A blog about physics, mathematics, and data analysis by Jason Cole.
Magnets - how do they work? For a brief enlightened period in my life, I could have told you. I subsequently forgot completely, and was poorer for it. But now I know again! And thankfully so, because understanding how a simple table clamp works took me on a delightful path full of my favourite things - undergraduate physics, enlightened by simulation.
It's been a long time since this site has had a refresh - the last time was 12 years ago when I decided to go for a purple fractal theme... Needless to say, it's been long overdue some love! Let's see what's fresh.
It was just over 10 years ago when I wrote my original blog post on WiFi. Looking back on it, it's incredibly nerdy - did I really include a sparsity plot for a matrix? Nevertheless, it blew my mind how viral it went, along with the Android app that came shortly afterwards (written in a mad microwave-curry-and-energy-drink-dash). I therefore have it to thank for the inspiration to continue to…
I'll be the first to admit, this is a post I wrote mainly to scratch an itch of mine and so may have an audience of approximately 1. Fortunately in my previous life as a physicist I found that approximations can actually encompass many orders of magnitude, so perhaps we're on to a winner here? Let's find out.
Forgive me for writing yet again about the weather, but 1. It's part of my national heritage, and 3. This summer has had genuinely terrible weather. Of course it remains to be seen exactly how terrible, and in great and unrelenting detail. How better to honour the time-worn traditions of my people?
Matt Parker, employing the enviably pithy prose typical of a content creator forged on the unforgiving fires of social media, asked the simple question back in 2018: > How thick is a three-sided coin? Translated into mathematician-ese, this means > What aspect ratio of a flipped coin leads to the chance of landing on either edge being the same as landing on a particular face? Such is Matt's reach…
Here's a fun question - let's consider, purely in the abstract, the notion of quickly putting on a lot of weight. If, hypothetically, one were to weigh themselves every day and, conceptually, throw away all of the results which showed an increase in weight, what, in a strictly Platonic sense, are the odds that actually they're just a fat shit not actually losing any weight?
It's always exciting when a new 3Blue1Brown video emerges - Grant has an incredible sense for the intuitive visualisation of complex concepts (pun intended). His most recent on Newton fractals however really pushes the bar, and I couldn't help but have a go at emulating it.
Matlab is an archaic piece of software, is stupidly expensive, has a ridiculous syntax, horrible UI, and a whole host of bizarre quirks that you just put up with because that one grad student 10 years ago wrote a controller in it for a camera from a company which no longer exists and your supervisor refuses to buy a new one because apparently that's a ridiculous price for only 14 bits of dynamic…
After my last post, where I noted that 45 degrees was the optimum angle to shoot a projectile the farthest, a commenter asked if the same was true for jumping from a swing. "Of course!" I initially thought. As we shall see, it isn't actually that simple.
I've got a house now which, amongst other things, means that all of my future posts will be depressingly domestic. In particular, as I sat watching a sprinkler water my new well-shaded lawn, I noticed that some parts of grass were being watered more than others. It wouldn't be right to fix these kinds of problems without first wringing all possible interest from them however, so let's first…
Since the start of lockdown, I've found ever more reasons to be grateful for the surprisingly sunny postage-stamp of a garden I enjoy here in London. I am however moving to a new house soon, and have been curious to know how the new garden will fare in comparison. Hopefully so are you, as we're about to enjoy it in painful detail.
One of the many sad consequences of the current lockdown, possibly the most unfortunate of all, is that the famous Cooper's Hill Cheese-Rolling competition will almost certainly not be taking place this year. In the spirit of finding light in the darkness, let's at least have a look at how we may improve it for next year. With maths!
Once again, the world is facing the emergence of a nasty disease. I was last prompted to investigate the dynamics of infection in 2014 during the Ebola outbreak. Here I thought I'd examine a slightly different model to see what, if anything, can be learned.
It's winter again in the UK which means even more rain than usual, often accompanied by oddly-named storms. Sadly this also occasionally means flooding for many parts of the country, a fact which I usually watched with some detachment from the other (safer) side of a news report. This year is different - I have bought a house quite near the river Avon, which makes the issue more immediate. I…
It's been that time of year again, where I am forced to face my one and only weakness: wrapping presents. Rather than confront my failings, I've once again turned to my old friends: maths, computers, and bad puns.
This post is a classic example of the malady known as Jason-itis - idly wondering about a thing, and then having to dive deep down a rabbit hole to satisfy a geeky wish. In this case the thing was 'I wonder how you make a 3D shape which looks like different shapes from different angles', and the rabbit hole bottomed out at this GPU-accelerated demo. Let's look at the stuff in-between.
I recently got a new phone, and have read online that its camera performance leaves much to be desired. As I bristle at the suggestion I could make a poor purchasing decision, let's put this to the test. With maths!
Regular readers of this blog will note that 2019 has not been a particularly fecund time for new posts. This is principally due to my getting married recently - typically weddings are events with minimal overlap with the kind of topics I write about here. Unless, of course, one of the people getting married happens to be me.
A few years ago, a building in London known as the 'walkie-talkie' (actually 20 Fenchurch Street, but ever since the Gherkin it has been mandatory to give big expensive buildings extremely silly names. Can of Ham anyone?) started setting fire to shops and expensive cars. Let's have a look at why that might be.
As I was watching an episode of Only Connect the other day, I learned an (almost) interesting fact about London tube stations: > St. John's Wood is the only tube station not to share any letters with the word mackerel > > Someone, for some reason, some time. This was such a delightfully pointless fact, that my curiosity was instantly piqued. Why this station? That word? Is it unique, or unusual…
This post is about me finally getting over a slight irritation that happened nearly a decade ago, one which was almost completely inconsequential. Fortunately, it was related to physics, so is fair game here.
Sitting in traffic in the middle of London gives you a lot of time to think. Here's a fun problem born entirely of frustration sat waiting to cross the Hammersmith bridge.
Let's get pedagogical. Often when analysing a system, it is useful to break a component down into pieces, and figure out which are the important ones (if any). There are many techniques for this, here I'll look at one called 'singular value decomposition' in the context of image compression.
Now that we've entered the knockout rounds, I thought I'd see how my predictions stacked up against reality, and how this new data changes the prediction of the winner.
The world cup is almost once more amongst us, which means interminable weeks of breathless coverage, punditry, and heartfelt professions that each match will be played at 110%. In an effort to inject some more quantitative rigour to a field which, apparently, could do with some, let's try and predict how the whole thing will play out.
I was in Rome airport not long ago, and noticed that the reflection of the striped ceiling looked warped and bent due to the non-flatness of the reflecting surface:
I recently tried my hand at throwing axes at a wall, courtesy of Whistle Punks in London. While this was a fun and satisfyingly macho activity, I noticed that the attendants were careful to position people at various distances from the target to increase their chances of success. This piqued my curiosity, so here I'll have a look at why that might be.
Since Christmas, at my house we've been cooking with 5 ingredients or fewer thanks to the acquisition of Jamie Oliver's new book, the contents of which are mostly available online here. The recipes are unanimously very tasty, but that's besides the point. The real mark of culinary excellence (in my humble opinion) is how efficiently one can buy ingredients to make as many of the recipes as…
Those who know me know that I am a fierce proponent of the digital-native lifestyle. Online shopping, cashless payments, the fewer physical components the better in my book. Except for my books.
Intriguing title, no? These are the first eleven words of Neal Stephenson's novel Seveneves, which set up the remaining 600 pages as an extended treatise on the future of humanity as it copes with certain annihilation. I thoroughly recommend it, as long as you can deal with hundreds of pages of orbital mechanics. In this post I will numerically explore this post-lunar age, to verify for myself if…
A break from physics to show something which might be actually useful to some people. Normal service will resume shortly.
I wrote this blog post because I saw a woman throw a banana at Russell Brand. Bear with me on this one.
Recently the extractor fan in my bathroom has started malfunctioning, occasionally grinding and stalling. The infuriating thing is that the grinding noise isn't perfectly periodic - it is approximately so, but there are occasionally long gaps and the short gaps vary slightly. This lack of predictability makes the noise incredibly annoying, and hard to tune out. Before getting it fixed, I decided…
As a poor student, I always tried to keep a close eye on what I spent. This usually amounted to skimming statements and manually keeping track of what went where, a decidedly sub-optimal solution. Thanks to an initiative called MiData, you are now able to download transaction histories from your current account in CSV format, which is ripe for analysis. I built a small tool for myself, which I put…
Here's a fun problem I came across when trying to analyse some data, which I thought I'd write up to illustrate the kind of interesting puzzles I get paid to solve as a physicist. Perhaps have a go yourselves and let me know if there are more intuitive solutions.
In this third of a trinity of posts involving the travelling salesman problem, we finally use the sophisticated algorithms at our disposal as they were intended: drinking with peak efficiency. With the aid of a well-placed Christmas present detailing the best pubs in London, I found the optimal route around a reasonable subset of them.
This is the second in a series of posts involving the travelling salesman problem, somehow even more frivolous than the first. This is no coincidence, as I have recently been reading the excellent book 'In Pursuit of the Travelling Salesman', which goes into great detail on the history of the problem and algorithmic techniques for tackling it. The topic which caught my eye was decidedly less…
In the finest traditions of christmas, how about a timely blog post meant to cynically cash in on a blogosphere craving seasonal articles about nothing much in particular (see previous, sadly failed, attempt). What are the implications of Santa flying around the UK in a single night?
I saw a 'simple' puzzle on the internet which I thought I'd have a crack at in an evening. Several furious scribblings on the bus and the sofa later, I finally have an answer. I'm so relieved I can't help but share the joy.
Way back when I was analysing London house price data for the Summer Data Challenge, I made a histogram of the distances from a random point in London to the nearest tube station. I noted that it peaked around half a kilometre, but ignored the shape of the distribution itself. This is an unfortunate faux pas for the accomplished procrastinator, so let's right that wrong with the help of some…
Here's a post which combines my favourite bits of writing a blog - fairly mathematical, not too simple or difficult to implement, mostly based around pictures, not covered in my undergraduate education, and pretty damn useful in my job. Excited? You should be.
The last time I looked at house prices it went pretty well, and I ended up winning a data science competition. There I was only dealing with a million or so records, and a relatively small 120 MB dataset. Then I found out it was possible to download 3.7GB of property sale records for all of England and Wales since 1995, so let's have another go.
This blog has been getting a bit too pop-science for my tastes recently. Card games? Word clouds? Urgh. Let's do some proper physics. I hope you're paying attention at the back.
When taking a picture of my new 55" TV (humblebrag) I noticed a diffraction pattern of the reflection of the camera flash. Fortuitously, I had also recently bought a slightly too-powerful laser pointer from China which is the perfect tool to investigate such problems. Here's a little write-up of my DIY measurements.
It's done! After 58,627 words, 233 pages, 369 references, 162 figures and 3 lonely tables I finished my PhD thesis. Weighing in at 161.8MB, it was unceremoniously uploaded and that was that. Here are a few tips and observations I made on the way, which are probably only useful to those of you battling through a long Latex document. Never fear, normal blogging service will resume shortly.
A quick note this time, compiled entirely over a course of a 45 minute train journey, but nevertheless with some cool pictures.
I've been a little busy recently for blog posts, what with a pesky thesis to finish and all, but such an occasion as this deserves the highest honour possible - making lots of plots. That's right, the hallowed HTML files under this domain name have been yanked from a poor Wordpress server somewhere over 1 million times now, almost coinciding with the first anniversary of the blog. I think it's a…
Holidays are so relaxing. You know the drill: lounge around, eat and drink haphazardly, play card games, simulate several million card games to gain an advantage over your opponents, go for walks, visit the seaside, derive relationships for expected values of card hands, buy chocolates, smash unsuspecting opponents through brute force, send a postcard, etc. etc.
Given a few of my previous posts it's obvious that I'm a fan of the physics and mathematics that that comes along with the theory of classical optics. To make the number of lens-based posts a nice round three then, here's a simple Matlab App I made over the last few days which lets you play with lenses interactively, hopefully giving a bit of useful insight into the underlying principles.