# # The Surprising Power of Paper: How Folding Transcends Limits

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## Understanding the Paper Folding Phenomenon

Imagine jumping from the height of a piece of paper that has been folded 16 times. The impact would be catastrophic; your legs would buckle, and you'd suffer severe injuries. This raises an intriguing question: how can something as seemingly inconsequential as a piece of paper become a source of such potential danger?

The concept of folding paper multiple times can be mind-bending, even for those familiar with the puzzle. While there are no practical uses for this exercise—such as stowing away old newspapers or crafting origami structures to travel to other worlds—it serves as a fascinating academic exploration of how our brains struggle to grasp extremely large numbers, particularly when dealing with exponential growth.

However, let's ground ourselves in reality. A typical piece of printer paper, measuring 8.5 inches wide and 0.004 inches thick, can only be folded a maximum of seven times. Interestingly, some MIT students managed to fold a roll of toilet paper, measuring 13,000 feet, 13 times. Yet, generally, we hit a physical limit quite quickly.

Nevertheless, let's venture into the realm of abstraction, where we can explore the concept of folding without limitations. But brace yourself: understanding the resulting thickness after multiple folds is one of the most counterintuitive thought experiments imaginable.

### The Thickness of Paper: A Case Study

The thickness of the paper we are discussing is approximately 0.1mm (around 0.004 inches). Before diving deeper, I wanted to gather some intuitive guesses from friends regarding how high a piece of paper folded 100 times would reach. I set two conditions: (a) they were unfamiliar with the folding puzzle, and (b) they couldn’t use any mathematical calculations. The estimates ranged from the height of a skyscraper to just below one friend's nose, about 1.7 meters. These answers highlight the stark contrast between our intuition and reality.

Now, let’s explore the unfolding mystery with minimal mathematical jargon, focusing instead on the concept itself.

Every time we fold our hypothetical piece of paper, the first fold results in a thickness of two sheets (0.2mm)—nothing extraordinary.

The next fold increases the thickness to four sheets (0.4mm), and the subsequent fold makes it eight sheets thick (0.8mm). At this point, we are merely doubling the thickness with each fold—mathematically represented as 2^x, where x is the number of folds. After just three folds, we're at 0.8mm, far from the height of any skyscraper.

However, something remarkable occurs: after just 23 folds, the paper reaches a height of 838 meters, surpassing the Burj Khalifa, the tallest skyscraper in the world. How can this be?

### The Journey Beyond: Exponential Growth

If we continue folding the paper to reach 100 folds, it would extend beyond the atmosphere, past the sun (which is about 147.1 million kilometers away), and stretch an astonishing 13,398,978,947.1 light-years across. This illustrates the bewildering nature of exponential growth; the numbers can become incomprehensibly large.

A key misconception arises when we perceive a folded piece of paper as a simple unit of measurement. We see the thickness after a single fold (0.2mm) and mistakenly think that subsequent folds will merely add that same small increment. Additionally, we oscillate between large objects, like skyscrapers, and the seemingly trivial number of folds, which confuses our understanding.

When the paper is folded 23 times—equivalent to the height of a skyscraper—we should consider that the next height will surpass two skyscrapers, and so on. Each fold effectively doubles the height and the number of sheets involved. For instance, after 23 folds, we have 8,388,608 sheets of paper stacked together, which is roughly the equivalent of 41,943 books.

To grasp the scale of a piece of paper folded 100 times, it equates to:

2^100 = 1,267,650,600,228,229,401,496,703,205,376 sheets of paper.

In simpler terms, that’s one nonillion, two hundred sixty-seven octillion, six hundred fifty septillion, six hundred sextillion, two hundred twenty-eight quintillion, two hundred twenty-nine quadrillion, four hundred one trillion, four hundred ninety-six billion, seven hundred three million, two hundred five thousand, three hundred seventy-six.

Who needs SpaceX to explore Mars when the power of a simple piece of paper can take us on a journey beyond our imagination?

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