Answers to previous questions of Do You Know? 1. I have heard of the “birthday paradox”, what is it? Ans: The birthday paradox answers the following question. Suppose there are 10 people in a room? What is the probability that at least two of them share the same birth day (same month and date, need not be the same year). The exact statement of the birthday paradox is, "How many people should there be in a room so that there is a 50% chance that at least two of them will share a birthday?" You can see that this involves probability or chance, but 50% chance means it is highly likely. The answer is a small number, which is 23! So if there are more than 23 people in your class, it is highly likely that two will share the same birthday. In the extreme limit, if all of the people had different birthdays, then you need at least 366 people for birthdays to repeat (the remaining have birthdays on different days of the year). So with 366 people, you are 100% sure that at least 1 pair have the same birthday. For 50% chance, you may have thought (like most other people) that you will need half that number, or 366/2=183 people. But you only need 23. That is why it is called a paradox or seemingly absurd or illogical statement. Let us try and understand why this number is so small. In probability, the word "at least" has a very important meaning. We need to calculate the probability that at least one pair of people in the room have a common birthday. There may be another pair of people with the same birthday as well. For instance, two people may have been born on 27th September and another two on 18th November. (We are not counting the cases where three people have the same birthday; that is a different problem). So we have to add up all the probabilities: that one pair of people have the same birthday, two have the same birthday and so on. So if there are 22 people in the room, we have to add all the probabilities upto the probability that 11 pairs (22/2) of people have a shared birthday. This looks hard. Instead, it is easier to ask, what are the cases that do not come under the possibilities we have listed? There is only one case: where no pair share a birthday. Every other case (from one pair to all pairs sharing a birthday) have to be included to get the total probability that at least one pair share a birthday. So let us calculate the probability that no pair share a birthday. Then, since the total probability adds to one (one of all the cases must hold), the probability that at least one pair share a birthday is given by (1-probability(no pair shares a birthday)). The birthday paradox then requires us to find out the total number of people needed to be in the room so that this probability is at least half. How do we calculate the probability that no person shares a birthday with any other person? Suppose there are only 2 people in the room. Let us say the total number, n=2. Then let one person have been born on 27th November. The other person could have been born on any of the 365 days in a year (let us not worry about leap years). The probability that this other person was also born on 27th November is 1/365 (one day out of 365 possible days). So the probability that the other person was not born on the same day as the first person is 1-1/365=364/365. If there were three people in the room, then we have to compare the birthdays of all pairs. Labelling the people as P1,P2,P3, we have to compare the birthdays of the pairs (12), (13), and (23) (that is person P1 with person P2, etc). Again, let us assume that the first person was born on 27th November. The probability that (12) don't share a birthday is 364/365, which we just calculated. The probability that (13) also don't share a birthday is the same. But we have to also consider (23). While P2 P3 may not share a birthday with P1, they may share a birthday with each other. We have already established that neither of them were born on 27th November (otherwise they will match with person 1). So person 2 was born on some other of the remaining 364 days. For P3 not to be born on that day, she should have been born on one of the 363 days which is not P2's birthday. So the chance that she was not born on the same day as P2 (and also not on the same day as P1) is 363/365. Hence the total chance of none of them sharing a birthday is (364/365)x(363/365). Another way of looking at it is to think of how three persons can all have different birthdays. The first person P1 can pick any day in the year. The second can pick any 364 (not P1's birthday). The third can pick 363. The total probability is therefore P_none=(365/365)x(364/365)x(363/365). Then the probability that at least one pair of them will share a birthday is 1-P_none. You can now write a general formula for n number of people in the room. It is P_none = (365/365)x(364/365)x(363/365)x ... x((365-(n-1))/365). (Did you understand the logic of (n-1)? Look at the formula for n=3 above.) If you have a calculator at home, you can calculate this probability as a function of n. It will look like the graph in the figure. For n=22, you will get 1-P_none=0.507. So if there are 22 or more people in a room, there is a very high chance (more than 50%) that two of them will share a birthday. Do you want to try it out in your class? 2. Why does soda fizz? Ans: There are many naturally carbonated beverages that fizz. But soda fizzes because it is made to fizz! The fizz in soda consists of bubbles of carbon dioxide, or CO2. Carbonated drinks are infused with this colourless, odourless gas at high pressures during production until the liquid becomes supersaturated with the gas. Modern carbonated sodas can be traced to English clergyman and scientist Joseph Priestley, who is nicknamed "the father of the soft drinks industry," for developing a carbonating apparatus in 1772, according to Britannica. By 1794, Swiss jeweler Jacob Schweppe was selling carbonated artificial mineral waters to his friends in Geneva. Even today you can buy Schweppe's soda in shops in India. At first, bottled carbonated water was used medicinally. Flavors were added later — ginger by about 1820, and lemon in the 1830s. In 1886, pharmacist John Pemberton in Atlanta, Georgia, invented Coca-Cola, the first cola drink. When soda is bottled, the soft drinks are kept very cold because carbon dioxide dissolves better in soda at low temperatures. After soda is infused with carbon dioxide, the gas effervescently escapes due to a principle in physical chemistry known as Henry's law, proposed by British chemist William Henry in 1803, according to Britannica. Henry's law states that the amount of a gas dissolved in a liquid is proportional to the pressure of that same gas in the liquid's surroundings. British chemist William Henry stated a law in 1803: the amount of a gas dissolved in a liquid is proportional to the pressure of that same gas in the liquid's surroundings. So when soda is canned or bottled, the space above the drink is usually filled with carbon dioxide at a pressure slightly above that of standard atmospheric pressure. Then it is sealed. Because of this, the carbon dioxide that's dissolved in the beverage stays within the fluid. However, when a soda container is opened, the pressurized carbon releases into the air. Why does this happen? There is a very small amount of carbon dioxide in the air, about 0.04% of Earth's atmosphere. When soda is exposed to air, the carbon dioxide in the soft drink naturally wants to reach the same concentration in the fluid as in the air. The result is that most of it fizzes out of the liquid as tiny CO2 bubbles. This venting gas produces the signature hiss one expects to hear from a newly opened soda bottle or can. So a soda bottle is effectively a pressure vessel that will hold that pressure in until you open the top. When you open the bottle, gas on top escapes, and so does the the gas within the liquid. The bubbles of gas leaving the liquid is what makes the soda fizz. You may have noticed that the fizz is more if you shake the bottle before opening it. Here, if you shake the bottle, the gas trapped within the liquid can escape from the liquid to join the gas above the beverage. This increases the pressure in the gas above the fluid. Now when you open the bottle, the soda bursts out almost like an explosion. Soda fizzes even more when it is poured into a glass because the act of pouring greatly increases the surface area of the liquid and helps the bubbles escape. One trick to reduce the amount of bubbling during pouring — and thereby enabling a soft drink to stay fizzy longer — is to pour the soda along the side of the glass. That drastically decreases the surface area of the pour and thus preserves more CO2 in the liquid. Carbonation not only leads to a dancing froth, but also reacts with the water to generate carbonic acid, resulting in a slightly tangy flavor. The carbonic acid and other flavour-enhancing acids that soda-makers add to soft drinks has been linked to tooth damage, adding to that from the huge amount of sugar in cola and other soft drinks. 3. I keep hearing that if I keep eating very spicy food, it would give me “acidity”. Is this true? Ans: This is one of those questions that doesn't have a simple yes-or-no answer. Acidity is a non-technical word that is used to express stomach discomfort. This is because there are always mild acids in our stomach. They are needed for digestion. However, in some cases, there may be more acid which may reflux into your oesophagus (gullet or tube through which food from the mouth reaches the stomach) and causes heartburn. The symptoms of heartburn is chest pain, ingestion, acidity, or a bitter taste in your mouth. The pain may worsen when you bend over or lie down. In fact it is called heartburn because the symptoms can be mistaken for a heart attack. Heartburn typically develops after you eat certain foods or if you eat too much. There is a 1-way valve (just like in a cycle tyre) at the entrance to the stomach so that food does not escape back into the oesophagus. Some conditions, including some foods, can cause the valve to open and allow food to back up towards the throat. That causes the burning sensation that can sometimes rise up into the throat, and also cause nausea and a bitter taste in the mouth. (Similar sensations are felt when you vomit). When this happens repeatedly, it is called gastroesophageal reflux disease, or GERD. Symptoms may include sore throat, pain when swallowing, cough, hoarse voice, and even constant vomiting. Spicy foods are notorious for causing heartburn. The reason is twofold. First, many spicy foods contain capsaicin, which slows down digestion and causes food to sit in the stomach longer. The longer food is in the stomach, the more risk of you having heartburn. Second, spicy food can irritate the lining of the esophagus, which can worsen heartburn symptoms. People who have heartburn, esophageal issues, or an ulcer often experience heartburn quicker and with more intensity when eating spicy foods than others do. High fat foods also cause heartburn because they are difficult to digest. Fried foods, chocolate, soft drinks, tea and coffee, all can make acidity worse. But no single food stands out. For some people, spicy food can cause acidity, for some, chocolate or soft drinks. In the end, only you can tell what suits your body the best. Perhaps you can eat all the spicy food you want, but should stay away from chips! 4. I love dragon stories. Can fire-breathing animals truly exist? Ans: Old and new literature (and TV) is full of fire-breathing dragons. But the she short answer is no, not in real life. There are other animals, though, which don't spit fire, but many chemicals and toxins to protect themselves. The spitting cobra, for instance, spit venom from their fangs when threatened which can blind you. So also some scorpions in Africa. The bombardier beetle can synthesise a mixture of hydrogen peroxide and hydroquinone. When the beetle is threatened, it puts the mix into a combustion chamber, and enzymes provoke the chemicals to react, producing a toxic substance called benzoquinone. It then squirts this boiling-hot liquid into the eyes of an assailant. Sources: https://www.livescience.com/32492-why-does-soda-fizz.html https://www.quora.com/Are-there-any-examples-of-animals-who-could-produce-fire https://www.livescience.com/65227-can-animals-breathe-fire-like-dragons.html