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Thinking Is Slow. Copying Is Fast. | Michael Gomes Vieira

Tue, 25 Aug 2026 17:05:49 +0000

Thinking Is Slow. Copying Is Fast.

Monday, 24 August 2026

Nearly all behavior of biological species is ultimately a result of what is effectively the giant reinforcement learning algorithm in nature. It incentivizes the generation of agents with behaviors that are more likely to reproduce.

In hostile and dynamic environments, adapting to a new environmental pressure is often crucial to a gene’s chances of continuing through time.

Species currently have four means of adopting new behaviors, with trade-offs between speed of adoption and speed of active use.

Speed of adoption is how quickly a species, or an individual member of a species, can learn a new behavior. Speed of active use is how quickly an individual can carry out a behavior when it is called to do so.

Here are the four means of adopting new behaviors, by speed of adoption:

Positive selection for genes encoding new innate behaviors (slowest adoption, fastest active use). It took many millennia for animals to adopt behavior to respire using oxygen from the atmosphere. Barring some major disability or injury, anyone can breathe in quickly without conscious thought.
Pavlovian reinforcement mechanisms (slow adoption, fast active use). The organisms of many species can be induced to quickly act a certain behavior when it has been strongly associated, over a period of its lifetime, with a reward or punishment. Pavlov demonstrated how ringing a bell in the presence of a dog feeding can, after several repeat incidents, induce a dog to start salivating upon hearing the ringing of that bell. Nature has allowed for the shortening of the reinforcement learning mechanism from generational timescales to the timescale of an individual organism.
Imitating the behavior of others (medium adoption, fast active use). Humans are (probably) unique in imitating the behavior of others to learn new behaviors. Nature again speeds up the reinforcement learning mechanism by allowing for the transference of learnings by other organisms.

Most of our skills are learnt from copying others. Children learn from adults how to tie their laces. This is much faster than each child having to use logic to deduce a knot that will keep their shoes firmly attached to their feet, or to go through the entire Pavlovian process of randomly trying knots until they learn that a certain knot keeps their shoes on.
The application of conscious logical thought (fastest adoption, slowest active use). Behaviors that are the consequence of logical thought have the fastest adoption. They do not need any historical examples to be learnt; they can be deduced from first encounter. They have the slowest active use. It can take a lot of time and brainpower to deduce, in a novel scenario, the desired behavior.

The trade-off between how quickly a behaviour can be adopted and how quickly it can then be used.

What has catapulted the human species to its current dominant position in the earth’s ecosystem is its ability to accelerate the adoption of new behaviors. It does this by the synthesis of conscious logical thought and the innate imitation of the behaviors of others.

Behavioral imitation is especially powerful. As soon as one individual can, either by random experimentation or the application of conscious logical thought, perform some new behavior that leads to a great increase in utility, others can imitate and also benefit from this successful behavior.

Humans further leverage the mimetic instinct by mimicking what are perceived as higher-status individuals. Teenage Napoleon devoured the biographical accounts of the life of Julius Caesar, who idolized Alexander the Great. Teenage Erling Haaland modeled his football game on Cristiano Ronaldo. Teenage Coco Gauff modeled her tennis on Serena Williams. Oprah Winfrey modeled herself on Maya Angelou.

To see why this is so, consider that being high-status is typically associated with wealth: that is, the ability to command resources. In our evolutionary history it was often the case that the behaviors the high-status person enacted are probably what allowed them their advantage in their command of resources.

In a sprouting agrarian society, anyone who could imitate the farmer with the bountiful harvest’s use of the first primitive plough would accrue for themselves the same advantage. Similarly, in our modern world, Erling Haaland, by following the techniques of Cristiano Ronaldo, is able to leverage these techniques to score many goals, providing value for himself and his team.

This instinct is so powerful in humans that we have even displayed the capacity to learn from other species. There are incidents of feral children walking on all fours and eating raw meat after being raised by wolves.

Dina Sanichar was raised feral in Victorian India

Next week I will write about what culture is and how it spreads.

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Gatekeepers are Dead, Long Live the Gatekeepers - BiteofanApple

Mon, 24 Aug 2026 18:49:50 +0000

Before the Internet things were different; this was the First Age.

If you wanted to get your message out there you needed either a lot of money, fame, or power. Usually you needed some combination of all three. Barring that you needed to find someone with money, fame, or power (or some combination) who was also willing to help you. These people were often elites of some kind. They could be professionals with an industry journal, the editor of a local magazine, a rich patron with connections, or even political party officials. These were the people who held the keys needed to pass into the public sphere: gatekeepers. Their job was to search out people of interest, people with something interesting to say, and promote them. Musicians needed talent scouts, authors needed agents, writers needed editors.

Guarding the entrance to the bridge.
The Saturday Magazine, 1836–03: Vol 8 Iss 240

Attention was infinite and quality content was scarce. Gatekeepers filtered through the trash and surfaced the gems. The public paid attention because that was all that could be done.

The Internet broke this system; we entered the Second Age.

Self-published books made it so anyone can get their book out there. Self-service distributors allow anyone to publish music, YouTubers to self manage, and blogs (and more importantly social media) give anyone a platform to speak. This system didn't replace the gatekeepers (traditional publishing and record labels still exist) but it broke open the floodgates. A lot of this new content was bad but some of it was amazing.

Attention became the currency of the land, a finite resource sure but one similar to oil: plentiful enough to build entire industries on. Tools existed to help filter it all. They became our gatekeepers: the feeds, then the algorithms. At first it was easy to find good, new content. Over time that got harder, but the system seemed to be stabilizing.

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Large Language Models broke this system; we are now in the Third Age.

Now the Web is flooded with text, images, video, and audio not made by any human. Books exist now which no human (including its supposed author) has ever read. We have reached a breaking point. Where before there was always at least one person who'd seen every piece of content, now it seems likely most content will never be read except by the unsuspecting fool who mistakes it for real work.

Will we build castles to save us?
The Saturday Magazine, 1834–08-23: Vol 5 Iss 137

Yet in this new age, where attention is a scarce resource compared with the glut of content to consume it, we have found ourselves bereft of those who can wade through the cruft and the noise and surface real wisdom. The legacy gatekeepers exist still, but they guard their own hoards. The feeds exist but few resort to them. Algorithms are still king, but will they be able to keep up with this barrage of meaninglessness?

We humans want to be distracted, to be entertained. That is what modern social media does for us. Yet people seek meaning too, and wisdom. In the prior age (and still somewhat today) that wisdom lies hidden in the muck, surfaced by legacy gatekeepers and by algorithmic feeds. I only wonder if this dam will hold.

For centuries, the Romans kept their enemies at bay. Cities that once needed walls abandoned them. The inner lands were safe. Then the institutions failed. Enemy armies roamed the heartland and nowhere was safe. The walls returned.

Speaking for myself these days I seek brand name goods on Amazon where I can. I find myself scrutinizing labels and FCC approval stickers. I buy what WireCutter recommends because at least I know that the product actually exists and has seen human hands. I prefer books published by Penguin/Random House or others of the Old Guard. I discover YouTubers via recommendation from those I already trust and treat algorithmic recommendations as inherently suspect. In short: I seek gatekeepers, not to surface diamonds in the rough, but to hold back the oncoming tide.

Am I alone in this?

Amathia, or: How I Lost Respect for My Father – Householder Karl

Tue, 25 Aug 2026 08:33:16 +0000

Amathia, or: How I Lost Respect for My Father

24 Aug, 2026

Alack then, Alcibiades, for the plight you are in! I shrink indeed from giving it a name, but still, as we are alone, let me speak out. You are wedded to amathia, my fine friend, of the vilest kind; you are impeached of this by your own words, out of your own mouth; and this, it seems, is why you dash into politics before you have been educated.¹

We are prone to thinking the problems of our modern age are unique. A cursory study of history would disabuse us of such a foolish notion. We are a ridiculous species.

Succinctly defined, amathia is willful ignorance. It has nothing to do with intelligence. In the quote above, Socrates isn’t calling Alcibiades stupid; he is accusing him of embracing falsehood despite being smart enough to know better.

Thanks to social media, we see amathia play out on our screens every day, from political figures to preachers to influencers. Sometimes it’s malicious, and other times it’s just a symptom of the human condition.

Dear Old Dad

I think the concept of amathia goes hand-in-hand with the idea of epistemic collapse, or the breakdown of a shared reality caused by the inability to distinguish what is true and what is false. Perhaps it’s more accurate to say that the latter is a consequence of the former.²

When people cling to ideas or beliefs without a rational foundation, or even worse, hold them closer in the face of conflicting evidence, then we lose the ability to communicate. Truth becomes relative and accountability loses all meaning.

And it’s one thing to discuss this topic while it’s comfortably at arm’s reach, a problem with society at large, but it’s a different beast when it appears in your own family.

Put simply, I’ve lost my dad to religion. He was always a religious person; he “found Jesus” during a crisis and felt something resembling peace. But now, in his dotage, he has fully embraced a MAGA/Christian Nationalist identity. Fox News is too liberal; it’s all about OAN. Demoncrats deserve to be shot in the street, along with gays. He blames most of our societal woes on the Marxist-Islamist-LGBTQIA+ cabal.

Over the years, his theology has morphed in strange and radical ways. He is convinced of an unseen cosmic war between Elohim and Satan. He expounds at length on the complex eschatology and our role in the conflict. Any attempt to push back is met with accusations of not being redeemed. See, if you had “the spirit,” then you would know what he says is true. If you disagree, it means you’re bound for hell.

Retirement only made things worse. Now he has all the time in the world to argue online and convince himself that it’s him versus the world.

We no longer exist in the same reality, and it’s incredibly sad. The man who once could do no wrong in my eyes has been reduced to a bitter, mean recluse, full of hate masquerading as Christian love.

I think we all reach a point in our lives when we see our parents for what they really are: fallible humans like ourselves, just trying to make ends meet. It’s just unfortunate that the fall-off had to be so dramatic.

Plato, Alcibiades I 118b–c, trans. W. R. M. Lamb, in Plato, vol. 8, Loeb Classical Library 201 (Cambridge, MA: Harvard University Press, 1927).↩
Peter Woit, "Notes on Epistemic Collapse," Not Even Wrong (blog), June 27, 2025, https://www.math.columbia.edu/~woit/wordpress/?p=14999.↩

#philosophy #reflections

Dido 和 Aeneas 的故事

Fri, 21 Aug 2026 13:55:23 +0000

Aeneid 是古罗马文学家 Virgil 创作的史诗，是荷马史诗的续集，是罗马帝国立国的典籍，是经典拉丁文学的巅峰之作。这篇史诗中最被人津津乐道的就是迦太基女王 Dido 和史诗主人公，罗马先祖 Aeneas 的爱恨情仇。这段经典故事两千年来在无数绘画，雕塑，歌剧，小说重现，人们无不感慨命运对一双璧人的不公。且让我们看看这个故事背后还有什么值得挖掘的。

故事梗概

Dido 自杀

Aeneas 是特洛伊的一个将军，特洛伊城破的时候，带着家人和部属逃了出来。他们在海上漂泊，想找一个新家园。经过在克里特岛和西西里岛等几次不成功的尝试后，他们来到了迦太基，也就是现在突尼斯在地中海南岸的一个城邦，受到了迦太基女王 Dido 的招待。在漂泊数年过程中，Aeneas 的老婆和老爸都去世了，家里就只有一个十来岁的儿子。

Dido 本是腓尼基公主。腓尼基大致在当今黎巴嫩沿岸，离迦太基有上千海里。Dido的爸爸，也就是老国王，有一子一女，老国王去世的时候儿女都不算大，安排儿子继位为国王，女儿嫁给了国内二号实权人物。但是七年之后，新国王，也就是 Dido 的兄弟，把 Dido 的老公抓起来杀了。这种权力冲突在历史上很常见，但 Dido 的反应很不常见。她带着幼子，夫家人，和其他自己的追随者上船逃了出来，辗转来到了千里之外的迦太基建立了新家园。到 Aeneas 一伙人来的时候，迦太基城已经建立了好几年了。

Aeneas 和 Dido 年纪相仿，背景相似：都是逃亡的部落领袖，饱经风霜又年富力强的中年人，还都是单身父母。很快，他们就堕入爱河。可惜故事再反转：Aeneas 他们修好船，补给好之后不告而别，驶向意大利继续寻找自己的新家园。心碎的 Dido 在海边用匕首自尽，死前发下诅咒：要迦太基和 Aeneas 的后人生生世世为仇，不死不休。

问题在哪里

我们可以探讨一下女王可以嫁给谁。女王择偶是自主了，可惜难度可比登天。首先，找自己的手下很有问题。手下有多个，找谁都会引起其他人不满，这对一个创业团队是很致命的。第二种选择可以是嫁给别国国王，例如 Dido 自己就有隔壁城邦的国王向她求婚。但是这样也有很大问题：这隔壁城邦的国王不仅想要娶你做老婆，还想要你的产业，吞并你的城邦。不管对方动机与否，自己手下一定会觉得将来会被矮化边缘化。出于上述两个选择的不可靠性，后世英国著名的女王伊丽莎白一世终身未嫁。Aeneas 的出现是很难得的：一个外人，有自己的队伍所以地位超然，他有求于己，所以没有被偷家的风险，这简直是女王的天赐良缘啊！所以说：Dido 肯定乐意找 Aeneas 成亲，假如我是 Aeneas 我肯定也愿意。可惜，Aeneas 不是一般人，没多久还是跑了。这是为什么呢？原著说这是宿命，是神的安排，但我不信。

在古代带一队人无目的，无后方基地去远方寻找新家园是一件很困难的事。一个完全没有开发过的处女地是无法做新家园的：他们工具肯定带不齐全，盖房，种地都需要很长的一个周期才能起步。就算吃住问题可以解决，孤注一掷的一群人不会多，没有足够的基因多样性也繁衍不下去。何况这样的远征队伍肯定是男远多于女，女人不够分，住下去自己就打起来了。所以说，新家园必须有原住民，这原住民还必须军事水平低于远征团队，否则远征团队人又少，只有被打跑这种后果。Aeneas 团队在克里特岛和西西里岛的两次失败尝试就是这样。即使机缘巧合，所有外部条件具备，内部条件也困难重重。能带团队，征服原住民，吸收原住民，建立新秩序，没有一个有人格魅力，有远见卓识的领袖是不行的。Aeneas 和 Dido 都是这样的领袖。

现在我们回到 Aeneas 的选择。上面说过Aeneas 是有远见卓识的政治领袖，他这样做肯定是出于政治考量。在当时，他代表的希腊/特洛伊文明和 Dido 代表的腓尼基/迦太基文明相比，其实是稍逊的。腓尼基现在没什么名气，但它是航海术和拼音文字的起源地，对地中海文明有极大贡献。在迦太基招亲形同入赘，继承人会是谁，是自己的儿子还是 Dido 的儿子？自己死后自己的团队还能不能保持独立性？百年后迦太基还有没有自己的印记呢？继续远行虽然困难重重，但还是有一丝成功的可能的。最终，Aeneas 他们在意大利找到了自己的新家园。

Aeneas 能用使命感压制自己的感情，Dido 只可能比 Aeneas 更牛。她一个女人，在暴力压倒一切的古代男权社会能在蛮荒之地带一群人艰苦创业，这比 Aeneas 更难的多，纵观上下五千年，我只找到这一例。电视剧《权力的游戏》里，女王 Daenerys 有龙，Dido有的只有自己的领导力。这么牛的女王，一定不会为个男人轻贱自己的性命的。

真相是什么

真相谁也不知道。但是根据考古和其他文献对应，我们可以接近真相。首先，罗马和特洛伊的传承在考古上没有任何证据。何况时间对不上：特洛伊城破到罗马建立有三百多年的间隔，罗马有文献再过几百年。就算罗马不是一天建成的，这三百多年无文献的历史，几百年的后的人想编啥不行，慢慢地，吹牛就变成传说了。Aeneas 的故事大概率是编的，虽然编的人一定不是Virgil 。

但是，Dido 的故事有不少真实性哦。首先，有确凿考古证据可以证明，迦太基确实是腓尼基文化的继承者。其次，从迦太基灭亡到Virgil写书虽然也有两百年，但是这两百年属于经典时期，有大量文献，Virgil 不能彻底胡编，一定是要依赖现在找不到，但他当时可以接触到的迦太基自己的传说。所以说，迦太基建城时期时的领袖是一个女王这种非常罕见的事应该不是空穴来风。

Virgil 的文学创作在于把 Aeneas 和 Dido 串到了一起，再加上英雄为宿命放弃美人，美人心碎自杀的桥段，再用美人临死时的诅咒点出布匿战争的前世渊源。罗马是圆满了，可惜，Dido 这样一个超级女强人被写成了个怨妇恋爱脑，谁让历史是胜利者书写的呢。

The Schrödinger Email

Sat, 22 Aug 2026 12:00:49 +0000

Contents

1. The Problem
2. Attempt #1 - Outlook Rule
2.1. The First Clue
2.2. The Authentication Stuff
2.3. The Original Email Was Fine
3. Attempt #2 — Add an @outlook.com alias
4. Attempt #3 — Cloudflare Email Routing
5. Attempt #4 — Email Worker
6. The Final Solution

How hard can emails be? Or so I thought. Boy, was I wrong. This post is basically me fucking around with email infrastructure and finding out the hard way.

#The Problem

As a person with multiple credit cards (no judging!) — I like to track all of them in a single place using apps such as CRED or Fold. They often ask for email access to read the statements and I don’t want to give complete access over my emails.

Hence, I have a separate email where I forward emails via mail rules, but the problem is forwarding them removes the original sender information i.e. the bank here and I want to retain all this information.

In an ideal world, this would’ve just worked and I will not be writing this post :P

#Attempt #1 - Outlook Rule

I created a rule to redirect any mail to my Gmail address for testing purposes. The rule itself works but there’s no status indication anywhere, so you cannot tell if it failed or not? Bad UX.

Gmail’s postmaster luckily sends a notification that the redirection failed stating: “Gmail has detected that this message is likely suspicious due to the very low reputation of the sending domain.” This is a hard SMTP rejection and this is where things get interesting.

#The First Clue

The original test email was sent from Gmail to Outlook. When Outlook received it, the authentication results were perfectly fine:

SPF:   PASS
DKIM:  PASS
DMARC: PASS

Why was Gmail rejecting it when Outlook tried to send it ahead? The important detail is that email forwarding creates another SMTP delivery.

So, the flow essentially is:

The authentication that happened on the first hop doesn’t automatically mean the second hop will be accepted.

#The Authentication Stuff

So what do SPF, DKIM and DMARC actually have to do with this? These are standard email authentication protocols designed to verify where an email came from and help prevent spoofing and abuse.

#Sender Policy Framework (SPF)

SPF is basically:

Is this server allowed to send mail for this domain?

If example.com sends an email through its own mail servers, SPF can verify that those servers are authorized. But forwarding changes the server that delivers the message.

The original message might have come from Google’s infrastructure:

After Outlook redirects it:

Gmail is now receiving the message from Microsoft’s infrastructure rather than the original sender’s infrastructure. This can make SPF complicated.

#DomainKeys Identified Mail (DKIM)

DKIM works differently. The original sender can cryptographically sign the message. That signature can survive forwarding, provided the forwarding system doesn’t modify the signed parts of the message.

This is one reason DKIM is particularly important for forwarded mail.

#Domain-based Message Authentication, Reporting and Conformance (DMARC)

DMARC ties the authentication results back to the domain in the visible From: address. The policy is published as a DNS TXT record under _dmarc:

_dmarc.example.com TXT "v=DMARC1; p=reject"

Here, p=reject tells receiving mail servers to reject messages that fail the domain’s DMARC policy.

Forwarding can therefore create a mismatch between:

who originally sent the message,
who is now transmitting it,
and which domain the message claims to be from.

There are mechanisms such as ARC that can preserve authentication information across forwarding hops, but the receiving mail server still gets to make its own delivery decision.

And Gmail doesn’t only look at SPF/DKIM/DMARC. It also has spam and reputation systems to prevent abuse.

#The Original Email Was Fine

Looking at the headers of the test message, Outlook had successfully authenticated the original Gmail message:

spf=pass
dkim=pass
dmarc=pass

So the first hop was fine. The failure happened when Outlook’s forwarding engine attempted the second hop. The headers gave me another clue:

Resent-From: <xyz@outlook.in>
auto-submitted: auto-generated
x-ms-exchange-generated-message-source: Mailbox Rules Agent

In other words, this wasn’t me manually sending another email. Outlook’s Mailbox Rules Agent was generating the redirected delivery.

#Attempt #2 — Add an `@outlook.com` alias

I found out that this exact issue was supposed to be fixed in 2024?? Microsoft has documented the issue involving country-domain addresses and Gmail rejecting messages with essentially this same error.

The documented workaround was to add an @outlook.com alias. So I added one as abc@outlook.com to the same Microsoft account.

I also switched @outlook.com address as the primary alias instead of @outlook.in. Then I ran the exact same redirect test again. It still failed as the headers for the redirected message still contained:

Resent-From: <xyz@outlook.in>
x-ms-exchange-generated-message-source: Mailbox Rules Agent

The new @outlook.com alias hadn’t changed the identity used by the automatic redirect. So, the alias workaround wasn’t useful for this particular redirect path.

#Attempt #3 — Cloudflare Email Routing

Okay. If Outlook doesn’t want to deliver directly to Gmail, maybe I can put another mail routing layer in between. I have routing rules set up such as abc@yashgarg.dev to forward emails to Gmail.

The idea was to let Cloudflare handle the forwarding instead of having Outlook directly deliver the redirected message to Gmail.

Unfortunately, that didn’t solve the problem either. Adding another forwarding layer doesn’t inherently solve the authentication and reputation problems that can happen when mail crosses multiple SMTP hops.

At this point my email architecture was starting to look like this:

Needless to say, this didn’t work either.

#Attempt #4 — Email Worker

I was thinking, instead of redirecting directly to my Gmail address, what if I use abc@yashgarg.dev and route it through an Email Worker, then forward the message myself?

Something as simple as:

The idea was that I’d get the message into my Worker and then have full control over what happened to it. But I didn’t realize that Cloudflare performs its authentication checks before the message reaches the Worker. If the inbound email fails those checks, it’s rejected before my code ever gets a chance to run.

Cloudflare performs SPF, DKIM, DMARC, and ARC checks on incoming mail. Messages that fail authentication according to the sender’s DMARC policy are rejected.

So, there goes my last hope.

#The Final Solution

I did the thing I really didn’t want to do. I moved all my banking-related emails from Outlook to my Gmail address manually.

Not exactly the elegant solution I was looking for, but after all that, it was simply easier than fighting email infrastructure. I spent more time than I would’ve liked on this but nonetheless, it’s done.

Until next time! 👋

Demolition：我们为什么用悲伤证明爱 – Notes Against Certainty

Sat, 22 Aug 2026 12:00:18 +0000

Demolition：我们为什么用悲伤证明爱

22 Aug, 2026

Jake Gyllenhaal 演的《Demolition》在我的电影清单上躺了很久。今天终于看了。一直对这部电影很好奇，是因为主人公身上表现出的情感解离，和我自己身上的某种麻木似乎有点像。

电影里，Davis 是在妻子突然离世之后，才诚实地意识到自己的麻木。现实中，我意识到自己的麻木是在 2018 年 5 月。那天，婆婆去世了。

我至今记得那个早晨。阴雨连绵的密西根，空气里透着寒冷。我坐在校车里，头靠在车窗上，看着玻璃上的哈气和缓缓滑落的雨滴。美国校车的座椅就是两个很硬的平面，外面裹着一层皮子，又冷又硌，让人浑身不舒服。

周围的同学叽叽喳喳地讨论着《创造101》——谁昨晚熬夜给哪个成员刷了票，哪个成员最好看。

他们真的很吵。我不喜欢。

我没有想象中的难过，也没有大哭。只是流了几滴眼泪，望着窗外掠过的芦苇荡，心里觉得无比地空。心情当然是低沉的，可那好像又不是悲伤。我的心就像死了一样。

那一刻我觉得自己像个冷血的怪物，甚至暗自庆幸身边的老师同学没有人知道我家里发生了什么。不然，他们会怎样看我呢？

这个状态一直持续到上课。直到周围突然再次变得聒噪起来，我的脑海里才终于浮现出婆婆的样子。

婆婆走之前其实已经病重很长时间了。之前有次视频通话，她说，她要争取挺到小斯斯放假回国。我当时心里莫名就有一种很不好的预感。所以，也许是因为潜意识里，我已经做了很久的心理准备。

就像 Davis 后来开始怀疑自己和妻子之间是否真的有过爱情，那时的我也开始反问自己：我是爱婆婆的吗？

答案当然是肯定的。

我至今仍然能回忆起和她经历的很多细节。小时候陪她逛菜市场，我非要一个人拎两个大购物袋，不肯让她拿任何重物。买完菜，我喜欢和婆婆一起坐三蹦子回家。她和司机讨价还价的样子很飒。我会给她写很多温暖的、表达爱意的贺卡；陪她一起看《养生堂》，然后假装自己是医生，给她写病历、开药。

2017 年，我高一。婆婆因为低钠血症短暂失忆。我从学校赶去医院，发现她不认识我了，于是躲进医院的厕所里哭得特别伤心。我的记忆里，那好像是我哭得最伤心的一次。也是那一次我才知道，原来人极度悲伤的时候是哭不出声音的。只是难以控制地把嘴巴张开、撇得很大，呼吸仿佛停滞了一样。原来心脏真的会疼。

所以，我是爱她的吧。

可为什么现在她去世了，我却哭不出来呢？

我依旧清晰地记得她的模样，依旧会在看到一些东西、做一些事，或是去到一些地方的时候想起她。

但也只是想起她。

也许，在回忆里不断挖掘那些细节，就是我爱她的方式？还是说，因为我的理智知道，婆婆继续活着只会遭受更多痛苦，所以对于“死”这件事本身，我其实并不为她感到悲伤？

我不知道。

当然，我的“麻木”应该还是比电影里 Davis 的“麻木”好上很多。在很多事情上，我依然有能力感知幸福和悲伤。

至少，我自己仍然这样认为。

说说电影吧。

看《Demolition》的时候，我总是不禁想到《局外人》里的默尔索。

两个故事的开头很像。Davis 和默尔索都有一种很强的情感错位：他们不是完全没有情感，而是他们的情感反应和社会预设的剧本对不上。妻子死了，我“应该”悲痛；母亲死了，我“应该”哀悼。可他们没有表现出社会认为该有的感情。

不同的是，默尔索似乎并不觉得这有什么需要解释的。他不会怀疑自己是不是不爱母亲，也不会努力寻找一个符合爱情的答案。他只是拒绝伪造情感。反倒是社会非常在意他有没有表现出“正确”的情感。他自始至终就天然地不太进入那些社会已经替我们规定好的意义。阳光、汗水、海水、身体的不适、别人说话的方式，他都看得很清楚，但对于这些东西“应该意味着什么”往往没什么兴趣。直到最后面对死亡，他才真正意识到并接受世界的“温柔的冷漠”。

Davis 不一样。他是真的不知道自己为什么会这么冷漠，他很困惑。

妻子的死对他来说是一个 anomaly。按照他原本的理解，他过着一套世俗意义上看起来完美的人生。那么妻子突然去世以后，他理应非常难过。可他没有。

这个反应让原来的那套意义结构失效了。

所以我很喜欢电影里拆东西这个设定。Davis 不是突然想通了人生没有意义，而是真的在试图弄明白到底哪里坏了。所有看似摧毁的动作实际上是他在重新检查过去的人生。所以与其说他在寻找意义，我觉得“破解”可能更准确一点。

默尔索没有这个 anomaly。他的反应并不会摧毁他对自己的理解，因为他本来就没有那么相信社会提供的那套解释。Davis 却原本是一个彻底的“局内人”。他不是因为看见世界荒诞所以疏离，而是先在一个框架里活得越来越麻木，直到妻子的死暴露出一个他再也没有办法忽略的矛盾。

Davis 和默尔索所处的世界都有一种很荒诞的地方：充满了虚伪的自我感动，以及一套关于人应该怎样生活、怎样爱、怎样悲伤的现成剧本。

比如 Davis 的岳父岳母。面对女儿的死亡，他们表现出的是一种高度社会化的悲伤——哭泣、纪念、成立基金会、讲漂亮的话。我并不怀疑他们真的悲伤，但这种悲伤又很快被整理成一套体面而有意义的仪式，甚至要求 Davis 一起参与。Phil 急着为女儿的死亡建立意义，却没有真正理解 Davis 为什么根本无法进入这套意义。

从外面看，他们当然比 Davis“正常”太多了，可正常并不意味着更真实。社会判断一个人的内心时，极度依赖这些可以被看见的仪式。于是“按照规范表达爱”很容易被当成爱本身，而一个人拒绝或者无法完成这些仪式，又很容易被理解成“没有爱”。

想到这里，我发现这和自己当年坐在校车上时害怕的事情其实很像。我那时候为什么会暗自庆幸老师同学不知道婆婆刚去世？大概就是因为如果他们知道，我会立刻意识到自己正在被观察。我应该是什么表情？应该哭到什么程度？如果我还是正常上课、说话，他们会不会觉得很奇怪？其实根本没有人在审判我。但我心里知道，一个人面对死亡“应该”是什么样子。

还有一点我觉得 Davis 和默尔索很像：他们看起来都很麻木，但其实都是高度敏感的人。只是顺序不一样。

默尔索一直对具体的感官经验很敏感。他注意阳光、炎热、身体、声音，只是不太把这些感觉继续解释成更抽象的东西。Davis 一开始则是真的麻木。直到妻子的死亡让原来的生活出现裂缝以后，他才突然开始观察周围，观察别人，观察自己以前根本不会注意的东西。

所以默尔索是先敏感，再和意义保持距离；Davis 是先疏离，然后通过重新观察恢复敏感。

我好像处于这两者之间。

从这个角度看，我甚至觉得 Davis 的结局比默尔索更困难一点。

默尔索最后接受了世界没有意义，走向刑场。这当然不容易。但接受无意义本身其实可以处于一个稳定的位置。

Davis 继续往前走了一步。他重新允许世界对自己变得重要，但这也意味着重新允许自己受伤。

那么问题又回到了最开始：

我们为什么如此习惯用悲伤证明爱？

Davis 的经历告诉我们，麻木不一定意味着没有情感。有时候一个人确实在经历什么，只是情感无法被自己辨认。悲伤也不一定非得表现成哭泣。悲伤可以长得不像悲伤。

默尔索则在质疑：也许我们根本不应该预设，一个人在某种情况下必须拥有某一种“正确”的感情。母亲死了为什么一定要哭？没有哭为什么就能够说明一个人缺乏感情，甚至缺乏道德？

而我的困惑是：我是爱婆婆的，可为什么她去世的时候，我就一定应该非常悲伤？

当年我因为没有崩溃而怀疑自己不够爱她，其实已经默认了一个很简单的逻辑：爱得越深，失去的时候就应该越痛。

可我现在不确定这个逻辑是否成立。

如果我知道她最后已经非常痛苦，继续活着对她而言未必快乐，那么对于她的死亡，我是否也可以有悲伤之外的感受？解脱、接受，甚至某种平静，都一定意味着我爱得不够吗？

当然，也许是我在为自己的麻木开脱。我不知道。

可爱的真实性，或许本来就不应该靠失去以后的悲伤强度来倒推。

然后…… “失去”又该如何定义呢？死亡是不是一种彻底的缺席？记忆还在算不算失去？

#notes

you SHOULD be bored sometimes – RNOTTÉ Animation

Sat, 22 Aug 2026 00:58:05 +0000

RNOTTÉ Animation

you SHOULD be bored sometimes

21 Aug, 2026

ask any artist what their source of inspiration is, and they'll tell you. what's mine, though?

being alone. in silence. with my thoughts.

yes, really. i strive to be bored and have a quiet moment to process things. in a tech-dominated age of... you know what... it's rare to have a quiet moment anymore. but you should do your best to find one, in spite of everything.

i know what it's like. you're stressed from long days at work or school, so when you get home, you just want to turn on the TV and binge netflix or youtube to have some form of solace. i get that. but doesn't that just make you feel even more stressed? i find that my best work comes from sitting in silence and wondering, "would this be a good idea? or maybe this?"

one need only look at nature. many social animals have schedules, including humans. most of their day is spent resting or socializing, after the couple hours they spend working, foraging, or hunting. what i'm trying to say is that being constantly stimulated is not natural nor healthy. your brain needs time to slow down. it's not "laziness", it's what animals are supposed to do after a long, hard day.

you SHOULD be bored sometimes. don't listen to anyone telling you that being bored is a bad thing.

#social thoughts

thinking about friendships – ava's blog

Tue, 18 Aug 2026 23:42:00 +0000

thinking about friendships

18 Aug, 2026

Currently taking stock of my social life, and throughout life, the same patterns emerge.

I’ve always been a more solitary person. I’m an only child, and my parents were rather neglectful and homebodies as well; so we never really went on trips, they never took me to the playground or anything.

I played in my room, alone. I went out to play in the shared garden by myself, I went to playgrounds and forests alone (I grew up in a small town/village). I occasionally played with other kids I met outside, but not always. I have always preferred my hobbies to be something I don’t need other people for and that I can just start on my own, whenever, exactly because of the way I am and how I grew up. At kindergarten, there was one other child I talked to and played with, and absolutely no one else. If she wasn’t in that day, I’d just be alone. I couldn’t stand anyone else.

Having anyone over or having to bring me to any other kid’s place was always treated as this impossible task by my mother, and would result in her being mad at me and abusing me, so I soon just didn’t ask for that anymore most of the time. I didn’t wanna cause any issues.

Later on, it meant a lot that I was able to help out at horse stables, earn riding lessons, and have community there. Adults who trusted me, a topic to bond over with people (esp. people my age), a shared interest, shared responsibility. I wasn’t ever enrolled in any team sports or anything, so that is the closest I had. I’m no longer involved in equestrian sports for a multitude of reasons, but I’m glad it was there for me back then. At least I could socialize there.

School was a sensory nightmare for me, extremely draining, overstimulating. My skin felt like it was raw, every sound felt like nails on a chalkboard. I had to use the breaks between classes to retreat to a quiet place and recover before the next class, but this also meant never hanging out with people between classes. The few times I tried, standing with others in these giant halls, people talking loudly and screaming and laughing everywhere around us, I just zoned out. I could barely listen or think of anything to say because everything was too loud. Then I entered the next class regretting how I spent my break.

I always thought things would improve with time. Next year, or when I reach university, and so on. But it never did. At my first university, I tried hard to make friends and attend events, but most connections simply fizzled out, and people dropped out. It didn’t help that I could otherwise barely interact with university life; the public transport home stopped at 9pm (bad for parties!), and other than that, my mother used our dog to guilt trip and control me all the time. I was going in for a class or two and otherwise staying home for him. I could never stay after class for lunch or going to a café together because she’d be throwing a fit and I relied on her for housing.

After that, I started a traineeship with some school parts. It started promisingly, and I indeed felt like people liked me in class. Unfortunately, trying to see anyone outside of it was like pulling teeth; I tried to organize hangouts at the park, barbecues, game evenings at my place etc., but most never materialized. I think some people showed up at my place once, some cancelling shortly prior, the few coming like 1-2h late and leaving early. It never happened again. After the traineeship ended, we all dispersed and didn’t keep contact with one another.

Surely, things would improve with full time work, right? Not really. It’s harder to bond with coworkers who are either much, much older or live a very different life in general, especially with kids, houses, vacations. I know what to ask them, and I do - is your aunt feeling better? How is your kid? Did he pass the difficult exam? What summer vacation are you planning/how was Egypt? How’s the garden project coming along?

But they don’t know what to ask me, and I totally get why. They can’t ask me about things they bond to each other about, and they don’t understand anything about me. Sometimes they ask if my wife found a job yet, and I still have to give the same answer, and then that’s it. I share stuff about myself, but am never asked about that.

I thought things would change when a new, similarly young coworker started here and got seated in my office. I put a lot of effort into being her guide, showing her everything, helping with the start, complimenting her work, bringing her coffee one time (which she didn’t touch for the entire day and then probably dumped, woohoo), spending lunch together, and all that.

But now, 2.5 years or so later, I have to admit it failed again. I make sure to always ask about how she is today or how her weekend was when I come in, I share stuff from my life to signal openness and to give her something to ask about or something, but it doesn’t help. We greet each other, say we feel alright, complain about public transport, and then spend 6-8h in complete silence in the same room until one of us leaves for the day.

There is no ease, no jokes, no conversations emerging inbetween. I also feel like when we have good weeks where I try extra hard and it flows better, it takes just one office day of being a little more quiet, or just a week of time off or sick, and then I have to start at zero again. I feel that way about lots of people, as if my progress with them is constantly reset by something.

Everyone else seems to bond just fine with her (and vice versa) despite the age difference and different lifestyle, so I guess it really wasn’t that; it was just me. I often have to rely on a group setting at work to find out stuff because people will just not tell me much directly for some reason.

Now that I have been in an online/distance university since 2022, there is even less contact with other students. Everyone I befriended in the beginning or had a study group with dropped out and disappeared. I no longer even join any groups or interact much because it’s pointless; I study the material, do the exams, and that’s it. All alone, no one to talk to about it, no one to ask or practice with. It’s easier that way than dealing with the flakiness.

In general, I think I just don’t seem to read people correctly, or I put too much stock in what they say or do, somehow, and expect it to follow the indicated pattern?

This year I suggested meeting up at a conference in a group, someone else made a group chat for that meetup, people joined voluntarily, and then I didn’t see most of them because they made no effort actually making plans in that group chat or reacting to my efforts to meet up. No feedback, no replies, no “sorry can’t make it”, just silence. You’d think there’s interest when people accept the idea, make a group and join it, but apparently I must have misread the intentions somehow. In the era of nonchalance, I guess it’s my fault for showing interest and enthusiasm.

I’ve also noticed that online friends, especially the ones more far away, and general real life friends that live very far away (because you or they moved away) make much more of an effort. They text more, they make online plans, they make an effort to meet irl when it fits. Meanwhile people local to me… you might as well not exist. I’ve tried to change LGS/Magic the Gathering connections into something deeper and broader, and it just fails. I make an effort to ask people about their interests, they don’t ask back. I make an effort to note that someone’s cat has been sick, and to check back in about the cat’s health later, and get completely ignored. Or the usual “This was great, we should do this again soon!” and then you’re the only one trying.

My wife and I are really great hosts. We have an option for guests to stay in my wife’s apartment. We stock the fridge for them. We bake cookies and gift people bread we bake. We cook great meals for people when they visit. We have a decent collection of boardgames and card games we invite people over to play, or bring to their place. We can watch your pets while on vacation, we can water your plants, we can bring you soup when you’re sick. We’re happy to go to museums and cafes and other stuff with you. But for some reason, actually establishing all that is painfully hard with local people.

People love to complain about a loneliness epidemic, but at this point, I consider that many people just wanna be lonely and make no effort to change that, or are saturated with what they have, or don’t actually have what it takes to build and maintain a “village” (“It takes a village”, if you want a village you have to be willing to be a villager and help, yada yada). Me too, probably; there seems to be something wrong with me, it’s probably my autism. But at least I try, which is more than I can say for most people who live close.

Right now, almost all friends I have are through my wife. They are hers, or ours, but never just mine. I even “lost” people to her when I introduced them. The vast majority of days, the only person I talk to in real life is my wife. 1 of 2 office days per week, I don’t say a single word at the office because I don’t see anyone; everyone is in their own little room, and my team mates are not there. I don’t really grocery shop, and when I do, I use the self checkout. Cashier contact gives me nothing.

Anywhere in public, no matter if shops or public transport, I don’t get these sort of whimsical stranger interactions others do. I make a joke and people don’t get it or don’t hear it, people say something to me in public and I am too surprised to say something of value or anything that would keep the conversation going, and the moment passes. The same happens in work hallways or the work kitchen.

I chat occasionally via Matrix or Signal, and that’s it. Every other month or three, we play Magic with some people and I get to socialize. Or friends from far away come visit.

But other than that, nothing. And I don’t think anything is gonna change that. I don’t understand people, and they don’t understand me. The only times it has ever really worked reliably is if they were romantically or sexually interested. There is always this invisible wall between me and other people, and in many cases, an effort mismatch and an importance mismatch.

I’m at a point where I might just accept it; hold the people close who really love and understand me, and otherwise be content with my solitary little hobbies and special interest. At least those can’t leave and aren’t unavailable. It just sucks when everyone you rely on so much (because you don’t have many others), have what feels like a sea of people available to them. You always have to share them, but they never have to share you.

Published 18 Aug, 2026

#2026

联邦德国历史博物馆，2026 – Yanwei's Blogs

Mon, 17 Aug 2026 04:41:13 +0000

写于2026年8月15日，Santa Clara, CA

2026年8月1日，我去伯恩 (Bonn) 参观了联邦德国历史博物馆（House of the History of the Federal Republic of Germany）.

House of the History of the Federal Republic of Germany

二战中的罪恶

希特勒的帽子

这是一件很珍贵的文物。没想到我还能近距离看见元首的军帽。

星条旗报巴黎版号外

纳粹集中营的尸体

可以看得出严重的肌肉流失，说明死前营养不良很久了。

纳粹钢盔

铁十字

当时美国国旗上是48颗星，阿拉斯加州和夏威夷州还没有加入美国

东西德对峙，冷战时期

东德镇压民众抗议的盾牌与警棍

东德警察

看来东德政府是对人民下过死手

柏林墙

顶部扣圆环，防止攀爬

东西德分界线

东德

西德时期的发展

美国在战后给予了德国大量的援助

这些援助，帮助了西德重建，也奠定了美国在世界上的地位。

西德总理维利·勃兰特的诺贝尔奖证书

这个证书我没有看见，是下载的。

我以为这个电视机是日本发明的呢，原来德国早有同款

我家的第一台12寸黑白电视机与这个一模一样，日本三洋的。我在纺院幼儿园大班时，还住在东楼时，家里买的。当时我去接弟弟从幼儿园回来，我当时骗他说家里新买了一辆坦克。

西德的绿色贝雷帽，鹰绣得真好

奥地利共和国国徽

鹰戴着王冠，显然不符合德国法律。爪子攥着镰刀、锤子，并戴着脚镣，虽然链子断开了，但拖在地上也不方便，飞起来也飞不动。羽毛爆炸，活像一只通了电的炸毛鸡。我不知道展览里它出现的含义，只是觉得这个鹰很恐怖又滑稽。

Photo by 史庆茹

参观途中，遇到一个柏林人，佳能摄影爱好者。用的照相机是Canon R5 + Canon RF 28-70mm f/2 L Lens，我和他攀谈了几句。硕大的镜头，95毫米Filter Size, 非常沉，1.43 公斤，最近对焦距离 39 厘米，B&H 售价 3400 美元。他问了我关于如何看待 AI 发展的问题。

荷兰国家美术馆，2026 – Yanwei's Blogs

Mon, 17 Aug 2026 04:41:13 +0000

荷兰国家美术馆，2026

2026年8月3日，Rijksmuseum 荷兰国家美术馆

The Milkmaid by Johannes Vermeer, 1660

镇馆之宝 — 维米尔^[注1]的《倒牛奶的女仆》

维米尔留下并被学界认可的作品数量非常少，通常只有三十多幅。Rijksmuseum自己收藏了四幅维米尔：《倒牛奶的女仆》《小街》《情书》和《读信的蓝衣女子》。一幅公认的顶级维米尔，本身就已经是世界级珍品。《倒牛奶的女仆》又属于维米尔最成熟、最容易一眼认出的作品之一。

《夜巡》The Night Watch

伦勃朗的《夜巡》是 Rijksmuseum 的第一号宝物。

A Young Woman Warming her Hands over a Brazier

欲戴王冠，必承其重

莎士比亚名句 — “Uneasy lies the head that wears a crown. ” 王冠果然很沉。

荷兰摄影师：范德埃尔斯肯

注释

[注1] 维米尔（Johannes Vermeer，1632–1675）是那种作品极少、题材极小，却后来被抬到西方绘画最高殿堂的画家。跟梵高、伦勃朗相比，他既没有传奇人生，也没有大量名作，更不像米开朗基罗那样到处留下巨型作品。

如果先用一句话概括他：伦勃朗画人的命运，梵高画自己的情绪，维米尔画“光落在普通生活上的那一刻”。

维米尔1632年出生在荷兰小城 Delft（代尔夫特），一辈子基本没有离开那里，1675年去世，只有43岁。这正是荷兰的“黄金时代”。当时荷兰靠贸易、航海、金融迅速富裕，城市中产阶级大量购买绘画。与意大利和法国不太一样，荷兰画家不一定天天给教皇、国王画圣经和神话故事，而是开始画：自己的房子、妻子、女仆、街道、餐桌、音乐、地图、酒杯。维米尔就是把这种“小日子”画到极致的人。

先记住他的三幅画

《戴珍珠耳环的少女》
《倒牛奶的女仆》
《代尔夫特风景》

Girl with a Pearl Earring, 1665

View of Delft, 1660

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The Universe of Discourse : There are two kinds of theorems

Wed, 12 Aug 2026 17:28:32 +0000

Tue, 11 Aug 2026

There are two kinds of theorems

In mathematical study there are two kinds of theorems, which serve very different purposes. Math instruction follows the same pattern. Students are often very puzzled by this, and rightly so, because it's never explained, or at least I've never seen it explained. There is this crucial, critical piece of mathematical methodology which is never made explicit, students just have to figure it out on their own, and many of them never do.

When we do mathematics, we construct a simplified model of some phenomenon. For example, Euclidean geometry is a simplified model of how shapes and lines actually work.

In formal geometry, things are simple: lines have no thickness, and three or more lines might all intersect at the exact same point. There are perfect circles, where every point is the exact same distance from the center, and there are perfect rectangles with perfectly straight sides and perfectly equal angles.

Real shapes aren't like this. Nobody can draw an infinitely thin line. Nobody has ever seen a geometrically perfect circle or rectangle. Three lines, however carefully drawn, will always intersect in three different places. That's okay! The point of geometry is to construct a simplified model that is easier to deal with.

When we're setting up a mathamtical model, we start by describing its basic objects, like points and lines, and with axioms and postulates, what properties we intend the objects to have. For example, Euclid has:

A line is breadthless length.
A circle is a plane ﬁgure contained by one (curved) line with a point inside, the center, so that the segments from the center to the boundary of the circle are always of equal length
All right angles are equal.

Having done that, we state and prove the theorems of the first kind. We're not studying the actual phenomenon yet. We're not yet trying to learn anything new about shapes and circles. Instead, we're investigating the model itself:

Is the model accurate? Does it seem to lead to wrong conclusions? What happens if we try to prove things that we know are are false? The proofs should fail! If they don't, something is wrong with the model, and we need to fix it.
Is the model powerful enough to prove at least simple things about the actual phenomenon? If it can't encompass the simple aspects of the phenomenon, we haven't much hope of using it to understand more complex aspects.

So for example Euclid starts by proving extremely simple theorems. For example, propositions 4 and 5:

Proposition 4: If in triangles !!ABC!! and !!A'B'C'!! we have !!AB=A'B'!! and !!AC=A'C'!! and !!\angle A = \angle A'!!, then the two triangles are congruent.

Proposition 5: If two straight lines cut one another, then they make the vertical angles equal to one another.

(That is, !!\angle CEB = \angle AED!! and !!\angle CEA = \angle BED!!.)

Obviously, yes, anyone can see that! We didn't need to develop a whole mathematical theory in order to discover that vertical angles were equal. Everyone already knew that, long before Euclid. The point of proving this theorem, the real discovery, is: our simple model is strong enough to demonstrate that vertical angles are equal. The theory didn't explicitly include anything about vertical angles, but the vertical alngle theorem was latent in the model anyway.

Consider the opposite situation, where we couldn't prove that vertical angles were equal. Or worse, what if the model allowed us to construct a pair of unequal vertical angles? Would this tell us something about vertical angles? Obviously not. Vertical angles are equal, regardless of what the theory does or doesn't prove. It would, though, tell us something about the theory, namely that it wasn't fit for purpose, and we'd better try a different model.

This is a common pattern in all mathematics education and indeed in all mathematics, but I've rarely seen it called out as such, not even with a passing remark like “here's why we're doing this”. In nearly every undergraduate class I've ever been in, someone was puzzled about why we were doing this. Why is Euclid proving all these theorems that are obvious?

In Euclid the mode goes back and forth: Euclid will do some model-verifying theorems, then move on to interesting-result theorems, then back for a while to introduce something new to the model, then forward again to prove interesting theorems about the thing he introduced. The first transition happens around proposition 32 or 36 or so. Up until that point there were a lot of proposition like this:

Proposition 20 In any triangle the sum of any two sides is greater than the remaining one.

and this:

Proposition 25 If two triangles have two sides equal to two sides respectively, but have the base greater than the base, then they also have the one of the angles contained by the equal straight lines greater than the other.

But then very soon after, the theorems start to have a different flavor:

Proposition 36: Parallelograms which are on equal bases and in the same parallels equal one another.

That is:

This is actually an interesting fact about parallelograms, and not intuitively obvious. Even though the two parallelograms are not at all the same shape, they have equal areas, since they lie between the same parallels and !!AB=CD!!. (Interactive version)

The same issue comes up in many different contexts. We develop the theory of the Peano numbers, define addition, and prove that addition is commutative, Was that because we didn't know how to do addition? No. We already knew that addition was commutative. The point of the theorem is to show that Peano arithmetic knows that addition is commutative. But I have more than once seen instructors demonstrate the proof, via a double induction, and then finish with a remark like “therefore, addition is commutative!” The students, to their credit, were suspicious of this. They knew something wasn't quite right, even if they weren't sure what. The right announcement would have been something like “therefore, the Peano axioms aren't complete rubbish!”

Or: We explore Dedekind cuts, we define a model for the real numbers as cuts of rationals, and a construction that we claim characterizes addition. And then we prove a batch of theorems that are intended to show things we already know about addition, not because we want to know whether addition is commutative (news flash: it is) but to show that it's plausible that our construction really does characterize addition. One of these, that the addition operation we defined on cuts, which looks nothing like the addition we defined on rational numbers, actually agrees with it when the cuts themselves correspond to rationals. Another, that if !!a < b!! then !!a+c < b+c!!.

Taking a look at Rudin Principles of Mathematical Analysis, I see that the first fifteen or so pages are like this, theorems like !!\lvert z\rvert = \lvert \bar z \rvert!!, which is a basic property of the fundamental notions !!\lvert z\rvert!! and !!\bar z!!. And then the mode starts to shift, first a little bit, with

Let !!z!! and !!w!! be complex numbers. Then !!\lvert z+w\rvert ≤ \lvert z\rvert + \lvert w\rvert !!

Okay, that's a triangle inequality again… and suddenly, seemingly out of nowhere, something not at all obvious: Theorem 1.35, the Cauchy-Schwartz inequality for !!\Bbb C^1!!:

$$ \left\lvert\sum_{j=1}^n a_j\bar b_j\right\rvert ^2 ≤ \sum_{j=1}^n\lvert a_j\rvert^2 \sum_{j=1}^n\lvert b_j\rvert^2 $$

A completely different kind of theorem, not a basic property of anything.

Remember the whole point of the process: We wanteded to model some object of study, we built a model, we proved a lot of theorems to lend plausibility to our model, to verify that the model wasn't broken, to confirm that the model captures the properties of interest. And then came time to use the model, and we started to prove theorems that told us new things about the original object of study.

Does Rudin announce this shift? Of course not, Rudin never announces anything. (Usually he mutters, and sometimes if you are especially unlucky he fixes you with a glare that dares you to question the remark he throws away in an undertone.) But Rudin is Rudin, and nobody else seems to announce this shift either. Almost always, it's passed over, usually without remark, even in gentler textbooks that give more attention to pedagogical matters. Sometimes the shift is sudden, sometimes gradual, but it's almost never pointed out.

In advanced study, that's okay, because advanced students should be expected to recognize the pattern. But why do we expect high schoolers and undergraduates to understand this without explanation?

In summary:

There are two kinds of theorems.
- The purpose of the first kind is to validate the model we've built, to check it for power and correctness.
- But the second kind is the kind we're really after, to apply the model to the problem we want to study.
This pattern, of building a model, validating it, and then using it, is a fundamental and universal methodology in all mathematical study.
Secondary and tertiary mathematical education should explain this methodology, but rarely acknowledges it at all.

[Other articles in category /math] permanent link

What is a product? - One more thing

Fri, 07 Aug 2026 22:19:24 +0000

I've seen, and probably you have seen too, far too many prototypes out there created with AI treated as products, because it is that easy to prompt two sentences and get something that resembles a real thing. Do you want a website to sell your old furniture? Done. You want an Instagram clone? Done. What about a full-feature LinkedIn replacement? Done. Except, it is not really done.

Every other week, Anthropic or OpenAI launches a new version of their models, and every other week, the internet is flooded with examples of what those models are capable of. Beautiful designs and prototypes fill up our feeds, giving us, simple mortals, a taste of what the future looks like, on localhost. No link needed.

I am impressed. Are you impressed? Well, you should be. But when I think about this for two seconds, I realized that four years after Sam Altman tweeted about his new chatbot, I haven't seen any real competitor of YouTube, or Figma, or Google, or Instagram created solely with AI. If this thing is so powerful, where is all the innovation? Shouldn't all of us be creating our own version of GTA 6 from our garage – I mean, our couch – at this point?

It turns out a prototype is not a product. Most of what we see on YouTube that was created by the dude, who never touched a line of code before, between two cups of coffee is not even a prototype; it's nothing. If you are generous, you can call it a demo, a draft, maybe?

A real product is hard to build. I'm not saying there aren't people out there creating useful stuff in record time. What I am saying is that you shouldn't be impressed by everything you see online. Don't feel bad if you don't have anything to show up with all the free intelligence available nowadays. Almost nobody has.

A real product has real users, a real market and solves real problems.

When I think about most of the products we use daily, like X.com or Google, I wonder why nobody has a real competitor of these things before. It was not a lack of intelligence or know-how. Many companies were created with this goal in mind, but none succeeded because a product is more than the parts that compound it.

I could prompt a basic Instagram feature in a few hours, maybe a few days, but would it mean I created a product? If nobody uses it or cares, is it still a product? What makes a product is its users. If nobody is using the thing you built, you don't have a product, you have a toy. Have fun playing with it.

Taste Is All That's Left | Blog

Thu, 06 Aug 2026 17:25:34 +0000

For most of the time I have been writing software, the hard part was making the thing exist at all.

You had an idea, and between the idea and the working program stood hours— sometimes weeks—of typing, of reading manuals, of misunderstanding an API and slowly grinding the wrong version into a slightly less wrong one. Production was the wall. Everyone hit it. It was the thing that separated the people who could from the people who could only talk about it.

That wall is gone. Or rather, it has been rented out. ¹ You can describe a thing now and receive a plausible version of it faster than you could have typed the first function by hand. The idea-to-artifact distance, the one that defined the entire craft, has collapsed to almost nothing.

Though, you have not been warned about one little thing: the value you built by learning to climb that wall does not disappear. It moves.

The Bar Went Somewhere

We keep asking whether the machines are any good. It is the wrong question. The output is good enough—that is the problem. Good enough is a solvent. It dissolves the reason to do better. For as long as making things was expensive, the expense did quiet work on our behalf. It rationed output. It meant that anything which existed had, at minimum, survived the cost of being made. You know what I mean? Effort was a filter, and like all filters it was invisible until it was removed. Nobody shipped a thousand mediocre variations of a feature, because a thousand mediocre variations cost a thousand times as much as one. The economics enforced a floor.

The floor is now gone. And when the floor goes, the thing that decides what is worth keeping is no longer the cost of making it. It is you. Your judgement. The verdict you reach when you look at three plausible versions of the same function and know, somehow, that two of them are wrong. That verdict has a name we are slightly embarrassed to use in engineering circles, because it sounds soft and unfalsifiable and vaguely aristocratic.

Taste.

What Taste Actually Is

I want to be careful here, because “taste” is doing a lot of work and it is easy to hear it as decoration. A matter of preferences. Whether you like your braces on the same line.

That is not what I mean.

Robert Pirsig spent an entire book circling a word he refused to define, because he had convinced himself that defining it would kill it. He called it Quality. His argument, roughly, was that you recognise Quality before you can explain it— that the recognition comes first and the reasons arrive later, if they arrive at all. A good mechanic knows the engine is wrong before he knows why. A good editor feels the sentence sag before she can name the clause that failed. ²

Taste is that. It is the compressed, wordless verdict you reach faster than you can justify. It is the “no, again” you say to yourself with total conviction and no available argument. And it is not soft at all. It is the hardest thing in the work, because it is the only part that was never mechanical to begin with.

Everything downstream of the verdict—the typing, the syntax, the wiring of one library to another—was always, in principle, automatable. We just had not gotten around to it. The verdict was the thing the machine could not do for you.

It still cannot. It can only make the absence of it cheaper to ignore.

Taste Is Downstream of Friction

Here is the uncomfortable mechanism, the part I would rather not think about.

Where did your taste come from?

No really. Where did it come from, was it genetic? Were you abducted by aliens one day that forcefully injected your sense of taste into your mind and wiped your memory?

I’ll tell you this much: it’s not from consuming good work. You cannot read a hundred excellent programs and absorb the judgement by osmosis, any more than you can become a chef by eating in good restaurants. Taste is built the slow, stupid, humiliating way: you make something bad, you are forced to live with it, it fails in front of you, and some part of you files the failure away. Then you do it again. The palate is an accretion of your own mistakes, sat with long enough to sting.

The friction was not an obstacle to developing taste. The friction was the curriculum. Every wall I cursed while climbing it was, without my noticing, teaching me which walls were worth climbing. The cost that rationed my output also educated my judgement, because paying the cost over and over is how you learn what is worth paying for.

So watch what happens when you remove the friction for the next person.

They can generate fluently from the first day. They will never ship the bad version and be forced to sit in it, because the tool offers them a competent version for free. They will climb no wall, and so they will learn nothing from the climb. They will arrive at fluency having skipped the entire apprenticeship that fluency used to require—and they will be more productive than I was at their stage, by every metric anyone bothers to measure.

They will be able to make anything, and unable to tell (or stop to think) whether they should. Not necessarily through any fault of their own. We removed the part of the process that would have taught them, and we called it progress, and by most definitions it was.

The Economics Are Against You

Suppose you have taste. Suppose you paid the full price and you can feel the sag in the sentence and the wrongness in the function.

Congratulations! You now ship at exactly the same speed as the person who cannot.

This is the quiet cruelty of the situation and I do not have a comforting way to phrase it. Taste is slow. It says “no, again.” It sends the plausible thing back because plausible is not the same as right, and while it is doing that, the person without it has already shipped, closed the ticket, and moved on. The market timed you both with the same stopwatch and it did not see the difference. It cannot see the difference. Taste does not show up in the diff.

It is unmeasurable, uncreditable, and invisible on a dashboard. You cannot point to the disasters it prevented, because prevented disasters leave no trace. You carry a cost—the extra hours, the returned work, the refusal to ship the fine thing when the right thing is still reachable—and you carry it alone, against an incentive gradient that runs the other way.

Harry Frankfurt once drew a careful line between the liar and the bullshitter. The liar at least respects the truth enough to work against it. The bullshitter does not care about the truth in either direction; he is simply indifferent to it. ³ Slop is the bullshit of engineering. It is not wrong, exactly. It is indifferent. It works, it passes, it is fine. And fine, produced without friction and shipped without judgement, is now the most abundant substance in the field.

The Flood

Sturgeon said it decades ago, defending science fiction from a critic: ninety percent of everything is crap. He meant it as consolation. Ninety percent of every field is bad, so do not judge the field by its bulk. But the ratio was never the danger. It held steady for centuries. What held the flood back was that producing the crap cost something. Bad novels still took a year to write. Bad software still took a month to build. The ninety percent was throttled at the source by the sheer inconvenience of making it.

We have now removed the throttle and left the ratio intact. Ninety percent of an infinite output is still infinite. The signal did not get worse. The noise became free, and free noise rises without limit, and every real thing you make now arrives into a sea of plausible nothing that looks, at a glance, exactly like it.

Which means the scarce act is no longer making. It is choosing. Deciding what, out of the endless generated plausible, deserves to exist and be kept. Curation was a minor virtue when things were expensive to make. It is the whole game when they are free.

What Deserves to Exist

There is a rhyme here, if you go back far enough.

When the factories came, they could suddenly make everything—cheaply, uniformly, by the thousand. And a handful of people, Morris and Ruskin among them, looked at the flood of cheap identical goods and asked a question that sounded, at the time, sentimental and doomed: not can we make this, but should this be made, and made this way, by no one, for no reason but that the machine could.

They lost the economic argument. They were always going to. But they were right about the thing that mattered, which is that when the making becomes free, the choosing becomes the craft. The human question stops being “can I build it” and becomes “does this deserve to exist”—and that question was always the more serious one. We just could not afford to ask it while we were busy climbing walls.

I keep coming back to this turn. It is not consolation but a correction.

The tools did not devalue the skill. They stripped away everything that was not the skill. All those years I thought the work was the production—the typing, the wiring, the wall—and production turns out to have been the toll. The tax you paid for the privilege of exercising judgement. Now the tax is close to zero, and what is left standing, exposed, with nowhere to hide, is the judgement itself. The part that was always the point.

Taste did not become less valuable. It became the only thing that was ever scarce. We just could not see it, because it was buried under all the labour it used to take to get to it.

A Defense, Then

So here is the defense, such as it is.

Anyone can generate now. That race is over and it was never worth winning. The discipline that remains—the one the machine cannot rent you and the dashboard cannot see—is in the deletion. In the “no, again.” In caring about the difference between fine and right when nothing external will ever reward you for caring, when the market has timed you and shrugged, when the plausible version sits there working and passing and asking only to be let through.

Refuse it anyway. Not out of nostalgia for the friction—I do not miss the wall, and I will not pretend to. Refuse it because the verdict is the last part of this that is actually yours. It is unmeasurable, which means no one can take it from you by measuring it. It is unautomatable, which means no one can sell it back to you. It is slow, which in a field optimising for infinite speed is starting to look less like a handicap and more like the only remaining evidence that a human was here and gave a damn.

Everyone can make anything. Almost no one can tell you what is worth making.

That was always the harder skill. It is now the only one left.

Footnotes

There is an older word for this arrangement. You no longer own the means of production; you rent them, by the token, from whoever trained the model. An English teacher of mine—a committed socialist—would have had the whole thing diagrammed on the board before I finished the sentence: the worker separated first from his tools, then from the labour itself, then sold a frictionless substitute for the labour and told this was liberation. He would also, I suspect, have been the first to note the one part of the process that cannot be rented back to you, because it never left your head. Draw your own conclusions about which part that is. ↩
Zen and the Art of Motorcycle Maintenance, if you have not read it. It is about a great deal more than motorcycles, and almost nothing about Zen. ↩
On Bullshit. Frankfurt, 2005, though the essay is older. Yes, that is the real title. ↩

北欧：从海盗窝到福利社会

Tue, 04 Aug 2026 21:13:19 +0000

上周我走马观花地访问了北欧的丹麦和瑞典两个国家，看了很多博物馆，系统地了解了北欧的历史。北欧不大：瑞典人口只有一千万出头，丹麦六百万，其他国家更小。它们都是经济发达，人民幸福指数超高的地方。了解一点历史的朋友应该知道，这里一千年前可是杀人不眨眼的北欧海盗 Viking 的起源地。本文以丹麦为视角，带你走过它的文明进化史：只要军事上一直输，连输几百年，就文明了。

1520年：瑞典独立

Gustav Wasa

很久以前，瑞典和挪威是从属于丹麦的附属国。它们都是中世纪欧洲典型封建国家，各自有不少的封建领主，领主效忠于国王，而这国王习惯性地来自实力最强的丹麦，兼任丹麦，瑞典，挪威三国王位，要在三国分别加冕。这一年丹麦的国王是克里斯蒂安二世，瑞典有不少领主不欢迎他来瑞典坐王位，他们起兵反抗。克里斯蒂安二世带的丹麦军队虽站上风，但瑞典反对派也一时半会打不掉，怎么办呢？

双方开始谈判，反对派愿意放弃抵抗，条件是得到完全宽恕。克里斯蒂安二世同意了。过了两个月，克里斯蒂安二世到瑞典斯德哥尔摩加冕瑞典王的时候，所有领主都到场宣誓效忠。结果克里斯蒂安二世背信弃义，抓住并杀掉了全部反对派领主，这个事件史称斯德哥尔摩大屠杀。被杀的一位领主有个儿子叫古斯塔沃瓦萨，他潜回领地，再举反旗。

这下反叛彻底压不住了。三年后，丹麦只能承认瑞典独立。古斯塔沃一世就是瑞典开国之君。

1658年：哥本哈根围城

丹麦国王

瑞典从丹麦独立后一百多年，两国之间一直有小规模的战争，丹麦一直是优势一方，可惜在种种原因综合影响下，两国国力逐渐逆转，在这一年战火重燃，瑞典连战连捷，兵临丹麦首都哥本哈根城下，围城长达六个月！

1658年的冬天奇寒彻骨，哥本哈根城外的海峡全部冰封。丹麦人引以为豪的海军成了摆设，陆军更强的瑞典人踩着冰面直接攻到城墙下。假如这城破了，丹麦可能就亡了。最终，丹麦人靠着万众一心，将将守住了哥本哈根。围城的瑞典人也磨不下去了，于是两国达成和议，瑞典人解围而去。和平的条件是丹麦割让全部 Scania给瑞典。从此，哥本哈根以东隔着一条不宽的海峡皆为瑞典，从王宫的高塔上就望的到。

打败丹麦后瑞典在军事上进入了一个黄金时期，直到几十年后东方出了个彼得大帝，俄罗斯开始崛起。丹麦割让给瑞典的Scania占丹麦领土的25%，全是沃野良田，从维京时代就是丹麦本土。想必丹麦不甘心吧。可惜，就算是瑞典被彼得大帝修理的最惨的时候，这片土地丹麦人也没打回来。

1807年：丹麦海军之亡

丹麦海军

这一年欧洲大战的主角是拿破仑，他带着法国独挑欧洲其他各大国（以英俄为主），端的是勇气可嘉。本来跟丹麦扯不上关系，但英国对丹麦发了最后通牒：把全部海军舰艇交出来！理由是：要是拿破仑打过来，控制了丹麦的海军（当时规模不小），将会对英国的海上霸权形成挑战，所以，英国要先下手为强。

这明明是一个强盗逻辑。英勇的丹麦人当然不能受这个屈辱。可惜，日不落帝国的海军不是丹麦海军能挑战的，最终，在顽强抵抗之后，丹麦还是失去了全部海军舰艇，英国海军甚至还炮轰哥本哈根，大批民房，宫殿，教堂被夷为平地。之后，丹麦为报海军灭亡之辱，毅然加入了拿破仑一方，然后陆军又输了一遍。

1814年战后清算法国，重新划定各国边界。丹麦屈指可数的海外殖民地全部被英国拿走，又被逼交出了挪威（丹麦附属国）给到瑞典，作为瑞典（反法战胜方小弟）承认俄国（反法战胜方大腿）吞并芬兰（瑞典附属国）的补偿。挪威人当然不愿被当成筹码转来转去，开始搞独立，到挪威终于独立的那天，已经是近百年后了。

1864年：丹麦普鲁士之战

普鲁士大炮

丹麦王室从古以来一直控制着三个南部大公国，这三个大公国南界和汉堡市隔河相望，居民以说德语为主。在1849年丹麦已经和平转型成民主政体，而德语区在神圣罗马帝国被拿破仑打散后，还是散沙一片。这一年，神圣罗马帝国故地有一个新的大国崛起，就是普鲁士。普鲁士在威廉一世和首相俾斯麦带领下立志要统一德语区，成立德意志帝国！

普丹之战其实没有任何悬念。普鲁士人口，装备，组织能力都不是区区丹麦能相比的。普鲁士轻松打下丹麦属下德语三区，然后放过丹麦转头向南了。它心目中的真正对手是奥匈帝国，是法国，不是小小的丹麦。普丹战争只不过是普奥和普法两场大战的开胃前菜，1871年，大败法国的普鲁士国王在法国凡尔赛宫加冕德皇。

失掉德语三区之后，丹麦领土又小了30%，人口少了40%。战后，丹麦人痛定思痛，下定决心，再也不能打仗了：大国争霸还有赢的可能，小国永远是受伤害的。所以一战的时候丹麦置身事外。二战时丹麦继续中立，但还是被德国占领，成了个令人哭笑不得的被占领中立国。谁让德国就这么近呢？

战场之外

在战场上丹麦屡战屡败。战场以外呢？1520年之战催生了宗教改革，丹麦和瑞典都摆脱了罗马教廷的束缚。1658年之战催生了丹麦第一份宪法，使得丹麦逐渐脱离封建成为现代国家，1807年之战催生了丹麦文艺的黄金时代，并最终导致了民主转型。1864年之战又导致了政治左转，社会民主党上台，国家转型为高福利社会。今天北欧四国丹麦，瑞典，挪威，芬兰殊途同归，都是小国寡民的乌托邦式国家。

那几百年的国仇家恨呢？日不落帝国已是昨日黄花，德意志也被拆掉爪牙，关进笼子。哥本哈根和斯德哥尔摩市民都通晓英语德语，服务于满大街操英语德语的游客。丹麦和瑞典的世仇也早已和解了：十九世纪开始两国王室重新开始嫁娶，到现在都是欧盟成员国，大家边界开放，还有跨海大桥。所谓国仇家恨，不外乎是沉没成本罢了。

丹麦只有六百万人，相当于香港的规模，但丹麦对世界文明的贡献远高于它的体量。光是在20世纪，丹麦就贡献了在量子力学里的赫赫有名的哥本哈根学派，建筑设计里的丹麦风，当然还有我最爱吃的蓝罐曲奇。假如时光回到1520年，克里斯蒂安二世是一个彼得大帝级别的雄主，丹麦能一统北欧，进而与英国德国俄国争雄，甚至殖民亚非拉，丹麦之外的全世界人民当然不愿意，我想今天的丹麦人恐怕也不愿意吧。

I'll do it by hand. – a giant glacier

Thu, 06 Aug 2026 08:14:07 +0000

I'll do it by hand.

06 Aug, 2026

In university I took small jobs in town whenever I could. It was an excuse to get off campus, it meant a little cash in my pocket, and I got to interact with townspeople, most of whom had strong opinions about my school. The jobs were usually one-offs and involved gruntwork of the handyman variety. One day I might be hauling away piles of old boards, the next repairing a shed or cleaning out a basement.

Once I was working with a gent from school to replace floorboards in the closet of an old house. It was a simple carpet thrown over 2x4s, so all we had to do was remove screws, swap boards, and attach. The screw removal process was involved, though, as whoever had built this floor apparently thought 20 screws per board was the norm.

I sat on the floor of this dusty closet with my work pal, each of us removing screws one by one. The homeowner had given us two tools: a plain old screwdriver and a battery powered drill. I had the former, and as we worked, each of us commented on our methods' pros and cons. His was faster but more prone to error (and the errors were larger). Mine was easier to control, but slow and painstaking.

We both said we preferred the manual method, and we even swapped when removing boards from another closet. Why the preference? Because the screwdriver connected us to what we were doing, while the drill separated us. You felt every turn with the former. The latter, it was over too fast to know what was going on.

This reminded me of a section of Paul Kingsnorth's Against the Machine. Paraphrased:

Simple technologies were not much used by the ancient Egyptians. The issue was not a lack of knowledge but a concern about what their use might do to the shape of reality. To them, even simple technologies had moral and cosmic implications, as using them required treating matter as if it were no longer the dwelling place of spirit, but as if it were simply mass with little more to it than extension, density and weight.

I'd never thought there were gods in objects, but I did think there was something different about manual, hand-to-object interactions. I could feel it that day with the screwdriver, and I notice it now whenever I pick up a tool. Battery-powered grass trimmer? No thanks. Give me the little pincer thing that goes snik. There's something deeply satisfying about that action, that sound, the time it requires, the muscles involved, the senses it engages.

What about efficiency? Can't I cut more grass faster and with less effort using a machine? I suppose so, but what's the point? To finish what I'm doing or to do what I'm doing?

Tools give us new abilities, and they make tasks easier/less harmful for us. You're not going to hammer nails with your first or go diving without goggles. But our tools are so good they replace our interactions with shortcuts to the end. Shortcuts necessarily cut out something, though, and that something might just be important.

But for human-level jobs, tools feel like they can distort what we're doing and remove us from the process. It becomes about getting to a destination rather than the job itself. And when you're that goal-driven, the only thing you can do after you reach the goal is to set another and start working towards it. Don't pause to appreciate or reflect, just go go go.

I've had the same feeling about work, hobbies, tasks of any kind. All this AI stuff got me thinking about it, too. The process of doing (and failing at, and mastering) something is pushed aside in favor of being at the final product. Faster, cheaper, easier...but you're never done, are you? And even if you are, you're never satisfied.

Chrono Trigger 30 years ago:

We've got some great tools at our disposal these days. But don't confuse the tools with the thing you want to do. I'm embarrassed to think about how many times I've needed a lightweight notes app only to spend two hours finding just the right one. I should have just picked up a pad of paper, shouldn't I?