Sense of number : Ep.1 – Go to the moon
Imagine if you want to go to the Moon.
The distance from the earth is around 384,400 km.
Apollo11 took 70 hours and 38 minutes to travel to the moon (~3 days)
By driving a car 120km/h, you can arrive the moon in 3,203 hours (~133 days) without considering gravity.
Before starting the question, I have an easy simple rule to ask you all. You have to answer within 5 seconds after finish reading the question, so just pick the first number that comes to your mind
the question is….
Define the thickness of an A4 paper to be 0.1 mm.
If you want to make the paper thick enough to reach the moon, how many times do you have to fold the paper?
What’s the first number that you think about? or the answer is more than which number?
OK! Answer!!!
Alright! let’s check it out together
The distance from the Earth to the Moon is 384,400 km.
= 384,400,000 m.
= 38,440,000,000 cm.
= 384,400,000,000 mm.
Accordingly, you have to stack a pile paper around 3,844,000,000,000 sheets
Let say folding a paper each time doubles its thickness.
… still folding …
Finally, after folding for 42 times
2⁴² = 4,398,046,511,104 sheets
If you just fold only 41 times, not enough because
2⁴¹ = 2,199,023,255,552 sheets (still need more than 1000 billions sheets)
Just imagine about it, 42 is not a big number and you can fold the paper once in a few second. Doing it 42 times, you should be able to finished in less than 3 mins, but it can take you to the moon.
This is the power of “Exponential Growth”
If you fold hundreds of times, it might take you to another galaxy. haha
The interesting thing that I found out after asking this question to many friends is
Many people answered million to billion
Some of programmers said “It’s exponential!!!” immediately after they know the question but the range of answers is around 1000 - 100000
And only few people answered between 40 - 90
Why I’m talking about this story?
In coding, we always deal with number. Most variable types that store integer have 32 or 64 bits. When I change the question to
Can you store 384,400,000,000 in Long(64bit Integer)?
Most programmers will answer “ absolutely yes ”
If so, why they answered more than “ 64 ” in the question above?
You should know and decide how to store variables efficiently. You also have to aware of algorithms that serve your business logic.
Many straightforward ways to solve problems are exponentially in runtime. This shouldn’t happen unless it’s necessary.
Even they know, they still underestimate about it.
This sample shows you, you can reach 4000 billion by doubled just 42 times. Let’s think about more than 42? or tripled or quadrupled it?
If you don’t believe me, you can fold your paper to prove it ;)
Thanks : Pattara Sukprasert for the idea.
Enjoy
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