I’m going to come right out and say this is a great video, it shows people how to handle objects in a way that minimizes transmission of virus from surfaces. Apparently the controversial part though is where he dumps his oranges in soapy water? Are you kidding me? Everyone should be washing their produce at all times people! Have you ever heard of e-coli?

A frequently heard thing in the “anti” group is something along the lines of “there is zero evidence that xyz”, such as “there is zero evidence that food packaging is a significant source of infection” or “there is zero evidence that washing your food in soapy water is good for you” or whatever. This is typical “Null Hypothesis Significance Testing” type logic… Until we have collected a bunch of data rejecting the “null hypothesis” that “everything is just fine” then we should just “act as if everything is just fine”. Another way to put this is “until enough people have died, you shouldn’t take precautions to protect yourself”. Put that way it’s clearly UTTERLY irresponsible to “debunk” this video using that logic.

What we KNOW is that viruses are particles, essentially complex chemicals, which sit in droplets, which can be viable after floating in the air for 3 hours, which can settle out onto cardboard and be viable for 24 hours, and which can be viable for 3 days on plastic and steel. Guess what your groceries come in? Plastic bags, cardboard boxes, steel cans, plastic jars…

The assay used in the NIH study that established those timelines was to actually elute (wash) the virus off the surface and then infect cells in a dish with it and see how many were infected. It wasn’t just detecting the virus was there, but actually showing that it was active and viable.

So, there’s your evidence. There is *direct* laboratory evidence that the virus *can* be transmitted off the surfaces into cells and infect them.

Whether this is a significant source of infection or not is more or less irrelevant. How do you make a decision as to whether you should spend ~ 1hr every 2 weeks cleaning all your groceries?

Here’s the Bayesian Decision Theory:

Suppose two actions are possible: 1) do nothing, or 2) handle your groceries carefully and wash your fruits and vegetables in dish-soapy water

Costs of (1): probability p0 of getting infected from contaminated surface. We don’t know what p0 is, but leave it as a symbolic quantity for the moment. Let’s just use 0.5% chance of dying if you’re infected as the dominant problem, and a “statistical value of a life” as on the order of 10M dollars… so p0*.005*10000000 = 50000*p0

Cost of (2): probability of getting infected from contaminated surface reduced to p0/100000 perhaps, the same 0.5% chance of dying if you’re infected, plus 1 hr of cleaning time. So cost is 0.5*p0 + w*1 where w is an “hourly wage”. Suppose you are willing to work for a median type wage, 50k/yr. This is 25$/hr. So, what does the probability p0 need to be to “break even”? Ignoring negligible quantities 0.5*p0, we have 50000*p0 = 25 so p0 = .0005. If you think there’s something like a .0005 chance you could transmit virus from your grocery items to your face by “doing nothing” then YOU SHOULD BE CAREFUL and wash your items. For me, I’ll spend some time quarantining my groceries, and washing my produce… I also find it keeps the produce from spoiling and hence lasts longer in storage, so that should go into the “plus” side as well.

As to what to wash your produce with. I’m using sudsy water from dye and fragrance free dish soap (main ingredients: Water, Sodium Lauryl Sulfate…). I’m washing my fruit and veg, and then rinsing it thoroughly. The quantity of soap I’m ingesting is substantially the same as if I hand washed a glass, rinsed it, and then filled it with water and drank it… It’s substantially less than you get from brushing your teeth with a typical toothpaste. If you are afraid of washing your dishes with soap, or of brushing your teeth, then by all means don’t wash your fruit with soap either… For the rest of us, do a good job rinsing just like you’d rinse your glasses or bowls before putting food in them.

```
library(ggplot2)
t = seq(1,40)
realcases = 100*exp(t/4)
realincrement = diff(c(0,realcases))
testseekers = rnorm(NROW(realincrement),4,.25)*realincrement
maxtests = 20000
## now assume that you test *up to* 20k people. if more people are
## seeking tests, you test a random subset of the seekers
## getting a binomial count of positives for the given frequency
ntests = rep(0,NROW(t));
ntests[1] = 100;
confinc = rep(0,NROW(t));
confinc[1] = 100;
for(i in 2:(NROW(t)-1)){
if(testseekers[i] < maxtests){
confinc[i] = realincrement[i]
ntests[i] = testseekers[i]
}
else if(testseekers[i] > maxtests){
confinc[i] = min(realincrement[i],rbinom(1,maxtests,realincrement/testseekers))
ntests[i] = maxtests
}
}
cumconf = cumsum(confinc)
cumtests = cumsum(ntests)
ggplot(data.frame(t=t,conf=cumconf,nt=cumtests,real=realcases))+geom_line(aes(t,cumconf),color="blue") + geom_line(aes(t,nt),color="green")+ geom_line(aes(t,real),color="red") +coord_cartesian(xlim=c(0,35),ylim=c(0,400000));
ggplot(data.frame(t=t,conf=cumconf,nt=cumtests,real=realcases))+geom_line(aes(t,log(cumconf)),color="blue") + geom_line(aes(t,log(nt)),color="green")+ geom_line(aes(t,log(real)),color="red") +coord_cartesian(xlim=c(0,30),ylim=c(0,log(400000)));
```

]]>That’s a bad thing, because that represents the really “peaked” shape that overwhelms healthcare facilities. Many people died who otherwise might not have…

But if we make that slower, then also the peak occurs later, and the duration is longer, we might need, say 80 days of rather intense social distancing to make that happen. If we figure lockdowns are going to start now and build up through the next 10 days (it’s already something WaPo and The Atlantic and etc are saying)… And then we need 80 days after that… you’re talking 90 days which is 3 months, and puts us starting to return to work around June 1.

Now let’s talk food supply. Unlike China, this virus is spreading country-wide. It’s not contained to a particular place. So mobilizing the national guard to bring food from the midwest to WA because people in the midwest are ok… is not a possibility. How do we feed our country for 80 days without people having to be in contact with each other? We need food delivery systems.

Fortunately, as people get the virus and then recover, they should be immune for at least some period of time. Recovery to the point that they’re not shedding the virus is however probably 30 days? Just a guess, we’ll have to see with serology and PCR combo tests (to test that someone had the virus at some point, and doesn’t shed it now).

This doesn’t help us a lot. We have to do 90 days of relative isolation, and during the first 30 days people are getting the thing and then over the next 30 days those early people are recovering… by the time we hit 90 days, if you haven’t gotten it, you’re running pretty lean on food and things even if you’re well stocked now (and most people really aren’t). Obviously we’ll need to distribute food throughout the 90 days. This is going to require coordination from govt I believe, otherwise we’ll have sick people out there handling food… not good.

]]>Here’s the facts out of Italy: about 10% of tested positive cases require ICU ventilation. The death rate for people under age 65 is probably only ~ 1% **if you get the ventilators to the 10% needing ventilation**… If you overwhelm the hospitals, the death rate will go to ~10% which is on the order of magnitude of about 10x as bad as pandemic influenza in 1918.

The current trending idea is #flattenthecurve to describe to people HOW IMPORTANT it is to start *NOW* avoiding the spread of the disease. This avoidance of overloading the infrastructure is a core idea in Civil Engineering (my PhD is in CE).

Reducing the spread of the disease is not important just because fewer people will eventually get it (though that is probably true) but because the peak number of people who need ventilators and other intensive type care will be lower, so that fatality rates can stay low. If all the ICU beds are full, and 300 patients show up needing ICU today… all 300 patients will die. Since 10% of cases may need ventilators, it’s a serious situation.

Does social distancing, closing schools, etc work? Evidence out of 1918 says HELL YES: Unfortunately servers are getting swamped, so the best way for me to link you to this info is via twitter, who will probably stand up to the pounding.

So, what do you need to do? TODAY make plans to not be at work by the end of the week. Why? Because the virus is doubling the number of symptomatic verified cases outside china about every 2-4 days, let’s call it 3 days. And, btw it takes 5 days to onset of symptoms and for many people ~ 10 or 15 days before they say “hey I need to go to the hospital” (though for the elderly… it can be like 1hr after onset of fever). So, whatever’s going on in a hospital near you… it’s maybe what was the case 3 or 4 doubling periods ago, so today it’s on the order of ~ 10x worse than that. 10 days from now, it will be 100x worse already, but that will show up at the hospital about 20 days from now.

Early, proactive and significant reduction in interaction with other people WORKS and is one of the only things we can do. So we WILL be doing it. If we wait, we’ll be doing it AND have a massive tragedy. If we start now, we’ll be doing it but have less of a massive tragedy. The boulder is rolling down the hill, we can start walking off the path now, or get hit.

]]>I personally view it as inevitable that PUSD will decide to close schools. I don’t know what their timeline will be, but as these are typically committee decisions and there is risk either way (too early vs too late) I expect them to be delayed until the choice becomes obvious. On a doubling every 5 days trajectory, that probably means somewhere in the 10 to 15 to 20 days from now (which would mean somewhere around 800 to 3000 cases in the US). Spring break being Mar 30, I could imagine they’ll try to stay open til the 25th or so, and then not reopen after spring break. Though more pro-active decision making might mean closure in the next 5-10 days or so now that Pasadena has declared state of emergency. All this is more or less my own opinion based on reading the growth charts, and seeing the responses from large organizations canceling conferences and things.

Now, at what point is it actually logical to pull your kids from school? I’m going to do this just for a family with a stay at home parent, because the calculation for lost days of work is much harder and depends on a lot of factors. We can back of the envelope calculate this as follows: Costs of lost days of education is on the order of a couple hundred dollars a day. Let’s say $20/hr x 6hr/day = $120/day. If the stay at home parent can provide some of this education, the cost might drop to say $50/day…

Now, what’s the costs associated with sickness? Let’s just do the calculation of one parent gets seriously ill and dies. For a child in elementary school let’s just put this around say $10M.

Now, what’s the chance of death if you have definite exposure? It’ll be something like 100% chance of getting sick and 0.5% chance of death (assuming parent doesn’t have underlying conditions and isn’t unusually old)… So the expected cost is $10M * 0.005 = 50000… So by this logic, you should be willing to avoid that by pulling your kids from school about 1000 days early. Of course, it’s way too late to be 1000 days early, so basically you should pull your kids from school TODAY.

Now, suppose you have a job making $100k/yr, and you just get cut off from that job. That’s $385/day (which you don’t take home all of, but whatever). So if you add $50/day to that for educational loss, you should be willing to pull your kids about 115 days early. It’s also too late for that… So again, pull your kids TODAY.

Any way I back of the envelope this, it’s time to pull your kids from school… I don’t see a big enough flaw in all these calculations that would lead to waiting another 20 days.

]]>This is because all those questions are actually answerable to some extent (probabilistically at least) but there isn’t a group tasked with doing the analysis. It would be a good idea. Like, what the heck is the WHO doing if not at least staffing say 10 people who develop disease modeling software, and have several racks of computers to run MonteCarlo scenarios?

Well, whatever, if they were going to hire some people to do this stuff, what does the analysis look like? Here’s the general idea:

- Describe the factors that are associated with costs…
- Loss of Quality Adjusted Life Years (QALYs). This is the cost associate directly with “you don’t feel well for N days” all the way up to early death… The direct real-world cost of loss of healthy time.
- Loss of productivity: people who are sick don’t provide services to other people, they don’t produce goods, etc.
- Cost of treatment: people who are sick require other people to take care of them. They require medicines. Etc etc.

- Describe the factors associate with reduction of cost, or creation of benefits (or increasing costs above what they otherwise might be):
- Treatment of a person may shorten their sickness time.
- Treatment of a person may avoid them spreading the disease.
- Quarantine or Social Distancing may reduce spreading rate.
- Fast spreading rate may result in overwhelming local medical care, resulting in lack of care and much worse symptoms even death.

Once we put all these different factors into a model of the costs of any given scenario, we have the structure for a decision, but we still don’t know what the right values are for the parameters. For example, what’s the right cost of loss of worker time in India, how about in Vietnam… in Canada? How about the cost of health care, or the number of hospital beds etc? One needs to collect data, and estimate quantities. Some quantities will need to be estimated during the outbreak, like the growth rate of the number of cases in each country and the effect on this growth rate of different kinds of responses… Some numbers we will never know particularly accurately, but we will need to “borrow strength” from estimates across nearby regions, or similar cultures.

So, after specifying all that… we need to run a tremendous number of simulations, using the posterior distribution of the estimated quantities, predict the costs of different responses. From this we will get a variety of distributions over costs for different scenarios, and can calculate what seems to be the best response choice. If we make that choice, we continue to collect data and figure out what is going on, going forward, and continue to estimate what is the best choice… possibly changing the response through time as things become clearer whether they work. There’s some reason to think that that we should try different responses in different places, so as to collect information about what might work, and then switch people to the apparently most effective thing as time goes on.

]]>The result is that if you plot N vs time it is an exponential curve, or log(N) vs time is a line… which is exactly what you see when you click the “Logarithmic” graph of cases vs time in the Johns Hopkins data display. (actually it’s more complicated, you first see an alarmingly fast line, then it turns over and continues at a different slope, this probably reflects our response, which is delaying and slowing the spread). Eventually enough of the population is sick that there aren’t new people to infect, or everyone becomes extremely wary of being around sick people, and the curve stops growing exponentially. So the result is only exponential in the initial stages (described by mathematicians as “asymptotically for small times”).

Now, exponential growth is *really fast*. Most people can’t really “get” it. Think of it this way, if you start with a ruler that’s 1 foot long, and you double it every day. It takes you 30 days to get the moon, 39 days to get to the sun, and 57 days to get to Alpha Centauri. Since it’s 4 light years to Alpha Centauri, evidently somewhere in the first 40 days or so you substantially exceeded the speed of light extending your ruler…

Next let’s talk about bias in measurement. In general there are two ways to get a biased estimate of how many people have a disease. One is that a bunch of people get the disease, it’s not very bad, and they don’t get tested or counted. This biases you LOW. Obviously the very sick do get tested, and so they are the only ones counted. If there is variability in symptoms, and there always is, you are essentially *always* biased low looking at the “confirmed cases”. The other bias is when people stop testing for the disease and report that everyone with some broad set of symptoms probably had the disease. This biases you higher… It’s primarily an issue with rare diseases rather than epidemics.

In general how big this bias is is unknown for any given disease, but for coronavirus which is known to only cause “a bad cold” in many people, and often very mild symptoms in the young, it’ll be significantly biased low.

As of this morning (Mar 2 2020), there are 86 confirmed cases reported on Johns Hopkins data display, and 2 deaths mostly involving people with existing health complications. The largest outbreak in CA is in Santa Clara County (Silicon Valley) with 6 confirmed cases. How many actual cases are there in the US? We don’t know, but given the known bias that people with mild symptoms will never be tested, and the fact that there are circulating cases (people who got it from an unknown source) it would be silly to estimate less than say 2x the number of confirmed cases, and it would be reasonable to estimate perhaps up to 10x. So that means somewhere between around maybe 160 and 860 real cases in the US today. If you look at the “other locations” graph, you’ll see that in the month of February the reported cases doubled about 6 times, or doubling every 5 days or so. If there are say 200 actual cases in the US, how many will there be by saturday when the Southern California Linux Expo is supposed to take place? The answer is perhaps 400. How many reported cases would there be? Perhaps 400 * 86/200 ~ 170. How many cases will there be 1 week from then? Around 800, how many by Mar 21… about 1600. With reported cases around 700.

The good news is this reflects a substantially reduced growth rate compared to the early days in China, when cases went from 200 to 10,000 in about 10 days (Jan 20 to Jan 30). If we had that kind of spread rate here in the US, we could expect 10000 cases *reported* by Mar 12. That’s a lot faster than the numbers above, and even more scary. In general it’s good to slow the spread, because slowing the spread prevents the health care system from being overwhelmed and unable to care for people. That leads to much higher death rates than would occur at a slower rate of spread.

So, what can we do about all this? The number one thing for a virus that sometimes has mild symptoms but occasionally very bad, is to start *early* infection control procedures. Social distancing is the term used for things like closing schools, working from home, canceling conferences, canceling sporting events, etc. When should we start social distancing? The answer is basically right now or very soon at least. On the order of 7 to 10 days from now. Remember, exponential growth? In china on Jan 20 the epidemic would have seemed not that big a deal, 278 people in China were reported having the disease. By Jan 30 it was 10,000! Anything we can do to slow the spread of the virus thereby reducing the number of cases at any given time that need severe treatment will save lives.

I won’t be going to the SCALE linux conference, even though it’s right here in Pasadena, and even though my kids get free entrance through their schools. It simply doesn’t make sense for our family, as the value we’d get isn’t high enough to overcome the general risk of being around maybe ten thousand people or more milling around sneezing. And they will be sneezing… it’s allergy season in LA.

]]>The frequency distribution for photons with both slits open is an “interference pattern” which has an oscillatory nature. For example from the Wikipedia article on the double slit experiment:

So, suppose we observe a photon in the general brightest central region. Suppose that it flashes within one of those “dark bands” that the double-slit pattern shows. Obviously psi_double^2 is very small in this region whereas psi_single^2 is large. Therefore the posterior probability that the particle went through the first slit because the second slit is closed… is very high. On the other hand, if we see the flash in one of the regions that is bright in both the diffraction and the interference pattern, then we have a harder time knowing whether the second slit was open or closed, though if the brightnesses are slightly different, then we infer that one vs the other was more probable.

What about the situation where we know the second slit is open, and we see a flash at a particular spot. Consider the 2 slit picture from above. If the flash comes from say far to the right where the diffraction pattern is quite dark, but the interference pattern has more light… Then when we run the Bohmian mechanics we will probably find that the photon came from one or the other slit with higher probability. Not having done the calculations I just don’t know, but let’s suppose for example it has a 80% chance of coming through the second slit. What does this matter? In particular, the pattern is the way it is because the apparatus is the way it is… in other words the second slit is open, there is nothing interfering with the passage of particles through that slit, there is no special magnetic fields or electron clouds or glass pieces or anything in the way, and so the physical scenario is such that the wave function does a particular thing, and voila… If we did something to perturb the apparatus, a different wave function would get set up, and a different path would be taken by particles initially coming from the same place as the original particle, and so it wouldn’t hit in the same place and might go through a different slit. What physical consequence can our knowledge that the particle had a high probability that it came through a given slit have? It’s a fact about the past, so we can’t act on it to change the past. It might matter if it would help us decide whether the particle might have interacted with some apparatus along the way, but if there were an apparatus along the way, the wave function would have been different and we’d have a different probability that the particle went along the path.

It seems to me this is one of the essential features of the problem of “whether a particle went through one or the other slit or both”. People whose interpretation of QM is that the particle doesn’t exist until it hits our detector are interpreting “there is no physically observable consequence of inferring the path that a particle took in the past” as evidence that “the path that the particle took in the past doesn’t exist”. This is rather odd. The fact is, by coupling our knowledge that the path might more likely have been X to knowledge of what things might have affected that path (such as the shutter) we can potentially infer that stuff we don’t know was more likely to be one way or another… For example, perhaps we can infer that there was unlikely to have been radioactive decay in the shutter mechanism.

]]>We set up a classic “two slit” apparatus. A laser fires single photons towards an intermediate screen with two slits in it, and then on towards a white screen where the photon position can be recorded (say by a fancy CCD).

One of the slits in the intermediate screen has a little shutter which can be open or closed and which is fed by a source of quantum noise. Like for example every time a geiger counter detects a radioactive decay the shutter flip-flops, or it goes back and forth based on some radio noise from the atmosphere or something, but in the long run the fraction of the time that it’s open = 1/2.

Once the far detector receives the photon and records its position, the apparatus beeps. Finally, a photograph of the position of the shutter is also taken at the time the photon is fired, so we can determine whether it was open or closed, but only by reviewing the record.

Now, let’s talk about Probabilities, denoted P, taken to mean Bayesian plausibility measures over facts about the world… and Frequencies denoted F counting how often a given thing happened in an ensemble of those things. Let’s assume that in addition to whatever I condition on below, we also add | Setup, that is, assuming our knowledge of the experimental setup as described above.

- Write down the probability p( Flash at X | Beep)
- Note that all we have is our knowledge of the setup, and the fact that a photon was received at some point on the detector. We would use our QM knowledge to calculate Psi(x)^2 for the two cases, one with the shutter open and one with the shutter closed, and create a 50/50 mixture model of the two.

- Write down the probability p(Photon went through the first slit | Beep)
- This is intended to be a trick question. It stabs right at the heart of QM interpretation. As far as I can tell, there are *some* interpretations of QM in which a photon has a well defined position at all times (nonlocal hidden variable theories such as Bohm’s) and *some* interpretations in which the photon doesn’t exist until it comes into being by colliding with the final detector (this is generally how the Copenhagen interpretation looks, though it doesn’t seem to me to be a well defined single interpretation, but for example this is how Griffith describes the interpretation in the intro to his standard textbook ~ pg 6). And maybe some other interpretations, like the Many Worlds one where the photon goes through both slits, it’s just a question of which world we happen to be in.
- Nevertheless, if we take a Bohmian type interpretation, then based on only the Beep, we can say there is a 50% chance the shutter was closed, so it must have gone through the first slit, and a 50% chance the shutter was open, and if the shutter was open things are more complicated… see below.

- Write down the Probability p(second slit was open | flash at X, Beep) (in this case the Beep just tells us that the photon fired… so we don’t have to include the option “no photon has landed yet”, we’ll drop the Beep)
- We can write down p(flash at x | second slit open) p(second slit open) = p(second slit open | flash at X)p(flash at X)
- p(flash at X) we use our knowledge of the apparatus to induce our only way of assigning probability, which is to calculate psi^2 for each situation, and mix them: psi_open^2 * 0.5 + psi_closed^2 * 0.5, and p(second slit open) is just 0.5, also p(flash at X | second slit open) is psi_open^2, so we have:
- psi_open^2 * 0.5 / (psi_open^2 * 0.5 + psi_closed^2 * 0.5)

- Now calculate p(Second slit was open | flash at X, photo of second slit, Beep)…
- Trick question, photo of second slit tells us all we need to know about whether the second slit was open or closed. This is either 1 or it’s 0.

- Lets start quantifying our knowledge of where the photon went under additional information… write down p(photon went through the first slit | flash at X, photo of second slit, Beep)
- You may see where this is going. If we know from a photo that the second slit was closed, then the photon to the extent that we allow it to have a trajectory, must have gone through the first slit.
- On the other hand, if we show that the shutter was open, then the photon either went through the first slit or the second slit, but we don’t know which. If we go along with Bohm, information about where it struck the detector should inform us somewhat about which slit it went through… So we calculate the wave function, and the strange trajectory of the particle. We run an Approximate Bayesian Computation type calculation. We select a photon initial position at the aperture of the laser according to our best guess of the distribution of photons at the aperture (let’s say uniform across the aperture), we propagate that photon through space according to Bohm’s equation, and we observe where it hit on the final screen. We do this in a tremendously large number of trials, taking only those photons that actually strike the screen within the range x +- epsilon where epsilon is the width of the CCD pixel or whatever. Then we calculate which fraction of these photons went through the first slit. This is p(photon went through the first slit | flash at X, both slits open).

Now, let’s examine instead the frequencies:

- F(flash at X | beep) = either 1 or 0, you have to ask the CCD if the flash occurred at X and find out. At the moment, at best we can put a Bayesian probability on this F. The Bayesian probability could be calculated from calculations above!
- F(flash at X | CCD) = {1,0} one or the other, our Bayesian probability of the frequency being one or the other collapses down to either 1, or 0. Is this “wave collapse?” no, it’s conditioning on information.
- Write down F(second slit was open) = {0, 1} either 0 or 1 depending on what actually happened. However we can put a Bayesian prior of 1/2, 1/2 on each because of how we arranged the flip-flop shutter.
- Write down F(second slit was open | record of the shutter) = a single number either 0 or 1 just look at the record of the shutter position and find out. Again, not wave collapse but it was caused by either geiger counter detected or didn’t.
- Write down F(second slit was open | flash at X) = {0, 1} depending on what X is… If X is the actual value of the X where the flash occurred, then = 1 otherwise = 0.

Clearly, we drive a strong wedge here between the interpretation of probability (meaning plausibility of what happened given information that we have) and frequency in repetitions. Furthermore we make a strong argument for the utility of a Bohmian viewpoint, because *it lets us calculate the probability that a quantum particle went through a particular region of space on its way to interacting at a detector*. Classically speaking, a Copenhagen interpretation says “the particle doesn’t exist, or the question of where the particle is is not meaningful until it is detected”. For Bohm, this is bunk. Conditional on knowing where the particle landed, we have a straightforward way to back out which paths are more or less likely…

Is that a desirable property of a theory? That it gives us probabilities for intermediate outcomes? It is to me. Is it desirable enough to put up with the nonlocality of Bohm’s equation? I actually think the nonlocality of his equation is pretty nifty, I’m not sure what the heck is wrong with physicists that they tend to reject that outright. It seems like a lot of them are wishy washy on this topic. I *can* understand why physicists would not want classical information traveling faster than light. But it doesn’t seem Bohm’s theory allows this anyway, so it’s not a real objection.

]]>```
## regression discontinuity such as:
## https://statmodeling.stat.columbia.edu/2020/01/09/no-i-dont-think-that-this-study-offers-good-evidence-that-installing-air-filters-in-classrooms-has-surprisingly-large-educational-benefits/
#generally is garbage that ignores what's essentially a correlary to
##the well known Runge phenomenon... we demonstrate here.
library(ggplot2)
set.seed(131211)
datasets = list()
for (i in 1:20) {
datasets[[i]] = data.frame(x=runif(20,0,2),y=rt(20,5))
}
plotgraph = function(d){
g = ggplot(d,aes(x,y)) + geom_point() + geom_smooth(data=d[d$x < 1,],method="lm") + geom_smooth(data=d[d$x >= 1,],method="lm")
return(g)
}
graphs = lapply(datasets,plotgraph)
pdf("discplots.pdf")
sapply(graphs,print)
dev.off()
```

In almost every plot there is “something going on” at the discontinuity, either the level of the function has changed, or the slope, or both. And yet, the whole thing is random t-distributed noise…

I don’t know what that paper did to calculate its p values, but it probably wasn’t simulations like this, and it should have been.