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Eight or nine misconceptions about Astra. See if you can spot the biggest fallacy.

Yesterday I wrote that a lot of the special functions that pop up in mathematical physics are solutions to second order linear differential equations with polynomial coefficients. More generally, holonomic functions are defined to be those functions that are the solutions to linear differential equations, of any order, with polynomial coefficients. Most special functions are […]

The post Holonomic functions first appeared on John D. Cook.

In this post I mentioned two series which I denoted t(n) and c(n). The former is the number of unlabeled rooted trees with n nodes. The latter is the cumulative sum of the former, i.e. The sequence c(n) is also the number of constrains on an n-step Runge-Kutta method; that’s how I became interested in it. Now the t(n) sequence has […]

The post Estimating a cumulative sum first appeared on John D. Cook.

Engineers often complain that visibility should be their manager’s job. In other words, they think engineers should be able to focus on the code, while their manager figures out who’s doing well and rewards them. This attitude is an extension of the “school fantasy”: the ide...

We must know. We shall not know.

Open letters about AI development I wrote this summary of the past few weeks of open letters as a section of my sponsors-only newsletter but I've decided to share it here as well. Open Weights and American AI Leadership was shepherded by Microsoft, dated July 24th, and signe...

The June edition of my sponsors-only monthly newsletter is out. If you are a sponsor (or if you start a sponsorship now) you can access it here.

This month:

• Accidental cyberattacks by OpenAl and Anthropic models under test
• GPT-5.6 Sol, Terra, and Luna
• Claude Opus 5
• Kimi K3 and DeepSeek-V4-Flash-0731
• Open letters about Al development
• A fireside chat and a podcast
• Reigniting my interest in MCP
• Other model releases
• My projects
• What I'm using at the moment

Here's a copy of the June newsletter as a preview of what you'll get. Pay $10/month to stay a month ahead of the free copy!

Tags: newsletter

As is typical here in the Floodgap lab, it all started so innocently: rebuilding a flaky Apple Workgroup Server 9150, the odd duck of the Workgroup Server line and older cousin to our beloved Apple Network Server. And then I just had to pimp it out for MkLinux. Before th...

For the first time I'm choosing my daily driver models on tokens per second rather than raw intelligence. Why ~100tok/s might be the new 100ms, where the speed gains stop mattering, and the price war that's coming.

at openai, many people hook their chatgpt up to slack.

people really don't like when a coworker's chatgpt contacts them asking for help with a task, even when they'd be perfectly happy doing that same work if asked by that coworker.

reinforces how much people care about human relationships and helping each other, and want AI to give time back — or enhance time together — rather than become a layer separating people.

— Greg Brockman, President and Co-Founder, OpenAI

Tags: ai-ethics, ai-misuse, generative-ai, openai, ai, llms

Release: datasette-apps 0.2a0

Changes that improve Datasette Apps when created and edited using Datasette Agent:

• New app_debug() tool allowing agent to open an app (invisibly) and test it using JavaScript. #33
• New app_list() tool for listing apps the user has permission to edit, so the agent can edit them. #36

The app_debug() tool is pretty neat: it works by displaying the app in a opacity: 0 iframe with pointer-events: none (so it can't be seen or interacted with) and then executing agent-provided JavaScript inside that sandboxed iframe. This means the agent can smoke test that the app is working and even do things like measure the dimensions of different elements.

This uses the new context.browser_task() mechanism added in datasette-agent 0.4a0.

Tags: iframes, datasette, datasette-apps

Ten advances in mathematics and theoretical computer science A few days ago it was Anthropic discovering cryptographic weaknesses with Claude using Mythos Preview, spending $100,000 on tokens and with prompts that included "again we are not looking for low hanging fruit, we ...

Release: llm-mcp-client 0.1a0

See this blog entry.

Tags: llm, model-context-protocol

Tool: Slack Emoji Maker

I wanted to create a new Slack emoji, and their tool recommends a square that's 128x128 and has a transparent background... so I had Fable build me this simple image editor against those requirements.

Tags: tools, slack

Release: datasette-agent 0.4a0

• New await context.browser_task() mechanism allowing agent tools to run code directly in the user's browser. #33

This is an exciting new capability: it makes it easy for Datasette Agent plugins to provide tools that execute custom JavaScript in the user's browser.

Tags: datasette, llm-tool-use, datasette-agent

The pricing gun should have been a dead technology years before it actually was. But state laws artificially kept it around as a shield against the scary barcode.

Second order linear differential equations with polynomial coefficients form their own area of study. This seems like a narrow class of equations, but it’s very important in applications. This class of equations seems like a mathematically natural topic, but why is it so important in applications? I did a PhD in differential equations without ever […]

The post Why polynomial coefficients? first appeared on John D. Cook.

Combinatorial problems can be interesting for their own sake, but they are more interesting when there is a connection to a problem outside combinatorics, and the more unexpected the connection the better. Counting the number of unlabeled rooted trees [1] with n nodes is a pure mathematics problem. Designing numerical methods for solving differential equations […]

The post Counting rooted trees first appeared on John D. Cook.

The textbook version of the Runge-Kutta method for solving differential equations has 4 stages and has 4th order error. For lower order versions of RK the number of stages s also matches the order of the error p. But in order to achieve error on the order of p ≥ 5, you need more than p […]

The post Runge-Kutta order versus stages first appeared on John D. Cook.

Today's links Why businesses lie about AI: Humoring the boss all the way into bankruptcy. Hey look at this: Delights to delectate. Object permanence: Vinge x NYT; Syklarov x publishers; Human hair castles; Gingrich's bot army; Accessibility v Web DRM; David Byrne x WinXP; Fur...