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.