Bacteria, scholar

Intelligence is an idea that is hard to catch in a definition. There are a million varieties of intelligence. If solving a mathematical equation is intelligence, so is deciding which spice will suit which dish. Selecting the right move in a chess game is intelligence, and choosing the right shade of colour in a painting is intelligence too. These are all high profile varieties of intelligence. But even activities that appear very simple to us require complex calculations, so scientists have realised.

One such simple but ever present activity is moving towards the target. Pause here, give it a thought and you can see that no animal can survive without this skill. Animals have to find food, which means they have to detect food and move towards it (with the possible exception of the lucky animals who can order food at home).

Detecting food and moving towards it requires high degree of intelligence – we just don’t recognise it because we take it for granted. Take mosquitoes for instance – they find you by smell. Or take ants and bees, which have an army of food finders and use elaborate signals to tell others that they have found it. Bats use ultrasound waves to detect their food – a mechanism called Echolocation which is so complex that when you understand it you will treat the mouse like creatures hanging from a neighbourhood tree with definite respect.

But the hero of this article is an unlikely candidate – bacteria. A primitive living being, neither animal nor plant, and visible only through very powerful microscopes. Let alone a brain, it does not even have a neuron. But with the limited means at its disposal, it does a wonderful job of moving towards its food. Bacteria were the first form of life on earth, they are still around, and most probably they will be there when we humans take our exit, which means they are finding their food alright. The mechanism they use for moving towards their food is so basic, yet so fantastic!

Dip a thin glass tube in a jar of water and pass a bit of glucose through the tube. The bacteria in the water will move and reach the tube to eat the glucose. A bacteria is really really small - 1000 bacteria can sit side by side in one millimetre mark on your scale, without the slightest discomfort. So even detecting glucose one centimetre away is like you detecting a freshly fried Batatawada from ten kilometres. How do they do it? They don’t even have noses.

Glucose, like everything else, is made up of molecules. The molecules are much smaller than the bacteria. As we drop glucose in water, these molecules spread in water, some finally reach the bacteria.

What happens next is an arresting sight, if only you can zoom it by a billion times. When the glucose molecules reach the cell wall of the bacteria, they act like a key for a lock. What does the key-lock mean here?

On the cell membrane of the bacteria, there are special sites, like our airstrips, for the glucose molecules to land. But the shape of these sites is such that only some molecules can land there. This is why I called it a key-lock mechanism.

Once the key is in the lock, the membrane opens a little bit. Certain ions from the outside liquid (like calcium or sodium) enter into the cell. (Ions are electrically charged particles that are present in all solutions.)

These ions enter in style – like a bollywood hero entering a villain’s den, and create the same kind of brisk activity. The end result of this activity is moving the small hair like extensions on the wall, called cilia (search ‘Cilia bacteria’ in Google and see the images). The movement of these cilia propel the bacteria in the right direction, like a rowboat.

But how does the bacteria know where to go, where the glucose source is? The bacteria does something very clever. It moves in a zig-zag motion, which we human beings can reproduce by drinking large amount of alcohol. But the bacteria is merely sensing the number of glucose molecules in its path. The direction in which the number of molecules of glucose goes up is the direction of the source. If it finds lesser molecules as it moves, it’s wrong direction, so it comes back and tries another direction.

Isn’t it fascinating? It tells us at least two things. First, the things at small scale are as spectacular as those we can see. Second, behaviour that appears intelligent can be produced purely by chemistry.

100 Words – Life in the sea is in danger

We burn a lot of carbon – like petrol, diesel, coal and gas for our energy needs. This makes huge amounts of carbon dioxide (CO2) – 36 billion tonnes in 2013. Half of this CO2 dissolves in the oceans, just like we make our fizzy soft drinks. A small part of it generates Hydrogen ions (H+) – Hydrogen atom minus the electron. The concentration of H+ in oceans has gone up by 30% in last 250 years of industry. This increased concentration of H+ is killing creatures like sea snails. The impact will be on bigger animals in sea and land, including us.

Of tortoises and school buses

This article is for the students, especially those who are enjoying a peaceful life after the board exams. If you belong to this lucky group, you might want to spend a little time reading this bit of wisdom from the past. It’s actually like a cool FB post, only about 2500 years old, by a guy called Zeno. Make friendship with Zeno now and he might help you in college, with all the math’s stuff you are going to find there.

2500 years ago, around the same time Buddha was preaching in India, the little country of Greece was teeming with all kinds of scholars. They had no FB and WhatsApp to share their status updates, but their teaching was earnestly learned and kept alive by their students. One such scholar was Zeno.

Zeno liked giving strange little problems to others. He told people to imagine a race – a race between a tortoise and a young man called Achilles. I mean, isn’t this like your school cricket team against Australia? Everyone knows how this race will end. But Zeno gave them a different story. It goes like this:

Suppose Achilles is ten times faster than the tortoise. To make the race fair, let’s place the tortoise 100 meters ahead of Achilles.

Let the race begin.

First, Achilles has to run the 100 meters. The tortoise is ten times slower. So it will run 10 meters while Achilles covers the 100 meters gap. Now there are 10 meters between them.

Next, Achilles has to run 10 meters. In this time, our tortoise is going to run 1 meter.

Achilles does not take long to run 1 meter, but tortoise has raced ahead by 10 centimetres!

Take out a forgotten notebook now, and try to write the next steps in this story. Well, you will finish all the notebooks, but this story will never end. No matter what you do, the tortoise will remain a little bit ahead. Achilles will never overtake the tortoise.

But we know Achilles actually overtakes the tortoise in real life. Such things are called Paradoxes. A Paradox is something you know to be false, but you can’t point out what is wrong with it.

There is another way in which Zeno’s Paradox is told. Suppose your school bus is standing 100 meters from you. You have to run and catch it. Now, to cover the 100 meters you have to first run 50 meters. Now only 50 meters remain. But before you run 50 meters, you have to go 25 meters. You run half the distance, but half still remains. No matter how much you run, a tiny bit will still remain. This means you can never catch the bus, even though it is standing still! But in real, you do catch the bus, almost everyday. That's what a Paradox is.

When scholars see such Paradoxes, their eyes light up. ‘Let me try my hand at this now’, they say to themselves. And so over the years, many clever people have tried to answer Zeno in their own way. Some fellows have applied mathematical ideas to the problem. You will probably like one of these ideas - it’s called a ‘convergent series’.

To understand convergent series, let’s go to the school bus again and try to cover the 100 meters. The distance you cover first is 50, then 25 and so on. Let me write it down:

50, 25, 12.5, 6.25, 3.125, and many more. To get the next number, just make half of the last one.

Let’s add all these meters that you ran:

50 + 25 + 12.5 + 6.25 + 3.125 + ...

(These three little dots at the end mean -‘Picture abhi baki hai’, or the story does not end here, there are going to be many such numbers).

What do you think the total of all these numbers will be?

Remember that you were 100 meters away from the bus? So the total will never be more than 100. But it will never be exactly 100 too. See for yourself:

50
75
87.5
93.75
96.875
...

Can you calculate the next totals?

You are going to meet these funny convergent series in college. The method to find totals of such series is called Integration, and once you master integration and things like that, there is no stopping you. One day you will possibly build a Jupiter Mission for India.

Prime numbers and credit cards

This article is about prime numbers. What! Skipping already?? I know you had enough of them in school and would like to get over the painful memories now. But can you hang on for a few more lines please? I am going to tell you two or three simple things about primes that will tell you a lot about security on the internet.

As we all know, prime is a number that can be divided by only two numbers – one (1) and that number itself. 31 is a prime number, because you won’t find a number- other than 1 and 31- that can divide 31. In other words, no multiplication table contains 31.

How do you decide that a number is prime? It’s easy, but completely donkey work. Take 31. You have to carry out the following steps-
- Is it a multiple of 2, if not,
- Is it a multiple of 3, if not,
- Is it a multiple of 4 ....and so on, all the way to
- Is it a multiple of 30?
If you a get a Yes to any of the above question, stop – it’s not a prime.

Now for a two or three digit number, you can work it out if you have nothing else to do, now that the world cup is over. For larger numbers, like 5437629789890011, you can use a computer to test its Primality, which is just a fancy name for being a prime.

For the computer nerds, this has become a kind of game. Since even computer take really long to test immensely big primes, the geeks run a race to find faster methods of testing primes. The largest prime found so far has 17,425,170 digits!

Now let’s take two primes and multiply them. What do we get? A larger number, of course. For example – 5 X 3 = 15. Easy enough.

But what if I give you 15 and ask to find the two prime numbers that made it in the first place? You can do it, it’s only a little trial and error. You find 3 and 5, and we call them the prime factor of 15.

But what if I give you 10873 and ask you to find its two prime factors? You wouldn’t try it, even if you have a long weekend ahead. You would turn to the computers and they will find the factors for you – 83 and 131.

Now let’s twist this a bit and make the computers groan. Take two large prime numbers, multiply them – you will get a very big number. Give this to the computer and ask it to find the prime factors.

It will huff and puff. Even very powerful computers will take a long long time to find the factors. If you give the most powerful computer existing today a 300 digit number, it will take more time than the age of the universe (13800 crore years) to come up with the result, and it will be a decidedly tired looking computer.

Some clever people used this fact to design a scheme for security of data on the internet. When you put your credit card number on Flipkart or Jabong, it is sent over the wires. It can actually be intercepted and read by anyone snooping on the way. This snooper will obviously then become quite comfortable in life, buying clothes, sofa and books on the internet. But it doesn’t happen. And the reason why this doesn’t happen has to do with what we just learned about prime numbers.

The basic technique (called RSA encryption) is very simple. When you put your credit card number, it is coded and changed beyond recognition before sending over the wires. The coding uses a very large number. When the coded credit card number reaches Flipkart (or Amazon, or whatever...), it is decoded back. But this decoding requires two prime factors of the original large number.

Now you see how clever it is? Anyone can find the public large number. But it does not help you. If you want to decode, you will need its two private prime factors. Finding these factors, as you seen, takes forever, so no one even attempts it.

Overall it is a pretty satisfying scene, isn't it? But wait....something is going to soon spoil the party. It’s called the quantum computer. Quantum computers are not yet really here, but when they come, they will crack a 300 digit RSA code in- hold your breath- less than 4 minutes!

It’s not just about credit cards. Most international top secret communications today use RSA encryption. Quantum computers will render them about as secret as writing on a postcard.
But what is a quantum computer? For that we will have to wait for a future article.