explain xkcd - User contributions [en]

2210: College Athletes

2019-10-02T02:06:53Z

172.68.226.106: /* Explanation */ missed an apostrophe

{{comic
| number = 2210
| date = October 2, 2019
| title = College Athletes
| image = college_athletes.png
| titletext = Their signature play is the three-point combinator, a recursive offense which is guaranteed not to halt and continues accumulating points until the buzzer.
}}

==Explanation==
{{incomplete|Created by a Steph Curry. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

The comic is about the [https://leginfo.legislature.ca.gov/faces/billNavClient.xhtml?bill_id=201920200SB206|California Fair Pay to Play act], which was signed into law on September 30, 2019. It gives college athletes the rights to their name and face for financial gain, in contrast to NCAA rules which require that athletes be unpaid.

In this comic, Cueball claims that all members of his college basketball team changed their name to Steph Curry, after the NBA Player of the same name. In particular, one player copied the name from the NBA player, then another member of the team copied the name from that player, and so on.

This process is called "Currying", a play on both the name "Curry" used here, as well as the mathematical procedure called {{w|currying}}, wherein a multivariable function is broken down into a sequence of single-variable functions, each of which outputs a new function until the final variable is consumed. For example, the function f(x,y,z) can be curried into f(x)(y)(z), where f is a function that consumes x and produces a function f(x), which in turn consumes y, yielding the function f(x)(y), and that in turn is a function f(x)(y) which consumes the parameter z to finally produce f(x)(y)(z), which is equal to the original f(x,y,z). This is not commonly used in most areas of math except for foundational logic and pure functional programming.

White Hat’s question regarding the form ‘''Stephs Curry''’ is referring to the pluralization of phrases where a noun is followed by a modifier of some sort, such as ''attorneys general'', ''parts unknown'', ''heirs apparent'', ''mothers-in-law'', and so on. In these cases, plurals are formed by pluralizing the noun parts of the phrases; however, some of these are rare or foreign enough that speakers of English don't always identify them correctly and pluralize the last word instead, e.g. *''attorney generals''.

The title text is a computer science joke, saying that their signature play is the "three-point combinator", a joke on y-combinators (?), which is recursive (see: recursion) and does not halt (see: the Halting Problem).

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[Cueball, Ponytail and White Hat are having a conversation.]
:Ponytail [checking phone]: Oh, huh. California passed a law giving college athletes full rights to their names and images.
:White Hat: Good, I think?

:Cueball: That's nothing. ''Our'' state gave college players rights to use the names and images of ''any'' California athletes.
:Ponytail: It did not.

:Cueball: Sure it did!
:Cueball: That's how our school fielded a basketball team made up entirely of Steph Currys.
:White Hat: Or is the plural "Stephs Curry"?

:Cueball: They didn't all copy the original Steph, though. One player got the rights to his name, then the next player got it from them, and so on.
:Cueball: This process is known as "currying".
:Ponytail: ...I hate you so much.

{{comic discussion}}

2210: College Athletes

2019-10-02T02:05:52Z

172.68.226.106: /* Explanation */ Expanded paragraph on plurals

{{comic
| number = 2210
| date = October 2, 2019
| title = College Athletes
| image = college_athletes.png
| titletext = Their signature play is the three-point combinator, a recursive offense which is guaranteed not to halt and continues accumulating points until the buzzer.
}}

==Explanation==
{{incomplete|Created by a Steph Curry. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

The comic is about the [https://leginfo.legislature.ca.gov/faces/billNavClient.xhtml?bill_id=201920200SB206|California Fair Pay to Play act], which was signed into law on September 30, 2019. It gives college athletes the rights to their name and face for financial gain, in contrast to NCAA rules which require that athletes be unpaid.

In this comic, Cueball claims that all members of his college basketball team changed their name to Steph Curry, after the NBA Player of the same name. In particular, one player copied the name from the NBA player, then another member of the team copied the name from that player, and so on.

This process is called "Currying", a play on both the name "Curry" used here, as well as the mathematical procedure called {{w|currying}}, wherein a multivariable function is broken down into a sequence of single-variable functions, each of which outputs a new function until the final variable is consumed. For example, the function f(x,y,z) can be curried into f(x)(y)(z), where f is a function that consumes x and produces a function f(x), which in turn consumes y, yielding the function f(x)(y), and that in turn is a function f(x)(y) which consumes the parameter z to finally produce f(x)(y)(z), which is equal to the original f(x,y,z). This is not commonly used in most areas of math except for foundational logic and pure functional programming.

White Hat’s question regarding the form ‘''Stephs Curry''’ is referring to the pluralization of phrases where a noun is followed by a modifier of some sort, such as ''attorneys general'', ''parts unknown', ''heirs apparent'', ''mothers-in-law'', and so on. In these cases, plurals are formed by pluralizing the noun parts of the phrases; however, some of these are rare or foreign enough that speakers of English don't always identify them correctly and pluralize the last word instead, e.g. *''attorney generals''.

The title text is a computer science joke, saying that their signature play is the "three-point combinator", a joke on y-combinators (?), which is recursive (see: recursion) and does not halt (see: the Halting Problem).

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[Cueball, Ponytail and White Hat are having a conversation.]
:Ponytail [checking phone]: Oh, huh. California passed a law giving college athletes full rights to their names and images.
:White Hat: Good, I think?

:Cueball: That's nothing. ''Our'' state gave college players rights to use the names and images of ''any'' California athletes.
:Ponytail: It did not.

:Cueball: Sure it did!
:Cueball: That's how our school fielded a basketball team made up entirely of Steph Currys.
:White Hat: Or is the plural "Stephs Curry"?

:Cueball: They didn't all copy the original Steph, though. One player got the rights to his name, then the next player got it from them, and so on.
:Cueball: This process is known as "currying".
:Ponytail: ...I hate you so much.

{{comic discussion}}

2210: College Athletes

2019-10-02T01:33:09Z

172.68.226.106: /* Transcript */ punctuation, formatting, one missing word, description

{{comic
| number = 2210
| date = October 2, 2019
| title = College Athletes
| image = college_athletes.png
| titletext = Their signature play is the three-point combinator, a recursive offense which is guaranteed not to halt and continues accumulating points until the buzzer.
}}

==Explanation==
{{incomplete|Created by a Steph Curry. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

In this comic, Cueball claims that all members of his college basketball team changed their name to Steph Curry, after the NBA Player of the same name. In particular, one player copied the name from the NBA player, then another member of the team copied the name from that player, and so on.

This process is called "Currying", a play on both the name "Curry" used here, as well as the mathematical procedure called {{w|currying}}, wherein a multivariable function is broken down into a sequence of single-variable functions, each of which outputs a new function until the final variable is consumed. For example, the function f(x,y,z) can be curried into f(x)(y)(z), where f is a function that consumes x and produces a function f(x), which in turn consumes y, yielding the function f(x)(y), and that in turn is a function f(x)(y) which consumes the parameter z to finally produce f(x)(y)(z), which is equal to the original f(x,y,z). This is not commonly used in most areas of math except for foundational logic and pure functional programming.

White Hat’s reference to ‘Stephs Curry’ is likely referring to State Attorneys General. Though commonly called ‘State Attorney Generals’, ‘generals’ is an incorrect pluralization, according to convention.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[Cueball, Ponytail and White Hat are having a conversation.]
:Ponytail [checking phone]: Oh, huh. California passed a law giving college athletes full rights to their names and images.
:White Hat: Good, I think?

:Cueball: That's nothing. ''Our'' state gave college players rights to use the names and images of ''any'' California athletes.
:Ponytail: It did not.

:Cueball: Sure it did!
:Cueball: That's how our school fielded a basketball team made up entirely of Steph Currys.
:White Hat: Or is the plural "Stephs Curry"?

:Cueball: They didn't all copy the original Steph, though. One player got the rights to his name, then the next player got it from them, and so on.
:Cueball: This process is known as "currying".
:Ponytail: ...I hate you so much.

{{comic discussion}}

Talk:2170: Coordinate Precision

2019-07-03T22:40:37Z

172.68.226.106:

The coordinates seem to show a NASA building, so in the end you're still soing something space related. [[Special:Contributions/172.69.55.196|172.69.55.196]] 19:47, 1 July 2019 (UTC)Some random European.
:The more precise coordinates are actually in the middle of the Rocket Garden at the Visitor's Center of the Kennedy Space Center complex. [[User:Ianrbibtitlht|Ianrbibtitlht]] ([[User talk:Ianrbibtitlht|talk]]) 19:58, 1 July 2019 (UTC)

The atom-level coordinates are obtained by appending digits of e and pi to the Rocket Garden coordinates. [[User:Ichoran|Ichoran]] ([[User talk:Ichoran|talk]]) 20:21, 1 July 2019 (UTC)

I always find it very funny to see all those decimals. Regular GPS devices have an uncertainty of 3 meters if there is no interference from trees, buildings or whatever. That puts you at about 4 to 5 decimals I guess. [[User:Palmpje|Palmpje]] ([[User talk:Palmpje|talk]]) 20:26, 1 July 2019 (UTC)
:A Google Maps webpage URL includes coordinates to seven decimal places. [[User:EmuSam|EmuSam]] ([[User talk:EmuSam|talk]]) 20:48, 1 July 2019 (UTC)
::Sure but out there with your handheld GPS or normal consumer device that includes a GPS receiver you won't get more precision than about 3 meters. And when your at the higher latitudes you're probably not getting that. [[User:Palmpje|Palmpje]] ([[User talk:Palmpje|talk]]) 20:52, 1 July 2019 (UTC)

So combining this comic with #2169, is Randal suggesting he'll be at the Rocket Garden on July 28th (much as he did in #240)? [[Special:Contributions/108.162.216.208|108.162.216.208]] 20:47, 1 July 2019 (UTC)
:It says ''June'' 28th. --[[Special:Contributions/162.158.126.22|162.158.126.22]] 20:52, 1 July 2019 (UTC)
::No, the date of that comic is June 28, but the title text says: [AT THE JULY 28TH MEETING] --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 21:51, 1 July 2019 (UTC)
:::Ah, that makes sense. For some reason my app only showed the first part of the tirle text --[[Special:Contributions/162.158.126.94|162.158.126.94]] 23:04, 1 July 2019 (UTC)
::::The COMIC says "June 28th." The TITLE TEXT says "July 28th." Apparently the government computer predictive text was trained from different input. [[User:Mwburden|mwburden]] ([[User talk:Mwburden|talk]]) 15:26, 2 July 2019 (UTC)

Regrettably, there are two dimensions missing, Z and T. Without Z (elevation)+/- you could be in space or in a neutrino detector. T is only relevant for dynamic objects, but there again, the Americas are going West at a measurable rate! [[User:RIIW - Ponder it|RIIW - Ponder it]] ([[User talk:RIIW - Ponder it|talk]]) 21:30, 1 July 2019 (UTC)

The seventh row is likely a reference to comic number 1358 where two stick figures try to find waldo via satellite. [[Special:Contributions/172.69.226.125|172.69.226.125]] 21:44, 1 July 2019 (UTC) kisara, 21:42, 1 July 2019 (utc)

10^-40 degrees on the surface of the earth translates to about 0.7 planck lengths. [[Special:Contributions/162.158.106.234|162.158.106.234]] 21:50, 1 July 2019 (UTC)

Do the coordinates 28.5234°N, 80.6830°W really correspond to the tip of the Delta rocket? I checked and it was pointing to a small patch of ground next to the rocket, not the tip of the rocket itself. [[User:Herobrine|Herobrine]] ([[User talk:Herobrine|talk]]) 00:20, 2 July 2019 (UTC)
:No, you need to go to five decimal places to get the rocket. In that respect, I think he might be off by one digit of precision in his descriptions. [[User:Jeremyp|Jeremyp]] ([[User talk:Jeremyp|talk]]) 12:04, 2 July 2019 (UTC)
::Someone corrected it in the explanation, the coordinates 28.52345°N, 80.68309°W do correspond to the Delta rocket. [[User:Herobrine|Herobrine]] ([[User talk:Herobrine|talk]]) 12:46, 3 July 2019 (UTC)

I would like to mention that neither number seems to fit into a standard double float value. I made a fiddle showing this. [https://dotnetfiddle.net/k7yK0Y#] [[User:Ansarya|Ansarya]] ([[User talk:Ansarya|talk]]) 01:48, 2 July 2019 (UTC)
:Floats are stored base 2, so representing them exactly as decimal often requires many more digits than is actually necessary (for complicated number theory reasons, a float can always be represented exactly as decimal, which would not be true if floats were stored in base 3). For this reason, programming languages that can format floats round them, usually to a number of digits where it will be possible to reconstruct the original float (though C# apparently takes off a couple extra digits, since those digits are almost never significant). To illustrate this, I used Rust to print many more digits of a float than would be shown normally [https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=6796c2459ceabea1a03d7113b676dd8f]. The latitude coordinate in the comic could be the result of printing a double precision float, but the longitude coordinate could not be. Also note that it takes almost 50 digits to reach an exact base 10 representation, even though only 14 or 15 of those digits are actually needed to reconstruct the original float. [[User:Probably not Douglas Hofstadter|Probably not Douglas Hofstadter]] ([[User talk:Probably not Douglas Hofstadter|talk]]) 18:01, 2 July 2019 (UTC)

May be my pet peeve... ...but adding an additional error to every piece of input data [and maybe every intermediate result] in order to show that either the precision the original measurement ends here or that all further digits of the measurement read "0" often introduces an error that can add up surprisingly quickly => I personally prefer raw floats that indicate there probably was no error analysis to rounded data and won't get tired on telling people to explicitely state what precision they can expect.[[Special:Contributions/162.158.114.70|162.158.114.70]]

If the smallest subnormal 32 bit float is a Planck length, then the largest 32 bit float is 10 sextillion times the diameter of the observable universe. If the value 1.0 of a 64 bit float is a cubic Planck length, then the largest float is 100 sextillion ''googol'' times the volume of the observable universe. [[User:Probably not Douglas Hofstadter|Probably not Douglas Hofstadter]] ([[User talk:Probably not Douglas Hofstadter|talk]]) 17:21, 2 July 2019 (UTC)

It'd be neat to have a map that shows the precision of given coordinates; like how Google Maps shows transparent blue circle with a wider radius if it's location detection isn't very precise. [[Special:Contributions/172.69.170.76|172.69.170.76]] 19:10, 2 July 2019 (UTC)

Something about the formatting of the table seems to be messing up the main page. Not sure what it is, but it happens just after the '110 km (70 mi)' so might be related to the span. Not a major problem as it's fine on the comic page and the main page will change tomorrow anyway. [[User:A(l)Chemist|AlChemist]] ([[User talk:A(l)Chemist|talk]]) 19:43, 2 July 2019 (UTC)

/\
/ \
/____\
information is people
[[Special:Contributions/172.68.34.172|172.68.34.172]] 01:27, 3 July 2019 (UTC)

"more than a quintillion times smaller" that's short scale quintillion, right?
[[User:Kventin|Kventin]] ([[User talk:Kventin|talk]]) 08:04, 3 July 2019 (UTC)

<q>This is probably a reference to the fact that persons are animate, and different persons can occupy the same position at different times.</q>
No it is not. The comic itself explicitly states that it's a reference to the geodetic datum when it says, <q>but since you didn't include datum information, we can't tell who</q>.

<q>As the comic notes, different persons can occupy the same position at different times</q>. Where does it note that? Am I looking at a different comic? [[Special:Contributions/162.158.38.166|162.158.38.166]] 09:57, 3 July 2019 (UTC)

Is there supposed to be a comma after the dash in the description on 15 decimal places? I thought the "beginning - interjection - end of sentence" structure doesn't require a comma since the interjected section is basically a comma in itself. [[Special:Contributions/172.69.44.146|172.69.44.146]] 16:51, 3 July 2019 (UTC)
:As I learned it, a sentence with an interjection should be structured and punctuated as if the interjection were not there, be it enclosed in parentheses or dashes. See “Let's hunt – and then eat –, Grandma!”. [[Special:Contributions/172.68.226.106|172.68.226.106]] 22:40, 3 July 2019 (UTC)

2170: Coordinate Precision

2019-07-03T13:36:47Z

172.68.226.106: /* Chart */ Integrating previous edits

{{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. Each table entry needs to be individually explained. Do NOT delete this tag too soon.}}

This cartoon gives increasingly precise latitude and longitude coordinates for a 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 increasing precision of coordinates in this cartoon are similar to the increasing magnification in the short documentary {{w|Powers of Ten (film)|"Powers of 10,"}} which can be found [http://www.youtube.com/watch?v=0fKBhvDjuy0 here]. (Also parodied in [[271|#271:Powers of One]]).

The coordinates at [https://tools.wmflabs.org/geohack/geohack.php?pagename=Cape_Canaveral&params=28.52345_N_80.68309_W_type:landmark_region:US-FL_scale:10000 28.52345°N, 80.68309°W] (in {{w|decimal degrees}} form; in {{w|geographic coordinate system}} form using degrees, minutes, and seconds, 28° 31′ 24.24.4″N, 80° 40′ 59.1″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 probably a reference to the fact that persons are animate, and different persons can occupy the same position at different times. It might also be a reference to the various ''{{w|geodetic datum}}'' or ''geodetic systems'' — different ways of dealing with the fact that the earth is neither perfectly spherical nor perfectly an oblong ellipsoid. The various data 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 {{w|False precision|meaninglessly precise}} because the measurement wasn't that {{w|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 ''π'' (3.14159265358).

The title text references how at sufficiently small distances, our understanding of reality itself begins to break down. Smaller than the {{w|Planck length}}, which is more than a quintillion times smaller than the diameter of a proton, the ideals of Euclidean geometry no longer apply and space itself may be composed of a {{w|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.

The actual number of longitude digits needed to identify a point with particular precision depends on your latitude. Near the equator, you need more longitude digits than at the poles. The number of latitude digits for some particular accuracy stays essentially the same everywhere. Close to the poles, the chart is increasingly wrong for this reason.

==Chart==

{| class="wikitable"
|-
! Decimal places
! Resolution*
! In the comic
! Location
! Explanation/notes
|-
| 0
| 110 km (70 mi)
| Something space-related
| Somewhere near the east coast of Florida
| This resolution is enough to point out a large-scale feature like a country, a mountain range, a large lake, or a significant island on a map of the world. It can also be used to tell if certain celestial phenomena are visible from a given location.
|-
| 1
| 11 km (7 mi)
| A specific city
| Cape Canaveral
| Cities typically span a couple kilometers/miles in diameter and are far enough from each other to distinguish them at this resolution. There are exceptions though, and the veracity of this statement depends greatly on the definition of a “city”, which varies by location and history.
|-
| 2
| 1.1 km (¾ mi)
| A neighborhood
| Kennedy Space Center Visitor Complex
|
|-
| 3
| 110 m (360 ft)
| A suburban cul-de-sac
| The Rocket Garden at the Kennedy Space Center
|
|-
| 4
| 11 m (36 ft)
| A particular corner of a house
| Somewhere near the center of the Rocket Garden
|
|-
| 5
| 1.1 m (3½ ft)
| A specific person in a room (given geodetic datum information)
| 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 Thor-Delta] rocket in Rocket Garden
| As the comic notes, the differences between {{w|geodetic datum}}s – different ways to map geodetic coordinates to specific points on the Earth's surface – become large enough that one needs to specify the one in use when supplying coordinates to this degree of precision (or greater, of course). Since the Earth is not a perfect ellipsoid, different parts of the planet conform best to ellipsoids of slightly different proportions, resulting in different coordinates for a specific location; not to mention that locally used datums have local reference points, which means that the local and global standards are slowly drifting away from each other with the tectonical plates.
Note that the comment in the comic concerns only the {{w|North American Datum|NAD 1983}} datum which is fairly close to the international, “one size fits all” standard {{w|WGS-84}}. Other datums may be shifted by tens or even hundreds of meters (yards), making geodetic datum specification necessary for less precise coordinates as well.
|-
| 7
| 1.1 cm (⁷⁄₁₆ in)
| Waldo on a page
| Presumably the very tip of the rocket.
| This refers to ''{{w|Where's Wally?|Where's Waldo?}}'', a series of books and magazines containing various scenes (densely packed with people) where one must find Waldo, a character wearing a red and white striped shirt. In the puzzles, he usually stands less than 2 cm (1 in) tall.
Finding Waldo on a page using satellites was also referenced in [[1358:_NRO|#1358]].
|-
| 9
| 0.11 mm (4⅜ thou)
| A specific grain of sand
| rowspan=3 | N/A
|
|-
| 15
| 110 pm (1.1 Å)
| Raw floating point precision or an individual atom
| A double-precision (64-bit) floating point variable stores 52 significant bits (with an implicit 1 in front), so that 180.00000000000000 and 179.99999999999997 may be represented as distinct values. (This is only 14 decimals, however; the larger the integral part, the fewer bits remain to represent the fractional part.) This level of precision is useful for mitigating rounding errors in computations, but this advantage only shows if the last few digits are treated as non-significant and thus, ideally, hidden from view. To work with data that is actually this precise – like tracking individual atoms or representing continental drift up to the second –, one must make allowance for these additional non-significant digits and store the coordinates in ''quadruple'' precision.
To track atoms, however, one needs very sensitive (and expensive) equipment with a severely limited range (according to our current understanding of science and technology). Using a global-scale coordinate system when a micrometer-scale would fit much better is either an abuse of the system and a great waste of memory and computing power, or it means that a significant portion of the Earth's surface has been blanketed by quantum microscopes, which would be an abuse and a waste of many other things as well.
|-
| 40
| 1.1 × 10–11 ym (1.1 × 10–35 m)
| Near (or past) our current understanding of the nature of distance
| This is where the resolution reaches the Planck length (1.6 × 10–35 m). At this scale, the very structure of spacetime (and thus, the notion of distance) may be different than what we know; measuring anything to Planck length precision would necessitate such tremendous amounts of energy in one place that would create minuscule black holes, warping spacetime further (in addition to wreaking havoc with whatever you were trying to pinpoint).
|}
<nowiki>*</nowiki>Since the Earth is not exactly spherical, the actual length of one degree of latitude varies between 110.574 km (68.707 mi) at the equator and 111.694 km (69.403 mi) at the poles, while one degree of longitude is 111.320 km (69.171 mi) at the equator, 55.800 km (34.673 mi) at lat. 60°, and 0 km (0 mi) at the poles.

==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}}

2170: Coordinate Precision

2019-07-03T12:42:18Z

172.68.226.106: Reverting special chars

{{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. Each table entry needs to be individually explained. Do NOT delete this tag too soon.}}

This cartoon gives increasingly precise latitude and longitude coordinates for a 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 increasing precision of coordinates in this cartoon are similar to the increasing magnification in the short documentary {{w|Powers of Ten (film)|"Powers of 10,"}} which can be found [http://www.youtube.com/watch?v=0fKBhvDjuy0 here]. (Also parodied in [[271|#271:Powers of One]]).

The coordinates at [https://tools.wmflabs.org/geohack/geohack.php?pagename=Cape_Canaveral&params=28.52345_N_80.68309_W_type:landmark_region:US-FL_scale:10000 28.52345°N, 80.68309°W] (in {{w|decimal degrees}} form; in {{w|geographic coordinate system}} form using degrees, minutes, and seconds, 28° 31′ 24.24.4″N, 80° 40′ 59.1″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 probably a reference to the fact that persons are animate, and different persons can occupy the same position at different times. It might also be a reference to the various ''{{w|geodetic datum}}'' or ''geodetic systems'' — different ways of dealing with the fact that the earth is neither perfectly spherical nor perfectly an oblong ellipsoid. The various data 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 {{w|False precision|meaninglessly precise}} because the measurement wasn't that {{w|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 ''π'' (3.14159265358).

The title text references how at sufficiently small distances, our understanding of reality itself begins to break down. Smaller than the {{w|Planck length}}, which is more than a quintillion times smaller than the diameter of a proton, the ideals of Euclidean geometry no longer apply and space itself may be composed of a {{w|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.

The actual number of longitude digits needed to identify a point with particular precision depends on your latitude. Near the equator, you need more longitude digits than at the poles. The number of latitude digits for some particular accuracy stays essentially the same everywhere. Close to the poles, the chart is increasingly wrong for this reason.

==Chart==

{| class="wikitable"
|-
! Decimal places
! Resolution*
! In the comic
! Location
! Explanation/notes
|-
| 0
| 110 km (70 mi)
| Something space-related
| Somewhere near the east coast of Florida
| This resolution is enough to point out a large-scale feature like a country, a mountain range, a large lake, or a significant island on a map of the world. It can also be used to tell if certain celestial phenomena are visible from a given location.
|-
| 1
| 11 km (7 mi)
| A specific city
| Cape Canaveral
| Cities typically span a couple kilometers/miles in diameter and are far enough from each other to distinguish them at this resolution. There are exceptions though, and the veracity of this statement depends greatly on what constitutes a “city”, which varies greatly by location and history.
|-
| 2
| 1.1 km (¾ mi)
| A neighborhood
| Kennedy Space Center Visitor Complex
|
|-
| 3
| 110 m (360 ft)
| A suburban cul-de-sac
| The Rocket Garden at the Kennedy Space Center
|
|-
| 4
| 11 m (36 ft)
| A particular corner of a house
| Somewhere near the center of the Rocket Garden
|
|-
| 5
| 1.1 m (3½ ft)
| A specific person in a room (given geodetic datum information)
| 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 Thor-Delta] rocket in Rocket Garden
| As the comic notes, different persons can occupy the same position at different times. It might also point to the differences between {{w|geodetic datum}}s – different ways to map geodetic coordinates to specific points on the Earth's surface – become large enough that one needs to specify the one in use when supplying coordinates to this degree of precision (or greater, of course). Since the Earth is not a perfect ellipsoid, different parts of the planet conform best to ellipsoids of slightly different proportions, resulting in different coordinates for a specific location; not to mention that locally used datums have local reference points, which means that the local and global standards are slowly drifting away from each other with the tectonical plates.
Note that the comment in the comic concerns only the {{w|North American Datum|NAD 1983}} datum which is fairly close to the international, “one size fits all” standard {{w|WGS-84}}. Other datums may be shifted by tens or even hundreds of meters (yards), making geodetic datum specification necessary for less precise coordinates as well.
|-
| 7
| 1.1 cm (⁷⁄₁₆ in)
| Waldo on a page
| Presumably the very tip of the rocket.
| Finding a cartoon character on the page of a book. Specifically refers to ''{{w|Where's Wally?|Where's Waldo?}}.'' Finding Waldo on a page using satellites was also referenced in [[1358:_NRO|#1358]].
|-
| 9
| 0.11 mm (4⅜ thou)
| A specific grain of sand
| rowspan=3 | N/A
|
|-
| 15
| 110 pm (1.1 Å)
| Raw floating point precision or an individual atom
| A double-precision (64-bit) floating point variable stores 52 significant bits (with an implicit 1 in front), so that 180.00000000000000 and 179.99999999999997 may be represented as distinct values. (This is only 14 decimals, however; the larger the integral part, the fewer bits remain to represent the fractional part.) This level of precision is useful for mitigating rounding errors in computations, but this advantage only shows if the last few digits are treated as non-significant and thus, ideally, hidden from view.
To actually track individual atoms (which may be as close to one another as 32 pm) or to represent continental drift up to the second, one would need to work with coordinates in ''quadruple'' precision. Tracking atoms, however, needs very sensitive (and expensive) equipment with a severely limited range (according to our current understanding of science and technology). Using a global-scale coordinate system when a micrometer-scale would fit much better is either an abuse of the system and a great waste of memory and computing power, or it means that a significant portion of the Earth's surface has been blanketed by quantum microscopes, which would be an abuse and a waste of many other things as well.
|-
| 40
| 1.1 × 10–11 ym (1.1 × 10–35 m)
| Near (or past) our current understanding of the nature of distance
| This is where the resolution reaches the Planck length ( 1.6 × 10–35 m). At this scale, the very structure of spacetime (and thus, the notion of distance) may be different than what we know; measuring anything to Planck length precision would necessitate tremendous amounts of energy in one place. This would both create minuscule black holes and, more importantly, move whatever particle you were trying to pinpoint.
|}
<nowiki>*</nowiki>Since the Earth is not exactly spherical, the actual length of one degree of latitude varies between 110.574 km (68.707 mi) at the equator and 111.694 km (69.403 mi) at the poles, while one degree of longitude is 111.320 km (69.171 mi) at the equator, 55.800 km (34.673 mi) at lat. 60°, and 0 km (0 mi) at the poles.

==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}}

1964: Spatial Orientation

2018-03-07T17:21:21Z

172.68.226.106: ayy

{{comic
| number = 1964
| date = March 7, 2018
| title = Spatial Orientation
| image = spatial_orientation.png
| titletext = Here, if you know the number of days until the vernal equinox, I can point you to the theater using my pocket Stonehenge.
}}

==Explanation==
{{incomplete|Created by a DISORIENTED STICK FIGURE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
Title -Spatial Orientation
- I'm facing Westm so the Earth's spin is carrying me backward. But our orbit is carrying me forward around the Sun.
The Sun is passing over my left shoulder. I'm at 39ºN, so I'm tilted. But wait, Earth's axis is tilted by 23º. Do I add or subtract that to get the tilt of the Solar System?
Of, I see the Moon. It follows the Sun's path, but is it moving toward it or away? I know it orbits counterclockwise from the North...
My Head hurts. Let me start over.
- He's just standing there. Hey, do you know which way the theater is or not?
- Let's ask someone else.
Subtitle - I spend way too much time trying to work out my orientation relative to other stuff in the universe.
{{comic discussion}}