Equinox
September 22, 2026 at 7:05 PM by Dr. Drang
The episode of The West Wing that’s always bothered me is “Evidence of Things Not Seen,” which is Episode 20 of Season 4. It takes place on the day of the equinox (in March, not September, but I remembered it because today is an equinox), and one of the continuing subplots is C.J. trying to convince the others that you can stand an egg on its end at the exact moment of the equinox and only at that moment. Oh, and it has to be the vernal equinox, not the autumnal one.1
That someone in the glorious Bartlet White House believes in nonsense isn’t what bothers me. Lots of smart people believe silly things. What’s wrong is that it’s C.J., the primary female character, who believes in superstition while the men around her are pooh-poohing it. I’m sure plenty of women will tell me that’s par for the course for Aaron Sorkin, but it still bothers me.
There are two small counters to the general sexism of the egg subplot. First, the men who tell C.J. she’s full of it are themselves wrong. They think you can’t balance an egg on its end, even though it’s not really that hard.
This photo was taken today (yes, on the equinox but not the vernal equinox and not at the exact moment) on my back patio. I didn’t do any tricks like slightly crack the shell or put it on a bit of salt and then blow the salt away. I just kept adjusting its position again and again until it stood. The plain fact is that it just takes a little time to balance an egg on its end, time that most people aren’t willing to spend. (And yes, it helps to have a rough surface.)
The second counter is that Jed seems willing to believe the egg story. He doesn’t defend C.J., but he does try to stand an egg on end in his office. In some ways, this is worse. For all his faults, Jed is supposed to know at least a bit about science. Remember the episode in which C.J. has to remind him to let the NASA experts handle the science questions coming in from schoolkids? If anyone should be instantly dismissive of the standing egg myth, it should be Jed.
At the very end of the show, C.J.’s alone and manages to balance an egg on its end, justifying her faith. The title comes from Hebrews 11:1, which she recites earlier in the episode. I guess this is supposed to get us to think that she hasn’t been spouting nonsense all this time, but what it really means is that she can do what anyone can do if they take their time.
What bothers me the most is the setup for her balancing act. Before trying, she looks pointedly at the clock, which shows midnight. Recall that the balancing is supposed to work only at the exact moment of the equinox. Does Sorkin think equinoxes always occur at midnight? Does he think the audience is dumb enough to believe that? The episode aired in April 2003, so I guess its events take place on March 20 of that year. In Washington, the 2003 vernal equinox occurred at about 8:00 pm, not four hours later. Was the show set a year or two earlier? No midnight spring equinoxes those years, either.
If you’re interested in the history of the egg balancing myth, Martin Gardner wrote an article about it in 1996. You can see the text on the Wayback Machine.
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No one ever asks whether the egg balancing would work if they were in Buenos Aires instead of Washington. ↩
Cleaning up after Matt Parker
September 16, 2026 at 11:36 PM by Dr. Drang
This video Matt Parker posted a couple of days ago really pissed me off:
It’s cheating to say that a result arrived at through classical mechanics—in this case, that is the kinetic energy of a particle—is wrong because it’s only an approximation to relativistic physics. Of course that’s the case, and I swore at my phone when the “reveal” came.
By the end of the video, though, I had calmed down because I knew I could put together a quick post of my own by rewriting the infinite series equation he derived in a better form. Also, I could provide a general expression for the individual terms.
Let’s start with this result: that the kinetic energy of a particle (including relativistic effects) is
where m is the mass of the particle, c is the speed of light, and
is the Lorentz factor, with v as the velocity of the particle. The video gets to this result at about the 8-minute mark.
Matt then does a series expansion of the term to get
The leading 1 of this series gets canceled by the 1 that’s subtracted from γ, giving
for the kinetic energy. The leading term is the one we get from classical mechanics and the others are essentially zero unless you’re in a particle accelerator (which is discussed later in the video).
I don’t like this form for the equation. It’s cleaner if you factor out all the terms that give the expression the units of energy and then have a nondimensional expression afterward. Like this:
Isn’t this nicer? The expression in the parentheses is a function of the ratio of the velocity of the particle to the speed of light. If we call that
then the kinetic energy is
and it’s much easier to see why the terms after the 1 are vanishingly small for most situations—all the situations for which classical mechanics applies.
One last thing. Matt sort of explained how to calculate the terms of the expansion of γ in the companion video, but there was a lot of handwaving and he bailed out after the second term. It doesn’t take too much effort to show that the series expansion of γ can be written like this:
That means the kinetic energy, , is
You can confirm that these terms match the equation we saw earlier by plugging values of n from 2 through 8 into this expression. And now we can extend the series as far as we like, even though the additional terms add essentially nothing.
Apple drawings
September 14, 2026 at 8:09 PM by Dr. Drang
Everyone’s favorite Apple archivist, Stephen Hackett, wrote a short post last week in which he linked to Apple’s page with dimensional drawings of its products. He included this drawing of the iPhone 17 Pro:
You can click on it to see a 300 dpi version. The Apple page linked above will give you infinite-resolution PDFs.
When I zoomed in on Stephen’s page, I was initially confused, but then I realized what seemed odd to me. You see, I’ve spent an awful lot of the past 40 years looking at engineering drawings, and I can’t think of any that looked like this. That’s because the drawings I’m used to are for making the depicted product, but the drawings Apple’s offering up here aren’t for that.1 These are for others—not Apple and not its suppliers—to use for making cases and other accessories. I figured it was worth a quick post on what makes a drawing like the one above so different from what I’m used to.
First off, there are so many dimensions. Drawings of full products are typically called assembly drawings, and they have almost no dimensions. What they do is show how the various component pieces (subassemblies) are put together. The subassemblies have their own drawings that show how they are put together from their components, which are themselves typically subassemblies. Eventually, you get down to the individual part drawings, which depict a single piece of metal or glass or plastic. At each level in this hierarchy, the drawings tend to include only the dimensions necessary to build the object depicted. You don’t include the length and diameter of a screw on an assembly drawing; you simply call out its part number (which is also its drawing number).
Speaking of drawing numbers, if you look in the title block you’ll see that there is no drawing number. Design drawings always have these. They also have the names or initials of the draftsmen and checkers and, usually, a list of revisions. These public drawings don’t reveal any of that internal information.
There are names for many of the items and dimensions: product length, display active area, volume button, rear sensor, etc. These are not common in design drawings because they tend to be of no value to those doing the manufacturing. You don’t need to know what this hole is for; just make it this big and put it here.
Which leads us to tolerances, which are absent. Dimensions and positions are given to the nearest hundredth of a millimeter and there is no give or take. To the outside world, Apple’s dimensions are absolute and invariable. Inside Apple and its suppliers, people know better.
Also absent is any specification of material, other than a few generic mentions of glass. While assembly drawings don’t usually include materials, parts drawings always refer to material specs, usually included in another company document.
The last thing I’ll mention is the Notes section in the upper left corner. It has instructions clearly meant for people outside of Apple and making accessories. If I’d zoomed in on this section first, I probably wouldn’t have been even momentarily confused.
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Obviously. Apple isn’t going to post its design drawings; they’re among its most tightly controlled proprietary documents. Even for a company that considers everything a secret, the design drawings are really secret. ↩
New Apple Watches have ears
September 9, 2026 at 10:42 PM by Dr. Drang
Starting about 45 minutes into today’s Apple Event, during the segment on the new Apple Watch, Ron Huang introduced a couple of features of the Series 12 and Ultra 4 that struck me as both disturbing and possibly illegal. They certainly seem at odds with Apple’s commitment to privacy.
First came Live Rewind, a feature that lets you “go back in time” to pick up on something you missed that was said in the past 15 seconds. Here’s how Apple describes it on the website:
Live Rewind catches what you missed. Did someone say something you couldn’t hear in a loud restaurant or share cooking instructions you didn’t quite catch? Just double-click the Digital Crown, and Live Rewind transcribes what was said in the last 15 seconds. You can ask Siri about the content of the transcript or save it to the new Siri app to revisit later.
In the Event, this was illustrated by a waitress going through the restaurant’s specials too quickly for the diners to remember all of them. One of the diners double-clicks the crown on his watch and reads what she said.
It seems like your watch will be listening continuously, keeping the last 15 seconds in a buffer, ready to be transcribed when you ask. That’s fine for you, because you know it’s happening, but what about those around you? Did they agree to this? I doubt wait staff will be upset with their spiel being transcribed, but the idea behind Live Rewind seems to be that everyone and everything near your watch is being recorded for 15 seconds. Surely, some people wouldn’t consent to that if they were asked. Significantly, though, they’re not being asked. I’m sure Apple will argue that there’s no privacy issue because the recordings aren’t being saved. But if there’s a transcription, isn’t that a type of saving?
And then there’s the question of legality. A great variety of law, both in the United States and across the world, concerns the recording of electronic and in-person conversations. I’m sure Apple has considered this, but I have to think some jurisdictions will frown on Live Rewind. If Apple has to defend it, that’s fine. What’s one more squadron of lawyers to Apple? But if an Apple Watch owner has to defend a transcription made innocently—made with Apple’s encouragement, in fact—that seems like an unfair burden. Maybe Apple should indemnify all future Watch buyers from privacy-related legal action.
Right after Live Rewind, we get the introduction of Siri Recap. From the Series 12 web page:
Siri Recap can summarize your chats to refresh your memory. Siri Recap transforms your conversations into high-level notes, so you can stay focused and present. Each Siri Recap includes a title, a summary, and key points that you can review in the Siri app on your Apple Watch or iPhone. You can turn Siri Recap on or off at any time from Control Center or choose where and when it takes notes, such as only at work or never at night.
Siri Recap does a summary, not a transcription, and it’s not automatic the way Live Rewind is, although it does sound as if you can set it up to always record when you’re at a certain place, so that’s kind of automatic. Apple touted Siri Recap’s privacy with three bullet points:
I think Apple is slicing the baloney pretty thin when it says audio isn’t recorded. Surely there’s some recording because summaries require context; they can’t be made on the fly. Maybe a transcription is done in near-real time and the summary is drawn from that. If so, the transcription is a type of recording, albeit one that isn’t stored after the summary is made. As for not identifying the speakers, I don’t see how that matters. Old-fashioned audio recordings don’t identify speakers, either, but they’re still intrusions on the speakers’ privacy if they didn’t give consent.
Apple has always focused on the privacy of its customers: your information is encrypted, your data stays on your device. It’s following that same pattern here, but the privacy concerns of Live Rewind and Siri Recap aren’t limited to the owners of Apple Watches. Apple now needs think about the privacy of non-customers and be able to explain how that’s being protected, too.
And while an argument can be made that textual transcriptions and recaps aren’t as invasive as saved audio recordings, that doesn’t mean they aren’t invasive at all. That little lock animation Apple’s been using to describe its commitment to privacy has been very effective, but its binary nature doesn’t fit when the products start putting privacy on a sliding scale.
Update 10 Sep 2026 8:14 PM
On Mastodon, Bill Lloyd sent me a link to this longer document from Apple with further explanation of Live Rewind and Siri Recap. The hoops Apple jumped through to avoid certain words is pretty funny. For example, in the discussion of Live Rewind, we learn that
Audio from the microphone flows into the audio buffer inside the Secure Exclave on the S11 chip.
You think your watch records the audio around you? No no no. The audio flows into the Secure Enclave, and flowing is definitely not recording because it’s a different word. Apple’s documentation poets liked flow so much, they also used it in the description of Siri Recap:
If a conversation is detected, audio flows into a protected buffer inside the Secure Exclave on the S11 chip.
Note also that the audio flows into a protected buffer inside the Secure Enclave, so that must make it doubly private.
Thanks for the entertaining link, Bill!