2586: Greek Letters

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Greek Letters

Title text: 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

This explanation may be incomplete or incorrect: Created by O R B S PRO®- Missing explanations for some letters. Do NOT delete this tag too soon. If you can address this issue, please edit the page! Thanks.

Mathematics uses lots of Greek letters, typically using 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 several advanced equations which use pi to represent variables other than the ratio of the circumference to the diameter.)

• 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 on.

• 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) — In lunate form, typically used to signify set membership. Given that set theory is a very pure branch of mathematics, the comic suggests it can be ignored. Alternatively, the normal 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.

• υ,ν (lower-case upsilon and lower-case nu) —

• μ (lower-case mu) — The SI prefix for "micro" = 10^-6, representing very small quantities: a micrometer (μm) is tens of times smaller than the width of a human hair, a microgram (μg) is one single fine speck of flour, both of which are barely visible with the bare human eye nor feelable through the skin.

• 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 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 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 alpha radiation, which certainly could kill someone.

• Ω (capital omega) — This symbol has been used for a variety of mathematical functions. Also used for the symbol for ohms, a unit for electrical resistance.

• ω (lower-case omega) — Lower-case omega is used for the 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.

• 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) —

• 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) —

• ψ (lower-case psi) — Psi looks exactly like a trident. This is hilarious. 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

This transcript is incomplete. Please help editing it! Thanks.

[Header:]

What Greek letters mean in equations

[What follows is a list of Greek letters, with explanations (quote unquote) 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 Trition, ruler of the waves.

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Discussion

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 ((edit: by some random IP: "...finite application of...")) addition, multiplication, exponentiation, and epsilons subscripting. EDIT: phi is used for the Veblen hierachy. GcGYSF(asterisk)P(vertical line)e (talk) 05:11, 26 February 2022 (UTC)

I wouldn't normally internally spellcheck/factcheck someone's signed Talk comment, as I think it's rude to do so (especially 'invisibly'), but an IP added some words to yours (without clear indication) probably with good reason but also with slightly bad typing. So I've highlighted their (corrected) addition, which at first sight seems a valid clarification but I haven't double-checked. And now this is me taking fully (IP-)signed ownership of what I changed. Would have been simpler for the prior editor just to have made a signed-reply, like this but far shorter, but they didn't! Ah well... 172.70.90.121 14:03, 1 March 2022 (UTC)

Don't you have an English saying: simple/easy as π? 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. 162.158.107.230 08:08, 26 February 2022 (UTC)

sqrt(-1) 2³ Σ π and it was delicious Elektrizikekswerk (talk) 08:30, 28 February 2022 (UTC)

Related: https://xkcd.com/2520/ 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. Douira (talk) 14:50, 26 February 2022 (UTC)

Uppercase xi is used by Alan Turing in his essay *Systems of Logic Based on Ordinals* to represent ordinals. I consider this to be a possible example of an alien mathematician among us. 17:11 26 October 2022

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? 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. Kazzie (talk) 16:11, 27 February 2022 (UTC)

Isn't the capital psi used for the wavefunction? 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 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. --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).

Yes it is distinct, but then the used typeface in the comic looks more like the epsilon for "element of" then for the usual epsilon in analysis (ie. for definitions of continues functions).

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. 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? 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".172.70.174.219 10:10, 27 February 2022 (UTC)

π is also commonly used as the 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. 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. 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 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. 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. 172.70.131.122

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

My sibling's in an advanced calculus course, when she saw the joke about lowercase omega she laughed for a different reason, remarking how accurate it was and how impossible it is to use in her class? (I can't remember exactly.) I don't understand what she meant, I'm in a lower class. Could somebody add an alternate explanation possibly? 123.456.7890

Differential forms? 172.70.230.111 03:24, 2 March 2022 (UTC)

Yes, that's it. I still have no idea how they work, though. 123.456.7890

O R B S are chanted with such gravitas in the Games Done Quick speedrunning fundraiser events. I would say this is a niche pull, but it seems up Randall's alley.

Why is Randall so good at making me crack up? Am I really that much of a nerd? (Okay granted I needed an explanation for some of this, hence my presence here, but still, Addition® and Multiplication® Pro® got me so...)--Twisted Code (talk) 17:10, 4 March 2022 (UTC)

It just occurred to me Poseidon could be written as Poψdon. Then his trident is in his name. Bwisey (talk) 13:11, 5 March 2022 (UTC)

One thing missed so far, the lowercase epsilon is also used in automata theory. There usually words (strings of symbols from an alphabet), which do contain lowercase epsilons, are equivalent to the same word, after removing any occurence of lowercase epsilon from the string. Ie. the lowercase epsilon there denotes the "empty symbol" (or "empty letter"). For further reading ie. look up non determitistic finite automata with (and without) epsilon transitions. Also in other branches of theoretical computer science the lowercase epsilon is usually used as "empty symbol" or "empty letter".

My favourite use of Greek letters in maths is that (in my experience) ψ is used as a backup for φ (so when you have already used phi, you use psi as the second one), and χ is sometimes used as a reserve for that. This means you can have an equation involving all three. This is perfectly clear on paper, but any discussion surrounding it is a nightmare, as they all sound exactly the same... Also this is generally φ rather than ϕ. The former is generally used for functions (specifically homomorphisms in groups) and the latter for spherical polars. Although they both have other uses, and that is a pretty vague rule... 172.70.86.44 18:21, 16 March 2022 (UTC)

the natural numbers under '<'

What does this mean?

Ordinal analysis

Why keep all the unnecessary ordinal-related stuff (beyond omega)? Ordinal analysis is an _extremely_ niche field - most professional mathematicians never even heard of it - so it is quite safe to assume Randall did not have it in mind. I don't think it helps explaining the comic any more than saying rho is the usual symbol for the Gaussian mass of a Euclidean lattice (i.e. not at all). -- Laurus (talk) (please sign your comments with ~~~~)

Taking a close look at the comic, I think you're right. It pains me a bit, but I think you're right, the ordinals ought to go. Vandalbane (talk) 01:23, 27 May 2022 (UTC)

I can't believe that the article is being edited again, over this, for the Nth time! 141.101.98.11 08:00, 27 May 2022 (UTC)

Was there some kind of debate over it? Vandalbane (talk) 15:32, 27 May 2022 (UTC)

Not that I'm aware of, that was just a pune on the term 'ordinal'. Here's the missing smiley that makes it more obvious. -> ;) 141.101.98.221 18:22, 27 May 2022 (UTC) ( :p <-- And here's the other one that this comment might need.)