Johannes @[email protected]

贝多芬所有的晚期作品——不同于他中早年的战斗或者期待光明的直观感觉——几乎是无奈与痛苦到近乎自虐。席夫对op110的评价是“like a phoenix emerging from the ashes”,但并非以光明的方式:贝多芬将最美的赋格主题深藏于乐曲中的每个角落，直到它在末乐章中终于第一次以完整的独立的形式出现，而从这一刻开始，力量开始汇集，音乐也不可避免地走向崩塌。我猜测这正是他想传达的某种东西:自我毁灭
https://open.spotify.com/track/5QaEBz7nwANqZzjE2Dz36z?si=xBavKTd_Qm22h92u4f1S6w&utm_source=native-share-menu

我想起了我高中数学课外班的老师讲过的故事，他说他在美国的某大学读本科的时候（我记得好像是哥大，反正是很好的学校），两个教授一块教一门课，考试题两个人各出一半。结果两个人发现都不会做对方的题，最后给他们学生算分的时候就把分数开根号乘十。我当时心想这题至于吗，开根号乘十拿个90分不是有手就行？很多年过去了，我估计我上学期那看起来还凑合的分数就是这么算出来的

这学期上了一门随机过程，教这课的教授上学期也教实分析。这教授感觉在整个系里无人不知，课程和作业难度高到逆天，上个学期的实分析是数学专业的必修，于是他成功折磨了三十个人；这学期的随机过程是选修课，结果一共就只有五个人上这课（一开始七个人，后来两个老哥光速跑路了）。不管是期中考试还是期末考试，他永远要在开头写一句“it’s not necessary to get a near-perfect score to do well; just do as much as you can.”这意思好像就是“我知道我出的卷子你们肯定不会做，但我就是要这么出”。

https://open.spotify.com/track/6hN9Dziy8GQCpSDFthmuF0?si=-ULt573YRG2eC-Qbvkcn-w&context=spotify%3Aalbum%3A62VlldLNKK8OGw8vbyIFED

很多人好像都会说“xxx维持了我的精神稳定”，我觉得我是正好反过来，每天都没什么动力，只有听音乐是特例，一旦开始就停不了。如果有人让我说说自己是怎么感受这些音乐家的，我会客观地、尽量不用比喻地描述每个音乐家；最后说到了贝多芬，我就说“他的音乐是真正的火焰”

我发现在中国有一种独属于左人的幽默感：他们明明做的事、说的话，都和中国政府如出一辙，但为了体现出自己作为左派的进步，于是在一个红得不能再红的视频里面评论：“最后一期”。

刚交上去的一次作业，关于带号测度和积分收敛之间的关系

这题折磨了我几个小时，一开始看到积分收敛就不由自主地往法图引理（Fatou‘s Lemma）上靠，但很快就发现走不下去了。如果你观察集合Ｂ的设立，应该能发现我想用法图引理（在Ｂ上gn属于L+，所以可以积分换序）

不过我很快就发现了更好的东西。实际上，Ｂ和Ｂ补就是关于测度νn-ν的一个若尔当分解（Jordan Decomposition),使得它的positive variation和negative variation互为奇异（mutually singular）。更进一步，根据若尔当分解定理，这个分解方式应该是唯一的。依据此性质，结论应该是易证的。

但是这个证明还是有瑕疵，我不清楚νn-ν整体的分解是否和分别分解相等。如果区别只是一个零测集的话，这个证明应该还是成立；但如果不是的话，这个证明很可能错得很远。

等助教判完这次作业之后去和她讨论一下

想在象上发点我觉得好的数学题，不知道会不会有人看

自从又开始上课之后，所有时间都花在研究数学和睡觉上，可能一周才看一次中国的新闻。现在每次看中国发生的事情都会被震惊到…关于捕杀流浪狗的政策，我大概花了三十分钟才搞清楚究竟发生了什么。我的脑袋对于学测度论来说够用，但对于理解中国来说还差得太远，好累

摘抄昆德拉
很喜欢这分开的几段，让我们把它们连起来看吧

在《不朽》第三章中，昆德拉写到：
In our world, where there are more and more faces, more and more alike, it is difficult for an individual to reinforce the originality of the self and to become convinced of its inimitable uniqueness. There are two methods for cultivating the uniqueness of the self: the method of addition and the method of subtraction. Agnes subtracts from her self everything that is exterior and borrowed, in order to come closer to her sheer essence (even with the risk that zero lurks at the bottom of the subtraction). Laura’s method is precisely the opposite: in order to make her self ever more visible, perceivable, seizable, sizeable, she keeps adding to it more and more attributes and she attempts to identify herself with them (with the risk that the essence of the self may be buried by the additional attributes).

在第五章中，在阿涅丝生命的结尾，昆德拉写到：
How to live in a world with which you disagree? How to live with people, when you share neither their suffering nor their joys? When you know that you don’t belong among them? Agnes is driving down a quiet road in her car and she answers herself: love or the cloister. Love or the cloister: two ways you can reject the Creator’s computer, and escape it
……
What is unbearable in life is not being but being one’s self. The Creator, with his computer, released into the world billions of selves as well as their lives. But apart from this quantity of lives it is possible to imagine some primordial being that was present even before the Creator began to create, a being which was — and still is — beyond his influence. When she lay on the ground that day and the monotonous song of the stream flowed into her, cleansing her of the self, the dirt of the self, she participated in that primordial being which manifested itself in the voice of fleeting time and the blue of the sky; she now knows there is nothing more beautiful.
The route she drove on to from the highway was quiet, and distant stars, infinitely distant stars, shone over it. Agnes drove on and thought: Living, there is no happiness in that. Living: carrying one’s painful self through the world.
But being, being is happiness. Being: becoming a fountain, a fountain on which the universe falls like warm rain.
……
For the last time the basic pattern of her life was repeated: she was running and someone was chasing her. Paul was chasing her. And she had nothing in her hands; neither brush, nor comb, nor ribbon. She was disarmed. She was naked, dressed only in some sort of white hospital gown. She found herself on the last lap where nothing could help her any more, where she could only rely on the speed with which she ran. Who would be faster? Paul or she? Her dying or his arrival?
The fatigue grew deeper and she had the feeling that she was rapidly moving away, as if someone were pulling her bed backwards. She opened her eyes and saw the nurse in a white coat. What was her face like? She couldn’t make it out. And then the words came to her: ‘No, they don’t have faces there.’

阿涅丝与她的父亲在死前做着一样的事：父亲撕碎了自己的每一张照片；阿涅丝则拼命地与自己的丈夫赛跑，在他到达之前死去。不朽，在昆德拉的眼中是一件如此可怕的事情。人的全部的生活，在不朽中被扭曲。正如歌德害怕被贝蒂娜追逐，海明威害怕被他的情妇和读者们追逐一样，一旦阿涅丝被追赶上，她就将永远存在。昆德拉的下场最终还是与歌德、海明威重合了，他注定无法获得与阿涅丝一般的美好结局。他获得了不朽，也将在不朽的法庭中接受审判。
让我来续写这一幕悲剧吧

Eternal trial
Hemingway, Judge
Kundera, Defendant

Hemingway. "You have been making us say nonsense. Now it's someone else's turn to make you do so. Because of your novels and exile, I judge you to have immortality. Does the defendant have anything to say?"

Kundera looks around. "No, I forsaw this scenario the moment I started writing."

Hemingway. "You seem very accepting of your end."

"Because I don't see Goethe here. I'm sure now that he's enjoyed the pleasure of nonexistence. Good luck to you, Ernest. Good luck to us. And good luck to both us to go to have a bluish sleep some day.＂