Editing 3033: Origami Black Hole

{{comic
| number    = 3033
| date      = January 3, 2025
| title     = Origami Black Hole
| image     = origami_black_hole_2x.png
| imagesize = 272x480px
| noexpand  = true
| titletext = You may notice the first half of these instructions are similar to the instructions for a working nuclear fusion device. After the first few dozen steps, be sure to press down firmly and fold quickly to overcome fusion pressure.
}}

==Explanation==
{{incomplete|Created by a PLANET-SIZED SWARM OF SELF-REPLICATING NUCLEAR POWERED PAPER COMPRESSION ROBOTS - Please change this comment when editing this page. It needs an explanation for the title text. Do NOT delete this tag too soon.}}

This comic shows what at first appears to be an actual page of {{w|origami}} directions, like [https://origami.me/crane/ this one] or [https://origami.guide/origami-animals/origami-rabbits/origami-sleeping-rabbit/ this one], except labeled "How to fold a real origami black hole".

The "real" part draws a contrast to whatever the reader might presume is a symbolic origami black hole. A piece of origami can be made to appear like one of the various images, diagrams, or artistic depictions of a black hole. It seems black-hole-like origami does exist, as created by [https://parchmentandallthingspaper.wordpress.com/2011/11/16/folding/ Richard Sweeney]. The implication is that while the linked origami only resembles a black hole, Randall's instructions create a {{w|black hole}} out of origami paper.

The instructions just repeat folds in half. While practically impossible, the theory suggesting one can create a black hole with bare hands is comical. The difficult details in actually carrying out such a thing are left implied and ironically unexplained - and they turn out to be surprisingly complex.

The number of folds is likely based on the {{w|Schwarzschild radius}} of a piece of paper. The Schwarzschild radius is a characteristic of every object that depends on the object's mass. If an object is compressed into the volume of a sphere with its characteristic Schwarzschild radius, then that object will become a black hole. (More specifically, it will become a {{w|Schwarzschild metric|Schwarzschild black hole}}.) As such, if a piece of paper were folded sufficiently many times so as to fit within its own Schwarzschild radius, it would become a black hole. However, this would require compressing the paper into a flat sheet at every step, otherwise the paper would have a thickness greatly exceeding its Schwarzschild radius.

If we assume standard {{w|origami paper#Kami|kami origami paper}} with a side length of 15cm and a weight of 70 grams per square meter, we get a Schwarzschild radius of 2.339×10<sup>-30</sup> meters corresponding to a mass of 1.575 grams. It follows that, ignoring the paper's thickness, we would need to halve each side length -log<sub>2</sub>((2 × 2.339×10<sup>-30</sup> m)/0.15 m) = 94.69 times to fit each side length within the "Schwarzschild diameter" of the paper. Using the square folding technique in the comic, this would take approximately 95 * 2 = 190 steps to complete, the exact number given in the comic.
Note that the radius of the resulting black hole is 10<sup>-15</sup>th the size of the {{w|Proton#Charge radius|charge radius of a proton}}. {{w|Micro black holes|Black holes this small}}, if they can be created at all, are believed to quickly disintegrate by losing energy by {{w|Hawking radiation}}. If those predictions are correct, it would result in an energy release of 33.8 kT of TNT equivalent, roughly equal to two atomic bombs dropped on Hiroshima, in approximately 1.57×10<sup>-28</sup> seconds. (This is the energy equivalent to the mass of the paper, by E = mc<sup>2</sup>.)

In actual fact, it's not possible to fold a piece of paper this many times, because the amount of paper 'wasted' in each fold will quickly surpass the length and width of the paper. For an ordinary letter-sized sheet (A4 or 8.5x11) the maximum number of folds is 7. The [https://www.guinnessworldrecords.com/world-records/494571-most-times-to-fold-a-piece-of-paper world record] for the total number of folds is 12, done with a length of tissue paper 3/4 mile (4000 ft, 1219 m) long. A group of MIT students demonstrated 13 folds using multiple miles of paper, but had to lay separate pieces together as it made them too thick to tape them. Materials other than paper, such as thin foil, can be folded more times. Not only that but, as the title text alludes to, prior to reaching any creation of a black hole, the pressures generated by the resulting {{w|Nuclear fusion#Confinement in thermonuclear fusion|fusion of its atoms}} must be overcome. Electron and neutron degeneracy pressure would also have to be overcome.

Naively, the instructions would produce a paper stack of shrinking area, growing in thickness exponentially. This would become impossible long before the 190 folds in half that the instructions require. In fact, with a paper thickness of around 0.1 mm, the sum of the lengths and width of the paper would need to be around 10<sup>110</sup> meters for it to be possible to fold it 190 times.

The {{w|mathematics of paper folding}} were augmented with [https://web.archive.org/web/20051102085038/http://pomonahistorical.org/12times.htm work by a California high school student in 2001] who wrote equations that [https://web.archive.org/web/20211116013626/http://teachersofindia.org/sites/default/files/folding_paper_in_half.pdf  related the size of paper to the maximum number of folds it could make], which has not yet exceeded the low teens in human competition. This could be exceeded by scoring the paper to cut and flatten the outer layers of the folds, but its thickness would immediately surpass its length, and compressing it beyond the size of its fibers would require some way to hold it together.

Since this folded paper would typically have growing thickness, the instructions wouldn't really create a black hole unless one somehow additionally compressed the paper commensurate with its decrease in width and length. Perhaps the comic imagines the folded paper retaining the same thickness as a single sheet; then the density and pressure required would likely reach a point where fusion between hydrogen atoms begins to occur (a la [https://what-if.xkcd.com/1/ What If #1]). This is later alluded to in the title text.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:How to fold a '''''real''''' origami black hole:

:Step 1.
:[A square sheet of paper shown folded in half, with a dashed line going across the middle, and an arrow pointing from one half to the other.]

:[In each step from Step 2. to Step 9., the paper is shown folded in half again and depicted in the same manner as Step 1. The aspect ratio of the sides alternates between 2:1 and 1:1.] 
:Step 2.
:Step 3.
:Step 4.
:Step 5.
:Step 6.
:Step 7.
:Step 8.
:Step 9.

:Steps 10-189.
:[Text shown between tall square brackets:]
:Fold paper in half another 180 or so times.

:Step 190.
:[A labeled arrow points to a dot]
:Black hole!

{{comic discussion}}

[[Category:Physics]]