3086: Globe Safety

Globe Safety

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Title text: Frankly, given their extreme gravitational fields and general instability, even 12-inch globes should probably be banned.

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Explanation

This explanation is incomplete: This page was created by an EARTH MASS BOT THE SIZE OF A REGULAR BOT. Don't remove this notice too soon. If you can fix this issue, edit the page!

For any given amount of (stationary) mass, a value can be calculated known as the Schwarzschild radius, which denotes the radius of a spherical volume of space. If the mass somehow is compressed into this volume, it becomes so dense that it forms a black hole. The Schwarzschild radius corresponding to the mass of the Earth is about 0.35 inches (roughly 9 mm, or a diameter of 7/10" or 18 mm), meaning that if you could compress the Earth into a ball that small, it would be a black hole. The object at bottom right in the comic, with a triangular warning sign next to it, is a depiction of a black hole.

Globes, in this context, are miniature re-creations of planet Earth, used to show its features without any of the typical problems of a flat map. Randall claims that safety standards are in place to ensure that globes are not manufactured at, below, or even close to the Schwarzschild radius of the Earth. The suggestion is that any globe of the Earth shares the same mass as the Earth and hence the same Schwarzschild radius. Such a globe might be made by creating a literal 1:1 replica of Earth and then shrinking it without distortion until it has the required size. This would, of course, give the most perfect maps; however, for each globe like this put on Earth, the Earth's mass would increase by its original amount. In addition, it would be impractical to make globes this way: such small amounts of matter of this density would immediately explode, vaporizing most or all of the Earth, unless the unknown process that produced the shrinking was maintained.

The title text suggests that globes up to 12 inches (30.5 cm) should be banned, due to their extreme density and gravitational field. The surface gravity of an object varies inversely with the square of its radius. Since the globe would have the same mass as the Earth, such a globe would exert massive, catastrophic gravitational forces at its surface. For a 12-inch globe, this would be 1.75 quadrillion times normal Earth gravity. The changes at the Earth's surface caused by these forces would immediately reduce the accuracy of the globe's representation of the area in which it is located. The gravitational effects on objects at a distance would be the same, but adding an Earth mass for each globe would still affect the orbits of satellites, other planets, etc. However, extreme gravity would exist for Earth-mass globes of any size that globes are commonly used for, so the 12-inch cut-off is no less arbitrary than the 4-inch one.

Transcript

[A standard globe of the Earth is shown. It stands on a typical stand which holds it by two arms at the poles, so it can turn around like the Earth does. The Earth is turned so it shows Australia at the bottom and most of Asia, including the entire India to the left. Only the very tip of Alaska can be seen of the Americas. Above the globe there is a double ended arrow that goes to two small lines that align with the edges of the globe (indicating the diameter). The arrow has been split in the middle and two lines of text are written in the gap. Above this text there is another line of text.]

Remember:

4 inches minimum

[Beneath the globe there are two small drawings. The left shows the Earth and to the left of the Earth there is a double ended arrow ending at two lines that indicated the diameter of the Earth going from top to bottom. The distance of this is written in inches to the left. From the Earth an arrow points to another drawing, this time the typical depiction of a black hole, with a "hat" like shape. A triangular warning sign is shown a the top right of the black hole with an exclamation mark inside.]

7/10"

[Caption below the panel:]

The Earth's Schwarzschild radius is about 0.35 inches, which is why safety regulations require desktop globes to be at least 4 inches in diameter.

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Discussion

You are welcome to comment on the April Fools' Day talk page

Hey, I thought we could revamp the old April Fools' Day comics page. I proposed a table or a list, and it would be nice if you commented. It should be a small project. You are welcome to comment here. Thanks!--FaviFake (talk) 18:02, 9 May 2025 (UTC)

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Hello! First time i got to a comic first --172.69.176.76 06:17, 8 May 2025 (UTC) 104.23.175.202 (talk) (please sign your comments with ~~~~)

Well first of all remember to sign your comments :-). But congratz... --Kynde (talk) 05:42, 8 May 2025 (UTC)

Sorry. I now realize that that was an extremely trollish thing to do. --172.70.92.140 07:09, 8 May 2025 (UTC) ٠ـ٠

Also i MAY OR MAY NOT have permanently altered the editing process of this talk by including arabic numbers in an emoticon. 172.70.92.140 (talk) 07:09, 8 May 2025 (UTC) (please sign your comments with ~~~~)

I believe he indicates that a globe is made by making a copy of the Earth, and then compressing it until it fits on a desktop. Hence having the same mass and thus the same Schwarzschild radius as Earth. I have changed the explanation a bit because of this observation.--Kynde (talk) 05:42, 8 May 2025 (UTC)

Gotta wonder what kind of a desk could support a desktop globe that weighs as much as the Earth --StumbleRunner

[...] desk? Convince me that such a globe wouldn't plunge straight through the Earth's crust and into the mantle. I sense a marketing problem. 172.71.147.69 07:07, 8 May 2025 (UTC)

Radius. Is there a typo in the comic where 7/10" should be 7/20", i.e., 0.35" as later written? Or would a 7/10" Earth collapse into a black hole nonetheless?172.71.154.129 06:40, 8 May 2025 (UTC)

Nope… the Schwarzchild radius is 0.35", which is indeed 7/20", but the measurement shown on the globe is the diameter, not the radius, so 7/10" is correct. 172.71.178.143 06:49, 8 May 2025 (UTC)

Isn't there also a jab at the weird way USsians use power-of-two fractions for inch measurements? I've never seen something like 7/10" before, it would be approximated as 11/16".172.71.95.69 09:18, 8 May 2025 (UTC)

It isn't a weird USian thing - it's just the historical way that inches (being a non-metric unit) were divided. The same way that an inch is a 1/12 division of a foot, which is a 1/3 division of a yard, etc. 141.101.98.83 10:23, 8 May 2025 (UTC)

I think we have a bigger problem: there are millions of globes on Earth! I haven't done the calculations, but that might be enough to turn Earth into a black hole already; if not, I expect at least it would turn it into a star. --104.23.190.34 11:44, 8 May 2025 (UTC)

BTW. what would be a 12-inch object with a mass of Earth? Neutron star? Neutron planet? Neutron meteoroid? -- 12:46, 8 May 2025 (UTC)

Crunching the numbers (thanks to Copilot.microsoft.com):

• A sphere with a 30 cm radius has a volume of about 1.13×10^-2 m³.
• Compressing Earth's mass into that volume gives a density of roughly 5.3×10²⁸ g/cm³.

That is way way denser than a neutron star. It's doubtful that such a sphere would remain at that density; it would likely explode immediately, or if prevented from doing so, continue to shrink down past 9mm and become a black hole. 172.70.110.59 (talk) 13:26, 8 May 2025 (UTC) (please sign your comments with ~~~~)

False precision: .889 cm? Could someone please check "0.35 inches (0.889 cm)"? I'm concerned that this is a matter of false precision, with two significant digits for the customary / imperial system precisely converting to three significant digits in SI (similar to the way people obsess over 98.6F, which is a precise conversion of the estimate of 37C.). Also, I'd suggest that millimeters are preferable to centimeters. 104.23.170.118 14:11, 8 May 2025 (UTC)

2 × 6.6738×10^−11 m^3⋅kg^−1⋅s^−2 × 5.972168×10^24 kg / (299792458 m⋅s^−1)2 = 0.00887 m , so the current 8.9mm looks good. Nosh (talk) 19:16, 8 May 2025 (UTC)

Why are globes over 12 inches safer than those less than 12 inches? The density calculation above seems to indicate that an earth mass object of 12 inch diameter is much denser than a neutron star. (Of course that calculation was done with an AI - so may not be right.) I did a little searching for things denser than neutron stars - didn't find much. So what is special about 12 inches that makes earth mass things of that size change in safety regime 172.68.22.75

I'm pretty sure there aren't any things denser than a neutron stars. (There are black holes, of course, but those are not really things and may not actually HAVE a meaningful density.) -- Hkmaly (talk) 05:07, 9 May 2025 (UTC)

')DROP TABLE Talk:3086: Globe Safety; 162.158.108.51 (talk) 07:22, 9 May 2025 (UTC) (please sign your comments with ~~~~)

So, I'm guessing you've never heard of the theoretical Quark star (a specific example of an Exotic star, which is hypothesized to exist between the two). SammyChips (talk) 18:13, 9 May 2025 (UTC)

I think that's part of the joke. There's no safe cut-off at which globes made in this fashion would be OK - placing an Earth-sized Earth-mass object immediately adjacent to the Earth would be utterly catastrophic, never mind anything smaller.172.71.26.107 08:32, 9 May 2025 (UTC)

I'd just like to point out the the Schwarzchild radius of one Planck mass is two Planck lengths (obvious from the standard formula). Since the mass unit is an incredibly huge 22 micrograms, this makes me nervous about all those bacteria for some reason. 104.23.209.191 17:43, 10 May 2025 (UTC)

I have three globes in my home office. I wondered why they were so heavy. These Are Not The Comments You Are Looking For (talk) 00:58, 11 May 2025 (UTC)
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