这些无法翻译的外语单词有哪些故事/典故?

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tumblr的舶來品?原文英語,譯作中文更爲冗長,但真地要這麼多字才能表達嗎?原作恐有故意嘮叨博取噱頭之嫌。

再者很多詞(包括但不限於我認識的)也並不神奇。

waldeinsamkeit = wald + einsamkeit = forest + loneliness = 林中孤獨(孤感?)
почемучка = почему + чка = 爲什麼 + 指小的後綴,實則專指小孩,《简明俄汉词典》的“小問號”之譯乃至勝過原詞。
木漏れ日 = 木(樹) +漏れ(漏れる)+ 日(太陽),譯作漢語也許去掉假名即可。
dépaysement = dépayse(r) + ment,化dépayser(離鄉,或者「遷」我看就行)爲名詞。有的詞典作好感,有的詞典作不適,還有一「流放」的廢意。「離鄉」之類也是古意。
sobremesa = sobre + mesa = on table = 桌上(的),不同語言(乃至不同地區,比如南美和歐洲?)引申大概不同,可能指最後一道甜點,可能引申作一串好事的最後一件(葡語),西語則作飯後閒聊,然而還是要據上下文,按原樣解作桌上也並無不可。
cualacino乃culaccino之訛誤,源自culaccio(牲畜的臀部),引申作「留在玻璃杯底的濕印」也可接受。

早先還有ten most difficult words to translate之類,也可以維基untranslatability。

多是由於原語言用了並不明瞭的構詞法(單純地疊加)或引申了,而別的語言卻追求口語化、清晰但冗長的構詞法,且要道出引申義。其實原語言詞典中的解釋也是如此,例如:

waldeinsamkeit: Abgeschiedenheit des Waldes——樹林的孤獨。
почемучка: ребёнок (реже взрослый), задающий много вопросов. ——常問問題的小孩(鮮指成人)。
木漏れ日: 木の葉の間から差し込んで来る日光。——插進樹葉間的陽光。
culaccino: Il residuo di un liquido che resta nel fondo di un bicchiere o altro piccolo recipiente——液體殘留在玻璃杯或別的小容器底部的遺蹟。
dépaysement: État d’une personne dépaysée. Changement agréable d’habitudes.——人更換環境的狀態。習慣的可喜改變。

成熟的語言之間並無無法翻譯一說,無非是長度變化罷了。現代語言之間互有長短,況且文語口語大有區別,不能一概而論。要追求短長之差,不妨翻譯文言(文),到任何一種語言,恐怕長度至少都得翻倍。

(原发于果壳问答

于 2013 年 12 月 22 日

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Reading Russian Lines of Cloud Atlas (4)

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ОБЛАЧНЫЙ АТЛАС

Острова Тихого Океана, 1849 год.

Дело сделано, мистер Юинг, теперь сей контракт свят для исполнения… почти как Десять Заповедей.
сделано: done
сей: this
свят: holy
исполнения: execution, fulfillment
почти: almost
Заповедей: commandment

Благодарю, Преподобный Хоррекс, мой тесть с нетерпением ждёт завершения этой сделки.
Преподобный: Reverend
тесть: father-in-law
нетерпением: impatience, hurry
ждёт: wait for, expect
завершения: completion
сделки: transaction

Хаскель Мур — великий человек. От таких как он зависят судьбы грядущих поколений, он не боится говорить правду.
великий: great
От: from
таких: such
зависят: depend on
судьбы: destiny
грядущее: coming, approaching, future
поколений: generation
боится: fear, be afraid of

Именно так.
Именно так: Quite so!

Когда я впервые столкнулся с творениями Хаскеля Мура, его проницательность показалась мне откровение Божьим.
впервые: for the first time
столкнулся: run into
творениями: creation
проницательность: perspicacity, insight, keenness of perception, discernment, clairvoyance, acumen, sagacity
показалась: show one self?
откровение: revelation
Божьим: God’s

Мы с просвещенным доктором, не одну ночь провели за обсуждением его этического трактата.
просвещенным: enlightened, luminous
провели: conduct
обсуждением: discussion
этического: ethical
трактата: treatise

Я только полагаю, что он весьма убедительно объясняет, почему мы наслаждаемся этим божественным ягнёнком, а Купака стоит и всего лишь нам прислуживает.
полагаю: suppose
весьма: highly, very
убедительно: convincingly
объясняет: explain
наслаждаемся: take delight in, revel in, enjoy
божественным: divine
ягнёнком: lamb
стоит: stand
всего: in all, only
лишь: only
прислуживает: serve

В самом деле. Эм, Купакатебе ведь по душе жизнь в нашем доме, не так ли?
деле: affair
ведь: you know(?)
душе: soul
не так ли: isn’t it?

Ох, да, Преподобный, господин. Купака очень счастливый здесь.
господин: gentleman, sir
счастливый: happy, fortunate

Вот видите, это и есть по Муру лестница цивилизации, определяющая порядок вещей в мире
видите: see
лестница: ladder
цивилизации: civilization
определяющая: determining, determinative
вещей: things
мире: world

Прошу тебя, помолчи. Я слышу от тебя одно и тоже… давайте лучше послушаем мнение его зятя.
Прошу: request, ask
помолчи: be silent
давайте: let us
лучше: better
послушаем: listen to
мнение: opinion
зятя: son-in-law

Ох, что же… Он исследует вопросы воли Божьей, природы человека, мужчин.
что же: what on earth
исследует: investigate
воли: willpower
Божьей: God’s
мужчин: man

А что он думает о женской природе?
природе: nature

Боюсь, что этот вопрос он обходит молчанием.
Боюсь: fear, be afraid
обходит: evade
молчанием: silence

И он далеко не первый.
далеко: far

Итак, мистер Юинг, продолжайте.
Итак: so, thus
продолжайте: continue

Ну что ж… он ставит вот какой вопрос… если мир сотворён Богом, как узнать, что мы вправе в нём изменять, а что должно остаться святым и нерушимым?
ставит:
сотворён: was created
узнать: get to know, learn
вправе: have a right
изменять: change
должно: should
остаться: remain, stay, be left
святым: holy, sacred
нерушимым: inviolable, indissoluble

Преподобный Хорекс установить чёткий правила как управлять плантацией. «Как в Джорджии» — так он говорить.
установить: establish
чёткий: clear
правила: regulations
управлять: govern, rule
плантацией: plantation
Джорджии: Georgia

Бог мой, нестерпимая жара. Как они выдерживают?
нестерпимая: unbearable
жара: heat
выдерживают: endure, hold

Преподобный говорить рабы как верблюд — пустынное племя. Он говорит… они не чувствовать жара как цивилизованные.
Преподобный: Reverend
рабы: slave
верблюд: camel
пустынное: of desert
племя: breed
чувствовать: feel
жара: heat
цивилизованные: civilized

Лучше бы Вам уйти с солнца.
Лучше бы: had better
уйти: leave
с: from
солнца: sun

А что это… что это за шум такой?
что за: what kind of
такой: like this, that sort of

Tuesday, August 13, 2013

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Reading Russian Lines of Cloud Atlas (3)

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— Здравствуйте.
— Ваш пропуск.
Смотрю вы начеку?

пропуск: pass, admission
начеку: on the alert


Я был издателем Дермонта Хоггинса, а не психоаналитиком или астрологом, и это чёртова, чёртова правда, я и понятия не имел, что он сделает в тот вечер.

издателем: publisher
психоаналитиком: psychoanalyst
астрологом: astrologer
понятия: idea
имел: have
тот: that
вечер: evening


Когда-то этот пляж был банкетным залом для каннибалов, здесь сильные пожирали слабых, а вот зубы, сэр, зубы они выплевывали, ну как мы с Вами вишнёвые косточки. Знаете полфунта этого добра сколько стоит?

Когда-то: once upon a time
пляж: beach
банкетным: of banquet
залом: hall (After future or past tense of быть, an instrumental case is used)
каннибалов:
сильные: strong
пожирали: devour
слабых: weak
зубы: tooth
выплевывали: spit out
вишнёвые: of cherry
косточки: kernel, nucleus
полфунта: half-pound
добра: property, assets
сколько: how much, how many
стоит: be worth, deserve


Помните, это не допрос и не судебное заседание. Ваша версия истины — единственное, что важно.
Истина всегда одна. Любые её версии — это … ложь.

Помните: remember, keep … in mind.
допрос: interrogation, questioning
судебное: judical, legal, forensic
заседание: sitting, meeting, conference, session
версия: version
истины: truth
единственное: only, sole
важно: importantly
Истина: truth
одна: one
ложь: lie, falsehood


И пусть не говорят, что я покончил с собой из-за любви. Да, у меня случались увлечения, но мы то оба знаем, кто был моей настоящей любовью
за мою короткую, но яркую жизнь.

пусть: let
покончил: finish
собой: myself
из-за: because of
любви: love
случались: happen
увлечения: passion, love
то: ?that
оба: both
настоящей: utter, real
любовью: love
короткую: short
яркую: bright, brilliant

Thursday, August 8, 2013

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Quotes From Cloud Atlas (I)

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Теперь я понимаю, что границы между шумом и звуком условный. Любые границы условный, и созданный, чтобы их переступать. Всё условности преодолимый, стоит лишь поставить для себя эту цель.

граница: limit, confine
между: between
шум: noise
звук: sound
условный: conventional
созданный: established, created
переступать: transgress, outstep
условность: conventionality
преодолимый: surmountable, vincible
лишь: as soon as
поставить: put, affix
для: for
себя: oneself
цель: objective, goal

Now I understand, that all bounds between noise and sound are conventional. Any bound is conventional, and is created so as to be transgressed. All conventions are surmountable, if only one sets this goal for oneself.

Saturday, August 3, 2013

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Polynomials and Power Series (I)

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Today we discuss something on polynomials.

Over a Commutative Ring

Nilpotents and units are closely related. In a commutative unital ring R, if x nilpotent, a unit, then a+x is again a unit. If 1+x y is a unit for every y\in R, then x\in\mathfrak{R}, the Jacobson radical, approximately nilpotent.

Let A be a commutative unital ring, and A[x] the polynomial ring over A.
Let f=a_0+a_1x+...+a_n x^n. If a_1,a_2,...,a_n are nilpotent, so will be f-a_0. If moreover a_0 is invertible, f will be invertible; if instead a_0 is nilpotent, f is nilpotent. The converses are both true. For nilpotency, the highest degree term of f^m is a sole a_n^m x^m, if f is nilpotent, a_n is forced to be; but then f-a_n x^n is again nilpotent. For invertibility, immediately a_0 is invertible; Suppose fg=1 with g=b_0+b_1x+...+b_r x^r. Then a_n b_r=0,a_n b_{r-1}+a_{n-1} b_r=0,.... Multiplying the second by a_n, we get a_n^2 b_{r-1}=0; repeating this yields a_n^{r+1} b_0=0, and b_0 is invertible so a_n is nilpotent.

In particular, these implies the nilradical \mathfrak{N}=\mathfrak{R} in polynomial rings. If f\in\mathfrak{R}, then 1+xf is invertible. This means a_0,...,a_n are all nilpotent, hence f nilpotent. In the proof of the Hilbert Nullstellensatz, we will see that this is valid also in prime quotients of polynomial rings.

If f is a zero-divisor, then a_0,..,a_n are all zero-divisors. Indeed, if fg=0, then a_n b_r=0, and f a_n g =0, with \mathrm{deg} a_n g<\mathrm{deg} g. Repeating this, eventually a_n g=0. This yields (f-a_n x^n) g=0. Then a_i g=0,a_i b_n=0,\forall i.

A general version of Gauss’s lemma holds: if (a_0,...,a_n)=(1), then f is said to be primitive. If f,g are primitive, then so is f g. The proof is analogous: If (c_0,...,c_n)\in\mathfrak{p} for some maximal p, then in (A/\mathfrak{p}[x], we have f g=0. Since this is a domain, either f,g is 0, a contradiction.

The above is easily generalized to several variables (actually arbitrarily many, since a polynomial always involves only finite terms), keeping in mind A[X_1,...,X_n]=A[X_1,...,X_{n-1}][X_n].

The case of power series is different in many aspects. First, if f=a_0+a_1 x+..., then f is invertible if and only if a_0 is. This is because suppose g=b_0+b_1 x+..., then f g=a_0 b_0 + (a_0 b_1+a_1 b_0)x+(a_0 b_2+a_1 b_1+a_2 b_0)x^2+... where a_i can be solved inductively as long as a_0 b_0=1. Second, although f nilpotent implies a_i nilpotent for all i, via some similar induction focusing on the lowest degree term, the converse is not true. In fact, there are some restrictions on the vanishing degree: if f^s=0, then a_0^s=0, so (f-a_0)^{2s}=0; then a_1^{2s}=0, so (f-a_1 x)^{4s}=0. In general a_i^{2^i s}=0. If the least s_i for a_i^{s_i}=0 increases rapidly, making 2^{-i} s_i\rightarrow\infty,i\rightarrow \infty, then f is not nilpotent. For example take s_i=3^i,A=\prod_{i\in\mathbb{Z}^+}\mathbb{C}[x_i]/(x_i^{s_i}),a_i=x_i. The argument also applies in the polynomial case, but then n is finite.

If 1+g f is invertible iff 1+a_0 b_0 is invertible. So f\in\mathfrak{R}(A[[x]]) iff a_0\in\mathfrak{R}(A).

The ideal F(\mathfrak{I}) of f with a_0\in \mathfrak{I} is an ideal of A[[x]]. Moreover A/\mathfrak{I}\cong A[[x]]/F(\mathfrak{I}). So if \mathfrak{I} is prime, so is F(\mathfrak{I}); same for maximality. In fact, the same holds in A[x].

The above topic is from Atiyah, M. F.; MacDonald, I. G. (February 21, 1994). «Chapter 1: Rings and Ideals». Introduction to Commutative Algebra. Westview Press. p. 11. ISBN 978-0-201-40751-8.

The case of countable variables is also of interest. We will discuss this in later posts.

Thursday, August 1, 2013

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Reading Russian Lines of ‘Cloud Atlas’ (2)

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Вот тогда-то я и свёл знакомство с доктором Генри Гуссом, с человеком, который, как я надеялся, сможет излечить мой недуг.
Вы что-то ищите?


тогда-то: then, at that time
свёл (свести): took; свёл знакомство с: made the acquaintance of
который: who
надеялся: hope
сможет: be able to
излечить: cure
недуг: ailment, illness
что-то: something
ищите: look for, search after


That’s when I made the acquaintance of doctor Henry Goose, with the man, who, as I hoped, is able to cure my illness.
You looking for something?


Вопрос первый:
Что за тайна была в докладе Сиксмита, за которую его могли убить?


Вопрос второй:
Есть ли основания предполагать, что ради сохранения этой тайны они снова пойдут на убийство?


Если да, тогда третий вопрос: Нахрена мне это?


тайна: secret
докладе: report
могли: be able
убить:
Есть ли:
основания: basis
предполагать: surmise
ради: for the sake of
сохранения: conservation, preservation
снова: again, anew
убийство: murder
третий: third
Нахрена: Why the hell


Question 1st:
What in secret was in the report of Sixsmith, out of which he could be murdered?
Question 2nd:
Is there any basis surmises, that to preserve this secret they will again go into murder?

If yes, then the third question: What the hell am I doing?


Да, богатый опыт редактора привил мне отвращение ко всяким флешбэкам проспекциям и прочим новомодным приёмчикам, но проявив немного терпения, дорогой читатель, ты поймёшь, что только таким образом, и можно рассказать эту безумную историю.


богатый: rich
опыт: experience
редактора: editor
привил: instilled
отвращение: disgust
ко: to
всяким: any, every
флешбэкам: flashback
прочим: other
новомодным: new-found
приёмчикам: tricks
проявив: show
терпения: patience
поймёшь: understand
образом: manner
безумную: crazy


Yes, rich experience of editor instilled in me disgust of any flashback, prospection and other new-found tricks, but having showed a little patience, dear reader, you will understand, that only in this manner can I narrate this mad story.


Мой дорогой Сиксмит, Сегодня утром я выстрелил себе в рот, из Люгера Вивиана Эйерса. Истинное самоубийство — дело размеренное, спланированное и верное.
Многие проповедуют, что самоубийство — это проявление трусости. Эти слова не имеют ничего общего с истиной. Самоубийство — дело невероятного мужества.


дорогой: dear
выстрелил: shoot
себе: 
рот: mount
Люгера: Luger, a kind of gun
Истинное: veritable
самоубийство: suicide
дело: business, affair
размеренное: measured
спланированное: planned; Word-formation: 
верное: correct
Многие: many
проповедуют: preach, sermonize
проявление: manifestation, display
трусости: cowardice
имеют: have
общего: general
истиной: truth
невероятного: incredible, unbelievable
мужества: courage, fortitude

My dear Sixmiths, tonight I shot myself at the mouth, using Vyvyan Ayrs. True suicide — measure affair, planned and correct. Many preach that suicide — this is the display of cowardice. These words don’t have anything general with truth. Suicide — affair of unbelievable courage.


Если возникнут проблемы, нажмите эту кнопку.
Благодарю.
От имени Министерства, и будущих поколений Единодушия, я благодарю Вас за эту последнюю беседу.


возникнут: arise from, come into being
проблемы: problem
нажмите: press
кнопку: button
Благодарю: thank you!
имени: name
Министерства: ministry
будущих: future
поколений: generation
Единодушия: unanimity
последнюю: last
беседу: conversation, talk


If problems arise, press the button.
Thanks.
In the name of the Ministry, and the future generation of Unanimity, I thank you for this last conversation.

Sunday, July 28, 2013

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Discussion on Exercises of Commutative Algebra (I)

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  1. Units
    , nilpotents, and idempotents lift from A/\mathfrak{N} to A.

    Proof: Units and nilpotents are obvious. In fact they lift to any of their representatives.
    For idempotents, if x^2=x\in A/\mathfrak{N}, then (1-x)x=0 \in A/\mathfrak{N}, so (1-x)^kx^k=0\in A for sufficiently large k. And (1-x)^k+x^k=1-x+x=1\in A/\mathfrak{N}, so lifts to a unit (1-x)^k+x^k. Moreover, its inverse u=1\in A/\mathfrak{N}. So (ux)^k(u(1-x))^k=0,ux^k+u(1-x)^k=1\in A and ux=x,u(1-x)=1-x\in A/\mathfrak{N}.
    This can be interpreted by sheaf theory, which is to be discussed in later posts.

  2. Prime ideals of A_1\times...\times A_n is of the form A_1\times...\times p_i\times ... \times A_n, where p_i is a prime ideal of A_i. What about countable products? (Profinite exists. Boolean Ring)

    Proof:
     Multiplying by (0,...,1,...,0) we see I=I_1\times...\times I_n. Then (A_1\times...\times A_n)/I=A_1/I_1\times...\times A_n/I_n. It is a domain iff n-1 factors are 0 and the other is a domain. Actually the index set does not matter, as this is a product. Direct sums are of interest, and we will discuss it later.
    The projection onto each factor corresponds geometrically to inclusion into the disjoint union. Multiplication by (0,...,1,...,0) means restrict the function to i-th component. The above demonstrates that ideals of a product works independently on factors, and so the subset is irreducible, iff it is restricted in one part, and irreducible there.
    1. Let f:A\rightarrow B be surjective. Then f(\mathfrak{R}(A))\subseteq \mathfrak{R}(B). The inclusion may be strict. What about \mathfrak{N}?
    2. If A is semilocal then the above is an equality.

    Proof:

    1. Since 1+f^{-1}(b) a is invertible, so is 1+b f(a) for all b\in B. Let f be the quotient map from a domain A by some principle ideal generated by a power. Then \mathfrak{R}\supseteq \mathfrak{N}\supsetneq (0)=f(\mathfrak{R}(A)).
      For non-surjective morphisms, the two thing may have no relation at all. For example, let A be a local domain and f the embedding into B, its field of fractions. Then f(\mathfrak{R}(A))=\mathfrak{R}(A) is very large but \mathfrak{R}(B)=0.
      Since prime ideals always pull back, we always have f(\mathfrak{N}(A))\subseteq \mathfrak{N}(B). For Jacobson radicals, the reason actually is the same since when f is surjective, maximal ideals pull back. This is like saying, if a function vanishes on every closed point, then it vanishes on every closed point of a closed subset. If it vanishes on every point, then its pullback vanishes on every point. In the polynomial case, since \mathfrak{N}=\mathfrak{R}, this reduces to trivial intuition.
    2. Denote the kernel by I and the collection of maximal ideals \mathcal{M}. It is equivalent to \cap_{\mathfrak{m} \in\mathcal{M}}\mathfrak{m} + I=\cap_{\mathfrak{m}\supseteq I}\mathfrak{m}. Passing to A/\cap_{\mathfrak{m} \in\mathcal{M}} \mathfrak{m}\cong \prod_{\mathfrak{m} \in\mathcal{M}}  A/\mathfrak{m}, it is equivalent to I=\cap_{\mathfrak{m}\supseteq I}\mathfrak{m}. This is a product of fields, so by 2. above, all ideals are products of the whole field or 0. I has 0 in the components of \mathfrak{m}\supseteq I while k_i otherwise, which is exactly equal to \cap_{\mathfrak{m}\supseteq I}\mathfrak{m}. This does not work when |\mathcal{M}| is infinite, because then Chinese remainder theorem does not hold.
      Continuing the discussion of a., this is saying if in addition closed points are finite, then a function vanishing on a subset of them must be induced by some function vanishing on all of them. Taking the example of \mathbb{Z}, p vanishes on the single point \mathrm{Spec}(\mathbb{Z}/p^2\mathbb{Z}), but cannot be induced by some elements vanishing on all of \mathrm{Spec}\mathbb{Z}: such elements must be 0. This happens because we fail to let it vanish at all other primes simultaneously: infinite product does not make sense. However in \mathrm{Spec}(\prod_{p=2,3,5,...}\mathbb{Z}/p^2\mathbb{Z}), this holds, as we can always pull back to (2,3,5,...).
  3. An integral domain A is a UFD iff both of the following are satisfied:
    1. Every irreducible element is prime.
    2. Principle ideals satisfy A.C.C.


    Proof:
     For UFDs, it is crystal clear that these are satisfied. Conversely, we can easily split a into a finite product of irreducible elements, by A.C.C.. The product is unique because irreducibles are prime. We should care about the cases when irreducible element is not prime.

  4. Let \{P_{\lambda}\}_{\lambda\in\Lambda} be a non-empty totally ordered (by inclusion) family of prime ideals. Then \cap P_{\lambda} is prime. Thus for any ideal I, there is some minimal prime ideal containing I.
    Proof: If ab\in\cap P_{\lambda}, then for all \lambda, either a,b is in P_{\lambda}. So the one of the collections of primes containing a and b respectively is not bounded below. Thus either of a,b is in the intersection. The corollary then follows from Zorn’s lemma.
  5. Let A be a ring, P_1,...,P_r ideals. Suppose r-2 of them are prime. Then if I\subseteq \cup_i P_i, then \exists i:I\subseteq P_i.
    Proof: This is mysterious. Proof is not hard, but I do not know why. I will write when I know its meaning or usage.
  6. In a ring A, if every ideal I\subsetneq \mathfrak{N} contains a nonzero idempotent, then \mathfrak{N}=\mathfrak{R}.
    Proof: Notice when A is reduced, this amounts to say if every ideal contains a nonzero idempotent, then \mathfrak{R}=0: If a\ne 0, then (a) contains a nonzero idempotent e=ka, with e(1-e)=0, so 1-ka is not a unit, and a\notin R. The general case follows by passing to A/\mathfrak{N}. But this is more like an awkward exercise.
  7. A local ring contains no idempotents \ne 0,1.
    Proof: Otherwise it would split as a direct product. By 2. above, it has at least two maximal ideals. Geometrically, a local picture cannot be a disjoint union.
  8. The ideal \mathfrak{Z} of zero-divisors is a union of prime ideals.
    Proof: Non-zero-divisors form a multiplicative set: If a,b are not zero-divisors, and a b x=0, we have b x=0 and x =0. The primes in the localization with respect to this set corresponds exactly to primes consisting of zero-divisors. Everything is clear. This is similar to the case of non-nilpotent elements is out of some prime ideals, or that localization with respect to a prime ideal is local.

The topics are from Matsumura, H. (June 30, 1989). «Chapter 1: Commutative Rings and Modules». Commutative Ring Theory. Cambridge University Press. p. 6. ISBN 978-0-521-36764-6. and Atiyah, M. F.; MacDonald, I. G. (February 21, 1994). «Chapter 1: Rings and Ideals». Introduction to Commutative Algebra. Westview Press. p. 11. ISBN 978-0-201-40751-8.

Friday, August 2, 2013

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A Simple Combinatorial Problem and Related Thoughts

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Problem: If the decimal expansion of a contains all 10 digits (0,...,9), then the number of length n strings (shorted as n-strings) is greater than n+8.

If you’ve established the simple lemma, the solution is instant. Otherwise very impossible.

Lemma: The number C_n of n-strings is strictly greater than C_{n-1}, that of n-1-strings.
Actually,  we always have C_n \ge C_{n-1}: Every n-1-string corresponds to an n-string by continuing 1 more digit. The map is clearly injective. If C_n=C_{n-1}, it is bijective, meaning we have a way to continue uniquely, which means rationality. Rigidly, at least one of the n-1-strings occurs infinitely, but all digits after some n-1-string is totally determined by it. So if an n-1-string appears twice, it must appear every such distances, and so do the digits between.

(Further discussion: For a rational number, split it into a finite part, and a recurring part. If the minimal length of recurring string is n, then any m-string starting in the recurring part has exactly n variations, if m \ge n. Additional variations brought by the finite irregular part is finite (regardless of m), as the starting point is finite. So C_n in this case is not decreasing but bounded. So it reaches some certain number and stays stable. In a purely recurring case, the number is exactly n (meaning afore-defined).

Now C_n \ge C_{n-1}+1 \ge ... \ge 9+1, as 10 > 9=1+8 holds, the problem is solved.

This may not be really hard. But the most important thing is to see the principle behind it.

(I  WILL FURTHER COMPLETE THIS POST.)

Saturday, August 10, 2013

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Reading Russian Lines of ‘Cloud Atlas’ (1)

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Тоскливая ночь.
Обыватели печальный, ветер пробирает до костей.
В нём я слышу…голоса.
Это вой, вой предков, они рассказывают свои истории.
Их голоса сплетаются в хор.
Но один голос особенный…
Этот голос, шепчет, преследует тебя из мрака.
Клыкастый дьявол, сам Старина Джорджи.
Приготовитесь слушать, и я расскажу тебе о том, как мы встретились в первый раз, лицом к лицу.




Words:

Тоскливая: depressed, sad
ночь: night

Обыватели: citizens
печальный: sad, wistful, derived from печаль (grief). 
ветер: wind
пробирает: penetrate
до: as far as
костей: bone (plural 2nd case)


слышу: hear

голоса: voice (plural 4th case)


вой: howling

предков: ancestors (plural 2nd case)
свои: their


сплетаются: intertwine, interlace
хор: chorus


особенный: especial


шепчет: whisper

преследует: pursue
из: from
мрака: darkness (singular 2nd case)


Клыкастый: sharp-toothed

дьявол: hellhound, belial
сам: himself
Старина: Antiquity


Приготовитесь: get ready

слушать: listen to
расскажу: (I) will tell
о том: concerning, about
встретились: encountered
первый: first
раз: time
лицом: face (singular 5th case)
лицу: face (singular 3rd case)




Translation:


Dreary night.
Residents sad, wind penetrating to the bone.
In it I hear … voices.
It’s howling, howling of ancestors, they narrate their history.
Their voices interlace in the chorus.
But one voice is special…
Sharp-toothed devil, he is Old Georgie.
Get ready to listen, and I will tell you, how we met for the first time, face to face.
Monday, July 22, 2013
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A Quote From ‘Cloud Atlas’

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На улице тяжёлый снег падал на шиферные крыши и гранитные стены. Подобно Солженицыну, томившемуся в Вермонте,
я буду трудиться
в изгнании.
Но в отличие от Солженицына, я буду не один.



Explanation:

green: radical
red: prefix
blue: suffix
dark red: preposition
orange: auxiliary ingredients
purple: declension
grey
background
: accent

 

 

underline: proper noun
Friday, July 12, 2013
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Faith

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When I was a child, I was attracted by the world beyond our planet. I did not have the opportunity to see a really starry night, for the I did not often live in the country side. But I could still imagine. I bought I lot of books which introduced efforts humans had made on exploring the outer world. I also watch cartoons related to this topic. My yearning for the vast world first led me to science.

Years have passed. Now I’ve been concentrating on mathematics. But the deep spaces still play an important role in my life. I am not fond of money, honor, reputation or something else, for I believe that there is something far greater. Money, honor or reputation only works in human society and the duplicity, deception and disguise intended for these things are simply nothing but abjection in front of the universe.

But I am somewhat worried. In the early period of human civilization, men used to respect the earth. But as they became stronger, they no more respect it. If one day men knows much enough about the universe, will my faith become absurd?

I might not be able to live long enough to see the answer. Even if that happens, I can still consider it holy regardless of the society. But anyway, I hope to find the answer.

By the way, I have just found Microsoft OneNote very useful.

2010-09-23

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An Animation and the Middle Age

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1

This weekend I came across the anime Spice and Wolf. The character Horo is so cute, but this is not what I want to mention most.

It was in the Middle Age, Lawrence, the main character is a travelling merchant. Therefore trading activities and religious organizations(sorry I can’t find an equivalent word) are often mentioned in the story. That inspired me to the imagination of the Middle Age.

It was a dark age that religious power controlled the society, and however, an age of merchants. There were villages, towns, cities, ports and kingdoms. There were missionaries, knights, mercenaries and kings. It was hard to transmit information. It was hard to transport substances. It was a solid age. And it was merchants, who traveled everywhere for more benefits, that liquefied the age.

Merchants were(maybe are) crafty as I knew before and see from the animation. It is not a good manner today. But at that time, the time people had to follow strict religious provisions and to live for gods but themselves, it was the worldly characters merchants had that bring the light that people should live for themselves.   And it was the lust for more wealth that led to the desire for freedom. And it was the success of merchants that inspired people to belief in themselves instead of gods.

I haven’t read much about the Middle Age. Maybe what I know is more romance than reality, but I still believe that era was full of romances of merchants, and it was these romances that pushed ahead the world.

2010-09-12

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1

Diary (Sep 4, 2010)

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The book From Calculus to Cohomology by Madsen looks a nice book. Well, it’s the first time I saw an introduction to topology from CALCULUS so I believe it amazing. Maybe I am too ignorant in mathematics.

I’m studying Commutative Algebra and Topology recently. As far as I’m concerned, categories are fundamental in mathematics so I’m particularly fond of algebra in favor of the concept of category. I saw some one says geometry and topology structures are much more interesting than algebra structures. I don’t understand it very much. Maybe in my mind all structures are algebraic. Well, maybe when we adopt measures and Cauchy sequences we are entering the field of Analysis, Geometry and Topology? Actually in my heart it is still algebraic. I think continuity doesn’t mean non-algebra.

Huh…The above seems almost all stuff. At my level of mathematics I’m not likely to understand much of them. I even used to reject algebra because at that time I think algebra is a boring collection of axioms. I also used to reject categories when I first knew them.

The society in China is weird. Teenagers need to study a lot of things neither interesting nor important in order to survive. As a result they do not have time to do things they like. Students with high grades are expected to be talents, but most of them do not have dreams to live for. All they do is to study for higher grades and to play. Most of them do not have their view in politics, culture, etc.

Because of these, I start to feel that I don’t really have friends. I am in a serious lack of emotions. Actually I don’t think anyone around me really has friends. I impute it to the weird society. It doesn’t allow people to dream, to love. So the lack of friends are natural.

The blog is desolate. Perhaps no one will see this post. But I believe one day here will be crowded, if I will.

By the way, Japan in World History by James L. Huffman is also a good book.

2010-09-04

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How do we think?

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When I say «apple» ,an apple will appear in your mind. You can understand it. People may explain it as some correspondence between images and specific signs. And the signs themselves are images so actually we associate the images with sounds and then sounds with signs. Humans have evolved so much that today they can understand written language in silence, not needing to read them out.

The understand of concrete things may be as easy as the above. But what about that of abstract things, concepts and statements? That should be hard to explain because explanation itself is an abstract statement, which I must use my understanding system of abstract things to understand.

I used to guess, the approach to solve this problem is up to science. That is, to study the brain. But there is still a critical obstacle that we still have to think using our brain.

Is that the unreachable acme of human cognition? Do humans have to continue evolving to answer it? Or never?

2010-09-04

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A Testing Post

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Human and Natural Disasters

Human activities are largely involved in the formation of some natural disasters, while not involved in the formation of some others.

As we all know, it is obvious that humans have nothing to do with the formation of volcano eruptions or earthquakes. But some other disasters, for instance, sandstorms, are related to human activities. Overgrazing and overcutting ruin vegetation, in turn causing desertification. When sands meet a windstorm, a sandstorm comes into being. Another instance is acid rain. Waste gas produced in industry activities, mostly in thermal powering, goes up to the clouds. It then blends with the water vapors. As a result, the rain from the clouds becomes acid, doing a lot of harm to humans, animals, plants, etc.

Therefore, we humans should actively take action to prevent the disasters which are mainly caused by us from happening. Education should be implemented to let more people realize the harm they are doing to the nature. Laws should be made and harsh supervision should be conducted to ensure no overgrazing or overcutting. Technologies that enable us to gain power while doing no harm to nature, such as transforming solar energy to electricity, should also be developed with exertion.

We should also actively deal with the disasters of which the formation does not involve human activities. Education is also important here. Comparing the earthquakes in Haiti and Chile, why did a much heavier earthquake cause a much slighter consequence in death numbers? One of the factors is people in Chile are well educated about how to survive earthquakes, while people in Haiti are not. Technologies are important as well. With better technology, we can develop more effective methods of surviving, forecasting and maybe even controlling the disasters.

To sum up, humans are responsible for a certain portion of natural disasters. We should positively deal with natural disasters in order to survive. Actions should be taken both as not to cause disasters ourselves and to reduce damage disasters can deal.

2010-08-27

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