Physical intuitions for impedance matching and critical damping

This semester I took an introductory class on electrical circuit analysis. One of the concepts introduced was impedance matching: the idea that if you want to deliver maximum power to a load, the amount that the load “pushes back” on the power source should be equal to (the complex conjugate of) the amount the rest of the circuit pushes back. If you were writing a textbook, you would convince your readers like so:

But what if you weren’t writing a textbook, and wanted to convince someone who was planning on simply getting up and walking away the moment any of those libertine little d’s or, god forbid, the imaginary unit (or the jmagjnary unjt, as the case may be) made an appearance?

Then you could say, imagine you are playing that game where you put a jump rope on the ground and send a pulse through it. You want to try to make sure that the pulse that reaches some given point on the jump rope is, as precisely as possible, exactly the same as the pulse that leaves your hand. You have two choices.

First, you could use two jump ropes tied together, where the two ropes have different thicknesses, or might be made of different materials, or maybe one of them is that beaded kind that hurts like a #!%$ when you hit yourself in the ankle with it:

Or your second option, you could just use one really long jump rope, that has the same thickness and material used throughout.

It’s intuitively obvious that, if there’s a possibility of you being asked to transmit that as-faithful-as-possible pulse to the far side of the rope, you’re way better off with the one long rope. If that isn’t obvious, it’s obvious that you can go buy some jump ropes and try it out for yourself. Of course, the rope that has the same “impedance” throughout is going to transmit the pulse more faithfully, while the tied-together bit is going to muck things up.

A piece of physical intuition that was less obvious to me at first was that for critical damping. In one assignment, we simulated in software and built in meatspace three different versions of an LRC circuit: an underdamped one, overdamped one, and then figuring out what resistive value to swap in to get it critically damped.

Of course, an underdamped circuit oscillates, as seen in both the simulation and the oscilloscope hooked up to a breadboard:

And an overdamped circuit decays exponentially:

A critically damped circuit– i.e., one where the characteristic equation of the circuit has repeated roots, and there is only one natural frequency– decays faster than an overdamped one:

Why, though? When the words are spoken, it sounds like the thing called “overdamped” should do the thing called “decaying” the fastest. The math, of course, is entirely clear: with repeated roots to the characteristic equation, the solution to the differential equation has an exponential decay term multiplied by the independent variable of time, while the overdamped case has no such thing. So of course the critically damped case has to decay faster. But that’s just a property of multiplication, not a good explanation (and we lost the no-libertine-d’s-or-i’s-or-j’s observer some time ago.)

The physical intuition, then: imagine you are dropping a little ball into a glass of some kind of fluid. Your goal is for the ball to come to rest on the bottom of the glass– equilibrium– as quickly as possible. If the fluid is not sticky enough to slow down the ball before it hits the bottom, it will bounce (underdamped.) If the fluid is sticky, it will slow down the ball enough that it won’t bounce– but there is a point of stickiness beyond which any extra stickiness isn’t actually helping to prevent bounces, it’s just delaying the ball reaching the bottom. Just the right stickiness to prevent bouncing, without slowing down the ball’s progress more than necessary, is critical damping; excessive stickiness is overdamping.

does not have the desired rhetorical effect

Things that the Messiah makes seem cool and fun and sexy:

Things that the Messiah makes seem boring and lame:

A basic technique lost and found

I was playing a concert recently with a rather speedy Bach continuo part. As I was practicing, it occurred to me to wonder what exactly had happened to the technique of double-tonguing on the bassoon in the first part of the 20th century.

Plenty of Baroque continuo parts, including those usually including bassoon, contain passages that only the most freakish of wagglers could single-tongue. It seems obvious that Baroque bassoonists must have been able to double tongue; and sure enough, in JJ Quantz’s chapter on articulation, after describing several tonguing techniques including double tonguing, he notes:

Why Quantz thinks you can’t double tongue on the oboe is a mystery for another day (or for a Baroque oboist to tell me); the point is, bassoonists were known double-tonguers in 1752, if not known good-reed-havers.

Why, then, did double-tonguing seem to disappear from the toolbox for a period of time? That it did is of course anecdotal, but it does seem to me that among the generation of professional bassoonists who got jobs in the early or mid 20th century, it was very much an optional technique. That generation is largely gone from the active playing scene, but many people still have stories of teachers or older colleagues who didn’t double tongue, and I have even heard it said by some of those players that bassoons don’t double tongue, or that if they do it is a new invention. (This does seem to be largely true on clarinet. “Fucking slur two tongue two… shit!”)

Bassoon historians slide into my DMs…

The Only Good Smartwatch

In August, a sixteen year old student reverse-engineered iMessage, and published an open-source Python library allowing anyone to send and receive encypted messages with Apple users right from the command line. Crucially, he didn’t “break” the encryption; he simply figured out how to use it, meaning that while Apple has been forcing its users to communicate with all non-iPhone users via insecure, unencrypted SMS messages if they want to use their default messaging app– which they’re also not allowed to change for a different default– JJtech had figured out how to allow the rest of the world to meet iPhone users in their own walled garden when they refuse to or can’t leave it. In a climate where the tech robber-barons are finally undergoing some antitrust scrutiny, interoperability of messaging platforms is an obvious issue to address; and indeed, after years of pressure and openly admitting that lack of interoperability was the goal in order to force people to buy iPhones, Apple has finally said it will adopt RCS in 2024, a secure standard that will replace SMS and, hopefully, if Apple doesn’t break it for their own users on purpose, fix the problems with group messaging that currently exist on the iPhone-Android divide.

Reverse-engineering for the purpose of interoperability is explicitly protected by the Digital Millenium Copyright Act; so a company called Beeper hired JJtech and rewrote his code to create the beginnings of a universal texting app, which would start just as a way for Android users to send iMessages but planned to incorporate RCS, Discord, Whatsapp, and Matrix chats all into one space. Apple moved to shut it down, Beeper got itself back up, and the two are currently in a (probably protracted) cat-and-mouse game of adverserial interoperability.

That’s not actually my point. My point is that I got curious about Eric Migicovsky, Beeper’s CEO; who, it turned out, had also created the first functional and widely available smartwatch.

But not just any smartwatch. The Pebble was the first Kickstarter campaign to raise over $10 million dollars, and created the demand for smartwatches that Apple would later exploit. And, indeed, Apple eventually ran over Pebble like a, well, Mac truck. But Pebble, amazingly, survived, and in a way that Apple devices could never. From ifixit’s Rebble with a Cause: How Pebble Watches Were Granted an Amazing Afterlife:

The next wave of Pebbles focused on fitness, something Apple was already pivoting toward with its second Watch, but Pebble didn’t have Apple’s money. After months of last-ditch fundraising attempts, Fitbit paid a scant $23 million for Pebble’s software assets and engineer hiring rights in December 2016. While Fitbit would not officially support Pebble’s customers, Migicovsky worked out a deal that would refund Kickstarter pre-orders, and, he hoped, keep the more than two million Pebbles sold, and their apps, working for as long as possible.

In hindsight, he nailed it. Pebble has been the most successful hardware company failure in history. Compare this to Revolv, whose acquisition by Nest led to an abrupt shutoff of smart homes around the world, or personal cloud device Lima, or, really, any Android device more than a couple years old.

From the rubble formed Rebble, a team of motivated fans, developers, and ex-employees, rushing to reproduce years of development in a matter of days. Frantic to document critical APIs and development tools before the servers shut off, they grabbed everything they could. The first replacement app store appeared quickly, aptly code-named Panic App Store. Within a few days, they had firmware, core and third-party apps, all the dev tools, and more. And they preserved it all on a wiki, right down to the pinouts.

Meanwhile, Fitbit kept the servers running longer than expected. But the axe would fall in June 2018, and a replacement was needed. Using her inside knowledge of Pebble’s server setup, and painstakingly working through a man-in-the-middle proxy, Berry, the ex-Pebbler, created replacement web services for nearly everything Pebble had provided. With just 16 days until the shutdown, Rebble opened up account sign-ups. When Fitbit finally killed Pebble’s servers, Rebble was ready the next day.

More than 177,000 people have connected their devices to Rebble’s services. Not everything can be free, because the APIs for voice dictation and weather are not cheap—$750,000 per year, if 100,000 people used them, Berry said. And yet, nearly 9,000 people pay yearly subscriptions. Full disclosure, in case you haven’t guessed: I pay for Rebble’s services on my Time Steel, which I wore in our video about … the Apple Watch.

The Rabble project not only has replacement web services, it also has a network of resources for replacing the batteries in Pebbles, 3D printing replacement buttons and cases for them, and is even working on creating entirely new hardware for RebbleOS to eventually run on.

So, I went on Facebook Marketplace and searched them up– and sure enough, there was one for sale close by for a whopping $10. Admittedly, the price point was probably partly because it was one of the very first generation of the watches, probably manufactured around 2013. While later versions were somewhat more refined aesthetically, the original looks like exactly the smartwatch that time travellers from 1960 would expect to find people wearing in 2013:

Anyway, I charged up my new Pebble and followed the instructions on the Rebble setup guide, and within a few minutes had a fully functional smartwatch, with an all-freeware watchface and app store, at my disposal. I joined the very active Rebble discord, where development of both hardware and software is still ongoing, and where they recently hosted their first hackathon for apps and watchfaces, but turned out not to need to ask any questions at all about the process– it just worked.

It’s hard to remember, sometimes, that “being on the computer” used to be fun. Owning and using tech has turned from something that feels like a frontier of discovery and possibility into a kind of grim obligation; the vast majority of devices and internet services are predatory and bad, but you need to use them anyway, and they’re designed to try to make you keep using them even when you actively want to stop, and they’re spreading misinformation and misunderstanding, but what are you going to do about it?

Pebble is fun. Pebble is a good device in the way basically nothing manufactured since is. Although it can put through any level of notification from your phone that you want, and you can install plenty of apps giving you different ways of interacting with those notifications, some of the best apps available for it are things that have nothing to do with your phone at all.

One of my favourites, for instance, is called “wristronome”. It is the best metronome app I have ever encountered. It uses the three buttons on the side of the watch as up/down tempo and start/stop, then uses the very strong vibrations of the Pebble as a metronome. Although there are all sorts of android and iOS metronome apps, almost all of them come with ads, and have weird unusable interfaces that take way too much time just to turn your metronome up a few clicks; so I have been using the same Korg TM-40 since, well, before my Pebble was born. This is the first app that provides a genuine challenger to it. Not only does it do everything it needs to do as a metronome, the vibrations make it appropriate to use in crowded warmup rooms at gigs or auditions; whereas having a loudly ticking metronome on your stand in a room where everyone else is trying to practice and warm up too is kind of rude, this is unnoticeable to everyone but the wearer.

Another of my favourite apps is called Tilt Calculator. Unlike Wristronome, this is, admittedly, not a better calculator than any calculator I’ve tried before. In terms of its ease of use, it’s, well, kind of insane. But that is the point: Tilt Calculator is a completely insane piece of software, something that has never existed before or since, something that could only exist in this particular ecosystem. To operate Tilt Calculator, you tilt the pebble until the cursor rolls over the number you want like a ball bearing in one of those little maze games, and then press the side button to select it.

Indeed, this is not a convenient way of doing arithmetic. But it is an entirely new way of physically manipulating numbers, unheard of until now all the way back to the invention of drawing in the dirt with a stick. Apple would simply never think up something this fun.

There are plenty of other genuinely useful apps– tiny maps for your wrist, health tracking, apps to set a location that it will then lead you back to, etc– as well as plenty of gloriously useless ones. One of the best features of the Pebble, though is probably its battery life; because it has a transflective liquid-crystal display that requires no backlighting in bright environments and draws almost no power to continue showing an image, a new Pebble battery lasts for about 7 days, and even my ten-year-old battery lasts for four days. Compare that to the Apple watch, for which the company claims a new device’s battery will last 36 hours or up to 3 days if you use “low power mode.”

The only downside to my Pebble is that it’s, well, kind of ugly. But then, there are quite a few nicer-looking ones– and now that I’ve discovered the secret of the Only Good Smartwatch, I’ll probably pick one up when it comes up on marketplace of kijiji near me.

Imaginary

Learning phasor analysis; contemplating that it’s almost too metaphorically on-the-nose that analysis of purely real functions can become vastly easier when they are given an imaginary component. A similar feeling to that evoked by the process for solving the Gaussian integral, in which turning a one-dimensional problem into a two-dimensional problem provides an almost offensively simple answer to a seemingly intractable problem.

A musician being nice about a conductor?

Linhan Cui is the real deal, as a conductor, and will soon be snapped up by a major orchestra if there’s any justice in the world; in the meantime, I treasure every concert I get to play under her direction.

Blanche Neige

What if Clive Barker had a fever dream of Snow White as imagined by Angela Carter? This is the question nobody but me asked, but I imagine Angelin Preljocaj’s Blanche Neige to answer.

Winnipeg is one of my favourite orchestras to play with, and recently I was invited to play guest principal for the Royal Winnipeg Ballet’s production of this show. The draw for musicians is that it’s a new ballet constructed entirely out of Mahler symphonies; but once I watched a video of a previous production sent to the orchestra, I was also excited for the reaction to the work, which is– look, I don’t think it’s particularly controversial to say that this is a very sexy ballet. The costumes were designed by Jean Paul Gaultier. The sexy cats had headgear intended to convey the danceable impression of ball gags. When Snow White eats the apple, it’s less a trick and more of an orgasmic force feeding.

I’m not casting aspersions. It all– in my opinion, from the production I did watch and the reaction of the Winnipeg audience– worked great. There is something about the project of presenting Mahler as anything other than an integral whole symphony that invites, nearly demands, a certain amount of enjoyable grotesquerie; Ken Russell comes to mind. That said, the music was not as chopped up as you might think it would have to be; no crazy cuts and very few significant alterations to make the music fit the dance. There were even two entire movements, the Purgatorio of the Tenth symphony and the third movement of the First, which accompanied probably one of the most memorable stagings in the show: the introduction of the seven dwarves (I think credited here instead as “miners”), an entire vertical ballet taking place on a sheer rock face, one of the pieces of it that is available online:

The only really wacky alteration was this section, from the very end of the 3rd movement of the Third symphony, being repeated eleven times:

…which is how I learned that in the Brothers Grimm version of the story, the happily ever after is that the Prince orders the evil Queen to dance herself to death while wearing a pair of red-hot iron shoes, which is what is happening during the above. Disney sure didn’t mention that part!

Anyway, I’m very much hoping that the National Ballet or some other company around these parts picks this up, as I’d like to see it properly!

NMC

The last time I was at the National Music Camp, I was 14 and played a bassoon for the first time in the beginning bassoon elective. This summer I returned as a faculty member. (Full disclosure… once I started playing bassoon in earnest, my allegiance was firmly to the other music camp, on the grounds that the dining hall was quieter and they didn’t make you do “evening program,” so I never actually attended as a camper on bassoon.)

I didn’t take all that many pictures– one of the excellent things this camp did was take away all the camper’s phones, so there just wasn’t much photo-taking culture in the absence of ubiquitous devices. To be honest, I suspect a lot of the kids (those who didn’t sneak them in anyway, that is) were relieved to have them gone for a week. Hey, maybe they’ll do the same for the faculty in the future!

Laurel leading a very cozy band sectional

A bat taking a rest outside the bassoon studio (I realize this does not exactly look like the peak of bat health, but at least it flew away and we didn’t have a dead bat to deal with…)

Not a camper any more… they can’t force me to stay in the loud horrible dining hall… ate all my meals on the dock with my buddy Montaigne.

Very good doggo getting ready to listen to faculty wind quintet rehearsal

Pulled out the 2nd cello suite for a faculty concert

Garden Walk

Arcady Ensemble’s “Garden Walk” concert– the first half was a setup where, instead of musicians assembling in a central location for a concert, musicians are spread out through the Whistling Gardens playing solo works with related thematic material, and the audience walks around through them. Ronald Beckett’s music is always fantastic and the dedication of his audience to the ensemble is impressive.

My spot in the garden

The entrance to the performance space

Who am I to disagree?

His Second-Last Bow