How can a piece of paper folded 103 times be larger than the observable universe?

Folding a paper is not as easy as it looks like. If you take an ordinary A4 size paper and start folding it, each time you fold, its width will increase exponentially.

Let’s suppose that your paper is 1mm wide. When you fold it, the width will get doubled and become 2mm. The next time you will fold your paper, its width will increase from 2mm to 4mm. When you reach your seventh time, your paper will have a width of 49mm. Just like this, every time, the paper will increase its width by the square of the number of the total folds.

To understand this concept, let us consider a real-life example. If someone gives you 1 penny today, and promises to give you twice as much money tomorrow, and twice of that the day after, and so on. By the end of the month, you would have received a total of 5 million pennies by then.

Similarly, every fold increases your paper’s width twice as much as the last width. Therefore, if a regular piece of paper has a thickness of 0.0039mm, it grows exponentially with every fold. You can also verify this through a calculator.

Take your scientific calculator and enter the thickness of your paper. Now, with every fold, take a square of the existing width. You will see that by the time you reach your 60th fold, your calculator will start giving errors. This is because you will surpass the value that your calculator is capable of processing.

But why folding a paper 103 times exactly makes it larger than the observable universe? Well, the answer to this question is quite simple.

The dimension of the observable universe is approximately 93 billion light-years. Now, if you were to fold a paper for 103 times, its diameter would exceed this huge quantity. That is why, we can safely say that a piece of paper if folded 103 times, exceeds the limits of the observable universe. Let’s just take a minute and appreciate how wonderful mathematics is.

Although it is impossible to carry out this experiment, you can still try to fold it to some extent. However, if you want to do this experiment at home, you will need some papers and a calculator.