2170: Coordinate Precision

2019-07-01T22:53:29Z

123chess456: /* Explanation */

{{comic
| number = 2170
| date = July 1, 2019
| title = Coordinate Precision
| image = coordinate_precision.png
| titletext = 40 digits: You are optimistic about our understanding of the nature of distance itself.
}}

==Explanation==
{{incomplete|Created by a CARTOGRAPHER. Provide examples for each table entry. Do NOT delete this tag too soon.}}

Coordinates are data points used to identify a person's location on the planet Earth. However, a given coordinate covers a square region of land, and thus leaves some ambiguity; thus, greater precision requires an increasing count of decimal points in your coordinates. This comic uses this information to roughly identify how precise a given coordinate length might be.

The coordinates at [https://tools.wmflabs.org/geohack/geohack.php?pagename=Cape_Canaveral&params=28.5234_N_80.6830_W_type:landmark_region:US-FL_scale:10000 28.5234°N, 80.6830°W] (in {{w|decimal degrees}} form; in {{w|geographic coordinate system}} form using degrees, minutes, and seconds, 28° 31′ 24.24″N, 80° 40′ 58.8″W) are pointing to the {{w|Rocket Garden}} at {{w|Kennedy Space Center}} in {{w|Merritt Island, Florida}} (usually referred to as '''{{w|Cape Canaveral}}''')—specifically, the tip of the [https://www.kennedyspacecenter.com/-/media/DNC/KSCVC/Blog-Images/Rocket-Garden/rocket-garden-with-labels.ashx?h=860&w=1173&la=en&hash=7B9ADC7AFF5370E462AC98D9651945B806B77B2C Delta] rocket.

The sixth entry in the table, with seven digits of precision, includes the caveat that, while your coordinates map to areas small enough on the Earth's surface to indicate pointing to a specific person in a room, "since you didn't include datum information, we can't tell who". This is a reference to the various ''{{w|geodetic datum}}s'' or ''geodetic systems'' — different ways of dealing with the fact that the earth is neither perfectly spherical nor perfectly an oblong ellipsoid. The various datums do not make much difference at six digits of precision, but at seven, there is enough skew depending on which system is in use that the person in a room you are referring to with the coordinates is ambiguous. It is unstated, but the remaining lines in the table with ever-greater precision suffer from this same issue and are equally ambiguous without datum information.

The final entry, with seventeen digits of precision, suggests that either the user is referring to individual atoms in the much-larger-scale whole-Earth coordinate system, or (perhaps more likely) has not bothered to format the values from the GPS module for viewing in the software UI in any way whatsoever, resulting in a value that is [https://en.wikipedia.org/wiki/False_precision meaninglessly precise] because the measurement wasn't that [https://en.wikipedia.org/wiki/Accuracy_and_precision accurate] to begin with. Even if the value is accurate, locating individual atoms by coordinates is not actually useful in most cases, and the motions of multiple systems within our physical world (continental drift, subtle vibrations, etc.) would render the precise value obsolete rather quickly.

For the decimal places past the 5th on the latitude, the digits given are actually the decimal expansion of the constant ''e'' (2.7182818284), while for the decimal places past the 6th on the longitude, the digits given are the decimal expansion of the constant ''pi'' (3.14159265358).

The title text references how at sufficiently small distances, our understanding of reality itself begins to break down. Past the [https://en.wikipedia.org/wiki/Planck_length Planck length], which is more than a quintillion times smaller than the diameter of a photon, the ideals of Euclidean geometry no longer applies and space itself may be composed of a [https://en.wikipedia.org/wiki/Quantum_foam quantum foam] where the very geometry of spacetime itself fluctuates, meaning coordinate systems based on an assumption that space doesn't change would no longer work. String theory, on the other hand, assumes that at a short enough distance the world is composed of ten space dimensions, which precludes the use of a two-dimensional coordinate system.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Single panel containing a table with two columns for "Lat/Lon Precision" and "Meaning" and a caption above the table.]
:Caption: What The Number of Digits in Your Coordinates Means

:[Row 1]
:Lat/Lon: 28°N, 80°W
:Meaning: You're probably doing something space-related

:[Row 2]
:Lat/Lon: 28.5°N, 80.6°W
:Meaning: You're pointing out a specific city

:[Row 3]
:Lat/Lon: 28.52°N, 80.68°W
:Meaning: You're pointing out a neighborhood

:[Row 4]
:Lat/Lon: 28.523°N, 80.683°W
:Meaning: You're pointing out a specific suburban cul-de-sac

:[Row 5]
:Lat/Lon: 28.5234°N, 80.6830°W
:Meaning: You're pointing to a particular corner of a house

:[Row 6]
:Lat/Lon: 28.52345°N, 80.68309°W
:Meaning: You're pointing to a specific person in a room, but since you didn't include datum information, we can't tell who

:[Row 7]
:Lat/Lon: 28.5234571°N, 80.6830941°W
:Meaning: You're pointing to Waldo on a page

:[Row 8]
:Lat/Lon: 28.523457182°N, 80.683094159°W
:Meaning: "Hey, check out this specific sand grain!"

:[Row 9]
:Lat/Lon: 28.523457182818284°N, 80.683094159265358°W
:Meaning: Either you're handing out raw floating point variables, or you've built a database to track individual atoms. In either case, please stop.

{{comic discussion}}

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2170: Coordinate Precision