A few days ago, I posted this image on Mastodon: | Continue reading
My fundamental rule is Don’t, but a single word wouldn’t make for much of a blog post. | Continue reading
I noticed today that the Cubs and Yankees have the same record. I knew that the Cubs have had some extreme ups and downs this year, but I wasn’t sure if the Yankees had, so I decided to plot their progress over the course of the season so far. | Continue reading
The indispensable Michael Tsai has an interesting post up today about Apple Park and whether its design isolates the people who work there, despite its having been designed—in part, at least—to encourage collaboration. | Continue reading
Yesterday I watched the most recent Numberphile video, in which Ben Sparks explains a few finite series and the equations that simplify the calculation of their sums. He derives the formulas graphically, and it’s all very cleverly done, especially the one for the sum of cubes. | Continue reading
A couple of days ago, Casey Liss took a break from arguing about temperature scales to tweak me about the recent passage of the Sunshine Protection Act by the House. The Act would make Daylight Saving Time permanent, something Casey knows I disapprove of. A similar bill passed th … | Continue reading
You’ve probably seen somewhere that the density of Saturn is less than that of water. If there were a bathtub big enough to hold it, Saturn would float. I think I first read this in one of Isaac Asimov’s collections of science essays. If you do an image search, you can easily fin … | Continue reading
I saw this article at Inside Higher Ed this morning, guided by a Mastodon post from Techmeme. The title of the article is “Brown Professor Suspects Majority of His Class Used AI to Cheat,” so if you’re sick to death of reading about AI—pro, con, or caveated—don’t feel obligated t … | Continue reading
There’s been a lot of talk lately about Mac application icons and “squircle jail.” Inspired by this post from Paul Kafasis on the Rogue Amoeba blog,1 many Mac-adjacent people have taken up his cause to “Free the Icons.” | Continue reading
I visited my eighth and final Louis Sullivan jewel box bank yesterday morning. The Purdue State Bank (now a Chase branch) is in West Lafayette, Indiana. As a graduate of the University of Illinois, I have thoughts about Purdue University and its substandard engineering program, b … | Continue reading
Yesterday I visited the Home Building Association Bank in Newark, Ohio, a Louis Sullivan jewel box bank built in 1914. It’s currently owned by the Licking County Foundation (oh, grow up), which restored it at considerable cost over several years and reopened it to the public last … | Continue reading
Last year, around Labor Day, I visited five of Louis Sullivan’s jewel box banks: | Continue reading
This week’s episode of Upgrade (which I listened to on a longish drive yesterday) has a preview of Jason Snell and Myke Hurley’s upcoming Designed in California podcast. No, not the “Road to the Apple II” series they’ve been squeezing into the Upgrade feed these past few weeks. T … | Continue reading
I’ve been thinking about 1984 lately—the year, not the novel. What got me thinking about it was the reduction in gas prices over the past few weeks, | Continue reading
At the end of yesterday’s post about the combinatorics of the World Cup group stage, I said “this is good enough for me.” Turns out that was a lie. Today I rewrote some of the code to come up with a slightly more detailed result. | Continue reading
We’re in the middle of the first set of games in the group stage of the 2026 World Cup, and I’ve been thinking about how many ways the points can be distributed among the teams in a given group. I used Python to help with the enumeration. | Continue reading
I took a bike ride this morning on a portion of the I&M Canal Trail from Romeoville to Joliet and back. It’s a fairly short ride, eight miles each way, and that distance got me thinking about using Mathematica to do some calculations after I got back home. | Continue reading
After my last post—the one about using Fourier series—I started thinking about how to use Mathematica to develop Fourier series.1 I could, of course, use the Integrate function to determine the Fourier coefficients, but Mathematica has other functions that can do the job directly … | Continue reading
We’re finally here, at the end of all things. In this post, we’ll use a Fourier series to get the formula for the center deflection of a simply supported beam with a uniformly distributed load. We’ll see some of the same math that we saw in the previous Fourier series solution, b … | Continue reading
This would have been the last post in the series if I hadn’t realized recently that another method deserved a post. So this is the penultimate. It was described in this 1943 paper by Nathan Newmark and is known—or was known—as Newmark’s method. | Continue reading
We’re in the home stretch of this series, so ANIAT will soon go back to complaining about Apple’s UI choices.1 Next week’s WWDC keynote should provide some inspiration. | Continue reading
The biggest problem I face when writing posts in this series is deciding how much background explanation to put in. If I included only the stuff I do to get the answer, the posts would be very terse: one sketch and a dozen or fewer lines of math. A full explanation, though, could … | Continue reading
Continuing our series on the many ways to get the center deflection of a uniformly loaded beam, we come to another energy-based technique: Castigliano’s method. | Continue reading
Today we’ll use the Rayleigh-Ritz method again, but this time we’ll avoid dealing with an infinite sum. In case you’ve forgotten, this is our problem: | Continue reading
I just learned that people are listening to music pitched slightly down because it makes them feel better. Instead of the A above middle C being set at 440 Hz, they have it tuned down to 432 Hz. | Continue reading
Continuing our trip through various methods to derive the equation for the center deflection of a uniformly loaded simply supported beam, today we’re going to do the first of two solutions using the Rayleigh-Ritz method. | Continue reading
The sixth way we’ll derive the formula for the center deflection of a uniformly loaded simply supported beam is the Myosotis method, which I wrote about over a decade ago. This is the method popularized1 by J.P. Den Hartog in his Strength of Materials textbook. | Continue reading
The next technique we’ll use to derive the formula for the center deflection of a simply supported beam with a uniform load is the slope-deflection equation: | Continue reading
The fourth way we’re going to derive the formula for the center deflection of a simply supported beam with a uniform load is the conjugate beam method. This is probably tied with the moment-area method for the simplest and fastest way to get the formula—at least if you’ve memoriz … | Continue reading
In Paul Krugman’s post today, he includes two charts. One is fine, the other isn’t. | Continue reading
Continuing our odyssey through various ways of calculating the deflection at the center of a simply supported beam with a uniform load, today we use the moment-area method. | Continue reading
In the introductory post to this series, I mentioned that the shear is the derivative of the moment. It’s easy to see that for our specific problem, the simply supported beam with a uniform distributed load, | Continue reading
Here’s the first of the derivations for the center deflection of a simply supported beam with a uniform load. | Continue reading
A few years ago, I wrote a post describing how I asked ChatGPT to solve a couple of elementary beam bending problems and how its answers were persistently wrong, even after I told it the mistakes it had made. For the first problem, determining the deflection at the center of a si … | Continue reading
I mentioned last week that some wording in a news article struck me as odd. A similar thing happened when I read this Scientific American piece (that’s an Apple News link—I don’t have a SciAm subscription). In this case, I didn’t even have to read the article; the oddity is right … | Continue reading
Earlier this week, I saw this article in Apple News. It’s from the San Francisco Chronicle and discusses a recent report on the safety of the Golden Gate Bridge. The report is one of several reports spurred by the Francis Scott Key Bridge collapse a couple of years ago. | Continue reading
After yesterday’s post, I got an email from reader Ron Sprague outlining two ways to block sender addresses from the list view in iOS Mail. Both of these methods are efficient, and neither starts with choosing a command with a stupid name like View Contact Card. I knew about one … | Continue reading
Complaints about Apple’s design choices usually involve transparency, color, and other legibility concerns. These criticisms are legitimate, but the poor design choices that usually set me off are the ones involving the mechanics of commands—what I have to do to get something don … | Continue reading
I meant to write this last week, shortly after I finished listening to Episode 612 of Upgrade. But things didn’t work out the way I hoped, so now I’m rushing to finish these few paragraphs before this week’s episode comes out (they’re recording as I type). I have nothing to say a … | Continue reading
In this morning’s blog/newsletter,1 Paul Krugman included a couple of unusual graphs that I want to talk about. It took me a little while—longer than it should have—to figure out what he was doing and why, and I’m still not sure I agree with his plotting choices. Let’s go through … | Continue reading
During my seven-week Spotlight trial, I was reminded of how easy it is to make file and folder launchers in Keyboard Maestro. In case you’ve also forgotten, here’s a short post on how to do it. | Continue reading
I started using launchers shortly after returning to the Mac (from Linux) in 2005. The first one I used was the great Quicksilver. I’m sure I learned about it from Merlin Mann, who was Quicksilver’s biggest advocate, but I can’t point to which of his many posts on QS got me start … | Continue reading
Yesterday’s post included some behind-the-scenes calculations that I figured were worth talking about. They were all done in Mathematica, and here’s the notebook I used: | Continue reading
In its continuing attempt to teach us how calendars work, Scientific American has an article (Apple News link) up today that goes through Gauss’s algorithm for calculating the date of Easter. The article was written by Manon Bischoff, who also wrote the Friday the 13th article I … | Continue reading
Back in January, I complained about the Apple Watch’s Timer complication being too complicated. A couple of days ago, Dan Moren told me on Mastodon that my complaint had been addressed in watchOS 26.4, which was released earlier this week. After a surprisingly quick update of my … | Continue reading
I’ve been working my way slowly through Reingold and Dershowitz’s Calendrical Calculations. This week I hit Chapter 11 on the Mayan and Aztec calendars and came across a notation for modulo arithmetic that wasn’t familiar to me.1 I figured I’d write about it here on the off-chanc … | Continue reading
You may have seen this article by Joe Rossignol in MacRumors yesterday. It’s about a new feature in macOS 26.4 that’s designed to keep us from pasting dangerous commands in Terminal. If a user pastes such a command, this warning pops up: | Continue reading
I’ve been thinking about the new Apple Studio Display lately, mainly in the context of Jason Snell’s review of it on Six Colors and his further discussion with Myke Hurley on Upgrade. | Continue reading