Gro-Tsen Profile picture
Feb 25 25 tweets 5 min read
Looking at Ukrainian words from the perspective of someone who knows just a little bit of Russian gives the superficial impression that:
⁃ Russian ‘и’ and ‘ы’ match to Ukrainian ‘і’ and ‘и’,
⁃ Russian ‘е’ and ‘э’ match to Ukrainian ‘є’ and ‘е’.
But It's Complicated™. •1/25
Here's what I THINK I understood. First, Slavic vowels historically came into two flavors: normal and “iotated”, pronounced with a /j/ before them (disclaimer: this is probably a huge oversimplification). In Old Slavonic, they are (sometimes) written with a iota-ligature. •2/25
The iotated vowels, but also some front vowels that were not iotated (‘i’, ‘ь’, ‘e’, ‘ѣ’, ‘ѧ’) caused palatalization (“softening”) of the previous consonant in East Slavic languages, inc. Russian and Ukrainian (exc. ‘e’?). But some vowels also changed, and others dropped. •3/25
E.g., the ‘ѧ’ vowel (“little yus”, historically a nasal, maybe like Polish ‘ę’) became /a/, but it is still distinguishable from ‘а’ because of the palatalization it caused. However, ‘ѧ’, ‘ѩ’ and ‘ꙗ’ would have become indistinguishable by then: they became modern ‘я’. •4/25
Similarly, the yer vowels ‘ь’ and ‘ъ’ dropped in many places — see en.wikipedia.org/wiki/Havl%C3%A… — but since the latter caused palatalization, it was still felt on the preceding consonant. This is the basis for modern Russian orthography: … •5/25
… the vowel signs not only mark the vowels, but they also indicate whether the previous consonant is “soft”, i.e., palatalized (provided it is palatalizable); the sign ‘ь’ marks palatalization in the absence of vowel, or /j/ between soft consonant and vowel, … •6/25
… and ‘ъ’ marks hard consonants in the absence of a vowel (mostly removed post 1917) or before a iotified vowel. OK, but what about ‘і’, ‘и’ and ‘ы’, then? Well, pre-1917 Russian orthography had all three, the first two pronounced /i/, the third, /ɨ/. •7/25
The letters ‘і’ and ‘и’ are copied from Greek ‘Ι’ (iota) and ‘Η’ (eta), which had merged in pronunciation at the time the Cyrillic alphabet was created. In Old Slavonic, IIUC, they represent the same sound, are maybe even interchangeable. •8/25
(They even imported Greek upsilon as ‘ѵ’, also with the same pronunciation, but this was basically used only for Greek words.) In pre-1917 Russian orthography, ‘і’ was used (roughly) before vowels and in the word “міръ”, “world” to distinguish from “миръ”, “peace”. •9/25
This is a somewhat artificial orthographic distinction: my Old Slavonic grammar writes “миръ” for both words. (Also, cue the urban legend that Tolstoj's ‘Война и Миръ’, ‘War and Peace’, was really ‘Война и Міръ’.) Nowadays, both are “мир” in Russian AND Ukrainian. •10/25
Russian ‘ы’, /ɨ/, arose from a ‘ъі’ or ‘ъи’ digraph (in Unicode: ‘ꙑ’). It's unclear to me whether it was ever a diphthong or just an orthographic convention. The writing was simplified to ‘ы’, explaining the paradox that this “hard” vowel starts with a “soft” sign. •11/25
Now Ukrainian merged the Slavic vowels ‘i’ and ‘y’ (Russian ‘и’ and ‘ы’), into one, pronounced /ɪ/. So Ukrainian indeed has ‘и’ in many places where Russian has ‘ы’, e.g., “ти” (2d pers sg pronoun) for Russian “ты”. Orthographically, IIUC, it does NOT show palatalization. •12/25
But as I pointed out earlier, Russian “мир” (both meanings) is also Ukrainian “мир”, Russian “один” (“one”) is also Ukrainian “один”. So whence to the Ukrainian ‘і’ come from, then? Well, it can be of various sorts. •13/25
A good part of Ukrainian ‘і’ come from the historical vowel ‘ѣ’ (formerly something like /æ/), which still existed in pre-1917 Russian orthography (e.g., “бѣлый”, “white”) and became ‘е’ in modern Russian (accented as ‘е’, not ‘ё’). So Russian “белый” = Ukrainian “білий”. •14/25
Similarly, Russian “лѣсъ” then “лес” (forest) = Ukrainian “ліс” But ‘і’ also appears word-initially: Russian “имя” = Ukrainian “ім'я” (apostrophe marks that ‘я’ is pronounced /ja/, not by palatalizing previous consonant: analogous to Russian ‘ъ’ mark here). •15/25
And in Ukrainian declension paradigms, where we have ‘и’ in the hard stem, it corresponds ‘і’ in the soft stem, just like in Russian hard ‘ы’ corresponds to soft ‘и’. Or it can also come from other vowels. So Russian “ночь, ночи” (“night, nights”) = Ukrainian “ніч, ночі”. •16/25
At any rate, orthographically, IIUC, Ukrainian ‘і’ marks palatalization of the preceding consonant (if this makes sense), like Russian ‘и’. And it is pronounced /i/. There is also a special sign, ‘ї’, for the /ji/ combination. •17/25
So, yeah, there's a certain parallel between Russian ‘и’ and ‘ы’ and Ukrainian ‘і’ and ‘и’, but it's not systematic or anything, many Russian ‘и’ are still ‘и’ in Ukrainian, and many Ukrainian ‘і’ are ‘е’ in Russian (historically ‘ѣ’). •18/25
Concerning ‘е’/‘э’ versus ‘є’/‘е’, I understand even less. Russian ‘е’ tends to reflect to Ukrainian ‘е’ even though the former is “soft” (palatalizing) and the latter is “hard”. E.g., Russian “вечер” (evening) = Ukrainian “вечір”. •19/25
I think Ukrainian more or less matches the historical Slavic vowels, with ‘е’ and its iotified counterpart ‘ѥ’, the latter having become ‘є’ in Ukrainian. So ‘е’ in the hard stem tends to correspond to ‘є’ in the soft stem. •20/25
In Russian, ‘э’ (almost?) only occurs at the beginning of words and foreign loanwords or transcriptions. The hard counterpart to ‘е’ in grammatical paradigms is ‘о’. I'm not clear as to why, nor whether this ‘о’/‘е’ parallel exists in any form in Ukrainian. •21/25
(And when Russian has ‘ё’, the only-accented palatalizing vowel /o/, then Ukrainian seems to write ‘йо’, or ‘ьо’ after consonant, e.g., Ukrainian “ньому” (3rd pers. sg pronoun, locative) = Russian “нём”.) •22/25
Anyway, that's what I think I managed to figure out without having access to any really reliable source (and without knowing any Ukrainian or more than the rudiments of Russian). Because of that, there are probably many errors or at least oversimplifications: … •23/25
… in the first place, while Russian had its last major orthographical reform in 1917, Ukrainian had a number of them, in 1928, 1933, 1999, 2019, I'm not sure I understood correctly, and understanding their differences is way beyond me. •24/25
So basically this whole thread is more of a plea for someone more knowledgeable than I am to intervene and explain all of this more correctly — but if possible not more complicatedly 😅 — than I did! •25/25

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More from @gro_tsen

Feb 25
The latest xkcd comic xkcd.com/2585/ leads me to raise the following question: suppose u_0,…,u_n (we can assume w.l.o.g. u_0=1) are positive real numbers (“units of measure”) and we consider the following graph (“integer measurements with these units”): …
… vertices of the graph are pairs (i,k) where 0≤i≤n and k∈ℤ, and we have an edge (i,k) → (j,ℓ) iff ℓ is the closest integer to k · u_i / u_j (conversion of k units u_i to the unit u_j), maybe assuming u_i/u_j are all irrational so we never have doubts on rounding.
A question might then be: what are the strongly connected components of this graph like? Are they of bounded size? If so, how can we bound their size from u_0,…,u_n?

(Yeah, I know, “mathematicians are like Frenchmen”. 😅)
Read 4 tweets
Feb 25
Interesting question on MathOverflow: can we find a nonnegative Borel measure μ on ℝ^d which is not discrete and whose Fourier transform stays bounded away from 0 (meaning inf |μˆ(u)| >0)? (NB: if μ is abs. continuous, then |μˆ(u)|→0: Riemann-Lebesgue.) mathoverflow.net/q/416939/17064
Of course if μ is discrete this is easy to find (just take μ=δ₀, so δ₀ˆ = 1). But note that in ℝ the Fourier transform δ_a + δ_b + δ_c (i.e., exp(2iπ(a−u)) + exp(2iπ(b−u)) + exp(2iπ(c−u))) comes arbitrarily close to 0 if (b−a)/(c−a) is irrational.
In another related (and linked) question, I learned that if μ is the “uniform” measure on a Cantor set with dissection ratio θ, so that μˆ(u) = ∏_k cos(θ^k·u), then |μˆ(u)|→0 except if θ is a Pisot-Vijayaraghavan number (Erdős-Salem, no ref given). mathoverflow.net/q/98405/17064
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Feb 24
Je suis fasciné par la proportion de copies (genre 90%) qui veulent utiliser le théorème de convergence dominée pour justifier que si f_n → f dans L² et g ∈ L², alors ∫(f_n · g) → ∫(f·g). En lisant l'énoncé, je n'avais même pas envisagé une possible difficulté à cet endroit.
Et le pire, c'est que des malins s'en tirent quand même (la question était en fait que si ∫(f_n · g) = 0 pour tout n alors ∫(f·g)=0: ils prennent une suite extraite des f_n qui converge p.p. et qui est dominée dans L², et appliquent Hölder puis le thm de convergence dominée)!
Je ne dis pas ça pour dire «ces élèves sont nuls»: là c'est clairement un problème d'enseignement, nous leur avons donné l'impression que quand on veut passer à la limite dans une intégrale c'est forcément le thm de convergence dominée qu'il faut appliquer, …
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Feb 16
So, here's a good approximation of a regular pentagon on a square lattice (to save you the bother of counting, the vertex positions are, up to translation: (0, 55), (−29, 34), (−18, 0), (18, 0), (29, 34)). How did I find it? 🧵⤵️ •1/18
Easy, you say: just pick any regular pentagon in the plane, and replace each one of its vertices by the closest lattice point! Well… yes, but that will give a very shitty approximation. To be honest, I didn't bother to compute how shitty, … •2/18
… but if you don't use the freedom to choose the size and orientation of your near-regular pentagon arbitrarily in the lattice, you won't do a good job (much like if you try to approximate ξ by rational p/q, you shouldn't just pick q arbitrarily and take p close to qξ). •3/18
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Feb 15
I just received this spam:

«
Dear David A. Madore,

We’d like to inform you that [redacted dot com], a leading academic platform for researchers, has just released the 2022 Edition of our Ranking of Top 1000 Scientists in the field of Mathematics.
The ranking is based on the H-index metric provided by Microsoft Academic and includes only leading scientists with an H-index of at least 30 for academic publications made in the area of Mathematics.

The full world ranking is available here: [redacted URL]
The annual release of our ranking is regularly featured by leading universities worldwide, including the University of Maryland, Stanford Robotics Lab, or the University of Texas, and it is a great opportunity to explore where leading experts are heading.
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Full disclosure: at the time, I may have been part of the cult-like following around RMS that Laurent mentions.
In particular, I remember leading a group of free software geeks around a (ahem) “Linux” expo in the late 1990's (still fairly rare then, at least in France), chanting: “Join us now and share the software: you'll be free, hackers, you'll be free!” gnu.org/music/free-sof…
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