2586: Greek Letters - Revision history

172.70.85.107: Undo revision 338326 by 172.71.158.23 (talk) "Squaring the circle" does have a lot of complex arithmatic behind its proof of impossibility... I don't think it hurts to reference.

2024-03-28T06:02:31Z

Undo revision 338326 by 172.71.158.23 (talk) "Squaring the circle" *does* have a lot of complex arithmatic behind its proof of impossibility... I don't think it hurts to reference.

172.71.158.23: Given the rest of the topics and the other sorts of math referenced it's almost certainly a reference to advanced math, not squaring the circle.

2024-03-27T21:57:40Z

Given the rest of the topics and the other sorts of math referenced it's almost certainly a reference to advanced math, not squaring the circle.

172.69.247.57: /* Greek letters */

2024-02-14T15:00:10Z

‎Greek letters

172.71.242.159: /* Explanation */ Rationalising (and nicifying at edit-side).

2023-12-01T14:13:34Z

‎Explanation: Rationalising (and nicifying at edit-side).

141.101.99.81: /* Greek letters */ typo

2023-12-01T09:21:24Z

‎Greek letters: typo

Stubbly: /* Greek letters */

2023-09-12T11:38:51Z

‎Greek letters

172.70.34.187: this was uppercase phi; make it lowercase like the explanation says

2023-05-29T20:43:56Z

this was uppercase phi; make it lowercase like the explanation says

TenGolf MathHacker: /* Greek letters */ neutrino is more commonly nu

2023-04-08T02:11:33Z

‎Greek letters: neutrino is more commonly nu

172.69.162.141: /* Greek letters */

2023-03-20T02:19:46Z

‎Greek letters

Theusaf: fix escape of html entity

2022-12-04T19:27:54Z

fix escape of html entity

@@ Line 16: / Line 16: @@
 ===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.
+* '''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 {{w|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, so-called omega pi {{w|Pi (letter)#Variant pi|ϖ}} sometimes used for angular frequency instead of the more common (and very similar-looking) lowercase omega ω. In astronomy, ϖ is traditionally used to denote the {{w|Longitude of the periapsis|longitude of perihelion}}.)
 ** In a field of math known as {{w|algebraic topology|algebraic topology}}, it is standard to use π to denote the {{w|homotopy group}}s. Despite decades of study, the {{w|homotopy groups of spheres}} in high dimensions are unknown.

@@ Line 16: / Line 16: @@
 ===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.
+* '''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.
 ** 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, so-called omega pi {{w|Pi (letter)#Variant pi|ϖ}} sometimes used for angular frequency instead of the more common (and very similar-looking) lowercase omega ω. In astronomy, ϖ is traditionally used to denote the {{w|Longitude of the periapsis|longitude of perihelion}}.)
 ** In a field of math known as {{w|algebraic topology|algebraic topology}}, it is standard to use π to denote the {{w|homotopy group}}s. Despite decades of study, the {{w|homotopy groups of spheres}} in high dimensions are unknown.

@@ Line 30: / Line 30: @@
 * '''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 (positive) 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. This Greek lowercase letter has two common modern variants, ϵ and ε. ϵ is called the "{{w|Epsilon#Unicode|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 (positive) 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. neutrino) 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]].
+* '''<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. neutrino) 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]]. The use of both terms together is most commonly seen when performing integration by parts, a famously counterintuitive method of integration (one of ''those'').
 * '''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. Also used in statistics for the mean (average). 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 that 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 materials 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.

@@ Line 8: / Line 8: @@
 ==Explanation==
-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]].
+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.
@@ Line 17: / Line 17: @@
 * '''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, so-called omega pi {{w|Pi_(letter)#Variant_pi|ϖ}} sometimes used for angular frequency instead of the more common (and very similar-looking) lowercase omega ω. In astronomy, ϖ is traditionally used to denote the {{w|Longitude of the periapsis|longitude of perihelion}}.)
+** 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, so-called omega pi {{w|Pi (letter)#Variant pi|ϖ}} sometimes used for angular frequency instead of the more common (and very similar-looking) lowercase omega ω. In astronomy, ϖ is traditionally used to denote the {{w|Longitude of the periapsis|longitude of perihelion}}.)
-** In a field of math known as {{w|algebraic topology|algebraic topology}}, it is standard to use π to denote the {{w|Homotopy_group|homotopy groups}}. Despite decades of study, {{w|Homotopy_groups_of_spheres|the homotopy groups of high-dimensional spheres}} are unknown.
+** In a field of math known as {{w|algebraic topology|algebraic topology}}, it is standard to use π to denote the {{w|homotopy group}}s. Despite decades of study, the {{w|homotopy groups of spheres}} in high dimensions are unknown.
 * '''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'').
@@ Line 40: / Line 40: @@
 * '''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 a 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.
+* '''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 a 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]].  In aviation, α refers to {{w|angle of attack}}, which could cause a deadly {{w|Stall (fluid dynamics)|aerodynamic stall}} if it gets too large.  Another dangerous meaning for α comes from ionizing 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}}, the {{w|first uncountable ordinal}}, and {{w|Absolute Infinity}}. 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 reportedly 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 (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}}, the {{w|first uncountable ordinal}}, and {{w|Absolute Infinity}}. 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 reportedly 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'''.
+* '''ω (lowercase omega): A lot of work went into these equations and you are going to die here among them.''' — Used for the least {{w|transfinite number}} of ordinals, 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.

@@ Line 18: / Line 18: @@
 * '''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, so-called omega pi {{w|Pi_(letter)#Variant_pi|ϖ}} sometimes used for angular frequency instead of the more common (and very similar-looking) lowercase omega ω. In astronomy, ϖ is traditionally used to denote the {{w|Longitude of the periapsis|longitude of perihelion}}.)
-** In a field of math known as {{w|algebraic topology|algebraic topology}}, it is standard to use π to denote the {{w|Homotopy_group|homotopy groups}}. Despite decades of study, the {{w|Homotopy_groups_of_spheres|the homotopy groups of high-dimensional spheres}} are unknown.
+** In a field of math known as {{w|algebraic topology|algebraic topology}}, it is standard to use π to denote the {{w|Homotopy_group|homotopy groups}}. Despite decades of study, {{w|Homotopy_groups_of_spheres|the homotopy groups of high-dimensional spheres}} are unknown.
 * '''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'').

@@ Line 66: / Line 66: @@
 :δ Something has changed and it's a mathematician's fault.
 :θ Circles!
-:Φ '''''O R B S'''''
+:ϕ '''''O R B S'''''
 :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''.

@@ Line 55: / Line 55: @@
 * '''ρ (lowercase rho): Unfortunately, the test vehicle suffered an unexpected wing separation event.''' — Used in statistics to measure the association between variables. Lowercase rho often represents volumetric mass density, such as the density of air that a wing might be traveling 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 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 ≡. Coincidentally, it also resembles the Chinese or Japanese character for the [https://en.wikibooks.org/wiki/Chinese_(Mandarin)/Numbers number 3] (&amp;#19977;). Randall thinks it most closely resembles alien writing.
+* '''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 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 ≡. Coincidentally, it also resembles the Chinese or Japanese character for the [https://en.wikibooks.org/wiki/Chinese_(Mandarin)/Numbers number 3] (&#19977;). 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 classical mythology, {{w|Triton}} is one of the gods of the sea, alongside his father Poseidon, and tridents are commonly associated with sea gods. 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, the supergolden ratio, and other purposes.)

2586: Greek Letters - Revision history

172.70.85.107: Undo revision 338326 by 172.71.158.23 (talk) "Squaring the circle" *does* have a lot of complex arithmatic behind its proof of impossibility... I don't think it hurts to reference.

172.71.158.23: Given the rest of the topics and the other sorts of math referenced it's almost certainly a reference to advanced math, not squaring the circle.

172.69.247.57: /* Greek letters */

172.71.242.159: /* Explanation */ Rationalising (and nicifying at edit-side).

141.101.99.81: /* Greek letters */ typo

Stubbly: /* Greek letters */

172.70.34.187: this was uppercase phi; make it lowercase like the explanation says

TenGolf MathHacker: /* Greek letters */ neutrino is more commonly nu

172.69.162.141: /* Greek letters */

Theusaf: fix escape of html entity

172.70.85.107: Undo revision 338326 by 172.71.158.23 (talk) "Squaring the circle" does have a lot of complex arithmatic behind its proof of impossibility... I don't think it hurts to reference.