See also: https://www.explainxkcd.com/wiki/index.php/3033:_Origami_Black_Hole
The math there lines up with Randall's. -Tim > On Jan 3, 2025, at 3:20 PM, Laura R via Origami > <origami@lists.digitalorigami.com> wrote: > > 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 >> <mailto: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 >
