explain xkcd - User contributions [en]

Talk:2586: Greek Letters

2022-02-28T20:06:56Z

ThomasGauss:

Pi also shows up in lots of extremely advanced equations as pi, not as something else, adding edit. 123.456.7890

zeta_0 is also used for the first transfinite ordinal that is unreachable through addition, multiplication, exponentiation, and epsilons subscripting. EDIT: phi is used for the Veblen hierachy. [[User:GcGYSF(asterisk)P(vertical line)e|GcGYSF(asterisk)P(vertical line)e]] ([[User talk:GcGYSF(asterisk)P(vertical line)e|talk]]) 05:11, 26 February 2022 (UTC)

Don't you have an English saying: '''simple/easy as π'''? [[User:Nukio|Nukio]] ([[User talk:Nukio|talk]]) 05:51, 26 February 2022 (UTC)
:the saying is '''easy as pie''' as in the dessert. sometimes we write it '''easy as π''' as a nerdy joke. [[Special:Contributions/162.158.107.230|162.158.107.230]] 08:08, 26 February 2022 (UTC)
:: sqrt(-1) 2³ Σ π and it was delicious [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 08:30, 28 February 2022 (UTC)

Related: https://xkcd.com/2520/ [[Special:Contributions/162.158.103.224|162.158.103.224]] 08:59, 26 February 2022 (UTC)

I've found a use for capital Xi: https://en.wikipedia.org/wiki/Harish-Chandra%27s_%CE%9E_function that seems to be from the field of Harmonic Analysis. [[User:Douira|Douira]] ([[User talk:Douira|talk]]) 14:50, 26 February 2022 (UTC)

The part that says the farad is "unusually large" is incredibly biased IMO. On the scale of planets its "unusually small", In fact, on the scale of EV's its even pretty normal. The writer is only considering small electronic circuits. Also the Henry is very well scaled to the Farad so how "unusual" is it really? [[Special:Contributions/108.162.241.33|108.162.241.33]] 17:13, 26 February 2022 (UTC)

:Apologies for the incredible bias. You're right in saying that I'm only considering small electronic circuits; I haven't worked on power distribution systems or applications with large capacitor banks, so my only hands-on experience of components measured in whole farads would be supercapacitors. In consumer electronics, where capacitors are typically labelled in pico, nano or microfarads, the whole farad is rarely encountered. I do still think that capacitors are a good counter-example of items using Mu that you can see and touch, in so many modern electronic devices. But as my previous use of language was so divisive, I'll let someone else attempt to reintegrate the point, if they feel it's useful. [[User:Kazzie|Kazzie]] ([[User talk:Kazzie|talk]]) 16:11, 27 February 2022 (UTC)

Isn't the ''capital'' psi used for the wavefunction? [[User:GcGYSF(asterisk)P(vertical line)e|GcGYSF(asterisk)P(vertical line)e]] ([[User talk:GcGYSF(asterisk)P(vertical line)e|talk]]) 19:35, 26 February 2022 (UTC)
:Yes, but rarely. The lowercase ψ is much more common (AFAIK it dates back to [https://commons.wikimedia.org/wiki/File:Grave_Schroedinger_(detail).png Schrödinger himself].

How sad that there is no '''η'''! Missed chance to blame steam machine engineers for not trying harder to invent the perpetuum mobile. --[[Special:Contributions/172.70.242.177|172.70.242.177]] 20:01, 26 February 2022 (UTC)

The lowercase epsilon is used much more often for something else - usually to denote that the "variable" on the lefthanded side is a member of the "set" of the righthanded side of the lowercase epsilon. Of course, this is totally unimportant ;-).
:You are referring to the "element of" sign, which is distinct from lowercase epsilon (although based on it).

I highly doubt that the use of Ξ has anything to do with it "looking like a UFO." Rather, I'd suggest it's because it's essentially never used, at least among the English speaking mathematicians in the US, and probably Europe. [[User:Douira|Douira]] went out of their way to find an example, and found something increadibly obscure, which supports the point. ''Why'' Ξ is rarely used is another question. Maybe because it could easily be confused for an E or Sigma, with lazy handwritting? Maybe because it's a Greek letter without a direct Latin counterpart, so doesn't correspond with the first letter of any common words? [[Special:Contributions/162.158.63.49|162.158.63.49]] 22:50, 26 February 2022 (UTC)som

In my experience lower case eta, zeta, (and xi) most commonly show up as dummy variable in an integral. Any two may be used for a double integral and all three for a triple. Double and triple integrals are often quite terrifying, particularly when somebody cannot write all three symbols consistently and distinctly, so many integrals become "integral squiggle squiggle dee squiggle dee squiggle".[[Special:Contributions/172.70.174.219|172.70.174.219]] 10:10, 27 February 2022 (UTC)

π is also commonly used as the [https://en.wikipedia.org/wiki/Prime-counting_function prime-counting] function in number theory. Most problems regarding primes are usually considered hard, like the twin prime conjecture.

Lower-case sigma is also used in sigma-algebras, which is part of the theoretical background underlying statistics, among other things. I second that the lower-case epsilon drawn by Randall is the lunate variant that looks indistinguishable from the "is an element of" symbol and should probably get mentioned. On an unrelated note, there's a story of someone using capital xi at a math conference specifically to annoy some other mathematician who *really* didn't like them. [[Special:Contributions/172.70.211.26|172.70.211.26]] 20:30, 27 February 2022 (UTC)

:Yeah I came to comment this, lower-case sigmas come up in sigma-algebras and are absolutely terrifying (bias) in that context. The joke about ‘someone trying very hard to apply this’ works with sigma-algebras in the context of measure theory -- someone trying to actually apply measure theory to a real problem. [[Special:Contributions/162.158.129.117|162.158.129.117]] 10:48, 28 February 2022 (UTC)

Alpha is also used in aeronautics for the angle of attack of the airflow over a wing. Exceeding a critical angle of attack leads to an aerodynamic stall, which has been cause of many fatal accidents.

Uppercase phi looks like an obvious reference to [https://twitter.com/nathanwpyle/status/1178152201392447488| this comic and author], as he normally uses the term orb to refer to spheres and balls (as part of the intrincate language of the characters), besides he normally uses that typographic resource of writing a word with its letters separated by spaces, i.e.: e x p e r i e n c e, in the example link. I'm missing the math context on why refering to orbs for uppercase phy, but it could be just because due to the form of the character. [[Special:Contributions/172.70.86.54|172.70.86.54]] 10:28, 28 February 2022 (UTC)

The lowercase gamma symbol and description may also be a reference to the downward-looping flight path of enemy ships in the video-game Galaga, which zoom down the screen at the player's starfighter while shooting at them, then retreat and zoom back up. [[Special:Contributions/172.70.131.122|172.70.131.122]]

Why was my remark on the impossibility of {{w|squaring the circle}} removed? (https://www.explainxkcd.com/wiki/index.php?title=2586:_Greek_Letters&diff=227689&oldid=227680) [[User:ThomasGauss|ThomasGauss]] ([[User talk:ThomasGauss|talk]]) 20:06, 28 February 2022 (UTC)

2586: Greek Letters

2022-02-26T18:43:23Z

ThomasGauss: π -> impossibility of squaring the circle

{{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. 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.

The letters are:

* '''π (lower-case pi)''' — Typically used to refer to the constant ratio between a circle’s circumference and its diameter (approximately 3.14). This usage of pi commonly applies to equations in introductory geometry classes, which would be considered "simple" by advanced mathematicians. However, pi also shows up seemingly randomly in extremely advanced and complicated equations (that have nothing to do with a circle), as part of the solution to an infinite series or whatnot. (There are also {{w|Pi_(letter)#Lowercase_Pi|several advanced equations}} which use pi to represent variables other than the ratio of the circumference to the diameter.) "Impossible" may mean the impossibility of [https://en.wikipedia.org/wiki/Squaring_the_circle squaring the circle] (a consequence of π being transcendental).

* '''Δ (capital delta)''' — Typically used to refer to a change in quantity.

* '''δ (lower-case delta)''' — Also typically used to refer to a change in quantity, but unlike the capital delta, this is only for infinitesimal changes and is used in derivative and integration expressions in mathematics hence the text's reference to "a mathematician's fault".

* '''θ (lower-case theta)''' — 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.

* '''Φ (lower-case phi)''' — 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.

* '''ϵ (lower-case lunate epsilon)''' — Epsilon is typically used to refer to very small quantities which go to zero in the limit. In this interpretation, the comic suggests that because these quantities are very small, they are unimportant, when in reality the study of quantities that go to zero gives rise to limits and calculus. Also used for the series of transfinite numbers that are unreachable from ω (see below) using addition, multiplication, and exponentiation, and in statistical modelling to denote observational noise.

* '''υ,ν (lower-case upsilon and lower-case nu)''' — If these are being used it implies that the normal u & v characters are already assigned as constants or variables, and thus the math is probably of a higher level. Common in college level physics and engineering equations.

* '''μ (lower-case mu)''' — Among others, ''μ'' is used in category theory, measure theory, and as the symbol for the Ramanujan–Soldner constant, all uses with highly abstract applications. It is, however, also employed in statistics and various physical fields, e.g. as the symbol for the coefficient of friction, which is a concept most people are well acquainted with – at least empirically if not formally. Another common use of ''μ'' – outside of equations – is the symbol of the SI prefix ''micro-''.

* '''Σ (capital sigma)''' — Typically used as a symbol for summation of a series of numbers.

* '''Π (capital pi)''' — Typically used as a symbol for multiplication of a series of numbers.

* '''ζ (lower-case zeta)''' — Frequently used with number theory, in particular the {{w|Riemann zeta function}}, which is a the focus of a famously unsolved problem in highly advanced mathematics.

* '''β (lower-case beta)''' — 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. 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 (lower-case alpha)''' — Possibly referring to the {{w|fine-structure constant}} which shows up in high energy physics, atomics physics, quantum electrodynamics, and at least [https://explainxkcd.com/1047/ one other xkcd comic]. Could also refer to {{w| alpha radiation}} or {{w| alpha particles}}, which could kill someone, but could also be blocked by ordinary sheets of paper. Alpha could also refer to {{w|angular acceleration}}, or the acceleration of spinning systems, which are capable of killing people in a number of [https://explainxkcd.com/123/ interesting ways]...

* '''Ω (capital omega)''' — Omega is the last letter of the Greek alphabet, and thus often seen as momentous (the end, the final word, death). This symbol has been used for a {{w|Omega_function|variety of mathematical functions}}. Also used as the symbol for {{w|ohms}}, a unit for electrical resistance, and for the first uncountable ordinal.

* '''ω (lower-case omega)''' — Lower-case omega is used for the {{w|Transfinite_number|lowest transfinite ordinal number}}, a specific way of referring to a type of infinity in a mathematically robust way. The line about dying here among the transfinite equations may be in reference to the literally infinite scope of the branch of mathematics. It is also used in physics and electrical engineering for angular frequency, equal to 2πf.

* '''σ (lower-case sigma)''' — In statistics, commonly refers to the standard deviation of a distribution. Statistics often attempts to use simplified models to explain real-world phenomena.

* '''ξ (lower-case xi)''' — Randall comments that this looks like a strand of curly hair. Xi is used in the {{w|Riemann Xi function}}.

* '''γ (lower-case gamma)''' — Gamma ray is the most powerful classification of electromagnetic radiation AKA "light", and powerful lights are frequently associated with high-tech, futuristic devices and weapons, hence "space noises". Alternatively, this might be a reference to the Lorentz factor, an important variable in special relativity calculations.

* '''ρ (lower-case rho)''' — often used to measure density, such as air density that a wing might be travelling through.

* '''Ξ (capital xi)''' — Resembles the icon of some {{w|Stack Exchange}} [https://stackexchange.com/sites# sites]. This character is also identical to Besh, the second letter of the {{w|Aurebesh}} alphabet [https://starwars.fandom.com/wiki/Aurebesh] used in ''Star Wars.'' According to the comic, anyone using this letter is likely a being from another planet.

* '''ψ (lower-case psi)''' — Psi looks exactly like a trident. In quantum mechanics it's used to describe the wave function of a particle, leading to a bad 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.)

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

:[Header:]
:What Greek letters mean in equations

:[What follows is a list of Greek letters, with explanations next to them.]
: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 '''''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''.
: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:Language]]