The Full Problem, Finally Solved Twelve years ago, in 2014, I was helping my girlfriend’s sister with her maths homework. The question was about a farmer with a fixed length of fence trying to enclose the largest possible area against a wall. It had the tidy A-level answer you’d expect, but it planted a question I couldn’t shake: what if the fence could be bent into a circular arc — and what if the wall were a circular lake? I wrote up the in-between version first — an arc of fence against a straight wall, which turns out to be a semicircle — in “A farmer out standing in their field, their field was not mathematics” . Then I took on the lake itself in “The full problem” , carried the differentiation about as far as I could, and stalled on a transcendental equation I couldn’t solve. That post ends with the confession that the tools I needed were not yet in my mathematical toolbox. They are now — though not, strictly speaking, mine. After twelve years I have finally solved i...

Sortis - A paper empire game I settled on the name Sortis from the Latin because you don't play every turn in the game instead you skip ahead and calculate what happened at the point you want to make a genuine change to what's going on. Its a way of having the mechanics of the computer adding 1 wheat each turn without you having to manually add 1 wheat each turn. The literal translation is "of the lot/ of fate/ of oracle". Its etymology stretches back to a series, chain or row; which is equally relevant to this game. I'd love for the word to come to mean computationally reducible, a generalisation of closed form.  I have been working on a game recently that is played on paper but has the emergence of a procedural game like Minecraft, without forcing the player to do all the computation that would normally require.  What I wanted from this game was the feeling of progression, automation and discovery without needing anything other than pen and paper. I als...

 I've been working on an extension of the Voxel mesh in three JS that I built in this blog post and I'm thinking of developing it into an upcoming game at ManicVoxels.com To be able to expand the reach of the game to lower-power devices I needed to make the program more efficiently rendered. This would allow the players on the lower-powered devices to still have a reasonably sized world around them. When looking at the Greedy meshing tutorial from 0fps I really struggled to work out what the algorithm was. I then realised what is actually going on; you start in the top left, you go as far right as you can and then you go as far down as you can. You then repeat this until you have a new mesh. Once I'd worked out what greedy meshing was doing I could start to code it up. I've also added an animation of the algorithm below. In the animation, you can see the cursor moving from the top left to the bottom right. As if goes if the square is to be included in a new mesh then ...

  I have for a long time wanted to make a system that would allow me to code on a beach. In recent years I’ve had two approaches to this, one has been to try and produce some sort of virtual reality desert island with a beautiful break . The other has been to try and produce a screen that I can see in direct sunshine. But modern screens are far better at being seen in the sunshine you might say. Just get an anti-reflective coating you might say. Both of these are good solutions but as you can see from the picture below both pale in comparison with my creation. The screen I present here is the culmination of 5 attempts and over £100. The device has 80w of led draw producing a lighting power for which a back panel full of heat sinks cannot dissipate in high ambient temperatures.   So far I haven’t been able to test the device outside of my flat and I know from previous experiments that ended up in the prototypes being smashed that the power pack I have cannot support both the sc...

 I often get confused with joins so I looked over the many cheat sheets on google images. The problem I have with the classic cheat sheets is that they all display the joins in terms of Venn diagrams and I've never really understood if the Venn diagram represented the columns or something to do with the data. I've been working to move some code from R in which joins are heavily used to python where pandas has some join functionality but not everything I wanted. To bring across that join functionality I had to understand the nature of the joins at a depth that I just never had before. The following image is what I came up with.

Sometimes I don’t know the function I need to perform a task I want. Often its something simple like; I have two dataframes and I want to create a new dataframe which has all the rows of the first followed by all of the rows of the second. I can for a small example create the two data frames and I can try and describe what I want to find through google, however, often the phrases that I type into google, being natural language, are ambiguous an imprecise of what I’m trying to describe. In this example of concatenating data frames, I more often came across joining the two dataframe by adding the columns of one to columns of the other rather than adding rows. This test of the function I’m currently building passes managing to find the function in the pandas library which concatenates the two objects. This is still very much a pre-useful stage as in the test I’ve had to put the two dataframes in a list as, having found the solution through google...

  As mentioned in a previous post I built my own computer about a year ago. One of the issues I have had with using it is constantly being undecided on what OS I should use for it. While my preference would be Ubuntu all the way I have since getting my oculus quest 2 wanted to be able to make use of the graphics capabilities for VR. Unfortunately, to do this I need to be running windows, which for all other tasks I would loth to use. My first thought was virtualisation. Virtualisation is the process of running a second OS on top of a first as if the second os was just a program like any other. This often comes with a lot of complications that simply running any other program doesn't. A lot of those issues come from the fact that what the os outside of the pretty things the use sees is a lot of management of the hardware and of the drivers between the hardware and the software running on the os. Modern operating systems do a lot of work to make sure that software can't access h...