Covid 10/21: Rogan vs. Gupta
I finally got my booster shot yesterday. I intended to get it three weeks ago, but there was so much going on continuously that I ended up waiting until I could afford to be knocked out for a day in case that happened, and because it's always easy to give excuses for not interacting with such systems. When I finally decided to do it I got an appointment literally on my block an hour later for that and my flu shot, and I'd like to be able to report there were no ill effects beyond slightly sore arms, but I'm still kind of out of it, so I'll be fine but if I made some mistakes this week that's likely the reason. I also had to wait the fifteen minutes. I would have simply walked out the moment they weren't looking, but they held my vaccine card hostage until time was up.
We now have full approval for every iteration of booster shots, including mix and match, for those sufficiently vulnerable. If you're insufficiently vulnerable but would still rather be less vulnerable, there's a box you'll need to check.
I got a chance to listen to the Rogan podcast with Gupta, and have an extensive write-up on that. It was still a case of 'I listen so you hopefully do not have to' but it was overall a pleasant surprise, and better than most of what passes for discourse these days.
Executive Summary
Conditions continue to improve.
Booster sequences including mix-and-match have been approved.
Rogan did a podcast and I listed to it so you don't have to.
Let's run the numbers.
The Numbers
Predictions
Prediction from last week: 481k cases (-12%) and 9,835 deaths (-11%).
Results (from data source unadjusted): 472k cases (-15%) and 11,605 deaths (+1%).
Results (adjusted for Oklahoma which will be baseline for next week): 472k cases (-15%) and 10,705 deaths (-3%).
Prediction for next week: 410k cases (-13%) and 9,600 deaths (-10%).
Wikipedia reported over 1,100 deaths in Oklahoma this week. That's not plausible, so I presume it was a dump of older deaths or an error of some kind, and removed 900 of them from the total.
There's no hard and fast rule for when I look for such errors or how I do the fixes, so you can decide if what I'm doing is appropriate. Basically if an entire region gives a surprising answer I'll look at the individual states for a large discrepancy, which is at least slightly unfair since sometimes it makes the number look 'normal' when it shouldn't, but time is limited.
This is still more deaths than I expected, but given cases continue to drop I expect deaths to keep dropping. It's possible there was another past death backlog I didn't spot because it wasn't big enough to be obvious.
Deaths
Chart and graph are adjusted (permanently) by -900 deaths this week in Oklahoma.
Death counts seemed higher than plausible in general even after the fix, but it's a small mistake. Next week will tell us whether or not it is a blip.
Cases
The South's situation continues to improve rapidly, and it now has fewer cases than multiple other regions, but we see improvement everywhere. Solid improvement in the more northern states is especially promising in terms of worries about a possible winter wave. Can't rule it out, but it seems somewhat less likely.
We are now down more than 50% in cases from the recent peak, and over the last five weeks, although regionally that is only true in the South. But we've clearly peaked everywhere.
Vaccinations
Nothing ever changes. Which at this point is good. Steady progress is more meaningful each week as more of the population is already vaccinated.
Vaccine Effectiveness and Approvals
In the words of Weekend Editor: Today the FDA formally authorized Moderna boosters, J&J boosters, and all the mix-and-match combination boosters. This is very aggressive for them!
Indeed, and congratulations to the FDA for doing the right thing, at least on this particular question. When someone does the right thing is the time to thank them, no matter how long overdue it might be.
As per procedure now the CDC gets to have all the same discussions, because if there's one thing we need enough of it's veto points. We'll know the outcome on that next week.
Vaccine Mandates
Support for older vaccine mandates is declining. This could end up being quite bad.
There continue to be claims that there will be massive waves of people quitting over vaccine mandates, this time in New York City. No, we are not going to lose half our cops, no matter how excited that prospect makes some people these days. We'll find out soon enough:
On the one hand $500 is in the 'let's actually get it done' range and worth it if it works, and should smooth over any general grumbling, on the other hand it's enough that I'm pissed off that they're getting that many extra tax dollars for what they should have done anyway.
Here's a Zeynep thread on the psychology involved. Lot of good food for thought.
A vaccine mandate carries with it the requirement to verify that it is begin followed. This in turn means verifying people's vaccine status and ID at various points. When does this end? Some people who based on their previous writings really should know better are seemingly fine with 'never' and I notice I am most definitely not okay with that for everyday activities. There will be a point these mandates \(\) everyday actions turn negative, and it's not that far off, and then we'll have to figure out how to unwind them. Would be increasingly happy to start now.
This post looks at vaccine persuasion in Kentucky, notes that $25 Walmart gift cards were a big draw, doesn't seem to offer much hope that persuasion via argument would work. But have we tried bigger gift cards?
California state works are somehow vaccinated at a rate much lower than the state average. Ignoring for the moment that they don't seem to be doing much to fix this problem, one can draw various conclusions about how the state government operates and hires based on this. And one can wonder why, if the state is willing to impose so many other restrictions, they can't or won't take care of business in this way. However, the article also notes that this is comparing the number who provided proof of their vaccination status as employees, versus the number who actually got vaccinated as adults. It seems that some employees may have simply decided not to provide proof, either as a f*** you to the demand for proof of vaccination, or because it seems that if you don't vaccinate they 'make' you get tested a lot but that's free and some people like the idea of getting tested frequently, so whoops.
Washington State's football coach is out:
So is an NHL player, and even if you oppose mandates I hope most of us think that faking a vaccine card is not a permissible response.
This is a remarkably high tolerance of importantly fraudulent behavior. Very much does not seem like a sufficient response.
Not endorsed, but noting the perspective that the unvaccinated are holding us hostage, because the threat of potentially running out of health care capacity is the reason we still take major preventative measures, and if everyone got vaccinated we would go back to normal. I find the hostage situation metaphor apt because hostage situations are mostly because we choose to care about them. Every so often, someone on a show will grab a hostage, and the response will quite correctly be 'I'm not going to reward threats to destroy value by giving you what you want' and I wrote a contest essay back in grade school arguing this should be standard procedure. Instead, we're more like a DC hero who thinks that if you point a weapon at any random citizen they are forced to hand over the world-destroying superweapon codes. I will leave it to you to draw the appropriate metaphor to our current situation on other fronts.
NPIs Including Mask and Testing Mandates
From New Zealand and Offsetting Behavior comes the story of Rako. Rako offered to scale up their Covid-19 tests, the government said they weren't interested, then when it turned out the tests were good they reversed course and decided to take what tests and capacity that did exist without much paying for them, among other disasters going on there, and hope that somehow anyone will be interested in helping with such matters next time around. It doesn't look good. Neither does the Australian decision not to securely keep the police away from the contract tracing records.
How much should you update on a Covid-19 test? We've got a new concrete reasonable attempt answer that, although it still uses the PCR test results as their 'gold standard' and thus is underestimating the practical usefulness of other testing methods.
The Bayes factors for positive tests are pretty high. The ones for negative results are less exciting, but if you're focusing on infectiousness, I believe you end up doing a lot better than this. Those who do math on this stuff a lot are encouraged to look into the details.
It turns out Rapid Antigen Testing works rather well at telling who is infectious. Here's a thread explaining why they're much more accurate than people thought, which is that when the PCR tests came back with what were effectively (but arguably not technically) false positives, not matching those was a failure. The fallback general official response has for a long time been something like this.
Where 'have Covid' is defined as 'have or recently have had any trace of Covid' although that's rarely the thing that has high value of information. It is very reasonable for someone to want to know if they have (or others have) Covid, and it is also very reasonable for someone to know if they are (or others are) infectious. Different purposes, different tools, and it turns out both tools are highly useful. The mistake we made for over a year was saying that because people might also want to know if they have Covid, the test that is very good at detecting infectiousness and less good at detecting Covid was illegal, so we should instead not test at all or use a test that was more expensive, slower and less useful in context. It is good that things seem to be coming around a bit.
Restaurant that isn't as good as Shake Shack lets people in, is now told they are out.
This was only a temporary shutdown of one store, since they only have one store in San Francisco. Depending on exactly where their stores are, this could be a very smart move, as it wins them massive points with the outgroup.
Permanent Midnight
Some of us think the ultimate goal is to become complacent about Covid-19 once it's no longer a major threat, and return to our lives. Our official authorities say, madness.
This is an explicit call for vaccinated children to be forced to mask permanently. This is utterly insane. If not them, then who? If not now, then when?
I sincerely hope the kids neither forgive nor forget that this happened to them.
This also brings up another of my humble proposals of 'maybe we should teach children that skipping a meal every so often is fine, so they have that valuable skill in life that's done me worlds of good' but mostly it's that they are literally forcing children to go outside in the rain to eat.
Remember.
Here's Sam Bankman-Fried going over why calls for large permanent interventions are nowhere near ever passing cost-benefit tests, and giving an attempt at a calculation and thus an opportunity to nitpick and refine.
Semi-constant mask wearing costs a lot more than 0.4% of GDP. I don't know exactly what you'd have to pay people to get them to wear masks indefinitely (with no other benefits) but I'd be stunned if it's under 1% of consumption. Even if we knew it would work on its own with no help I have no idea why you'd even consider this.
Staying home if you have a sick housemate, to me, seems mostly like a good idea even before Covid-19. You can call this a cost of one day per year, but you have to make a bunch of assumptions to get there. Days of work can't be fungible, so taking a random day off means your productivity is lost and can't be made up later, and there aren't substantial benefits from taking that extra day off on the margin. But that's kind of weird, since if there was such a big net loss from losing a random day of work it strongly implies you're not working enough at the baseline. And it seems likely to me that you save the office collectively a full day of productive work (since being low-level sick makes work less effective on top of less fun) by avoiding additional infections.
The exception here would be if work on that day can't be done from home, and isn't fungible with either other times or other people, so you lose something close to a full day's productive value. I think that is rarely the case, and that Sam's history of being stupidly productive at all times makes this a blind spot. For most people, my model says that either (A) you can mostly get others to cover for you without too much loss and (B) most of the work where this isn't true can be done remotely for a day or two.
Zoom meetings are a mixed bag, but this week I had my first work in-person meeting in over a year and it was incredibly more productive than a similar Zoom meeting would have been. There are big advantages the other way, so this won't always be the case, but I strongly agree that giving up on seeing people in person is a productivity (and living life) nightmare that costs way more than we could plausibly give up. But on the margin more Zoom meetings than 2019 is good actually.
That leaves the vaccines, which he estimates at a day of cost, and I don't understand this number at all. Sometimes the vaccine will knock one out for a day, but this does not need to be the case and I wrote most of this the day after getting my booster shot. Over time, we'll figure out the right dosing and regimens and the side effect impact will decline, and you can plan ahead so you choose a day when it's not that expensive to be somewhat out of it.
If we end up passing a 'everyone must miss a work day after the shot so everyone feels permission to get the shot' law then it could end up costing a day, I guess, but also giving people some paid time off at the time of their choice that they plan for seems like it isn't even obviously a bad idea?
Rogan Versus Gupta
I got the chance to listen to Joe Rogan's podcast with Dr. Gupta. It's a fascinating combination of things, some of which are great and some of which are frustrating and infuriating, from both of them.
The opening is a discussion of why the two of them were willing to sit down together. Gupta sat down with Rogan to try and understand Rogan's thinking process and because Rogan can reach a huge audience that is otherwise exceedingly difficult to reach, and to convince Rogan on vaccines. Rogan sat down with Gupta because Gupta's public changing of his mind on marijuana (which they talk then about a bit) revealed to Rogan that Gupta is willing to look at the data, change his mind and admit when he's wrong.
In this past, both of them acquitted themselves well. The central point here was well taken. On its surface it was about the potential of marijuana and why we should not only legalize but embrace it and research what it can do for us, and I'm while I don't have any desire to use it myself I am totally here for that.
The real point was that one needs to think for oneself, look the data with your own eyes and an open mind, be curious and come to conclusions based on where that takes you, and that doing this is how you earn many people's respect. That Gupta was here with the ability to engage in (admittedly imperfect, but by today's standards pretty darn good) discourse because he'd shown himself in the past to be an honest broker and truth seeker acting in good faith.
They then started getting down to it and discussing the situation in earnest. Compared to my expectations, I was impressed. Joe Rogan came in curious and seeking truth. He had many good points, including some where he's more right than and where he was wrong, he was at least wrong, making substantive claims for reasons and open to error correction and additional data and argument. He was continuously checking to see if Gupta's story added up and whether it lined up with Rogan's model of the world in general, but was quite open to learning more.
Like any discourse or debate, there were many ways all participants could have done better.
Several people have noted that Joe Rogan is drawing a distinction between vaccines, where the burden of proof of safety is being put on the vaccines, and on various other things like Ivermectin, where he largely puts the burden on others to show they are not safe, and holds them to a very different standard. In general, it seems like Rogan is hunting for an angle whereby the vaccines will look risky. Not full solider mindset, but definitely some of that going on.
It's worth noting that Rogan explicitly states in minute 59 that the risks from the vaccines are very, very small. This is despite Rogan listing off people he claims to know who had what he thinks are deadly serious adverse reactions, so it's not clear to me that he in his position should even believe these risks are all that small.
Rogan's point that Gupta is at far greater risk as a vaccinated healthy older adult, than a child would be unvaccinated, is completely correct and a kill shot when not tackled head on. None of our actions around children and this pandemic make any sense because we refuse to reckon with this. Gupta has no answer. The response 'I think you have to draw a distinction between those that have immunity and those that don't' is not a meaningful answer here - saying the word 'immunity' and treating that as overwriting age-based effects is Obvious Nonsense and Gupta is smart enough to know that. As are his attempts to move back and forth between risk to self and risk to others when dealing with kids. If he wants to make the case that vaccinating kids is mostly about protecting others, that's a very reasonable case, but you then have to say that part out loud.
Which is why Rogan keeps coming back to this until Gupta admits it. Gupta was trying to have it both ways, saying he's unconcerned with a breakthrough infection at 51 years old, and that young children need to be concerned about getting infected, and you really can't have this one both ways. Eventually Gupta does bite the bullet that child vaccinations are about protecting others, not protecting the child (although he doesn't then point out the absurdity of the precautions we force them to take), and frames the question in terms of the overall pandemic.
The question of protecting others was a frustrating place, and the one where I'm most disappointed in Rogan. Rogan pointed out that vaccinated people could still spread Covid-19 (which they can) and then said he didn't see the point of doing it to protect others, whereas he's usually smarter than that. Gupta pointed out that the chances of that happening were far lower, although he could have made a stronger and better case.
Gupta was very strong in terms of acknowledging there was a lot we didn't know, and that he had a lot of uncertainty, and that data was constantly coming in, and in engaging the data presented with curiosity and not flinching, if anything taking Rogan's anecdata a little too seriously but in context that was likely wise.
The key moment where Rogan turns into the Man of One Study seems to start in minute 62. In response to Gupta referring to the study, Rogan has it brought up. The study's surface claim is that for some group of young men, the risk of the vaccine causing myocarditis is 4.5x the chance of being hospitalized for Covid-19. Gupta had previously pointed out that the risk of myocarditis from Covid-19 is higher than that risk from the vaccine, and tries to point out that the study here is not an apples-to-apples comparison, as it's comparing hospitalization risk to diagnosis risk. Rogan grabs onto this and won't let go. It takes a few minutes and Gupta stumbles in places, but around the end of minute 65 Gupta gets through to Rogan that he's claiming myocarditis risk from the disease is higher than from the vaccine. Rogan responds that this is inconsistent with the data from the study, which seems right. Then Gupta gives the details of his finding, but his finding is based on all Covid-19 patients in general, which is consistent with this particular risk being higher for young boys from the vaccine than from Covid-19, and potentially with the results of the study.
At another point, Gupta threw the Biden administration under the bus on the issue of boosters, blaming them for daring to attempt to have an opinion or make something happen without waiting for word to first come from the Proper Regulatory Authorities, and claiming this was terrible and caused two people to resign and treating their decision to resign as reasonable (Rogan was asking about the resignations repeatedly). He equated 'data driven' with following formal procedure and only accepting Officially Recognized Formats of Data. I wasn't happy about this, but the alternative would be to start speaking truth about the FDA.
My model is that Rogan's take on vaccines differing from the standard line comes mainly from Rogan placing an emphasis on overall health and the strength of a person's immune system, and from taking these questions seriously and spotting others not taking the questions seriously.
Rogan's entire model of health and medicine, not only his model of Covid-19, consistently gives a central role to maintaining overall good health. People should devote a lot of time and effort to staying in good health. They should eat right, exercise and stay active, maintain a healthy weight, take various supplements and so on. This is especially important for Covid-19, whose severity seems highly responsive to how healthy someone is, with large risk factors for many comorbidities, although not as large as age.
From Rogan's perspective, one option against Covid-19 is vaccination, but another option is to get or stay healthy. As Gupta points out multiple times, this is a clear 'why not both' situation, except that there's complete silence around helping people get healthy, even though it's a free action. It's worth getting and staying healthy anyway, why not use Covid-19 as an additional reason to get people started on good habits? And if you're unwilling to help people get healthy, why should we listen to you about this vaccine? Which is a fair point, you mostly shouldn't listen to these people in the sense that their claims are not in general especially strong evidence. It's that in this case, it's very clear for multiple distinct reasons that they are right.
Minute 88 is when they get into Ivermectin. Joe Rogan is not happy that he was described as taking 'horse dewormer.' As he points out, this is very much a human medicine, regardless of how some people are choosing to acquire it, and those people are not him: "Why would they lie and call it horse dewormer? I can afford people medicine, motherf***er, this is rediculous. It's just a lie. Isn't a lie like that dangerous? When you know that they know they're lying?"
So then he played the clip, and the CNN statement wasn't lying, exactly. It was technically correct, which as we all know is the best kind of correct - it said that he said he had taken several drugs including Ivermectin. Then it said that it was used to treat livestock, and that the FDA had warned against using it to treat Covid. Now all of those statements are technically correct - the FDA definitely warned about it and doesn't want you doing that, and among other things Ivermectin is used to treat livestock, although it is also often used for humans and Rogan had a doctor's prescription.
Now, in context, does that give a distinctly false impression to viewers? Yes. Are they doing that totally on purpose in order to cause that false impression? Absolutely. Is it lying? Well, it's a corner case, and technically I guess I'm going with no? Gupta's response is that they shouldn't have done it, but he's not willing to call it a 'lie' and is denying that there was glee involved. (Morgan Freeman narrator's voice: Oh, there was glee involved.)
Rogan asks, if they're lying about this, what do we think about what they're saying about Russia, or any other news story? And my answer would be that this is the right question, and that it's the same thing. They're (at least mostly) going to strive to be technically correct or at least not technically wrong, and they're going to frame a narrative based on what they want the viewer to think, and as a viewer you should know that and act accordingly.
Later on comes the part that should be getting more attention. In minute 125, Rogan explains that he almost got vaccinated, but didn't, and what happened.
The UFC got some doses and offered one to Rogan. He accepted.
Logistical issues. Rogan had to go to a secondary location to get it, his schedule didn't allow it, had to be somewhere else, planned to take care of it in two weeks.
During the two week period, Johnson & Johnson got pulled.
Also, his friend had a stroke and Rogan connected this to the vaccination, whether or not this actually happened.
Rogan goes "holy ****" and gets concerned.
Another of Rogan's friends has what looks like a reaction to the vaccine, gets bedridden for 11 days. And another guy from ju-jitsu that he knows had what looked like another issue, having a heart attack and two strokes.
A bunch of these reactions don't get submitted to the official side effects register.
Rogan concludes that side effects are likely to be underreported.
Rogan goes down a rabbit hole of research, finds opinions on shape of Earth differ.
Rogan doesn't get vaccinated, thinking he's healthy and he'll be fine.
Rogan gets Covid-19, his family presumably gets it from him (Minute 135), it isn't fun, but he gets over it and he's fine, and they get over it and they're fine.
Rogan tells these stories to millions of people, teaching the controversy, but still advocating vaccination for the vulnerable and for most adults, but is highly skeptical about vaccinating kids and thinks people should be free to choose.
Gupta tries to get Rogan to get vaccinated despite having been infected, while admitting Rogan has strong immunity already, which goes nowhere.
Rogan says repeatedly that he's not a professional, that you shouldn't take his advice, to listen to professionals, that he is just some guy with no filter. But this includes naming The Man We Don't Talk About as an expert.
But of course, he knows that saying 'my advice is not to take my advice' mostly never works.
The first thing he mentions in his story, the start of this reversal, is when they pulled Johnson & Johnson to 'maintain credibility.' This is a concrete example of the harm done by that action. It contributed directly to Rogan not being vaccinated. That speaks to how many other people had similar reactions, and also Rogan then shared his thoughts with millions of people, some of whom doubtless therefore did not get vaccinated.
The bulk of his points were about side effects in particular people that Rogan knew. From his perspective, the side effects looked very much like they were being severely underreported, especially since these particular side effect cases weren't reported. How could he not think this? From his epistemic position, he'd be crazy not to think this. He has quite a lot of friends and people who would count as part of the reference class that he'd observe here, and the timing of some of what looked like side effects could easily have been a coincidence rather than causal, but still, he saw what looked like three of these serious cases in rapid succession, in people who seemed otherwise healthy. Meanwhile, similar risks are being used as a reason to pull one of the vaccines.
He responded to all this quite strong (from his position) Bayesian evidence, combined with his good health and his model that Covid-19 was unlikely to be that bad for him, did a bunch of research that under these circumstances put him in contact with a bunch of Covid-19 vaccine skeptics, and declined the vaccine.
I strongly feel he made the wrong decision, took an unnecessary risk and would have been much better off getting vaccinated. But mostly the heuristics and logic used here seem better than blindly trusting a bunch of experts. Sometimes that gets you the wrong answer, but so does trusting the experts.
Given he continues to mostly advocate for vaccination of adults, and seems to have come around to believing the generally accepted vaccine safety profile, that both speaks highly to his epistemic process used since he was exposed to a bunch of his good friends who were peddling other conclusions rather forcefully, and also makes me think I know here he did make his mistake.
My guess (and I could be wrong, he didn't make this explicit) is that the decision ultimately came down in large part to blameworthiness in Rogan's mind. In the frame most of us have, vaccines are safe and effective, so if you get Covid-19 without being vaccinated that's on you, and if you have one of the exceedingly rare serious side effects (many or more likely most of which are a coincidence anyway) then that's not on you. The incidents with his friends reversed this for him, combined with thinking that outcomes from Covid-19 are tied to health. In his mind, if Covid-19 got him, that was his fault for being unhealthy. If the vaccine got him, that would be on him for seeing these things happening to his friends, and taking it anyway. So he did what most people do most of the time, especially when he saw the decision as otherwise only a small mistake, and avoided what he thought of as blame, and did what he could feel good about doing. And of course, the decision was in many ways on brand. But the undercurrent I sense is that yeah, he knew it was objectively a mistake in pure health terms, but not a huge one, so he just did it anyway.
One thing that reinforces this is that Rogan comes back repeatedly to individual examples of people, especially young healthy people, who had problems that happened after getting vaccinated, and says that it was overwhelmingly likely that that particular person would have been fine had they gotten Covid-19. Which is true, but it was also far more overwhelmingly likely that they would not have had the problem they had if they got vaccinated. If you trade one risk for another smaller risk, sometimes the smaller risk happens to you. That's what a risk is. But if you instinctively use forms of Asymmetric Justice, what matters is that this particular person is now worse off, even if on net people who took such actions are better off, therefore blame.
That of course is an aspect of vaccines being held to a different burden of proof. In his mind and many others, they're unsafe until proven safe, and that includes long term data, and the prior on 'artificial thing we made to do this' in some sense is stronger than any of our 'this is how this mechanically works or when we'd see the effects show up' style arguments could hope to be. Whereas he puts his assortment of other stuff into a different bucket, with a different burden and a radically different prior. Which isn't a crazy thing to do, from his perspective, although I don't see it as mapping to the territory.
They finish up with a discussion about the lab leak hypothesis, and they certainly don't make me less suspicious about what happened on that front.
That's a giant amount written about a three hour podcast I listened to (mostly at 1.5x speed) so you didn't have to. It was less infuriating than I expected, and contained better thinking, and is to be hailed for its overall good faith. We need to be in a place where such actions and exploration are a positive thing, even when they make mistakes and even when they end up causing people to be pushed towards worse decisions in many cases.
In Other News
Bioethicists have profoundly inverted ethics.
No, seriously, imagine speaking this sentence out loud. Say, to whoever is listening, "We don't ask people to sacrifice themselves for the good of society."
Then realize that bioethicists are far more insane than that, because what they're actually saying is, "We don't allow people to sacrifice of themselves, or take risks, for the good of society."
Over half of respondents to this survey report being lonely, with only a small effect from identifying as autistic. We had a crisis of loneliness before and Covid-19 had to have made it much worse, and at this point I worry about such effects far more than Covid-19.
Not Covid, but a good politician never wastes a crisis, so here's a look into the child care portion of the Build Back Better bill. I solved for the equilibrium, and I doubt anyone's going to like it.
As the weeks continue to blend into one another, it seems like it's getting to be time to formally write up my lessons from the pandemic. I don't know when I'll have the bandwidth, but I'm authorizing people to periodically ask why I haven't finished that yet.