The Birthday Paradox

By Anupum Pant

Imagine you meet a random person in the street and ask him/her when is their birthday, there’s a huge chance that the person’s birthday will not be the same as your birthday. In fact, the probability of both your birthdays being on the same day is around 0.27%. Fat chance. At the back of our heads, this is something that is very clear to all of us.

Again, if you repeat this by asking about 22 people the same question, the chance of you finding someone having the same birthday as yours is still around 5%. Too less. This is too is a very intuitive piece of information.

But consider this. If I put all of the 22 guys and you in a room, there’s a big chance that 2 people in that room will have the same birthday – a 50% chance. Moreover, if there are 70 people in the room, this chance increases to about 99.99%. This is called the birthday problem or the birthday paradox.

So, what changed when 20 people went into the room? It was just the fact that in the room, we are picking 2 people from a group of 23 people. That is equivalent to this – everyone is asking everyone their birth dates. Everyone doing it simultaneously makes the probability much higher. The probability of two people sharing a birth date among a group of 23 people is far higher than you alone going around and asking all the 22 people, and finding someone having the same birthday as your’s.

Suppose there are 200 people in the room. The probability of 2 people sharing their birthday is massive (and yet not definite). There is in fact a 99.9999999999999999999999999998% chance!

1024px-Birthday_Paradox.svg

Finally, if you had 367 people in a room, at least a pair among these 367 people in the room would definitely have the same birth date. The 99.99% chance shoots up to a definite (100%) probability if there are 367 people in the same room. Think about it for a minute.

A Piece of Paper as Thick as the Universe

By Anupum Pant

Linear growth is only what we can visualize well. Estimating things that grow exponentially, is something not many of us can do properly.

Here’s what happens when you fold a piece of paper. A paper of thickness 1/10 of a millimetre doubles its thickness. On the second fold it is 4 times the initial thickness and so on. It doesn’t really seem like it would grow a lot after, say, 10 folds, right?

After 10 folds, the paper which was about the thickness of your hair, turns into something that is as thick as your hand.

Without any calculation, how thick do you think would it become if you could fold it 103 times?  (I know, no one has ever folded a paper more than 12 times)

Think about this for a second: How many times do you think would you have to fold a paper to make it 1 kilometre thick? The answer is 23. Yes, it takes just 13 more folds to go from the thickness of a hand to a whole kilometre.

Turns out, if you manage to somehow fold a paper 30 times, it would become 100 km tall. The paper would now reach the space.

For the sake of imagining how exponential growth works, a paper folded 103 times would be about 93 Billion light years thick – which is also the estimated size of the observable universe.

Watch the video below to see one other great example of how exponential growth can mess with you.

Crickets – Nature’s Weather Reporters

By Anupum Pant

Background

An annoying Cricket’s treet-treet-treet noise is really unbearable sometimes, especially when a house cricket ends up under your bed and treets all night long. To others, it’s pleasing, they associate it with the night time, and it makes them go to sleep.

Whatever it is for you, there’s one interesting thing universal about that noise they make. If you can count the number of chirps, you can almost accurately estimate the atmospheric temperature using a simple formula! Good ‘ol farmers used to do this.

I know all of us have smartphones these days, so counting cricket chirps to estimate temperature probably makes no sense to you. Still, I’ve said it back then and I say it again, it’s never bad to know anything.

Here’s how you do it

For doing it, you somehow should be able to measure 14 seconds. In those 14 seconds, count the number of times a single cricket chirps. Suppose there are 35 chirps heard, you save that number and add it to 40 (always 40). And this gives you the present temperature in Fahrenheit.

35 chirps + 40 = 75 degrees Fahrenheit

Now, since only a handful of countries use Fahrenheit to measure temperature, you might want to convert it into Celsius scale. I personally am comfortable with only the Celsius scale. But you don’t have to go through the trouble of converting because, to measure the temperature in Celsius scale using the cricket’s treet, this is what you have to do.

Simply count the number of chirps it makes in 25 seconds. Now divide the number by 3 and add 4 to it. There you have your ambient temperature in Celsius scale. Suppose the cricket chirps 50 times…

(50 chirps/3) + 4 = 20.67 degrees Celsius 

Why it works

To know that it is first important to understand how a cricket makes that sound. Remember only male crickets of a few species make this sound. They do this by a process called stridulation – rubbing 2 body parts to make a sound. Rubbing the underside of one wing with the upper side of the other wing does this trick – as they have rough and hard structures over there.

To move these wings it requires a particular chemical reaction to happen in their muscles. The speed of this chemical reaction is dependent on how hot or cold it is. The hotter it is, the faster the reaction happens and the faster it is able to move its muscles to produce more sounds in those 14/25 seconds…

via [Scientific American] and  [Howstuffworks] and [Farmer’s Almanac]