$$ \newcommand{\rmap}[3]{#1:#2\rightarrow #3} \newcommand{\lmap}[3]{#1:#2\leftarrow #3} \newcommand{\map}[3]{\rmap{#1}{#2}{#3}} \newcommand{\reals}[0]{\mathbb{R}} \newcommand{\xreals}[0]{\mathbb{R}\cup\{\infty\}} \newcommand{\ub}[1]{\rm{ub\ #1}} \newcommand{\lb}[1]{\rm{lb\ #1}} \newcommand{\glb}[1]{\rm{glb\ #1}} \newcommand{\lub}[1]{\rm{lub\ #1}} \newcommand{\ftom}[4]{\glb{ \left\{#2#1 |\, {}^*#2 = #3\ \rm{and}\ #2^* = #4\right\}}} \usepackage{mathrsfs} \newcommand{\alg}[1]{\mathscr{#1}} \newcommand{\complexes}[0]{\mathbb{C}} $$

The Alphabet

Mathematics has an insatiable appetite for symbols. We use digits to represent numbers, we use letters to denote variables. In computer science we just use words, or arbitrary strings of letters, to give us all the variables we could want. That strategy doesn't work well in mathematics, however, because verbose identifiers obscure the structure of expressions, and in mathematics we can't afford to obscure structure. Insight into structure is the heart of the business. While mathematics makes use of Fraktur font characters for Lie algebras, and the first letter of the Aramaic alphabet to label cardinalities, and a borrowing from runic writing, the vast majority of characters come from either the Roman alphabet, or its parent, the Greek.
chiseledinkedRoman versionsnamepronunciationsorority pronunciation
ΑαAalphaæl̩fʌapple pail/shovel fan onion
ΒβBbetabeɪtʌbat acorn teatree onion
ΓγC Ggammaɡæmʌgear apple mittens onion
ΔδDdeltadɛl̩tʌ dice elephant pail/shovel teatree onion
Εε ϵEepsilonɛpsɪlɑnelephant pea sun igloo lamp octopus nose
ϜϝFdigammadaɪɡæmʌdice iron gear apple mittens onion
ΖζZzetazeɪtʌzebra acorn teatree onion
ΗηHetaeɪtʌacorn teatree onion
Θθ ϑdiscardedthetaθeɪtʌthimble acorn teatree onion
ΙιI Jiotajoʊtʌyarn ocean teatree onion
Κκ ϰKkappakæpʌkey apple pea onion
ΛλLlambdalæmdʌlamp apple mitten dice onion
ΜμMmumumitten tooth/shoemjumitten yarn tooth/shoe
ΝνNnununose tooth/shoe
Ξξdiscardedxiksikey sun eagle
ΟοOomicronoʊmɪkrɑnocean mitten igloo key rake octopus nose
Ππ ϖPpipipea eaglepaɪpea iron
Ρρ ϱRrhoroʊrake ocean
Σσ ςSsigmasɪɡmʌsun igloo gear mitten onion
ΤτTtautaʊteatree owl
ΥυU V W Yupsilonupsɪlɑntooth/shoe pea sun igloo lamp octopus nose
Φφ ϕQphififan eaglefaɪfan iron
ΧχXchihihat eaglekaɪkey iron
Ψψdiscardedpsipsipea sun eagle
Ωωdiscardedomegaoʊmeɪɡʌocean mitten acorn gear onion
What I've labeled Roman versions aren't really Roman; mostly they're later adaptations forced by certain medieval sound changes. But that doesn't really matter here — the point is to make it easy to learn the Greek alphabet by relating it to letters you already know. The symbols most commonly used in mathematics are the inked forms. As you can see, they're like the chiseled forms, but better suited to the rounded flow of a pen rather than the straight line of a pounded chisel.

The pronunciation of Χ is actually more subtle than described above; it starts with the /x/ sound that ends loch. That's probably why /kaɪ/ is commonly substituted.

The discarded items are instructive. Ο and Ω are similar; micron means small and mega means big. While Latin had long and short vowels, Latin writing didn't make the distinction; not a problem if you grew up speaking Latin. The Τ/Θ distinction in Greek was the difference between the t sounds in stall and tall. You may never have even noticed that distinction, but if you put your palm in front of your lips as you say both words aloud, you'll instantly perceive the difference. Latin didn't have that distinction. English has it but doesn't care much about it, certainly not enough to need separate letters for them. Greek did care, and so had two distinct letters.

The others, Ξ and Ψ, are much more interesting. They weren't actually needed, even in Greek, because Ξ could have been written ΚΣ and Ψ could have been written ΠΣ instead. Each is a blend of two sounds in sequence. That statement was either immediately obvious to you, or is somewhat puzzling to you, depending on how you learned to read. Because it turns out that the skill of fusing sounds together into syllables, and of analyzing syllables into constituent sounds, isn't obvious or intuitive, but must be learned or discovered. The alphabet itself was an accident — a result of adapting a syllabic writing system to a language that happened to have an exquisitely simple syllable structure, with only open syllables and no consonant clusters and virtually no lexical significance to vowels. In adapting that to Greek, which does have consonant clusters, whoever created that adaptation seems to have had limited knowledge about analyzing consonant clusters, and so created new symbols for the clusters. It's as though, in English, we had a unique letter to represent str or spl. Interestingly, the Athenians did not use them, but for some reason at some point chose to adopt the less sophisticated Ionian version, which did.

These pronunciations, while conventional, don't match the ancient pronunciations of the names. You can find those by searching for the history of the Greek alphabet.

It turns out that for most people the biggest obstacle to literacy is that their teacher either doesn't herself have that skill, or doesn't realize that it is a skill, that needs to be explicitly taught. While it's possible to learn to read without that skill, it's dramatically more expensive and difficult. This skill is (sophomorically) called phonemic awareness; both words are wrong. It's not quite at a phonemic level, nor is it wholly at an allophonic one. In practice, for example, the allophonic distinctions exhibited by rake and earth, as well as by lamp and pail/shovel do matter, while the various allophones of p and t do not. Nor is it an awareness. You can't just point it out. It requires a small but nonnegligible amount of teaching and practice to develop the skill. Great enough that it is quite costly to gloss over it, but small enough that those who have the skill generally retain no memory of having acquired it in the first place, and so neglect its importance.

I've given pronunciations using both the international phonetic alphabet, and also using words exemplifying those sounds. Where one word is given, the initial sound of that word is being represented. Not every sound in English can be word-initial. I use pairs of words sharing the desired sound in those cases, and in one other case for reasons not worth going into here.
IPAexemplary wordsas IPA
ppeaspiz
bbatbæt
tteatreetitɹ̠i
ddicedaɪs
kkeyskiz
ɡgearsɡiɹ̩z
ffanfæn
vvolcanovɑl̩keɪnoʊ
θthimbleθɪmbl̩
ðlathe/featherleɪð/fɛðɹ̩
ssunsʌn
zzebrazibɹ̠ʌ
ʃsharkʃɑɹ̩k
ʒmeasure/garagemɛʒɹ̩/ɡɹ̩ɑʒ
hhathæt
çhugeçjudʒ
xlochlɑx
cherriestʃɛɹ̩ɹ̠iz
jacksdʒæks
mmittensmɪtn̩z
bottom/fathombɑtm̩/fæðm̩
nnosenoʊz
kitten/ladenkɪtn̩/leɪdn̩
ŋring/tongueɹ̠iŋ/tʌŋ
ɹ̠rakeɹ̠eɪk
ɹ̩earthɹ̩θ
llamplæmp
pail/shovelpeɪl̩/ʃʌvl̩
wwellwɛl̩
jyarnjɑɹ̩n
ʍwheelʍil̩
æappleæpl̩
ɪiglooɪɡlu
ɛelephantɛləfn̩t
ɑoctopusɑktəpʊs
ʌonionʌnjən
ʊhook/foothʊk/fʊt
ieagleiɡl̩
utooth/shoetuθ/ʃu
ɔorangeɔɹ̠n̩dʒ
əcommakɑmə
ironaɪɹ̩n
acorneɪkɔɹ̩n
ɔɪoilwellɔɪl̩wɛl̩
owlaʊl̩
oceanoʊʃn̩

It's possible that your dialect of English makes no distinction between wile and while, in which case you can pretend that ʍ is w. It's also possible that your dialect uses ɔ where mine uses ɑ, or even a third vowel. I don't think that affects any of the Greek letter names. In any event, since I don't make those distinctions in normal speech, I'm not a reliable guide to those dialects. When I'm being careful, I might distinguish caught from cot, but usually I don't.

I'm Andrew Winkler. I hope you've enjoyed exploring these ideas with me. Thanks for your time. If you've got any questions, send an email to 4af502d7148512d4fee9@cloudmailin.net.

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