2800: Down

Explain xkcd: It's 'cause you're dumb.
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It's just that I get nervous about heights.
Title text: It's just that I get nervous about heights.


The direction that we call "down" is usually defined as the direction in which objects on Earth fall, which, for all intents and purposes, is the same as the direction that points toward the center of the Earth. This direction is therefore relative, as it depends on where you are located in relation to Earth's center, and is different for people in different locations. For example, from an outside viewpoint, the direction of "down" for people in Madrid, Spain is the opposite of the direction of "down" for people in Weber, New Zealand, as these two places are located at antipodal points on Earth.

It is possible to redefine "down" by choosing a different point of reference, such as the center of a different planet, which is the situation shown in this comic. We see Megan seated at a desk, which would be perfectly normal if not for the fact that the scene is shown at a completely unnatural, almost upside-down angle. Megan explains to Cueball that the direction of "down" was redefined to be relative to Mars instead of Earth. Since Mars is located in space many millions of miles away, this means that "down" could potentially be in almost any direction.

Redefining down to be relative to Mars would be impractical for people on Earth,[citation needed] as Mars is constantly moving with respect to Earth; this means that the direction of down will drift over time. Additionally, as Earth rotates once per day, the direction of down would also experience a 24-hour periodic wobble. It would be very difficult to keep track of this constantly-changing direction. Setting down relative to Earth's center avoids these problems (at least for beings on Earth!), as the Earth's center is static in relation to the motion and rotation of Earth.

Megan does not explain who exactly redefined down, or why they have the authority to do so, but it is most likely some scientific body such as the International Astronomical Union or the General Conference on Weights and Measures, which have the power to make such decisions - for example, the IAU defined planet and dwarf planet in 2006, and the GCWM redefined the kilogram in 2018. In reality, in addition to there being no governing body which determines the direction of down, such definitions are made only when there is compelling reason to, and they work hard to minimize the changes. (For example, the redefinition of the kilogram was done in order to prevent the mass of the kilogram from changing in the future by attaching it to physical constants.) Nonetheless, in the world shown in this comic, redefining 'down' appears to happen frequently enough for Cueball to be frustrated but not fazed by it.

It should also be noted that redefining down does not automatically alter the direction of gravity, which will still act in the same direction it did before. Therefore, it is unclear how Megan or Cueball are even aware of the change in definition, unless they are somehow aware of the comic they are in and "know" that they are oriented at a strange angle.

Cueball mentions that the redefinition of down is a side effect of redefining the origin of their coordinate system. A coordinate system is a way of representing locations in space using a set of numbers, where each number (called a coordinate) measures a distance travelled in one of the spatial dimensions. In order for these numbers to be meaningful, it is always necessary to define a single point as the origin, where all coordinates have the value 0. Locations can then be measured relative to the origin.

For example, a commonly-used coordinate system for Earth is the Earth-centered, Earth-fixed coordinate system, which defines the origin to be Earth's center of mass, and uses three pairs of points on the Earth's surface to define the directions of the three spatial dimensions; this allows any point relative to Earth to be specified as a triplet of three coordinates. Presumably, the coordinate system now used in the comic is a "Mars-centered, Mars-fixed" coordinate system, which would be good for things like launching satellites from Mars, but otherwise not very useful for most Earthly situations.

In the title text, Cueball states that he gets nervous about heights. Height is the distance between two points at different elevations, and elevation depends on which way "down" is - therefore, redefining down also redefines the concept of height. Since down now points toward Mars, and Mars is millions of miles away (about 34,000,000 mi or 55,000,000 km at closest approach), this means that Cueball - and indeed, everyone on Earth - is now standing at a height of about 34 million miles above Mars. While fear of heights is a common cause of anxiety, it doesn't really make sense for Cueball to be nervous in this instance - usually, when people are afraid of heights, it's because they are afraid of falling. However, gravity still points toward the center of the Earth, so Cueball is in no danger of falling to Mars. The joke is that Cueball is scared solely due to the redefinition of the situation - where previously he was standing on solid ground, now he is "perilously" clinging to the underside of a planet with a 34-million mile drop beneath him.

The only advantage of using Mars as down, is that everyone on Earth agrees on the direction of down, since Mars is so far from Earth that even those on either side of Earth orthogonal to the direction towards Mars, would still almost agree on the down direction.

In the recent game comic 2765: Escape Speed, the planet outside of the Crystal Sphere, based on the Click and Drag comic, doesn't have it's own gravity. So the space ship is pulled towards the Crystal Sphere no matter what side of this planet the space ship is located. This makes navigating difficult. Only the fact that landing on the surface (and sticking to it) is possible, makes it possible to explore the planet properly.

The comic could also be a reference to the novel Ender's Game by Orson Scott Card, in which the protagonist, Ender, helps his team to orient themselves in a zero-gravity battle by noting that the directions "up" and "down" are arbitrary in space; he summarizes this with the mantra "The enemy's gate is down". This insight gives his team an anchoring point of reference which makes it easier for them to function in the gravity-less arena. This aspect of Ender's Game was previously referenced in 241: Battle Room.


[Megan is seated at a desk, in front of a laptop. The scene is rotated by 150° clockwise, so she appears to be upside down and angled.]
[Cueball enters the scene from the right side, behind Megan. He has three question marks below his head, oriented upright in frame.]
Megan: They announced that "down" is relative to Mars today.
Cueball: Ugh, I hate when they make another planet the coordinate system origin.

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Shouldn't it be geolocated, to be rotated accordingly? 12:35, 10 July 2023 (UTC)

You need to know where and when you are. Taking the 220 degrees (why not 140?) currently in the transcript as correct, that means Mars is at 50° azimuth, which a versatile but overly-fiddly astronomy app I have (why doesn't it remember I do manual orientation? ...it's flat out wrong when it tries to do it from device settings/current orientation!) suggests that Mars will reach 50° 'up', for me, at about 16:30 local time (could have checked when it fell back down to that again, but I didn't) at which point I could easily be sat facing whichever direction puts "Mars down" at a similar angle to the one seen in the comic. But it will change throughout the day, every day that it applies. 13:05, 10 July 2023 (UTC)
I guess that's why Randall hates it so much, it changes continuously. Although he missed a great opportunity for a clever animated comic -- it could calculate the rotation of the scene based on the reader's location and time. Barmar (talk) 14:20, 10 July 2023 (UTC)

Why didn't Orson Scott Card get cowriting props for this one?

I'm TenGolf and I started the explanation! 15:03, 10 July 2023 (UTC)

I'm not so sure about the "relative to gravity in actuality" - there's no objective reason why "down" must follow gravity. (Take Ender's Game - "The enemy's gate is down") DownGoer (talk) 15:07, 10 July 2023 (UTC)

That's not the directional sense of "down". When it's used as a direction, it's towards the center of whatever body currently exerts the most gravity -- if you're on Earth it's towards the Earth's center, if you're on the Moon it's towards the Moon's center, etc. "Down" has other senses, like "the computer is down" that just refers to whether it's functioning. Barmar (talk) 17:16, 10 July 2023 (UTC)
241:_Battle_Room Relevant here? —Purah #126 (talk) 00:41, 11 July 2023 (UTC)
For the case of Ender's Game, it isn't a matter of ignoring/spiting gravity, but the disorientattling lack of gravity in the arena makes tactics difficult to maintain when everyone has a different 'up' (when going concentrating on 'forward to the enemy').
Rethinking it as being 'down to the enemy' (and perhaps revisualising as cylindrical/spherical coordinates as you are looking 'down that well') gives you a better resilience of comprehension whenever you get spun around and need to make sure you're still singing to the same (directional) hymnsheet as your team.
Though, if I recall the film correctly, they re-established the "single orietation standard" whereby (whatever the script said) there seemed to be the obligatory common (and perpendicular to the line of attack/defence) 'up', just for the sake of the audience's own 2D-plane (with maybe 0.5d of 'elevation') sensibilities. 07:54, 11 July 2023 (UTC)

This may be a reference to the band named Down Left Forte. 23:37, 10 July 2023 (UTC)

When I first tried to access this comic, Explain XKCD's server didn't respond. For a second I thought it was some sort of joke page in the same vein as 404. -- 10:49, 12 July 2023 (UTC)

I am over 2 bottles of wine deep tonight. This comic looks like I feel.

In the space opera board game Twilight Imperium, one of the factions, the L1Z1X, has labelled their home planet "[0.0.0]" and their flagship "[0.0.1]". This would imply that their coordinate system, both orientation and distance, is dependant on the relative positions of these two objects. -- 11:17, 13 July 2023 (UTC)