Matematika, kalba, poezija: sąveikos ir traukos

S aipsniai / A icles 227 GIEDRIUS ALKAUSKAS The Uni e si y o Vilnius ORCID id: o cid.o g/0000-0002-5747-363X Resea ch a eas include modula o ms, unc ional equa ions, p ojec ed lows, na u al aspec s o musicology; The language and o m o poe y. This Regula ion shall en e in o o ce on he wen ie h day ollowing ha o i s publica ion in he O icial Jou nal o he Eu opean Union. Ma hema ics, Speech, and Poe y: Wha a e some o he bene i s? The ollowing able is inse ed in Annex I: Ma hema ics, language and poe y: In e ac ions and A ac ions This Regula ion shall en e in o o ce on he wen ie h day ollowing ha o i s publica ion in he O icial Jou nal. The a icle in es iga es s uc u es a he in e sec ion o wo a eas o knowledge (ma hema ics, language, poe y) ha imply non- i ial conclusions o he hi d o hem. Fo example, i examines how o c ea i ely in e p e a Li huanian ex while keeping s ic ma hema ical and g amma ical ules. Fu he , based on ma hema ics, he co e o he e ia y o m is e ealed, a he same ime his poe ic in en ion o Dan e allows he o mula ion o a heo e ical (and in some cases p ac ical) ask. The a icle also discusses he assump ions ha de e mine when he in e ac ions o se e al disciplines a e (o can be) ui ul. The ollowing wo ds a e included in he lis : sequence, ixed o m, e ia y, quin ile, Ba anauskas, Dan ė, penkiaeilis, bidiscipliniškumas, conc e e poe y, synonym, me a ezė, mnemonic, Luhno o mula, opai. This Regula ion shall en e in o o ce on he wen ie h day ollowing ha o i s publica ion in he O icial Jou nal. In his pape , we in es iga e he s uc u es buil a he in e sec ion o wo domains o knowledge (ma hema ics, language, poe y), which imply non- i ial consequences o he emaining domain. Fo example, we explo e he possibili ies o how o c ea i ely in e p e he Li huanian ex whose o m is s ic ly limi ed by ma hema ical and g amma ical ules. Fu he mo e, ma hema ics helps us o e eal he co e o he hi d hyme by Dan e and allows us o pose a pu ely heo e ical (and in a ew cases p ac ical) p oblem abou i s GIEDRIUS ALKAUSKAS The Ac a Linguis ica LXXVI discusses he assump ions unde which he in e ac ions o se e al domains o c ea i i y a e (o can be) e ile. KEYWORDS: Ve si ica ion, o ms ixed, hi d hyme, i h hyme, Ba anauskas, Dan e, pen as ich, bidisciplina y, conc e e poe y, synonym, me a hesis, mnemonic, Luhn algo i hm, ope. This is he i s ime I' e seen his. 1. The en e p ise Imp o izacija poezijoje y a s a biausias dalykas, gene aliza ions. We also bu be o e ha he e mus be a con en ed whole ašan ysis u i išmany i i iziką, i ma ema iką. Sigi as and Geda 1.1. The con ex . This a icle is he hi d in a se ies o ou ex s. The i s was o he speech o poe y (2019), he second o he sound o poe y (2020). The las pa will discuss he w i ing o poe y: he easons o he un o una e w i ing (his o ical, poli ical, echnical, pe sonal, a ge ed) and i s po en ial a is ic capaci y; g aphs, syllables, logog ams, hie oglyphs, pic og ams and g aphics; Pe oglyphs, li home e s and bus s. he poe ic dimensions o he w i ings (e.g. Wes A ican Adlamo and N[…]ko, Enocho languages) and he abili y o ex apola e his in o he Li huanian language. Indeed, he ques ions abou he exolinguis ic de ici and p o iciency in he Li huanian poems o he g ajdanka2, o he books o he Li huanian Ta a s in Russian A abic cha ac e s (in he case o he book by I ano Lucke ičius) a e in iguing. And also, does he shape o he s one dic a e he nex space- ime o he ex s o be exca a ed? Is Lewis Ca oll's Jabbe wocky di e en om a ex ha has ailed o be unde s ood, bu which does indeed make sense, e en hough i has been los o e e ? The ideas o he ou h pa will succeed in such o bi s. The pu pose o his a icle is o cla i y se e al cons uc s based on he in e ac ion o wo ields (poe y, language, ma hema ics) ha imply he non- i ial 1 Measu emen o he S one (li ho […] me on). This e m is mo e app op ia e he e han land measu emen (geome y) The ollowing de ini ions apply: The monog aph o Gied ius Subacius (Subacius 2010) is de o ed o ano he aspec o his heme. Poe y ca ed in s one combines in i sel bo h he a o ime and he geome y o space. The Eilengesch i , w i en in one o he o ms o he quin e s discussed below in his ex (2.2.), namely 13213-2431-4214 (S anda d Quin e Module 4), is insc ibed on a 1 × 1 × 2 ec angula s one s ele nex o he g ani e, concealing e en he di ec ion o ime. 4 Abou he linguis ic s uc u e o his poem, see h ps: en.wikipedia.o g/wiki/Jabbe wocky. This is amazing! No wonde , because Lewis Ca oll ( eal name Cha les L. Dodgson) is a p o essional ma hema ician. A icles by A icles 229 Ma ema ika, kalba, poezija: są eikos i aukos he s uc u e o he hi d a ea. This is done acco ding o he wo k on he analogy o music and ma hema ics (Alkauskas 2018), whe e he bounda ies o common knowledge a e examined no om he exac sciences (as w i e s […] and mos o hem […] a ely ee hemsel es om he schemes o na u al science hinking) ną (2.2.), nepa eikiama. Taigi šis eks as – ik idėjų daigynas. Be ne i nedygus kanko ėžis isą alksnio ( aip, alksnio!) p o aizdį sa yje jau u i. 1.2. Kon s a egija. I is ik: a ski akilmių kū ybinių jėgų są eika ga- bu om he a side. Exhaus i e examples, excep ha i 's ui ul? The heme is no i ial: al hough cu en scien i ic documen s a ibu e a sel -e iden alue o mul idisciplina y knowledge, he in e sec ion o se e al ai s mo e o en co e s he sho comings o all he sec ions han opens a new po al. Fi s , wha does he i le o he pa ag aph i sel mean? Al hough i is only a game, his wo d accu a ely e lec s he spi i o he a icle and in oduces he ui ul pa o he ma hema ics-language-poe y in e sec ion. S uc u al and ma hema ical linguis ics will only be ouched upon b ie ly in he ex (much mo e […] calcula ed), bu i is emphasized ha he a en ion o a ional consciousness o he i a ional in all in e ac ions be ween a and science has been and is much g ea e han ice e sa. Two cha ac e quo es. The i s […] Zeligo S. Ha is: Howe e , he deb o ma hema ical linguis ics o ma hema ics is chie ly he a i ude and he way o hinking a he han any pa icula esul . I is pe haps no acciden ha mos g adua e s uden s in his ield come om ma hema ics o logic a he han om linguis ics. The second is Oleg G inbaum: «Главной причиной [малой интенсивности использования математических методов в литературоведении] мы считаем отсутствие в арсенале ученых- стиховедов, оперирующих понятием художественной целостности, такого формального аналитического аппарата, в котором целостность стиха могла бы быть представлена и описана на языке математики» (Гринбаум 2002: 12).7 5 Ex ending he idea o he ma hema ical e m by An ano Ba anauskas, and e en mo e so by […] Jono Jablonski (who sugges ed he plu al plu al ins ead o he acqui ed plu al): how do you name each pa o […] in he union o se e al adjec i es? And a he c oss oads o se e al s ee s? This is he con luence o wo i e s, whe e each o hem can be called a con luence (su ekmuõ). Su ekmė (‘san aka), ekmė, įs u is (‘į aka, žio ys) a e no sui able. 6 „Reikia pasaky i, kad ma ema inė ling is ika iš ma ema ikos g eičiausiai pasiskolino požiū į i I 's a way o hinking, bu i 's no a conc e e esul . I is he e o e no su p ising ha mos g adua e s uden s in his ield ha e comple ed unde g adua e s udies in ma hema ics and logic a he han in linguis ics. 7 […]In ou opinion, he main eason why ma hema ical me hods a e a ely used in li e a u e is ha schola s who s udy o de and use a is ic uni y GIEDRIUS ALKAUSKAS 230 o he Li huanian Language Ac LXXXVI The e o e, hose a e cases when he poles change, when a ela ionship o i a ionali y inspi es a a ionali y, a e pa icula ly aluable. So wha 's he name o he game? The h ee Li huanian wo ds an sk ydis, be gžjias, and kon ž algyba ha e i e syllables each. The wo d coun e -s a egy (measu es o elimina e he impac o he opponen 's s a egy) wi h six coun e -balance keys, used in specialized li e a u e, con ains algo i hmically inco ec ly and p ac ically sup og amuojamo8 op imiza imo užda inio g ūdą: as i isus mo ologiškai, o- possible Li huanian wo ds wi h he maximum possible unc ion om he meaning o he sequence o le e s o ming he wo d. The wo d he e is iden i ied wi h he da ančių aidžių seka. Pažymėkime ją . Tegul y a isas hipo e inis lie u ių dic iona y o he con e sa ion. Examples o such unc ions a e: 1. i he e is a leas one owel in he wo d, do no add a; in he opposi e case, he numbe o o es. 2. i he e a e wo owels o wo consonan s in he wo d; In he opposi e case, he leng h o he wo d. 3 is he leng h o he longes sequence made up o he balls alone. Le s look a he las example. The unusually li ely-sounding name o he Kėdainiai Paeismilgio (small illage Smilgai is, old Eismilga) s ee indica es a possible sea ch a ea. Thus, when he wo d "moun ain" is eplaced by he wo d "moun ain" wi h he nea by meaning "moun ain", we ge "moun ain". This wo d is also used in he se en h song o he poem […]Šiau iniai elics[…]. The op imiza ion p oblem is o mula ed as ollows: is i ue ha In ha case, le 's look o he wo ds. O cou se, w i en ma hema ical (logical) o mulas only o malize sen ences ha a e easie o exp ess in wo ds. S ill, I deeply belie e ha only a egula back-and- o h be ween me apho s, o mulas, ja gon, as one ex eme, and poe ic language, as he o he , gi es he cou age o speak o he ue ela ionship be ween ma hema ics and poe y. Regula de alua ion and e alua ion o old alues. And he ligh keeps ib a ing. Ba anauskas and ma hema ics 1.3. Al hough i is g a i ying ha Jonas Kubilius has ini ia ed he inko ma ema ines Ba anausko dieno aščių i laiškų ie as, be dėl š y uoklės in ingemen o his s udy An anas Ba anauskas and ma hema ics (Kubilius 2001) is conside ed ese ed. The book is in ended o in oduce s uden s o he basic concep s, he e is no o mal analy ical appa a us ha can be used o p esen and desc ibe he uni y o he sequence in he language o ma hema ics. An algo i hm is some hing ha can be done by a ini e Tu ing machine. 9 Fo mo e in o ma ion abou he poem, see Alkauskas in he yea 2022. 10 The unc ion and elemen no a ion symbolizes he i s wo images: all he elemen s o which. A icles o he T ea y Ma ema ika, kalba, poezija: są eikos i aukos ma hema ical concep s: p imi i e numbe s, E a os henes' equa ion, asymp o ic laws, deg ees, c yp og aphy, he A chimedean cons an , he squa e o he ci cle, in ini y, and his is wha i achie es. Howe e , he eade who wan s o know Ba anausk will be disappoin ed when he eads i , because many ex s ha e li le in common wi h i . And mo e. The i s o hese was he poem "The Found Fo mula" by Ka l Hoss eld, published in 1890 in he jou nal Zei sch i . In ac , i s alue is no ü Ma hema ik und Physik: „[...] as ezul a as mėgėjui Ba anauskui bu o s a - g ea (Kubilius 2001: 30). The ligh bulb is s uck a one end. And wha does a s uden ead on his pillow? When is Ba anauskas a lose ? Ano he example: Kubilius discusses he Ba anausko publica ion published in Wa saw in 1897 en i led "O p og esji anscenden alnej o az o skali i syłach umysłu ludzkiego". In i , he su agan bishop o he Low Coun ies cons uc s a sequence o each ecu ence, which he calls anscenden al. Fo example, i a1 = 2, hen a2 = 4, a3 = 256, and a4 al eady has 617 digi s. In mode n ma hema ics, such numbe s a e no exo ic. In he heo y o Tu ing machines, he e a e unc ions ha g ow as e han any symbolic unc ion, such as (n) = an. As old by Toliau Kubilius (see also pa ag aph 84): […][In Ba anausko's wo k] he p ope ies o [ his] p og ession a e discussed, he hough s abou in ini y al eady quo ed om ou le e s a e augh . Howe e , he main pa o he wo k is de o ed o ques ions o philosophy and heology. The essen ial […] p ecisely hose ques ions […] a e also omi ed. I 's good ha wo w i e s men ioned hem: Sigi as Geda: […][Ba anausko] The i anic na u e is wi nessed by ano he […] u opian idea. I said ha a eally g ea poe mus ha e u opian ideas. Calcula e he ou o hell! Saulius Šal enis: "When I coun , I would say ha you ha e u ned he e il o he whole wo ld in o a ma hema ical o mula like a sponge. Cling o Sa an like a igh ened bee le o a piece o ginge and in oduce God's o de ! The o bi o he ligh house is o med by a con inuum o equal- alued poin s. Bu which one o hem is mos likely o be highly un ep esen a i e? Quo ing Ged once again: The e is no essen ial di e ence be ween highe ma hema ics and poe y o music. This cosmic plan o Ba anauskas also p o es ha e e y hing he did in he hea o he momen was mani es ed in o he ways in o he ac i i ies (ibid., 156). 11 This is no a uni e sal law. Fo example, in he heo y o complex a iable unc ions, all local (one-poin en i onmen ) in o ma ion abou he analy ic unc ion desc ibes i globally. GIEDRIUS ALKAUSKAS 232 Ac a Linguis ica Li huanica LXXXVI Ve y li le only hal a page o Kubilius' book is de o ed o Ba anauskas as he ounde o Li huanian ma hema ical e ms. You'd wan mo e: w i ings, speeches, speake s' commen s, exce p s om a co espondence wi h Hugo Webe . Kubilius, who himsel ini ia ed he c ea ion o he ma hema ical e minology dic iona y (MTZ), is conside ed he successo o Ba anausko's wo ks. A beau i ul o e iew o he his o y o hese e ms is w i en by Vidman The Commission shall be empowe ed o adop delega ed ac s in acco dance wi h A icle 26 o supplemen his Regula ion by laying down de ailed ules o he applica ion o his Regula ion. 1.4. Poe y and a . Acco ding o Benedik Januše ičius, " isual poe y" is a e bal ex ha gi es a new, addi ional dimension o li e a u e ha is no a isual a angemen (RP 17). Bu i seems ha his supplemen is gi en only in a ew pages o he book Raidžių pa eikslai. Some o he wo ks a e ex s, bu hey a e no s uc u ed in he o m o meaning ul s anzas, bu in he o m o quo a ions, passages, e c. (Who knows wha a mill looks like?) O he s, on he con a y, a e d awings om g aphemes. Bu , acco ding o he au ho , "a book o poe y" is no a newspape o a publica ion o in o ma ion, i mus be en i led o be meaningless o incomp ehensible. Don' you ge i ? Unde s ood! Bu nonsense? I he e's no meaning, any hing is possible? I 's like he ulga hough o Fyodo Dos oe sky. Bu i 's no en i ely ulga , because he e's some kind o connec ion be ween ai h, meaning, and poe y, as his quo e om Elio by Tom S e ns shows: "An allego y o a wise poe is no di e en om a pu e isual image. And pu e images become much s onge when hey make sense -- we don' need o know wha he meaning is, bu when we become awa e o he image, we need o know ha i makes sense. Howe e , Januszewicz's o mula "g aphic poe y" is a poem ha p e ends o be a d awing, because i gene ally i s he de ini ion o in e disciplina i y: emphasizing he quali y o he g ain, in i ing o y he wo k (a solid po only om good g ain). Theology disguised as physics his applies o some o he a icles in Česlo o Ka aliausko's Theology Dic iona y (Ka aliauskas 1992). I is ue ha i is he mos di icul o play he cha ac e o a poe wi h a g aphic mask. The e a e wo easons o his: physical and physiological. Li e a u e is he a o a non-homogeneous ime, and g aphics is he a o a homogeneous space. The cu a u e o spaces can be ei he o e y la ge dimensions, o o illuso y igu es, and he o hogonali y o poe y is ob ious. I is also ex emely iniams. Kinas, muzika elpa į homogeninį laiką12. Tai, aišku, sąlygiška, be g a- di icul o one o he wel e li e a u es, as he a o he pas , and he music, as he compulso y exp ession o he hy hm-seman ic in e al as a con inuum. Bu he idea o Rim ydas mojo laiko meno, ski is, no s dažnai paminima, nė a isiškai į ikinama, ypač apmąs an me- S anke ičius (S anke ičius 2015) ha he poe An anas Kalana ičius was pa icula ly ond o he u u e equency o ime (applies o p ecep s - o u n o e bs om e bs, o example, o epea , o p omise) […] i would seek o see each ac ion as happening now, which would o e u n he o he o hese dimensions. In addi ion, he e a e eac ions known in b ain science called limai nu odo į li e a ū os i muzikos sin ezę, y a nepap as ai įdomi. A icles by A icles 233 Ma ema ika, kalba, poezija: są eikos i aukos e en - ela ed po en ial (ERP) (HNL). Thei esea ch cla i ied how long i akes o he senses o pe cei e a wo d and o adap he wo d o he con ex . The known momen when access o seman ic in o ma ion occu s. And i 's all subconsciously. Wi hou unde s anding he meaning, i is u he cla i ied a he le el o consciousness. In he case o he in e ac ion o g aphics and poe y, i jus akes oo o en a conscious alignmen o an unde s anding o meaninglessness. This ac i i y simply s imula es he b ain. Yes, g aphic poe y is a b oad concep ha encompasses many echniques and ideas. Abs ac s (and ma hema ics) o he poems o Donald Apana ičius in his book a e among he s onges . This is he ime, nyksmas (RP 80[…]81), c yp ogalba, kabala (a he same ime, 79), genezė ab o o (a he same ime, 78). In pa icula , he h ee OM econs uc ions (simul aneously, 75[…]77) whe e he mixed language, ma hema ics, mandala, iba, phoneme, symbol, mys e y a e in luenced; The mind eac s s ongly o i (Pic u e 1). I econs uc ion I econs uc ion I econs uc ion II econs uc ion II econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I econs uc ion I z 1 PAV. O he D. The ip ych o Apana ičius The book also includes nominal ma hema icians: Euclid's i h pos ula e (see 4.1) is mined by Rimas Vėžys (RP 23), and Vilma Fiokla Kiu ė (ibid, 51) uses ma ices (deja, e e y hing in his composi ion is o e w i en; e en he logical e o 13 is mo e un o una e). Among he good ideas is Ma o Gimžausko's play […]Suahilidada[…] (same, 86), whe e he a y um is w i en in pseudo-Swahili syllaba ies […]Tau iška giesmė[…] s ongly co ela es wi h 4.2 (Remembe ing) and he ou h pa o his se ies o a icles men ioned abo e. O S. Gedos' "Vienna's D awing by Jonines" (ibid., 73), which he c i ics seem no o ha e examined in de ail ye 14. The ollowing is a b ie and highly subjec i e analysis o his g aphic ex (Figu e 2). The men ion o Jonah p o ides a gua an eed e lec ion o he sola calenda . Bones a e di ided in o 24 pa s. So we ha e luna phases whe e he odd numbe , like he yea 13 A=MATRICA IR 4R, has kiekis k ad a o k aš inėse kin a nuo 1 iki 7, ad šios k ū elės pe ime ą pada- o be 3R. In addi ion o he abo e-men ioned, he e a e also a numbe o o he examples o he use o he e m "spa ial" in he con ex o space explo a ion, such as in he case o G. No ille's in e iew, which in ui i ely men ions space he e. l /2012-02-22-gy is-no ilas-eile as is-p ieglobscio-zona/). GIEDRIUS ALKAUSKAS 234 Ac a Linguis ica Li huanica LXXXVI And he beginning o he mon h (when you' e young, you' e alone) ma ks you h. The gi en d awing is he mos popula o me sola -moon calenda among a ious cul u es. The Chinese, he Heb ews, and he Indians s ill use i oday. I was used by he ancien Scandina ians, because his The wen y- hi d pa ag aph o he […]Va ūdnio eilių[…]: Mundil io is is he a he o Mėnesis, Saulė is his daugh e . They a e des ined o a el h ough he skies e e y day […] so we coun he ime (PE 101). In Scandina ian my hology (as well as in Sume ian, Indian, Heb ew, and G eek), and e en mo e so in cosmic my hology, Geda was o pa icula impo ance. Odin, Tho , and Loki a e men ioned in one cycle o "Se en y Summe Songs". Fu he mo e, Jeho ah's a angemen - he comple ion o he wo ld's c ea ion, he se en h day o God, he balance o powe - ep esen s he equinox o sp ing and au umn, he se en cubi s on he le and he se en cubi s on he igh . The e, he wo ld's assembly is he s onges , he kiss is he slowes . The whole mass o he wo ld, e en isually, is concen a ed a hese s a iona y poin s, and he sun's e u n is a b eak, a ansi ion, a shock, a singula i y. The uppe uni ( iena ė, singula is) is […] Joninės, he lowe one is […] Kalėdos. The i s day o God's calenda is he eme gence o o de om chaos. The in e sion o chaos is Tobuli y. O de is a he edge o he hand, in he abyss (g . χάος). O de , ine i ably esembling chaos. And also: be o e he calenda was s anda dized ac oss he plane , he win e sols ice in he Sou he n Hemisphe e coincided wi h he summe sols ice in he No he n Hemisphe e. Bu o hose wo ds e e y hing is jus i ied by one o Coun ess Gedas poems. 2 PAV. O he S. Gedos […]Viena ės piešinys pe Jonines[…] 15 S uc u alis , p ecisely ma hema ical music compose s unexpec edly no iced ha he composi ions o Tokia di e ed li le om he alea o ical p inciples c ea ed. A icles by A icles 235 Ma ema ika, kalba, poezija: są eikos i aukos 1.5. Signa u es and ag eemen s. In ma hema ics, a numbe is an elemen belonging o a ce ain s anda d s uc u e. Since o he (excep 4.1.4.3.) will no be equi ed, he numbe he e means ei he he na u al numbe om he abyss = {1, 2, 3, 4, ...}, o he in ege numbe om he abyss = {0} . The meaning o he p i eiks ik są okos g upė, ku i bus apib ėž a ėliau. s uc u e is p ecise, bu when M, N, he unc ion M mod N (numbe ed ‘M moduliu N) indica es he only in ege L, 0 ≤ L ≤ N 1, such ha M L is di isible by N wi hou a emainde . Fo example, 20 mod 7 is 6. In he case o a poem, he capi al le e deno es he masculine, he lowe case […] he eminine, he lowe case […] he dac ylic ime (when he hi d le e is c ossed om he end). The index o his le e will show he numbe o ee ( wos o h ees) in he ow. I all he ows o he pe iod ha e he same numbe , i 's jus a ou -legged s ool. 3-am ib achis i pan. 2.POSMAI IR GRANDINS The endency o mode n languages o di e en ia e abs ak ų mąs ymą ( he only uni e sal language oday is ma hema ics), bu he uni e sal p ope ies o he La in language a e cha ac e is ic o Dan e's Flo en ine dialec s. This is Thomas S e ne Ellio . 2.1. Eilėda a and he language. A pa o he a o hy hm is he adap a ion o ma hema ics (in he b oades sense) o a pa icula language, i we conside hy hm, phone ics, ins umen a ion, o m, hyme as exp essions o s uc u e, symme y, balance and analogy. He e a e a couple o examples. In he classical syncopa ion, he in e als a e 0, 1, 2, o 4 unci cumcised syllables. Juozas Gi dzijauskas s udied he s uc u e o he la e and ound he ollowing ac s: In Li huanian poe y he e a e wo syncopa ed g oups wi h six main me e s and eigh een de ailed a ian s. Almos all a ian s o syncope (excep one) a e domina ed by he non-ci cula ing wo-pa in e al ( om 51 pe cen o 75 pe cen ). This is because o i s dominance in he 16 h cen u y, when he e m "poe y" was used. Ma ulai ienė was bo n in 1997. 17 The e m was in oduced by Kęs učio Nas opkas. In he case o ype V and ype VI syncope, he in e als o 3 and 5 a e allowed (Gi dzijauskas 1978: 220–230). GIEDRIUS ALKAUSKAS In he Ac a Linguis ica Li huanica LXXVI aBaaB, Co nelius Pla elis […]Mėnulio da želis[…] (1984, 5-am ib achis aBaaB), V. Mykolaičius-Pu inas […]Hymn o Pessimism[…] V (1925, 4-am ib achis aBaaB), Albino Be no o […]Ilgo yl[…] (4-8, Anakam ib achas aBaaB), V. Mačinio […]Žmogus (1943, jambilis a7B7A8a5B5) and […]**[…] ( he i s h ee lines o which ha e a dak il a4a4a4a4a4B; h ee o which ha e a dak il a1a4a4b), E iko […]Baladė w o e abou he beginning o he poems in he beginning o he poems (1987, jambalis j4A4A3A4A4A4A4A4A4A12). The e a e pauses a all o hese s ages: ca alec in (a lack o one's skiemens), he na u al b ea hing o he ex in such a i e-s ep sequence equi es pauses. I is di icul o imagine a a ba pėdà su umpėjusios eilu ės. Eks apoliuojan ai į k in inas, galima eig i: na u al ex low when each ime co esponds o bo h 3 masculine and 2 eminine cadences (o ice e sa). I 's he second op ion. The e's one excep ion, hough. A pu e hendekasilab jam is also sui able o quin uses. He e each line ends wi h a pause, illing i up o six ee . The wid h o zės mãža, be ki os eilu ės anak uzė, eikdama kaip p ieš ak is, pauzę a y um one is up o wo skis. And indeed, he i s disco e ed poem wi h he hyme scheme 12112, which coincides bo h wi h he numbe o syllables in he lines and hei ypes o cadence, is Aido Ma čėno's […]Iš pak aščių į cen ą[…] (2000, 5-jambas abaab). In he con ex o his chap e , he i s pa ag aph simply mus be quo ed: "Dan e has isen, he oo h is bleeding, he old man is whe e he was yes e day, he landscape is glued om agmen s, he sky and he ea h, he woman and he lu e, he ligh , as i hell begins he e" (CHLP 142). The e ame e is less sui able, because i he pause we e coun ed, each ow would be i e, and he pe iod would be […] 25 ee . The inequali y o his numbe elimina es he sudden u ning in he ex . In his way, he h ee […] cho us, he dac yl and he jambo […] eme ge in a o m sui able o he quin e s: 2 1 3 2 1 ∪∪∪∪ ∪∪∪ ∪∪∪∪ ∪∪∪∪ ∪∪∪ ∪∪∪∪∪ ∪∪∪ ∪∪∪∪∪ ∪∪∪∪∪ ∪∪∪ ∪∪∪∪∪∪ ∪∪∪∪∪∪ ∪∪∪∪∪∪ ∪∪∪∪∪∪ ∪∪∪∪∪∪. As men ioned, he mos ypical Li huanian language is he wo-syllable non-ci cula skiemen in e al. I is o his eason ha he yped example is used in his a icle S aipsniai / A icles 243 Ma ema ika, kalba, poezija: są eikos i aukos The au ho 's poem "The Relics o he No h" begins wi h he song "The Fi s Ba le wi hou The gua d. The i s wo s ages: The deep-sea ed a ea o he no he n idge, he he idge, he idge ha has no won, he idge The e e nal he Skelia is co e ed by Ge ian idge... The idge, has won, he idge ha ha has no won, he idge ha has no won. Only gi en by A e ia Visa e ėja wheel. I' e go he blue one. 2.4. The Sep uagin Canonical se en hs a e less p ac ical. Because, i s o all, e e y hyme would epea i sel se en imes, and ha 's a se ious one-line . Secondly, he hyme cycles would shi only a e se en lines. When conside ing a ious 7-cycle sequences, i would be mo e p ac ical o ake each second s ep. Thus, some e y a ac i e sep ums a e ound. This is he i s o he ou poems in he second e alogy, Alkauskas 2022. S age one h ee one ou wo h ee ou wo S age wo 5 3 6 45 6 4 S age h ee se en i e eigh six se en eigh six Unequal hymes a e epea ed h ee imes wi h spaces o 3, 3, and equal […] ou imes wi h co esponding spaces o 2, 4, 2. 3. The GROUP Ma hema ics, along wi h language and music, is one o he i s exp essions o he ee c ea i e powe o he human mind. This is He man Weill. G oup s uc u e and me a hesis. Bina y ope a ion i s such a wonde ul box wi h doo s on he le , igh and op. By inse ing an elemen om bo h sides, he box also gene a es some hing ha can al eady be emo ed om he op. Ma hema ically, his is w i en as a □ b = c. Fo simplici y's sake, ins ead o he symbol □, he s anda d symbol is used o ma k he box. G oup (Γ, ) is also a bina y ope a ion i he pai sa is ies he ollowing axioms: o each a Γ; 1) Neu alusis elemen as ( iene as): egzis uoja oks e ∈ Γ, kad a ⋅ e = e ⋅ a = a 2) The in e se elemen : o e e y a he e exis s a b such ha a […] b = e; GIEDRIUS ALKAUSKAS 244 Ac a Linguis ica Li huanica LXXXVI, which was published in he O icial Jou nal o he Eu opean Union. Axiom A = b = c (a) Axiom A is he only elemen ha is neu al, and he only elemen ha is opposi e o i . The la e is hen ma ked wi h a[…]1. I 's called mu a ion. In he eal wo ld, his is no ypical: i 's no he same as he i s passenge o die Bina inė ope acija gali enkin i i lygybę a ⋅ b = b ⋅ a. Tokia g upė adinama ko- jumping ou o i . The simples elemen s in he g oup a e he uni a e he kojinę, a au i ba ą. I ne as pa s, kas į yks a anksčiau: au obuso sus ojimas a elemen s o he second ow (i hey exis ) o which a […] a = e applies. The opic o mi o e lec ion is no new in he con e sa ion. This is also he case wi h me a esis (li . kep i // sla . peek i), and Algi do Pa acko's de eloped opology (Pa ackas 2014: 85), which desc ibes he meanings and symbolic connec ions o wo ds: pla -us // alp-us; gyl-is is equal o 34 and so on. Wi hou looking a he well-dese ed c i icism o he speake s, he la e phenomenon should no be dismissed as comple ely un ue (Sauda gas 2014: 100). Mo eo e , acco ding o Dainiaus Razausko, he wo ks o A. Pa acko and A. Ža skumi emain ele an in ela ion o Vienna. I is p ecisely in hem ha one can see an a emp by S. Valen o o de ec he linguis ic phenomenon unde conside a ion a he highes philological le el [in he book Mė(lynojo)nulio linguis ics] no in au ho 's poe y, bu in he Li huanian language i sel " (Razauskas 2006: 59). The heme o mi o e lec ion can be ex ended, bu on a comple ely di e en p inciple. Le 's call his e e se ex design (RTD). I is a o m o c ea i i y in which he means o cons uc ing he ex a e limi ed by p econcei ed ules, lea ing ull eedom o i s in e p e a ion, in e p e a ion in con ex , allusions and manipula ions. Below a e au ho examples. The a o emen ioned p elimina y ule becomes clea a e se e al o hem. 3.2 The ex Me amo phosis is he p ocess o changing he subjec 's mind and body o change he subjec 's mind and body o change he subjec 's mind and body o change he subjec 's mind and body o change he subjec 's mind. *** Abou he cold and he ine i able No embe anxie y I 's all igh . I 's all igh . *** Apie ko o mėnesį nuskaid ėjan į ainų gy enimą p ie Išika io upės 33 Essen ially, wha is being discussed he e is he composi ion o unc ions, which by de ini ion a e al eady associa i e, bu hei commu a i i y is […] ex emely a e. 34 Pa icula ly in e es ing ma hema ical cases: leng h […] ou , e ical […] ho izon al. A icles and a icles 245 Ma ema ika, kalba, poezija: są eikos i aukos SAKUROS VĖLEI. VAKARO SIELIAI. *** The omance o an unhappy lo e o he cello solo GLS RŽIA […] CHÈL GRIEŽIA. This is he i s ime I' e been o his place. *** Tell me abou he money, he ake and he ake c eam. The eins a e ull o milk. *** The pa adise o he Ojibwe li ing by he G ea Lakes I 's all igh . I 's all igh . I 's all igh . *** Abou he cu iosi y o he be y and he oy obo s in childhood I'm no going o lie o you. I 's called LIEKA RL. *** The my h o he So ie s and he bu ial o he dead in he wa e s o DLS VLUOJA. I 's a wo-way s ee . *** As on ea h, so in hea en. (The s o y o he Queen o Bi ds, like he hea enly Ma y An oine e, who du ing a amine answe ed hose who asked he o ood: "Is he e no b ead? Ea cake!") Wha a lo ely way o ea . *** La gale o Del u a and Nalsia in he 7 h cen u y. The S.L.I.N.A. is V.L.E. I'm so y abou ha . *** The Sa io 's Se mon on he Los Kingdom and he Gaining o he Kingdom o Hea en (Luke 9:24, jus e old in he Ma ke place o Skopje) VIELÕS CELĖS – CÍELOS VĖLĖS. *** The s o y o an old seduce who, wi hou digging, ound a slab om he second emple o Je usalem, he WORLD OF ZABAL. The GABLAS yellow. I 's all igh . I 's all igh . *** The i s communi y o hun e s and ga he e s (in which hun e s also become ga he e s by using spices) PELS STRING […] STRLS PINGA. *** The s o y o A ila he Hun, wi hou any chi al y, won by he hand o Ildik A g ea sho , a g ea sho . *** GIEDRIUS ALKAUSKAS This Regula ion shall en e in o o ce on he day ollowing ha o i s publica ion in he O icial Jou nal o he Eu opean Union. Wha is he smalles bu mos impo an pa o a g ea hing? DRELĖS – RATAS, RELĖS – DRATAS. *** I all makes sense. Physicis s will con i m ha he essen ial mechanism o he coil (n. wo ld. d el) is he coil, and he elays […] he elec omagne , consis ing o a wi e (n. wo ld. wi e) coil and a e omagne . O he schemes o he applica ion o ATD may also be sugges ed. Le 's ake cha ac e is ic ph ases, p eposi ions, jus u ned in o oxymo ons o puns. Fo example, you' e no going anywhe e. You' e going o ha e o ge ou o he e. he b idge is no abou o be bu ned; We'll see i we can see ha . I 's been ha way since ime immemo ial. he c op is no longe cul i a ed; No one's eady o ake o hei clo hes and so on. The mos in e es ing hing, o cou se, is o in e p e such a one-way s ee . Bu he idea ha he seman ic cha ge o he i le o he poem can be decisi e is no eally new. The […] pa o he eilių in S. Geda's book The Hidden Spi i o he Seeke (Geda 1994) is enc yp ed only a pos e io i by epea ing he i le. 3.3. Synonyms and oo s o he uni . Fi s ly, he de ini ion: Tik aisiais synonyms a e wo ds wi h a simila o simila meaning ha mean he same concep and a e used o deno e di e en shades o meaning o s ylis ic ea u es. [...] Due o polysemy, a wo d in some o i s meanings may en e in o synonymous ela ionships wi h ce ain wo ds and in o he meanings […] wi h o he s[…] (Lybe is 1981: 3). Now, le 's imagine ha he wo ds α1 and α2 a e ue synonyms. Ideog aphically, žan iniai, emociniai, da ybiniai – inka isi. I už iksuo i žodyne, i naujai su- cons uc ed, i only he linguis ic sense does no con adic he synonymi y gi en. Le s ma k his ela ionship as α1~α2. Le now ollow α1, α2, α3, ..., αn each adjacen pai will be synonyms (in ski ing pai s he same wo d can be used homonymically). I we we e looking o examples wi h α1~αn, we would ha dly a oid one synonym kekes. Bu he addi ional equi emen p, 1 < p < n: α1 αp, al eady c ea es he necessa y ol age. The nex ques ion is, when is α1~αn? In o he wo ds, can he chain o synonyms lead o he an onym? The e's poe y in ha ques ion. I 's a me apho o he ela i e and he absolu e. To quo e Lybe ia la e : Win e , when you close you whi e shoes, you pumpkin is cu g een (Mai onis). He e he wo d is ue, one o he pa alai eikšmę ‘sniegas’ įgyja ik kon eks e i y a aizdinga me a o a“ ( en pa ). ypes o me apho is he con ex ualiza ion, gi ing di e en wo ds o ph ases synonymous ea u es. Bu he con ex ualiza ion can be eplaced by an algo i hm ha b ings he wo d α1 synonyms in a chain o he wo d αn. Thus, his chain acqui es me apho ical ea u es. Synonyms ha don' con lic wi h he linguis ic in ui ion, he c ea ion o pseudopa izds can also be good poe y. A icles and a icles 247 Ma ema ika, kalba, poezija: są eikos i aukos Le i be n[…]. The complex numbe ρ is called he n- h deg ee oo o minus one i ρn = 1. Fo example, 35, G andin α1~αn and is he linguis ic oo o he minus uni analogue. Fo example, hea , hea , hea , cold, cold, cold, cold. The wo d džio a is used he e homonymously bo h as saus a and as ube kuliozė. In he o mula ion o Libe ian, he synonym […] is a shade. Ano he colo ha can be synonymous wi h op ical colo s is he colo o double whale equency. Fo example, ed ligh (400 e ahe z) is synonymous wi h iole ligh (800 e ahe z). I his is no con incing enough in op ics (bo h equencies a e in he egime ligh pai s), acous ics helps, because he doubled equency co esponds clea ly o he synonymous (common wo d) in e al o he pu e oc a e ( o example, he i s and second oc a e sol). The e o e, in he case o op ics and acous ics, he an onym would be exac ly ac oss he middle, whe e he wa e equency a io is […] 1.4142. Howe e , i is clea ha i is possible o mo e slowly om one o he o he only h ough shades and shades. In he con ex o language, such cases a e singula . Tha 's wha makes hem in e es ing. The example o hea […] cold gi en abo e may no be pa icula ly in e es ing (i 's cold and i doesn' ma e ), bu he heme i sel is some hing deep in he language. I 's jus a ma e o u ning he wheel. 4. Poems and ma hema ical exe cises In Sibe ia, I became in e es ed in he exac sciences - physics, ma hema ics. A nigh , I s udied he heo y o cha ac e s and w o e poems. This is M . Česlo as Ka aliauskas. The A chimedean cons an The numbe π is he mos impo an o he so-called pe iods38. The alue o his cons an is equal o he a io o he leng h o he ci cle o i s diame e , app oxima ely 35 The uni i sa is ying he equa ion i2 = […]1 in ma hema ical Pla onic eali y is a eal, exis ing objec , bu such a misleading designa ion has been his o ically used. The acous ic wa es o he nea by equencies a e s ongly dissonan due o he so-called "blowing e ec ." Bu i he echo […] is a memo y- epea ed sound (geome y) whose equency may de ia e somewha om he o iginal, hen he echo becomes a di ec analogue o he op ical shade. 37 The opposi e o his oolish allego y is he ph aseology o he wea ing o he swo d, bo h o which a e almos synonymous wi h he i s . The de ini ion o he e m is qui e echnical (c . Kon se ich, Zagie 2001). GIEDRIUS ALKAUSKAS 248 Ac a Linguis ica Li huanica LXXXVI 3.1415926535897932384626433832795. Tha 's igh , he e is no o iginal de ini ion. Euclidean geome y ope a es in he plane wi h lines and poin s, whose ela ionships a e desc ibed by Euclidean pos ula es. When you hea he wo ds poin and line ma hema ically, you imagine eal objec s, bu you can only ope a e wi h concep s ha a e subjec o p ede ined ela ionships called axioms. These a e […] du ies, g ains, g owing c ops ( heo ems) and ha es s ( heo ems). Example o he axiom: The only s aigh line ha does no c oss i passes h ough a poin ha is no in he gi en line. This is he amous i h pos ula e (axiom) o Euclid, which has long been ied o de i e om o he s. I i had wo ked, a i h would ha e been unnecessa y. The poe and ma hema ician Oma Khayyam w o e a commen a y on he i s pos ula es o Euclid's book (a ound 1100), in which he hough he had ound he solu ion. Un o una ely, in he nine een h cen u y, i was p o en ha Euclid's i h pos ula e is independen o he o he s. His al e na i es ga e bi h o he so-called non-Euclidean geome ies. I an Ka amazo spoke o Alyosha abou he la e : «Между тѣмъ находились и находятся даже и теперь геометры и фило- софы, и даже изъ замѣчательнѣйшихъ, которые сомнѣваются въ томъ, чтобы The whole uni e se, s ill as , "e e y hing ha exis s was c ea ed only by Euclidean geome y, and i is e en d eamed o , ha wo pa allel lines, which, acco ding o Euclid, can ne e each he ea h, can be, and would be, in some in ini e way" (Dos oe sky 1879: 396). Only he au ho , by he way, is no en i ely accu a e he e: by men ioning he Euclidean, he is mo e likely o desc ibe he essence o p ojec i e geome y. In he la e case, he s a emen is always ue: wo con adic o y u hs in e sec a one poin . This geome y has ano he peculia i y: i you pu he concep s o do s and s aigh lines in any o i s heo ems, you ge he co ec heo em. The i s claim has a dual asse ion: he only s aigh line passes h ough wo di e en poin s. A he same ime, i 's a g ea illus a ion ha he line and he do a e abs ac ions. By imagining a seman ic language in which he meanings o he wo ds " igh " and "w ong" a e linked, all Li huanian heo ems a e alid and meaning ul. Fo his objec , kad bū ų pa yškin a, kaip ma ema inė abs akcija ski iasi nuo aizduo ėje esan- i is wo h men ioning ha one o he models o he p ojec i e plane is a h ee-dimensional space wi h a ixed ze o poin O, in which […] aškas[…] […] i is pe O i iesė, o „ iesė pe du aškus“ – pe d i okias ieses iš es a plokš uma. Todėl einang e a Dos oe sky i s pe ec ly and Jus in Ma cinke ich: All he ime I' e been looking o one poin om which all he u h comes ou . I'm always looking o a wo d, e en hough I know I'll ne e ind i . A icles and a icles 249 Ma ema ika, kalba, poezija: są eikos i aukos The law in he in ui i e de ini ion o π is now explained simply. The Euclidean geome ijos ėmuose iesiog neįmanoma apib ėž i k ei ių (pa yzdžiui, apsk i- Timo is long. This equi es ano he b anch o ma hema ics, analysis, wi h i s own axioms. The i s de ini ion o π may be su p ising: his in eg al […] a g ea . s epping s one o Dan e's […]Red[…] hi y- hi d o he o y- i h song: Qual èl geomè a che u o sa ige measu e he ci cle, and did no e u n, ealized, hinking, wha p inciple ondelli Saky um geome as, whe e he ied o o u n he ci cle in o a squa e, inally indige. I 's a was e o ime and e o . Why, in his case, is measu ing a ci cle and u ning i in o a squa e a ai ly accu a e ansla ion? Dan é is alking abou he an ique sc ibbling squa e p oblem. This one asks i i is possible o cons uc a squa e wi h he help o a sc ibe and a line, he a ea o which is equal o he a ea o a uni sc oll. The ac ha he answe is no was p o ed by Fe dinand on Lindemann in 1882. π and he geome ic s uc u e o he poem i sel , p ecisely planned by he au ho himsel (see Ha 1987). Dos oe sky men ions Už ašuose om he house o he dead, compa ing he p oblem o w i ing a squa e wi h he un esol abili y o i wi h he combina ion o punishmen s o he same c imes. This ac is omi ed in he a he comp ehensi e The Palg a e Handbook o Li e a u e and Ma hema ics (PHLM). 4.2 The Mnemonics Da ijo Kas eljanos (Cas ellanos 1988: 152[…]153) discusses he mnemonics o a ious languages ha help o emembe π in he digi al decimal coun ing sys em. The code he e is simple: he numbe o le e s in a wo d co esponds o he numbe o men. A well-known English a ian , somewha less […] G eek: How I wan a d ink, alcoholic o Ai he God o Megas Geome y, he cycle cou se, a e he hea y lec u es on he leng h o he edge o he diame e , pa agene in ol ing quan um mechanics! he numbe o ou s anding... Toliau au o ius pa eikia imuo us pa yzdžius p ancūziškai i ispaniškai. I is clea (and esea ch con i ms his) ha poe y is mo e sui able o his pu pose han p ose (Le i in 1999: 200 […] 211). Indeed, a pe son's memo y o de ails is qui e weak: many people emembe only accen , emo ion, and mood om a casual con e sa ion. In ligh o his ac , he memo y o he old ballads and epics pe o me s seems almos phenomenal. Vis ik y imais a skleis a, kad a likėjai isų de alių neįsimena: i mas, imas, ali e acijos, melodika, g ama ika, seman ika eks o lais ę iboja, kas i padeda GIEDRIUS ALKAUSKAS 250 Ac a Linguis ica Li huanica LXXXVI is no w ong. Simila ly, ac ile sensa ions s eng hen he memo y o pianis s. Howe e , a e a pause, i was epea edly poin ed ou by ele en epic poe s ha he ex is no always epea ed iden ically, bu is subjec o seman ic and poe ic cons ain s: he lexicon a ies synonymously, and smalle wo ds, wi hou changing he meaning, some imes change he meaning. In he con ex o memo y eco ds, his is whe e he po en ial dange lies. The poe y being sung will encode a lo o π digi s, bu one un o ge able synonym can uin e e y hing. Fo example, Cas ellanos (1983) p o ides a 1717 F ench poem based on a calcula ion o 126 π digi s. Un o una ely, he numbe 113 is inco ec . When his was no iced, he wo d sec o (7 le e s) had o be eplaced by quad an (8), and he co esponding an e io (9) by p eceding (9). The e's ano he d awback o his coding. The e is no doub (al hough i has no ye been p o en) ha he numbe π is no mal in all sys ems o calcula ion. Tha is, in i s en h exp ession, he numbe 0 will occu asymp o ically wi h he p obabili y 39. Since he e a e no b aid wo ds, ze o can be encoded as decimals. Secondly, one-syllable wo ds in poe y may include o and in o, a ew su ixes, a comma,40 and he unusually used le e o he alphabe .41 Howe e , i is ob ious ha i e e y en h wo d is singula , he ex will no be na u al. All hese wo ds belong o a sepa a e class hey do no encode any hing uni o mly. 4.3. con ol o memo y. The solu ion o he p oblem o un eliabili y o memo y de ails was p oposed by an algo i hm ins alled in he b owse and a ious QR (quick esponse) codes, c edi ca d numbe s, book labels, ISBN and EAN sys ems. In pa icula , he con ol amoun me hod (S akėnas 2007: 127). I you wan o emembe he digi s 3603735 he simples con ol numbe is olded like a og on a couch42 o con ol he leng h o wo ds, you can add se en wo ds, o muo bū ų 3 + 6 + 0 + 3 + 7 + 3 + 5 mod 10 = 7. Taigi, siekian eilu ės jau kny- example, al eady olded like a og on a couch in on o a book (yes, ha 's a ope). Some ex -obedien mis akes (like → and, like → how) will be no iced, bu i you acciden ally decla e, you will be sucked in. The e o e, he e is a ce ain a ying in e nal s uc u e, and he s a is ics a e no a ec ed. O en, he desi ed p ope y is demons a ed p ecisely by ouching his 39 Ta kime, eikia į ody i, kad aibė u i am ik ą sa ybę, ku i nė a būdinga ipinei, s a is inei ai- s uc u e. On he o he hand, he asks ha ask o p o e ha a pa icula numbe sequence (π digi sequence) is subjec o s a is ical laws a e he mos di icul . 40 The amous […]Anykščių šilelio[…] (o , bu , he ogi). 41 Juozo E licko's a ou i e s ylis ic de ice, o example, "Mo e gi es joy o he soul and so on", "A ain ha an om A o B and wen o C a e wa ds" and so on. 42 Eilu ė iš S. Gedos eilė aščio „Ka aičių kaime, ku is užpus y as smėlio“, ik o iginalus i pakeis as A icles and a icles 251 Ma ema ika, kalba, poezija: są eikos i aukos The wo ds in he book and he places whe e hey' e been s i ched oge he wouldn' ha e damaged he jambon and he cezu a, bu he check numbe o his e o , un o una ely, won' be eco ded. Ma hema ics can s ill help mo e signi ican ly, because he algo i hm chosen is no good enough. I Luhn's o mula we e used, i would eco d bo h single-digi misma ches and almos all e o s in swi ching be ween wo adjacen digi s (only e o s o 09 […] 90 would no be obse ed). 4.4. The algo i hm A gi en ini e sequence o digi s {s1, s2, s3, s4, s5, s6, ..., s }. I is a subs i u able sequence K = {2s1, s2, 2s3, s4, 2s5, s6, ...}, i.e., each second membe is doubled. All wo-digi numbe s in K a e subs i u ed o hei nume ical sums (e.g., 12 → 3,14 → 5, e c.), hus p oducing he sequence L3. All he membe s o L a e added oge he , and he desi ed con ol numbe is equal o his sum modulo 10. Fo example, le 's look a he same 3603735. This is K = {6, 6, 0, 3, 14, 3, 10}, L = {6, 6, 0, 3, 5, 3, 1}. The con ol numbe is 6 + 6 + 0 + 3 + 5 + 3 + 1 mod 10 = 4, so he wo d "end" will be ixed wi h mo e possible e o s han he wo d " on ". The mnemonic-con olled algo i hm will now be desc ibed only oughly, as i equi es ca e ul s a is ical analysis o he sample ex and discussion o possible complica ions. Ins ead o using he Luhn me hod, he Du ch ma hema ician Jacobus Ve hoe 's algo i hm is used. inka da daugiau klaidų, aip pa i 09 ↔ 9043. The ex is w i en in classical e na y, whe e each line has 11 syllables. A li le bi o s a is ics. The g aphic depic s Sigi o Gedos ansla ing […]P aga o[…] X songs in all 45 hi ds long le e s (sepa a ion ma ks a e no coun ed). All ows excep one in he hi d, 7, 11, 21, 23, 30, and 33 (whe e he numbe o syllables is ei he 9, o 13) ha e 11 syllables. Ma hema ically, he lines o "non-den is " ha e been co ec ed. This is al eady a s ic ly hendekasilabinian jambo ex and is used o s a is ics. The a e age numbe o le e s in a e ia y is 84,44, and he a e age numbe o le e s in a semicolon is 2,558. The black line indica es he no malized dis ibu ion unc ion, in e pola ed e ically44. Algo i mas. Tegul {ps, s ∈ } bus skaičiaus π skai menų seka. T. y., p1 This is equal o 3, p2 is equal o 1, p3 is equal o 4, p4 is equal o 1, p5 is equal o 5, and so on. Le 's b eak i down in o 10 nume ical blocks. Now le 's ake one block and pu i in he con ol digi acco ding o 43 in he Du ch language, numbe s a e usually coun ed in pai s. J. Ve hoe […]as, when s udying pos al indexes, calcula ed ha phone ic e o s, when he numbe 1x is mixed wi h x1 ( o example, 15, Vij ien and 50, Vij ig) accoun o 0.49% o all e o s. I 's an unknown, bu isible pa . The p obabili y dis ibu ion unc ion o a andom size Z (Fx) = Px (Zx) indica es he p obabili y wi h which mę, mažesnę už x. Tokios unkcijos maksimumas y a 1. G a ike ši eikšmė padaugin a iš 5, kad i acqui es signi ican da a om a single illus a ion.