B R Sitaram
Here are the answers to last month’s questions.
Q 1. When we go to buy electric bulbs, we are given a choice: warm yellows or cool whites. What is wrong with these choices and why do we make these mistakes?
A. An object (e.g., a star) that emits white light is hotter than an object that emits yellow light. The Wein Displacement Law, in fact, says that the temperature of an object that is emitting light and the frequency at which most of the light is emitted are proportional to each other. Thus, for example, Sirius, which is a white giant star, has a surface temperature of about 9,500° C, while the sun, which is yellow in colour, has a surface temperature of about 5500° C. Thus, it should actually be “cool yellows” and “warm whites”! However, we associate yellow and white with the two most prominent sources of light, the sun and the moon! Sunlight of course is hot and moonlight cool! Hence the inversion!
Q 2. Why is -2 x -4 = 8? Why not -8 or even 217?
A. You can define a system of mathematics in which -2 x -4 = -8 or even 217 which is consistent. However, this system of mathematics has a problem that makes it not very useful: it no longer obeys the distributivity law of multiplication over addition! To understand this, start with -2 x (4 – 4). One way of doing this calculation is to replace 4 – 4 by 0, calculate -2 x 0 as 0 and hence get the answer 0. Another way is to distribute the multiplication: -2 x 4 + (-2) x (-4). The first term gives you -8 (you are adding -2 four times). If you want the final answer to be 0, (-2) x (-4) has to be 8. Any other value will give you a consistent system of mathematics, but the two answers you get by doing the calculation in two different ways will be different.
Q 3. This book, written in four parts, of which the first one is more famous than the next three, is a satire. It is often mistaken to be a children’s book. Which book am I talking about?
A. The book is Gulliver’s Travels. Only the first book (The Voyage to Lilliput) is popular while the second book (The Voyage to Brobdingnag) is reasonably well-known. The other two books, describing the voyages to Laputa and to the land of Houyhnhnms are far less known. The first two books are in fact satires on travellers’ tales, the third on science and scientists and the fourth on the political system prevailing in England!
Q 4. Uttarayana is celebrated in India on the 14th of January. What is wrong with this date?
A. Uttarayana means “northward motion” and refers to the apparent northward motion of the sun from the Tropic of Capricorn. At any given instant of time, the sun appears to be exactly overhead at a certain point on the Earth’s surface, called the sub-solar point. This point has two motions: east-west (daily) and south-north (annual). On the summer solstice (around June 21), the sub-solar point is on the Tropic of Cancer. Following this, the point moves southwards, reaching the equator in the Autumn Equinox (around September 21), moving further southwards till it reaches the Tropic of Capricorn during the Winter Solstice (around 21 December). Following this, the point starts moving northwards, which means that Uttarayana starts on the day of the Winter Solstice!
Questions for this month
- On WhatsApp, I got a message that March 2019 would be special, as, for the first time in 560 years, there would be five Sundays in the month. Why should I dismiss this statement as hype?
- How long is a day (in hours)?
- One of the persons referred to in Harry Potter and the Sorcerer’s Stone, who is credited with discovering the Sorcerer’s (or Philosopher’s) Stone is a historical figure. Who is he?
- Sheep, mutton; Cow, beef; Swine, pork; Deer, venison; Calf, veal; House, palace; Home, mansion; Knave, servant; Horse, cavalry; Wool, cloak; Cloth, raiment; Wife, spouse; Skirt, gown; Begin, commence; Depth, profundity; Happiness, felicity; Meal, repast; Believe, trust; Friendly, amicable.
In each pair, the first word comes from Old German, while the second comes from Old French. Also, the first word has more to do with the common man and the second with nobility. What important historical event is responsible for these features?
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