While it is still fresh in my mind, I want to describe the conversation I had with a publicly available version of ChatGPT, the much-discussed large language model, LLM, for conversational artificial intelligence.... 続きを読む >>

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... 続きを読む >>

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... 続きを読む >>

Camille Jordan (1838-1922)... 続きを読む >>

The ACM Special Interest Group on Programming Languages, SIGPLAN, expects to hold the fourth in a series of conferences on the History of Programming Languages in 2020, see HOPL-IV. The first drafts of papers are to be submitted by August 2018. That long lead time gives me the opportunity to write a detailed history of MATLAB. I plan to write the paper in sections, which I'll post in this blog as they are available. This is the seventh, and final, installment.... 続きを読む >>

Pi DayHappy Pi Day, 3/14.Here are 10,000 digits of π. Notice the six consecutive 9's in the sixth row, digits 763 through 768. n = 100; % Get pi from Symbolic Toolbox. p =... 続きを読む >>

Two days ago I wrote about random points in a square. At the last minute I added the paragraph asking about the generalization to random points in a cube. I have to admit that I didn't check the Web to see what was known about the question.... 続きを読む >>

How far apart can you expect two points chosen at random in the unit square to be? I found this problem on the YouTube channel maintained by Presh Talwalkar, Mind Your Decisions. He correctly calls it a very hard puzzle. At first, I guessed the answer might be $1/2$. But the correct answer is more interesting than that.... 続きを読む >>

I first encountered the Hilbert matrix when I was doing individual studies under Professor John Todd at Caltech in 1960. It has been part of my professional life ever since.... 続きを読む >>