AI Should Build Its Own Research World Model

01 · 唯一讲道理的一节

01 · the only section that argues

§1把 AI 扔进无规则游戏：科研需要显式的世界模型，而非盲目依靠权重

§1Into a Game With No Rules: Research Requires Explicit World Models, Not Just Weights

为了做这个实验，我们需要为 AI 找一个完全未知的环境，让它可以自己去探索并理解底层的物理规律。通过探索、总结、反思和提出假设的循环，慢慢沉淀出对这个世界的显式理解，最终通关。这个环境可以是一片前沿的科研领域，但在这里，我们选择用 ARC-AGI 里的一个互动谜题作为实验对象，来探索 AI 在持续的抽象与反思能力上的进展。

To run this experiment, we needed a completely unknown environment for the AI, where it could explore and understand the underlying physics on its own. Through the loop of exploration, summarization, reflection, and hypothesizing, it would slowly precipitate an explicit understanding of the world to eventually clear the game. This environment could be a frontier of scientific research, but here, we chose an interactive puzzle from ARC-AGI as our experimental subject to explore AI's progress in continuous abstraction and reflection capabilities.

而这只是一个例子。它可以是一个游戏世界，也可以是一段蛋白质、一个没被解过的方程、一片还没有人绘制的科学前沿。我们真正想知道的，不是 AI 能不能通关，而是把它放到一个谁都没去过的地方时，它能不能像科学家那样，自己走出来。

And this is only one example. The world could be a game; it could just as well be a stretch of protein, an unsolved equation, a patch of scientific frontier nobody has charted. What we actually want to know isn't whether an AI can clear a game; it's whether, dropped somewhere no one has ever been, it can walk out the way a scientist would.

科研，不该只被压缩进权重和直觉里。

Research shouldn't live compressed in weights and intuition.

02 · 阶梯一 语言

02 · rung one language

§2给未知事物起名建档：发明表征是建立理解的第一步

§2Naming and Filing the Unknown: Inventing Representations is the First Step to Understanding

这个实验是这么跑的：

Here's how we ran it:

现在，看它睁眼时看到的东西。

Now, look at what it saw when it opened its eyes.

第一关，第一帧。这就是它能看到的全部。没有规则，没有目标，没有教程。只有四个方向键，和每按一下就短一格的底部横条。 Level 1, frame 1. This is everything it can see. No rules, no goal, no tutorial. Just four arrow keys, and a bar along the bottom that gets one cell shorter with every press.

如果是你，会先按哪个键？

If it were you, which key would you press first?

它四个都按了。有的方向走得动，有的撞上去纹丝不动，但底部的横条照样短一格。撞墙不免费。这个世界连犯错都收钱，还不给你价目表。接下来它就是瞎摆弄：把那个灰帽紫身的方块挪来挪去，踩过一个不起眼的黑点，左下角框里的图案跳了一下；把方块推进上面那个框，输了；等图案对上再推，整个屏幕重画，第二关。

It pressed all four. Some directions moved; others hit something and didn't budge, but the bar at the bottom got shorter all the same. Hitting a wall isn't free. This world charges for mistakes and doesn't post the prices. What followed was basically fiddling: it shoved the grey-capped purple block around, stepped across an inconspicuous black dot, and the pattern in the bottom-left frame jumped; pushed the block into the frame up top, lost; waited for the pattern to match and pushed again, and the whole screen redrew. Level 2.

第一个 session 收工前（不妨叫它第一夜），它做了博物学家落地荒岛会做的第一件事：给从没见过的东西起名字。会动的方块叫 block；踩了会让图案跳动的小点叫 switch；上方那个装着目标图案的框叫 key-box；地上那种说不清用途的稀有斑点，它随手叫作 speck。谈不上有想象力，但都好用。名字起好，它开始往一份文件里写词条。

Before closing out its first session (call it the first night), it did the first thing a naturalist does after washing up on an island: it named the things it had never seen. The square that moves became block; the little dot that makes the pattern jump when stepped on, switch; the frame up top holding the target pattern, key-box; the rare floor spots with no obvious purpose it offhandedly called speck. Not imaginative names, but they all worked. Once they were settled, it started writing entries into a file.

ara-ls20/logic/concepts.md · «switch» 词条 · 原样引用ara-ls20/logic/concepts.md · the «switch» entry · quoted verbatim

switch

A rare color-0/1 floor speck the block steps onto to toggle/cycle the lock pattern shown in the panel. Not consumed (still present after the block moves off). The per-level transform differs: L1's switch (R6C3) toggles only the middle row (2 states); L2's switch (R9C9) is a 4-state cycle (C09, C10).

开关：一种稀有的地面斑点，方块踩上去会切换面板上的锁图案。不会被消耗。每一关的变换规则不同：第一关的开关（第 6 行第 3 列）只翻转中间一行（两个状态）；第二关的开关是四状态循环。

我第一次翻这份 concepts.md 的时候，也在 R6C3、color-0/1 这些地方卡了一下。先不急着解释。这种"读不懂"本身就是证据：这些词条从第一行起，就不是写给人读的。

The first time I opened this concepts.md I got snagged on R6C3 and color-0/1 too. Let's not rush to explain. The unreadability is itself evidence: from their first line, these entries were never written for humans.

第一夜的账单：首次摸清这一关花了 24 步；事后最短通关只要 13 步；死亡 0 次。收工时，它的世界模型里已经躺着七条它敢写下来的规律（在它的档案里，这叫 claim，逐条编号），包括那条日后救它命的 C07：锁满足时，封死的钥匙盒才会打开。

The first night's bill: 24 steps to work the level out the first time; 13 steps for the shortest clear afterwards; 0 deaths. By close of session, seven laws it was willing to commit to writing already lay in its world model (it calls these claims, each numbered and filed), including C07, the one that would later save its life: only when the lock is satisfied does the walled-shut key-box open.

命名，是把混沌切成可以思考的零件。

Naming is cutting chaos into parts you can think with.

人类的智慧开始累积，不是哪一代人突然变聪明了，而是我们发明了语言：经验第一次可以离开产生它的那颗脑袋。它在这个小世界里重演的就是这一步：先有词，才有可以传下去的理解。

Human wisdom started to pile up not because some generation suddenly got smarter, but because we invented language: for the first time, experience could leave the head that produced it. That's the step it re-enacted in this little world: first the words, then an understanding you can pass on.

不过到这里为止，它写的东西跟一本旅行日记还没什么两样：看见，记下。变化出现在第五关：它发明的词，开始自己做数学。

Up to this point, though, what it wrote was still nothing more than a travel diary: see, record. That changes at level 5, when the words it invented start doing mathematics on their own.

03 · 阶梯二 数学

03 · rung two mathematics

§3从发现运算到纸上推演：AI 能自主提炼并利用抽象数学结构

§3From Discovering Operations to Derivation: AI Autonomously Extracts and Uses Abstract Mathematical Structures

第五关有两个斑点。正常的开关是"按了就到某个状态"，第一关的开关就是这样，来回翻同一行。这两个不是。踩第一个，面板图案往前循环一步，六步回到原点；踩第二个，整个图案顺时针转 90°。

Level 5 has two specks. A normal switch is "press it, land in some state"; level 1's switch was like that, flipping the same row back and forth. These two are not. Step on the first and the panel pattern cycles forward one notch, coming back around after six; step on the second and the whole pattern rotates 90° clockwise.

它们不是按钮，是动作。

They aren't buttons. They're operations.

动作和按钮的区别，要命在一点：顺序开始要紧了。先转再循环，和先循环再转，结果不一样。玩过魔方的话你已经懂了：没有哪个单独的转法能复原魔方，解法是一串转法拼成的"句子"，而且有些状态你永远转不到。它面前这把锁，就是一个 3×3 的小魔方。这事没人告诉它，是它自己发现的。而它接下来做的几件事，恰好就是数学家拿到魔方会做的头几件。

Operations differ from buttons in one lethal way: order starts to matter. Rotate-then-cycle is not cycle-then-rotate. If you've ever held a Rubik's cube you already get it: no single twist restores the cube, a solution is a "sentence" spelled out of twists, and some states you can never twist your way into. The lock in front of it was a little 3×3 Rubik's cube. Nobody told it that; it found out on its own. And the next few things it did happen to be the first few things a mathematician does when handed one.

第一步，起名。它把循环动作记作 P，把旋转动作记作 Q。这两个符号后来在 claims 和 trace 里被跨文件反复引用；同一个动作要反复指认，就得有个稳定的名字。少年费曼自学三角的时候也干过一样的事：嫌 sin、cos 记号歧义，发明了一套自己的符号，用得飞快；后来放弃了，他说，"我发现如果要跟别人说话，就只能用标准记号。"费曼有听众，所以他投降了。这个 agent 的唯一听众是未来的自己，所以它留下了费曼放弃的东西。而且从棋盘里面看，P 和 Q 比任何人类词汇都更贴身：它不需要"循环"和"旋转"的比喻，它需要能拼句子的字母。

Step one: naming. It wrote the cycling operation as P and the rotation as Q. The two symbols then get cited across files, in claims and trace alike; referring to the same operation over and over needs a stable name. Teenage Feynman did the same while teaching himself trigonometry: finding the sin and cos notation ambiguous, he invented symbols of his own and worked fast with them; later he dropped them. "I found out that if I was going to talk to anybody else, I'd have to use the standard symbols." Feynman had an audience, so he surrendered. This agent's only audience is its future self, so it kept what Feynman gave up. And seen from inside the board, P and Q sit closer to the skin than any human word: it doesn't need the metaphors of "cycle" and "rotate," it needs letters that can spell sentences.

第二步，把动作画成地图。它笔下的面板状态长这样：110/011/101，又是密文。但这串字符其实是一块 3×3 的灯板，1 是亮、0 是灭。画出来就不是密文了：

Step two: drawing the operations as a map. In its notes a panel state looks like this: 110/011/101. Ciphertext again. But the string is really a 3×3 board of lights, 1 lit, 0 dark. Drawn out, it stops being ciphertext:

P 的全部家当就这六个状态：一步一格，六步转回原点。这个圈它记作 orbit B（轨道）：光按 P，出不了这个圈。一百九十年前 Babbage 说过，代数记号的本事，就是"把大量的意义压进狭小的空间"。

These six states are all P owns: one notch per press, back where you started in six. It calls the circle orbit B, an orbit: press only P and you never leave it. Babbage said it a hundred and ninety years ago: the whole point of algebraic notation is to "condense into small space, a large amount of meaning."

Q 只干一件事：把整块板顺时针转 90°。左边的状态转一下，就成了右边。这一转在第七关还会出现。

Q does one thing: rotate the whole board 90° clockwise. Turn the left state once and you get the right one. The same turn shows up again on level 7.

第三步，发现轨道与桥。第六关把难度加倍：两把锁，其中一把的目标图案，光按 P 怎么按都到不了：它在 P 够不着的另一个圈里。它没接着撞，停下来写了这一段：

Step three: discovering orbits and bridges. Level 6 doubles the stakes: two locks, and one lock's target pattern won't come no matter how much you press P: it lives in another circle P can't touch. It didn't keep banging; it stopped and wrote this:

ara-ls20/logic/claims.md · C14 · L6 战况 · 原样引用（节选）ara-ls20/logic/claims.md · C14 · the L6 situation · quoted verbatim (excerpt)

P is a genuine period-6 NON-permutation (on-bit count varies), and — the new structural fact — P has orbits … can NEVER reach the target in orbit A — the LOWER alignment GENUINELY requires a {P,Q} WORD where Q bridges between P's orbits, then P walks to the target within the right orbit. … the LOWER word QQPPPPPQ (offline BFS over {P-cycle,Q}) is forced and ENDS in Q

P 有轨道：目标在 P 永远够不着的 A 轨道里；解必须是一个由 P、Q 拼成的"词"，其中 Q 充当两条轨道之间的桥。下方那把锁的词是 QQPPPPPQ，由离线 BFS 搜出（BFS：在纸上把所有能到的状态一层层穷举一遍），别无选择。

第四步：不可能定理。引文里有一个大写的 NEVER。它找了一路捷径，最后找到的是一条"捷径不存在"的证明：光靠 P，那个目标永远到不了，这不是还没试够，是数学上到不了。试错只能告诉你什么行得通；只有理论能告诉你什么永远行不通。知道这一点的那一刻，它停止了在死路上花钱。

Step four: an impossibility theorem. There's an all-caps NEVER in that quote. It went looking for a shortcut, and what it found instead was a proof that no shortcut exists: by P alone, that target can never be reached; not "hasn't tried hard enough," mathematically unreachable. Trial and error can only tell you what works; only theory can tell you what will never work. The moment it knew this, it stopped spending money on the dead road.

现在回头看这一节的两个词是在哪里找到的。第五关的 PPQQ、第六关的 QQPPPPPQ，都不在游戏里，在纸上。这个世界里每走一步都花钱、走错了要赔命；但在写下来的规则上推演，一分钱都不用。它把 P 和 Q 的规矩写清楚，在纸上把状态搜了个遍，找到解，回游戏里照着按。

Now look back at where this section's two words were found. Level 5's PPQQ, level 6's QQPPPPPQ: neither came from inside the game; both came from paper. In this world every step costs money and a wrong one can cost a life; deriving on written-down rules costs nothing. It pinned down how P and Q behave, combed through the states on paper, found the solution, then walked back into the game and pressed the keys.

ara-ls20/logic/claims.md · C14 · 证据行 · 原样引用ara-ls20/logic/claims.md · C14 · the evidence line · quoted verbatim

(2,3) period-6 + (7,3) 90°-rotation, offline BFS gave the forced word PPQQ, verified live to reach 101/110/011, then delivered → levels 4→5

两个控制：周期六的 P、旋转 90° 的 Q。离线 BFS 给出唯一的词 PPQQ；回到游戏里实测，面板走到目标状态，交付，第五关通过。

每关首次通关后的最短步数。第五关比第四关更难，步数反而更短（56 A2->(10,5). Phases (each idempotent, callable separately so I can supervise): colour -> set colour % at selector (8,1) p N -> catch P' (left row-8 corridor cols2-3) N times q N -> catch Q (right col-10) N times deliver -> goto (9,5), A2 into (10,5)"""

它把答案写成了带阶段的脚本：定颜色 → 捉 P′ 五次 → 捉 Q 两次 → 交付。下面右侧的动画，就是这个脚本跑起来的样子。

尝试一 · 举灯侦察attempt one · recon by lamplight515 步 · 未解515 steps · unsolved

尝试二 · 问过世界模型attempt two · after asking the world model决胜 63 步 · WIN63-step finish · WIN

同一间黑屋子，前后两世。左：第一个 context 的摸索。右：新 context 带着查询得来的判断直奔主题（含探雾全程 399 步，其中破局后的干净执行 63 步）。 The same dark room, two lifetimes apart. Left: the first context feeling its way. Right: the new context heading straight for the point with the judgments it queried for (399 steps in all including fog-scouting, of which the clean

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