Another little chess puzzle

Here’s another little chess puzzle by Martin Gardner, taken from the same paper as earlier. The task is to place two rooks, two bishops, and two knights on a 4 by 4 chessboard so that no piece attacks any other. As before, there are two basic solutions, here and here,

Multiplying by quaternions on the left and right

The map that takes a quaternion x to the quaternion qx is linear, so it can be represented as multiplication by a matrix. The same is true of the map that takes x to xq, but the two matrices are not the same because quaternion multiplication does not commute. Let q = a + bi

Embeddings, Projections, and Inverses

I just revised a post from a week ago about rotations. The revision makes explicit the process of embedding a 3D vector into the quaternions, then pulling it back out. The 3D vector is embedded in the quaternions by making it the vector part of a quaternion with zero real

Why Your Automation Needs AI Decision-Making (And How Wordware Delivers)

Discover why traditional automation tools fall short for complex workflows and how Wordware's AI decision-making capabilities transform business processes through intelligent context understanding, adaptive learning, and natural language programming. Continue reading Why Your Automation Needs AI Decision-Making (And How Wordware Delivers) on SitePoint.

Alternative exp and log notation

The other day I stumbled on an article [1] that advocated writing ab as a↑b and loga(b) as a↓b. This is a special case of Knuth’s up arrow and down arrow notation. Knuth introduces his arrows with the intention of repeating them to represent hyperexponentiation and iterated logarithms. But the emphasis in

Decimal Separator and Internationalization

This morning I ran across the following tip from Joost Helberg on Mastodon: TIL don’t report numbers with three digits after the decimal point. People may interpret the decimal point as a thousands separator. Using 2 or 4 digits, although wrong, avoids off by a factor thousand errors. I usually

A crowded little chess puzzle

Here’s a puzzle by Martin Garnder [1]. Can a queen, king, rook, bishop, and knight be placed on a 4² board so no piece attacks another? There are two solutions, plus symmetries. Note that in all non-attacking chess puzzles, the colors of the pieces are irrelevant. In the solutions I

Is the enterprise (actually) ready for AI?

Maryam Ashoori, Head of Product for watsonx.ai at IBM, joins Ryan and Eira to talk about the complexity of enterprise AI, the role of governance, the AI skill gap among developers, how AI coding tools impact developer productivity, what chain-of-thought reasoning entails, and what observability and monitoring look like for

Chris’ Corner: CSS Deep Cuts

Sometimes we gotta get into the unglamorous parts of CSS. I mean *I* think they are pretty glamorous: new syntax, new ideas, new code doing foundational and important things. I just mean things that don’t demo terribly well. Nothing is flying across the screen, anyway. The Future of CSS: Construct <custom-ident> and <dashed-ident> values

JavaScript Location.reload() Explained (With Examples)