Folding Our Minds
Here's the question for you:
If you fold a piece of paper 50 times, will it reach the Moon?
Let's assume that we're folding our imaginary sheet of paper exactly in half each time.
A rectangular shaped sheet is better to use but a square one will work too.
Ok, these are things we need to know:
How far away is the Moon?
Well, it's about 384,400 kilometres away.
How thick is a sheet of paper?
Umm, that depends on the quality of paper and the manufacturer, etc.
BUT a typical sheet of standard office paper (80 gsm) is about 0.1mm thick.
And, it also makes it easier to have all numbers used in our calculations equivalent to the same unit of length.
So, since we're talking about the Moon's distance, let's convert the 0.1 Millimeter paper thickness to Kilometers --> 0.0000001 kilometres.
Ok.
The common misconception is, "if we fold a sheet of paper 50 times, the resulting stack will be 50 times thicker".
Nope. Wrong.
Think about it this way --
(and feel free to grab any sheet of paper and carry out the actions as you read along):
Fold a piece of paper in half once.
The "stack" (or combination of 2 paper thicknesses) is now twice as thick as it was, right?
Yup. You'll notice that this is correct.
Now fold the sheet in half, once again.
Overall, this folded bundle (stack) is now twice as thick as it was last time.
Right?
If you've got the paper in front of you, you can now simply count the layers:
1, 2, 3, 4.
Yup, right.
The layers of paper folded on top of each other is now four times as thick as the original piece of paper.
Fold the stack in half once again.
If you count the layers, you'll see that it's now eight (8) times thicker than the original sheet.
and so on...
By now, it's apparent what's happening.
Each time you fold the stack, you're doubling the overall thickness of all the paper layers.
That means it's fairly easy to see the eventual endgame here.
There is a method of calculating the thickness of the stack of paper after 50 folds...
You start off with the thickness of one sheet, and then double it.
Double it again.
Double once more.
Double again.
And again.
And again...etc............
Keep going until you've done it 50 times.
If you're into "button-mashing" on a calculator, you could also simply type this into any calculator:
0.0000001 (<--conversion of a thickness of paper to
KMs, as above)
x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
(which is the same as----> 0.0000001 X 2^50)
2 to the power of 50
Because the original number (0.0000001) was assumed to be Kilometres , we know that the answer is obviously in Kilometers as well.
The product?
112,589,991 kilometres thick! (rounded off)
So, back to answering the original question:
Would this reach the Moon?
Well, we only have to compare two numbers.
The distance to Moon is 384,400 km
.
The height of our paper stack, folded over 50 times, is 112,589,991 km
.
112,589,991 km ----> paper stack
384,400 km --------> distance to moon
So we have our answer: YES, if you folded a sheet of paper 50 times, it could easily reach to the Moon.
But it would be boring to stop here.
So divide the distance to the Moon into the paper stack thickness:
112,589,991 / 384,400 = 292.8
That means that our folded paper stack would reach nearly 300 times further into space than the distance the Moon is from Earth!
So what's that? How far out from Earth is that? Here's some perspective...
Travelling in an inward direction, from Earth to the Sun, we'd cross the orbit of Venus after climbing up the side of no more than about a third of our stack tower of folded paper.
If we could keep climbing to the very top of the paper stack and stand on top of it, we'd find ourselves about 3/4 way of the distance to the Sun from Earth.
But hold on, one more...
Suppose we could fold that paper stack just one more time --- so to a total of 51 total folds (and it would be soooo sooooo soooooooooo very very difficult) --- we'd now discover that the top of the paper stack tower is now reaching well BEYOND the Sun from the Earth's surface!
Well beyond by approximately 75 million Kilometers!
...Ain't math grand?
*burp X 2*
