482: Height

Explain xkcd: It's 'cause you're dumb.
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Interestingly, on a true vertical log plot, I think the Eiffel Tower's sides would really be straight lines.
Title text: Interestingly, on a true vertical log plot, I think the Eiffel Tower's sides would really be straight lines.


Ambox notice.png This explanation may be incomplete or incorrect: Lots of the little references aren't even mentioned, e.g. Human Altitude record, the space elevator, and I just added an explanation for "All Hail Discordia!" This is nearly there, but not yet.
If you can address this issue, please edit the page! Thanks.

The comic is a companion piece to 485: Depth, which explores a logarithmic scale from Earth's atmosphere down to the interior of a single proton. Height begins this process by viewing logarithmically smaller scales showing several objects in the universe, both real and fictional, from farthest (top) to closest (bottom). The comic starts with Black Hat throwing a cat off the edge of the universe, probably a reference to Schrodinger's cat (as since it is outside the observable universe (for us), it exists in a super-position of both living and dead until we actually 'observe' it and force it to be in one of the states). It may also refer to the common myth that a cat will always land on its feet, a myth Black Hat appears to be testing to the extreme. The top of the universe is shown as the distance from which the oldest rays of light reach Earth.

Displaying height logarithmically while displaying width linearly noticeably distorts the shapes of the terrestrial objects. The title text notes that this distortion would approximately cancel out the curve of the Eiffel Tower's profile, and speculates that the cancellation might in fact be exact enough to convert its silhouette to a straight-edged triangle.

The age of the universe is currently stated as 13.8 billion years. But the Observable universe is about 14.0 billion parsecs or 46 billion light years, as shown on the top of the image.

Fictional Objects

  • Cat on a keyboard in space.
  • Ford Prefect, character from The Hitchiker's Guide to the Galaxy (franchise), shown near his home star; Betelgeuse.
  • The Romulan Neutral Zone, marking the edge of the Star Trek Federation.
  • Federation Sector 0-0-1, the sector of space assigned to Earth in Star Trek.
  • "missing WMDs", a reference to the controversy about Iraq and weapons of mass destruction.
  • Bupkis is Yiddish for "nothing". Only a handful of objects are known to orbit between the outer edge of the Kuiper Belt and the inner edge of the Oort Cloud, hence "Bupkis".
  • A comet scheduled to hit earth in 2063, to coincide with the latest date for a supposed Biblically prophesized end of the world.
  • Life on the moons of Jupiter and Saturn, which may or may not exist.
    • The arrows most likely points to the following moons:
    • Jupiter’s moon Europa which may be covered by a deep ocean of water - which is again covered by layer of ice many kilometers thick. In such an ocean life could have formed.
    • Saturn’s moon Titan is the only known moon to have an atmosphere - although nothing like the one on earth. There may be oceans on the moon, but not filled with water but with liquid methane and ethane. It is way too cold for liquid water. Still in such oceans life could also have formed.
    • For either moon the oceans cannot be viewed from earth either due to thick ice or opaque atmosphere.
  • The little spaceship from Asteroids (video game).
  • The Discovery One from 2001: A Space Odyssey, referring to the quote "open the pod bay door, HAL."
  • The spaceplane is most likely the Planet Express from Futurama, where Fry once discussed "a big heaping bowl of salt." However, it could conceivably refer to these instead:
  • A lunar lander with someone inside proclaming "In retrospect, they shouldn't have sent a poet. I have no idea how to land". The goal of Lunar Lander (arcade game) is to land the vehicle without crashing it. The quote is a reference to Contact (1997 film) where the main character Ellie Arroway after witnessing a celestial light show up close says "Poetry! They should've sent a poet.". The actual vehicle in the movie was round and not shaped like a lunar lander.
  • Cory Doctorow's balloon. (first referenced in 239.)
  • Cueball, who is apparently still using Python as shown in comic 353.
  • A Space elevator is a proposed method of transporting cargo or people into orbit, consisting of a station in a geosynchronous orbit, a cable connecting it to the Earth, and a climber that can scale the cable. No space elevator has been built to date, but according to the comic, one will be deployed "one of these days, promise!"

Real Objects


[Map of the universe from observable universe to Earth. Each area of item is labelled.]
[Labels left to right, up to down:]
[Black Hat is standing on top, throwing a black kitty down.]
Black Cat: mrowl!
Top of Observable Universe
46 Billion Light Years Up
Hubble Deep Field Objects
-One Billion Light Years-
Great Attractor
Antennae Galaxies (Colliding)
Holy Crap Lots of Space
-One Million Light Years-
Magellanic Clouds
Edge of Galaxy
Galactic Center
Crab Nebula
Orion Nebula
Horsehead Nebula
Romulan Neutral Zone
Ford Prefect
-Expanding Shell of Radio Transmissions [Arrows are pointing up.]-
Edge of Federation Sector 0-0-1
Missing WMDs
Alpha Centauri
Barnard's Star
-One Parsec-
-One Light Year-
Oort Cloud (?)
Comet which will destroy Earth in late 2063
Pioneer 10
Eris (All hail Discordia!)
Voyager I
Pluto (Not a planet. Neener neener.)
Aircraft: Hey a heaping bowl of salt!
"Open the fridge door, Hal."
Human Altitude Record (Apollo 13)
2nd Place: Snoop Dogg
Space Elevator - One of these days, promise!
-Geosynchronous Orbit-
GPS Satellites
Lunar lander: In retrospect, they shouldn't have sent a poet. I have no idea how to land
International Space Station
Space Junk
-Official Edge of Space (100 km)-
-1/10 ATM-
High Altitude Balloons
-1/2 ATM-
Cory Doctrow
Shuttle Columbia Lost
Cueball: Woo Python!
-800 m-
-1 km-
[Height progressivly gets smaller and smaller.]
Burj Dubai (~800 m)
Eiffel Tower (325 m)
Great Pyramid (140 m)
Redwood (115 m)
Pop Fly
Oak (20 m)
"Hey Squirrels!"
Tallest Stilts
Brachiosaur (13 m)
Giraffe (8 m)
[Megan and Cueball.] Folks
The Observable Universe, from Top to Bottom ~On a log scale~
Sizes are not to scale, but heights above the Earth's surface are accurate on a log scale (that is, each step up is double the height.)

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Are you sure it reads "missing winds"? It looks like "missing WMDs" to me, which would suggest a political reference to the US engagement of 2003 in Iraq. 02:48, 22 May 2013 (UTC)

Yeah. Agreed. Changed. PinkAmpersand (talk) 11:23, 23 May 2013 (UTC)
"The comic starts with Black Hat throwing a cat off the edge of the universe, probably a reference to Schrodinger's cat" 
Has the editor here never heard of the "cats always land on their feet" myth? Black Hat would appear to be testing this from the extreme. Anonymous 01:43, 4 December 2013 (UTC) (and yes, that would be WMDs)
If I am not mistaken, this is a wiki; there is no set editor. If you have a suggestion for how to improve a page, it would be apt to edit it yourself. The discussion tends to be a forum for matters that may be tangentially related to the comic, or uncertain suggestions for improving the article. Davidy²²[talk] 03:18, 4 December 2013 (UTC)
Sorry, I wasn't aware of the proper terminology. I'll add my line shortly. Anonymous 05:13, 13 December 2013 (UTC)

Why is there a "(?)" in "Oort Cloud"? 02:10, 15 December 2013 (UTC)

Because it's not known if this cloud really does exist. Many objects are assumed to be there at that vast distance to the sun, but that distance is also the reason they could not be detected from earth. Voyager 1, the farthest humanmade object from Earth, will reach that region in many thousand years. --Dgbrt (talk) 21:37, 15 December 2013 (UTC)

Why is Snoop Dogg in space? (talk) (please sign your comments with ~~~~)

Because he's high as shit, man--he's so high, he's the second-furthest any person's ever been from the earth. 10:12, 6 February 2014 (UTC)
Diameter of milky way: 100 - 120 kly (Lets call it 110 kly)
Suns distance to galactic centre: 27.2 kly
Distance to edge of galaxy: (0.5*110)-27.2 = 27.8 kly = 263E18

Is my understanding and maths right? --Pudder (talk) 08:08, 11 September 2014 (UTC)
Conversion of pixels to height

Because it is a log graph for the y axis

heightfinal = heightinitial * factor
pixels = Logbase(height)

Using identities to show that a vertical distance on this graph represents a multiplicative change in true distance from the starting point of measure, and that a vertical change (delta) in the same number of pixels represents a corresponding multiplicative factor on total height.

pixelsfinal = Logbase(heightinitial * factor) = Logbase(initial) + Logbase(factor)
pixelsfinal - pixelsinitial = Logbase(factor) = pixelsdelta

Solving for the factor and the base of the log function

factor = basepixelsdelta
base = factor1/pixelsdelta

From the diagram it appears that a change (delta) of 550 pixels represents a change of x*1000000 therefore we can determine the base and determine the multiplicative factor for any change in pixels in the original drawing.

base = 10000001/550 
factor = (10000001/550)pixelsdelta = 1000000pixelsdelta/550


heightfinal = heightinitial * 1000000pixelsdelta/550
The above can be used as an equation to estimate and validate the heights on the diagram, where heightinitial is the height of the reference point in meters, pixelsdelta is the vertical change in pixels on the diagram, and is positive if height increases and negative if height decreases. 12:40, 30 September 2014 (UTC)

We just need to be careful that the existing heights (which in most cases have been fairly thoroughly researched) are not replaced by heights determined by their 'pixel position'. --Pudder (talk) 11:16, 1 October 2014 (UTC)
Wrong, the explanation is intended to explain the comic not the real world. Before you get excited though let me explain, we may be on the same page.
Many height values can be determined from external research, and can be shown to be consistent with the graph (e.g. center of the galaxy). In these cases the researched number should be used in the height column, as clearly these numbers represent the authors intent.
There or other cases where the height is labeled. These should always be used as height, as these numbers represent the authors intent. If they are inconsistent with the scale of the graph this should be noted in the description.
There are other cases, such as where the space shuttle disintegrated, where we can research the numbers, but they are inconstant with the graph by more than an order of magnitude. Any large inconsistencies should be noted in the description, but in these cases the graph position, not the actual position should be in the height column, because this is the closest representation we can have to authors intent. 11:50, 1 October 2014 (UTC)

Completely agree with the basis that authors intent is priority, and with pretty much everything written above. What I was concerned about was the possibility of someone indiscriminately changing existing height values based solely on its pixel position, with no cross-checking against the real world height. I would venture that the heights of the real items on the graph are intended by Randall to be at their correct positions, but there may be exceptions. I have a personal bias here, in that I spent quite considerable time doing research on many of the heights. That said, I don't in any way expect the height entries I worked on to be taken as correct, simply that there is some degree of reasoning behind the existing heights, and to change them without checking any discrepancies would be reckless. --Pudder (talk) 12:48, 1 October 2014 (UTC)
The Bodes Law ratio of one planet to the next but one is:
Pi^(9/4Pi): 20Pi^(3/2Pi)
thus rendering:
  • Mercury : Mars
  • Venus: Jupiter
  • Earth : Saturn
  • Mars : Uranus
  • Asteroids : Neptune

Not that the inner asteroids appear between Mars and Jupiter on the right hand column.

I used Google News BEFORE it was clickbait (talk) 01:09, 31 January 2015 (UTC)

I think the "pulsar" at the top right might actually be a quasar (an active galaxy). They certainly are distant objects, so someone more versed with the wiki may want to have a look. 20:10, 14 April 2015 (UTC) 15:00, 18 August 2015 (UTC)

Randall is stating that this is the longest distance that a ray of light has ever traveled to reach Earth, which implies that the universe is about 46 billion years old

Never hear of the expanding space? 15:00, 18 August 2015 (UTC)