 When I was first thinking about this, I was motivated by the problem of schools, to be honest. Even MIT as a university, we also shut down basically because of the six foot rule. And so that was actually my initial motivation. Should we really be doing this, or should we be doing something else? Maybe some spaces are actually safe, others are not safe. We've also sent all our students home, maybe they could actually be here. Or maybe they shouldn't be here. So that was the question that I wanted to address. And so I would say that was the initial thinking of a little bit larger spaces, more people in it, and really understanding the role of ventilation and everything else. The story that came out recently, given the fact that we're on the holidays, Thanksgiving in the US and Christmas coming up as well, people were very concerned about, can I attend my holiday party? And so people were running the app for really small numbers of people, like six. And it might say with no mask, of course, you're eating without mask, you could be there only for a short time. And so essentially then it says we can't have Thanksgiving dinner, we can't have Christmas with our relatives. Okay. And I'm necessarily necessarily saying you can, you should be aware of the issues that are raised by the app. But you also be kind of careful in how you use it. It comes back to this issue I mentioned earlier, that I was thinking initially more along the lines of like, should the New York City public schools open? For example. Okay. That's a big question. And there you're really worried about, are these people in these spaces, the students, the teachers contributing to the spread of the pandemic? It's kind of a community-spread decision made at a higher level. And it's kind of a blanket statement. Are we going to be open? Are we not? Okay. And I think that, you know, the information I provide, I think can be very helpful actually in making such decisions. And also I was thinking of cases like nursing homes, you know, where there could be a, you know, a short but very high-risk transmission. And I want to understand, you know, when, when that can be an issue. Because they're like, it's so sensitive, you know, just, it doesn't happen very often. But when someone comes like, this can be deadly actually. So, you know, it's, it's with much higher probability. So I was very concerned about those kinds of cases. But when you apply it to the case of say, a Thanksgiving dinner, you know, let's say the app gives you, you know, for your space, you have very poor ventilation. I mean, you're going to have, you know, 10 people total, let's say, and your nuclear family is maybe five, and you're going to have a few relatives over. It might tell you you've got, you know, three hours. And you might say, oh, maybe I can't really have that dinner. And I would say, you know, perhaps that's the case. We have to look carefully at the situation. On the other hand, that's not necessarily the right way to use the app, actually. Because as I mentioned earlier, we have to, for a specific incident, what we really care about is the total probability of a transmission, including the possibility that an infected person is there in the first place. So, you know, in some parts of the country, right, I mean, the prevalence of infection is very low actually. So like the chance that there is an infected person is extremely small. So what you need to do is multiply the conditional probability of transmission that we're essentially using with the probability that there is an infected person. So you take your gathering size, multiply by the prevalence of the infection, which potentially you can look up and find in some database. And then you finally have a lot more time, because actually the chances are that there won't be an affected person. You know, even in fairly stricken areas, like I said, maybe there's a 3% infection rate, you know, in the population. It's not, it's not 90%, you know, it's still like the chance that an individual person comes in is actually COVID positive and also importantly doesn't know it. Because of course, if they're positive and they've been tested or they have symptoms, they're not going to come to your party. So these are people coming who think they're healthy, the fraction of those people who actually have the disease and don't know it, it's significant, but it's not 100%, it's not even 50%, it's not even 20%, it's probably like a couple percent at most and maybe lower than that. So that's one factor. The second factor, again, in terms of using the app in a way that is more kind of tailored for a certain situation, is this idea that, you know, we live in a household where we have a certain set of people, let's say, you know, like my family is, you know, I have four kids, I have a family of six. A household, or more generally, you know, people live in pods or other kind of, you know, more kind of familiar arrangements, that's a group of people who know and accept the risk of transmission. So, you know, another criticism that happened when our app, you know, ended up on some stories and websites is there, if you read the comments, a lot of people are really angry saying, well, this is BS because, you know, this professor is saying we're going to get sick over dinner, but we have dinner every night and we're not sick, you know, so like, how is it, what's he saying? We've been living together for three months or, you know, no one's gotten sick and now he's saying we're going to have a dinner with like one extra person and suddenly we're going to be sick in three hours? No. So in the specific case of a holiday party, what you really should be thinking is there's a certain number of people that are potentially bringing you the infection and it's not everybody because you're, let's say, relatively comfortable with your immediate family, either you're tested or you're spending a lot of time quarantined together or you just simply accept the risk of transmission between you and you're really worried about the outsiders. You're inviting your grandparents or your cousins, so there's some people coming from the outside that are going to be joining you for a period of time. So what you really want to take primarily is that number of people, times that probably they're infected, to estimate how many infectors there would actually be or what's the chance there would be an infected person. That's much lower than the probability that's essentially in the app right now, which is a hundred percent chance, right? So it's a totally different question. So if you want to know, like, can I actually have a Christmas dinner with a few visitors? Chances are you probably can and that requires using the app in a slightly more subtle way. Unfortunately, when those news stories started running, I became the Grinch that's still Christmas, among other things. And so that's, again, not my intention. Now I'm happy to be the Grinch if the news you need to get is a tough medicine saying, hey, don't have this gathering. Like I might be saying that, but I think many times I'm not saying that. And so it boils down to understanding what the app is calculating, what the theory is telling you and how to use that information. So we're working on improving, actually this was a good thing, by the way, that just happened this last week. We are right now working on improving the app with just including that effect of prevalence of infection into your decision-making. But we also don't want to be right on the front where you have to enter a bunch of numbers to kind of take away the beauty of it. So we're trying to find ways to kind of keep the user experience simple, but to convey these kind of two different ways of thinking. One is just sort of from the perspective of like a high level policymaker, let's say in charge of the New York City Public Schools wanting to like control the spread of infection in general versus an individual who's deciding, should I go to a party or should I go to a store for a certain period of time? Those are two very different questions. 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