Trust me, this is interesting, and very important, even though it involves math

Alright, so the question was, if you fold 0.1mm newspaper 50 times, how high would it be? (Well obviously, you can't fold a newspaper 50 times, but let's just say that you can).

So what are your guesses?  about 2 inches?  about a yard?  a meter?  may be even up to the roof?

Actually, it would reach the moon and some more.  Even if you said to the moon, you're grossly underestimating.  It's probably closer to the sun

If you don't fold the newspaper at all, it's:  1 x 0.1mm = .1mm
Fold once: 2 x .1mm = .2mm
Fold twice: 4 x .1mm = .4mm
Fold three times: 8 x .1mm = .8mm

right?  even if you failed high school algebra, this should be obvious.

Does anyone see a pattern? 

Fold zero times: (2^0) or 1 x .1mm
Fold once:         (2^1) or 2 x .1mm
Fold twice:        (2^2) or 4 x .1mm
Fold 3x:            (2^3) or 8 x .1mm

So on, until you fold it 50 times, which would be 2^50.  Now, take out your calculators and tell me what 2^50 is (drum rolls please)


2^50 is whopping 1,125,899,906,842,624

I don't even know what that's called.  Let's count together:

1,125,899,906,842,624
                            thousands
                      millions
               billions
        trillions
quadrillion

So 2^50 would be 1.125 quadrillion.  To finish off our calculation, let's multiply 1.125 quadrillion x 0.1mm

1.125 quadrillion x 0.1mm = 112.5 trillion mm

112.5 trillion mm x (1km/1,000,000 mm) = 112.5 million kilometers. 


The distance from earth to the moon?  approximately 384,403 kilometers, which is far, far, far less than our stack of newspaper, which is 112 million km.

The distance from earth to the sun is about 149 million kilometers, which is somewhat closer to our 112 million figure.

Now, do you understand how we humans grossly underestimate exponential functions?  Let me give you another example:

The legends has it that a king wanted to award the mathematician who invented chess.  He went up to the king and said, "my wishes are modest - first day, I want a single grain on the first square of the board, second day, two grains for the next square, and third day, four grains; double the grain everyday until the last, or the 64th square..." 

The king thought to himself, 'what a foolish man,' but you tell me, was he foolish?

Let's just see how much grain he would receive on the very last day alone, which should be easy to calculate:  it's 2^63, which is ....

9,223,372,036,854,775,808 grains, or 9.2 quintillion grains.  Let's say that a grain of wheat weighs 1 milligram, then

9,223,372,036,854,775,808grains x (1 mg/1grain) x (1kg/1,000,000mg) x (1 metric ton / 1,000kg) = 9.223 billion metric tons of wheat

The world produced 607 million metric tons of wheat in 2007.  It turns out, the mathematician was not so modest.

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So when things double, it will grow quickly, quickly... The numbers will be out of control sooner than you can imagine.  Why is this important?  It's SUPER IMPORTANT for many reasons... but I'll explain more later.