangakuvara from Wikimedia Commons CC4.0 - I've no idea what the guy with the cue thinks he's doing.

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Why is an insect like a leased aircraft?

Lewis Carroll famously came up with the nonsense riddle ‘Why is a raven like a writing desk?’ - which was never intended to have a meaningful answer. But for some reason a piece of science news I read in Physics World inspired the question in the title of this post: why is an insect like a leased aircraft?

The leased aircraft in question was one that British Airways borrowed from Aer Lingus. The plane was then repainted in BA colours for the duration. But part of the deal involved repainting the aircraft in the Irish airline’s livery and generally putting it back with the configuration Aer Lingus required before returning it. When the engineers finished, they fixed a little plaque to the instrument panel in the cockpit reading ‘FLY GREEN SIDE UP.’

The science story that made this come to mind was the answer to a long-term puzzle: why do insects seem to be so attracted to lights at night? I had heard the suggestion that they used the Moon to help with navigation - but the study shows that they don’t fly towards light. Instead they turn their backs to the light, apparently because with a natural light source this essential gives them the correct orientation for ‘fly this side up’. Light is treated as an indicator of upwards, which is why, for instance, they often fly around a light at an angle. You can read the details here.

One last thing. Previous generations wondering why a raven is like a writing desk could not consult an AI. I asked ChatGPT and Gemini (the renamed Bard) for their thoughts. Of the two I preferred the answer from Gemini, which is below:

This famous riddle from Lewis Carroll's "Alice's Adventures in Wonderland" has no definitive answer, and that's part of the point! Carroll himself offered several playful solutions:

Because it can produce a few notes, though they are very flat; and it is never put with the wrong end in front! (Early versions spelled "never" as "nevar," mirroring the reversed letters in "raven.")Because Poe wrote on both. (Referencing Edgar Allan Poe, known for his dark poems and stories.)Because they both come with inky quills.

However, the beauty of the riddle lies in its openness to interpretation. Here are some other creative solutions people have come up with:

Because one has flapping fits and the other has fitting flaps.Because one is good for writing books and the other better for biting rooks.Because a raven is nevaR backwards and a writing desk is for Words. (A play on words and spelling.)

Ultimately, the answer depends on your perspective and playful creativity. What do you think makes a raven like a writing desk?

As Gemini hadn't answered my question directly I asked what it thought:

As a large language model, I don't have personal opinions or beliefs. Therefore, I can't truly "think" there's one definitive answer to the riddle. My role is to present the various interpretations and let you, the user, decide which one resonates most with you or sparks your own creative response.

However, I can offer some observations based on the history and nature of the riddle:

Lewis Carroll intended it to be ambiguous and humorous. He enjoyed wordplay and logic puzzles, and this riddle serves as a playful challenge to think outside the box.There are multiple layers of meaning. The most obvious level involves their physical qualities (feathers/quills, flat surface), but deeper interpretations draw on wordplay, literary references, and abstract connections.The best answer is the one that delights you. Don't feel pressured to find a "correct" solution. Instead, have fun exploring the different possibilities and appreciating the open-ended nature of the riddle.

So, while I can't point to a single "right" answer, I encourage you to continue exploring and enjoying the imaginative possibilities!

Image by Miguel Angel Sanz from Unsplash

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When is 99% less than 99%?

Asking when 99% is less than 99% sounds like a riddle - but it's not. I recently heard a Sky Mobile radio advert in which they claimed 99% UK coverage. In the 'small print' words at the end, they said this meant they covered 99% of the population.

I don't know about you, but unless I'd heard that proviso, I would have assumed that 99% coverage meant you could connect to their service in 99% of UK locations - I expected the figure to be based on area of coverage, rather than population.

It might seem like this is splitting hairs, but it really isn't.

Let's just imagine an unlikely version of the UK where 99% of the population lived in London (this is, after all, what most advertising people think). Having 99% coverage by Sky's definition would mean that you could only use your mobile phone in 0.65% of the country. The whole point of a mobile is to be able to use in on the move, not just at your home location.

Of course, the real UK is not like my imagined version. Yet the country has far more open space than many assume. Only around 10% of the country is built up. This means you could make Sky's claim and still be inaccessible in much of the other 90% of the country. 

In saying this, I'm not just getting at Sky - I'm sure other mobile providers make similar dodgy claims. From my own personal experience travelling around the country (using O2, not Sky), quite often I can't get 4G and there are plenty of places still with no signal. 

If you want to use statistics in your advertising, it's a good idea to use numbers that mean what people will assume they mean. Otherwise, it's more than a touch deceptive.

I have contacted Sky to ask about how they came up with the 99% figure, but as yet have had no reply.

Image by Resume Genius from Unsplash

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The surprising views of Fred Hoyle

The late Fred Hoyle was one of my favourite scientists. He did impressive work on astrophysics, wrote imaginative science fiction and was an excellent science communicator, famously devising the term 'Big Bang' in a radio broadcast when he was throwing doubts on the theory.

In the late 1940s, Hoyle, along with colleagues Hermann Bondi and Thomas Gold at Cambridge came up with the steady state theory as an alternative to the Big Bang. One of the driving reasons behind this was that they felt that the Big Bang theory was too uncomfortably close to alignment with theological creation, and Hoyle was a staunch atheist.

When I was growing up, with Hoyle as one of my heroes (a fellow northerner, if from the wrong side of the east/west border), I was sad that steady state was disproved. Hoyle never gave up on it, modifying it to match observation (just as, to be fair, Big Bang had to be modified to match observation), but it dropped out of fashion as Big Bang made an easier match to the view of the early universe (steady state had no concept of an early universe, because there was no beginning).

I mention all this as a precursor to discovering a sort-of quote from Hoyle in reviewing A Chorus of Big Bangs. It seemed so out of character for Hoyle, that I had to follow it up - I was sure that it must be a fake. Here's the text:

A common sense interpretation of the facts suggests that a superintendent has monkeyed with the physics, as well as chemistry and biology, and that there are no blind forces worth speaking of in nature. I do not believe that any physicist who examined the evidence could fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside stars.

A lot of the websites quoting the words above online were fringe, and none gave a clear reference for the source, but in a blog post on the Guardian website, the author of the post indirectly references a 1990 book called The Mirror of Creation by Edmund Ambrose. I ordered a copy of this (long out of print) book to see where Ambrose got his quote from. Ambrose did not include the final sentence, but referenced an essay from the early 1980s by Hoyle called The Universe: Past and Present Reflections. This is primarily about the development of his version of panspermia theory with Chandra Wickramasinghe (and is interesting in its own right, as it provides more detail than is usually given when dismissing the theory). Right at the end Hoyle says this:

A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.

Leaving aside the presumed autocorrect that turned superintellect into superintendent, as you can see, the final sentence is totally different. The second part of the original 'quote' was indeed by Hoyle, but comes from a totally different source: a slim volume entitled Religion and the Scientists dating back to 1959, which is a collection of a series of talks given by Cambridge scientists including Hoyle, Neil Mott (then Cavendish Professor) and G. P. Thomson, which were intended to help theologians get a better feel for the scientific view of 'some of the facts of existence'. 

Many of these talks were, as the preface puts it, 'incompatible with orthodox Christianity, and sometimes opposed to it' - these were not apologists for religion. Yet in his talk Hoyle did include the 'I do not believe that any physicist' sentence. He was reflecting on the fine tuning required for the production of heavier atoms in stars, and later goes on to add the extra fine tuning required for life to exist. There is no doubt at all, from reading this talk, that Hoyle had, by 1959, a form of religious belief.

However, those who use this kind of quote to bolster a particular religion should also be aware that he was very clear in the same speech that there is an irreconcilable clash between the rigidity of (at least parts of) formal religions and science. He says 'There is a clear reason for this. All formal religions were devised at earlier times when man's understanding of the physical world was far less developed than our present understanding. It is natural therefore that modern science should find itself at odds with these earlier attempts at an expression of the religious impulse of man.'

It's quite possible that Hoyle would have agreed with the panpsychist view of philosopher Philip Goff. What Hoyle suggested is that if we take away the dogmatic trappings of traditional religion, science should have no problem with having a religious viewpoint. He draws a parallel between religion and mathematics, pointing out that mathematics has a validity 'independent of any observational test' and once we admit the validity of mathematics in this way, how can the validity of religion be excluded? I will leave you with Hoyle's expansion of this view:

It may surprise you when I say that I have yet to meet a person who was not imbued by a religious sense. The great difference between us lie in our varying attitude to formal religion. Religion in a non-formal sense I take to mean that a man will look up at the stars at night with a sense of awe, that he will feel that the majestic play of the universe has some deep laid purpose, and that his own small role in the play must make sense, if only he has the wit to find it. By contrast, by a formal religion I mean a belief in the miracles of Jesus and of the Virgin Birth, belief in those events that if they ever occurred must have contradicted the very fabric of the world as we know it.

(Note that though Hoyle's specific example here of formal religion is Christianity - the talks took place in a church - he elsewhere dismisses the other formal religions as well.) I don't agree with everything Hoyle said, but for me this shows the dangers of just labelling someone as 'an atheist' or a 'religious believer' - it is only the fundamentalists of either atheism or religion who feel they know for sure exactly what is behind our existence.

The image is from a series of mosaics by Boris Anrep in the entrance hall of the National Gallery in London. Somehow it's distinctly appropriate for this exploration of Hoyle's position that he is portrayed as 'a steeplejack, climbing up to the stars.'

Image by Anne-Lise Heinrichs from Wikipedia under CC 2.0

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