Alphanumeric Sheep Pig

On Matrix Inversion in Python

noreply@blogger.com (Alphanumeric Sheep Pig) — Wed, 03 Jun 2015 10:09:00 +0000

In the introductory programming course that I lecture, the big programming project that I set for the students involved writing a number of matrix operations in pure Python (that is, using built-in functions only - I specifically disallowed the use of any imported modules like NumPy). Transposition and matrix multiplication are fairly simple to do, but the challenge is in writing a function to invert a matrix.

Of course, Gauss-Jordan elimination (which should be covered in any first year algebra course) is one of the easier ways to do this. I wrote a fairly long but simple-to-understand function to give out to the students as a model solution at the end of the project, but I was wondering, how short could a working matrix inversion function be?

I came up with the function below, complete with partial pivoting, which seems to work correctly. It could probably be even shorter, but I think I achieved what I set out to do:

The input argument A is simply a nested list, such as
A = [[1,2,3],[1,5,9],[7,5,2]]

Line 3 simply augments the matrix with the identity matrix. The for loop on line 4 loops through each row, and sets the element on the main diagonal to 1, and every element above and below that element to zero. This happens in three steps. The first step, on line 5, is a simple pivoting step. It sorts all of the remaining rows such that the current row will be divided by the number with the largest possible magnitude (to avoid division by zero, and improve the accuracy if the matrix contains very small numbers). The second step (line 6) is to divide each element in the row by the element on the main diagonal, leaving a 1 on the main diagonal. The third step (line 7) is a little more complicated. For each row that is not the current row, we subtract the current row multiplied by the element in the column index equal to the index of the current row. This will set each element in the current column to zero, except for the element in the current row, which remains 1.

The net result is that the left hand side of the augmented matrix becomes the identity matrix, while the right hand side becomes the inverse. All that's left is to separate the two, and return the inverse. This happens on line 8.

I don't know who would find this post useful, because it's better to just use numpy, but it is certainly a fun exercise.

On My 13 Favourite Pieces of Metal Music

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 02 Sep 2014 19:25:00 +0000

The music I listen to falls mainly into the genres of metal and classical music. A while ago, I put together a list of my 13 favourite pieces of classical music, so I decided it was about time to put together a list of my favourite metal music. Funnily enough, I find that classical music gets me worked up, and if I want to relax, no other music works quite as well as metal. I'm not very good at having favourites, so I should probably point out that there may be some more deserving songs out there that were accidentally overlooked, and my favourites change from day to day. However, these are the ones that I'd have to consistently include near the top of a list like this, but they are in no particular order. Once again, I have limited myself to one song per artist, and I have not listed songs that have made lists on this blog before.

    1. Moonsorrow - Raunioilla

Moonsorrow is my all-purpose music. No matter what mood I'm in, I'm in the mood for Moonsorrow. It's my first choice when I have to concentrate on work, or when I want to sit back and relax, or when I'm stressed, or sad, or really happy.

    2. Rhapsody of Fire - Queen of the Dark Horizons

Rhapsody of Fire's album Rain of a Thousand Flames is considered a filler album, as it only plays a small side role in the epic story they tell through their music. Still, it contains some of their best work, and Queen of the Dark Horizons is easily my favourite song of theirs. It is a perfect mix of symphonic and power metal, and I love every second of its 13 and a half minutes.

    3. Cradle of Filth - Nymphetamine (Fix)

My brother went through a phase where he listened to nothing but Cradle of Filth. Musically, I think they are brilliant, but I never liked Dani Filth's screaming. With exposure though, I did grow accustomed to it eventually. The one song that stood out was Nymphetamine (perhaps because Liv Kristine sings a large portion of the song), from the album of the same name. The song appears twice on the album, but the first version (the overdose) has a mismatched intro and outro which just don't fit in with the rest of the song. For that reason, I prefer just the fix.

    4. Deathstars - Razor End

While I had heard a little of the Deathstars' music before I met my girlfriend, I had never heard Razor End. We'd been dating for just a couple of weeks when she had my taste in music completely figured out. She burned me a CD, which had this song on. It's a pity it's not on any Deathstars album, because I feel it's easily their best work. Four and a half years later, it was still one of the easiest songs to choose when I started putting together this list.

    5. Anathema - Eternity, Part I

I've always had a taste for depressing doom metal, and that's what led me to Anathema. I enjoy almost all of Anathema's music, from their work in the early 90's, up to their latest albums. Listening to all of their albums in order and hearing the progression in style from doom metal to through to alternative rock is a fascinating experience in itself. Eternity, Part I is the first of three parts, and is written in a rather heavy doom metal style. The second part is a soft instrumental piece, and the third part closes off the first with a more progressive style, and cleaner vocals. I encourage you to listen to all three parts, but the first is definitely my favourite.

    6. In Flames - Come Clarity

In Flames is a band I have mixed feelings about. There are many of their songs that I thoughroughly enjoy, and then there are others that I cannot stand. Come Clarity is one of their softer songs, and I'm not sure what it is about the song that makes me love it so much.

    7. Wintersun - Death and the Healing

There are a couple songs from Wintersun which were strong contenders for this list. Beautiful Death was probably at the top, but it has already been listed on this blog as part of the soundtrack for the end of the world. Instead, I chose Death and the Healing. The slower pace and clean vocals make the song really stand out from the melodic black metal that makes up the rest of the album.

    8. Metallica - No Leaf Clover

When Metallica reached 30 years old, I compiled a list of my 30 favourite Metallica songs. Of them, 27 were released in the first 15 years of their career, and only 3 in the second 15 years. Also, I really don't like live music. It's rather funny then that my absolute favourite Metallica song was only released in the band's 19th year, and only ever as a live recording. I think it has something to do with the symphonic elements. I just wish there was a studio recording of the song.

    9. Nightwish - Phantom of the Opera

For a long time, Nightwish was my favourite band. For the last few years, however, there just seems to be something missing from their music (I wonder what it could be?) Even though it's not an original song, Phantom of the Opera seems to epitomise everything I loved about the band when they were at the peak of their career.

    10. Lordi - It Snows in Hell

The piano intro to this song is really simple to pick up and play, and really catchy, and I'm constantly getting the chorus stuck in my head. There's also something about the guitar solo that makes me think of a lazy Sunday afternoon.

    11. Bathory - The Lake

Although the album Blood on Ice was written in the late 80's, it wasn't released because the band were worried that it was too different to any of their other music. At the time, Bathory was known for their fast-paced black metal. Through the first half of the 90's, they changed their style, and began to define the Viking metal genre. In 1996, the band finally decided that they were ready to releace Blood on Ice. The Lake was the first song on the album that I heard, and remains my favourite to this day.

    12. Therion - To Mega Therion

Therion is the metal band that has experimented (mostly successfully) with more styles than any other band I have heard. To Mega Therion is from their album Theli, which was the first album to drop their death metal roots entirely. To Mega Therion features a full orchestra and choir, interspersed with raspy male vocals and catchy guitar and keyboard solos.

    13. Green Carnation - Light of Day, Day of Darkness

Yes, this song (if it can be called that) is just over an hour long. When I first heard about it, I expected it to be drawn out and repetitive, but it is far from it. The style and tempo of the music varies throughout the song, so that it easily maintains my interest for the full hour. I once heard a shortened version in which the song had been cut to ten minutes, and even though the editing had been done extremely well, and the transitions fitted in perfectly, I found that the song was seriously lacking. The full hour needs to be heard in one go. In my opinion, not a single second can be cut out.

Legal notice: I obviously don't claim to own any of the songs or videos in this post. Copyrights belong to the respective publishers.

On Rubik's Cube

noreply@blogger.com (Alphanumeric Sheep Pig) — Wed, 09 Jul 2014 20:29:00 +0000

I love Rubik's cube. It's a puzzle that many people associate with intelligence, mathematical ability, and good problem solving skills, but being able to solve it actually has nothing to do with any of those. The only things you need are basic pattern recognition and muscle memory - both of which everyone has anyway.

    1. My first cubes

My first Rubik's cube was even older than I am. My dad bought two of them (one with standard colours, and one with pictures of fruit) some time in the early 80's when they first became popular, together with a short book explaining how to solve them. I found the book in 1996, shortly after we'd moved house. I asked my dad about it, and he found the two cubes for me. Not wanting to cheat, I scrambled one and tried solving it myself. It didn't take long to figure out how to solve one side, but I quickly realised that any turn inevitably messed up four sides, got frustrated, and moved on.

I came back to them a couple years later. This time, I actually tried reading the book. The first chapter was all about the internal mechanism, and how to take the cube apart. Naturally, I stopped reading there and did exactly that. I took them both apart, and put them back together in a solved state, and began to look at how various turns affected the faces. Whenever I got stuck in a position that I couldn't solve, I would take the cube apart, and put it back together. After a while, the core of one of the cubes broke while I was taking it apart. Having made very slow progress, and having lost a cube, my 12 year old brain decided it had more interesting things to do, so I moved on.

    2. Solving the damn thing

Once again, I came back the the cube a few years later. I think I was about 17 years old this time, and far more patient. I only had the cube with the fruit stickers left, so I had to be more careful. I decided to read the book, and I approached it the same way I would approach a school text book. I took a notepad and a pencil, and began to take notes.

The book described a very simple layer-by-layer method for solving the cube. You would start by inserting the four edges on the top face, and then execute a simple algorithm until they cycled into the correct positions. Then you would insert the four corners of that face, then the four edges of the middle layer. At this point, the top two layers of the cube were solved. To finish the last layer, you had to switch some corner pieces in the bottom layer to get them in the correct position, then execute an algorithm over and over until they were oriented correctly. Then, you would execute an algorithm to cycle the last four edges, until they were in the correct position, and finally you would execute one of three algorithms to flip them into the correct orientation. The book claimed that the method required an average of about 120 moves to solve the cube. There were a total of nine algorithms to learn, and it only took a couple of days to memorise them all (it's surprisingly easy if you just let muscle memory take over).

The catch was the centres. The book assumed that the cube had stickers with a solid colour, but my cube had little pictures of fruits. All of them would point the same direction except for the centres. I later learned that a cube like this is called a supercube, and some people draw arrows (or buy stickers with arrows) to turn their Rubik's cubes into supercubes. I was not content having my centres pointing the wrong way, so I sat down and figured out a couple of algorithms myself that would allow me to orient five of the six centres while solving the cube. I noticed that a couple of the algorithms I already knew rotated one or two centres if I repeated them three times, and with that, I could solve the cube, centres included.

Solving a Rubik's cube is a very relaxing task. It takes very little brain power, and is actually very meditative. Apart from occasionally glancing down to see which algorithm you need to execute next, you don't even really have to watch what you're doing. I used to solve my cube several times a week, just to meditate and relax.

    3. Moving on: new Cubes and new methods

My fruit cube lasted a surprisingly long time. After several years, it began to lock up occasionally. A couple years after that, pieces began to pop out every now and then. By late 2012, the pieces became so loose that it reached a stage where it would lock up on almost every turn, and it became almost impossible to solve without the whole thing exploding in my hands. I needed a new cube, so I bought one: a cheap Chinese cube from a flea market stall. The stickers lasted less than two weeks, and it was less than a month before one of the edges broke in half.

It was then that I decided to take things seriously. I went online and did some research, and discovered the fascinating world of speedcubing. I discovered that the world record at the time was less than six seconds, and that more than a thousand people around the world can solve a Rubik's cube in under fifteen seconds almost all the time! It put my two and a half minutes to shame.

I found out what makes of cube were actually considered good quality, and found a stickerless DaYan GuHong on sale. While waiting for my new cube to arrive (it took two months, thanks to a useless Postal service), I found a Rubik's 2x2 cube in a local toy store. I could solve it by adapting the 3x3 method, but it felt very slow and inefficient. I learnt to solve it using the Ortega method, which is a much faster method specially developed for 2x2 cubes, which is also fairly light on algorithms (you actually only need two of them, but learning up to eleven makes things faster).

Conveniently, my GuHong arrived the day before I left for America to present a paper a conference. A 15 hour plane flight is absolutely perfect for learning a new method. I made a short cheat sheet with the algorithms for the ZZ method, and between the two plane flights, I managed to memorize them.

    4. Speedcubing: attempt #1

Last month, a toy store near my girlfriend's house held a Rubik's cube competition. When I had first looked in 2013, there were only six South Africans ranked by the World cube Association, and speedcubing in the country seemed pretty much non-existent. I was fairly surprised to see an actual competition. I checked the World Cube Association website, only to see that the first official competition had been held a few months before, and more than thirty people had attended, two of whom had managed to set times under fifteen seconds.

It led me to find speedcubes.co.za, a South African online store that stocks a range of the world's leading speed cube brands. I told myself that if I could solve my cube ten times with an average time less than 90 seconds (a minute faster than a year before), then I would allow myself to buy a new cube. I made it, but only just. In ten solves, my best time was 1:22, with an average of 1:29.8.

I ordered my new cube, a DaYan ZhanChi (since my stickerless GuHong is technically not competition legal), as well as a new 2x2 (my Rubik's brand one had a cracked core), and a 4x4 cube. With these new cubes, together with a couple of key rings, I can officially say that I have begun a bit of a collection.

I thoroughly enjoyed my first competition. By some miracle, I actually won the 2x2 category with an average of just over 16 seconds (my five solves took 13, 15, 15, 18 and 32 seconds). In the 3x3 category, I came nowhere near the winning average of 45 seconds. My best time was 53 seconds, and I averaged just over a minute.

5. Next goal: An official WCA ranking

There's going to be an official WCA ranking event in Johannesburg on 23 November, and one in Cape Town on 30 November. This leaves me four and a half months to practice and get my times down. My goal is to set at least one time less than 30 seconds at that event. I'm improving fairly quickly. As of 30 June, my average time over 100 timed solves was 1:15.62. By 8 July, my average time over 100 solves had dropped to 57.93 seconds, and my current personal best is 42.65 seconds. 30 seconds may seem ambitious, but I'm fairly confident that I will be able to do it.

On The Fuel-Optimal Ascent Speed in Kerbal Space Program

noreply@blogger.com (Alphanumeric Sheep Pig) — Thu, 01 May 2014 19:10:00 +0000

Kerbal Space Program is a sandbox-style spaceflight simulator game developed by Squad. The player designs and assembles spacecraft by piecing together a wide range of components, and then launches and flies them. The game places an emphasis on the realistic modelling of various physics, including structural failure of components, aerodynamic lift and drag, and accurate orbital mechanics. It should come as no surprise to learn that I absolutely love this game.

It is widely known and claimed that the most fuel efficient ascent speed for a spacecraft in Kerbal Space Program is the terminal velocity. However, not many people can actually explain exactly why this is. The whole thing has given rise to a number of misconceptions about terminal velocities and aerodynamic drag, so I felt I had to clear these up.

I'll also go through the math to calculate the actual fuel optimal ascent speed (which just happens to be equal in magnitude, but opposite in direction to the terminal velocity), because I couldn't find it explained anywhere else. I didn't really believe the claims until I did the math myself, so hopefully this will help those who are not convinced by all the half-baked whishy-washy arguments out there.

    1. What is the terminal velocity?

Many people seem to think that the terminal velocity is the maximum speed a rocket can reach. I don't know where this comes from, but it's absolutely false. The terminal velocity of an object is the speed at which an object will fall through air in the absence of all forces other than gravity and air resistance. That is, the only forces acting on the object are gravity and air resistance, or aerodynamic drag. Finding the terminal velocity is as simple as equating the weight of the object (a constant) to the drag (which varies with the square of the speed), and solving for speed. If an object is falling faster than the terminal velocity, air resistance will cause it to slow down. If it's falling slower than the terminal velocity, gravity will speed it up.

To get an object to fall faster than the terminal velocity, one simply needs needs to apply a downward force in addition to gravity.

Another thing to note is that the terminal velocity is always directed down. That's because at the terminal velocity, gravity and drag are equal in magnitude, but directly opposed.

    2. What does this have to do with going up?

The terminal velocity applies only to falling objects in the absence of other forces, so what is the relevance of the terminal velocity when your rocket is going up? The answer is, not much. It's just a useful reference point. Below the terminal velocity, your engines are doing more work to overcome gravity than drag. Above the terminal velocity, your engines are doing more work against drag than gravity. At the terminal velocity, exactly 50% of the work your engines do goes to overcoming gravity, and exactly 50% goes to overcoming drag. There's no reason why you can't just apply more thrust to ascend faster, or less thrust to ascend slower.

    3. Calculating the terminal velocity

From here on out, we're doing math. Hopefully this doesn't scare you off. As we've already pointed out, the terminal velocity occurs when the weight of the object acting downwards exactly balances the drag acting upwards. The weight is given by

where is the object's mass, and is the gravitational acceleration (which we can assume is constant if we're considering only very small changes in altitude).

The drag depends on several factors: the air density, , the cross-sectional area of our rocket, , the drag coefficient, , and the square of the object's velocity, . The equation is

The terminal velocity occurs when these two forces are equal. That is, when

To find the terminal velocity, we simply solve for to get

4. Calculating the optimal ascent speed

We're now going to calculate the optimal ascent speed. As far as we're aware (at this stage), that has nothing to do with the terminal velocity, so we're going to start from scratch.

To do this, we're going to try find the mass of fuel that needs to be burnt to increase altitude by a small amount, and then use some basic calculus to find the speed that minimizes that. First, we'll need an expression for the change in altitude at a given speed. That's easy to do if we assume that the speed is constant. This is approximately true, provided we're considering a very small change in altitude:

where is the speed, and is the time taken to change the altitude.

We don't actually know what this change in time is, so we'd like to find another expression for it, preferably one that doesn't involve speed. To do that, we're going to make use of the rocket's impulse:

If we assume that we're looking at a very short period of time, so that the thrust is approximately constant, then this simplifies to

Now we need to calculate this impulse. Fortunately, the impulse, as you might guess, is very closely related to the specific impulse, which is a property of the engine, and is readily available for various engines in KSP. The specific impulse is defined as the impulse delivered per unit weight (at standard gravity, , which is the gravity at sea level on Kerbin) of propellant burned. Therefore, we can calculate the impulse from the weight of fuel burned, and the specific impulse of the engine:

Substituting this into our expression for impulse above, and solving for the time, we get

And so our expression for the change in altitude at a given speed becomes

So, solving for the amount of fuel burned, we get an expression for the fuel required to increase altitude by a certain amount at any given speed:

We don't know how much thrust we need to produce to maintain the optimum velocity. However, we can calculate what this value needs to be based on the two assumptions we've already made. We've assumed that the thrust is constant, and we've assumed that the velocity is constant. This means that thrust will be exactly balanced by the sum of the rocket's weight, and drag, . Therefore, we can write the thrust as

Since we're considering a very short period of time, we can assume that the weight of the rocket is constant. We've already got expressions for weight and drag, but we'll repeat them here. They are

and

We can substitute these into our equation for thrust to get

Then we can substitute that into our expression for fuel required to get

This can be simplified to give a simple expression for the fuel required to increase altitude by a small amount at any given speed.

We want to find the speed that minimizes the fuel required. This is a standard optimisation problem, and means we need to set the derivative of the objective function to zero.

That derivative is fairly easy to get with basic calculus. It leaves us with the following equation to solve:

This is easy to solve. Move the first term across to the other side, cancel and on each side and then multiply through by . This leaves the following expression:

Does that look familiar? It should. This is the exact same equation we had to solve to calculate the terminal velocity. The term on the left is simply the weight, and the term on the right is the drag. This means that the speed that minimises the fuel required to increase in altitude just happens to be the speed at which weight and drag are equal.

This means that the velocity that gives a fuel optimal ascent is equal in magnitude to the terminal velocity, but in the opposite direction.

On QuickCoords - A tool for quickly capturing coordinates across a series of images.

noreply@blogger.com (Alphanumeric Sheep Pig) — Fri, 14 Mar 2014 08:51:00 +0000

I needed an easy way to manually track the positions of features across a series of more than 600 photographs. Loading each individual photo and copying the coordinates of each point one at a time gets very tedious very fast, and none of the programs that I tried really seemed to support a rapid workflow.

That's why I wrote my own. QuickCoords v0.1beta is now available, either from Sylvermyst Technologies or from GitHub.

It's still in beta, so if you have any need for a program like this, try it out. The following features are fully functional:

Select a folder, and load images from that folder.
Quickly switch between images using a range of keyboard shortcuts.
Click anywhere in the image to get the coordinates of that point with sub-pixel accuracy.
Select and remove points individually, or in groups.
Shift points around if your initial click was a handful of pixels off.
Copy a list of points for pasting into most spreadsheet programs.
Export the points as a CSV file or plain text.

Any feedback is welcome, and if you encounter any major bugs, please report them (if they haven't been reported already).

On the Elusive Doctor of Philosophy

noreply@blogger.com (Alphanumeric Sheep Pig) — Wed, 19 Feb 2014 18:21:00 +0000

The number one problem with a PhD is that no one really knows what you need to do to get one. Over the past few years, I've been asked too many questions like "When will you finish?" and "How many pages does your thesis have to be?" The answers are actually surprisingly simple: "When I'm done" and "Enough".

I'll start by telling you about the official Rules and Syllabuses of my faculty. This is a three hundred and something page document that goes into a lot of detail into what you need to get various degrees. For undergraduate courses, it will go into some detail about what courses of specific lengths you need to take, how many credits each course is worth, the minimum number of credits required in each year, and summarises the basic requirements for each course and how they are assessed and examined. When it comes to a PhD, though, the rules are pretty vague. Here's what it says:

Conditions for the award of PhD:

A candidate for the Doctor of Philosophy shall –

present for the approval of the Senate a thesis which must constitute a substantial contribution to the advancement of knowledge in the subject chosen, which thesis must be satisfactory as regards literary presentation.

present himself/herself for such assessment as the Senate may determine.

There's a little more about admission requirements, having an advisor, examiners, something about spending a minimum of two years, and a how many copies of the final thesis need to be handed in (it's five, by the way, not counting the electronic copy), but that covers the gist of it. In summary, I need to do some research and write a thesis on it. Nothing about a page count at all. There's just that one requirement: it "must constitute a substantial contribution to the advancement of knowledge in the subject chosen", whatever that may be.

Naturally though, after a few years of research, one can produce a hell of a lot of rubbish. When writing up a thesis, it's natural to start to wonder how much of that actually needs to go in. How much of it would be considered an acceptable amount of filler material to bulk up the actual content.

My University has been operating for a little under a century, and there's a basement level in one of the libraries that is packed with past theses arranged by subject. You could walk through there to try figure out how long a thesis should be, but there are many there that are five or six hundred pages long, and some that are just a few dozen. However, it's not to difficult to see that theses written under the same advisor often land up being similar lengths.

So, curious as to where I stood (and because I'm sick of endlessly processing results), I went down to the library and pulled down five recent theses in my field that had been written under my advisor. So, instead of plotting the results of my experiments, I plotted a breakdown of each of those theses and compared them to what I have at the moment. The similarities in length and structure are clear.

That's me on the right, just next to the average thesis. My introduction is a couple pages longer than average (with about 2 pages left to write), and my methodology is about 7 pages below average (although I shoved about 20 pages into an appendix, so maybe it's longer than average), and my conclusion is a blank page right now.

It's reassuring to see that my results are the only thing left to type up. And with more than 600 photographs from experiments to process, and 260 GB of data from computer simulations to sift through, I don't think I'm going to have a problem adding the 81 pages that will take me past the average thesis.

I was hoping to finish by the end of this month, but here I am procrastinating again. It looks like I may just need a little bit longer...

On... a fifth arbitrarily defined solar cycle?

noreply@blogger.com (Alphanumeric Sheep Pig) — Fri, 17 Jan 2014 07:52:00 +0000

It's hard to believe that the Earth has completed almost five trips around the sun (at least, it will have by 19:44 this evening) since I started this blog, one boring Saturday afternoon in 2009. Although I have been considerably less active over the past year, I still managed to find time for 18 posts. I had just under five thousand visits this year (although Blogger is reporting forty thousand for some reason), mostly from the US, South Africa, Canada and the UK. It's difficult to tell what Google searches bought people here, because Google no gives out that information for users who are signed in. It's mildly disappointing, but I'm actually glad that the world is taking privacy a little more seriously these days.

The most popular posts for the year were, well, from previous years actually. My post about petrol price hikes made it into sixth place, after four posts about Minecraft, and the post from 2011 about our Tullen Shears (which, incidentally, are still going). Other popular posts for the year include Amusing Hat Day (which was a bit of a flop - even I forgot my hat), and the posts about classical music (lots of links to a couple hours worth of music, so go listen if you haven't already), the age of star light, and the theory of relativity. I was disappointed that my first video game was not quite as successful (go download it and try it if you haven't. It's actually more fun than it sounds).

Outside of blogging, 2013 was a very eventful year. On the academic side, I actually made some serious progress toward my PhD (despite both a hard drive and a laptop deciding to retire, removing 700GB of simulations between them), and may actually finish it soon, and I was flown to the other side of the world (the USA) to present a paper at my third academic conference. I bought my first car (instead of just driving a car which technically belonged to my parents), and took out my first insurance policy. I think, somewhere during 2013, I turned into an adult. I'm still not exactly sure what that means, and I don't feel any different, but I'm sure I'll figure it out.

Anyway, hopefully I'll still be able to find some time to post for some years to come.

On a Sense of Scale in the Solar System

noreply@blogger.com (Alphanumeric Sheep Pig) — Mon, 13 Jan 2014 07:14:00 +0000

Cary Huang has an awesome Flash application that you might have seen before, called The Scale of the Universe. Although that app is awesome for getting a sense of the sizes of various objects, it is not very good at conveying a sense of distance. To convey a sense of size and distance, you need to portray both sizes and distances to scale, like the Earth and Moon in the image below. I've always wondered if I could make something that can convey that sense of distance.

Figure: The Earth and Moon with both sizes and distances to scale. [Source: Wikipedia]

I've been wanting to learn how to use HTML5 canvases and improve my JavaScript knowledge for a while, so I realised that this was a perfect opportunity to do that. On Christmas Eve 2013, I sat down and began to program it.

Here is what I came up with.

It's probably not complete, but an app like this could be added to forever, and it possibly will be. I'd like to go further than our Solar System, and add some neighbouring stars, the Milky Way Galaxy and it's neighbours, and so on, until I get to the observable universe.

The rest of this post will talk about the challenges I faced during development, so if that sort of thing doesn't interest you, you can move on. If it does, or you're bored enough not to care, then please read on.

Firstly, the distances between objects in our Solar System are just enormous relative to the sizes of those objects. For example, to display the Earth and Sun together in an image, with the sizes and distances to scale, the image would have to be well over eleven thousand pixels across for the Earth to even show up as a single pixel. That's six times the resolution of a widescreen monitor at 1080p.
The second problem is the range of orders of magnitude that need to be dealt with. Many moons in the solar system have diameters of just a few hundred kilometres and orbit tens or hundreds of thousands of kilometres from their planets, yet the gas giants orbit at distances of a few billion kilometres from the sun.

Thirdly, there is the shear number of bodies in our solar system. The four gas giants have a couple hundred moons between them, and there are more than half a million bodies in our Solar System actively being tracked by the Minor Planet Center.

Finally, the orbit of each body in our solar system traces a unique path in three dimensional space, each with a different inclination, eccentricity, and other orbital parameters. Each body is at a different position in it's orbit, and many of these orbits (especially bodies in the outer solar system) intersect. For example, although Pluto is currently further from the sun than Neptune, it was actually closer than Neptune between 1979 and 1999.

The solutions described below were applied to solve the above problems, in reverse order. Each of these solutions has implications, which are also described below.

The program was restricted to a single dimension. Inclinations were ignored, and distance of each body is averaged across its entire orbit. The implication of this is that all bodies are incorrectly shown on the same plane, and distances between each body are completely inaccurate. Only the average distance from the body to the planet or star about which it orbits is accurate. A future incarnation of the program may remove this restriction.

All eight major planets were included, but only the five dwarf planets recognised by the IAU at the time of writing were included. This means that some bodies such as Sedna, Quaoar, Orcus and Salacia were not included, even though they are widely considered by many astronomers to be dwarf planets. Moons are only included if they are either massive enough to be rounded under it's own gravity, or larger than 10% of their parent planet's diameter. There are only two exceptions: Mars's moons Phobos and Deimos. These were included because they are widely known, and are the best studied moons in our solar system other than our own.

The ability to zoom was essential in order to get a sense of scale over a wider range of distances, with orders of magnitude varying from as little as tens of kilometres up to trillions and beyond. A constantly scaling grid in the background is essential for maintaining the sense of distance as the scale changes.

A minimum size (currently 3 pixels) had to be enforced so that a bodies position could still be seen, even when zoomed too far out for it to be visible. Bodies gradually fade from view as they get too close to their parent bodies on the screen.

I think the final approach comes close to what I originally imagined when I originally came up with the idea, and I hope someone at least finds it interesting and educational.

On Space and Big Life Decisions

noreply@blogger.com (Alphanumeric Sheep Pig) — Thu, 05 Dec 2013 07:46:00 +0000

I don't know why, but I've always assumed I'd be going to space one day, and I still know that I somehow will, one day. When I was very young, I wanted to be president of the world and rule from orbit. As I grew into a teenager, I began to understand a little of how politics worked, and I quickly abandoned that idea. Instead, I wanted to make my fortune by starting a multi-national corporation involved in every aspect of people's lives, and run a private space agency. I still hang on to that idea, and dream of it every now and then, but reality gets in the way. The business needs to start somewhere, and that needs a big idea. While I have no shortage of ideas, I have an unfortunate tendency to analyse them to shreds.

I think I was 15 or so when I realised I wanted to be an engineer. When I finished high school, for some reason I can't remember, I decided to pick a career based on the pay and how many job opportunities were available. Being South African, and having grown up in a city with a deep history in mining, I chose to become a metallurgical engineer on a mine. After 18 months at university, I couldn't figure out why I was doing what I was doing, but I was doing incredibly well academically, and I was waiting to hear back from the big mining company that had flown me out to a mine for a second round of interviews for a really attractive bursary. I felt that my entire future had been decided, and that I was stuck. It frustrated me. I told my mom how I felt in the car one day. I made it quite clear. If I did get the bursary, I'd carry on. But if I didn't get it, I wanted to study something else.

I don't know what would have happened if I did get the bursary, or if my parents hadn't been so supportive, but I was lucky. At the beginning of the next year, I registered for a different degree, and a four years later, I graduated with a Bachelor's degree in aeronautical engineering. I went straight into a Master's program, which brought me to where I am now - just a handful of months from finishing off my PhD.

It may be a couple of years late, but this is where I wanted to be when I was 15 years old. Then, of course, there's a few years of some sort of work, and then space.

A few years of what work, exactly? It feels really weird to look back on things now and realise that I'd never really given it much thought. I kind of assumed that the right opportunity would come along, and I'd just go with it. And, to be honest, that's exactly what has always happened in the past, and I'm kind of waiting for it to happen again. For a while, I thought that I was stuck on the wrong continent, but of course, in Africa, there's no better place to be than South Africa. Two South Africans have already been into space - one as a test pilot, and the other by copying my idea of becoming a stinking rich businessman. The past few years have even seen the start of a proper space agency, and the induction of a South African company into the International Astronautical Federation.

Anyway, I'm at another awkward point in my life where I have to decide where to go next. There are two things that I really enjoy doing, and want to do for the rest of my life: accumulating knowledge, and sharing that knowledge. I do really enjoy research (it's why I landed up doing my PhD), so I really would like some sort of R&D job. But at the same time, I've sort of grown to like teaching. While a year ago, I thought I'd never want to be an academic, I now think that's a career I could really enjoy, especially if I'm allowed to take courses unrelated to my field on the side. But, how many academics get to go to space?

Anyway, I don't post enough pictures, so here's a picture of my giving a thumbs-up when I finally get into space, made using my very limited artistic talent. Yes, I know the stars are no where near as visible outside the atmosphere, but how else can I portray that I'm in space without the stars?

On Online Learning

noreply@blogger.com (Alphanumeric Sheep Pig) — Mon, 07 Oct 2013 18:45:00 +0000

There is probably a reason why, after 10 years, I'm still a university student. I can't say what it is, but I think I may be addicted to learning. At the beginning of the year, I discovered MOOCs (massive online open courses) through an article that randomly popped up on my Facebook feed. Eight months later, I've completed two courses through edX, and am on my way to finishing two more.

The key to the success of these courses, I find, are the entry surveys that they typically ask you to complete before the first lecture. One part of most of these surveys asks you to select a response to a series of sentences. The available responses go from "Not at all confident", through "Somewhat confident", to "Extremely confident". My reaction to these sentences often runs something like this.

      "I am confident that my English skills are sufficient for this course."
Of course. No doubt there. Extremely confident.

      "I am confident I can understand the main concepts taught in this course." I'm doing a PhD in engineering. I should hope I can understand this. Extremely confident.

      "I am confident that I can handle the assignments, the quizzes and tests in this MOOC." Once again, absolutely no doubt. It couldn't be much harder than anything I've handled before. Extremely confident.

      "I am confident that I will finish the course." The slap in the face question. It gets me every time. It's like the arrogant "Oh yeah, then prove it" that I just can't back down from. Over the next few weeks, I will find myself working late on Sunday nights just to finish some assignment for a deadline the next morning, feeling like a complete undergrad, wondering why I ever signed up for this torture. Every time, I will think to myself, I could just quit. "There's no obligation to complete the course and earn a certificate", the FAQ constantly reminds me. But I don't quit, all because of that one time, right at the beginning of the course, that a survey used my ego to blackmail me into admitting that I was "somewhat confident" that I would finish the course.

On the "Microsoft Service Center"

noreply@blogger.com (Alphanumeric Sheep Pig) — Thu, 29 Aug 2013 13:37:00 +0000

We regularly receive calls from people claiming to be from "Microsoft Service Center". Usually, I explain to them that I actually use Linux, and then rant on about how a computer technician should have at least heard of Linux until they hang up. Today, however, I decided to have some fun and see exactly what they wanted.

Turns out, its the stupid stuff. The internet is infected, apparently. Every time I connect, my computer starts downloading special viruses and trojans that can't be detected by normal anti-virus software.

They wanted me to run a command 'eventvwr'. This is just Window's built in system log viewer, and I know that it inevitably lists several errors and warnings. I told them I used Windows 98 on a very old desktop (keyword: "used"... a decade or so ago...), and that it was giving an error message telling me that the command was not found. After ten minutes of explaining to the guy that Microsoft made Windows 98 before XP, and that XP was not the first version of Windows, I finally got transferred to Dan, the senior technician.

(On a side note: Dan says that ten or twelve years is not old for a computer. Computers have a lifespan of at least twenty years... Yeah, sure, Dan. Whatever you say.)

Dan spoke nice and slow, so I pretended to type nice and slow too. He sent me to a website, which I did not recognise, so I told him so. Sounding frustrated, he told me that Microsoft has lots of websites and makes lots of products, and that Windows is just one of them, and this was another Microsoft website. I waited a little, and explained how the screen had gone red and said "This website is not trusted". He quickly told me to close it, and then slowly spelt out the website for TeamViewer, which is an address I do recognise (after a Google search, I now know that the first site he wanted to send me to was for remote desktop software as well). We waited five minutes while I pretend downloaded it, and apologised for having slow internet.

"I don't know what it is. It's gotten really slow over the last few months," I told him. "Yes," he said. It's the trojan virus slowing it down. It's busy downloading all the other trojans onto your Windows."

Eventually I'd finished pretending to download TeamViewer, so he asked me to install it, but I could see where things were going. He wanted remote access to my PC, but I wasn't at my PC, so things were going to reach a stalemate. I decided it was about time for my pretend PC to crash. "Oh no, your computer hasn't crashed," he told me. "It's the hackers. They've taken control of your computer. Don't panic sir. I'll help you through this." Too bad. I panicked. I unplugged the modem on my imaginary desktop so the hackers wouldn't be able to do anything.

This was where the guy began to offer some useful advice. "We're going to install Microsoft Security Essentials, sir." I told him how I already pay a fortune for an anti-virus package. Apparently, that doesn't do anything to stop hackers. But for only R 150, I could purchase Microsoft Security Essentials (which is actually free). All I needed was my credit card number. I could make the purchase right there and then, over the phone.

Credit Card? I used to get lots of calls trying to sell me stuff (they stopped completely when I registered on the Direct Marketing Association's National Opt Out Database over two years ago), so I know exactly how to stop this. I'm a student, I told him. I don't have a credit card. I do have a card, but it doesn't have an expiry date. It's not a Visa, it's not a Mastercard, and I can't use it to make payments over the phone. Beeep. Beeep Beeep. He'd hung up. Unfortunately. I was really having fun.

On Video Game Programming - Part II: Page Ripping Champion 2013

noreply@blogger.com (Alphanumeric Sheep Pig) — Mon, 12 Aug 2013 10:32:00 +0000

Back in May, I announced my intention to develop a game. I spent some time messing around with 3D engines, and was pretty happy with my progress. But then life and work got in the way, and it all ground to a halt. However, I did find time to lurk in the back of the last couple of meetings of the South African game development community (which is actually far more active and talented than I'd imagined). Last month, they ran a competition, with an actual deadline that motivated me to actually do something. The only constraint was that the game could only use two inputs.

So, I bring you a video game. No, it is not 3D, and actually has absolutely nothing to do with what I'd said I'd do, but it is more or less complete, relatively bug-free, and actually surprisingly enjoyable to play, if only for five minutes. I present to you: Page Ripping Champion 2013!

The player controls a pair of hands using the F and J keys and tries to pull out all 250 pages in a book. Points are awarded for good technique and deducted for bad technique. If you use a single hand for too long, then that hand cramps. If neither hand is moving, then all bonuses are dropped. If this happens too often, then it's game over.

It was written in Python, using pygame for graphics, and PGU for the text. Graphics were very quickly thrown together in Inkscape. The game runs on both Linux and Windows. I hope you enjoy it.

On Being a Lecturer around Exam Time

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 04 Jun 2013 19:32:00 +0000

My mind likes to work with concepts rather than images, so this blog does tend to be a little short on pictures. I don't think there's any question why I would take the time to make this particular one.

And of course, if any of my students writing my exam tomorrow happen to be reading this, then... Well, I would wish you luck, but I've always thought that if people can pass an exam with luck, then it wasn't a very good exam... So, I guess... I hope you've been studying?

On Why the Stars We See in the Sky are NOT Long Dead

noreply@blogger.com (Alphanumeric Sheep Pig) — Fri, 31 May 2013 09:02:00 +0000

The light from distant stars takes a long time to reach us. High powered telescopes can look at stars that are millions, even billions, of light-years away. Because of this, a surprising number of people believe that when they look up into the sky, they are seeing stars as they were millions of years ago. Unfortunately, that's not true. In most cases, you're only seeing the star as it was a couple of centuries ago, or in many cases, only a couple of decades ago. In fact, if you look at Rigel Kent (the left most of the two pointers to the Southern Cross) tonight, you'd be seeing it as it was back in January 2009.

In fact, for more than half of the 50 brightest stars in the sky, the light reaching us now left them some time in the 20^th or 21^st centuries.

It kind of ruins the popular anti-joke: "According to astronomy, when you wish upon a star, you're actually a few million years late. That star is dead. Just like your dreams." Pretty much all the stars we see are almost certainly still alive. The one that's expected to die the soonest is Betelgeuse (that's pronounced Beetlejuice), which we see as it was in the late 14^th century. Betelgeuse is due to explode any day now... Which in astronomical terms means some time in the next million or so years.

Just to give you an idea of how long ago the light left some of the stars in the sky, I used Stellarium to generate a map of the stars in the sky from Johannesburg, South Africa at 8 pm and 4 am last light. I've labelled most of the more prominent stars, and included the approximate date on Earth at which the light left the star. I didn't account for changes in calenders or anything, so some of the older dates may be a few days out, but it's still accurate enough to give you an idea.

Johannesburg, 30 May 2013, 8PM:

Johannesburg, 31 May 2013, 4AM:

As always, you can click on the images for a higher resolution version.

Unfortunately, the constellation of Orion (of which Betelgeuse makes up the armpit) disappeared over the horizon shortly after sunset, so it was not visible for very long last night. For the briefest instant at around 4AM, the very dim Mu Cephei would have popped above the northern horizon if you had a clear enough view. Mu Cephei is one of the largest and most luminous stars in our galaxy, and yet it's barely visible with the naked eye. Light from Mu Cephei travels a mere 6000 years to reach us. If you think that's a long time, consider that light takes 100 000 years to travel from one side of the Milky Way to the other, and about 2.5 million years to get from here to our neighbouring galaxy, Andromeda.

On Video Game Programming

noreply@blogger.com (Alphanumeric Sheep Pig) — Wed, 22 May 2013 19:09:00 +0000

I haven't really had much time in the last few years to spend time programming something for fun, and I think it's really starting to get to me. In an attempt to fix this, I've set myself a fairly ambitious goal. I'm going to attempt to program a fully functional 3D game, or at least a working prototype of one. The catch is that I'd like to release the game under a GNU General Public Licence, or something similar, and so any libraries or engines that I use need to be compatible with that licence. Even so, I'm strictly limiting myself to using only free and open source software to develop the game. That means I'm not even going to use my Windows laptop to make backups. The game will stay strictly between my Linux netbook and desktop (This is also to prevent me from being tempted to do anything on this project while I'm at work). However, I'd like the final game to be cross-platform if I ever release it.

    1. My Game Programming History

My experience with creating games is fairly limited. I completed my first "real" PC game about 10 years ago. It was a simple text-based fighter with a combat system fairly similar to that of the Game Boy's Pokemon games. I've made a couple of attempts at games since - all ridiculously simple - a vertically scrolling space shooter (where balls start falling from the sky that get progressively faster), a pointless game where you control a grim reaper figure and try herd one of several balls into various baskets on variously shaped fields. One of the most promising games I've made was a horizontal scrolling platform game inspired by Contra. You controlled a figure that resembled the guy from the toilet signs (I'm sorry. I drew all the sprites pixel-by-pixel in MS Paint), and the object was to make your way through the rooms of some form of hostile building. I finished the first level, started prototypes for the second and third, and realised that I had no clue about balancing difficulty. The result was... well, it's probably better if you just try it for yourself.

    2. The Concept

So, what am I going to try and make now? The concept is one that I think is really simple to implement. I want something that makes use of (at least approximtely) real life physics, but in an environment that is completely unfamiliar. I want people with an understanding of physics to be able to understand the game mechanics, but I want a person who works off of everyday experience to be thrown off, and hopefully spark a curiosity as to why things happen that way.

When it comes to physics, there are two phenomena that more or less govern all of our intuition when it comes to judging how things behave. Those two phenomena are gravity and physical resistance (be it friction, air resistance, whatever). So, getting rid of these two things will change the way everything behaves, and the behaviour will be physically possible, yet completely unfamiliar. You can see where I'm going with this. The game will be set in space. Or at least, on a space station in space.

When I was a teenager, I played a game called Descent. While I was never particularly good at the game, the game's unconventional use of 3D movement in an enclosed zero-gravity environment stuck with me. I was always fascinated with the way my mind would always pick a direction as "down" based on visual clues, and I would always needlessly try and orient my ship in that direction, even wasting time during combat to do so.

When I read Orson Scott Card's Ender's Game, I could not help remembering playing Descent, always needing to orient myself according to those visual clues. "Remember- the enemy’s gate is down" is a well known quote from the book - and refers to the fact that ignoring the visual clues, and over riding your instinct with a different concept of direction could give you a strategic advantage. I always wondered about how it would feel if I was in a Battle Room, with no ability to change direction or velocity until I touch an object, and with no sure way to stop myself. I've always toyed with the idea of programming something based on that concept. I've finally decided that I will make it into a game.

So, to sum it up, the game will consist of a room, with obstacles, in which players will float free from any effects of gravity or air resistance. The only means of controlling ones motion will be through physical interaction with the walls, obstacles, and other players. In this, I will incorporate a combat element, and hopefully later a team combat element, as well as a certain level of puzzle solving. I don't want to take the concept too far until I see how everything works.

    3. Starting Off

Programming a game is not easy. There are a lot of aspects that need to be taken care of, and the one thing that's always stood in my way is not knowing where to begin. In the past, I've falling into the trap of designing the GUI, the main menu, writing the help files, character design, and all the wrong things to start with. I know where to begin now. A prototype. I need a rectangular room with a sphere, and very basic camera controls. I can then make the sphere move, and then make it bounce off walls. Then I can worry about adding controls to allow the player to control how the sphere bounces. Once I've got that, I'll have a basic prototype. I'll then start thinking about how to add other players. Only once I have that am I going to try put in models, textures, a GUI, and all the rest.

    4. The Language Question

The first thing I need to decide is what language I'm going to write the game in. This section is going to have to start with a bit of a rant, and I apologise for that. Without a doubt, Python is my favourite language. Despite criticisms against it, it's actually not such a terrible language to use to make a decent game. The one thing I hate though is the general attitude some people seem to have toward Python. "Its slow because it's a scripting language!" It can be used as a scripting language, but it's got so many other uses. Also, it can call C libraries, which is almost as fast as if the entire game was written in C/C++ anyway. "But Python sucks with graphics!" Yes, but once again, C libraries... Personally, I can write code far quicker in Python than in any other language I've dealt with, and it's not just because I've got more Python experience. I also get fewer bugs with Python, and I find those bugs easier to find. I've often written a quick Python program to do menial tasks. I've never written a C++ code for anything other than university projects, and even then, I only used C++ because the choice of language was made for me. I'm not a big fan of C++. I love almost everything about Python.

But the fact remains, if I Google some problem I'm having in Python, I land up with a forum post swamped with useless comments like "learn a real language" and the like, even though the real solution is usually some really elegant and concise line of code, and it really gets on my nerves. When I Google the same problem for C++, I get several civilised answers on how to go about solving my problem.

So, for that reason, and because of the game engines available, I'm going to be programming this game in C++. Although I've read through and made minor modifications to bits of C++ code in the last couple of years, it's about 6 years since I did any serious C++ programming from scratch, but hopefully I'll pick it up quickly again. Project Euler time again, I guess.

    5. The Engine Question

So, I also mentioned that I'd be using C++ because of the engines available. If I was using Windows, I'd probably use Unity. I've heard a lot of good things about Unity, but it doesn't meet the constraints that I've set myself. I need something with a decent free software licence, and preferably something that works nicely on Ubuntu. The first engine I started looking into was Panda3D. It's a 3D library for Python, made available under a modified BSD license. However, after a week of messing around with it, I found it clumsy and messy. I also found it difficult to learn. The closest thing I could find to a tutorial are a set of poorly commented sample programs, which I had to manually read through to find what was relevant to what I wanted to do. I grew frustrated quickly and decided to start looking elsewhere.

There are a surprising number of 3D engines out there, but very few work well with Python. Once I broadened my search to include engines for other languages, I had better luck. I eventually settled on OGRE, which is made available under an MIT license, and seems to have a decent set of tutorials available. The advantage of OGRE is that it apparently works quite well with Bullet, an open source physics engine that looks like a good bet.

    6. Conclusion

I'm pretty sure this project will take me a while. It's possibly one of the most ambitious projects I've ever undertaken. That said, I'm hoping that once I get some sort of working prototype, the rest will be easy. I've written this for three reasons. The first is to get my plans down in a coherent form that I can follow. It forces me to iron out the concept, in a way that can be explained simply, and this gives me a solid foundation on which to start developing. Secondly, it makes a commitment that I will do this. It gives me some level of accountability, and hopefully my readers will remind me if I forget about the project (although, that's never really worked in the past). Thirdly, it exposes my idea to much needed criticism. If you have any improvements to the idea, or if you think it's rubbish and I should do something else altogether, please tell me.

On Why Resigning is not Usually the Honourable Thing

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 30 Apr 2013 07:49:00 +0000

Recent events in the news have lead to certain people saying "She should just resign and let someone else take over," and "at least he did the honourable thing and stepped down." I've always thought that resigning is precisely the opposite of the honourable thing. This is best explained with an analogy.

Imagine a party at someone's house. Things get a little out of hand, and someone is being stupid, messing around, doing stuff that they probably shouldn't be doing, and eventually, somehow, a table with several glasses and drinks gets sent flying. Imagine that you're the host, and you're staring down the culprit. If he said, "Sorry, here's some cash to cover the cost of the glasses, and where's the mop so I can help you clean up?", would that be the honourable thing? What if he said, "I'm not saying I'm the one who knocked over the table, but I'm going home"?

Another example. Imagine you have a daughter, and she winds up pregnant, and you weren't even aware that she was even seeing anyone, but you've got a pretty good idea who the father is. If this boy says "I may or may not have gotten your daughter pregnant," and then leaves town, is that really the honourable thing?

What I'm trying to say is that we shouldn't be calling for people to resign in the face of a scandal. We should be calling for people to take responsibility, and fix whatever mess they've created.

On What I Could Contribute if I had to Build Society from Scratch

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 02 Apr 2013 13:06:00 +0000

Imagine you're suddenly transported somehow into another planet Earth in some other universe. Everything in that universe is exactly like ours in every way except that, technologically, the inhabitants are around ten thousand years behind us. Luckily, their languages have magically and inexplicably managed to evolve the same ways as ours, so they understand everything you tell them, and you understand everything they tell you. They've got a pretty good idea of how to start fires, make sharp tools, and they're not too bad with farming, but they have little more than that. While their quaint rural lifestyle would probably seem nice and relaxing for the first few days, no doubt you'd start to miss some of your modern comforts after a while. You have all the knowledge of a late twentieth/early twenty-first century education. How much of ten millennia worth of technological advancement could you reproduce in the remainder of your lifetime?

    1. So... What am I starting from?

Lets set the stage. We're talking the equivalent of roughly 8000 BCE in our world, which is the middle of the Neolithic Era. People are still using stone tools - this is about a thousand years before the first copper came on the scene (and about three thousand more before it's use is widespread), bronze tools are still five thousand years away, and iron tools will only start appearing a couple thousand years after that. However, they're getting quite advanced with stone technology. They're not just bashing rocks until they have a sharp point any more. They're taking the time to grind and polish their tools, and getting pretty good at it too.

Domestic dogs, sheep, and pigs are pretty widespread, but the idea of domesticated cattle is a fairly new one. Farming plants is also a pretty new idea, and is mainly limited to annuals like pulses, grains and gourds. If you want fruit, you'd most likely have to find a wild tree or bush. There are lots of farms, and a handful of villages. There are even a couple of towns in the most developed parts of the world - with walls and towers and everything - although they only have a few thousand inhabitants each.

Not having to go hunting for food actually frees up a surprising amount of time, and these people are just starting to discover recreation. They're already carving crude statues and making jewellery from brightly coloured stones, but concepts like wheels and pottery are still 1500 years away.

    2. Why would I be able to contribute?

I supposedly have all the knowledge that comes from being educated in the last decade of the twentieth century. I have an engineering degree from the first decade of the twenty-first century. Lets assume that I'm a quick enough negotiator so that they don't consider me a threat and kill me, and that I somehow manage to convince them to listen to me. What can I offer to this backward civilisation?

    3. The Basics.

Well, the wheel is a pretty obvious place to start. I could also teach them them that mud can be used for more than just mud huts and teach them to use clay to do some basic pottery. Not that I'm particularly knowledgeable about pottery, but I'm sure I could convey some of the basic ideas.

Another obvious, and probably essential technology would be writing. They'd actually be about five thousand years away from inventing written language on their own. However, starting with very young children, and trying to mimic the methods that are used in millions of our own schools across the world, I feel I could have children reading, writing and understanding within about six to eight years. Following on from that, I see no reason why I couldn't introduce a crude wooden printing press, even though they're almost nine and a half thousand years from inventing it on their own.

Once that's out the way, a crash course in Western philosophy may be appropriate. It would be wonderful if I could somehow get deductive logic to be a permanent feature in the education system from the very start. And naturally, I could follow with mathematics. I feel that with my knowledge, I could teach them basic arithmetic, quite a bit of algebra, some introductory statistics, and I think it may even be a good idea to introduce some very elementary calculus. Of course, I'd have to start teaching some Newtonian mechanics to make it all make sense, and then I could teach them some basic engineering design to make it all useful.

I also think I'd have to teach ethics from very early on. In fact, I should probably lead with that.

    4. What Could I Contribute From My Education?

Well... I did spend two years in university specialising in metallurgy. Is that useful at all? They're not far off from working out how much you can do with copper. I could easily teach them everything they need to know to build a simple clay copper smelter, and how to work the copper to make tools. I could even bypass the whole copper age, and show them how to introduce tin to make bronze. I could tell them all about alloys, and how you can affect the properties of metals by mixing them in different ratios. There's one catch though, and it's a fairly big and embarrassing one. I actually have no idea how to differentiate copper ore in a pile of rock. I wouldn't be able to identify any metal ore, in fact. So unless they know what copper ore is, but just haven't figured out what to use it for, none of my metallurgy knowledge is going to be particularly useful at all.

I spent the following four years studying aeronautical engineering. Obviously they're not quite ready for aircraft, but there are some pretty important things I could teach them that they could put to immediate use. Windmills are incredibly useful for grinding grain. I could also probably teach them a bit about propellants, and maybe make some crude rockets, but I'm not sure if this would be a good idea. In fact, most of what I could teach them from my university education would have only military uses to a civilisation like theirs. I think I should most definitely lead with teaching them ethics.

    5. What Would Actually Happen?

The course of events that would actually take place becomes pretty obvious, the more I think about it. I would arrive in their world. I would encounter the first tribe, and convince them not to kill me. Knowing people, I'd presumably have to do this by demonstrating that I can provide some military advantage over their rivals. They'd be terrified that I'd be captured by their rivals, so they'd kill me to prevent my knowledge falling into the wrong hands. Progress would resume as if I'd never been there.

    6. Conclusion - What Should I Do?

The answer is simple. Remain isolated. Live as a hermit. Avoid all contact with the humans that inhabit that planet. Never reveal anything. Unfortunately, I'm too much of a show off, so even then, I'd probably try something stupid and get myself killed. So the safest thing to do is to avoid being transported to a universe whose human inhabitants are ten thousand years behind ours.

What would you do? What could you contribute?

[Editor's note: Proof-reading this post made me realise that it sounds like a very generic blog topic. In fact, it probably sounds like it came straight from a random writing prompt. It didn't. As usual, I've probably been playing too much Minecraft, and it got me thinking. This is not too far off what that game is all about.]

On Amusing Hat Day for Incompetence Awareness 2013

noreply@blogger.com (Alphanumeric Sheep Pig) — Mon, 11 Mar 2013 19:49:00 +0000

Incompetence can be cured, if only we'd all make the effort. Make the effort, and on Friday 23 August 2013, wear anything on your head that wouldn't normally be considered a hat. Don't forget to join the Facebook event too.

Every year, over 7 billion people are affected by either their own or someone else's incompetence. Somewhere along the line, being incompetent became something to be ashamed of. All to often, we belittle people for something they can't do. Quite frankly, that's half the problem. Being incompetent is not something that anyone does deliberately. Many incompetent people are too embarrassed to admit that they don't know what they are doing. More often, they're not even aware of their incompetence. If only these people could be made aware of their shortcomings so that they could take steps to learn. So often, an incompetent person needs nothing more than to be taken by the hand and taught how to teach themselves.

Of course, awareness can only go so far. Somewhere along the line, we also need to start doing something. If you have any spare books lying around, then donate them to a local library or school. Offer your services to help out at a school or children's home. If you have no books, and are too busy to help, then donate some money to an orphanage, and let them know you want it to go towards a child's education. If you have no money, then use your creativity. Wear your amusing hat, and if anyone asks about it, use the opportunity to ask them to help out too.

If we all work together, we can solve the problem of global incompetence, and with it, the vast majority of the worlds other problems.

On Why South Africans Don't Really Mind Petrol Price Hikes

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 05 Mar 2013 10:24:00 +0000

South Africans love to complain, but I never see their words affect their actions. Sure the petrol price has an obvious affect on how much you land up paying to fill up your tank, but there are other factors that influence it too. Its difficult to take someone seriously if they complain about the petrol price after they've just bought an SUV, and even more so when you watch cars flying past on the highway at 140km/h. If people were really concerned about the price of petrol, we'd see people buying smaller cars, and driving slower.

It's all very well to say this, but I'm basing it all on anecdotal evidence. It seems as if people are driving the same speed, and it seems that they're still buying larger cars, but what do the actual figures say?

It seems that no one in South Africa regularly reports statistics on traffic related charges. In fact, apart from a single report for KZN in 2007, I could not find anything about the number of speeding fines issued in a given period. Unfortunately, this means that my impression that people are driving just as fast as they were a few years ago will have to remain unconfirmed. However, we do have data on vehicle sales and the petrol price, so we'll just have to concentrate on those.

    Fuel Prices

It's quite easy to find out past fuel prices. The AA of South Africa kindly lists past fuel prices for each month going back to 2008. The fuel price, as you're probably aware, has been steadily increasing over over that entire period. The exact value of the fuel price depends on whether it is sold at the coast or inland, and on the octane rating, but since I live inland and use 93 octane fuel, I used that price. Whichever price you choose to look at, however, the trend remains exactly the same.

    Vehicle Sales

Data on vehicle sales is a little harder to find. The National Association of Automobile Manufactures of South Africa (NAAMSA) publishes vehicle sales data, broken down by manufacturer. The catch is that their public access "Flash Results" are the only freely available results that they publish, and they don't seem to keep data for previous months. Fortunately, our old friend Google does. There are a number of sites that publish the NAAMSA flash reports from time to time, and so using search phrases like "inurl:pdf naamsa 'new vehicle sales statistics' may 2011", I managed to find a complete record going back to January 2009.

These reports include a breakdown of sales by engine size for Associated Motor Holdings (Hyundai, Kia, etc.), and as of July 2009, Amalgamated Automobile Distributors (Chana, Foton, etc.). While ideally I'd like to include a lot more manufacturers in my analysis, and the reports do contain more detailed sales data for most other manufacturers, these figures don't help me unless they are combined and aggregated - a classic case of too much information being useless. (Of course, I could do this manually, but that would take too much time. I could also pay for access to more detailed information which just might contain the aggregated data I'm looking for, but I'd feel cheated if I paid for something which was essentially public information anyway.)

Just to get an indication of the market, we'll look at the combined AMH and AAD sales for the following four categories: small (1400cc or less), medium (more than 1400cc, up to 2500cc), and large (more than 2500cc) cars, and SUVs and 4x4 recreational vehicles. For reference, these figures cover roughly 10% of the total monthly sales for all manufacturers in South Africa.

    Effect of Petrol Price on Small Vehicle Sales

Ideally, if people are smart and don't like spending a lot on petrol, we'd expect to see them buying more small cars as the petrol price increases.

Vehicle sales fluctuate wildly from month to month, but we're not concerned at this point with total sales. We just want to know what portion of those sales were small cars. So we simply take the number of cars with an engine size of 1400cc or less and divide by the total sales in the four categories (and naturally multiply by 100 to get a percentage). Since there's a bit of a fluctuation from month to month, we smooth the data out into a three month average. To keep things balanced, we compare this to the change in petrol price over the three months. The data is plotted below.

Apart from the obviously steadily increasing petrol price, you can see that there's a definite seasonal fluctuation in the number of small cars purchased. There's a definite peak between October and March. I'd guess this is due to year-end bonuses and school leavers entering the vehicle market, but that's not really important. What is important is that if you ignore these seasonal variations, there is a definite downward trend. So while the petrol price is increasing, people are favouring medium to larger cars over the smaller cars - the complete opposite of what you'd expect.

If we take time out, and simply plot the 3 month sales figures against the 3 month change in fuel price, we see the picture a little more clearly.

There's obviously no linear relationship (for those who know their stats, R² is 0.00006), but if we try fit a trend anyway, we see that it comes out more or less flat - implying that the petrol price has very little effect on the percentage of small cars bought. Of course, in reality, this is not necessarily the case. It is more likely that there are other factors which buyers consider more important that petrol price when they're deciding what car to buy. Things like the state of the economy at the time.

Effect of the Economy on Small Vehicle Sales

The gross domestic product (GDP) is a pretty well recognised indicator of the state of a country's economy. Unfortunately, monthly GDP values are not published, but quarterly ones are. This suits us fine, because we're looking at sales date averaged over three months anyway. Lets plot the percentage of small cars sales against the GDP and see what happens. (Since the actual value of the GDP is not important, it's been normalised by dividing by the GDP at the start of our data - i.e. June 2009)

The scatter is primarily caused by the seasonal fluctuation I mentioned earlier. If we ignore that, we see a definite downward trend. As the GDP increases, we see people favouring medium to larger cars.

Conclusion

If people were concerned about the petrol price, we'd expect to see people favouring cars with smaller engines as the petrol price climbs, but we actually see the exact opposite behaviour. The country's economy is growing steadily at the moment, and the immediate future looks bright (because who thinks long term anyway), so who really cares how much it costs to fill up your tank?

Me? I drive a small car, and I've always made an effort to drive it economically. But I don't have much money to spare, and I realised long ago that I just don't think of things the way others do.

On My 13 Favourite Pieces of Classical Music

noreply@blogger.com (Alphanumeric Sheep Pig) — Thu, 28 Feb 2013 12:51:00 +0000

I felt like compiling another list of music I enjoy. I'm told that I listen to a fairly broad range of music, but I don't really. All of the music I really enjoy falls into the genres of metal, alternative rock and classical, and even within those genres, I'm quite discerning. Anyway, here is a list of the 13 pieces of classical music that I would list as my favourite, in no particular order. It wasn't easy, but I did try limit myself to listing each composer only once. Sit back, listen, and enjoy.

    1. Vivaldi's "Winter" from The Four Seasons

Antonio Vivaldi's music was incredibly advanced for it's time. Although it is a full concerto in it's own right (No. 4 in F minor), it is usually listed as the final part of the set The Four Seasons. The first concerto, "Spring" is probably the most famous (and you'd probably recognise the opening bars if you heard them), but of the four, it is definitely the one I like least.

    2. The Funeral March from Mahlers's Symphony No. 5

Gustav Mahler wrote a couple of funeral marches throughout his life. The first, "Hunter's Funeral", which served as the third movement of his first symphony is probably one you'd recognise - the melody is from the nursery rhyme "Are You Sleeping?". The opening movement of his 5th symphony, however, is far more powerful. It portrays such complex emotion, more than just the sadness which funeral marches tend to carry. It contains pieces which carry grief, distress, frustration, resignation, and gratefulness all pulled together in a single piece of music.

    3. Beethoven's Symphony No. 5, Movement I

There is a reason why Ludwig van Beethoven's 5th symphony is one of the most famous pieces of classical music ever written. I enjoy the majority of Beethoven's work from his middle period, but his fifth symphony (together with the more light hearted eighth symphony and the Moonlight Sonata) really stands out from the rest.

    4. Dvořák's New World Symphony, Movement IV

Antonín Dvořák's From the New World was apparently one of the pieces of music that Neil Armstrong chose to take with him to the moon. As far as epic music goes, the final movement is one of the best. Having been a big fan of this piece for years, I was incredibly excited when I first heard The Wizard's Last Rhymes (by the Italian power metal band Rhapsody of Fire) use it to such good effect.

    5. Tchaikovsky's "Scene" from Act II of Swan Lake

Although Pyotr Ilyich Tchaikovsky's 1812 Overture was the first piece of instrumental music that I heard that portrayed it's story perfectly (who can't love music that uses cannons as a musical instrument), but it's just not quite as beautiful as the Swan Lake's "Scene".

    6. Prokofiev's Dance of the Knights

I first heard this piece in the form of Lords of Bedlam (by the Austrian symphonic black metal band Hollenthon), and eventually went on a hunt for Sergei Sergeyevich Prokofiev's original from his Romeo and Juliet ballet. It's the sort of tune that gets stuck in your head for years, and never truly leaves.

    7. Chopin's Fantaisie-Impromptu

Limiting myself to listing Frédéric François Chopin only once was difficult, since Chopin's Prelude No. 4 in E minor is by far, the most emotional piece of music I have ever heard, and no single piece of music has quite as much effect on me. However, Fantaisie-Impromptu, which is heavily inspired by Beethoven's Moonlight Sonata (another work which maybe should have made this list) is easily one of my favourite pieces of pieces of piano music. Interestingly, it's the most complex piece I've ever tried learning on the piano. Too date, I have mastered the first two notes.

    8. Grieg's Piano Concerto in A minor, Movement I

Apparently, the only piano concerto Edvard Hagerup Grieg ever wrote is somehow the one of the most famous piano concerto's ever. It's the introduction that I enjoy most, but the rest of the piece is extremely relaxing and perfect background music when reading or working. As Bill Bailey's character Manny from Black Books says, "It's good isn't it. It's sort of relaxing."

    9. Rachmaninoff's Piano Concerto No. 2, Movement II

Sergei Rachmaninoff hated his second piano concerto. He wrote it while trying to recover from clinical depression and severe writer's block. I have mixed feelings about a lot of Rachmaninoff's work, but this particular piece is one that I always enjoy listening to. For some reason though, the depressing 1975 pop song (which will remain unnamed) that features the main theme from this movement is one song I can't stand listening to.

    10. Pachelbel's Canon

Apparently, Johann Pachelbel's Canon is quite popular at weddings. Having only been to one wedding in my life, I didn't actually know that. I enjoy it because of the complex harmonies that arise out of such a technically simple piece. For those who don't know, a canon is a single melody that is played, with one or more instruments picking up the same melody after a delay (much like rounds in singing). In Pachelbel's Canon, all of the variation and complexity in the music essentially comes from a single melody interacting with two delayed versions of itself.

    11. "Rondo" from Paganini's Violin Concerto No. 2

I was torn between listing Niccolò Paganini's original violin concerto and Franz Liszt's piano version, La Campanella. In the end, I chose Paganini. I'm not sure why. It's probably because of the violin

    12. Bach's Toccata and Fugue in D minor

Johann Sebastian Bach actually wrote three Toccata and Fugues for the organ - two of which were in D minor. Two of them (BWV 538 in D minor and BWV 540 in F major) are quite similar, and I'm not a big fan of either of them. In fact, I dislike almost all of Bach's music. The one exception, of course is the better known of the three Toccata and Fugues, BWV 565, which is one of the most recognisable organ pieces ever written. It is completely different to any of Bach's other works, and indeed contains many features that were either extremely rare or completely unique at the time. There are two possible explanations for this. The first is that it was not written by Bach at all (there is actually no manuscript signed by Bach), and the second is that it was actually written for violin and later transcribed for organ.

    13. "The Sea and Sinbad's Ship" from Rimsky-Korsakov's Scheherazade

Nikolai Andreyevich Rimsky-Korsakov had an incredible talent for telling stories through music, and most of his orchestral works are the sort of thing you can just sit and listen to at any time. Scheherazade is just one of my favourite examples of that. He was also renowned as an excellent teacher, describing his philosophy as "I will speak, and you will listen. Then I will speak less, and you will start to work. And finally I will not speak at all, and you will work."

On John

noreply@blogger.com (Alphanumeric Sheep Pig) — Thu, 21 Feb 2013 16:40:00 +0000

Crouching forward, glaring at the dull grey light emanating from the screen, the man appeared deep in thought. It took a while to realise that he was dead, and probably had been so for a day or so. Even after realising this, and seeing the red of the gunshot wound in the back of the man's head, John gave the body a quick nudge with the tip of his boot before checking for a pulse, just to make sure. Nothing. Of course.

He left the room, returning less than a minute later with a large black bag. He pulled the chair out from under the table, and tipped the body onto the floor. In the manner of one who has unexpectedly spent a decade or two too long in one job, he dragged the heavy body into the bag and pulled the drawstring tight. A thick, tattered cord was hastily tied through a pair of roughly cut holes in the bag's base, and John dragged it out into the hallway, carelessly knocking furniture on the way out. He passed by the too-long-out-of-order elevator doors, and made his way down the stairs, the body thunking violently down each step. A hobo lay in a pile of his own vomit, drunk at the bottom of the stairs. John carried on walking, dragging the bag over the hobo’s legs as if he weren’t there. The hobo mumbled something unintelligible in his sleep, but John lurched on.

It was late morning, although little more than wisps of light could pierce the deep mist curtains that hid the rest of the city away. John tossed the body into the back of a run-down truck. He spent a couple of seconds looking back at the building before clambering into the driver’s seat and heading off. He was tired of this.

It was several hours before he approached his destination. Two blocks away from the place he was looking for, he was forced to swerve at an intersection as a couple in a battered sports car hurtled through on a red light, sending John and his truck skidding out of control into the side of a grey brick apartment block. He yelled profanities after them, but they were already long gone. Mumbling under his breath, he pushed the airbag down and climbed out to inspect the damage. It wasn’t too bad – it could probably be repaired – but the truck would not be going anywhere for a couple of days. That was unfortunate. He doubted that he had a couple of days. He took the body bag and a steel shovel out of the back, and grudgingly dragged them the final couple of blocks.

There was a park on the banks of the river, beautiful trees dropping autumn leaves which drifted under a large stone bridge. He had always loved this park. It was so peaceful here. He found a quiet corner under a tree, and in the orange light of a setting sun, he began to dig.

He wondered briefly how strange it was that he felt nothing. It was as if he was fulfilling an almost forgotten promise to a friend with whom he’d long since parted company.

The body buried, he turned back toward the road. A woman stood watching, long, wispy grey hair blowing gently in the breeze. He was not surprised. He had been expecting her to be there. “It is difficult,” she said, a small tear glistening in her otherwise lifeless face. He shook his head. “An obligation owed. Nothing more,” he replied.

He took her hand, and the pair walked down the street to the nearby pub. It was deserted, save the sullen barman behind the counter. He gave them little more than a glance as they walked in and seated themselves at the bar. The two sat in silence for quite some time before ordering.

The hours passed by, and the dirty glasses piled up. The pub closed, and the two made their way to the woman’s tiny apartment.

The night blurred into early morning, and John awoke on the kitchen floor. The woman was gone, but empty bottles still lay across the table and floor. Feeling bilious, John staggered out into the street, barely registering that the sun was still not up. His stomach finally giving up the battle, he threw up violently over his pants and shoes. He walked through the doors of the building next door, and passed out in the lobby. He lay there for several hours. Few people walked by, but those that did looked down scornfully, before pretending that they hadn’t seen him.

The grey-haired woman woke him. “Hurry, we need to leave,” she told him. “If we don’t make it in time…” John nodded, understanding. The two climbed into her car and set off.

“We won’t make it in time,” John told her.

“We have to,” the woman replied, pushing down on the accelerator.

They soared out of the city, and up a windy pass. As they left the mountains behind, the clouds opened up, and the mid afternoon sun pummelled down on them. The distant blue of ocean flickered though gaps in the trees as they heedlessly bounced over the cracked asphalt.

Speeding through the narrow streets of the city, the woman rashly cut corners, leapt over sidewalks, and completely ignored the traffic signals, sending more than one car swerving out of her way. She came to a stop in the middle of the street outside a battered old building. The two leapt out of the car, and made their way up the stairs, cursing the elevator which was not working.

Sitting in the chair, John fired up the computer. “Come on, come on,” he mumbled under his breath. The screen lit up, and he began clicking the mouse furiously.

“Will it work?” the grey-haired woman asked.

“I’m not sure. We need more time,” John replied.

“We don’t have time. Will it work?”

“I think so.”

“We need to be certain.”

“Yes. It will work.”

“Thank-you.” She turned made her way to the door. Her hand on the handle, she stopped and turned. “And, John?”

John did not remove his eyes from the screen. “Yes?” he asked, exhausted.

“I’m sorry,” she said as she fired the gun. She scrambled down the stairs, out the door, across the road, hurried across the river at the bridge, and came to a stop on a small hill looking over a quiet corner of the park. There, she stood and waited patiently as an old man slowly filled a grave for a long-forgotten friend.

On the Seven-Year-Old Who Bought Stuff

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 12 Feb 2013 22:06:00 +0000

Sorting out some paperwork in my cupboard, I came across an invoice for a cheap keyring, dated 5 July 2009. Its not that I don't clean out my cupboard very often (I try do it at least every six months), but I kept that particular invoice for a reason. You see, it's only a copy of an invoice, printed a week after the sale, and I wasn't the one who made the purchase, and, actually, I have never even touched the keyring in question.

I printed and kept a copy of the invoice because, over that one little keyring, threats and accusations were made against me, and on two separate occasions, security guards were called. All thanks to a single cheap little keyring.

The whole issue revealed so many flaws in our society and the way people think that I just had to write a post about it. However, it didn't feel right posting it while I was still working at the shop where the incident occurred. After three and a half years of a two-sentence draft post sitting in my post list, and more than two and a half years since I stopped working at the shop, I finally feel that the time has come for me to write the things that I wish I had been quick enough to think of at the time.

Let me tell the whole story. It's pretty long, but I think I should include all the details.

It all started at about 4PM on a Sunday, where I was working as a casual in a small retail store. I about five hours into a nine hour shift (immediately after a three hour shift at my sound engineering job earlier that morning), and I was pretty tired. It had been a quiet afternoon, and I'd spent most of it doing reading for my final year research project that I didn't really understand. A small boy walked in alone, and spent quite a bit of time looking around. Now this wasn't unusual - the centre is primarily a casino complex (one of the most popular in the country), and an alarming number of parents would leave their kids to wander the centre while they were off gambling, rather than fork out money for the childcare facilities that were provided. Eventually, the child brought a keyring to the counter, and handed over his money. I ring it up, handed him his change and a receipt, and thought nothing more of it. If it hadn't been such a slow day (that was practically the only sale I'd made that afternoon), I wouldn't have remembered it at all.

(On a side note: The babysitting issue was pretty serious problem for us, but I'll get back to that later. We actually at one stage had a large TV in the store, and we used to play DVDs on it to attract customers. We got rid of it, because we'd inevitably land up with a row of kids seated in the middle of the store as parents left them for hours at a time while they went to watch a show or gamble.)

At around 6:30, the boy came back with a slightly older (maybe ten to twelve years old) girl. She holds out the keyring, and says "You have to take it back. His father will kill him if he finds out." The store had a no returns policy, but if an item was still in the packaging, I often used to do a refund anyway. Unfortunately, the boy had thrown away the receipt and packaging (so we'd never be able to resell it even if I had taken it back), so I apologised, and explained that I couldn't give a refund. The two left disappointed.

Closing time was officially 8PM, but I noticed pretty soon after I started working there that there that the store's busy periods coincided with the end of each show at the cinema. I could normally make half a dozen or so extra sales for the day if I kept the store open an extra 30 minutes, and that day was no different. I cashed up and closed off the day's accounts, switched everything off, packed up my stuff and left. Just as I turned away after locking the door (this is 45 minutes after the official closing time), a woman approached me.

"How could you sell this to my son!" she yelled, waving the keyring in my face. "He's a child of seven!" I noticed the boy now hiding behind her, terrified. Tired, and just wanting to go home, I asked her calmly if she wouldn't mind coming back the next day - someone else worked Monday's, and I was hoping that by passing off the problem, I wouldn't have to deal with it. She did not accept that. I repeated what I had told her children - that without the packaging and receipt, there was nothing I could do. If a child is old enough to carry money and walk around a shopping mall alone, he's old enough to buy stuff. After around fifteen minutes of arguing, I gave up and began to walk away, but she grabbed my arm and violently pulled me back. That was my trigger - no one touches me aggressively. The two years of Taekwondo training that I'd had at the time probably showed a little in the way that I twisted my arm out of the grip, and I murmured "Don't f****** touch me." Now, those who know me personally will be able to confirm that I almost never swear, and that I am almost always calm. In fact, this was the fourth time out of four that I have ever genuinely lost my temper in public. I turned and stormed off. I heard her calling for security, calling "Stop him! That man stole from my son." I walked through the centre, people staring, straight past the security check point at the exit, made sure no one was going to stop me, got in my car, and drove home. I made a very angry Facebook status update, followed half an hour later by an apology, both to my friends and the woman I swore at (who would obviously never read it).

The following Sunday evening, an angry man with popping eyes and throbbing veins on his forehead came into the store and started yelling at me. With an awful lot of cursing, he was demanding his money back, but it took me a full five minutes to figure out that he was the husband of the woman I'd dealt with the week before. I explained, as I had to his wife and daughter, that I could not do the refund without a packaging and receipt. he demanded that I get the store owner on the phone. I did so, and the store owner (who'd heard the whole story the week before, and supported the way I'd handled it) explained our no refunds policy to him. The man stormed out. Ten minutes later, he stormed back in. This time, he had a security guard with him. "This is the one. He's scamming children out of their money," he told the guard. The guard asked him to explain the whole story. The man started by explaining how I took advantage of his son's naivety and tricked him out of his money. Then he explained how I had not given his son any change or receipt, changing his story as he went along. Eventually, the story went that I did this all the time: I took advantage of children who had money and overcharged them for unmarked keyrings with no packaging from under the counter, and pocketed the cash. Naturally, I interjected to deny the allegations, to which he responded "Shut up. You'd better watch your back when you go home tonight, because I'll follow you and smash your face in." I could see the situation resolving in the security guards face, even as he explained to the man that threats wouldn't help anything. He asked the man to step outside so that he could ask me my side of the story. When the man had gone, I began to explain to the security guard what had happened, but he stopped me. "Its obvious what's happened here. Don't worry. We'll sort it out." He went out, and I didn't see the man again. Just to be on the safe side, I went back to the previous week's sales, found the transaction in question, and printed the copy invoice in case any more accusations came up. A security guard stood across the corridor for the rest of the day, and when I left that evening, I noticed a pair of security guards following me at a comfortable distance as I made my way through the car park. I put the invoice on my paperwork-awaiting-filing pile, and that's where it's been ever since.

That's pretty much the end of the story. I still have the father's eyes imprinted in my memory, and would almost certainly recognise him if I ever saw him again. I probably won't, but if I do see him again one day, I will direct him to this post. Unfortunately, it's a big world, and that's unlikely. Instead, all of you will be the ones who read this, and most of you are the ones who this least applies to. Nevertheless, I feel that it all still needs to be said.

First of all, the babysitting issue. I know childcare facilities can be expensive, and I know that a lot of people do not trust the people who work in them (they're mostly underpaid with very little experience and no qualifications anyway), but both of these points are easily addressed. The cost is easily argued away by pointing out that gambling is an extremely expensive habit in the first place. If a person cannot afford to pay for childcare services because of a gambling habit, one can't help wondering which other of the child's needs that person is neglecting. If this is a problem for you, you should probably seek free, confidential, expert help from the National Responsible Gambling Programme. The second point is even simpler: if a person doesn't trust the childcare staff, then what exactly is it that makes you prefer to put your trust in the roughly 9 and a half million annual visitors to the centre? I wish I'd thought to point out these flaws in their parenting at the time.

Second, the age issue. It turns out that the money that the child spent on the keyring had been intended to buy his dinner. One of the principle arguments that the mother had brought up was that it was irresponsible of me to be selling to such a young child. This is a terrible notion. I started receiving pocket money at around the age of five, and by then my parents were already teaching me the basics of saving up to buy bigger things. I was raised from the very beginning to learn to make sure I really wanted something before I bought it, and if I ever ever decided that I didn't want something after buying it, my parents would simply laugh at me and point out that there was a lesson to be learnt. So when I see a seven-year-old, eagerly handing over money, having been staring at an item on the rack for several minutes, I naturally put my seven-year-old self in his shoes, and imagine that they are coming to a final decision regarding hard earned money. It's not my place to remind him (even if I had known) that he needed the money to buy dinner. I think going hungry for a night would be the best way to teach him where his priorities should lie (this is exactly the same way life likes to teach this same lesson to children and adults alike). That aside, surely if it's irresponsible for me to be selling to a seven-year-old, then it's also irresponsible for a fast food joint to be selling to a seven-year-old? Not to mention giving a seven-year-old money, expecting him to buy stuff?

Thirdly, the blame and accusation issue, and this applies to people in general. Why on earth do some people feel the need to pile up accusation after accusation when they're angry? Even when the accusations turn out to be true (which wasn't the case in this situation), they are often irrelevant - merely constituting an argumentum ad hominem, one of the most common logical fallacies. In this case, of course, the accusations were actually relevant to the complaint, but the repeated exaggeration of the accusation, and adding additional false claims if the originals don't seem to have an impact is a deliberate malicious act. It only serves to weaken the case - inconsistencies in a testimonial form the biggest clue that it is false. It is completely irrational, and I don't think I'll ever understand the thought processes that would lead a person to do that sort of thing.

And finally, the threat. How on earth is threatening to smash a person's face in - in front of a security guard, no less - ever going to solve the situation. Especially since, from the security guards point of view, the party making the threats has been yelling and swearing excessively the whole time, while the other party just stood there calmly, unable to get a single word in. People do this all the time. They immediately want to revert to violence, when simple thought and calm debate would get both parties much further. Even if they can't reach agreement, there's always a compromise to be made.

Anyway, I'm glad that I've finally gotten around to writing this post. I'm sorry I lost my temper with a customer - something that I still feel guilty about today - and I'm sorry to everyone who saw me lose my temper. And even though she will never read it, I apologise to that woman. Most of all, I apologise for that poor little boy (who will be eleven this year), who has had to grow up with parents like that. I'm sorry.

On Applying the Theory of Relativity to Everyday Situations

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 29 Jan 2013 09:35:00 +0000

I came across a question on Reddit the other day, in which someone asked how much time a flight attendant would "gain" over the course of an entire career. It got me wondering about applying the theory of relativity to everyday situations. For those who are unfamiliar with relativity, let me start by giving a quick explanation.

If you're sitting on a small boat in a wide lake, aimed into the current, looking down at the water and watching the waves rushing past, its easy to imagine that you're cruising through the waves at speed. By looking at the shore, the illusion is broken, and you can see that you are in fact stationary, or merely drifting along. Now imagine the same scenario, but this time far out at sea, with no shoreline to look at to confirm your speed. It is impossible to tell how fast you are moving, if you are moving at all.

This effect was first described by Galileo Galilei in 1632, and is called the principle of relativity, and it basically says that you can't measure your absolute speed - you can only measure your speed relative to something else - and the laws of physics remain the same, regardless of what you choose to measure your speed against. So in a boat, you like to think of the shore as stationary, so you measure your speed relative to the shore, but you could just as easily have chosen another boat, or anything else with a constant speed for that matter. You should have covered this much in high school.

Fast forward two and a half centuries. People were thinking on a much greater scale. If we're on the surface of a rotating Earth, the Earth is rotating around the sun, the sun is in a spinning galaxy, so everything is in relative motion. It had to stop somewhere. Using the prevailing understanding of physics at the time, Albert Michelson and Edward Morley realised that it should be possible to work out the absolute velocity of the Earth in space by measuring the speed of light in different directions. They set up their experiment, and got extremely accurate results. The only problem was that they measured exactly the same speed of light in all directions. Turns out, it doesn't matter how fast you're moving, or in which direction, you will always measure the same value for the speed of light.

A couple decades later, and a young Albert Einstein tried putting the two together to see what came out. He started by assuming that there is no preferred reference frame, and that measuring the speed of light will give the same value in all of them. He got some startling results. For that to remain true, space and time would have to distort for a moving body. He derived formulae for the dilation of time and space for a body moving at a constant velocity, and called it the special theory of relativity. Special, because it only looks at the one special case of zero acceleration. Einstein then spent the rest of his life trying to remove that zero acceleration assumption, and eventually came up with a general theory of relativity, which could be applied to all moving bodies, and describes how space and time are distorted by gravitational fields.

It turns out that the passage of time slows down as you move faster, and speeds up as you move away from a heavy body (such as the Earth). So, if a particular journey causes the passage of time to go slower for a particular person, then they will have aged less than someone who did not go on that journey. To the stationary observer, it may appear that the traveller "gained" a certain amount of time, although to the traveller, time would actually seem to have passed normally.

The maths behind special relativity, as it turns out, is not too complicated - and space and time dilation depend only on the ratio of the object's velocity to the speed of light. The maths behind general relativity is a lot scarier, but for some simple cases (like constant gravitational pull), it reduces to some manageable formulae - the simple sort of plug-in-and-get-your-answer types.

So, can we apply some of these formulae to everyday situations? Like calculate the time that people who are up and moving are "gaining" over you, sitting in front of your computer? The answer is yes, and so I tried to do just that.

Lets start with something simple, like walking. A typical walking speed is just under one and a half meters per second, where as the speed of light is just under three hundred million meters per second. Lets put that ratio in numbers: 1/200 000 000, or in scientific notation, 1/2x10⁸. The time they'd "gain" over you is given by a simple equation:

where v is the traveller's speed relative to you, c is the speed of light, and t_you and t_traveller are the times that you and the traveller experience passing respectively.

All very well, but if you plug the ratio into the formula on your calculator, you get one - i.e. for every minute that passes for the walker, one minute passes for you, but that's not exactly right. Using a higher precision calculator, the actual answer is not far from 1-1.25x10^-17. That means that for every minute that passes for you, only 0.9999999999999999875 minutes pass for the walker. In other words, the walker "gains" an extra three quarters of a millionth of a nanosecond for each of your minutes he spends walking. Its not surprising that we don't notice time dilation in every day life.

Lets get a little faster. A car on the freeway travels at around 30m/s, which is a ten millionth of the speed of light. Plugging into the formula, we get about 0.999999999999995 minutes passing for the car for each minute that passes for you, the car "gains" three ten-thousandths of a nanosecond. Not much, but a lot more than walking.

Faster still, in an aircraft. Now things get complicated, because although you're quite happy at your 9.8 m/s² of gravitational acceleration in your chair, at the aeroplane's altitude of something around 35 000 ft (depending on flight conditions, of course), gravity is about a third of a percent weaker. This complicates things, because it means we can't just apply special relativity - we need to use general relativity to account for the differences in gravitational fields, and this means differential equations. Fortunately for us, they've been solved before, with a few approximations, so we can just use this simple equation:

Sure, it involves a derivative, but in our aircraft example, the entire right hand side is a constant, so finding the solution is as simple as finding the ratio between two constants. In the above equation, t_E is the time that the object under consideration experiences, and t_c is the time that passes for some stationary object too far away from anything else to be affected by any gravitational field. U is the Newtonian gravitational potential, which in this case is simply the Earth's mass times gravitational constant, divided by the distance of the object from the earth's centre.

If we assume that the aircraft is travelling at a speed of 250 m/s, we find that although the special relativity equation slows time down on the aircraft, the difference in the gravitational field actually counteracts this effect to a slight degree (although it's still a net "gain" in time). The aircraft effectively "gains" 9 hundredths of a nanosecond for every minute that passes for you. This experiment measured a 230 ns time shift on a round the world flight, which assuming 44.5 hours of flight time, can be converted to 8.6 hundredths of nanosecond per minute. I love it when my maths corresponds with reality.

Lets go faster still. It's not an every day situation for most, but lets consider the International Space Station. At 7700 m/s and an average altitude of 410 km, it's a lot higher and faster than the aircraft. Plugging the numbers into the formula, we get a "gain" of almost 23 nanoseconds for every minute that passes for you. That equates to astronauts on the ISS aging 0.006 seconds less than those of us stuck here on the ground Wikipedia puts that value at 0.007 seconds. I'd assume that Wikipedia's value is more accurate than mine.

Fascinating, but it's hard to imagine how the space and time dilation would look and feel. If you missed it last year, MIT Game Lab made a game to demonstrate various relativistic effects as you approach the speed of light. If you haven't tried it yet, download and play A Slower Speed of Light.

On the First Things I Do on a New Computer

noreply@blogger.com (Alphanumeric Sheep Pig) — Tue, 22 Jan 2013 15:43:00 +0000

Having formatted my desktop twice earlier this month, and with a new netbook due to arrive in the next day or two, I compiled a short list of things I do while setting up a new computer. Regardless of what operating system I use (and I firmly believe different OSs are suited to different tasks, so I use a couple), I make a few changes to the appearance and the default settings and software. This is a summary of some of the changes I usually make to a freshly installed OS.

    Noises.

Without fail, the very first thing I do is turn off system sounds. They're annoying, and who knows why they're still turned on by default on every system I've ever used?

    Space.

In Windows, I move the start bar to the side of the screen, because I feel that vertical real estate is far more valuable than horizontal on a wide screen. In GNOME, I disable the bottom panel for the same reason. I then shrink the icons to the smallest size that's practical and still looks good.

    Security.

I install an antivirus in Windows (usually AVG Free), or make sure that a simple firewall is installed and switched on in Linux (I like UncomplicatedFirewall). Along the same lines, I disable the guest login account if it isn't already.

    Browser.

I usually install Google Chrome, because the billions of saved passwords I have but can never remember are automatically synced. If Firefox comes installed by default (as on a number of Linux distros), I might just enable the Omnibar extension and put off this step until I need one of those passwords.

    Drivers.

I install any drivers that came with the computer, and update the graphics drivers with the latest version from the manufacturer's website.

    Dropbox.

Dropbox, or whatever cloud syncing app you use to make backups and store those things you can't do without.

    Desktop.

After setting the desktop wallpaper, I'll delete all of the icons (Oh how I wish Windows would let you delete Recycle Bin). I spend very little time looking at the desktop, so icons there are just a messy eyesore (I launch apps from the menu anyway). Its usually at this point in Ubuntu when I install Gnome Tweak Tool, and turn off "Have file manager handle the desktop".

    Screensaver.

I get rid of them. I set the display to turn off after 10 minutes and lock the computer. I never did like screensavers.

    Autorun.

Like screensavers, I've never liked software that runs itself when I insert a disc or plug in a device. I set the computer to do nothing on media insertion. On Windows, you can achieve this by going to Control Panel -> Hardware & Sound -> AutoPlay and setting it all to "Take no action".

    Appearance.

In Windows, there's not too much room here, but in any Linux distro, you can do almost anything. Firstly, I set the theme to something as dark but clear as possible. In Ubuntu and related distros, I install Ubuntu Tweak. I set the date format to a sensible order (day-month-year), and make sure it shows the day of the week (because I can never remember that). I also always move the close button to the left (because my clumsy clicking often closes when I meant to maximize). Other than that, I will spend several days trying out various settings and tweaking minor details until I am completely happy with the results.

    Software.

I cannot function on Windows without WinRAR, Notepad++ and WinDirStat, so I install those first. Second is a codec pack that includes Media Player Classic (K-Lite is all you really need). In Linux, it means taking a stroll through the package manager (I prefer to use Synaptic, so I'll usually install that first), and adding whatever you need. Ubuntu Restricted Extras are essential if you're going to be using the computer to play any media. Whichever OS I'm on, I'll install Calibre to manage my e-books and the Gimp to edit images.

    Shortcuts.

As I mentioned, I don't use desktop shortcuts. Although I launch almost all applications from the app search bar that most OSs have these days, I still like to have quick ways to launch a couple of my more frequently used programs. I pin a few programs (namely the browser and media player) the the taskbar or panel, and add a couple shortcuts (text editor and calculator) to the start menu .

Although I compiled this list mainly as a reminder to myself, I've shared it with you in the hopes that you find it useful. Don't be scared to experiment, and remember that if you stuff everything up, you can always just format and start over.

What are some of the first things you do on a freshly installed OS?

On... a Fourth Arbitrarily Defined Solar Cycle?

noreply@blogger.com (Alphanumeric Sheep Pig) — Thu, 17 Jan 2013 08:09:00 +0000

For those who were wondering, the arbitrarily defined cycle this year happens to be a day longer than I've used before. This fortunately significantly reduces the birthday shift down to just over 47 minutes earlier than the 14:38 at which the first ever Alphanumeric Sheep Pig post appeared. This time, I'm not going to repeat the embarrassing mistake that I made last year, when the shift of 18 hours and 54 minutes (that I had not at the time calculated) meant that my post landed up going out a day late.

This last year marked a big step for me. Apart from finally being officially enrolled at university for my PhD, I more or less succeeded at my first attempt at lecturing part of a course. Was I lecturing something related to my thesis topic? No. Maybe the stuff I spent 4 years studying to get a Bachelor's degree? The stuff I studied for two years before that before dropping out? Not even that. On the stuff I taught myself in a week one summer holiday 5 years ago and haven't really used since? Um... Yes... That.

But what about the blog? Yes, the frequency of posts have been getting slower these days (I blame Minecraft - the game that sucked me in almost two years ago, and hasn't let me go since), but my readership is higher than ever. According to Blogger's official count, I've had over 90 000 hits! Google Analytics says there were 31 265 unique visitors in the last year, from 123 different countries (amongst which South Africa has slipped to fourth place). Wait. I think this needs a map...

For the record, countries are coloured by the percentage of new visits, so South Africa appears slightly darker than the rest since those tend to be the people who know me personally (Thanks all of you loyal people, and the rest of you too).

Unfortunately, amusing Google searches have more or less disappeared off the radar. They are far overshadowed by searches for "minecraft bookshelf" (You're looking for this), "boeing 747 dimensions" (maybe this?), or "minecraft mining techniques" (obviously this, which may be quite old, but it's still valid), although searches for my explanation of the halos around the sun still feature quite prominently. I have to say that I'm disappointed at the poor performance at my first infographic attempt (using the moon to tell the time).

I will do my best to keep posting for another year, and hopefully after that. If you haven't already, encircle, like or follow using the links in the sidebar on the left. Speaking of which, are you aware of the mobile and tablet friendly version of the site I launched a couple of years ago? Top of the sidebar on your left, or type the address in your device's browser: bloggertouch.appspot.com/alphasheep. If you regularly read this blog on a phone or tablet, bookmarking that may be a good idea.