Couldn’t resist asking AI a silly question: how many times would you need to fold a piece of paper in half before it turns into a black hole?
Answer: The idea of folding paper until you create a black hole is rooted in an interesting thought experiment rather than something physically achievable. Here’s the reasoning: 1. Folding and Thickness Growth: When you fold a piece of paper in half, its thickness doubles. For instance, if the paper is initially 0.1 mm thick, after one fold, it's 0.2 mm thick. After n folds, the thickness is given by 2^n x (initial thickness). 2.Scale to a Black Hole: For a black hole to form, its mass must be compressed into a region smaller than its Schwarzschild radius, a theoretical boundary determined by its mass. If we assume the paper’s density remains constant during folding, the thickness would need to reach astronomical scales to contain enough mass to collapse into a black hole. 3. Number of Folds Required: Let’s approximate: - If the paper's thickness is initially 0.1 mm (0.0001 m), the thickness after n folds is 0.0001 x 2^n meters. - The Schwarzschild radius of a mass is roughly 2Gm/c^2, where G is the gravitational constant and c is the speed of light. To form a black hole, you'd need an unimaginable amount of paper mass compressed to such density. 4. Physical Limitations: - The strength of materials would fail long before reaching these scales. - Folding even a standard sheet of paper more than 7-8 times is practically impossible due to exponential thickness growth. So while the concept is fascinating, it's firmly in the realm of theoretical physics and thought experiments. In practice, you'll hit practical limits long before you fold anything into a black hole! > On Jan 3, 2025, at 4:49 PM, Robert Lang <rob...@langorigami.com> wrote: > > Today’s XKCD contains origami instructions! > > https://xkcd.com/3033/ > > I found the folding sequence quite easy to follow, but once I finished, my > stash of origami paper started to disappear, followed by my desk, room, > studio, etc. > > Robert
