Tuesday, December 20, 2011

On the Enchantment Level - Bookshelf Dependency in Minecraft

[Editors Note: For those who do not play Minecraft, you should. You can play it in your browser here, but I strongly recommend downloading the client from here.]

[Another Editors Note: This post is outdated. Updated versions are available for the enchanting systems introduced in version 1.1 and version 1.3]

After watching episode 125 of Etho's Minecraft series, and listening to him complaining about how long higher level enchantments take to find, I decided to work out exactly what the distributions of the various enchantment levels are, and find the optimum number of bookshelves to use when looking for a specific enchantment level.

Because there is an increasing scale for the amount of experience required to obtain each level, a lot of experience is wasted if you spend your levels on more than one enchantment at a time. For example, if you start at level 0, and gain 10 levels and spend them on a level 10 enchantment, and then gain another 10 levels and spend them on another level 10 enchantment, you will have had to kill roughly 154 hostile mobs to obtain those two level 10 enchantments. But, if you gained 20 levels, and then spent all of them on two level 10 enchantments, you would have had to kill around 294 mobs for the same net result.

As a result of this, it is necessary to find an enchantment that will use up all (or almost all) of your levels in order to minimise the amount of experience wasted.

When enchanting an item, the player is offered three possible enchantments of random levels. The levels of the enchantments that are offered depend on two non-random and three random variables. The non-random variables are the slot in which the enchantment is offered and the number of bookshelves surrounding the enchantment table, and the random variables are integers uniformly distributed between zero and the number of bookshelves, zero and half the number of bookshelves (rounded up), and one and five. The three random variables are added together, and multiplied by a factor of 0.5, 0.66 or 1.0, depending on whether the enchantment is being offered in the top, middle or bottom slot.

This means that with 30 bookshelves around the enchantment table, the maximum level that can be offered in each slot is 25, 33 and 50 respectively. In other words, an enchantment of level 34 or above can only appear in the bottom slot. However, it is possible for a level 1 enchantment to be offered in any of the three slots.

Because of this, the distribution of the enchantment levels offered is skewed significantly toward the lower levels, with the first, second, third, and fourth groups of 10 levels appearing on average 8.0, 18.2, 9.3, and 3.4 times more often than the fifth group of 10 levels for 30 bookshelves.

The resulting probability distributions for the bottom slot are shown in Figure 1 below. For clarity, the numbers of bookshelves for which the graph is plotted match the combinations available using Etho's piston mechanism for the variable bookshelf enchanting room (built in episode episode 112 of his series.

Figure 1: Distribution of enchantment levels appearing in the bottom slot

The likelihood of being offered a level 50 enchantment is 0.04%, which means that the expected value for the number of attempts required to obtain this is 2 480. At two attempts per second, this means that it would take on average, over 20 minutes of clicking to get a level 50 enchantment. However, with some considerable luck (and faster clicking) this time could be much shorter.

Since the enchantment levels offered in the middle and top slots favour the same distribution, albeit squashed on the horizontal axis, it is apparent that lower level enchantments are much more likely to show up. For example, with 30 book shelves, a level 17 enchantment is the easiest to obtain. Obtaining an enchantment of exactly level 17 is likely to be quicker than obtaining an enchantment of any level from 38 to 50 (requiring on average 6.4 attempts, as opposed to 7.4 attempts).

This sort of behaviour will be familiar to all players who make use of higher enchantments. What is more useful is to use the distributions to calculate the optimum number of bookshelves to maximise the probability of being offered an enchantment of a specific level. This is quite easy to do, and the results are shown in Table 1. Oscillations in the distributions of the top and middle slots are caused by the rounding error after multiplying by the slot factor, and these play a small but important role in the calculation (for an example, level 14 is most easily obtained with 22 bookshelves, while level 15 requires just 21).

Table 1: Optimum number of bookshelves for specific enchantment levels.

Level Bookshelves
2 and below 0
3 1
4 3
5 5
6 7
7 9
8 11
9 12
10 14
11 15
12 18
13 19
14 22
15 21
16 26
17 25
18 27
19 and up 30

This phenomenon is not present when using Etho's variable bookshelf design. In this case, the optimum number of bookshelves to use is 2 for levels 4 and below, 9 for levels 5 to 8, 16 for levels 9 to 12, 23 for levels 13 to 17, and 30 for levels 18 and above.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, December 12, 2011

On the Imminent Loss of the Ultimate Kitchen Instrument

[A picture stolen from ebay.co.uk]
Growing up, I always took the set of Tullen Shears (pictured right) mounted on our kitchen wall for granted. They could (and did) cut through almost anything, and I simply assumed that everyone had a pair. Unfortunately, over the last couple of years or so, they have been getting progressively less sharp. This is not that surprising, considering what they have had to cut through in their almost 29 year life: virtually everything, including plastic, cardboard, tin cans, chicken bones, a couple of pairs of sunglasses, and a glass window pane. Ironically, the one thing that it could never make a clean cut through was paper.

While the shears still work, they don't cut through some things (like plastic) quite as neatly as they once did, so we have been looking for a replacement pair for a while now. This has unfortunately been unsuccessful. After turning to the great power of the internet for an answer, we found (with some digging, in a forum dated five years ago, from someone claiming to be the daughter of the inventor of the shears) that Tullen New Zealand was sold to an English company in the late 1980s and they stopped making the shears shortly thereafter.

At first I was surprised that no one had ever seen the gap in the market and come up with shears that could match those once made by Tullen, but gradually it began to make sense to me. Those who have never heard of Tullen Shears do not know that such an incredible instrument is possible, and those that do know about them still have a working pair.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Sunday, December 4, 2011

On Irrational Driving Part 1: Only Accelerating on the Downhills

There seems to be a growing trend for drivers to apply non-optimal behaviour to their driving techniques. I do understand that I tend to analyse things a bit more in depth than the average person, but there are certain facts that seem obvious to me. One of those facts is that it is more economical (not to mention less frustrating for other drivers on the road) to maintain a constant speed while driving along a straight road. Despite this, some drivers tend to enjoy accelerating the car to its top speed on the downhill sections of the road, and then let the car's momentum carry it up the following uphill at a much slower speed. This is a horribly inefficient way of driving, and I am going to attempt to explain why now.

In a very simplified consideration of a car, kinetic energy (or speed) is gained primarily from two sources, and mostly lost in two ways. The car gets extra kinetic energy by burning fuel, or by losing altitude. That is, if the car starts at the top of a hill, then without burning any fuel, it can start moving, simply because it is on a downward slope. The car loses energy to aerodynamic drag (and friction and a bunch of other things, but at fast speeds, drag is the most important), and by gaining altitude. A car slows down much quicker on an uphill than on a flat road. These things are obvious to most drivers, I hope.

The general idea for maintaining a constant speed is to balance the energy you gain from going down the slope with the energy from burning fuel. That is, you ease off on the accelerator on the downhills, and accelerate harder on the uphills.

On to the irrational behaviour. Some drivers, for some reason, like to put all the energy into the car at once, i.e. accelerate only on the downhills. It is very simple to show why this doesn't work.

Consider a road that consists of a 50/50 distribution of uphill and downhill slopes of equal gradient. Now consider two drivers: one who goes as fast as he can on the downhills, say 120 km/h, but then goes much slower on the uphills, say 80 km/h; and a second who maintains a constant speed of 96 km/h. We will assume that the uphill and downhill stretches are relatively long, and that the first car changes speeds quickly (so that we can neglect the time spent accelerating and decelerating). The advantage of these numbers is that for a journey of say, 6 km (which I chose for the round numbers it gives), both cars will take exactly the same time to reach the destination, that is 125 seconds. We will also assume that there are equal numbers of up and downhills, so that the starting point and destination are at the same altitude - this just makes the calculations a bit simpler.

The difference comes into the power that the cars lose through aerodynamic drag, since this power lost is proportional to the cube of the velocity (that is, a car doing twice the speed will lose eight times the power to aerodynamic drag). So while the drag of the first car is 30.6% lower on the uphills than that of the second car, it is 56.3% higher on the uphills. The result of this extra drag is that the first car loses 12.8% more energy to drag than the second car.

Since a specific quantity of fuel will release a specific amount of energy when it is burnt in the engine, this means that the car that accelerates hardest on the downhills will need to burn 12.8% more fuel throughout the journey.

So to sum up, a car that accelerates to 120 km/h on downhills but only does 80km/h on the uphills will use 13% more fuel than a car that holds a constant 96km/h, but arrive at it's destination at exactly the same time.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Thursday, December 1, 2011

On NaNoWriMo Part IV: Type IV

Even though I did not finish, I would call National Novel Writing Month 2011 a success from my point of view. I managed to write over 16 days in November, and put out 22 186 words (or 44% of the novel's minimum length) - my contribution to the more than three billion words written worldwide. This is a big increase over NaNoWriMo 2010, during which I managed to write a total of 4 607 words.

Unfortunately, I won't be giving you a full novel, because I have decided over the course of the next few months, I will be finishing it. It will be released as a free e-book under a Creative Commons license as soon as it is finished (and hopefully proof read and edited too).

The novel, is titled Type IV(Working Title) is set in a world very similar to the world inhabited by Ashley of last year's novel, and Sarieth of this blog's opening post. It is a world that may or may not be our own, long after a technological civilisation, which may or may not be us, has fallen and receded. The story centres on our descendants who are living in and around the ruins of ancient cities. The story centres on two characters.

Amser is an extremely gifted girl who is obsessed with discovering things. Although the sciences of the ancients are long since forgotten in the isolated city in which she was born and raised, she is a genius when it comes to inventing. Her true gift however, is chemistry. Through a childhood of trials and experiments, she has learned how to create a vast range of mixtures and chemicals that can perform a whole range of apparently magical functions. These lead her to discover ways to temporarily restore books left behind by the ancients, and she explores the world, absorbing knowledge, and applying it where she can.

Llyr, aka Pedran, aka Elhaearn, is a man who is being hunted by the Company - a corrupt private law enforcement agency that has the entire country under its terrifying rule, much like the rule of Llyr's father (self-appointed lord of the city of Pyr, notorious pirate and marauder, and insidious conman) had once had over those very same people. Hunted in exile, he is searching for these mysterious creatures that have been prophesied to be the ones to bring freedom from tyrannous rule to his country. Funnily enough, he finds that these creatures have a very strange connection with the foreign girl, Amser.

Anyway, here's a short extract:

“This guy saved our lives back there. Don’t they have names?” he asked.

Amser shrugged. “Not really. I’m not good with names. I call that one Type I,” she said, pointing to the smaller of the bird-creatures upon whose back Llyr was now sitting. “I call this one here Type IV.”

“In that case, I’m going to call this one Sion. Strong name. Means ’saviour’.”

Amser laughed. “I’m sticking with Type IV. Accurate name. Means the fourth combination of ingredients that worked.”

And then because I have the habit of graphing things (more for show than for actual information),

And of course, since I promised you at least part of a novel, you can have a prologue.

Prologue: The Girl Who Explored

CAREFULLY, using a sharp, flat piece of metal, the girl pried the small square concrete slab out of place. Once it was loose, she began to lift it, ever so slowly, keeping it absolutely straight. As soon as it was clear of the slabs around it, she tossed it through the battered doorway where it joined a pile of other identical slabs. The girl let out a sigh of relief. The faint rust outline of a key was just visible on the coarse cement base beneath. She removed a thin square of paper from a wooden box she had taken out of her coat pocket and placed it over the outline. From a small glass bottle in the box, she poured a clear pungent chemical over the paper and then blew over it. The red outline of the key was gradually drawn through the paper. She mixed two more chemicals from the box in a small vial and poured the silver mixture into the area within the outline. Within seconds, it was glowing red hot, the paper curling in the heat. The girl was ready with a bottle of water as soon as the paper caught alight. Once the billowing steam had cleared, she lifted a rough key from the floor. After quickly filing the burs from the key, she placed it in a pocket of her coat, together with her wooden box, and after a nervous glance at the window, hurried out of the room.

Several hours later, she was several stories underground at the bottom of a narrow and broken flight of concrete stairs that had apparently been ineffectually repaired with wooden planks a number of times in their long history. Panting from moving some of the concrete slabs from the rooms above all the way down to bridge missing steps, she began to search her pockets.

She quickly found what she was looking for. She removed two small vials, one containing a clear transparent liquid, and the other containing a thick orange gel. She rubbed a small bead of the gel over her left hand, and then allowed a tiny drop of the liquid to spill over it. She closed her eyes as the combination erupted into blinding blue flames, engulfing her entire hand. The flames resided in an instant, leaving just a glowing blue aura around her hand which cast a faint but sufficient light several metres around her.

She was standing in a narrow stone passageway. The floor was slippery with moss, and the thick smell of damp hung in the air. She slowly advanced along the passageway. Every now and then, at somewhat irregular intervals, passageways identical to the one she was in would branch off to her left or right. Most of these she ignored, but every now and then, she would turn down one. After half an hour, the light emitted by her hand was no longer bright enough to show the path in front of her. She rubbed some more of the orange gel over her hand, and the light was restored.

Eventually, she approached a thick steel door. Here, the damp heavy air at the entrance had given way to a much dryer thin atmosphere. A thick layer of dust coated the floor and was thrown up by her feet as she passed. She stopped several meters away from the door, pulled a cloth over her nose and mouth, and moving very slowly, she pulled a small spray bottle from one of her pockets and began spraying a fine mist into the air. She waited while the dust settled, taking shallow breaths and exhaling very slowly. When the air was clear again, she moved forward, the dust remaining undisturbed bar a few faint foot prints.

When she reached the door, she examined it for several minutes. Finally, she fired a short burst of the mist from her spray bottle into the key hole, and then immediately blew into the lock. Out came her wooden box again --- this time so that she could take out a small bottle with a brush in the lid. She took out the key and painted over it with a thick red-grey grease. Slowly but forcefully, she slid the key into the lock, listening for each click as either the key or the catch in the lock gave way and sprang back into place. Once the key was fully in the lock, she sprayed it with a new bottle, this one containing a transparent fluid with a soft acrid smell which slowly ran out of the lock. She searched a coat pocket hurriedly for something, cursing under her breath when she couldn't find it. She eventually found what she was looking for in another pocket --- a small silver-grey rectangular stone. She held it a few inches away from the lock, and the fluid, stained slightly brown from grease, flowed towards the stone. She slowly moved the stone in a circular motion, spiralling first clockwise, and later reversing the direction. Once she had been round several times, she turned the key in the lock. With a loud grinding noise, the lock eventually turned. With a loud clang, the door was unlocked.

With no shortage of resistance, and a deafening squeal of resistance from the long neglected hinges, she finally got the door open. She quickly moved into the room and pushed the door shut behind her. A smile slid across her face as she walked across the floor. The rough concrete roof was only just higher than her head, and lined with cables with long perished white rubber insulation. Every few meters, bare glass bulbs dangled from the ceiling, and where they were missing, shattered shards lay on the ground. The room extended further than she could make out and was filled with rows and rows of crude metal shelves, many of which had buckled under the weight of books they had held for centuries.

She made her way to the centre of the room, taking care not to disturb anything. Where a shelf had collapsed, or books had fallen, she changed rows to pass them, rather than disturb the fallen heap.

When she reached the room's centre, she took off the large tanks that she had strapped to her back and placed them on the floor. She untied a small mask that was attached to the one and fastened it across her face. She opened the valves on the two tanks, first on the one her mask was connected to, and then the other. A thick yellow mist filled the room. As the gas filled the room, she began to lift books of their shelves seemingly at random, spraying the liquid she had used earlier to settle the dust. Turning the rigid pages one by one, she began to read...

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, October 31, 2011

On NaNoWriMo Part III

As I did last year, I will be taking part in National Novel Writing Month (NaNoWriMo). For the month of November, I will be attempting to write a fifty thousand word novel. In the mean time, you can keep yourself occupied by reading what I managed to write last year. Or, you could always just use the time you normally spend browsing pointless stuff on the internet (like right now) to be constructive and write a novel.

You can keep track of the progress of my novel here. Feel free to add me as a writing buddy if you're also doing it. I will be back with a novel for you (or at least part of one) in early December.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Thursday, October 27, 2011

On the Efficiency of Nether Wart Harvest Spacings in Minecraft

[Editors Note: For those who do not play Minecraft, you should. You can play it in your browser here, but I strongly recommend downloading the client from here.]

Once again, my mathematical mind found itself thinking about the efficiency of Minecraft. Obviously, the warning for high mathematical content which I developed and then never bothered to actually use, could be applied here.


The expected yield per hour of a Nether Wart plant that is left for a given time period before being harvested and replanted can be calculated using statistics. The expected yield for several interval lengths is calculated and an optimum interval of between 25 and 50 minutes is found to be sufficient to allow the majority of the plants to grow, without leaving fully grown plants too long to waste update cycles.

      1. Introduction

The game of Minecraft is an open sandbox construction game created by Markus "Notch" Persson. The basic gamplay involves the player manipulating blocks in an effectively infinite 3D environment. The player controls an avatar that is capable of placing and removing blocks to create various structures, artworks or creations[1]. A significant part of the gameplay for the advanced player is farming for resources.

Nether Wart was added to the game in the 1.9 pre-release, and is a plant which only grows in the Nether on Soul Sand [2]. Due to the importance of Nether Wart in potion brewing, and since it can only be grown in the Nether, optimum farming methods become necessary. After being planted, Nether Warts need to undergo two stages of growth in order to be fully grown.

      2. Methodology

The aim of this investigation is to determine the time for which Nether Wart should be left in order to maximise the number of seeds obtained in a given time period. It is useful to define our target variable as the net yield per plant, , measured in seeds per hour. Freshly planted and half grown plants will yield a single seed, while fully grown plants will yield two to five seeds [2]. The distribution of the number of seeds dropped by a fully grown plant appears to be uniform, for an average of 3.5 seeds per plant. Thus the yield per plant per hour is given by the formula

where represents the probability that the plant has undergone growth cycles, and is the actual time in hours since the seed was first planted.

The algorithm the game applies when checking for growth is as follows [3]. The game runs through an update cycle (I avoid the word tick, due to confusion with redstone ticks) every twentieth of a second. Each cycle, the game checks twenty random blocks in each loaded chunk for updates. A chunk is a 16 x 16 square with the full 128 block height of the world, and consists of 32 768 blocks. Thus the probability of a certain block being checked for updates is 20 in 32 768, or 0.061%. If a Nether Wart that is not fully grown is chosen to be checked for updates, then the probability of it growing to the next stage is one in 15.

After update cycles, the probabilities of the plant being at each stage of growth is given by

where is the probability of a plant growing in any given update cycle, which is given by

After a certain time in hours, the number of update cycles that have been applied are

From this, it is possible to calculate the expected yield per hour per plant for a farm that is harvested an replanted at regular specified intervals.

      3. Results

The yield per hour per plant was calculated for various time intervals. Exact agreement was found for the probabilities of various stages of growths with the work of Pernsteiner [3]. The probabilities of a plant being at each stage of growth and the resulting yield per hour per plant is shown in Table 1.

Table 1: Yield per hour per plant at various times after planting.
Time Fresh Plant Half Grown Fully Grown Net Yield
1 s 99.92% 0.08% 0.00% 0.00
30 s 97.58% 2.38% 0.03% 0.08
1 min 95.23% 4.65% 0.12% 0.17
5 min 78.33% 19.12% 2.54% 0.76
10 min 61.37% 29.97% 8.67% 1.30
20 min 37.67% 36.78% 25.56% 1.92
30 min 23.11% 33.86% 43.03% 2.15
35 min 18.10% 30.94% 50.95% 2.19
40 min 14.18% 27.70% 58.12% 2.18
50 min 8.70% 21.25% 70.05% 2.10
1 hour 5.34% 15.65% 79.01% 1.97
2 hours 0.28% 1.67% 98.04% 1.22
4 hours 0.00% 0.01% 99.99% 0.62

The results are plotted in Figure 1 below.

Figure 1: Plot of net yield per hour against time

      4. Discussion

Figure 1 shows a maximum yield at 36 minutes and 43.6 seconds. However, the relatively flat gradient between 25 and 50 minutes would suggest that any time within this range would provide a reasonable yield.

The method with the highest yield would obviously be to monitor the farm constantly and manually harvest and replant those plants that are fully grown, but leave those that have not yet started to grow. However, the method of harvesting all plants at once lends itself to large or automated farms.

The above analysis does not account for the fact that a farm would take a finite amount of time to plant. Assuming a planting rate of about two plants per second, a 16 x 16 farm would take just over two minutes to plant. Because of this, the first plants two be planted would have had roughly two minutes longer to grow than the last plants to be planted. This should be accounted for when harvesting.

It is tempting to spread the farm over several chunks. This has absolutely no effect on the growth rate, as each block still has the same 0.061% chance of being selected for update, regardless of which chunk it is in.

      5. Conclusions

The expected outcome for the net yield of a Nether plant after a certain time period is easily calculated using statistics. A formula to calculate the probability of a Nether Wart having reached its first and second stages of growth respectively was developed and was then used to calculate the length of time that an Nether Wart farm should be allowed to grow to maximise the yield in a certain time period. The optimum time between harvests was found to be 36 minutes and 43.6 seconds, but any time period between 25 and 50 was found to be reasonable.

      6. References

[1]. Curse, Inc.; Minecraft Wiki - The ultimate resource for all things Minecraft; September 2011.
[2]. Curse, Inc.; Nether Wart - Minecraft Wiki; October 2011.
[3]. Pernsteiner, S.; Minecraft Crop Growth Algorithm; October 2011.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, October 24, 2011

On Password Strengths

It annoys me considerably when I am signing up for something and the form insists that if my password does not contain capital letters or numbers, or some special character, then it is somehow an inferior password. The strength in a password lies not in the characters it contains, but rather in the characters that it could contain. Therefore, if a password contains only capital letters, for example, but could contain small letters or numeric characters as well, then any brute force attacker will not know this, and would waste considerable effort testing passwords that contain those small letters of numeric characters.

It is especially annoying when I generate a completely random list of letters and numbers for use in a password, and then have the signup form tell me that my password is weak, despite the fact that by some random chance, it has no capital letters (something which can happen on average once in 167 passwords with the algorithm I typically use). My passwords typically have an entropy between 36 and 95 bits, which is strong enough for most purposes (the average person's passwords typically have entropies in the twenties.)

(On a nice informative side note: the aesthetically pleasing arrangement of letters and numbers that forms part of the background to the header on this page was generated by the same Matlab script I originally wrote to generate passwords for me.)

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, October 17, 2011

On the End of the World Part II

I once did a forecast based on penguin migrations and determined that on the 25th of August 2011, penguins would take over the world. You may think that we had a narrow escape, but I have found that my fridge is ever so slightly colder than I thought it was set to - clearly evidence that the penguins have been using it as a hideout.

More importantly, according to Harold Camping, the world is going to come to an end on Friday (just before supper, unfortunately), so I thought I'd be nice and help set the mood for our impending doom. I have arranged a nice depressing soundtrack to the end of the world so that, just in case the world does end, we will be in the right mood for it.

The Alphanumeric Sheep Pig's Soundtrack to the End of the World

  1. Gustav Mahler - Symphony No. 5, I. Trauermarsch (7:45)
  2. Virgin Black - Of Your Beauty (4:00)
  3. Frédéric Chopin - Piano Sonata No. 2, III. Marche Funèbre (9:33)
  4. Lacrimosa - Satura (9:23)
  5. Anathema - Shroud of False (1:37)
  6. Visions Of Atlantis - Atlantis, Farewell... (3:39)
  7. Wintersun - Beautiful Death (8:18)
  8. Ludwig van Beethoven - Symphony No. 3, II. Marcia funebre (13:49)
  9. Counting Crows - Raining In Baltimore (5:13)
  10. The Foreshadowing - The Last Minute Train (4:09)
  11. Rhapsody of Fire - Symphony of the Enchanted Lands, I. Tharos' Last Flight; II. The Hymn of The Warrior. (4:09)
  12. Eluveitie - Anagantios (3:26)
  13. United States Army Band - Taps (0:48)

Total playing time: 75 minutes, 49 seconds.

You can listen to the complete playlist on YouTube. If you start listening at 4:44 on Friday afternoon, you should finish the album just in time for Judgement. And don't forget to have a good meal beforehand, because if Mr Camping is correct, you won't get another meal again, ever.

(Some rather irrelevant notes: My apologies to those who do not share my taste in music. If I were a video game character, I'd be the little guy on the second island of Black & White, who wanders around in the mountains cheerfully whistling Chopin's Funeral March. The final two movements of the Symphony of the Enchanted Lands are far too uplifting to be included in this list (plus, they'd make it too long to fit on a single CD). Even though I am not American, Taps has an emotional depth that Last Post can never have, no matter how well it's played (I don't think my grandfather would like me saying this though). And then, obviously, I do not claim in any way that these videos or the music therein are my own.)

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, October 10, 2011

On Door Knocking

I tend to knock on things a lot. When I was much younger, I could never work out how to knock on doors. What ever I tried either made almost no noise or caused a sharp pain or spasm to shoot through my arm. When teachers needed someone to send on an errand, I dreaded being picked. Then, one day (I think I was around sixteen), I worked out how to knock on doors. Looking back, I think I had learned to knock superficially from watching television shows, but had never thought that hard about how it all worked in principle (which is something I try to avoid doing now). Somehow, I subconsciously made the shift to knock with the correct part of my knuckle.

The net result of this is that I missed that all important childhood phase where I should have been knocking on everything. I entered adulthood just as I was learning that I could knock on things, and now I'm stuck as an adult who compulsively knocks on doors, walls and desks.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Tuesday, October 4, 2011

On the Indecisiveness of Cardboard Boxes...

... because they can never seem to decide what shape they want to be. They always seem to insist on collapsing in slightly when carried, especially in the rain. In particular, the cardboard box that I use to hold my backup drives used to fit perfectly into my middle desk drawer. For some obscure reason, it decided this morning that the drawer was ever so slightly smaller than itself and for several seconds, it refused to allow the drawer to open. This is in spite of the fact that it showed absolutely no sign of protest when it was put into that drawer yesterday evening.

Perhaps I am missing something. Perhaps it is the drawer that is shrinking. Perhaps penguins sneaked into my office in the middle of the night and switched my desk with another one, identical except in its marginally smaller size. That would be impressive on the part of the penguins. This desk mirrors my old desk so closely, even down to the exact location of that annoying scratch in the table that makes my mouse skip.

(On a side note: It is strange how, after speaking almost exclusively English my whole life, and having almost certainly used some past tense form of the word "sneak" on at least several occasions, I could not recall which form I had always used previously, and could not remember which form was correct. As it turns out, the Oxford Dictionary of English says "past and past participle sneaked or INFORMAL, chiefly NORTH AMERICAN snuck")

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, September 26, 2011

On Swearing

I don't swear often. In fact, apart from when I'm driving, I practically never swear at all. The main reason for this is not because I have anything against swearwords, but partly due to my mind's insistence on taking certain things literally, and partly due to the fact that I like to avoid using words incorrectly. For example, consider someone who states that their "f**king car" has broken down. Immediately my brain conjures up an image of a car in the process of having sexual intercourse which suddenly stops and (with much clanging, banging and smoke billowing from the engine) falls over sidewards (exhausted perhaps?). The image is more comical than anything else, and fails to convey the (presumed) anger, frustration, hatred or other negative emotion that the original statement was supposed to convey. Most absurd, of course, is the exclamation "F**k me!", to which I can only respond with a shocked "What, right here?"

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, September 19, 2011

On the Productive Use of Compulsory Leisure Time

For roughly two hours a day, I am forced to sit in a nice padded chair with absolutely nothing to do to but to sit back and listen to the radio. I enjoy this time to myself and find it one of the most relaxing times of the day. I cannot understand why other people have to see time spent in traffic as waste of time and a source of stress.

People who get the most frustrated by heavy traffic do not seem to me to fit the sorts of stereotypes that would have particularly happy home lives or enjoyable jobs. It seems absurd to me that these people would want to minimise the time they have to sit back and relax, and rather just get to work each morning as quickly as possible. The more time I have to my self to sit back and relax while listening to music, the better - even if it does require some attention to be on the road in front of me.

The most frustrating part of sitting in traffic for me is making the adjustment from tapping out the rhythm of the music with my feet (which I do all day at work) to drumming it out on the steering wheel instead.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, September 12, 2011

On an Analysis of Minecraft Mining Technique Efficiencies

[Editors Note: For those who do not play Minecraft, you should. You can play it in your browser here, but I strongly recommend downloading the client from here.]
[Editors Note #2: While the analysis in this article is still valid, the addition of abandoned mines in version 1.8 makes the use of existing shafts in these mines the most efficient mining technique and is far safer than spelunking, provided the cave spiders are avoided.]
[Editors Note #3: With the addition of enchantments to the game, a player can obtain 120% more diamonds through the use of Fortune III, and can mine 300% more blocks with Unbreaking III. This makes mining for diamonds even more efficient than before.]

I take a very thorough and calculated approach to almost everything in life, and the game of Minecraft is no exception. As a result, I have decided to take a very scientific approach to the development of an efficient mining technique.

(On a very early side note: my advice to you is to not take any technique that recommends the use of stone pick axes seriously, as iron is definitely common enough to make all tools, buckets and doors from iron, and still have enough left over to make an extensive minecart system. Furthermore, there are just enough diamonds in the game to justify using a diamond pickaxe for all but the most detailed construction projects.)


This study presents an analysis of various Minecraft mining techniques. A quantifiable mining efficiency is defined and compared for 24 different mining techniques. Spelunking proved to be the most efficient technique, involving no mining in order to reveal resources, while large scale open-pit mining was the least efficient, as it required mining every single block. The optimum compromise between safety and efficiency is offered by slope mining at a 71.6° angle for iron and coal, and branch mining with two block high tunnels for diamonds.

      1. Introduction

The game of Minecraft is an open sandbox construction game created by Markus "Notch" Persson. The basic gamplay involves the player manipulating blocks in an effectively infinite 3D environment. The player controls an avatar that is capable of placing and removing blocks to create various structures, artworks or creations[1]. There are two primary elements to gameplay - these being the placing of blocks, called "building", and the destruction of blocks, called "mining". In general, mining includes the act of destroying blocks that are automatically generated ("spawned") within the games environment in order to obtain resources that may be placed as is, or crafted into other objects which may be placed.

The most common blocks are stone and dirt, which vastly outnumber other more useful blocks such as coal, iron, gold, diamond and redstone ores. Due to the large surplus in supply of the common blocks and the limited storage space available, mining stone or dirt unnecessarily is usually avoided. In addition to this, the act of mining takes a significant amount of time which is mostly wasted if useful resources are not being generated. Since the world in the game is essentially infinite, but the amount time a player spends playing is limited by constraints of every day life, there is a great advantage to using a technique which involves a minimal mining, but maximises the number of useful resources obtained.

      2. Methodology

In order to make any direct comparison of mining techniques, we need to define a quantifiable "mining efficiency" that can be meaningfully applied to any technique, and that allows for a conclusive comparison between mining techniques.

Previous work has had a tendency to place emphasis on not missing any ores within the mining region [2,3]. Contrary to popular belief, the distribution of diamonds within a world is not completely randomly, but is in a manner that is biased towards a more uniform distribution (that is, each chunk is given an opportunity to spawn a single diamond vein only once). Thus, it is safe to assume for our analysis that diamonds are approximately uniformly distributed throughout the world (at the correct depths, of course). This would imply that all blocks in suitable locations have the same probability of containing a certain resource. Strictly speaking, this is not true, but it is still a very close approximation. It follows from this that the quantity of resources found by a particular mining technique will be directly proportional to the number of bocks that the technique reveals.

The most efficient mining technique would be a technique that reveals blocks without having to mine any blocks at all. Similarly, the least efficient technique would involve mining absolutely every block. A suitable equation for the efficiency can be derived by applying a linear variation between these two limits. The efficiency is thus given by

where gives the number of blocks revealed by the technique, but not mined, and gives the number of blocks that are mined in order to reveal those blocks.

      3. Results

There are several classes of mining techniques that need to be considered. These include
  • Spelunking or cave diving, which involves exploring naturally occurring caves in order to find exposed resources.
  • Open-pit mining, which involves mining out every block in a deep pit of a certain size.
  • Branch mining, which involves mining long straight tunnels from a central hub.
  • Slope mining, which is similar to branch mining, but the tunnels are dug along a downward slope at a certain angle from horizontal.
  • Cutting, which involves mining long, narrow slits into the surface.

For the majority of these techniques, the efficiency of the technique depends on the scale at which it is implemented. The efficiencies for each technique at various scales is shown in Table 1 below. The table is sorted from the most to least efficient.

Table 1: Summary of efficiencies for various techniques.
Technique Blocks Mined Blocks Revealed Efficiency
Spelunking 0 1 100.0%
Open-pit mining, 1x1 1 4 80.0%
Slope mining, 71.6°, 5 high 5 16 76.2%
Branch mine, 2 high 2 6 75.0%
Slope mining, 63.4°, 4 high 4 12 75.0%
Cutting, 1 deep 1 3 75.0%
Slope mining, 26.6°, 2 high 5 14 73.7%
Branch mine, 3 high 3 8 72.7%
Slope mining, 45°, 3 high 3 8 72.7%
Branch mine, 4 high 4 10 71.4%
Cutting, 2 deep 2 5 71.4%
Branch mine, 6 high 6 14 70.0%
Cutting, 4 deep 4 9 69.2%
Cutting, 6 deep 6 13 68.4%
Cutting, 8 deep 8 17 68.0%
Open-pit mining, 2x2 4 8 66.7%
Cutting, very deep 1 2 66.7%
Open-pit mining, 3x3 9 12 57.1%
Open-pit mining, 4x4 16 16 50.0%
Open-pit mining, 6x6 36 24 40.0%
Open-pit mining, 8x8 64 32 33.3%
Open-pit mining, 16x16 256 64 20.0%
Open-pit mining, 32x32 1024 128 11.1%
Open-pit mining, large-scale 1 0 0.0%

      4. Discussion

Table 1 clearly shows that the most efficient technique is spelunking, followed by 1x1 open-pit mining. Spelunking is indeed the most efficient mining technique, especially after the Beta 1.2 update, which increased the amounts of iron, diamond and coal in caves [4]. However, spelunking has several disadvantages, including a greatly increased risk of encountering hostile mobs and a significant risk of getting lost. It relies heavily on natural cave systems, placing the player at the mercy of the randomly generated map.

Open-pit mining in a 1x1 pit (which is the equivalent of mining narrow vertical shafts) is the second most efficient technique at 80%, but is the most dangerous technique. It involves an exceptionally high risk of mining through the ceiling of a tall cave, or mining into a pool of lava. Both cases are likely to involve death, and it is either very difficult or impossible to reclaim your items should this occur. This is the primary reason for the often quoted "Never dig straight down" slogan. The efficiency of open pit mining drops rapidly as the size of the pit increases. For a 2x2 pit, the efficiency drops to 66.7%, and tends towards 0% as the size of the pit increases.

Slope mining at a 71.6° angle (as shown in Figure 1) is the optimum combination of efficiency and safety. The angle of 71.6° is the steepest angle that can safely be dug without mining the block that the player is standing on. This technique is ideally suited for coal and iron mining, but is not suited for diamond mining, due to the rapid rate of decent, which will reach the lava or bedrock layers within a few iterations of the method when starting from one of the diamond layers. The primary disadvantage is that this technique requires a minimum of 0.4 ladders per block mined in order to exit the shaft. An alternative is to fill in at least two blocks for every five block high section.

Figure 1: Example of slope mining at an angle of 71.6°

A more suitable mining method for mining diamonds is the branch mining technique. The higher the tunnel, the lower the efficiency of the technique, so it is advantageous to keep the tunnel height to the minimum height along which the player can walk, i.e. two blocks. At 75%, the efficiency of this technique is only marginally lower than that of 71.6° slope mining. Since all mining is carried out at a constant depth, it is possible to mine very long branches, increasing quantity of resources that may be collected.

      5. Conclusions

In general, spelunking is the most efficient mining technique. However, in the absence of suitable natural caves, or if the player deems the risk to be unacceptably high, then mining downwards along a 71.6° slope proves to be the optimum combination of efficiency and safety when mining for coal or iron. When mining for diamonds, a branch mining technique involving tunnels of a height of two blocks is the most effective method out of those investigated.

      6. References

[1]. Curse, Inc.; Minecraft Wiki - The ultimate resource for all things Minecraft; September 2011.
[2]. Malavok; Minecraft Forum: Stripmining Tutorial - Finally!; September 2011.
[3]. IceGecko; Minecraft Forum: Branch Mining Technique; September 2011.
[4]. Curse, Inc.; Version History - Minecraft Wiki; September 2011.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Sunday, September 4, 2011

On the "Explenation Point" (sic)

Or so I have heard it called. This possibly reveals the primary reason for the unfortunate punctuation mark's excessive misuse. The fact that certain people believe that it is a punctuation to indicate an explanation rather than an exclamation (a fortunately much rarer occurrence in writing than in speech). Such a person would state "The sky is blue because the different wavelengths of light are refracted by differing amounts in the atmosphere!"

In general, an exclamation mark at the end of a long sentence is almost always being used incorrectly. Most often, an exclamation mark should appear after a single word or phrase (as in "Hey!" or "Shut up!") as a way of indicating that it would have been exclaimed had it been said in speech. The Oxford English Dictionary essentially defines "to exclaim" as "to cry out suddenly and vehemently; to cry out from pain, anger, delight, surprise, etc."

(On a side note: It is a little known fact that "sic" as in the title of this post is actually not an abbreviation, but rather a word of its own, derived from the Latin word "sīc" meaning "thus".)
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, August 29, 2011

On Calculators

And yes, I am talking about the little battery operated pocket calculator. The one I have used maybe twice in the two years since my final exams at University. In fact, I am not even sure if it still works. (Note: I just checked. It does work. It just needs a whack against the desk to get the display to turn on.)

The thing with calculators is that people tend to take them for granted. I have learnt the hard way that they are vastly overrated. During test and exams, both at school and university, students were required to take out the stationery that they would need, and leave their bags at the back of the venue. Since I've always had a tendency to take the more mathematical subjects, The majority of exams I have written have required a calculator.

The first time I remember forgetting to take my calculator out was during an accounting exam in high school. As soon as I realised that I had forgotten, I thought of raising my hand and asking if I could go fetch it, but something inside me saw it more as a personal challenge, and that raising my hand would be giving up. Instead, I wrote the exam without my calculator, doing all the adding in my head and doing the more complicated depreciation and interest calculations in the margins. Somehow, I managed an A for that exam, and I felt immensely more proud of myself than I would have if my calculator had done half the work.

A couple of years later, sitting done for my mid-year physics exam at university, I realised that I had not taken a calculator out of my bag. (The irony was that I had by that time started carrying a spare calculator to exams, just in case one stopped working.) Once again, I considered raising my hand, but something in me was excited about the challenge. This time however, the calculations were somewhat more challenging than mere addition and subtraction. Many of them involved trigonometric functions and square roots - the sorts of calculation I cannot easily work out on a piece of paper without considerable time. Needless to say, I failed the exam completely.

The moral of the story, I guess, is that I should not listen to the little voices in my head that get excited whenever something challenging comes up. The only problem is that I don't think I can.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, August 22, 2011

On Making Telephone Calls

I am a little shy in some situations. I have no problem getting up in front of a crowded room and talking, but some things make me extremely nervous. Telephone calls, for example. When receiving them, I have to take a couple of deep breaths to psych myself up before picking up the phone. During the conversation, I'll usually limit myself to yes or no answers, even in cases where it doesn't really answer the question asked. I often find myself saying goodbye prematurely, typically several times before the conversation actually comes to an end.

Far worse than receiving phone calls is making them. In general, I try keep most contact - both business and personal - to emails, texts and instant messaging. On those rare occasions when I receive the dreaded email, "Please contact me on 012 345-6789", my pulse starts to rise, and sweat instantly appears in the palms of my hands. After taking several deep breaths, I get up and walk to my phone. After several more deep breaths while just standing there, I go back to my computer, just in case I see a message, "Never mind, we can sort it out over email", which I have to date never received. I go back to my phone, sit down and start dialling the number. Before I finish, I cancel the call, and go to the toilet to empty my bladder. When I get back, I check my email again, still hoping for them to change their mind. Finally, I resign to the fact that I'll have to make the call, and just get on with it.

Fortunately, I don't have to do it often. I can get away with making as few as three or four phone calls a year, including calls to my family, girlfriend and friends. Fortunately the age where phone calls are a daily necessity has passed.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, August 8, 2011

On the Amusing Hat Day Part II

There are 18 days left (or something like that, I think) until Amusing Hat Day for Incompetence Awareness... I spent a full twenty-or-so minutes setting up a website some time last week, and after registering a domain, and spending several days procrastinating, it is on-line. You should find the official website at www.amusinghatday.za.org without having to do too much searching.

If you enjoy using the Short-Spam-Engine, then you can follow @AmusingHatDay on twitter. And of course, if you haven't already done so, then RSVP to the Facebook event.

If you still haven't thought of what hat you are going to wear, then consider one of the following: underwear; a pot plant; a cardboard box; a brick (if you have strong neck muscles); an inside out T-shirt; a wooden plank; a plastic cup (I would not recommend glass); a small electric appliance; a book (an old boring one that no one would want to read, preferably); or a plastic bag (don't suffocate yourself though).

If you have any ideas that are not listed here, then feel free to suggest them in the comments.

Feel free to send an email to the event organisers at amusinghat@alphasheep.co.za.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, August 1, 2011

On the Nasal Athlete: Part II

For as long as I can remember, I have always had an overly athletic nose in July. For the last couple of years, it seems to have been getting lazier. Last year, I was amazed at how long it stayed away, but this year definitely squashes the pie. It took until the evening of the 31st for the first signs of of a running nose to appear. It wasn't exactly an olympic medal winning performance - more along the lines of a (possibly reluctant) late afternoon jog - but it was a run, nonetheless. Of course, now that it is August, my nose has returned to it's usual peaceful pedestrian state, apart from what feels like a broken down truck in my right nostril.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, July 25, 2011

On "Security Measures"

Upon entering a store carrying a full shopping bag from another store, the security likes to put a tiny piece of red tape across the opening of the bag. I have yet to see this done with any real effect. In most cases, especially in a bag that is rather heavy, this little piece of tape is not enough to hold the bag closed any longer than 30 seconds. This is extremely awkward for me. It is like an unwritten agreement between you and the security guard at the door that you are allowed in the store only on condition that the bag be sealed by their tape. I feel compelled to honour that agreement and often have to resort to holding the bag in an awkward manner in order to reduce the strain on the tape.

The other day, however, the guard at the door had used the tiniest piece of tape imaginable to tape shut one of the fullest bags I had carried in a while. Despite my best efforts, I was unable to keep the bag sealed, and I eventually gave up after the tape tore down the middle. With visions of a number of armed guards pouncing on me to escort me out of the store, I clutched the bag in a way that obscured the torn tape from view. Eventually, at the till, I had to get my wallet out of my pocket. Without thinking, I removed my hand, and the security guard saw the broken seal. I know she saw it - she was staring directly at it. And yet she did absolutely nothing. I walked out of the store, and tried to nod acknowledgement at her in and inconspicuous manner, and she did nothing. I had always believed that the tape was there to prevent you from shoplifting by putting items in the bag and claiming you had bought them at another store, but considering the evidence against that hypothesis, I am not so sure now.

Speaking of sealed bags and security, I am highly upset with the man at the security check at a certain UK airport who decided that the knotted heavy duty butcher bag that I had put my deodorant in was inadequate. He insisted that I actually pay for one of their inferior resealable plastic bags. I felt like explaining that the so called "seal" on such a bag is to stop solid objects from falling out, and is not water tight. I would not be impressed if the deodorant leaked (which mine tend to be prone to doing) all over my bag. In any other circumstance, I may even have explained this, but fortunately I remembered an important rule that I try to live by - keep on security's good side.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Thursday, July 14, 2011

On an Official Sort of Announcement Part II

Due to me flying ten thousand kilometres from home to present a paper at a conference (read free overseas holiday), there will be no posts until at least the 24th of July. Unless you're lucky that is. I might just find time next week to type up a post or two. We'll see.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Thursday, July 7, 2011

On Perhaps Too Much Information

I am currently resisting the compulsive urge to extrapolate a fluid jet along a parabolic trajectory into the porcelain gravity-driven interface of a hydraulic bio-hazard disposal network.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, July 4, 2011

On a Rather Disturbing Thought

Consider a large group of people, all dressed in identical black and white suits, standing in the middle of an apparently open field in rather miserable weather. Every time you see them, some are just wondering around slowly, but most are simply standing there, looking around, but trying extremely hard to not focus on anything in particular.

If you are smart, you will pretend not to have noticed them, and just carry on with your business and try not to think about it any more. However, if you are unfortunate enough to have no control over what your brain chooses to think about (like me), your mind will immediately jump to one of a number of conclusions. One possible conclusion is the "secret service" option, and you may wonder which foreign head-of-state is currently visiting. If you like conspiracy theories, you may think "cover-up". Another possible conclusion that you may jump to is the "mafia" option - somewhere in the middle of that group, someone possibly has a shovel and is busy disposing of a body or two. The rest are just standing around to block the makeshift grave from view. There are few other explanations, especially during a raging blizzard, and most of them arouse suspicion.

It is for this very reason that I cannot bring myself to trust penguins. I mean, I like them. They are extremely cute and all that, but I would never leave my car keys where a penguin could reach them, and I most certainly would not let one into my house for any reason. Their general behaviour and actions are just far to suspicious for them to be up to any good.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, June 27, 2011

On Games of Logic

Very early on in my school career, I showed practically no mathematical ability (possibly due to a boring teacher, combined with a bit of ADD, my annoyingly slow brain with very little capacity when it comes to short term memory). At the age of around 8 or 9, I began to show an aptitude for maths that was somewhat higher than most kids of my age (probably around the time when maths became about working things out rather than memorising multiplication tables). As a result, my teacher recommended that I join the schools chess team.

There is a remarkably common misconception that people who are good at mathematics are good at chess. This is not true at all - to be good at chess requires two abilities: pattern recognition, and enough memory to hold a decision tree consisting of all possibilities for at least the next three of your turns . My pattern recognition is only average, and my memory has difficulty in holding even the moves available in the current turn. No surprises then that I landed up at the bottom of the team. I still cannot understand how people associate chess with a mathematical ability. It is merely a combinatorial game, and it's difficulty arises due to the shear number of posible locations for all of the pieces on the board. Also, chess requires very little in terms of reading your opponent, because it almost always safe to assume that your opponent will choose from a limited set of "good" moves that will lead to either an improvement in position or an advantage within three to five moves.

That aside, in high school, mathematics was a prerequisite for computer programming. This is something else I could not understand. Programming requires only one skill: the ability to break a problem down into a set of smaller problems - something which helps, but is not essential, for mathematics. There are many people I've met who are exceptional programmers who struggle with maths, and there are many people who have no problem at university level maths who struggle with programming.

All this shows is that no one actually knows what it takes to be good at mathematics.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Tuesday, June 21, 2011

On the Googles, Part X

The mysteries of Google's incredibly complex ranking formulae still evade me. In the mean time, I really enjoy the rather absurd Google queries that lead people to this site. For some obscure reason, almost 100 people a day pass over my blog in their Google search results. An impressive 20% of those are offered a link to my explanation of the 22° halo around the sun, with a third of those having searched for the term "sun diagram" (my average position on the search is around 160th). Hopefully those people were not disappointed with the answers they found. My nice little diagram often shows up on the first page of an image search for "sun halo diagram".

More importantly, I enjoy reading the absurd searches that actually lead people to my blog. Apart from the incorrect spellings such as "alphanumeric sheep pid" (which occured on a number of different occasions) there are several interesting ones, such as "alfanumetric wash your hands solution" or "motor driven moving pig targets".

Of course, I can't help but be proud of showing up consistently somewhere around the 87th postition for a search for "depth perception problems", or for being in the search results for "communicating with aliens", "oversized floppy hat", "what does bunnies eat" and "five legged sheep".

Most of all, I'm proud of Bing, who have finally started indexing my blog over the past couple of months. I have actually shown up in obscure Bing searches such as "in the heat of the night", "googlesaga winter holidays", "google-history of pie birds", "the sheep and chicken head feet problem", "something involving words", "googledo termites have wings", "is a pig as smart as a human being" and "sheep eating rabbits". It is however alarming at how many searches on bing contain the word "google". That may be something Microsoft would want to look into.

Not bad for the ramblings of some over-analytical, permanently bored engineer with a compulsive need to write absolute rubbish. I'm just disappointed that the penguins do not show up much. Or, perhaps that has been their plan all along. They must not want you to know about Amusing Hat Day for Incompetence Awareness.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, June 13, 2011

On Next Week Tuesday

It is widely believed that the seasons are centred about their corresponding equinoxes and solstices, and that the seasons are each roughly three months long - September means spring, December means midsummer, March means autumn, and June means midwinter (or cycle each month two seasons to the right if you live on the wrong side of the world). Some cultures believe the other extreme - that the solstices and equinoxes mark the separation of the seasons. I disagree with both, simply because of this idea of having well defined seasons is stupid.

Even though the winter solstice is hitting next week Tuesday (somewhere around quarter past seven in the evening), we are only just starting winter. Excluding the repeated buffeting from severe cold fronts, the weather has actually been warm enough to wander around with just a jeans and a T-shirt during the day. Each and every year, the real cold, where even the sun has no warmth, comes during July and August. It amazes me how people fail to notice this every year.

(On a side note, it is a common misconception that the solstices arrive on the same day each year. This is not true at all. In reality, it varies from year to year as the Earth follows its elliptical orbit, and its axial tilt does not change as the orbit moves around the sun. For example, the solstices this year are 20 March, 21 June, 23 September and 22 December (UTC), but next year they will fall on 20 March, 20 June, 22 September and 21 December (UTC, of course))

As with this idea that rain in June being "unseasonal and unusual" - it is actually rather common, and happens at least one, if not two, out of three years. Cold fronts almost always carry a bit of rain with them. Around the end of May or beginning of June, the cold fronts are pushed far enough North, and bring a day or two of rains, and another half a week of icy weather and wind. It is just as bad as those who believe that September brings rain, when really, more often than not, the first spring rains only fall somewhere around the end of October (which I wrote about before).

The best way to work out the seasons is by using nature, rather than just forcing on arbitrarily defined definitions. In Johannesburg in particular, you know Autumn has started when the majority of trees start losing their leaves (usually late April, early May); winter has started when the sun has no warmth on a clear day (around mid June); spring starts when the trees start shooting their leaves (mid September); and summer starts when the sun is hot enough to burn the grass (late October), but there is a fuzziness of some sort for two to three weeks which make up the transition periods in between, and these can move forward or backward by up to a month from year to year...

When I was 11 or so, I spent a lot of time developing a complex system of sixteen seasons, in which every sort of weather pattern was accounted for. In the end, I had to discard the whole idea on account of the fact that it did not resemble reality at all - something which most others unfortunately seem rather reluctant to do.

[Editor's note: Apologies for the rather late post due to technical errors - in this case a rather unfortunate configuration of synapses which have a tendency to fire electrical signals in such a way that it has lead to a case of chronic procrastination, even of tasks that themselves were originally meant as a form of procrastination. When you start putting off your procrastination until next week, you are most certainly in trouble. In return a long and boring post - 20 June 2011, 9:26 AM]

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Thursday, June 9, 2011

On the Abnormality of Standard Sizes

At 170 cm tall (that's 5 foot 8 inches), I am certainly not what anyone would consider tall, but I am not really that short either. Yet so often I find that things are designed for the most absurdly sized people. I am not particularly fat (in fact, apart from the bit of padding I've gained around my belly in the last couple of years, I am actually quite scrawny). However, whenever I try on pants, the size that fits me around the waist is almost always far to long and extremely baggy. If I get the size that fits my leg length and diameter comfortably, then the waist circumference is usually a good 5 cm too short to fit.

Perhaps the most confusing then, is that when I lie in bed and pull the duvet around my neck, I find that my feet stick out the bottom. I cannot work out how the standard length for a duvet was determined, but it was done wrong. How on earth people who are taller than me cope, I don't know.

I guess the five adult shirt sizes available in the shops show that the standards (if they can be called that, as poorly defined as they are) are completely arbitrary... On the shelves, you see S, M, L, XL, and XXL... implying that a mid sized person is considered large.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, June 6, 2011

On the Efficiency of Natural Night-time Heating

The other night, unable to sleep because I was too warm (despite winter beginning to set in properly), I began to solve the puzzle of my body's heating efficiency versus the insulation provided by my heavy down duvet. My body produces heat at a more or less constant rate, coupled with some spikes every now and then which vary with the frequency of flatulence (I can't help it when I'm sleeping, OK?).

I am very very far from an insomniac. I can (and have) managed to fall asleep in some of the most absurd places. However, I am occasionally (i.e. about 6 to 8 times a year) kept up by complex problems (surprisingly, these are only rarely work related). On this particular night, I could not fall asleep because I was too hot with my thick down duvet on, but too cold if I replaced it with my blanket. The compromise was to use the duvet, but with strategic holes left open to optimise cooling. But I'll get back to that.

The primary issue here is the human base metabolic rate, which is the energy that the human body generates whilst in a rest state. For an average human, it is between 50 and 75 W. It doesn't seem like much if you consider that the heater in my office is 1500 W, but in that tiny space, wrapped up by my super effective duvet, it is a lot.

Now consider the insulation provided by my duvet - an approximately 30 year-old 5 cm thick duvet stuffed with the down feathers of some unidentified (probably semi-aquatic) bird. It probably has a thermal conductivity of (and I'm taking a completely well-educated stab in the dark here) somewhere around 0.03 W/(m.°C). Although the area of the duvet is 1.7 m², I estimate that only 1.2 m² actually has a person underneath, and isn't just resting on the sheets. Assuming the air around my body has all reached somewhere around my body temperature (37°C), and is at steady state (although it is not, it is adequate for these simple head calculations), and that the air outside is a freezing cold 10°C (which I could have checked, if I'd thought of it at the time, since I keep two thermometers next to my bed, and then one in the study across the passageway (although I can't remember the last time I looked at any of them)), then the net rate of heat leaking through the duvet is just 20 W, meaning that somewhere from a half to a third of the body heat I generate is trapped in my duvet, and goes to making me uncomfortable.

Do the same calculation on the 8 mm thick synthetic and cotton blanket, and you get a heat leakage rate of 120 W. The perfect solution would be a duvet or blanket that lay somewhere between the two, but since that was not available, I had to work out the optimum size and location of a cooling vent. Here, the calculations proved to be not as simple, as the effectiveness of the cooling vents requires knowledge of the air flow in the room. Even though this is technically supposed to be my area of expertise, I am completely unaware of the frequency and strength of my night-time flatulence, so this was impossible for me to calculate. Instead, after setting up vents of various sizes and various locations and leaving them open for 5 or so minutes at a time, with little success (they resulted mostly in one part of my body being too cold, while the rest remained too hot), I decided that it would not work.

In the end, I managed to squeeze in a pathetic 6 hours of sleep by pressing my knees (which seem to be rather resilient to temperature changes) against the wall, and using that as a heat sink to dump the extra thirty something watts of heat I was generating.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Wednesday, June 1, 2011

On Methods for Concealing Baldness and Other Such Nonsense.

If you are one of those that are still impressed when an advert claims that a certain product is patented or patent pending, with the belief that if it can be patented it must work, I have bad news for you...A prime example which most people are familiar with is US Patent number 4,022,227. If you are bald on top but fortunate enough to have extra length hair around the sides of your head, you could "conceal" the bald part by carefully folding your hair over the bald area to conceal it in the classic hairstyle known as the comb over. Everyone (except perhaps those who have a comb over) knows that the comb over is an instant notifier of baldness, and in may cases, looks even worse than if they had just left it. It looks almost as ridiculous as a toupée.

The truth is that anything can be patented, provided that you have the time to write out a well worded patent application, and the money to throw to the patent office. Perhaps more absurd is the inventor Mitchell Kwok, someone with enough spare money to splash out on no fewer than six patent applications for a time machine. His plan is remarkably well thought out. The basic principle came to him while playing Prince of Persia on his PlayStation 2. Whilst playing the game, he came to the realisation that, in the video game world, the rules of time do not apply. He proposes programming human level artificial intelligence, and then letting these AIs loose in a video game environment where they can conduct research and develop an artificial intelligence that is much smarter than a human. He reasons that this would take humans 20 years to complete in the real world, but would take only a second in the video game world (an obvious sign that he has never used a computer to carry out research). It starts with US Patent Application number 2009/0164397, which claims
"A method and system for creating exponential human artificial intelligence in robots, as well as enabling a human robot to control a time machine to predict the future accurately and realistically. The invention provides a robot with the ability to accomplish tasks quickly and accurately without using any time. This permits a robot to cure cancer, fight a war, write software, read a book, learn to drive a car, draw a picture or solve a complex math problem in less than one second."

Using this method recursively, he believes that each iteration of the AI will be exponentially smarter, and he will eventually land up with an intelligence thousands of times smarter than a human. He will then ask this AI very nicely to calculate the exact positions and velocities of every single particle on Earth (presumably anything more than Earth would be asking too much), in the past and future with "pinpoint accuracy", and store these in a database somewhere (hopefully on the moon to avoid the paradoxes associated with self-containing systems). Following this, some prospective time traveller would be able to go up to some sort of machine and enter some sort of target date and time. Following this, "atom manipulators" scattered around the world will set to work and begin to manipulate atoms very quickly into position until the current environment represents that of the target date and time. This whole plan is outlined in US Patent Application number 2009/0234788.

Hey, at first I thought it was too good to be true as well, but then I found out that the idea is patent pending, so it must work.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, May 30, 2011

On Radio Advertising

There is currently an advertisement running its course for a certain car manufacturer’s “Auto Stop-Start” feature, which switches off the engine when the car is at a complete stop. The amusing part of the advert comes when it states that "when your car comes to a stop, all you will here is this..." Which is followed by a brief period of no noise apart from the sound of my own car's engine idling. I wonder if the marketing team that came up with the advert realised that a large portion of radio listeners do the majority of their listening while in the car, and would either already have a silent car, in which case their marketed idea would not appeal to them, or woud hear the sound of their own car engine during the period of silence. It's exactly the same as those TV adverts.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Thursday, May 26, 2011

On the Uneasiness of Electromagnetic Trespassing

It is particularly disturbing when I am sitting in my bedroom at home working on my laptop, and I get signal from my neighbour’s Wi-Fi. I know it’s somewhat less intrusive than having a neighbour’s cat walk muddy paw prints over my car, but it still gives me the vague impression that I am not alone. It is just as nerve-wracking to see the signal strength fluctuate eerily as the wind changes, almost as if the source of the signal is wandering around the house like a ghost. I’m comfortable with most technology, but that is the one thing that gives me the heebie jeebies.

I know there are an endless number of electromagnetic signals passing through my bedroom all the time, but none of them are as personal as Wi-Fi. They don’t have your neighbour’s name attached to them. Anyway, I’d better get on with my work... There are four different Wi-Fi signals roaming through my office, keeping watch.

If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Tuesday, May 24, 2011

On Towel Day Part II

I dislike regurgitating the same post, but that important time of year has come around again. In memory of the death of the great Douglas Adams on the 11th of May 2001, and in celebration of the premier of the Star Wars episode IV on the 25th of May 1977, I’d like to remind every geek and nerd out there to remember to carry their towels with them tomorrow.

For does the Guide itself not say:
      "A towel is about the most massively useful thing an interstellar hitchhiker can have. Partly it has great practical value - you can wrap it around you for warmth as you bound across the cold moons of Jaglan Beta; you can lie on it on the brilliant marble-sanded beaches of Santraginus V, inhaling the heady sea vapours; you can sleep under it beneath the stars which shine so redly on the desert world of Kakrafoon; use it to sail a mini raft down the slow heavy river Moth; wet it for use in hand-to- hand-combat; wrap it round your head to ward off noxious fumes or to avoid the gaze of the Ravenous Bugblatter Beast of Traal (a mindboggingly stupid animal, it assumes that if you can't see it, it can't see you - daft as a bush, but very ravenous); you can wave your towel in emergencies as a distress signal, and of course dry yourself off with it if it still seems to be clean enough.

      "More importantly, a towel has immense psychological value. For some reason, if a strag (strag: non-hitch hiker) discovers that a hitch hiker has his towel with him, he will automatically assume that he is also in possession of a toothbrush, face flannel, soap, tin of biscuits, flask, compass, map, ball of string, gnat spray, wet weather gear, space suit etc., etc. Furthermore, the strag will then happily lend the hitch hiker any of these or a dozen other items that the hitch hiker might accidentally have "lost". What the strag will think is that any man who can hitch the length and breadth of the galaxy, rough it, slum it, struggle against terrible odds, win through, and still knows where his towel is is clearly a man to be reckoned with."

Even if you never read the Guide and don’t understand the significance of Towel Day do it for the sake of Geek Pride Day tomorrow. And if you are really so geeky that a towel is not enough for you, then make sure to carry your hard boiled egg and lilac with you for the Glorious Revolution of the 25th of May, as a tribute to Terry Pratchett, and to help raise awareness for Alzheimer's research.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .

Monday, May 16, 2011

On My Neon Coloured Inflatable Safety Device

I carry my lunch in a neon green cooler bag (or a neon orange one, if I forget the green one in my desk drawer the day before). When people ask, I tell them that it is an inflatable safety device in case I fall into a lake. The real reason is simpler, but the full story is rather long-winded. I will give it a try, nonetheless.

All through school and for my undergraduate years at university, I carried only one bag around with me with all of my books as well as my lunch and juice. In high school, the sheer size of my bag earned me a bit of a reputation. Most people packed their bags in the morning or the night before, and only packed the books that they needed for that day. I was never the sort to be able to get into a routine (never mind have to work out what day it is, every single day), and after several occasions where I went to school taking books packed for the wrong day, I decided that such a system could never work. Instead, I adjusted the system to use terms instead of days. This way, I only needed to pack my bag with all of the books I would need in the next three months, and only needed to remember to do so every three months. (And although I often have difficult remembering what day yesterday was, I usually find it easier to remember which term the last one was (since three months does give it time to sink into my long term memory).)

However, at university, the books grew bigger, the distances between classes grew further, I grew lazier, and large bags grew more expensive. It did not take long for the immense compressive forces inside my bag to cause a bottle of grape juice to pop its lid – an accident which left my unfortunate chemistry textbook permanently disfigured (and stained pink, which I’m sure is the source of much teasing from the other books). Thanks to this (and one or two other close calls), I learned to leave my text books at home, and take only a notepad and some pencils with me to lectures, and then empty the previous days notes out when I got home. That way, I would lose at most one day’s work in case of a catastrophic leak. Unfortunately, by third year (which I reached in five years, due to my inability to decide what I what I want to be if I eventually grow up), I began to carry my laptop with me to classes, and still used only one bag. (Actually two on some days, because of the immense number of reference material that my aircraft design lecturer insisted we had with us all the time, but there was no way I was going to risk damaging the thousand odd pages of charts and tables and diagrams, so my laptop and lunch remained in one bag.)

(On a side note, when I did carry two bags, I had to tie them together. The awkwardness of having a piece of string to deal with every time you moved or pick up the bags was far preferable to realising that you had forgotten one bag somewhere several hours previously.)

I was very careful, and for almost one and a half years my laptop survived sharing a bag with not just one juice bottle, but a half litre water bottle as well. However, one day (19 January 2010, before 11:24 am, judging by my facebook status update regarding the event), The water bottle, apparently jealous of the bag being dry inside, decided that the bag should carry half the water as well. I pulled out my sopping wet laptop, pulled out the keys and patted it down with toilet paper. (Very bad idea. It sticks to everything when it gets wet, and it turns out that removing the bits of toilet paper is a real mission.) Fortunately, the laptop made it through with absolutely no damage (apart from toilet paper stuck to the backs of one or two keys).

From that day onwards, I have been carrying my juice and water bottles in a nice black cooler bag that my father once got for free at some company function.

Oh... wait. That explains the black cooler bag, and not the neon green one, doesn’t it? I started carrying the neon green one several months before the laptop-water incident because the large bowls of leftovers that I regularly take for lunch don’t fit in the bag with my laptop, didn’t I? Ah, apparently it's not so long-winded after all.
If you enjoyed this post, then don't forget to like, tweet, +1, or upvote on reddit. If you have any questions, comments or complaints, post them using the form below.
. . . . . . . . . . . . . . . . . . . . . . . .