All of cistran's Comments + Replies

Answer by cistran-10

In 12 months US experienced a rate of infection of about 33%. In 4 months, Indian infection rate will be about a third of that, so 10%, unless their dominant variant has a much higher R0.

cistran-10

How many cases of COVID were detected in your child's school in one year?

2Steven Byrnes
My kids really don't mind wearing masks. They really just don't care, they don't even think about it. Sometimes we'll get home and they'll just forget to take their masks off! Like, for a really long time! They just got used to wearing masks when going out, pretty quickly into the pandemic. Young kids are adaptable. :) I'm not really sure what your question is getting at. There's no sense in directly comparing my need for a mask to my kids' need for a mask. It's not like we only own one mask and need to fight over it...  For what it's worth, it wasn't my decision, but I am very happy that everyone in their school has to wear masks indoors. The benefit of reducing in-school COVID spread seems to me to overwhelmingly outweigh the (trivial) costs of making kids and teachers wear masks. I think that the prevailing COVID rates in the community would need to be very low indeed—maybe 10× or 100× lower than today—before I would endorse having kids in school stop wearing masks, at least until there's a vaccine available for kids.

If Alice also want to date Carl, David, etc, does she have to do it again and again every time? Wouldn't it be easier to do it once and put in into a blockchain?

cistran-10

Nobody seems to be doing any cost/benefit calculations on masks. Particularly when it comes to fully vaccinated people wearing them. Why are we not doing it, especially the cost part? The benefits at least are tractable. But the costs are not easy to calculate. Obviously they are bigger than the cost of masks themselves, time it takes to properly take care of them one way or the other, and the cost of their disposal.

2Steven Byrnes
Hmm, I think for me the dominant cost of masks is that they're mildly annoying. That's a much bigger cost for me than the monetary price or the time spent laundering them or whatever. I endorse not wearing masks when they provide zero or infinitesimal benefit. Like, where I live, there's a rule that people walking alone outside need to wear a mask. That's a really dumb and annoying rule. I expect to be doing more stuff without masks, and more stuff period, when I'm fully vaccinated, and so are my friends, and when the prevailing COVID rates in the community are much lower than they are now. Can't wait, and I think it won't be much longer, in my community anyway. :)
8Steven Byrnes
What are the complications? Death? Weeks in the hospital? Lifelong complications? I suspect that if there was even 1-in-100,000 chance of that kind of consequence from regularly wearing masks, I would have heard about it by now. But if you have a reference to actual incidents (not just speculation that it's possible, but actual people who had these kinds of very very serious problems), I'd be interested to see that. I want to consider possible impacts of my decisions that are either (1) common, (2) rare but catastrophic. MIS-C is not super catastrophic, but it's fatal if you're not promptly hospitalized, and occasionally fatal even if you are, if I understand correctly. So it enters into consideration, despite being rare. And even so I wound up declaring that MIS-C risk is too low to be decision relevant. I have a hard time imagining that wearing a mask will lead to consequences anywhere remotely as serious as MIS-C. So it wouldn't enter into my consideration unless it was very common, like >1%.
4Elizabeth
The linked article is low quality. It proposes a mechanism but gives no evidence for its frequency or severity or even if it actually happens at all.  It is clearly not doing cost/benefit calculations. Overall you seem to be putting the burden on Steven to prove that there isn't a risk to masks, rather than doing anything to demonstrate that there is. I agree with considering the costs as well as benefits of masks and would love to see real data on the costs of masks, but this is an unfair burden to put on Steven in particular as a reward for a pretty useful write-up.
8Steven Byrnes
Sorry, I meant "negative consequences of mask-wearing are rare", not "wearing moist and soiled masks is rare". I've worn moist and soiled masks from time to time, and nothing bad has happened to me so far, except perhaps looking a bit unprofessional :-) And I meant "rare compared to 100%". Like, if even 1% of mask-wearers got a throat bacterial infection, that would be millions of throat bacterial infections in my country, 50,000 in my state, hundreds in my town, and probably at least one or two among my friends and family and acquaintances. So if that's actually a thing that's happening at a 1% rate, I think I would have heard something about it by now. Unless those infections were really not a big deal, such that they don't rise to the level of even being worth mentioning to your friends. (How many people do you personally know who have gotten a bacterial throat infection from mask wearing? How bad was it? Were they hospitalized? How many days of work did they miss?) So I figure that bacterial throat infections from mask wearing is either <<1% likely to happen, or it's really not a big deal when it does happen, or (most likely) both.
4Steven Byrnes
Those don't seem to be worth worrying about, so far as I can tell. It seems like they are rare (or maybe nonexistent) (insofar as I haven't heard of any such issues through friends or family or the news), and they also sound like not that big a deal even if they do happen. You can tell me if I'm missing something.
Answer by cistran10

A potentially more interesting question is what vaccine effectiveness as a function of time looks like near its protection expiration date. Not much data to answer this one yet. May become relevant in 6 months in a worst case.

Here is another ironman for FDA decision based on nothing at all. What if they are scared of unknown long term effects and take any confirmed problem as a red flag pointing to unknown long term effects. This would push them away from moustache twirling villains category.

People between 12 and 16 not getting vaccines by the end of 2021 is not even a 90% proposition. Studies are already underway for this age cohort, and it is plausible that a vaccine will be available for teenagers as soon as September of this year.

2Primer
The clinical trials on children by Moderna and Biontech have end dates somewhere in 2022, thus I had supposed we won't see any approval in 2021. That assumption seems to be wrong and I'm happy to stand corrected. I still believe we're missing something when we complain about the "abundance of caution" concerning 19 year old women, but hardly talk at all about the abundance of caution delaying vaccinations of a 15yo.

I really appreciate this comment. I just want that good cautious people quit thinking themselves already guilty of manslaughter let alone murder. Just continue to be good cautious people. 

Infecting a reckless superspreader who will give it to everyone he meets did not occur to me.

 Paraphrasing a famous writer, the evil may triumph but not through me.

cistran-10

You severely overestimate your chance of actually murdering someone. Lets go through the numbers. Lets be generous and assume a 10% chance that you are an asymptomatic carrier. If you are, you have no more than 50% chance of infecting someone even if you don't wear a mask, so lets say with mask properly worn that is reduced to 30%. Now you are already down to 3% chance of infecting any person you encounter. Now, for you 80+ year old neighbor the chance of actually dying from infection is around 5%. So multiply your 3% chance of infecting the neighbor by 5% chance of death and you get 0.15% chance of murdering a person of advanced age. You'd need to encounter 7 of them to get to 1% chance of murder. 

1masasin
Which is still a huge probability. That being said, the precautions to prevent murdering others are exactly the same precautions that would reduce my probability of getting sick in the first place.
2Ann
Ignoring the fact this is then contagious from the people you infect (regardless of age) and also the number of people encountered doesn't seem like the most helpful napkin numbers for strategy against a contagious illness.

I understand the assumption of vulnerability. But how does one assume that one is an asymptomatic or pre-symptomatic carrier if the chance of that is less than 10% on any given day? By itself it doesn't seem rational because if you assume you are pre-symptomatic you have to do something about it. Like testing. Testing very often for no reason comprehensible to the outside world.

1masasin
Until I get symptoms, the highest probability was that I hadn't gotten COVID yet. On the other hand, even if there was a 1% chance that I was infectious (able to spread COVID to others) on any given day, it's not high enough to warrant a test, which is uncomfortable, and expensive unless it was positive or I had a confirmed exposure. At the same time, it was high enough that e.g. my neighbours (80+ years old) or the person at the supermarket might get sick from it, and be hospitalized, not to mention the secondary effects, so I made sure to breathe slowly around people, and wear masks and keep my distance. Most of my communication ended up being gestures (and even then it was mostly "thank you!") instead of words. In other words, 99% chance that I'm vulnerable, take precautions to avoid getting infected if I'm not infected already. 1% risk of preventably murdering someone else, take precautions to avoid that consequence just in case I am infected already.

There is also a risk of PEG immunity which will make one immune to lipid nanoparticle vaccine.

What is the best way to correct mistake 3 on your list?

3masasin
Assume you're both infectious and vulnerable to infection. I disagree with their #3. I've had a prior that I had an asymptomatic infection at less than the background rate of asymptomatic infections in the population in general. So, no symptoms would definitely not cause me to think I have been infected, unless I had more information (e.g., a test result). I certainly wouldn't act as if I was immune. At the same time, the probability that I had been infected without symptoms was high enough that I always treated myself as infectious, just in case. Even being conservative, I think 5% would be a big overestimate. When I was living on my own, it was less than 1%. When I moved in with my sister (who only interacts with people who keep their distance and take the same precautions she does), it went up a bit, and then went down a bit when she got vaccinated, because even if she would have increased her risk-taking, she'd be less likely to get infected, and less likely to be infectious, and, if she was infectious, it would be unlikely that my symptoms would be severe because of virus load. (In the end, she tested negative, so...) As for their #4, my symptoms (i.e., the cough) are already gone, and I didn't notice a decrease in e.g. breath holding ability, energy levels, or anything like that. I think the no long covid for me is 80+%.
Answer by cistran30

The new lipid nanoparticle delivery method can potentially target a much wider range of cells than older modalities. Any cell can ingest an LPN and start displaying spike protein epitopes. All the cells that are not professional presenter cells and do not have MHC-2 complexes will be destroyed by immune system. Some critical, sensitive, hard to replace cells might be so killed at random if enough LPN get into systemic circulation which can occur if for example a needle pierces a blood vessel during vaccination and a large portion of LPN spills into the vei... (read more)

You can sum expected utility of doing your your activity A K times like so:

Calculate expected utility of doing activity A K times with K chosen in such way such that p is approximately 0.5

Then your calculation becomes: E = KU-C/2. Is this E still positive? 

Another objection is that you assume that C is fixed, but it is actually a function of utilities of all the activities Ai with positive utility which you will be unable to do if infected.

Answer by cistran20

First, there should be competition between different virus variants for the cells to infect. This paper

( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4426218/) discusses competitive exclusion for shorter infection cascades.

Second, there are viruses that evolved to coexist with immune system and maintain stable populations inside human host without provoking super-exponential immune response. New variants of corona viruses that gain this ability will become permanent residents in people who are partially immune. Eventually these variants will constitute a majority of corona virus populations in human hosts.

1tkpwaeub
This reminds me - have you read about some of the connections between covid outcomes and cytomegalovirus? It's pretty fascinating. 
1anorangicc
Nice discovery! I will look into it. In my naive understanding, I imagine that each strain only infects a small fraction of all cells, so that two strains should rarely infect the same cell. On the other hand, the abstract explicitly mentions competition between strains, suggesting that there must be connection to multiple infection of cells.

Vaccination passports must come with an expiration date and we do not know what date is best yet (obviously not 90 days.) This is because we don't yet know for how long the vaccines provide protection and because  new strains with higher vaccine escapes may emerge which will eventually necessitate boosters designed specifically against these new strains. 

Census is explicitly prescribed in the Constitution. It is a very protected service which cannot be cancelled without a Constitution amendment. 

False negative is worse than no test at all. It gives a person additional incentive to ignore mask rules.

3AnthonyC
I realize this is going to be different for different people and in different places, but if you're in a place where mask compliance is high already, and rules are actually enforced, this isn't likely to be a thing. I mean, obviously it is to some degree, people get a negative test result (sometimes, too soon after exposure for it to even mean anything) and then see friends and family unmasked. But I don't think it's anywhere near significant enough to change my conclusion. If that were likely to be a major problem, I'd think we should already be seeing large numbers of people who've recovered from covid refusing to wear masks in public. After all, that's much stronger evidence of not having covid, and not being able to catch it, than a negative test result is. Also, better messaging could help mitigate that, "Sometimes tests are wrong, so you can't treat a negative test as a guarantee, but even if you could, a mask helps protect both you and others, so you should wear one to help you stay negative." Still: I don't mean for my list to be definitive. I was making examples based on my own assessments of the kind of reflection I'd need to see from major public health figures and institutions before I start trusting them to implement any policy that requires delicacy, nuance, precision, and care, to avoid causing significant harmful side effects.

I asked around my teacher acquaintances about the virtual classes. Turns out, no one is sending truant officers if kids do not attend their virtual sessions. All they have to do to get credit for a day is login in the morning. How is this worse than going back to prison?

2MalcolmOcean
Guessing that that varies by location—I've heard of online classrooms where you're not allowed to have your video off nearly all day. But even if it's all as you describe, one answer for how virtual classes might still be worse is that for kids whose home situations are abusive or neglectful, it makes a meaningful positive difference to get to be around teachers and other kids outside their home.

This is because little evidence is available. You are looking at vaccination as an urgent matter. But your average chances of getting infected are only one in 4 in a given year. That is an average exposure of about 250,000 microcovids per year. Since average chance also includes people who make very little precautions against infection, it is likely that your personal chances are better than average. There are some people here whose personal chances are an order of magnitude lower than average. If you calibrate it by 3-4 months it will take for vaccines to... (read more)

This neglects to account for a large group of people who have no opinion and will be swayed by any news, positive or negative. Overcoming a formed opinion is going to be harder.

One objection to that is that one must not just compare between vaccinating and getting Covid. One must also strive to pick the safest vaccine. 

Rotashield, the first rotavirus vaccine only caused one bowel obstruction in 20,000 vaccinated children, yet it was pulled from the market after a year because there were already vaccines 5 times safer.

If there is a large safety gap between different available vaccines, least safe must be declined in favor of most safe.

Another objection is that long term effects of any covid vaccine are not yet well-studied and there could be plausible mechanisms by which some of the vaccines could cause long term damage for example due to cumulative effects. 

2gwillen
Well, as to the vaccines available right now, I'm not aware of any evidence for one of them being more or less safe than another, so your choices seem limited to "vaccine" or "not". But even if they were different -- getting the safest one is only a usable strategy if it's available, i.e. there is not a vaccine shortage, which there currently is. If your choices are "get whatever vaccine is on offer" and "nothing", you should get whatever vaccine is on offer as long as the expected value of doing so is better than the risk of COVID exposure if you do nothing. This is definitely the scariest hypothetical, IMO, but I'm not aware of any evidence for it, only a lack of long-term data. How you weigh "unknown unknowns that are hard to measure" against the risks of COVID seems like a very personal choice. (I'm not aware of any past vaccines having hidden long-term side effects that didn't appear at all in trials or early use.)

I think I know why the deaths are below baseline as you said. A significant percentage of people who die spend many weeks on their deathbeds, and people on their deathbeds are too sick to be vaccinated.

Here is a simple question I got from my vaccine hesitant coworker: 

VAERS lists about 1400 deaths following vaccination by mRNA vaccines in 2021. 

He checked the flu vaccines deaths listed in VAERS and couldn't find more than 50 for each of 2016, 2017, 2018 and 2019. The question is why is there 30 times more deaths reported in VAERS following covid mRNA vaccination? Does it mean regular flu vaccines are 30 times safer? The total number of shots is comparable in tens of millions. 

2gwillen
Supposing hypothetically that those 1400 deaths were all caused by the vaccines -- wouldn't the math still be on the side of getting one? (Of course, most likely the relationship is not causal, as discussed by the CDC link below, as well as Zvi's reply, but hypothetically assuming it was.) from https://www.cdc.gov/coronavirus/2019-ncov/vaccines/safety/adverse-events.html: "Over 92 million doses of COVID-19 vaccines were administered in the United States from December 14, 2020, through March 8, 2021. During this time, VAERS received 1,637 reports of death (0.0018%) among people who received a COVID-19 vaccine." Chance of death from COVID for young healthy people is probably somewhere between 0.05% and 0.1%. (CFR seems to be around 0.2%, but IFR is lower. I'm eyeballing from https://link.springer.com/article/10.1007/s10654-020-00698-1 .) For older people it can be as high as 10-20%. Even if you are in the youngest, healthiest group, making the most optimistic assumptions about the danger of COVID, and the most pessimistic assumptions about the danger of the vaccine, that it caused every single death reported after receiving it -- it seems to me that COVID would still be at least 20x more dangerous. And realistically the difference is much higher than that, and for older people it's going to be orders of magnitude higher. Of course, if you think you can perfectly avoid exposure to COVID, then you could declare any amount of risk from the vaccine to be too much. But I think most people are both unable and unwilling to do that, and I suspect that most people who ARE able and willing to completely avoid exposure are also more likely to be getting the vaccine, not less.
7Zvi
1400 deaths from about 70 million shots after lag, so even if that was 100% the vaccine, that would be a death rate of 1 in 50k. Seems well worth taking. But also if life expectancy vis about 80 years, that's about 30k days, so if they report deaths that day, and vaccinate a lot of elderly, isn't 1400 deaths on 70mm shots below baseline? If you die after a flu shot no one thinks the flu shot kills you. If you happen to die after getting an mRNA shot they report it.

Right, there is a difference between your clone who is a few lessons ahead of you and a really good teacher. So, you don't learn from the best, but try to find the best teacher?

You should still want to learn physics from Richard Feynman

3George3d6
Wasn't Feynman basically known for: 1. His contribution to computing, formalizing problems into code, parallelizing, etc 2. His mathematical contributions (Feynman diagrams, Feynman integrals) 3. His contributions to teaching/reasoning methods in general. I agree that I'd want to learn physics from him, I'm just not sure he was an exceptional physicist. Good, but not Von Neuman. He says as much in his biographies (e.g. pointing out one of his big contributions came from randomly point to a valve on a schematic and getting people to think about the schematic). He seems to be good at "getting people to think reasonably and having an unabashedly open, friendly, mischievous and perseverant personality", which seems to be what he's famous for and the only thing he thinks of himself as being somewhat good at. Though you could always argue it's due to modesty. To give a specific example, this is him "explaining magnets", except that I'm left knowing nothing extra about magnets, but I do gain a new understanding of concepts like "level of abstraction" and various "human guide to word"-ish insights about language use and some phenomenology around what it means to "understand".
5Razied
Though even there, his lectures are famous for only being truly appreciated after you've first learned the material elsewhere. They are incredibly good at giving you the feeling of understanding but quite a bit less good at actually teaching problem-solving. When reading them, it was a common occurrence for me to read a chapter and believe the subject was the  most straightforward and natural thing in the world, only to be completely mystified by the problems.
1MikkW
Yes, although this is the exception rather than the rule- Feynman happens to both be a world-class physicist and a world-class communicator (in addition to being talented at many other things)- I suppose the class Feynman belongs to is that of polymath- he didn't strive to be the singular best at any one thing, but rather to be as good as possible in many different fields

At some point in the near future this rate will become unsustainable. Because vaccine hesitant and vaccine avoiders are a significant minority everywhere.

Injecting RNA into cells is not enough.  There are also interferon protein complexes that interfere with viral RNA doing anything inside the cells. They must be bypassed or overrun or there will be no viral replication. These intracellular defenses make many viral infections grow much slower. 

USA is not the only nuclear power. Other nuclear powers which begin to descend their cost curves might be tempted to export the cheaper tech, especially if the expensive precision components are not wanted by the buyer. See the nuclear tech connection between Pakistan and North Korea, but make the cost of technology an order of magnitude smaller. 

Limiting the spread of cheap nuclear weapons will never become as impossible as banning firearms, but it will become harder.

1Gentzel
This is what the non-proliferation treaty is for. Smaller countries could already do this if they want, as they aren't treaty limited in terms of the number of weapons they make, but getting themselves down the cost curve wouldn't make export profitable or desirable because they have to eat the cost of going down the cost curve in the first place and no one that would only buy cheap nukes is going to compensate them for this. Depending on how much data North Korea got from prior tests, they might still require a lot more testing, and they certainly require a lot more nuclear material which they can't get cheaply. Burning more of their economy to get down the cost curve isn't going to enable them to export profitably, and if they even started it could be the end of the regime (due to overmatch by U.S. + Korea + Japan). The "profit" they get from nukes is in terms of regime security and negotiating power... they aren't going to throw those in the trash. They might send scientists, but they aren't going to give away free nukes, or no one is going to let planes or ships leave their country without inspection for years. The Cuban missile crisis was scary for the U.S. and USSR, but a small state making this sort of move against the interest of superpowers is far more likely to invite an extreme response (IMO). 

The FDA must actually say that children are ok to vaccinate, do you think they'll do that by September?

I think you corrected your self later, but there was a sentence earlier about vaccinated children in classrooms.

That is not likely to happen this year. Vaccine trials for children are just getting under way

3Zvi
Vaccine supply will be ready for them the moment the studies are done, so this year seems realistic for getting children vaccinated. Chances seem very high the vaccines work on children, with the caveat that they aren't as needed, of course.  It's months away but I see no reason we couldn't make a September deadline if that was something teachers needed in order to come back. 

I think this post has a lot to do with shifting Overton's windows:

 https://www.lesswrong.com/posts/HLqWn5LASfhhArZ7w/expecting-short-inferential-distances

Any proposal that brings us closer to hundred million dollars nuke will probably be bad for preventing nuclear incident of the mushroom cloud kind. I think your proposal of reducing the size and yield of nuclear weapons also reduces its cost. 

A country like North Korea is unlikely to strike first with nuclear weapons precisely for reasons you mentioned. But possession of them is a significant deterrent against invasion by a conventional military force or insurrection aided by an outside military force, such as ones happened in Iraq and Libya. Any gove... (read more)

1Gentzel
Precision isn't cheap. Low yield accurate weapons will often be harder to make than large yield inaccurate weapons. A rich country might descend the cost curve in production, but as long the U.S. stays in an umbrella deterrence paradigm that doesn't decrease costs for anyone else, because we don't export nukes. This also increases the cost for rogue states to defend their arsenals (because they are small, don't have a lot of area to hide stuff, etc.), which may discourage them from gaining them in the first place.

A very important special case of this: There is no evidence that COVID vaccination reduces transmission.

All your examples point to self-inflicted reputation loss. I am talking about reputation loss inflicted from outside.

Here is my counter-example: Doctor Ignaz Semmelweis, the inventor of hand hygiene in medical (specifically OBGYN) practice. He was reviled and ridiculed and driven insane by the medical establishment of Vienne. 

3ryan_b
Aha; I failed to parse the second sentence in light of the first, and mistook them for an independent claim. Confusion resolved!

But dishonor is rarely used in its transitive meaning. It is difficult to reduce someone's honor by dishonoring somebody, only your own honor can be dishonored by you.

Your machine will make you permanently stupider than you could be in a real world since it would continue forcing reasoning errors on you. Once you realize that, how can you trust that machine experience will remain better in pain/pleasure balance. In other words, what makes you confident the machine won't extract a payment of pain out of you in exchange for all the bliss you received?

And yet, Piratebay stays online.

2crl826
This is a good, fair point (unlike the person who wrote me and told me I was spreading Nazi propaganda). Thank you. I confess I am not tech savvy enough to validate these arguments, but I have heard that Piratebay is much simpler (text files that point to other files) and is much easier to keep play cat and mouse games than, say, a social network. But, either way, you are right to point out that a determined opponent can keep up a fight for awhile.

PR is something that can be done to you as in negative PR. There is no negative reputation, or negative honor, there is only slander.

2ryan_b
I find this idea shocking. Could you talk a bit more about your thoughts here? By way of examples, how would you describe any the following: * The reputation of Exxon-Mobile or BP for environmental practices? * The reputation of the National Enquirer for news? * The reputation of the Soviet Union for free expression? Relating to honor specifically, what are your thoughts on shame?
Vaniver120

My dictionary has "dishonor" in it, as both a noun and a verb.

You are way better than average at avoiding infection then. CDC estimated that from February to December that there were a total of 83.1 million infections in US, over 20% of population.

Does accessing antibody test results break the double blind? Are you sure you didn't consent to not doing that?

1ejacob
Short answer is yes, it mostly does, but they'll test me anyway. I didn't have to agree to anything that could possibly prevent me from receiving the best healthcare I would otherwise get. I'm pretty sure/hope such a condition would not have been allowed by any IRB.  I spoke with a pathologist in my family and together we estimated that a positive blood antibody test ~2 weeks after the 2nd vaccine dose would have a likelihood ratio on the order of 50:1 or more in favor of having had a response to the vaccine. (This is specific to me - my lifestyle protects me very well from possible infection (I have close contact with very few people, most of whom have received a vaccine themselves or have recovered from covid a couple of months ago); I would reduce this estimate for an average person). So if we find antibodies in my blood about a month from now I would be quite comfortable concluding I received the vaccine (recall the prior odds are 2:1 in favor, updating based on the test makes it 100:1; a near certainty). Likewise a negative blood antibody test would strongly I did not receive the vaccine.

Is the JHU tracking site at https://coronavirus.jhu.edu/data very inferior to covid tracking project?

Trying to help them how? Education? Financial incentives to vaccinate? Social disincentives to hold out?

At least some forms of trying will not be cost-effective.

or, you could use unhealthy only to mean things which are likely to decrease your health (mental health included)

1Gitdes
Thats what I meant ofc.

That's the point of the post. Given a large number of contacts, P(infecting at least one of them) > P(you are infected)

Lets illustrate. Suppose P1(you are infected AND (you are asymptomatic OR you are pre-symptomatic)) 

P2(infecting any one of your contacts) = P2'*P1 = where P2' is the probability of infection per contact

Then P3(infecting at least one of your contacts out of N) = 1- (1-P2)^N provided none of the N contacts are themselves infected.

And in P3>P1 it is always possible to solve for N.

1mwacksen
Sorry for the late reply. I'm assuming you need to be "infected" in order to infect someone else (define "infected" so that this is true). Since being infected is a neccessary precondition to infecting someone else, P(you infect someone else) <= P(you are infected), and it's clear you can replace "<=" by "<". This is basic probaility theory, I can't follow your notation but suspect that you are using some different definition of "infected" and/or confusing probabilities with expected values..
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