When my oldest was a small boy, he took it into his head that not fastening our seat belts would cause us to get into an accident. He had clearly picked up associations we had made between the concepts of accident and seat-belt. The distinction between "in case we get into an accident" and "because we'll get into an accident" is not easy when you're three or four. No real harm done at the time. He fastened his seat belt willingly and we didn't think he'd graduate from highschool with that misapprehension.
There are a lot of theories and descriptions of the various ways people come to think they know things and what they trust. They are not mutually exclusive. We all trust our own experience while attaching some importance to what we hear happens to others. We all have authorities we trust, but also trust our own ideas and reasoning. We also have opinions about what other people trust in ways of knowing. We particularly dislike it when those benighted other folks trust the wrong authorities or exhibit poor reasoning. We also mix categories. In the long sorry state of CoVid commentary, we have had lots of complaints about people trusting "experts," always in sneer quotes, yet our solution is nearly always that they instead believe...different experts. Ones that we like better.
The other suggestions are usually worse. Too many people trust only what their personal experience is, believing this is somehow representative of the real world, and ignoring what people smarter than they are are saying. There are half dozen over at Maggie's - which has a wide readership and thus provides a forum where knuckleheads can have their say, which is very American - and even one at Grim's who have claimed "Y'know how I know this virus is all a hoax? Because I don't know a single person who's had it." My first temptation is to say "Dude, don't help any kids with their science homework, okay?" Yet it is true that we all are affected by what drifts by our dock on the river. Glenn Reynolds made the interesting observation that this may operate like AIDS in reverse. No one took that disease seriously until they knew someone who died from it, and then it suddenly went to the top of the list of problems the country needed to solve. He mentioned that he had C19, it wasn't a bad case, and most people he knew about didn't have bad cases, and thought that many people were going to conclude that the disease wasn't that big a deal. I think his prediction is likely true. I disliked his tone that this was a generally accurate, good conclusion to come to, though he refrained from going that far.
This gave me an immediate new example to draw from, however. I had many patients (and two coworkers) who eventually died of AIDS in the 1980s, and heard of more from my theater days in the 70s, even though I think I knew of none from any of my social circles by then. Most of my friends knew no one who had the illness. I knew that both their personal experience and their personal experience were not the whole story. The same is happening now. College professors are not likely to have a representative sample of the danger of the disease, they will have an underestimate, unless there is some other factor in their lives, such as a family member in assisted living. Health care workers are likely to have the opposite bias in their sample. They will know a disproportionate number of people who have the illness, and a disproportionate number who die from it. Their prism is slanted such that it skews to the other end of the spectrum. I will note additionally that when you know people who died, it just naturally has a large impact. In strictly logical terms, perhaps an excessive impact, but...death is an important consequence, y'know? Not one that human beings are supposed to be dismissing too easily.
There are other groups which are going to have more exposure to Covid deaths than others. Pastors and people who are on prayer chains do not only hear about their friends and immediate circle, but the relatives of their friends and their frightening circumstances. That is a biased sample, to be sure, but it is not pretend. I'm not sure what further groups would have too many representatives of the dead and which too few. Relatedly, those whose circles of exposure are those who are not in much danger even if they get the illness seem to focus on their own personal risk and their insistence that they should have the freedom to make that assessment, while those who know many who are at the mercy of the safety habits of others are more likely to favor controls to limit the damage of the poor decisions of those others. Neither is an unnatural bias, but you should know which tendency your life circumstances tilt toward.
I write all this not to tell you which experts you should choose. Others can advise you better than I on that. I am overconfident that I can sort through which experts to trust, but that needn't affect you. However, I am qualified to ask you to look carefully at what your sample and your experience is. What is the age group of the people you interact with most? What would you predict their level of danger would be in a general situation if they lived somewhere else? If they have relatives or friends who get injured or sick, is your situation such that they would tell you, or are you sheltered from that knowledge?
And next, how much does this personal bias, which is a natural but unscientific influence your assessments. There's no quiz on this. No one is grading your answers except yourself.
So, epistemology is interesting to me philosophically: how can you know something, and what does it mean to know? COVID is, however, a subject with which everyone is currently emotionally involved; it's hard to have fully rational conversations about things you fear or love, hate or admire.
ReplyDeleteSo I'd like to address your points by talking first about something else entirely: vampires.
There is a way of knowing (and what we sometimes call second-order knowing, i.e., 'knowing that you know' as well as 'knowing') that vampires do not exist. It's a mathematical proof. If vampires existed and needed to feed on someone every night, and that person became a vampire, then the next day there would be two vampires feeding. The day after that, however, there would be four; and then sixteen; and so the number would increase. By geometric progression, the entire human race would be vampires in about two years.
I read a version of this proof when I was a child, written up in a book for children, which was both a way of showing us that we didn't need to worry about vampire stories and also teaching us about math. I see that some physicists felt inclined to write it up formally just a few years ago.
The case is actually worse with exponential growth, which is what we were told to expect with the virus. When you hear someone say, "This is a hoax because I don't know anyone who has had it," you hear them say two things that are unlikely: first, that they're being lied to by all the experts, and second, that their experience locally should line up to the experience globally.
I don't know what 'hoax' means in various contexts, but I do know -- and know that I know -- that exponential growth can't be right. The proof is the vampire proof, but shifted to exponential growth. It's been long enough now that, if exponential growth claims were true, not only would I know someone who had it, everyone I know would have had it. One case doubling every three days would give you a billion at 90 days; by this point, it's far more than humans exist.
So we know, then, that at least one major claim was badly wrong. The guy who is objecting that what he's being told can't be true because he still doesn't know anyone who's had it was foolish 30-45 days in, but he's got a point given the status of the claim at 9 months in.
Now, epistemology: Mathematical knowledge is a form of knowledge that we can be much more certain about than most, because it admits of actual proofs (like the vampire proof). It's not extrapolation from limited experience, like most human knowledge, and it's not a mere appeal to authority, which can be fallacious. Like a logical proof, a mathematical proof is certain to transfer the truth of the assumptions to the conclusions assuming you follow all the steps correctly. So, if you can show that the math was done correctly, you can show that the conclusion is as true as the initial assumptions.
Usually we do that to show that we know the conclusion is true, because the assumptions were true and the steps were valid. You can work back, though: if you can show that the conclusion is false, then either a step went wrong or else (at least) one of the assumptions was false.
In March, I took those early experts seriously when they talked about exponential growth. I urged the shutdown of our schools and devised a program for school lunches to be delivered by schoolbus without human contact, in case this was an exponentially-spreading disease with a potentially horrible fatality rate.
Now, though, enough time has passed that we know it isn't that. The guy who says "I still don't know anyone who's had it" also, by virtue of the math, has a much better proof than he did in June or April.
Exponential equations can be affected by other factors, especially early on. x²-9x-2 is going to take a while to get off the ground before that exponent takes over. It was on that basis we were told that the disease would recede under our initial efforts but have a likely resurgence in late summer. It was actually later than that, but it came.
ReplyDeleteNow, what were they thinking might be the factors that would give us a false pause, that is the "-9x" in the equation? I don't know. I can't say if was sensible on their part or not. Other than the fact that people have contact with more than one other person, sick or well, I don't know why they called it exponential rather than geometric to begin with. But from October 1 to now the number of new cases looks like a steep curve. Deaths are also up, but don't show that rate of increase; but we know more about treating people, and a lot of the population over 90 isn't catching it because their number is now significantly reduced.
Similarly, WRT vampires, if they only need to feed once a year they could hang on longer without running out of fresh meat. That would also be subject to the same doubling effect, and that would go off the charts and be larger than the population of the world eventually as well. Even if they started as late as Bram Stoker's time, it would include all of us by now.
ReplyDeleteOTOH, if they only need to feed once every hundred years they might have been around for a thousand without us knowing it.
Sure: vampires might not feed that often; or they might not turn you into a monster at the first timey they fed. Maybe it requires an additional ritual. People like vampire stories for some reason, and want to continue telling them, so they keep coming up with new ideas about how to make the story more plausible.
ReplyDeleteBut they don't keep telling the old folk story. It's no longer a matter of suspension of disbelief, because it's no longer a matter of belief: we now know that the story wasn't true, and we know that we know it, and so we can't really entertain it anymore. That's where we are, I think, with the COVID issue too: you can tell me a new kind of story, if you can provide reasons for me to think it's plausible, but you can't keep telling me the old story.
A lot of this is also caught up in the problem of induction, which is the problem you're describing as generalizing from local experience. If you're learning from experience, you could always just not have run into the counter-example yet. (E.g., 'every whole number is prime' works great until you get a few steps down the line.) That's a big problem for strict logic (as well as for science when it operates from induction rather than from the process of elimination of hypotheses that is more strictly the scientific method).
The way strict logic gets around this feature of induction is by claiming that induction is a valid way to know if it can be done on any random member of the set you're describing. Now, that's a problem itself, because usually in reality we don't know everything we need to know about the set (e.g., the set of people who might get COVID), so we can't really appeal to this as a way of making the induction valid. Strict logicians thus often end up appealing to mathematical entities because we do know enough about them to make these kinds of inductive claims. That's not helpful, really, because all it shows us is that induction can work well with mathematical objects, which is really a claim about math more than about logic.
But the inductive nature of the claim does work in cases where the local knowledge and the global knowledge converge, as in the case of the guy who doesn't know anyone who's had the disease. At step 1, that's a useless claim; but at step 1+n, where the whole population is suddenly supposed to have been infected, it's useful. Now, you really could pull "any individual A" out of the set, and show that they ought to know someone (indeed, it should be everyone they know). So now you can prove by induction, because what you're claiming about A should hold for any, and indeed every, member of the set.
That's why I don't argue with people making claims of the sort you're describing there; at some point (specifically, the point any local and the global conditions should coincide), what was once a stupid claim becomes a valid proof by induction. It's a legitimate claim to knowledge, even if the only thing you can say you know for sure is that the original story was wrong. "What they've been telling us wasn't true" is a valid claim.
So what does the truth look like? That's a lot harder.
My county average age is very high, and my neighborhood even more so. On the other hand, we're a small county with a low population concentration. We've had 22 deaths out of about 30,000 people. Something under 600 reported cases, but presumably many more unofficial and unreported. The people who died were mostly rather elderly and mostly suffering from the usual pre-existing conditions. One young resident had an awful, awful time in the hospital for months and just barely pulled through.
ReplyDeleteI've got quite a handful of neighbors and friends now in their late 60s and 70s who've had it and recovered, which of course reflects the odds suggested by the national statistics.
WRT exponential change, of course we know that exp(ct) can shrink with time if c<0, but set that aside and just consider c>0. (We'll see if that html works.)
ReplyDeleteThe exponential growth model assumes a uniform probability of interaction.
For example, in radioactive decay, the probability that one nucleus decays is independent of the probability that any of the other do, and of its history. If the probability of a nucleus decaying within a year is 1/2, then for a large ensemble of such nuclei, after a year, about half of them will have decayed. Since the probability is independent of history, the same is true for the next year--half of the remaining nuclei decay. Presto--exponential decay, from uniformity.
What keeps growth from being purely exponential are factors of non-uniformity like isolation, prior interaction, and so on.
To keep with the vampire theme, if the vampire has to bite someone every night, and there are only two on the island, the second night there are two vampires, but every night thereafter they bite each other and there remain but two. Sooner or later the exponential growth has to stop. In this example it stops quickly, but once there are more vampires than people, the vampires will be more likely to bite each other, slowing the growth rate.
I have close contact with members of my family, but much less close contact with people at the hardware store--so the probability of transmission isn't the same.
Suppose there are two other island residents with the vampire. One gets bitten the first night, but the other island resident likes garlic pizza, and has a month's supply. Tribalism matters: if two adjacent groups don't interact...
Anyhow, to return to the real question. If I assume that there is such a thing as Wuhan 2019A, and that there are tests of some unknown accuracy for it, I'm still having to trust other people about numbers. If I'm told that Wisconsin has 5.86M people and has had 486K cases of the disease, overall that's about 8%. But that doesn't tell me about my exposure risk, because my environment isn't the average. Breaking the Wisconsin numbers down to something that speaks to my situation isn't easy. (The most likely transmission is via our children, who have non-public-facing jobs.)
If I just use that 8% number, and I know about 150 people, I expect to have seen about a dozen cases--which oddly enough is about the number I do know personally. (As I've said, 9 had "bad flu" and 3 were sick for 10-12 weeks--including one of my daughters, so if there's a genetic bit to susceptibility either I or my wife is at risk of really bad illness)
Obviously 12 is a pretty low number to try to base estimations on. 0 would have been a reasonable number to find: Not likely, but not terribly unlikely either.
Suppose I know 0, AND all my acquaintances know 0. There's some overlap there, so it isn't going to be 150*150, but more like 150*50, but 7500 is still a big enough pool to say "there's not much risk here." Either transmissibility is low to us (isolated, or maybe we're already immune?), or we didn't get very sick and nobody noticed, or maybe their numbers are goobered up.
Grim: I don't know what 'hoax' means in various contexts, but I do know -- and know that I know -- that exponential growth can't be right. The proof is the vampire proof, but shifted to exponential growth.
ReplyDeleteThat is incorrect. It depends entirely on the exponent. With no social measures, the reproduction number of COVID-19 is estimated to be about 2.5 or so. But people will naturally take measures to slow the spread. In the U.S., the reproduction number now varies from a bit more than one to a bit less than one, which itself varies among different sub-populations. The result is the ebbing and flowing of the disease through the population. Even with an exponent just over one, the number of cases can rise very rapidly.
Without counter-measures, the virus may have already burned itself out, at the cost of 2-3 million lives just in the U.S. Due to the poor response, the U.S. is swimming in contagion, so even those who are careful are at risk.
See reproduction number here:
https://covid19-projections.com/
Assistant Village Idiot: I write all this not to tell you which experts you should choose. Others can advise you better than I on that. I am overconfident that I can sort through which experts to trust, but that needn't affect you.
ReplyDeleteExcellent post, by the way.
When outside your field of expertise, nearly everyone relies on consensus of expert opinion. (Even within a field, experts often rely on other experts.) Fields of expertise will intersect with other fields, which helps define their validity. Of course, one can often test the findings of science in part. For instance, you could collect a few fossils from your local area to see if they match what geologists say, or you can repeat historical experiments such as Newton’s experiments with prisms or Darwin’s observations of earthworms.
https://scienceblogs.com/evolvingthoughts/2007/01/12/in-the-mud-1
"Fields of expertise will intersect with other fields..." This is true, and important. It does help with the sorting out. It is possible that someone from far outside a field will offer a new and important insight, but it is rare, and usually by application of analogy from their own field rather than understanding the basic principles of another discipline. An archaeologist might not know much about principles of linguistics, but may through her research be able to suggest that the cause of a language replacement comes from multiple sources, or even flows in the other direction.
ReplyDeleteThat is incorrect. It depends entirely on the exponent. With no social measures...
ReplyDeleteIt is true that, if you are constantly changing the exponent, you can map a range of geometric figures. But it is not true that you can draw a line that sometimes goes up, and sometimes goes down, and sometimes is flat, etc., and describe it as "exponential growth." You're just using an exponential function with a constantly fluctuating term to draw the figure.
Grim,
ReplyDeleteGrowth can be exponential with an exponent just greater than one, and still meet the condition you described above.
In any case, no one ever said that exponential growth of the coronavirus, or rabbits for that matter, is exactly like the simple mathematical curve. Exponential growth is the basic model of organic reproduction, but all exponential growths are limited in nature. So, in the case of COVID-19, the epidemic will grow exponentially — unless or until people socially distance, or the epidemic approaches herd immunity. With rabbits, the limit is food and habitat. Nonetheless, the growth rate is expressed as an exponent, a.k.a. the reproduction number.
You can draw a line using geometric functions that you change constantly to fit the curve or lack thereof you’d like too. Math can be used to construct all sorts of imagery; not just graphs but virtual worlds.
ReplyDeleteNevertheless, phrases like “linear growth,” “geometric growth,” and “exponential growth” are not equivalent to “any shape we could possibly produce with sufficiently shifting terms.” You could draw pretty much anything.
Even linear equations can create sophisticated shapes; vector scan graphics were built on them. Linear growth, however, doesn’t look like a flying saucer.
So if the claim is “of course it’s exponential because an exponential function could describe it if we change the terms constantly so the graph reflects the facts we observed after the fact,” we’re just not talking about the same thing.
Zachriel, you said "Without counter-measures, the virus may have already burned itself out, at the cost of 2-3 million lives just in the U.S."
ReplyDeleteIf you use 80% as the percent who need to be infected for community immunity (estimates range from 60-90%), the CDC estimated Infected Fatality Rate of 0.46%, and a 327 million population, you have an outside death count of 1.2 million, much less than 2-3 million.
Zach is correct here. I am partly at fault for using the simple mathematical graph early last year to show how quickly things can get out of control. The simple graphs usually show what exponential growth would be like if the exponent is 2, or 3. Yet in many real-world cases, the exponent is near 1, and does fluctuate according to conditions. With an exponent of 1.1, the numbers will not appear to rise all that quickly for a while, then gain steam and grow quickly. It is something like "the miracle of compound interest" they always tell you about in investing or saving. If the exponent is 0.9, things will stay about the same for a little bit, then drop to zero.
ReplyDeleteI am not the only one to write imprecisely about "exponential growth" and use such graphs. I'm sure if you google images of exponential graphs you will see lots of lines that head north quickly, because in teaching or explaining the concept, that gets the point across best. But it's not the only way such things can look.
James mentioned some limiting factors that keep the exponent lower, such as a closed population, or the fact that the human contacts of each person in a population have some overlap. Yet over time, anything over 1.0 can get large quickly if it is not interrupted. Zach is not describing any convenient retrofitting to make a graph look like what we want it to say. All contagion follows an exponential track, the only question being the size of the exponent. In the case of C19, the long period before one shows symptoms and the long period of contagion are big problems WRT to spread. They drive the exponent up, as every patient has the potential to infect more others. Since last February, the exponent has been near 1.1 but rises and falls because of limiting factors. Saturation will be the eventual limiting factor as the disease will have no new places to go.
Graphs can rise and fall for lots of reasons. They don't have to be exponential in their underlying nature to do that. But when each point on the line influences the next point, then an exponential function is likely. Contagion is a situation in which today's numbers drive tomorrows very strongly.
When I looked at the graphs last May and even mid-June I could think "those aren't dangerous curves. The exponent must be less than 1.0. This is going to go to zero." But as things went into a second rise, worse than the first, I got worried. Then that subsided, but a third wave, much worse than the numbers we thought were bad in April, started to arise. If one scrolls down to look at the Daily New Cases at https://www.worldometers.info/coronavirus/country/us/, one sees the rise, fall, rise, fall, rise. (Ignore the spikes that occur with regularity every week. they are artefacts of how states report their data.) When I look at that graph now I see clearly what I was told but did not fully accept in April and say to myself "Gee, that looks like some sort of exponential function with the exponent up and down near 1.1. Crap. That's not going to stop until something stops it." For deaths, one of the somethings will be running out of old people who haven't been exposed, because a large percentage of them got it and either recovered or died.
@ Brad - I also thought that seemed high, though I didn't do the arithmetic. It's upwards of a million, though, which is a big number.
ReplyDeleteThe COVID corollary to Godwin's Law
ReplyDeleteThe longer the thread discussing COVID, the more likely it is that both 'we have x deaths which is fewer than (big scary prediction from early 2020) because social distancing/masks/lockdowns' and 'we have x deaths because social distancing/masks/lockdowns were not implemented' will appear in the comments.
It does seem to be a stalemate, dead-horse discussion. But by March 1st we will have had a full year of unprecedented interventions and still have half a million deaths, so projecting we would have had double that or even more without precautions doesn't seem unwarranted.
ReplyDeleteI don't know if I'm just misunderstanding everyone's comments today, but there seems to be some confusion here about what exponential growth means. To use your example, AVI, x^2-9x-2 isn't an exponential equation. It's quadratic. Exponential growth is gong to be of the form:
ReplyDeleteP(t) = P(0)*e^(r*t).
Exponential growth means the exponent changes, not the base. So, I'm not sure why both Zachriel and AVI have said that you can get exponential growth with an exponent close to one. You'll have a point on your graph where your independent variable is close to one (t in my example), but you're not going to be there for long. Am I just misunderstanding what you're both saying?
Deevs: Exponential growth means the exponent changes, not the base.
ReplyDeleteThe exponent is time — which increases.
Exponential growth for reproduction is of the form p = p0 * r^t, where p is the population, p0 is the initial population, r is the growth rate, and t is time. For r > 1, the population will increase exponentially over time.
The pedantic question is whether to treat the equation as an exponential when r itself varies over time. Consider a couple of simple Newtonian examples.
"A body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force." In nature, no body will ever trace a straight line forever, but the equation of linear motion holds over finite intervals.
"a = F/m". We make our pretty plot on a graph. Then someone asks, "But what if the mass decreases over time?" All of a sudden our pretty plot doesn't apply. But the base equation still works over intervals, and we might use the calculus to make a more appropriate plot.
COVID will grow at a given exponential rate unless and until "acted upon by other forces." These forces could include natural or artificial immunity, or if social distancing decreases the r value. But we can still calculate the expected increase or decrease in the population by applying the changing growth rate using the exponential equation over intervals.
You are correct that I should not have used a quadratic. My error, I won't explain why, as it is too boring and will lead us into further confusion. You have not misunderstood me, and you seem to understand this better than I. I am working from memory of long-unused college math. However, I believe that in the overall concept, if there is an exponent of 1.1, the number of patients can grow quickly, but if steps are taken to depress contagion, that is the same as reducing the the exponent. But such depression might not be easy, and the exponent could rise again and the graph resume its upward climb. Please feel free to explain it better, especially WRT disease.
ReplyDeleteChristopher B: The longer the thread discussing COVID, the more likely it is that both 'we have x deaths which is fewer than (big scary prediction from early 2020) because social distancing/masks/lockdowns' and 'we have x deaths because social distancing/masks/lockdowns were not implemented' will appear in the comments.
ReplyDeleteHeh. Funny. The crux of the riddle is that social distancing measures are not black and white. When there are outbreaks, people tend to be more socially distanced. When the outbreaks wane, people tend to loosen up. The result is an ebb and flow of contagion. Of course, if measures were stringently applied and applied early, then much of the problem could have been avoided, as it has been in much of Asia.
Grim: the CDC estimated Infected Fatality Rate of 0.46%, and a 327 million population, you have an outside death count of 1.2 million, much less than 2-3 million.
ReplyDeleteThe infection fatality rate is still not known with precision. However, it is believed to have decreased over time due to better treatments.
Even granting the 0.46% figure, if the pandemic had been allowed to have spread unimpeded, then millions would have been in need of hospitalization in just a few months. While new treatments may have been introduced faster, the fact that hospitals were being overrun would have meant a higher case fatality rate. Not to mention the preventable suffering of millions of people.
On the other hand, people aren't without their own volition. People isolate even when the government is inept, or in the case of the U.S., undermining its own medical recommendations. The U.S. is subject to wide community spread, so even people who are careful are at risk.
Yes. The vampire model isn't actually a very good one here, because vampires are "contagious" forever, while disease sufferers aren't. The number of sick doesn't increase without limit because most of the sick recover, and stop being contagious.
ReplyDeleteI hesitate to guess how high or low the death toll might have been under different circumstances, without some careful looking at how the death toll did in fact vary in different places that tried different methods to curb transmission. Otherwise we're at risk of the kind of reasoning that led doctors to let blood from their patients, on the theory that it might not have improved their condition, but it surely prevented them from getting even worse. The other possibility, without solid data, is that they might have recovered faster without the blood-letting, or it might have had no noticeable effect. That's why we try to do controlled experiments, to get out of that kind of intuitive assumption mode, which often isn't much more reliable than superstition.
ReplyDeleteWhat's more, there's not much use speculating about how much worse things would have been without lockdowns unless we take careful account of how many bad things were added to the mix precisely by the lockdowns. We're in grave danger of merely waving our arms in various directions.
The only thing I'm confident of is that the disease exists and does kill some people, especially the elderly and ill. What makes it better or worse? I don't think we really know, or at least not without enough certainty to warrant browbeating each other over curative strategies.
Okay, thanks for the replies, and I now understand what AVI and Zachriel are getting at. It's a multi-variable problem. Time, of course, but whatever variables are affecting the that transmission rate (e.g., mask wearing, social distancing, etc.).
ReplyDeleteThat said, Zachriel, when you wrote, "For r > 1, the population will increase exponentially over time." I think you meant "For r > 0."
Speaking of social distancing and masks, my wife and I just spent the weekend in Preston, Idaho. That's the small town where Napoleon Dynamite was filmed all those years ago, so you may have seen parts of this place. Interestingly, mask wearing was non-existent at the stores and restaurants we visited with the exception of the staff. Now I want to go see what their Covid numbers look like, jump to conclusions, and assume Preston, ID is representative of everywhere else on the planet. Wait, what was this blog post about again?
texas99: I hesitate to guess how high or low the death toll might have been under different circumstances, without some careful looking at how the death toll did in fact vary in different places that tried different methods to curb transmission.
ReplyDeleteSure. Consider Norway and South Korea, or even China. Here's Wuhan at New Years celebrations. Consider that they were the epicenter of the initial outbreak, but have virtually no cases. When Qingdao had an outbreak, they tested every single person in the city within two weeks, 10 million people, while the U.S. struggled with testing. Still, everyone is wearing masks.
https://cdn.cnn.com/cnnnext/dam/assets/210101094624-wuhan-new-year-2021-p2-exlarge-169.jpg
We certainly can't expect the U.S. to meet the standards of a technological powerhouse like Vietnam, but the Americans might have done somewhat better than they did.
Country, deaths per million
Vietnam, 0.4
U.S., 1085
To be fair, most Asian societies have integrated social distancing measures into their cultural response to pandemics. Western cultures will probably do better next time.
Deevs: I think you meant "For r > 0."
We were using r for reproduction number, with r = 1 representing a flat distribution, consistent with the use here:
https://covid19-projections.com/
Oh, yeah. I see now. I misread the equation when I looked earlier. I saw e^rt instead of r^t. Gotcha.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteMy county & the adjoining one have nearly no COVID deaths, but it isn't that fact upon which I base my opinions. I just reason that any disease which has only killed one-tenth of one percent of the country's population isn't a pandemic. It would even make a pretty piss-poor epidemic.
ReplyDelete--Tennessee Budd
@ TB - thank you for changing from "Unknown" as we already have a regular using that sometimes.
ReplyDeleteZac: That guy you're answering in the last bit you @Grimmed is not me.
ReplyDeleteJames: The vampire analogy wasn't meant to be a model, least of all for viruses. It was meant to be an analogy to illuminate a curious fact about epistemology. An argument from ignorance can become an inductive proof under the right circumstances. Once you can establish that it's possible to make the shift, then you can ask the question about whether it's proper to claim that the shift can be made in the analog.
All analogies always break, so the question is where an analogy breaks and whether or not it breaks before it is useful. You raise a good point of disanalogy; but the time frame is also so far beyond what would have been needed for the original claim (which was, roughly, that numbers would double every three days) that I think it still holds.
Whatever this is, it isn't that; and the public debate would have gone rather differently if the claim had not been "exponential growth!" but "we're going to model change using exponential functions, which could mean that the graphs will show rapid growth, or no growth, or a decline, or really anything." We got to these massive interventions because experts pushed the line that it was going to be 'slow, then sudden,' leading to whole systems of healthcare being overwhelmed.
So we can say that didn't happen, and so we know the original models offered us were wrong. That doesn't tell us much about what right might be.
@ Grim - except wait. That (exponential growth) did happen. The NE cities had the first "sudden," but now the rest of the country has it. The growth curve of new cases for the US since October is enormous, way more than the spring. Florida, Texas, California, Georgia, and the Dakotas were bragging about how they had got it right and those other places were stupid and cowardly, but now over the last few months their numbers are worse.
ReplyDelete@AVI: That (exponential growth) did happen.... Florida, Texas, California, Georgia, and the Dakotas were bragging...
ReplyDeleteWell, now, the news I thought I heard out of the Dakotas today was that they'd seen cases drop dramatically -- and that even though one of them adopted a mask mandate etc., and the other one didn't.
https://www.postbulletin.com/newsmd/coronavirus/6824462-North-Dakota-got-a-mask-mandate-South-Dakota-didnt.-COVID-19-cases-have-plummeted-in-both
So that puts me back to "maybe we don't know what's going on, but it's not what we're told to expect," e.g., that adopting all these restrictions is necessary and/or sufficient for case rate drops.
But I'd rather discuss epistemology than COVID, for the same reason that I'm trying to discuss political philosophy more than politics at my place. It's both easier and better to try to get the principles right beforehand, than to argue about the particulars once you're in it.
Besides, I like you and enjoy your company, and I don't want to irritate you in your own house (as it were). So why argue the facts? They are what they're going to be, bot here and elsewhere: there aren't enough people either of us could persuade to change anything.
Grim: Well, now, the news I thought I heard out of the Dakotas today was that they'd seen cases drop dramatically -- and that even though one of them adopted a mask mandate etc., and the other one didn't.
ReplyDeleteMost people started wearing masks when they saw how dire the situation was becoming. A mandate's purpose is to preempt the spread, and not wait until the hospitals are overrun, and to maintain the countermeasure to minimize the threat of a resurgence, when people may be inclined to let their guard down.
The mandate in the North Dakota was late to preempt the spread. Your own article points out that North Dakota is recovering more quickly, though both have suffered dire hospitalization and death rates.
Grim: But I'd rather discuss epistemology than COVID
COVID-19 is an instance of how do we know what we know. A consensus of scientists can be wrong, but are much more likely to be right in their own field of expertise than people outside their field, especially if supported by findings in related fields.
The specific data supports the fact that COVID is an infectious disease spread through droplets that can expand in the human population exponentially, but for which people can take effective countermeasures. While all the details of the novel coronavirus weren't known a year ago, the basic principles of epidemiology have been borne out.
COVID-19 is an instance of how...
ReplyDeleteYes, an instance. One way we try to get to the universals is by generalizing from a set of particulars that instantiate the universals. The problem of trying to do so from a single or limited set of instances was covered before, in the discussion on the problems of induction. It's worse when the facts about the particular single instance are still being hotly debated, which is a good reason to shift to more solid ground.
A consensus of scientists can be wrong, but...
I hold with Popper's idea that science is really about the disproving of hypotheses (and not, then, the forming of consensus). One might say, in fact, that science advances precisely by undermining consensus.
There are two dangers to the scientific process from consensus. The first one is that, once you have accepted a consensus, you might stop doing the thing that is the real work of science, i.e., trying to disprove the hypothesis. Even if they continue to study the issue, the fact that the community to which they belong believes and approves of the hypothesis can create a kind of confirmation bias that may make the science less reliable.
The second problem is that people may take the consensus as an assumption for further study. As discussed above, even logical and mathematical arguments can only forward truths that are already contained in the assumptions. If the assumptions are false, what they will convey instead is the falsehood. The process is going to be convincing because it will look logical/mathematical/scientific, but the flaw in the assumptions will be reliably transmitted to the conclusions.
This can harden, of course, into doctrinaire oppression of attempts to question the consensus. That is less a problem in the specific case than in other cases, e.g., climate change, or whether the earth orbits the sun or vice versa. It does come up sometimes.
So I'd be wary of consensus in science per se.
But this is not really a discussion about who is more or less likely to be right on a particular technical question; it's about who should rule in matters of public policy. And at that point, you have left science behind and walked into philosophy. For now, regardless of who is right about the technical question, we have to balance that with all the other goods: liberty, constitutionality, economic goods, the harms of depression or suicide, etc. And on that, as Socrates and Protagoras agreed so long ago, all rightly have a say.
Grim: It's worse when the facts about the particular single instance are still being hotly debated, which is a good reason to shift to more solid ground.
ReplyDeleteActually, where knowledge is less than certain is the very heart of the scientific enterprise.
Grim: I hold with Popper's idea that science is really about the disproving of hypotheses
Not really, or Newtonian physics would have been *falsified* in the mid-19th century. Rather, the theory was modified to "Newtonian physics everywhere except for a small discrepancy in the perihelion precession of Mercury." That ad hoc generalization held until Einstein.
This brings up Azimov's Relativity of Wrong.
https://chem.tufts.edu/answersinscience/relativityofwrong.htm
All models are wrong, but some are wronger than others. Just because Newtonian physics is *wrong* doesn't mean it is as wrong as Aristotelian physics.
Grim: There are two dangers to the scientific process from consensus.
Consensus is only tangentially related to the scientific method. An argument to authority is just that, an argument. It's an inductive argument and can certainly be wrong. You can always address an argument to authority by reference to the evidence. Everyone relies on expert opinion. No one checks every possible fact before moving forward. You don't have to visit Paris to know it exists.
Grim: I hold with Popper's idea that science is really about the disproving of hypotheses
ReplyDeleteA bit more on this. When testing a claim, one attempts to devise an experiment or observation that cleaves the universe in two: one where the claim is true and one where the claim is false. In many cases, a single observation, a very narrow slice of the conceptual universe, can act as a falsification. But that is not always the case. The universe doesn't always cleave neatly along a narrow edge, but may have long, jagged and multifarious edges. The observation itself may be fraught with theoretical baggage. Still, scientific progress can be made, and the outlines of the universe can be slowly revealed.
All models are wrong, but some are wronger than others. Just because Newtonian physics is *wrong* doesn't mean it is as wrong as Aristotelian physics.
ReplyDeleteBut Aristotle was more right that Newton in some respects. Or don't you know? The biggest difference between Aristotle and Newton is whether or not the nature of the object matters to its being moved. For Aristotle, the nature of the thing was everything; earth falls below water because the nature of earth is to be at the center of things. Newton proved that the nature of the thing doesn't matter; a pound of iron or a pound of steel will have the same force with equal acceleration, F=ma.
But it turns out it does matter, just as Aristotle says, if the difference is a pound of iron or a pound of bird. The bird goes where it wants, and it wants to go where its nature impels it.
Maybe that's coherent with your claim that modern physics doesn't falsify Newton. You could argue that Newtonian physics and modern physics don't falsify Aristotle, who had a big point about conscious matter that our contemporary physics can't begin to handle. That's more or less what I'd say.
ReplyDelete