The Radioactive Lake of Kazakhstan

By Anupum Pant

If you haven’t heard about the operation Plowshare, it was a US operation focused at developing techniques that would help them utilize the massive power of nuclear weapons for peaceful construction purposes. Now if that sounds dumb, remember, it was the year 1961 when they thought of trying it out. Look back at other things from that time and you’ll realize how dumb those times were. Maybe the next generation will say the same for the year 2014.

How would someone use nuclear weapons for construction, you ask? If you think about it, using it to make huge holes in the ground, blasting rocks for mining seems like a good idea at first. How quick it would be, right? No.

After 27 such experimental blasts, the researchers from US learnt that this wasn’t a very wise thing to do, even if it seemed like a good idea. However, they ended up inspiring the Soviets.

While US had learnt about the ill effects of it and had stopped the operation by the year 1977, Soviets made their own version called “Nuclear Explosions for the National Economy” and continued doing it till the year 1989. 156 such tests were done by them.

Among all of them, one was done at the edge of a test site in Kazakhstan. In the year 1965, a 140 kiloton device was placed at about 180 meters below the surface, and detonated. As a result, a 400 meter wide and 100 meter deep hole was created in the ground.

This hole was planed to be a reservoir for an overflowing river nearby and it eventually got filled with water. A lake was formed. It has since been known as lake Chagan.

Lake Chagan contains water that remains radioactive till date. Even today the lake has “100 times more than the permitted level of radionuclides in drinking water“. Only at a distance of about 100 to 150 meters from the lake the radioactivity levels are at a background level.

Here is the video of the test that created this radioactive lake. The audio is in some other language, so you might have to do with just the video…

via [AmusingPlanet]

Lower Part of a Wheel Travels Slower

By Anupum Pant

Stick a colourful piece of paper on the side of a rim of a wheel and make the wheel roll away. If you observe carefully you’ll see, whenever the paper is near the ground, it appears clearly. However when the paper is at the top of the wheel, furthest from the ground, the paper appears hazy.

Also if you observe the spokes of a wheel of a moving cart, you’ll see that the spokes at the lower part of the wheel appear clearly. While the spokes of the upper part appear to blend into a single body, as if travelling much faster than the lower part.

It seems, the upper part of the wheel is travelling at a higher speed than the lower part of the wheel. How can that be, when both are physical extensions of a single object?

Yes, in fact the upper part does travel faster than the lower part. This sounds incredible, while it seems very ordinary to others who understand the simple physics of it. The physics involved really is very basic. So basic that I’m sure many reading this are cursing me for writing something so ordinary. But I find it really incredible. And believe me, there still are people who need to know this.

Let’s suppose the wheel moves at a speed of v in the right direction. However that is just the speed of the centre of the wheel. The upper part of the wheel for instance rotates at a speed of, say v, and also translates in the same direction at a speed of v. So, the speeds add up. And the top is travelling at a speed of 2v.

Similarly, at the bottom part of the wheel, the rotation is in the opposite direction (towards the left) and translation is in the right direction. Hence the speeds get cancelled and the lowest part of the wheel is stationary.

rims of a wheel

These are the topmost and bottommost points I’ve discussed here. For all the other points on the rim the rotational speed v gets split into a horizontal and a vertical component. So their speeds vary and lie in between 0 and 2v.

Some call it the cartwheel riddle.

Now, if you already knew that there’s something mind-boggling for you here. There’s another similar thing about wheels which blows my mind. Demonstrated in the video below…

Tickling Yourself

By Anupum Pant

In most cases tickling yourself is tough. That is because whenever you try to tickle yourself, at the back of your head (yes, really at the back, in a part of the brain called the cerebellum) you know that the sensation was caused as a result of your own movement. That way, the brain is able to predict the sensation and is able to nullify it.

When someone else tries it on you, the brain fails to predict the movement and the somatosensory cortex and the anterior cingulate cortex fire up to make you feel the tickle.

But have you ever tried tickling yourself with a fake hand? It still doesn’t work! Even when you don’t use your direct body part, your brain knows and can predict movement. Unless of course, the fake hand is being used by someone else. It’s interesting but believable that tickling yourself with a fake rubber hand doesn’t fool the brain. But there’s more.

In fact, if you had a tickling robot which could be controlled with a remote control, you still won’t be able to use the remote to operate it and make yourself tickle. While, if some one else had the control and they tried to control the robot to tickle you, you’d feel more ticklish. Unless, there’s a delay. It blows my mind to think about that!

What if, there was a robot which could control the remote control of a tickling robot, and you could control the first one with another remote control. Would you be able to tickle yourself using this contraption? I’m saying no, you still won’t be able to tickle yourself if there was no delay in between. What do you say?

Yes, delay is crucial here. Suppose you had a long contraption which would make movements after a few seconds of delay with respect to the control (which you have in your hand), you’d feel more ticklish, if you tried. Studies say, more the delay, the more ticklish it is.

Note: People with schizophrenia can tickle themselves, using their own hands, fake hand or something else.

Remember, I started the article with “most cases”. That is because there are a couple of ways to tickle yourself successfully. Try making little circles with a soft touch behind your knee for instance. Or use a feather on the sole of your foot. Or, try making circles with your tongue on the roof of your mouth where there’s a ribbed texture…

Weather Reporting Leeches

By Anupum Pant

Of all the creatures in the whole wide world, you’ll be surprised to know that leeches have played a fairly important role in the history of weather forecasting. An incredibly bizarre device invented by Dr. George merry weather, in the 19th century, called the tempest prognosticator, was basically a barometer powered by leeches.

Dr. George Merryweather, aptly named, was a surgeon by profession who was a lot into leeches. Since barometers were already being used for a long time then, to indicate approaching storms, he knew that air pressure was crucial in determining weather. However, Dr. Merryweather, an ingenious man, hell-bent on doing things the different way, had a different plan in his mind.

In his profession, he came across medicinal leeches all the time. In course of time, with a keen ability to notice details, he noticed that leeches were sensitive to electrical variations in the atmosphere.
He noticed a peculiar behaviour among these creatures. He observed that the leeches often started squirming around in a chaotic manner before a storm arrived.

Putting this practical knowledge to use, and experimenting with a number of designs, Dr. Merryweather devised a contraption. It consisted of 12 pint-sized bottles arranged in a circle. Each of which contained a leech in one-and-half-inch deep rain water. The top of every bottle had a tube into which the leech could crawl and disturb a mechanism, which in turn would activate a hammer to hit a bell – indicating that a storm is coming.

When a storm would come, the leeches were expected to crawl up the bottle, into the little pipe and activate a Heath-Robinson like mechanism which would make a hammer hit the bell. When the leech had completed its job it would fall down into the water and the hammer would go back to its place.

However, a number of times the leeches would give a false alarm. That was the reason he decided to use a jury of 12 leeches. And said,

The more of them that rang the bell, the more likely it was that a storm would be on its way.

If you ever go to Devon, you must take some time out to visit the Barometer World Museum to check out a full-scale working model of this device. Or you could go to the Whitby Museum in North Yorkshire to see the other working model.

Superstitious Pigeons

By Anupum Pant

B.F. Skinner was an American psychologist, a behaviorist, and a social philosopher. He was also the inventor of the operant conditioning chamber – A.K.A the Skinner box, is a box which is used to study animal behaviour. For example, you can use it to train an animal to perform certain actions in response to some input, like light or sound.

Using one of his favourite animals, he designed an experiment where he trained a pigeon in order to examine the formation of superstitious beliefs in animals. Here’s what he did.

He placed a couple of pigeons in his setup which was designed to deliver food to them after certain intervals. Of all the things, the timing of food delivery by this apparatus wasn’t related to one thing for sure – behaviour or actions of the bird.

And yet, after some time in this automated setup, the pigeons developed certain associations which made them belief that the food came when they did something. They had developed superstitious beliefs.

For instance:

One bird was conditioned to turn counter-clockwise about the cage, making two or three turns between reinforcements. Another repeatedly thrust its head into one of the upper corners of the cage. A third developed a ‘tossing’ response, as if placing its head beneath an invisible bar and lifting it repeatedly. Two birds developed a pendulum motion of the head and body, in which the head was extended forward and swung from right to left with a sharp movement followed by a somewhat slower return. – Wikipedia

The bird behaviour isn’t much different from what humans do…

The pigeons started believing in a causal relationship between its behaviour and delivery of food, even when there was nothing like that.

It’s almost like the humans blowing on the dice, or throwing it harder to make a favourable number appear. Even when blowing or throwing a dice harder doesn’t hold any causal relationship with the event of good numbers turning up.

During other times, when people bowl down a bowling ball and twist  their bodies towards right to make the ball go right, they have in fact unknowingly developed a superstitious belief, just like the pigeons that there’s a causal relationship between turning their bodies and curving of the bowling ball. In reality, there’s nothing like that. The ball goes where it has to, irrespective of how they turn their bodies.

Just like in the superstitious pigeon’s case, the food would have appeared anyway. The pigeon didn’t have to do something to get it.

via [Wikipedia]

The Hottest Place on Earth – Not Death Valley!

By Anupum Pant

For years I’ve known that the death valley was the hottest place on earth. Of course, not counting the lava, laboratory furnaces, hot springs and other such smart-ass answers, the death valley has always been, in textbooks and beyond, the hottest place on our planet.

On July 10th 1913, the temperature there was measured to be around 56.7 degrees centigrade. Nowhere else has the mercury risen to such high levels since then. Or so we thought…

Until, like always, a science channel from YouTube – MinuteEarth – decided to dive in a little deeper.

This is what the weather statistics do when they measure the temperature – The temperature outdoors are measured in shade at about 1.5 meters above the ground. Of course they had a standard procedure set to do that, and there must be a solid reason for that.

But, practically, who are we kidding. Anyone who has been on a beach, barefoot on a sunny day knows how hot the surface of sand can get in the sun, right?

The data from NASA’s satellites equipped with spectroradiometers has a different story to tell. A place somewhere in the Lut desert in Iran is the winner. The temperature averaged in a 1 square kilometre by the satellite shows that temperatures here have reached a whooping 70.7 degree Celsius. The place is somewhere inside the blue circle I made on Google maps.

lut desert hottest place on earth

You could literally cook eggs in the open there. Anyway, that isn’t totally new. Mr. Sargunaraj claims to have cooked an egg on the streets of Tirunelveli District in Tamil Nadu, India too. And I’ve also seen a video of a restaurant serving eggs cooked in the open (without fuel).

An 8000 km Long African Man-Made Forest

By Anupum Pant

The only desert larger than Sahara is a whole continent which is a desert – Antarctica. But Antarctica, unlike Africa’s desert, isn’t becoming bigger every year. It’s only the Sahara among these two which grows as time passes.

So, the expanding Sahara desert poses a great problem for the future generations of the southern nations (Sahel region) towards which it comes creeping. At least the ones just south of the Sahara desert, as the UN suggests, must be ready to face a hard life in the future.

Unless, an extremely ambitious and selfless plan being pushed for the good life of future generations, by a group of eleven African nations becomes a success.

The eleven nations across the African continent which stand to face the peril with a solid plan in place are Senegal, Mauritania, Mali, Burkina Faso, Niger, Nigeria, Chad, Sudan, Eritrea, Ethiopia, and Djibouti.

They have all come together and decided to create a massive Great Green Wall of Africa – a 15 km (9 miles) wide wall of man-made forest home to millions of drought resistant trees, stretching across the continent for about 8000 km (~5000 miles)! If complete, this is what it will look like.

The great green wall of africa

Since 2008, after spending about 6 million dollars, the enterprising leaders of Senegal, were able to finish a 330 mile long man-made forest. However in other nations where “short-termism” (to feed the present families) has taken priority over long-term good (of the future generations), the project faces a problem. Other problems like rebel groups, drought and famine doesn’t let this happen very easily.

The world bank has pledged 2 billion dollars for this massive project. If this great African dream does succeed, it will carry a huge lesson for all humans across the world to learn.

I earnestly hope it does succeed.

via [AtlasObscura]

Ants and Their Friends

By Anupum Pant

Background

If you consider the habits, social organization, communities, network of roadways, possession of domestic animals, and counting skills of ants, they are not very different from humans. Yes, ants even domesticate animals. And we’ve talked about their counting skills in the past. Then, I came across a very interesting experiment sir John Lubbock decided to do on ants.

Experiment

He had in his captivity a number of varieties of ants living in different colonies. One day he saw a group of ants feeding on honey together. He picked twenty five of them and managed to intoxicate them by some method, others were left there, feeding on honey.

Next, he picked twenty five other ants of the same species, from a different colony and intoxicated them too. He then placed all of these 50 intoxicated ants near the honey, in the path which the ants were using to move to and fro from the honey.

He watched them for hours and it was an amazing thing he found. The twenty five ants which belonged to the same colony of ants that were feeding on honey were treated much differently by them, than the other 25 ants of the same species that belonged to a different nest! Somehow they were able to identify the ants of their own nest – differentiate friends from strangers.

Twenty out of the twenty five friend ants (which belonged the same nest) were carried by the honey feeding ants to their home. While about 18 of the other intoxicated stranger ants were picked up and thrown into water.
There were just 5 friend ants which were thrown into water (probably accidentally) and 6 stranger ants which were carried back to home (probably accidentally, again)

Nevertheless, most ants were correctly identified as friends and strangers. Moreover, I think their reaction to drunk friends and drunk strangers was so much like what human beings would do!

Next Experiments

In an experiment which he did later, the researcher tried separating friend ants (of the same nest) for about 4 months. And when they met after 4 months they were able to clearly identify each other. They caressed each other with their antennae.

In other experiments when he introduced a stranger ants in a nest, the strangers were evicted immediately and sometimes even killed.

There are a couple of other interesting experiments he has mentioned in his article here. Do read it whenever you find time. [link]

10% of Our Brains? Oh, Come on Lucy!

By Anupum Pant

Have you ever heard people say that we use just 10% of our brains and 90% of it is lying dormant waiting to get awakened? I’ve heard this all the time, from parents, teachers and “self-help” gurus. And that what I believed  too, until a couple of years back when I read it on the internet that it was so not true! Later, I came across an informative science video (shared below) which explained otherwise. Of course it came from someone whose authority we can trust in – TED education.

The 10% thing is a myth has already hit most well-informed people, and yet I’ve heard it once again now. This is coming from an upcoming Hollywood movie trailer. I just watched it and it made me uneasy that people are still propagating it. This was the reason I wanted to make it clear to every one who reads my blog that “we use just 10% of our brains” is a pure myth.

Well, if you haven’t heard people say that, you will, in a couple of days, when the sci-fi movie Lucy will hit the theatres. Or you probably have already seen its trailer. If you haven’t seen it yet, watch it below. I was totally flabbergasted by the concept, I think this movie is based on. Pay attention at the 1:11 mark.

But, then it’s only a movie. When other sci-fi movies can show reverberating explosions in space making huge sounds, and people talking in space, it is only normal for Morgan Freeman, a neuroscientist in the movie, to say:

It is estimated most human beings only use 10 percent of the brain’s capacity. Imagine if we could access 100 percent. Interesting things begin to happen.

No!

The myth that humans are only capable of using around 10% of their brain capacity has floated around for a very long time. So much that more than 65% of the people believe that it’s true! There are a number of levels on how this statement is wrong, I cannot even begin to explain. TED makes it easier for me to put across the argument…

Some time ago, a MythBuster Tory Belleci, hooked himself up to a neuroimaging device (magnetoencephalogram) which is able to measure the feeble magnetic fields generated by the brain’s electrical activity. During this time, he involved himself in some memory drills, math calculations, word associations and image comparisons. 35% of his brain showed activity. But again, in order to prove the 10% myth wrong (which they did), it meant that only a certain percentage of the brain was lighting up.

35% might mean to someone that removing 65% of the unused brain shouldn’t make a difference in our cognition. But we know how even tiny lesions can impair normal function. So, myth busters didn’t mean that.

35% in only what we can measure. There’s a lot that happens in there without us having figured it out (yet). Or like the video puts forward a solid argument – “by now evolution would have gotten rid of 90% of the parts which the myth says we don’t use.”

However, not completely relying on what the myth busters “proved”, you might want to have a look at this insightful answer by a computational neuroscientist, Paul King. Turns out myth busters were not totally right. Again, that doesn’t make the 10% myth true.

We do not use all of the different areas of the brain at the same time because they have different functions.  The closest the brain gets to being completely active is during a seizure. At any time there is only a percentage of the brain active. – [Source]

Bad news for people looking to unlock the full potential of their brain by some mystical methods, one thing is for sure, the following is definitely not true.
we use only a certain percentage of our brain at one time, meaning we are not using it to its full potential. No!

This Tiny Sponge is Probably Set to Change The World

By Anupum Pant

Background

Things absorbing water from the air is nothing new. Hygroscopic substances – or substances which have ability to attract and hold water molecules from the surrounding environment – have always been around. Coffee powder for instance is one great example – leave the dry coffee powder in the open and it will turn into a mushy matter within hours. Thanks to the moisture present in the air that it absorbs.

Hygroscopy in Nature

In the nature too, hygroscopy – the ability to extract water from thin air – has some peculiar functions. One fantastic example is the seed of the needle-and-Thread grass. This seed, with the help of a hygroscopic awn attached to it, can twist and untwist the screw like structure by releasing and absorbing moisture from the air. This way, it is able to dig its way into the ground. But that’s just one of the many examples of how hygroscopy is all around us. Here’s another one…

Thorny devil – an Australian lizard – lives in the arid scrubland and desert that covers most of central Australia. It has a hard time finding water in this dry place. So, blessed by the evolutionary forces of nature, the lizard has developed tiny hygroscopic channels between the spines on its back. These channels, working in tandem with a capillary action mechanism, are able to draw water from the air. Then their precise design makes the water move into the mouth of the lizard. Fascinating!

Other Ways

Although not exactly using hygroscopy, the Namib desert beetle, also does something similar – drawing water from thin air. Unlike the hygroscopic grooves of the thorny devil’s back, the desert dwelling beetle has developed some patterns on its hard wings which help it in drawing water from the air. These patterns include an array of  hydrophobic and hydrophilic materials which are able to trap water from the foggy morning air and are able to channel it to the beetle’s mouth.

The Nanotube Sponge Mat

This particular beetle’s hard wings with magical patterns on it, intrigued a couple of researchers. They took cue from this natural material and were able to create an artificial mat which could absorb water from the air.

nanotube sponge

Although we do have commercial Atmospheric Water Generators (AWG) which can harvest water from the air and supply drinking water, the sad thing is that these things run on electricity. This new mat that was fabricated recently, using an array of carbon nano tubes sandwiched between hydrophilic and hydrophobic layers, doesn’t need any electricity to extract water.

This mat they’ve fabricated is smaller than your thumbnail, but it still works, and is able to extract about 1/4th of it’s weigh in water within a few hours. The researchers are working on it to make it more efficient. [more information] [Original Paper]

A couple of years back a US based startup, NBD Nano, was inclined on developing a water bottle based on the same Namib desert beetle principle. The much touted water bottle, they said, would be able to fill itself! I’m not sure where their project is headed today, but an auto-filling water bottle sure would be a product just too cool to not own by every kid at school!

Needless to say, it would probably make a huge difference by lowering greatly the number of people who don’t find clean drinking water every day – Just for the record, about 1/7th of the world population didn’t have access to clean water today.

A Massive 3200 Year Old Tree in a Single Picture

By Anupum Pant

If there’s one place I’d like to visit, it is the part of California where you find giant sequoia trees. The Giant forest is one such grove in the western Sierra Nevada of California. It is home to five of the ten most massive trees on the planet.

With a tree trunk measuring 36.5 feet in diameter, the Giant Sherman in the Giant forest grove, is the largest of the trees in this grove. It is 275 feet tall! (and yet there are taller trees in existence – Hyperion – again in California, which is about 379 feet tall)

While the President tree, 3200 years old, is another one of these Giant sequoia. It has seen hundred generations of humans pass by. Throughout its life it has survived a number of storms, fires, winters, earthquakes, and climate changes. And even today it grows faster than most other trees on the planet, adding one cubic meter of wood every year.

Its trunk measures around 27 feet in diameter.  In height, its topmost point measuring at 247 feet, is slightly shorter than the Giant Sherman. Still, the tree is massive. Its huge branches hold about 2 billion needles (leaves), which is more than any other tree on earth.

It is so huge that until recently it hadn’t been captured in a single photograph (excluding satellite shots and other such smart ideas). A team from National geographic magazine joined scientists to study and photograph the tree.

the president tree

[Video] Stunning Animation of How HIV Works

By Anupum Pant

Sorry, it was the FIFA WC finals, my favourite team (Germany) won, and I was too excited to write a lot today. So I searched my notes for something interesting to share quickly.

I found this 3D medical animation that I had bookmarked a long time from now. It is an animation of how the HIV replicates. It’s one of those videos with a lot of jargon where not everyone would understand what’s really happening, unless they are a lot into biology. If you are not, then I’d suggest muting the sound (don’t actually) and just watching the biological machines at work.

Still, it is amazing to see how things work at a very very tiny level and it’s an immense pleasure to appreciate how little biological machines work around in bodies to accomplish so much.

Moreover, it makes me very happy that we’ve come so far in science to understand so many things that we are now able to make mesmerizing animations of the extremely complicated and seemingly abstract biological mechanisms.

Script, Storyboard, Art Direction by: Frank Schauder, MD
Animation: MACKEVISION
Publicity: Dr.Rufus Rajadurai.MD. | D.DiaDENS

Subtle Differences

By Anupum Pant

Who’d have thought that a fun website like 9gag could teach you something useful. This is an artwork that I first saw on 9gag and wanted to find where it originated from (to give the artist its full credit). I believe, I Raff I Ruse is the blog which published it first. I could be wrong, but then the apparent source itself attaches no text that could confirms anything. And then it probably went on NPR, and consequently spread all over the web.

The artwork illustrates subtle physical differences between certain kinds of animals which look very similar to the untrained eye. It’s a very simple thing to know and you should definitely know it. The whole list includes differences between:

  • Ape and Monkey
  • Frog and Toad
  • Dragonfly and Damselfly
  • Ant and Termite
  • Wasp and Bee
  • Turtle and tortoise
  • Alligator and Crocodile

The Turtle and tortoise difference was one of these seven differences which I knew for sure. Then, I can definitely tell a wasp from a bee, an ape from a monkey, and an ant from a Termite, I still wasn’t very confident about the others. I bet you also knew at least one of these differences. And I hope you didn’t know at least one because I wish you learn something from this post.

alligator vs crocodile ant vs termite ape vs monkey dragonfly vs damselfly frog vs toad turtle vs tortoise wasp vs bee

via [9gag] and [NPR]

The Best Illusion of the Year 2014 Award

By Anupum Pant

You probably know the static Ebbinghaus illusion – where a circle appears bigger around smaller circles even when it is of the same size. It’s static because it works without moving. Well, if you don’t know, you should because it helps you lose weight in a very subtle manner.

A slight variation involving movement of the Ebbinghaus illusion won the best illusion award for the year 2014. Yes, there are annual awards for the best illusions (I never knew that!). This one which won the award was submitted by researchers from the University of Nevada Reno.

The new variation is called the Dynamic Ebbinghaus effect. This is what happens in it…

best illusion animation

There’s an arrangement of circles, exactly like the Ebbinghaus illusion, but there’s just one of the sets from the static illusion discussed above. While this arrangement of circles move, the central circle remains of the same size and the surrounding circles change in size.

Now, if you look into the central circle, you’ll see that it changes size too. In reality, it doesn’t. This effect is weaker when you look directly into the central circle. To make it more pronounced, you can shift your focus to the side and look at it through your peripheral vision. It’s totally mesmerizing. No wonder it won.

It works even when you  know about it.

An Elegant Proof of the Pythagorean Theorem by a Former US President

By Anupum Pant

Abraham Lincoln, the 16th president of the United States, was probably a math whiz. Doesn’t it sound like an extremely rare combination of things a person could possibly be? – a president and a math whiz. And yet, he was not the only one. James Garfield, the 20th president, was very much into mathematics too.

Garfield wasn’t a professional mathematician. He was a president. But, much like Abraham Lincoln, he was very much into geometry! Before he went into politics, he wanted to become a mathematics professor.

While he was a member of the US house of representatives, five years before he was elected president of the US, he came out with a very elegant and unique proof of the Pythagorean theorem (yes, another one of those Pythagorean theorem proofs). Here’s how he did it with the help of a congruent flipped triangle…

Doing it with a piece of paper is really easy…

Pythagorean theorem proofFold a paper and cut 2 exactly same right-angled triangles out of it. Now, put them together as shown in the image here (click the image). Next, write down the area of the trapezium – (a + b) . ½(a + b) – 1

Now write the area of all the 3 triangles and add them. This is what you’d get – 2 x ½ ab + ½ c2  – 2

Since both these areas are same, just written in a different way, equate them and solve. You’ll end up with the Pythagorean theorem!

a2 + b2 = c2 

Or, simply watch the video to understand better…