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SWING AND A MISS
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. Setup Let's first, as usual, define the problem. SIGNED DISTANCE FIELDS Signed distance fields (SDFs) This is a fancy name for something very simple. An SDF is just a function which takes a position as an input, and outputs the distance from that position to the nearest part of a shape. For example, the simplest possible SDF is that of a 2D circle, namely for a circle centred at with radius the function. THE MOON BLEW UP WITHOUT WARNING AND FOR NO APPARENT In the novel, one day the moon breaks up into 7 roughly equal-sized pieces. These pieces continue peacefully orbiting the Earth for a while, and eventually two pieces collide. This collision causes a piece to fragment, making future collisions more likely. The process repeats, at what Stephenson says is an exponential rate, until theEarth is
WHAT DO WE LOOK LIKE ON THE INSIDE? What do we look like on the inside? A quick note this time, compiled entirely over a course of a 45 minute train journey, but nevertheless with some cool pictures. In the news recently was an update from the Visible Human Project, where cadavers are sliced into very thin (300 micron) sections, and each one is digitised so that the full HELMHURTS – ALMOST LOOKS LIKE WORK A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn't. Well, spurred on by a shocking amount TWO COME ALONG AT ONCE a nice simple result. The odds that the next bus makes us wait at least as long as the first is 50% as we might imagine. The odds that the next bus will arrive in a time less than one tenth of the first is around 9%, which is quite a lot! One in ten bus journeys may conceivably be plagued by the ‘two at once’ curse then, by ourmodel anyway.
WIFI STRIFE
I've recently moved into a new flat, and to celebrate I bought a WiFi card for my PC rather than relying on a power line LAN adaptor - plug sockets are a valuable resource in a Victorian flat conversion and so shouldn't be wasted on such trivial things. Unfortunately, with my lovely new card freshly ALMOST LOOKS LIKE WORK Signed distance fields. 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 APPS – ALMOST LOOKS LIKE WORK WiFi Solver Chrome – the same Android app as above, bundled into a Chrome app. Currently limited to ChromeOS. Lens Lab – a Matlab app for simulating simple lens layouts. See the post here for more information. TEF Data Explorer – a web app based on Dash for exploring the results from the 2017 Teaching Excellence Framework. MATSLAB – ALMOST LOOKS LIKE WORK 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 supervisorSWING AND A MISS
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. Setup Let's first, as usual, define the problem. SIGNED DISTANCE FIELDS Signed distance fields (SDFs) This is a fancy name for something very simple. An SDF is just a function which takes a position as an input, and outputs the distance from that position to the nearest part of a shape. For example, the simplest possible SDF is that of a 2D circle, namely for a circle centred at with radius the function. THE MOON BLEW UP WITHOUT WARNING AND FOR NO APPARENT In the novel, one day the moon breaks up into 7 roughly equal-sized pieces. These pieces continue peacefully orbiting the Earth for a while, and eventually two pieces collide. This collision causes a piece to fragment, making future collisions more likely. The process repeats, at what Stephenson says is an exponential rate, until theEarth is
WHAT DO WE LOOK LIKE ON THE INSIDE? What do we look like on the inside? A quick note this time, compiled entirely over a course of a 45 minute train journey, but nevertheless with some cool pictures. In the news recently was an update from the Visible Human Project, where cadavers are sliced into very thin (300 micron) sections, and each one is digitised so that the full HELMHURTS – ALMOST LOOKS LIKE WORK A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn't. Well, spurred on by a shocking amount TWO COME ALONG AT ONCE a nice simple result. The odds that the next bus makes us wait at least as long as the first is 50% as we might imagine. The odds that the next bus will arrive in a time less than one tenth of the first is around 9%, which is quite a lot! One in ten bus journeys may conceivably be plagued by the ‘two at once’ curse then, by ourmodel anyway.
WIFI STRIFE
I've recently moved into a new flat, and to celebrate I bought a WiFi card for my PC rather than relying on a power line LAN adaptor - plug sockets are a valuable resource in a Victorian flat conversion and so shouldn't be wasted on such trivial things. Unfortunately, with my lovely new card freshly ABOUT – ALMOST LOOKS LIKE WORK My name is Jason, a physicist turned software engineer from London with a passion for physics, maths, and data visualisation. I currently work for Count, building the next generation of data analytics software. I host a (slightly outdated) public CV here, and my PhD thesis is publicly available here. Get in touch TwitterLinkedInGoogle ScholarGitHub Around the web Articles GOING VIRAL… AGAIN Going viral again. 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. In all the following, note that I am not an expert, andnothing
THE MOON BLEW UP WITHOUT WARNING AND FOR NO APPARENT In the novel, one day the moon breaks up into 7 roughly equal-sized pieces. These pieces continue peacefully orbiting the Earth for a while, and eventually two pieces collide. This collision causes a piece to fragment, making future collisions more likely. The process repeats, at what Stephenson says is an exponential rate, until theEarth is
WARPED IDEAS
This is why the reflection looks warped. Because the ceiling has a regular structure, I know what the reflection should look like, and therefore it is possible to figure out the local angle of the mirror surface, and from that the shape of the mirror. Doing the geometry, one can show that. Because the mirror is far away, must be quitesmall.
THE TRAVELLING ARTIST PROBLEM The Travelling Salesman Problem, or TSP, involves finding the shortest path between a collection of points (‘cities’ in the TSP literature). For the purposes of this post the points are assumed to lie on the 2D Euclidean plane, though this need not be the case – see here for an impressive example involving non-Euclidean geometry. HOW DOES A LENS MAKE AN IMAGE? I've talked before on this blog about the propagation of electromagnetic waves, and that's not stopping any time soon. This time, I'd like to go through from first principles and demonstrate how a lens forms an image in all the gory details. Beware, there be maths ahead In the beginning there was Maxwell Now, lightROLLING SHUTTERS
I remember seeing once the following photo from Flickr, and having my brain melt slightly from trying to figure out what went wrong: The issue was the propeller was rotating as the camera detector 'read out', i.e. there was some motion during the exposure of the camera. This is an interesting thing to think about, letsGOING VIRAL
With a high infection rate, the virus is merciless and sweeps its way through the country rapidly. Some more remote places hold out for longer, but everywhere is vulnerable apart from the most sparsely-populated of areas. To avoid infection, head to theSWYPE RIGHT
I wrote this blog post because I saw a woman throw a banana at Russell Brand. Bear with me on this one. Yes, upon witnessing this act of fruit-based aggression I immediately related the incident to friends by typing a message about it. It struck me that the effort required to type the words 'banana' IF PIXAR MADE HISTOGRAMS The simplest thing we can do is render the plot as above with the city made of a generic diffuse material, which looks a lot like white plastic. We can place the model on an orange plane for a splash of colour, and see what that looks like. This is a much better render, given that we’re now going for nothing other than eye candy. ALMOST LOOKS LIKE WORK 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 ABOUT – ALMOST LOOKS LIKE WORK My name is Jason, a physicist turned software engineer from London with a passion for physics, maths, and data visualisation. I currently work for Count, building the next generation of data analytics software. I host a (slightly outdated) public CV here, and my PhD thesis is publicly available here. Get in touch TwitterLinkedInGoogle ScholarGitHub Around the web Articles BOOK – ALMOST LOOKS LIKE WORK You can purchase a printed paperback book containing most of my blog posts from 2014 - 2017 on Amazon, called 'Almost Looks Like Work: A guide to healthy procrastinating'. The book is full colour, and a solid 340+ pages long. Amazon UK Amazon US For other countries in WHAT DO WE LOOK LIKE ON THE INSIDE? A quick note this time, compiled entirely over a course of a 45 minute train journey, but nevertheless with some cool pictures. In the news recently was an update from the Visible Human Project, where cadavers are sliced into very thin (300 micron) sections, and each one is digitised so that the full structure of the body can be visualised.. Slice of thorax, from Visible Human Project websiteHIGH FLOOD PRESSURE
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 - ALMOST LOOKS LIKE WORK What a fancy icon! You should probably click it. The recent attention this humble blog received was surprising to say the least. Despite continuing to be slightly bemused by it all, let it not be said I don’t listen to the comments I receive.There is therefore an Androidapp here
THE MOON BLEW UP WITHOUT WARNING AND FOR NO APPARENT 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 thisBLISSFUL UNITY
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 HELMHURTS – ALMOST LOOKS LIKE WORK A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn't. Well, spurred on by a shocking amountWIFI STRIFE
I've recently moved into a new flat, and to celebrate I bought a WiFi card for my PC rather than relying on a power line LAN adaptor - plug sockets are a valuable resource in a Victorian flat conversion and so shouldn't be wasted on such trivial things. Unfortunately, with my lovely new card freshly ALMOST LOOKS LIKE WORK 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 ABOUT – ALMOST LOOKS LIKE WORK My name is Jason, a physicist turned software engineer from London with a passion for physics, maths, and data visualisation. I currently work for Count, building the next generation of data analytics software. I host a (slightly outdated) public CV here, and my PhD thesis is publicly available here. Get in touch TwitterLinkedInGoogle ScholarGitHub Around the web Articles BOOK – ALMOST LOOKS LIKE WORK You can purchase a printed paperback book containing most of my blog posts from 2014 - 2017 on Amazon, called 'Almost Looks Like Work: A guide to healthy procrastinating'. The book is full colour, and a solid 340+ pages long. Amazon UK Amazon US For other countries in WHAT DO WE LOOK LIKE ON THE INSIDE? A quick note this time, compiled entirely over a course of a 45 minute train journey, but nevertheless with some cool pictures. In the news recently was an update from the Visible Human Project, where cadavers are sliced into very thin (300 micron) sections, and each one is digitised so that the full structure of the body can be visualised.. Slice of thorax, from Visible Human Project websiteHIGH FLOOD PRESSURE
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 - ALMOST LOOKS LIKE WORK What a fancy icon! You should probably click it. The recent attention this humble blog received was surprising to say the least. Despite continuing to be slightly bemused by it all, let it not be said I don’t listen to the comments I receive.There is therefore an Androidapp here
THE MOON BLEW UP WITHOUT WARNING AND FOR NO APPARENT 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 thisBLISSFUL UNITY
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 HELMHURTS – ALMOST LOOKS LIKE WORK A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn't. Well, spurred on by a shocking amountWIFI STRIFE
I've recently moved into a new flat, and to celebrate I bought a WiFi card for my PC rather than relying on a power line LAN adaptor - plug sockets are a valuable resource in a Victorian flat conversion and so shouldn't be wasted on such trivial things. Unfortunately, with my lovely new card freshly APPS – ALMOST LOOKS LIKE WORK I can be found on the Google Play Store under the developer name jasmcole here. Currently all future development will be Android-based as I don't have any Apple devices for development and testing. WiFi Solver FDTD - with this app you can model WiFi propagation through the interior of your house. See the post here for some explanation ALMOST LOOKS LIKE WORK I also used the surprisingly awesome export feature of OpenStreetMaps which includes building shapes and heights, then ran the export through the equally awesome OSM2World which spits out file formats readable by other 3D software – in this case, Blender.. A bit of modelling, importing, and rendering later, we get a lovely view of this chunk of the City, with some minimal external lighting: GOING VIRAL… AGAIN 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. In all the following, note that I am not an ALMOST LOOKS LIKE WORK I’ve spend an unreasonably significant fraction of my life sitting in traffic, particularly along the infamous M4 corridor in England. Now, living in London I’m well acquainted with THE MOON BLEW UP WITHOUT WARNING AND FOR NO APPARENT 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 thisTHE FULL PICTURE
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! The new phone in question is the OnePlus 7 Pro - it'sgreat! I haven't
ROLLING SHUTTERS
I remember seeing once the following photo from Flickr, and having my brain melt slightly from trying to figure out what went wrong: The issue was the propeller was rotating as the camera detector 'read out', i.e. there was some motion during the exposure of the camera. This is an interesting thing to think about, lets TWO COME ALONG AT ONCE As the old saying goes, you wait ages for a bus and then two come along at once (or more!). Is this true though? My own anecdotal evidence would suggest yes, every single bloody time. However, we love data and maths in this blog almost as much as we hate waiting for thebus, so
GOING VIRAL
Diseases have been in the news recently, for one reason or another, and journalists are engaged in an increasingly ridiculous race to construct the most alarming headlines possible. How about we cut through the noise and indulge in a calming bit of maths? There are many ways to model the spread of infectious diseases, the relevant equations can be made as intricate as required in order toAUGUST 25, 2014
1 post published by jasmcole on August 25, 2014Skip to content
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* Going viral… again * High flood pressure * Wraptimisation 2: The WrappeningSHADY BUSINESS
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. Continue reading →Comment
July 26, 2020
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BRIECHISTOCHRONE
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! Continue reading →Comment
April 13, 2020
jasmcole cheese
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GOING VIRAL… AGAIN Once again, the world is facing the emergence of a nasty disease. I was last prompted to investigate the dynamics of infectionin 2014 during the
Ebola outbreak. Here I thought I’d examine a slightly different model to see what, if anything, can be learned. Continue reading →Comment
April 7, 2020
jasmcole C++
Disease
Infection
Python
Simulation
HIGH FLOOD PRESSURE
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 suppose I could campaign for flood defences, or petitionmy new local MP
,
but for now let’s stick to what I know: data and maths. Continue reading →1
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February 23, 2020
jasmcole
Data analysis
Differential equationsFlooding
Mathematics
Python
WRAPTIMISATION 2: THE WRAPPENING 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 againturned to my old
friends: maths, computers, and bad puns. Continue reading →1 Comment
December 27, 2019
jasmcole Christmas
Mathematics
Optimisation
Python
SIGNED DISTANCE FIELDS 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. Continue reading →1
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October 3, 2019
jasmcole
Blender
Mathematics
React
Typescript
Web app
WebGL
THE FULL PICTURE
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!
Continue reading →Comment
June 23, 2019
jasmcole cat
fourier transform
Image processing
Mathematics
mobile phones
one plus
Python
BLISSFUL UNITY
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. Continue reading →Comment
June 9, 2019
jasmcole Android
App
Blender
c#
Python
wedding
WALK THE WALKIE, TALK THE TALKIE 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. Canof Ham
anyone?) started setting fire to shops and expensive cars. Let’s have
a look at why that might be. ------------------------- The obvious feature of this skyscraper (other than the almost complete incongruity with the surroundings) is that it is strongly curved inwards on its southern side:From Wikipedia
Any inward curvature like this will act to focus the incoming light upon reflection. The fact that the tower curves over at the top also helps reflect the incoming light downwards onto the buildings it loomsover.
Intriguingly, the designer of the walkie-talkie Rafael Viñolywas also
responsible for a similar ‘death ray’ in Las Vegas . Perhaps he assumed the notoriously feeble British sunshine could never be focussed to high enough intensities to ever cause damage? I’ll chronicle here my attempt to model this situation, inspired bythis paper
from
my alma mater. While the paper is thorough, follows best scientific practices, and uses proper solar irradiance profiles, the visualisations left me wanting more. Casting proper science aside, let’s right that wrong and dig in.THE BUILDING
My initial thought was to model everything in Blender, and just let the rendering engine do all of the hard work of calculating lightpaths.
To draw up the building, I used the floorplans available hereto get the
shape correct, and smoothly interpolated the building shape betweenthe floors.
Floor 7, featuring some pretty sweet corner offices. I also used the surprisingly awesome export featureof
OpenStreetMaps which includes building shapes and heights, then ran the export through the equally awesome OSM2World which spits out file formats readable by other 3D software – in this case, Blender. A bit of modelling, importing, and rendering later, we get a lovely view of this chunk of the City, with some minimal external lighting: Great (I thought). Let’s stick a sun lamp into the scene, and see which building it focusses on: This was a bit disappointing – a faint splodge of white was not the death ray I was hoping for. Much fiddling with materials, lighting and renderer settings improved the render slightly, but it was still a struggle to generate anything which looked like it might melt a car. DOING THINGS PROPERLY Leaving Blender behind then, I loaded the building model into python using trimesh , which also very helpfully does efficient ray-surface intersection calculations. Firing a load of rays at the building surface with direction , calculating where they hit, and calculating the reflected ray directionusing
(where is the normal direction at the surface), I could now trace the evolution of the reflected death ray intensity: Here the incoming rays are spaced evenly in the plane normal to their direction, and so the density of rays at any point gives the light intensity. This is a simplified approximation, but will suffice forour purposes.
Tracing the paths of many thousands of rays, we can start to see how the reflected light propagates: The rectangular region contains the intersections between the reflected rays and the ground. Here is actually the worst-case scenario – at an incident angle of around 16 degrees the light comes to a focus almost exactly on the ground. If we calculate the ray density on the ground, we can plot the ‘focal spot’ produced by the building: The units on the axes are arbitrary. Frighteningly, a significant portion of the entire incident light field is focussed to a small point, with the rest spread behind itlongitudinally.
Varying the incident ray angle, we see how the light comes in and out of focus (we don’t show the incident rays for clarity): The non-uniformities in the transverse direction are probably due to non-perfect smoothing of the building mesh – focal spots are very sensitive to departures from surfaces of constant second derivative. If we plot the maximum intensity of the focal spot as a function of ray angle, there is a clear peak: From this surprisingly cool site, we know
that in summer time in London, the sun is at 16 degrees at 8AM in the morning and 6PM in the evening. Given these are peak commuting times, the unwary commuter could have ended up with a nasty surprise! Indeed, the paper linked above concludes that sun intensities may have been boosted by a factor of up to 16 times. Fortunately, shortly after London started melting the developers applied some protective covers to the southern face of the building. This is much safer, and the right thing to do, but has the unfortunate side effect of completely ruining my chances of dropping the words ‘death-ray’ into casual conversation. Guess we’ll just have to wait for Rafael’s next great project.Comment
January 27, 2019
jasmcole Blender
London
Optics
Python
Skyscraper
A UNIQUE SPELL ON THE TUBE 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 for this to happen? Let’s, dear reader, find out forourselves.
Continue reading →Comment
January 6, 2019January 6, 2019jasmcole
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London undeground
node
words
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