一次隨機騎行

Like
Like Love Haha Wow Sad Angry
1

本来去讨论“英国历史与经典文献选读”的展示,完了之后突然想去沃爾瑪買奶酪,中途發現沒錢,索性騎到市區玩玩好了,結果卻騎到了萬象城。當然鑒於一分錢沒帶,就只能拍拍照啦。。。

Ralf Lauren的童裝櫥窗,擺設得有點意思。
Ralf Lauren的童裝櫥窗,擺設得有點意思。

途中本想在慶春路的書店停下逛逛,奈何拖延糾結中就過去了。好在萬象城也有家實體書店,Page One。它售賣的淨是些小資情調的書,什麼室內設計啦、烹飪飲食啦、文史哲啦,有很多英文書。

Continue reading “一次隨機騎行”

Like
Like Love Haha Wow Sad Angry
1

这些无法翻译的外语单词有哪些故事/典故?

Like
Like Love Haha Wow Sad Angry

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。

Continue reading “这些无法翻译的外语单词有哪些故事/典故?”

Like
Like Love Haha Wow Sad Angry

读《云图》的俄语台词 (4)

Like
Like Love Haha Wow Sad Angry

ОБЛАЧНЫЙ АТЛАС

Острова Тихого Океана, 1849 год.

Дело сделано, мистер Юинг, теперь сей контракт свят для исполнения… почти как Десять Заповедей.

сделано: 完成
сей: 这个
свят: 神圣的
исполнения: 执行, 完成
почти: 几乎
Заповедей: 戒律

Благодарю, Преподобный Хоррекс, мой тесть с нетерпением ждёт завершения этой сделки.
Преподобный: Reverend教士
тесть: 继父
нетерпением: 不耐烦
ждёт: 等待,期待
завершения: 完成,补完
сделки: 交易 Continue reading “读《云图》的俄语台词 (4)”

Like
Like Love Haha Wow Sad Angry

读《云图》的俄语台词 (3)

Like
Like Love Haha Wow Sad Angry

– 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

Continue reading “读《云图》的俄语台词 (3)”

Like
Like Love Haha Wow Sad Angry

《云图》中的一句话 (I)

Like
Like Love Haha Wow Sad Angry

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 Continue reading “《云图》中的一句话 (I)”

Like
Like Love Haha Wow Sad Angry

多项式和幂级数 (I)

Like
Like Love Haha Wow Sad Angry

今天我们讨论多项式

交换环上

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. Continue reading “多项式和幂级数 (I)”

Like
Like Love Haha Wow Sad Angry

读《云图》的俄语台词 (2)

Like
Like Love Haha Wow Sad Angry

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

Continue reading “读《云图》的俄语台词 (2)”

Like
Like Love Haha Wow Sad Angry

《交换代数》习题研讨 (I)

Like
Like Love Haha Wow Sad Angry

  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. Continue reading “《交换代数》习题研讨 (I)”
Like
Like Love Haha Wow Sad Angry

一个简单的组合问题及相关的思考

Like
Like Love Haha Wow Sad Angry

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. Continue reading “一个简单的组合问题及相关的思考”

Like
Like Love Haha Wow Sad Angry

生成函数和形式幂级数

Like
Like Love Haha Wow Sad Angry

今天我们讨论生成函数

Problem 1: Give a finite set of positive integers T. Let \mathfrak{T}_n be the collection of sequences (t_1,t_2,...,t_m), such that \sum_{i=1}^m t_m=n, and each t_i\in T. Let a_n=|\mathfrak{T}_n| for n\ge1 and a_0=1, and f(x)=\sum_{n=0}^{\infty}a_n x^n. Find out what is f(x) explicitly.

Solution: It is not hard to note the recursive relation a_n=\sum_{t\in T} a_{n-t} for n\ge1, if we set a_i=0 for negative i. So that f(x)=1+\sum_{t\in T} x^t f(x) and f(x)=1/(1-\sum_{t\in T} x^t), which is a rational function.

Variantion 1: If T is infinite, what would happen? Would f(x) still be rational?

We first analyze simple cases. If T=\mathbb{N}^+, it is expected that f(x)=1+\sum_{t=1}^{\infty} x^t f(x)=1+f(x) x/(1-x), so that f(x)=(1-x)/(1-2x)=1+\sum_{n=1}^{\infty} 2^{n-1} x^n. Indeed, in this case, counting the sequences amounts to divide a sequence of n objects arbitrarily. You can choose to divide between the ith and i+1th for 1\ge i\ge n-1, so in all 2^{n-1} choices, justifying the expansion.

I think it is equivalent to f being rational.

Theorem: \mathbb{Q}_p(t)\cap\mathbb{Q}[[t]]=\mathbb{Q}(t)

It is very interesting that this theorem is used for the rationality of \zeta-functions for algebraic varieties, which is part of the Weil conjectures.

2013 年 7 月 10 日

Like
Like Love Haha Wow Sad Angry

读《云图》的俄语台词 (1)

Like
Like Love Haha Wow Sad Angry

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

Continue reading “读《云图》的俄语台词 (1)”

Like
Like Love Haha Wow Sad Angry

《云图》中的一句话

Like
Like Love Haha Wow Sad Angry
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
Like
Like Love Haha Wow Sad Angry

信念

Like
Like Love Haha Wow Sad Angry

小时候,我就对地球以外的世界深感兴趣。虽然住在城市里,并没有看到满天繁星的机会,但我还是喜欢想象。我买了很多讲人类探索宇宙的努力的书,看了很多这样的漫画(主要是蓝猫淘气三千问)。正是这种憧憬带我走向了科学。

许多年过去了,我现在专注数学(而不是科学)。但是深邃的星空依然对我意味着许多。我不关心金钱、荣耀、名誉或别的什么,因为我相信有些别的东西远比它们伟大——它们只在人类社会生效,其背后的欺骗和伪装,在浩瀚的宇宙中,更是不值一哂。 Continue reading “信念”

Like
Like Love Haha Wow Sad Angry

An Animation and the Middle Age

Like
Like Love Haha Wow Sad Angry
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. Continue reading “An Animation and the Middle Age”

Like
Like Love Haha Wow Sad Angry
1

Diary (Sep 4, 2010)

Like
Like Love Haha Wow Sad Angry

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. Continue reading “Diary (Sep 4, 2010)”

Like
Like Love Haha Wow Sad Angry

我们如何思考?

Like
Like Love Haha Wow Sad Angry

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

Like
Like Love Haha Wow Sad Angry

A Testing Post

Like
Like Love Haha Wow Sad Angry

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. Continue reading “A Testing Post”

Like
Like Love Haha Wow Sad Angry