explain xkcd - User contributions [en]

2586: Greek Letters

2022-03-01T18:02:25Z

TreyHarris: /* Greek letters */ change υ,ν to serif—as the joke points at, they look just like the Latin letters in many common sans-serifs

{{comic
| number = 2586
| date = February 25, 2022
| title = Greek Letters
| image = greek_letters.png
| titletext = If you ever see someone using a capital xi in an equation, just observe them quietly to learn as much as you can before they return to their home planet.
}}

==Explanation==
{{incomplete|Created by '''''O R B S''''' PRO®- Missing explanations for some letters. The text for each letter should be in the explanation with an attempt at explaining it. This has not been included and many of the letters have no explanation of the given text, only for what they actually are used for. Do NOT delete this tag too soon.}}
Mathematics uses lots of Greek letters, typically using {{w|Greek_letters_used_in_mathematics,_science,_and_engineering|the same letter consistently}} to represent a particular constant or type of variable. This comic gives a (non-)explanation of what they typically mean, see [[#Greek letters|below]].

In the title text the joke about capital Xi from the main comic is continued. In the main comic those using Ξ (capital xi) greets us as Earth mathematicians, indicating they are not from Earth, but have come here to learn what we know of math. In the title text the idea that any one using Ξ must be aliens is made clear. So if you ever meet someone using this letter while doing math, then learn as much as you can by quietly observing them, before they return to their home planet. Either learn from their possible advanced math (that allowed them to construct a way to get from one star system to another), or learn about them as the aliens species they represent.

Previously [[Randall]] made a similar comic, [[2520: Symbols]], about math symbols.

===Greek letters===

* '''π (lowercase pi): This math is either very simple or impossible.''' — Typically used to refer to the constant ratio between a circle’s circumference and its diameter (approximately 3.14). In a common school curriculum, this constant first shows up in introductory geometry classes, which would be considered "simple" by advanced mathematicians. But often, pi can show up seemingly randomly in advanced equations that have nothing to do with a circle at first glance, such as in infinite series. And because pi is transcendental, it can sometimes be difficult to work with pi in those situations. The comic may also be a reference to the impossibility of squaring the circle.
* An alternate explanation is that the comic refers to how the symbol can sometimes be used as a variable where the 'p' sound might make sense, such as in the prime-counting function where it stands for "prime" or the Buckingham π theorem where it stands for "parameter." These uses can be confusing to students who have only ever seen a lowercase pi used for the circle constant. This has pushed college courses to use it less and less frequently for anything other than the circle constant, so that now you are only likely to see π as something else in higher math. (More confusing still is the variant lowercase pi ϖ sometimes used for angular frequency instead of the more common (and very similar-looking) lowercase omega ω.)

* '''Δ (capital delta): Something has changed.''' — Typically prefixes a variable to refer to a macroscopic change in or finite difference of that variable. For instance, Δ'''v''' may be the finite change in velocity '''v''' over some finite time span, while Δ[''f''](''x'') represents the forward difference of ''f'' at ''x'', defined as Δ[''f''](''x'') = ''f''(''x''+1) - ''f''(''x'').

* '''δ (lowercase delta): Something has changed and it's a mathematician's fault.''' — In many areas of maths we study systems by introducing small changes (perturbations) in input variables and observing how the system changes. The perturbations introduced are often written down as ''x'' → ''x'' + ''δx'' for some variable ''x'' we're perturbing, where ''δx'' is the change we've introduced. These are often applied in physics (perturbation theory, principle of least action, Noether's theorem,…). Since this change was purposefully introduced by the mathematician instead of occurring naturally, it is therefore their fault.

* '''θ (lowercase theta): Circles!''' — Typically used to refer to an angle, and is notably used in the polar coordinate system. The text refers to its close relationship with circles, on which the polar coordinate system is based. In European handwriting, the variant form ϑ is commonly used with the same meaning.

* '''φ (lowercase phi): ''ORBS''''' — Typically used to refer to another angle other than one referred to by theta. It's used in spherical coordinates, and the text refers to how spheres, or orbs, are important in spherical coordinates. Lowercase phi has two forms in modern typography which are confused by this website's default font. In the comic, it has a complete circle with a vertical line passing through it, which is what Knuth called "phi." The alternate form, ϕ, is what Knuth called "variant phi" and can be written in a single stroke. Most fonts reverse the way these symbols are rendered. There is no difference in meaning between the symbols.

* '''ϵ (lowercase epsilon): Not important, don't worry about it.''' — Typically used to refer to a very small quantity. ϵ may be an error term in a statistical model (which is usually small if the model is useful), a remainder term in an approximation (same), or an arbitrarily small quantity in analysis. Although a total cumulative change of "ϵ" is negligible, in analysis, ϵ is most often applied in a context of an infinitesimal change occurring with infinite frequency. The study of ratios of quantities that approach zero gives rise to infinitesimal calculus. Also used for a sequence of transfinite numbers that are unreachable from ω by finite application of addition, multiplication, and exponentiation. This Greek lowercase letter has two common modern variants, ϵ and ε. ϵ is called the "lunate epsilon" and may be more common in the U.S. A stylized version (∈) is used as the mathematical symbol for "is an element of." ε is what Knuth called the "variant epsilon" and is never used for the "element of" symbol but otherwise has identical meaning. Because epsilon represents an arbitrarily small quantity, there's no reason for anyone to worry about it from a practical standpoint.

* '''<span style="font-family: serif;">υ,ν</span> (lowercase upsilon and nu): Is that a v or a u? Or...oh no, it's one of ''those''.''' — Common in college level physics and engineering equations. <span style="font-family: serif;">ν</span> commonly represents wavenumber in physics as well as a wide variety of other variables, often with names starting in N (e.g. neutron) or V (e.g. viscosity). Lowercase upsilon is rarely used, probably to avoid confusion. The symbols look remarkably similar to Latin u and v, to the point that they are nearly indistinguishable in some fonts; Randall has complained about this before in [[2351: Standard Model Changes]].

* '''μ (lowercase mu): This math is cool but it's not about anything that you will ever see or touch, so whatever.''' — Used broadly in the abstract mathematical fields of category theory and measure theory. Physicists use Latin letters for the indices of the 3-vectors of classical physics and Greek indices, including μ, for the 4-vectors of special relativity. This leads to μ being ubiquitous in a field which is very far from everyday experience (where speeds approach the speed of light). It is also employed in statistics for the population mean, which is a quantity that the statistician never actually knows and frequently wants to estimate. Equations requiring a μ are thus impossible to apply directly. However, μ is used in physics for the coefficient of friction in the Coulomb model, typically used to approximate resistive forces between dry solids of different material sliding past each other. A very common use of μ in science and engineering is as the symbol of the SI prefix ''micro-'' for a millionth. Unicode has officially added a point for μ as the "micro sign," distinct from its usual codepoint as the lowercase Greek letter mu.

* '''Σ (capital sigma): Thank you for purchasing ''Addition Pro''®!''' — Typically used as a symbol for the sum of a series of numbers. The comic is making fun of summation, pointing out that it's essentially a complicated, "pro" version of simple addition. The capital sigma is often used as the icon for the all-important "sum" button in spreadsheet software. However, the sigma operator is often necessary for explicitly defining infinite sums, avoiding ambiguous notation like an ellipsis (...).

* '''Π (capital pi): ...and the ''Multiplication''® expansion pack!''' — Typically used as a symbol for the product of a sequence of numbers. The joke is the same as for summation. Here, it is advertised as an "expansion pack," a term used for a piece of software that cannot stand alone but adds features to some existing software. Any paid spreadsheet or database program should already have the ability to perform products. The ® symbol indicates that ''Multiplication'' is a registered trademark somewhere, which is unlikely, as the term is not unique. However, common words are registered as trademarks rather often.

* '''ζ (lowercase zeta): This math will only lead to more math.''' — Frequently used for the {{w|Riemann zeta function}} in analytic number theory, a function of complex numbers which is challenging even to define and which is the focus of a famously unsolved problem in highly advanced mathematics. Zeta is used much less often in other contexts, such as the ζ-potential in colloidal chemistry, and even there it is likely to just lead to more math.

* '''β (lowercase beta): There are just too many coefficients.''' — This could be a reference to the typical usage of beta to represent coefficients of independent variables in the {{w|Ordinary_least_squares#Linear_model|ordinary least squares regression model}}. Regression can potentially have a large number of independent variables, hence potentially many different betas (differentiated by subscript, or compacted into matrix notation) would be used, while there is only ever a single zeroth-order coefficient α in these models. Alternatively, the comic might suggest whatever source this equation is from has run out of Latin letters to use as symbols, and is now going through the Greek letters.

* '''α (lowercase alpha): Oh boy, now ''this'' is math about something real. This is math that could ''kill'' someone.''' — As the first Greek letter, α is used for a tremendous variety of purposes in math. For example, it is used to represent the probability of a Type-I error (false positive) occurring in a hypothesis test. It could also possibly refer to the {{w|fine-structure constant}} which shows up in high energy physics, atomic physics, quantum electrodynamics, and at least [[1047|one other xkcd comic]]. Alpha could also refer to {{w|angular acceleration}}, and a rapidly-rotating system is capable of killing people in a number of [[123|interesting ways]]. Another dangerous meaning for α comes from ionising α-radiation: while it can be easily blocked by even a sheet of paper, it has been {{W|Alexander Litvinenko#Poisoning and death|used for assassinations}} through ingestion.

* '''Ω (capital omega): Oooh, ''some'' mathematician thinks their function is cool and important.''' — The last letter of the Greek alphabet and thus often seen as momentous (the end, the final word, death). The capital letter has been used as the symbol for a {{w|Omega_function|variety of mathematical functions}} and for the {{w|first uncountable ordinal}}. It is commonly used in physics and electrical engineering as the symbol for {{w|ohms}}, a unit for electrical resistance. Capital omega has produced a fascination in common culture, perhaps due to God describing himself as "the alpha and the omega" in the Book of Revelation or due to its highly distinctive shape. It is often used to represent something of grave or transcendent significance. So using it to name your function (instead of a conventional symbol like ''f'' or ''g'') may mean you think the function is particularly important.

* '''ω (lowercase omega): A lot of work went into these equations and you are going to die here among them.''' — Used for the {{w|Transfinite_number|least transfinite ordinal number}}, the order type of the natural numbers under '<'. The line about dying here among the transfinite equations may be in reference to the "eternity" of the infinite set it represents. It is also used in physics and electrical engineering for angular frequency, equal to 2π times the frequency, and thus it is ubiquitous in equations dealing with all sorts of wave phenomena. '''ω''' is also used for the angular velocity of a rotating system, defined by '''v''' = '''r'''×'''ω'''.

* '''σ (lowercase sigma): Some poor soul is trying to apply this math to real life and it's not working.''' — In statistics, σ commonly refers to the population standard deviation of a distribution. Many simplified statistical equations substitute the population standard deviation σ for the sample standard deviation s for simplicity, even when this is not justifiable. A common example is using the normal distribution to model the mean of several identically-normally-distributed variables instead of the T distribution. The variant ς is used at the end of Greek words (called the "final sigma") but is rarely used in math or science.

* '''ξ (lowercase xi): Either this is terrifying mathematics or there was a hair on the scanned page.''' — Randall comments that this looks like a strand of curly hair. Xi is used in the {{w|Riemann Xi function}} and sometimes as a variable or function symbol in higher math. It is famously difficult to write in a way that is consistent and clearly distinct from other symbols.

* '''γ (lowercase gamma): ''Zoom'' pew pew pew [space noises] ''zoooom!''''' — Lowercase gamma is used for the Lorentz factor, an important variable in special relativity calculations. Its use implies that you are dealing with speeds approaching the speed of light and therefore with spaceships or other moving objects not confined to Earth. γ-rays are also the highest energy photons, so a space opera might have ships flying near the speed of light firing gamma-ray weapons that go PEW PEW. γ is also used as the symbol for the Euler-Mascheroni constant and occasionally as a variable or function name.

* '''ρ (lowercase rho): Unfortunately, the test vehicle suffered an unexpected wing separation event.''' — Lowercase rho often represents volumetric mass density, such as the density of air that a wing might be travelling through. The density of a fluid is directly proportional to the Reynold's number which dictates the sort of physics used to model motion through the fluid. Flying a plane in conditions with a Reynold's number well outside of what it was designed for could have catastrophic consequences. A variant symbol ϱ with the same meaning is common in European handwriting.

* '''Ξ (capital xi): Greetings! We hope to learn a great deal by exchanging knowledge with your Earth mathematicians.''' — Probably the least used Greek letter in math and physics despite being easy to write and to recognize. According to the comic, anyone using this letter is likely a being from another planet. It does see very occasional use, such as in the Riemann xi function or as the symbol for a class of heavy baryons in particle physics. It resembles, but is not to be confused with a "hamburger button" or a triple equals sign ≡. Randall thinks it most closely resembles alien writing.

* '''ψ (lowercase psi): You have entered the domain of King Triton, ruler of the waves.''' — Both capital and lowercase psi are shaped like tridents. In quantum mechanics, either psi is used to represent the wave function of a particle, leading to a pun. (Psi is also used in mathematics to represent the sum of the inverse of the Fibonacci numbers, the division polynomials, and the supergolden ratio, and other purposes.)

==Transcript==
:[A list with 21 explanations of different Greek letters. To the left the letter (on in one case two letters) are shown, and then the explanation is written to the right in one or two lines (and in one case on three lines). Above these explanations there is a header in a slightly larger font:]
:<big>What Greek letters mean in equations</big>
:π This math is either very simple or impossible.
:Δ Something has changed.
:δ Something has changed and it's a mathematician's fault.
:θ Circles!
:Φ '''''ORBS'''''
:ϵ Not important, don't worry about it.
:υ,ν Is that a v or a u? Or...oh no, it's one of ''those''.
:μ This math is cool but it's not about anything that you will ever see or touch, so whatever.
:Σ Thank you for purchasing ''Addition Pro''®!
:Π ...and the ''Multiplication''® expansion pack!
:ζ This math will only lead to more math.
:β There are just too many coefficients.
:α Oh boy, now ''this'' is math about something real. This is math that could ''kill'' someone.
:Ω Oooh, ''some'' mathematician thinks their function is cool and important.
:ω A lot of work went into these equations and you are going to die here among them.
:σ Some poor soul is trying to apply this math to real life and it's not working.
:ξ Either this is terrifying mathematics or there was a hair on the scanned page.
:γ ''Zoom'' pew pew pew [space noises] ''zoooom!''
:ρ Unfortunately, the test vehicle suffered an unexpected wing separation event.
:Ξ Greetings! We hope to learn a great deal by exchanging knowledge with your Earth mathematicians.
:ψ You have entered the domain of King Triton, ruler of the waves.

{{comic discussion}}

[[Category:Math]]
[[Category:Aliens]]

2170: Coordinate Precision

2019-07-01T22:24:32Z

TreyHarris: /* Explanation */ link syntax

{{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).

==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

2019-07-01T20:58:57Z

TreyHarris: /* Explanation */ Add DMS form

{{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 data}}'' 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.

==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

2019-07-01T20:49:30Z

TreyHarris: /* Explanation */ formatting, grammar

2170: Coordinate Precision

2019-07-01T20:42:22Z

TreyHarris: /* Explanation */ typos

2170: Coordinate Precision

2019-07-01T20:41:28Z

TreyHarris: /* Explanation */ change external links to template links

2170: Coordinate Precision

2019-07-01T20:36:41Z

TreyHarris: /* Explanation */ more links to geodata and location

{{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. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

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] are pointing to the [https://en.wikipedia.org/wiki/Rocket_garden Rocket Garden] at [https://en.wikipedia.org/wiki/Kennedy_Space_Center Kennedy Space Center] in [https://en.wikipedia.org/wiki/Merritt_Island,_Florida|Merritt Island, Florida], usually referred to as [https://en.wikipedia.org/wiki/Cape_Canaveral 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 [https://en.wikipedia.org/wiki/Geodetic_datum ''geodetic data''] or ''geodetic systems'' — different ways of dealing with the fact that the earth is not either 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.

==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

2019-07-01T20:24:31Z

TreyHarris: /* Explanation */ fix interwiki link

2170: Coordinate Precision

2019-07-01T20:15:11Z

TreyHarris: /* Explanation */ geodetic datum

2170: Coordinate Precision

2019-07-01T20:09:26Z

TreyHarris: /* Explanation */ spelling

1002: Game AIs

2015-06-19T16:44:28Z

TreyHarris: /* Humans Beat Computers */ Updated Arimaa section wrt computers vs AI in 2015

{{comic
| number = 1002
| date = January 11, 2012
| title = Game AIs
| image = game_ais.png
| titletext = The top computer champion at Seven Minutes in Heaven is a Honda-built Realdoll, but to date it has been unable to outperform the human Seven Minutes in Heaven champion, Ken Jennings.
}}

==Explanation==
To understand the comic, you have to understand what the games are, so let's go (but first, the years in parenthesis in the comic are the year that the game was mastered by a computer):

===Solved===

: These games are considered "solved", meaning the ideal maneuver for each game state (Tic-Tac-Toe, Connect Four) or each of the limited starting positions (Checkers) has already been calculated. Computers aren't so much playing as they are recalculating the list of ideal maneuvers. The same could be said for the computer's human opponent, just at a slower pace.

*'''{{w|Tic-tac-toe}}''' or '''Noughts and Crosses''' in most of the rest of the British Commonwealth countries is a pencil-and-paper game for two players, X and O, who take turns marking the spaces in a 3×3 grid. This game nearly always ends in a tie, regardless of whether humans or computers play it, because the amount of positions is minimal.

*'''{{w|Nim}}''' is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap.

*'''{{w|Ghost (game)|Ghost}}''' is a spoken word game in which players take turns adding letters to a growing word fragment. The loser is the first person who completes a valid word or who creates a fragment that cannot be the start of a word.

*'''{{w|Connect Four}}''' (or '''Captain's Mistress''', '''Four Up''', '''Plot Four''', '''Find Four''', '''Fourplay''', '''Four in a Row''', '''Four in a Line''') is a two-player game in which the players first choose a color and then take turns dropping their colored discs from the top into a seven-column, six-row vertically-suspended grid.

*'''{{w|Gomoku}}''' (or '''Gobang''', '''Five in a Row''') is an abstract strategy board game. It is traditionally played with go pieces (black and white stones) on a go board (19x19 intersections); however, because once placed, pieces are not moved or removed from the board, gomoku may also be played as a paper and pencil game. This game is known in several countries under different names.
:Black plays first, and players alternate in placing a stone of their color on an empty intersection. The winner is the first player to get an unbroken row of five stones horizontally, vertically, or diagonally.

*'''{{w|Draughts|Checkers}}''' (in the United States, or '''draughts''' in the United Kingdom) is a group of strategy board games for two players which involve diagonal moves of uniform game pieces and mandatory captures by jumping over opponent pieces.

===Computers Beat Humans===

:The below games cannot be "solved" due to the factors of random numbers, a near-infinite{{Citation needed}} number of starting positions, or the existence of multiple "ideal" maneuvers for each position. That said, a computer's faster reaction time, higher degree of consistency in making the right decision, and reduced risk of user error make the computer objectively better than the human opponent in nearly all situations.

*'''{{w|Scrabble}}''' is a word game in which two to four players score points by forming words from individual lettered tiles on a gameboard marked with a 15-by-15 grid.

*'''{{w|Counter-Strike|CounterStrike}}''' most likely refers to the popular multiplayer shooter video game about terrorists and counter-terrorists. Counter-Strike is notorious for the large variety of cheating tools that have been made for it; a computer would have essentially perfect accuracy and reflexes, essentially making it the {{w|aimbot}} from hell. It is theoretically possible for a skilled player to beat an AI, but it would be ''extremely'' difficult to do so.

*'''{{w|Beer pong}}''' (or '''Beirut''') is a drinking game in which players throw a ping pong ball across a table with the intent of landing the ball in a cup of beer on the other end.
:[http://hacknmod.com/hack/beer-pong-robot-precision-air-pressure/ Here's the video] of the University of Illinois robot mentioned in the comic.

*'''{{w|Reversi}}''' (marketed by Pressman under the trade name '''Othello''') is a board game involving abstract strategy and played by two players on a board with 8 rows and 8 columns and a set of distinct pieces for each side. Pieces typically are disks with a light and a dark face, each face belonging to one player. The player's goal is to have a majority of their colored pieces showing at the end of the game, turning over as many of their opponent's pieces as possible.

*'''{{w|Chess}}''' is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. Each player begins the game with sixteen pieces: one king, one queen, two rooks, two knights, two bishops, and eight pawns, each of these types of pieces moving differently.

*'''{{w|Jeopardy!}}''' is an American quiz show featuring trivia in history, literature, the arts, pop culture, science, sports, geography, wordplay, and more. The show has a unique answer-and-question format in which contestants are presented with clues in the form of answers, and must phrase their responses in question form.
:Ken Jennings, mentioned in the title text, is a famous Jeopardy champion who was beaten by {{w|Watson (computer)|Watson}}, an IBM computer.

===Humans Beat Computers===

:The below games are incredibly difficult to "solve" due to the near-infinite number of possible positions. Computers built in the early 21st century would take years to calculate a single "ideal" move. Worse, the human opponent has the ability to "bluff"; that is, to make a bad move, thus baiting the computer into a trap. Complex algorithms have been devised to make moves in a reasonable timeframe, but so far they are all highly vulnerable to bluffing. As mentioned in the comic, focused research and development is working on refining these algorithms to play the games better.

*'''{{w|StarCraft}}''' is a military science fiction real-time strategy video game. The game revolves around three species fighting for dominance in a distant part of the Milky Way galaxy known as the Koprulu Sector: the Terrans, humans exiled from Earth skilled at adapting to any situation; the Zerg, a race of insectoid aliens in pursuit of genetic perfection, obsessed with assimilating other races; and the Protoss, a humanoid species with advanced technology and psionic abilities, attempting to preserve their civilization and strict philosophical way of living from the Zerg. While even average Starcraft players can defeat the AIs that originally shipped with the games, Starcraft has since been adopted as a standard benchmark for AI research, largely because of its excellent balance. Thanks to that attention, computers can now challenge some expert players, and the trend does not look promising for human players.

*'''{{w|Poker}}''' is a family of card games involving betting and individualistic play whereby the winner is determined by the ranks and combinations of their cards, some of which remain hidden until the end of the game. It is also, however, a game of deception and intimidation, the ubiquitous "poker face" being considered the most important part of the game.

*'''{{w|Arimaa}}''' is a two-player abstract strategy board game that can be played using the same equipment as chess. Arimaa was designed to be more difficult for artificial intelligences to play than chess. Arimaa was invented by Omar Syed, an Indian American computer engineer trained in artificial intelligence. Syed was inspired by Garry Kasparov's defeat at the hands of the chess computer Deep Blue to design a new game which could be played with a standard chess set, would be difficult for computers to play well, but would have rules simple enough for his then four-year-old son Aamir to understand. On April 18, 2015, a computer won [http://arimaa.com/arimaa/challenge/|the "Arimaa Challenge"], so this comic is now out of date with respect to Arimaa; it should move above ''Starcraft'' or ''Jeopardy!''.

*'''{{w|Go (game)|Go}}''' is an ancient board game for two players that originated in China more than 2,000 years ago. The game is noted for being rich in strategy despite its relatively simple rules. The game is played by two players who alternately place black and white stones on the vacant intersections (called "points") of a grid of 19×19 lines (beginners often play on smaller 9×9 and 13×13 boards). The object of the game is to use one's stones to surround a larger portion of the board than the opponent.

*'''{{w|Snakes and Ladders}}''' (or '''Chutes and Ladders''') is an ancient Indian {{w|race game}}, where the moves are decided entirely by die rolls. A number of tiles are connected by pictures of ladders and snakes (or chutes) which makes the game piece jump forward or backward, respectively. Since the game is decided by pure chance, it occupies the limbo where a computer will always be ''exactly'' as likely to win as a human.

===Computers cannot compete===

*'''{{w|Mao (card game)|Mao}}''' (or '''Mau''') is a card game of the Shedding family, in which the aim is to get rid of all of the cards in hand without breaking certain unspoken rules. The game is from a subset of the Stops family, and is similar in structure to the card game Uno or Crazy Eights.
:The game forbids its players from explaining the rules, and new players are often told only "the only rule you may be told is this one." The ultimate goal of the game is to be the first player to get rid of all the cards in their hand. Computers would have a difficult time integrating into Mao either because they would know all the rules -- and thus be disqualified or simply ignored by the players -- or would need a complicated learning engine that quite simply doesn't exist.

*'''{{w|Seven minutes in heaven|Seven Minutes in Heaven}}''' is a teenagers' party game first recorded as being played in Cincinnati in the early 1950s. Two people are selected to go into a closet or other dark enclosed space and do whatever they like for seven minutes. Sexual activities are allowed; however kissing and making out are more common.
:As the game is focused on human interaction, there's not a whole lot a modern computer can ''do'' in the closet. It would need some kind of robotic body in order to interact with its human partner, and emotion engines that could feel pleasure and displeasure in order to make decisions. The title text claims that {{w|Honda|Honda Motor Company}} has invented a "{{w|RealDoll}}" (sex toy shaped like a mannequin) with rudimentary Seven Minutes in Heaven capabilities, but they pale in comparison to a human's.

And finally
*'''{{w|Calvin and Hobbes#Calvinball|Calvinball}}''' is a reference to the comic strip {{w|Calvin and Hobbes}} by {{w|Bill Watterson}}.
:Calvinball is a game played by Calvin and Hobbes as a rebellion against organized team sports; according to Hobbes, "No sport is less organized than Calvinball!" Calvinball was first introduced to the readers at the end of a 1990 storyline involving Calvin reluctantly joining recess baseball. It quickly became a staple of the comic afterwards.
:The only hint at the true creation of the game ironically comes from the last Calvinball strip, in which a game of football quickly devolves into a game of Calvinball. Calvin remarks that "sooner or later, all our games turn into Calvinball," suggesting a similar scenario that directly led to the creation of the sport. Calvin and Hobbes usually play by themselves, although in one storyline Rosalyn (Calvin's baby-sitter) plays in return for Calvin doing his homework, and plays very well once she realizes that the rules are made up on the spot.
:The only consistent rule states that Calvinball may never be played with the same rules twice. Scoring is also arbitrary, with Hobbes at times reporting scores of "Q to 12" and "oogy to boogy." The only recognizable sports Calvinball resembles are the ones it emulates (i.e., a cross between croquet, polo, badminton, capture the flag, and volleyball.)
::Long story short, the game is a manifestation of pure chaos and the human imagination, far beyond the meager capabilities of silicon and circuitry.

==Transcript==
:Difficulty of Various Games for Computers

:[A diagram. The left column describes various levels of skill for the most capable computers in decreasing performance against humans. The right side lists games in each particular section, in increasing game difficulty. There are labels denoting the hard and easy ends of the diagram.]

:'''Easy'''
:{|border="small"
| rowspan="6" | Solved - Computers can play perfectly
| rowspan="4" | Solved for all possible positions
| Tic-tac-toe
|-
| Nim
|-
| Ghost (1989)
|-
| Connect Four (1995)
|-
| rowspan="2" | Solved for starting positions
| Gomoku
|-
| Checkers (2007)
|-
| rowspan="6" colspan="2" | Computers can beat top humans
| Scrabble
|-
| CounterStrike
|-
| Beer Pong (UIUC robot)
|-
| Reversi
|-
| Chess
* February 10, 1996 - First win by computer against top human
* November 21, 2005 - Last win by human against top computer
|-
| Jeopardy (but just barely)
|-
| colspan="2" rowspan="4" | Computers still lose to top humans
(but focused R&D could change this)
| StarCraft (but just barely)
|-
| Poker
|-
| Arimaa
|-
| Go
|-
| colspan="2" rowspan="1" |
| Snakes and Ladders
|-
| colspan="2" rowspan="4" | Computers may ''never'' outplay humans
|-
| Mao
|-
| Seven Minutes in Heaven
|-
| Calvinball
|-
|}
:'''Hard'''

{{comic discussion}}
[[Category:Charts]]
[[Category:Video games]]
[[Category:Chess]]
[[Category:Calvin and Hobbes]]