3033: Origami Black Hole

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Origami Black Hole

Title text: 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

This comic shows what at first appears to be an actual page of origami directions, like this one or this one, except labeled "How to fold a real origami black hole".

The "real" part draws a contrast to an origami depiction of a 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 Richard Sweeney. The implication is that while the linked origami only resembles a black hole, Randall's instructions create an actual black hole out of origami paper.

The instructions just repeat the operation of folding the paper in half, ignoring the increases in thickness and difficulty of folding that occur. In addition, the idea that one can create a black hole with one's bare hands is far-fetched. The difficult details in actually carrying out such a thing are left implied and unexplained - and they turn out to be surprisingly complex.

The number of folds is likely based on the 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 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, as otherwise the folded paper would double in thickness at each step, greatly exceeding its Schwarzschild radius. Indeed, it would need to be compressed beyond the thinness of the original sheet of paper.

If we assume standard kami origami paper with a side length of 15 cm and a weight of 70 grams per square meter, we get a mass of 1.575 grams, corresponding to a Schwarzschild radius of 2.339×10^-30 meters. It follows that, ignoring the paper's thickness, we would need to halve each side length -log₂((2 × 2.339×10^-30 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 95 * 2 = 190 steps to complete, the exact number given in the comic. Note that the radius of the resulting black hole is 10^-15 times the size of the charge radius of a proton. Black holes this small, if they can be created at all, are believed to quickly disintegrate by losing energy via Hawking radiation. In this case, if those predictions are correct, it would result in an energy release equivalent to 33.8 kilotons of TNT, roughly equal to two atomic bombs dropped on Hiroshima, in approximately 1.57×10^-28 seconds. (This is the energy equivalent of the mass of the paper, given by E = mc².)

In actual fact, it's not possible to fold a piece of paper this many times^{[citation needed]}, because the amount of paper 'wasted' in each fold will quickly surpass the length and width of the paper. For an ordinary letter-sized (A4 or 8.5x11) sheet, the maximum number of folds is 7. The world record for the total number of folds of a sheet of paper is 12, done with a length of tissue paper 3/4 mile (4000 ft, 1200 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, prior to reaching any creation of a black hole, the pressures generated by the resulting 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, for it to be possible to fold it 190 times, the sum of the lengths and width of the paper would need to be around 10¹¹⁰ meters, a good 10⁸³ times the diameter of the observable universe.

The mathematics of paper folding were augmented with work by a California high school student in 2001 who wrote equations that 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 What If #1). This is later alluded to in the title text.

Transcript

This transcript is incomplete. Please help editing it! Thanks.

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 an apparently glowing black dot]

Black hole!

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Discussion

First post! RadiantRainwing (talk) 19:08, 3 January 2025 (UTC)

…really? sigh 42.book.addict^{Talk to me!} 02:27, 4 January 2025 (UTC)

Sorry RadiantRainwing (talk) 03:55, 4 January 2025 (UTC)

All six gross attempts to follow these instructions have ended with the attemptor vanishing into themselves before reaching step 175.172.70.47.105 19:17, 3 January 2025 (UTC)

e162.158.10.131 20:14, 3 January 2025 (UTC)

Should we also add a mention of the /Mythbusters/ doing this? I don't remember the details or I would put it in. MAP (talk) 21:48, 3 January 2025 (UTC)

I started convincing chatgpt to tell me how to fold this origami at https://chatgpt.com/share/67785de4-9a4c-800e-80f5-31d12d999999 before running out of free credits. 172.68.54.157 22:00, 3 January 2025 (UTC)

Nice 404 error --162.158.90.211 04:25, 4 January 2025 (UTC)

Using rice paper you could easily reach 9 steps by pure hand pressure, although reaching fusion point -at or around 80 steps- would definitely require strong fingers indeed. Black holes clearly cannot exist, because they would require folding Chinese paper more than a red-blooded American can do, and this is not an option. 141.101.68.192 (talk) 22:13, 3 January 2025 (please sign your comments with ~~~~)

The current explanation that it's impossible to create a black hole by folding paper is only right in practical terms. If you manage to keep folding while keeping the same thickness the density of the paper will be far beyond that of a neutron star.--Pere prlpz (talk) 22:42, 3 January 2025 (UTC)

I would be impressed if you did manage to keep folding, since the goal size can be measured in Planck lengths with only six digits. Would you define it as a 'fold' after the entire thing fits inside an electron? (Tangentially, I'm not sure what theory suggests here - can a black hole exist at a scale which makes quantum tunnelling trivial?) 172.68.210.114 (talk) 23:09, 3 January 2025 (please sign your comments with ~~~~)

I don't think we'll be able to answer that until we unify QM and GR. I don't think we currently have a theory that addresses quantum-sized black holes. Barmar (talk) 23:23, 3 January 2025 (UTC)

This strip loosely follows a routine by Emo Philips in the 1980's where he describes tearing a piece of paper in half repeatedly until it explodes. He didn't give a count though. 172.71.154.140 01:22, 4 January 2025 (UTC)

So, based on some quick math: If we take the 10^110 meters of paper needed to complete this many folds, then you definitely can easily make a black hole. Generously assuming a 1mm wide strip, this gives us a folded stack of paper 1mm wide, 10^53 meters tall and long. 1 light year is 10^15 meters. So this piece of paper is now 10^38 light years long and wide. I.e. something like 10^27 universes tall and long.

I for one, am totally ready to cut down all the trees needed to make this happen. SDSpivey (talk) 17:42, 4 January 2025 (UTC)

Using the 70g per square meter number used above, you get 7^105 kg total mass. One solar mass is roughly 2^30 kg. Our paper weighs something like 10^54 times as much as the observable universe. This is very likely enough to reverse the expansion of the universe, and cause the entire observable universe to turn into a black hole. Or would it be a new big bang? I wonder what theoretical physics would say about a universe with 10^54 times as much mass / energy.

Also how exact does this comment system work? Is it easier if I just make an account? -Nathan 172.68.22.223 (talk) 08:19, 4 January 2025‎ (please sign your comments with ~~~~)

Only one rule I'm aware of - always sign your comments with ~ (tilde sign) repeated four times. If you aren't signed in this will timestamp with your IP address, if signed in it will show your username as follows: Alcatraz ii (talk) 10:09, 4 January 2025 (UTC)

I think the closest anyone got to the origami was this guy from Finland, who I felt deserves an honourable mention here. Hydraulic Press Channel Hydraulic Press Channel "Closest" nevertheless still means a long way off. ;) PaulEberhardt (talk) 12:50, 4 January 2025 (UTC)

Alternate method: 1) get a large enough piece of paper; 2) wait for its gravitational collapse; 3) you have a black hole! This method is more convenient because the paper "folds" itself. --Itub (talk) 15:22, 4 January 2025 (UTC)'

Seems a lot like the instructions for a carbon atom. [1] N-eh (talk) 21:00, 4 January 2025 (UTC)

No, "fifteen orders of magnitude smaller than" doesn't mean it goes negative. I actually very much dislike phrases like "three times less" (just say that it's a third of what it was... or whatever you really meant, because you might actually mean a quarter or an eighth, for completely different reasons!), but I think that this was clearly "it is smaller by fifteen magnitudes of reduction", not "it is a value that is the original value minus one that is fifteen magnitudes higher than the original value". Anyway, no problem with the attempted edit, but I think the reasoning is misdescribed and/or the declared confusion is unnecessary. 162.158.74.119 00:46, 5 January 2025 (UTC)

Regarding the energy output, equivalent to the mass of the paper... do we also have to account for the work done to force the paper down to the required volume, past the barriers to compression? BunsenH (talk) 04:36, 7 January 2025 (UTC)

Not saying this to suggest some kind of plagiarism or anything but I'm amused this is very similar to a joke from Jeremy Shafer's 2001 book Origami to Astonish and Amuse (in which similar instructions were presented for a "Carbon Atom" (p.244 https://archive.org/details/origami-to-astonish-and-amuse-jeremy-shafer/page/244/mode/2up)). --172.68.3.36 20:12, 7 January 2025 (UTC)