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.

World’s Largest Building Has a Climate of Its Own

By Anupum Pant

A place where planes like the Boeing 747, 767, 777 and 787 are built, has to be huge. But this Boeing factory in Everett, Washington, home to 30,000 workers (working in 3 shifts), is so huge that the inside of the building has a climate of its own. It is the largest building on Earth. If you get a chance, you must not drop a chance to take the 90-minute tour of this factory (it costs $15 per adult). Here are a few things to note about it…

The size: The volume of this factory is 472 million cubic feet or 13.3 million cubic meters. That is enough to fit the whole Disney land and still be left with a 12 acre place to park the vehicles. In other words, it could fit 800 standard sized hockey rinks. Or it could fit in 75 football fields. Or it can hold about 12 empire state buildings! You get an idea how huge it is, right?

Largest Digital Mural: Being huge comes with its own side effects – another world record. The doors, like the building, are huge too. The factory has 6 doors, where each of them is 82 feet in height and 300-350 feet in width! You could bring in an NFL field (as in, fit the length of it) in through one of these. But what is more interesting about these doors is that they are covered with a 100,000 square feet of digital graphic. This is the largest digital mural in the world – printed by SuperGraphics, Seattle. It took the workers 27 days to install the digital mural.

Small City: Had this place been slightly larger, it could have had enough space to fit in a country – The Vatican city. Still, it isn’t small. The building is like a small city with it’s own fire department, security force, fully equipped medical clinic, electrical substations and water treatment plant. To move around in this little city, the employees use 1,300 bicycles.

Its own Climate? Now, since it is like a small city, it has to have its own climate, right? Yes. When the building was first built, clouds got formed inside and some say it even rained inside (mostly, not true). But rainbows have definitely been seen inside.
The temperature inside the building is controlled by those 1 million bulbs that are used in there. During winters, the bulbs bring warmth and during summers the doors are opened and air circulating fans are switched on to let the fresh Everett breeze come in.

Bonus fact: The network of 26 overhead cranes have about a total of 39 miles of ceiling rails inside the factory!

A Natural Explosion That Knocked 80 Million Trees

By Anupum Pant

In the year 1908 (June 30), a remote part of Siberia experienced something really mysterious and really huge. It was an explosion that took place at about 5-10 km altitude in the air which was estimated to be as powerful as 1000 (or 185 according to NASA) Hiroshima bombs!

No one could ever figure out what really caused it. However, scientists were pretty sure that it was either a huge meteorite of about 100 feet (some say 1000 m) in diameter which crashed into the earth’s atmosphere and disintegrated, or it just bounced off the earth’s atmosphere like a huge skipping stone. Besides the scientific theories, there are a number of other “UFO and alien” stories that have been associated with this event. This was called the Tunguska event.

The sheer size: The explosion was utterly gigantic. So big, that it is still considered to be the most powerful natural explosion in the known history. The shock-waves from the explosion knocked people off their feet, and these people were 40 miles away from where the explosion happened. It wasn’t just people, 80 million trees over an area of 2,150 square kilometres were knocked down in a radial pattern (with trunks pointing away from the epicentre). 80 million! Wow!

It caused a mini earthquake and a NatGeo article says that the lake Checko could have been created due to this impact.

Eyewitness’ account:

Suddenly in the north sky… the sky was split in two, and high above the forest the whole northern part of the sky appeared covered with fire… At that moment there was a bang in the sky and a mighty crash… The crash was followed by a noise like stones falling from the sky, or of guns firing. The earth trembled.
[NASA website]

Had this taken place above a metro city, the city would have been completely levelled by the event. But that is highly unlikely because cities take up a very small fraction of area on the earth’s surface. Moreover, very rarely do such events happen.

What is very likely is that such an event could happen over the part which covers 70% of the earth’s surface – the ocean. Such an event could create a huge Tsunami causing a lot of destruction on land.

The Coastline Paradox

By Anupum Pant

The length of Australia’s coastline according to two different sources is as follows:

  1. Year Book of Australia (1978) – 36,735 km
  2. Australian Handbook – 19,320 km

There is a significant difference in the numbers. In fact, one is almost double the other. So, what is really happening here? Which one is the correct data?
Actually, it depends. The correct data can be anyone of them or none of them. It completely depends on the kind of precision you decide to use while measuring the coastline. This is the coastline paradox.

The coastline paradox

The coastline paradox is the counter-intuitive observation that the coastline of a landmass does not have a well-defined length. – Wikipedia

The length of the coastline depends, in simple terms, on the length of scale you use to measure. For example, if you use a scale that is several kilometers long, you will get a total length which is much less than what you’d get when you would use a smaller scale. The longer scale, as explained neatly in this picture, will skip the details of the coastline.

This is exactly what happened when the two different sources measured the coastline of Australia. The first, Year Book of Ausralia, used a much longer scale than the one, Australian Handbook used. Ultimately, the great disparity in the result had to do with the precision of measurement. Had they used a scale just 1 mm in length, the result would have been a whooping 132,000 km.

This effect is similar to the mathematical fractal, Koch’s flake. Koch’s snowflake is a figure with finite area but infinite perimeter. Veritasium explains it better in this video:

Another factor is to take into account the estuaries to measure the length. Then,what about those little islands near the coast? and the little rocks that protrude out of the water surface? Which ones do you include to come out with the data?  And the majestic Bunda cliffs? Probably this article from the 1970’s clarifies what was included and what was not during the time the results were published.

So, the next time someone decides to test your general knowledge and asks you the length of certain country’s coastline, your answer should be – “It depends.”

The Standard World Map is Misleading

by Anupum Pant

Mercator’s projection

Most of us have this image of the world in our minds. This kind of a map, today printed in almost every textbook, known as the Mercator’s projection was first created to make work easy for navigators. Even Google Maps uses a Mercator-derived technique to project the world on a flat surface. But, Mercator’s projection has only deceived our idea of geographical area for all these years. For instance, it has led us into believing that Greenland covers an area which is almost equal to Africa (Also, have a look at the size of Antarctica there. Gosh!). The comparison of these two land masses actually looks like this.

According to this infographic, the actual size of Africa is larger than US, China, India, Mexico, Peru, France, Spain, Papua New Guinea, Sweden, Japan, Germany, Norway, Italy, New Zealand, the UK, Nepal, Bangladesh and Greece, all of them put together. In short, Africa is around 14 times larger than Greenland. Do not underestimate its area.

You can try playing with various combinations on this web app – map fight. Try these: Australia vs. Antarctica; US (contiguous) vs. Russia; and of course Greenland vs. Africa; they’ll leave you spellbound.

Why does this happen?

Since our planet is a sphere (an oblate ellipsoid really), to project it on a flat surface like paper, the actual shapes and sizes of landmasses have to be distorted to some extent. There is no way around it. Today, hundreds of different projection methods meant for various purposes are available, but none of them can exactly show the actual shapes & sizes of the landmasses. Some preserve the shape, some preserves the size, and others preserve direction…so on…

Mercator’s projection, the devious one discussed above, for example, uses a cylindrical projection. That means, it stretches the areas on a globe, which are nearer to the poles. Hence, the imprecise size of Greenland and Antarctica.

What is a perfect map, then?

Even after developing hundreds of projection method, we haven’t been able to spot the perfect method, nor will it happen in the future. But, to get the right sense of area, a projection method known as the Peters (also known as Gall-Peters projection) projection, is said to be the most accurate (in terms of area). It is also one of the most controversial maps.

Peter’s projection also has a huge fan following in spite of its terrible appearance.

Bonus Map Facts:

  1. National Geographic started using the, good looking, Robinson projection from the year 1988, and used it for ten years, then, it moved to the Winkel-Tripel in 1998.
  2. An ideal Mercator’s projection would have infinite height if it doesn’t truncate some area near the extreme poles.
  3. Peters pointed that the Mercator’s projection made developing countries seem much smaller than they actually are. He said that these errors made the struggles of developing nations near the equator looks much smaller to the developed world.
  4. XKCD published a comic on projections – “What your favorite map projection says about you.” 977. [see the explanation here]