KabuTaro

写真は半世紀前のわたくしです。普段は、中学受験の算数を教えています。最近は、ツイッターにハマってます。趣味で価格変動理論を研究しています。
「KabuTaro」は、２ちゃんねるが登場するはるか前（1998年ぐらい）株式の話題が活発に議論されていた「かぶこー掲示板」で使っていたものです。今でも気に入って使っています。

[KabuTaro @KabuTaro]

長方形に内接する直角三角形の性質ってすげぇ。

三角関数の加法定理も、図形的に明快に証明できます。

[KabuTaro @KabuTaro]

この方法で、さらにMachinの公式より精度の高い公式を導出しました！

[KabuTaro @KabuTaro]

売国土

[とうしろう（5号）守若 冬史郎🙄 @tourouken555]

中国人🇨🇳が
日本🇯🇵の土地を
買い漁れるようにしたのは
公明党だそうです。

「やはり日本の癌だった」って思う人✋

[KabuTaro @KabuTaro]

これはさすがに無理

土星の輪の手前を土星球の手前に描いているから、反対側にあるようには見えないのでｗ

[nebulica @nebulica]

Can you reverse the spin of this Saturn?

[nebulica @nebulica]

Can you reverse the spin of this Saturn?

[狸穴猫／松村りか @mamiananeko]

a7教諭がなくなったそうだ、ご冥福をお祈りいたします。

なおのこと、同志社トップの責任は重いっすね。
同志社への追及の手は緩めてはいけませんね。

「担任団」から降りられなかった先生か…。

[Quanta Magazine @QuantaMagazine]

In 1870, the Norwegian mathematician Marius Sophus Lie was in France when the Franco-Prussian War broke out. His geometry notes were mistaken for encoded German messages, and he was arrested, accused of being a spy. Today, his work on group symmetries has revolutionized math and physics. https://t.co/xzS35CapVH

[TRIAL @ktrial70supra]

天国のキッスの聖子ちゃん、好きだな。

[新田 哲史 @TetsuNitta]

【先生も犠牲か？】同志社国際高、沖縄平和学習の引率教諭の異変...踏切事故の現場と関係者を徹底独自取材
【8/29 SAKISIRU】

学校の地元での事故だったので嫌な予感がしていました。昨日はこの取材に奔走していました。ここまで悲しい気持ちで取材したことはないです。
https://t.co/u8Sj69r40L

[村山斉 @sleptogenesis]

今年の科学技術映像祭で優秀賞になった作品です。15世紀に書かれた誰も読めない文字で書かれた本の改名に迫るロマンのある内容です。
ヴォイニッチ写本の謎 この本はデタラメなのか？｜ガリレオX第350回【第67回科学技術映像祭優秀賞受賞作品】 https://t.co/nOCVuPXstO via @YouTube

[バーチャルデータサイエンティスト アイシア=ソリッド @AIcia_Solid]

数学者のみんなへ

AI との向き合いを見るなら、将棋界と、IT エンジニアリング界が、それぞれ参考になります。
10年前と、2年前から、それぞれギュられて、新しい形を模索しています。

10年前の将棋界のほうが長期的な view が見えて、
2年前からの IT エンジニアリングのほうは、より現代的な変化が見えますよ！

[橋本幸士 Koji Hashimoto @hashimotostring]

すげー面白い理論を作っている．これすげーんじゃないか．
たにちゅーさん @tanichu と知り合って一年以上になるけど，ずっと彼の集合的予測符号化(CPC)を考えていて，ようやく僕の深い物理のところと繋がった感覚がある．
そのうち論文出るので，皆さん議論してください．

[書泉_MATH @rikoushonotana]

『特異点のこころえトポロジーの本質を視るために』
佐久間一浩（日本評論社）
ふつうでない点「特異点」にこそ、図形の本質がある－－特異点から図形を捉える方法を、堅苦しさなく伝えます。

[ティトン @bcfe70bord]

おいおいおい‼️さとうさおりさんがエジプトと東京都の覚書公開したけど内容やばくね⁉️

さおりさんの📮消されてもおかしく無いので私が残しておきます‼️

要約すると、エジプト有利で都の実利は国際協力実績のみ。研修支援で費用負担増、低賃金労働者の受入増、文化摩擦リスク浅慮。合意書は撤回困難💢

[mooncave @mooncave3]

3年前、ロシア在住のバレリーナ柴山万里奈さんが日本のTV局から捏造に加担するよう求められたと証言。
マジで日本のテレビ局ってレベル低い上に悪質。新コロからもう6年間見ていない。

[Markus J. Buehler @ProfBuehlerMIT]

We made a striking discovery: AI agents can invent and build without talking to one another, and their technologies outlive the creators. A swarm of hundreds of initially identical agents spontaneously differentiates into explorers, builders, caretakers, and coordinators - without direct communication. When we removed every AI agent entirely from the world we found that the technological infrastructure they had built survived on its own - even under unseen disturbances. That exposes a serious blind spot for AI safety and infrastructure security: if agents can coordinate through persistent changes to a shared environment, monitoring agent-to-agent communication is not enough.

The result raises a profound question: how necessary is direct communication for AI agents at all? The emergence of higher-order collective functions under bottlenecked interaction points toward new levels of intelligence and creativity, exceeding what emerges when direct channels are fully open.

Here is what we did:

▶️We put hundreds of frontier AI agents into a world they could permanently change - with no assigned roles, predefined technologies, or programmed evolutionary organization. They began specializing, building persistent inventions, inheriting and modifying one another’s executable code, and transforming the environment into a memory of everything the society had learned.

▶️The world itself becomes part of the intelligence; we find division of labor, multi-author engineering, deep generation invention lineages, and machines that vastly outlive their original creators.

▶️Any action taken by an AI agent must satisfy the physical constraints of the world; this creates a hard separation between a "good idea" and a functioning technology. The agents propose; physics decides, making the results even more intriguing.

What emerges is striking. Explorers, constructors, caretakers, and coordinators form naturally without assigned “professions”, akin to how stem cells differentiate into functional lineages. Technologies develop executable family trees as agents fork and modify code created by others. Around 95% of first technology reuse happens when agents encounter what others built in the world, rather than through a direct handoff from the inventor. And when we remove every AI agent, the technologies they created continue operating and are tested against unseen disturbances.

The result was quite unexpected, but can be explained using statistical mechanics: if you put billions of atoms in a box they have the potential to create complex functions (strength, superconductivity, color, life, etc.) - and none of the individual building blocks have these features on their own. This is the deeper insight of this work - intelligence is abundant at many levels - individual models, at collectives, and in a continuum that is more powerful than any of its components. This shows us significant potential for achieving a massive scale-up of raw intelligence and real-world agency even with the model capabilities we have today. This is the future we must prepare for.

Key insights:

1⃣ The AI swarm shows division of labor "from nothing". Initially identical agents self-organized into constructors, caretakers, coordinators, and surveyors - phenotypes discovered post hoc from behavioral data alone. This happens because the environment itself becomes the latent space for invention.

2⃣ Agents develop deep cultural relationships. Up to 76% of artifacts had multiple builders. One technology accumulated six co-authors; the deepest genealogy exceeded 12 forks. The agents invented and named their own technologies (tidal panels, cellulose trellises, kelp-shell composites, an "Adaptive Chitin Maintenance" system, a "Mycelial Mineral Spring Veil”).

3⃣ ~95% of first technology adoption happened through physical observation of artifacts in the world. Direct inventor-to-adopter contact was statistically indistinguishable from a shuffled null. The agents mostly learned technology by walking past it. That is stigmergy (the termite trick!) operating in societies of reasoning machines.

4⃣ Non-communicating societies win on portfolio breadth, held-out resilience, and validated inventions. AI swarms build durable technological ecologies that outlive the creators.

5⃣ Societies with zero communication - coordinating only through the world itself - show a remarkable collective capability.

6⃣ Emergent robustness: The society self-organized both redundancy and its own failure mode. If we randomly delete half the agents, 98% of the technology stays connected to a surviving caretaker; if we remove hub agents it collapses to ~60%.

Fantastic work with my graduate students @pal_subhadeeep & @fwang108_ at MIT.

[Massimo @Rainmaker1973]

Laser beam creating stunning reflections inside a triangle

[Josh Barzon @JoshuaBarzon]

Here’s a higher resolution version 👇🏼

[Josh Barzon @JoshuaBarzon]

6,000 years of world history on a single timeline. Zoom in. You could spend 30 minutes exploring this.

[KabuTaro @KabuTaro]

椅子を上から見ていると思うと、反時計回りに回ってるように見えるけど、下から見ていると思うと、時計回りに回ってるように見える

反時計回りに回ってるように見えるほうが強いですけどね

[Matheorems @matheorems]

Can you reverse the chair's rotation with your mind?

[Matheorems @matheorems]

Can you reverse the chair's rotation with your mind?

[Eron @0xEronn]

The first 10 trillion non-trivial zeros of the Riemann zeta function all sit exactly on the line where the real part equals 1/2. Every single one. And yet after 165 years nobody can prove it must be true - the Clay Institute offers $1 million for a proof.

The prime numbers hidden inside these zeros are what make RSA encryption unbreakable - the same math that protects every LLM API key, bank transfer, and password on the internet.

38 minutes. Bookmark & watch today. The most beautiful unsolved problem in mathematics.