2 + 2 = 5

When I was in first year of college, a senior who was preparing for a competitive exam asked me to help him with his maths. For each hour of tuition he would treat me to biryani, which I considered an excellent deal.

In our second lesson, I explained how to solve quadratic equations by factoring by inspection.

Then I derived for him the general solution for ax² + bx + c = 0, the quadratic formula which in Indian textbooks is often called Sridhar Acharya's formula after the 9th century Indian mathematician who described a general method for solving quadratic equations:

I advised my friend that if a and c are integers with relatively few factors, factoring by inspection is quicker, so he should try it first before using the quadratic formula. He rejected this suggestion with an argument of such staggering irrationality and misplaced patriotic pride, that I could think of nothing to say in reply: "When there is a perfectly good method discovered by an Indian, why should I use another method?"

The incident came to mind because I noticed an amusing photo on the Guardian (online edition) front page today:

The teacher(?) is factoring a quadratic polynomial 2x² + 5x + 2, but the expression in the second line is incorrect: (2x + 2)(x + 1) actually equals 2x² + 4x + 2. The second line should read (2x + 1)(x + 2).

And yeah, there also should be a full-stop after 'charts'.

Shunbun no Hi: Llamas

Elsewhere on this blog I have extolled the virtues of the Isle of Dogs. But that list had one glaring omission: it made no mention of the llamas of Mudchute Farm. For this must surely be one of the top reasons for wanting to live in the area: when you're on the Isle of Dogs, no matter how bad things are, you can always take comfort from the fact that you are never more than 2 km from a llama.

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Llamapaedia's Common Llama Terminology page has a wonderful entry:

Overconditioned
The polite way of saying in the showring that a llama is overweight or fat.

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Last year I wrote:

If, as is not unlikely, Web 3.0 is created to allow people to share pictures of llamas, my llama photo will get its place in the sun.

Web 3.0 is still in the works, but while we wait, here is a llama photo taken by Sujaan at Mudchute Farm:

Clouds

My first attempt at a timelapse video of natural phenomena: clouds over my patio on Saturday morning. Click on the photo below for the video (0:18).

The video is composed of stills taken at 15-second intervals played at 15 fps, for an effective speed of 225×. Next time, I'll pick a shorter interval (and hopefully, more interesting clouds and scenery).

Several aircraft appear in the video, some only for the space of a single frame (less than 67 milliseconds). Still you can spot them if you look real carefully, e.g. near the end there are two specks in the 1st quadrant and a white streak in the 3rd quadrant.

Earthquake Memories

Today is the third anniversary of the Tōhoku earthquake and tsunami.

Tuesday, 8 March 2011, was the first day of my six-month secondment to my law firm's office in Tokyo. Upon arrival, I got a health-and-safety briefing which, among other things, introduced me to the earthquake pack under my desk. It had a hard hat, fire-blanket, rope, torch, whistle, bottled water, tinned food and biscuits. The biscuits interested me particularly. They were not very tasty, but when I ate a few and then drank some water, I felt as full as if I had eaten a big meal.

On Wednesday morning, there was a 7.2-magnitude quake off the coast of Japan, and the high-rise building I was in swayed noticeably. I was thrilled to be in my first real earthquake, but after that I left the biscuits alone.

Later that day I had a Japanese lesson. Among the first words my teacher taught me were emergency words, "just in case": 地震 (jishin: earthquake), 火 (hi: fire) and 火山 (kazan: volcano). "And of course, tsunami is already a word in English," she said.

On Friday afternoon there was a 9.0: one of the most powerful earthquakes in recorded history.

The alerts began to sound seconds before the tremors began. The recorded announcements were in Japanese, followed by English. My supervisor translated the Japanese announcements as they sounded, giving me a few seconds' advantage. The first one told us to put on our hard hats. The second one told us to get under our desks. It was not yet necessary to evacuate; we were actually safer in the earthquake-resistant building than in the street outside, where we might be endangered by falling objects.

When the tremors subsided, we were told to keep our hard hats on because there might be aftershocks. The Japanese people seemed composed; they went around switching off the air-conditioners because they said after an earthquake that size, some power stations had probably switched off. Some of the expats were freaking out, but I remember feeling excited rather than fearful or panicky (news from Fukushima was yet to filter through, so we had not realised the scale of the disaster). Rather than adding to the uproar, I went back to work. My supervisor was so amused that she took a photo on her phone.

Out of the whole episode, what impressed me most was Japan's disaster preparedness and recovery (at least so far as the earthquake is concerned; the Japan government's reaction to the Fukushima meltdown has perhaps not been beyond reproach). The earthquake registered an upper five in Tokyo, but there was little damage to property because the buildings, like in the parable of the Oak and the Reed, are designed to sway with the tremors rather than stiffly resist. In my flat, picture frames were askew and a few books fell off the shelves. The Tōkaidō Shinkansen resumed limited service late in the day, and the next day it was back to its normal schedule. By next week, my hotel was issuing notices about bicycle parking.

Waxing Crescent

Six-day-old moon over London, photographed through a 300mm lens
(click on the image to see names of some lunar features)