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.

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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.

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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]

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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.

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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.

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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.

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