To get started Tyler, I thought it's best to start with the big change this year Obviously the pandemic Started in March and that forced a change in the production of conversations with Tyler Unlike a lot of other podcasts. We had never done a remote interview before April I think well March was our first remote interview with Russ Roberts when we did the live bonus episode right after everything shut down Um, but we've had to make this abrupt shift from doing absolutely every episode face to face To now not being able to do any face to face and I wonder how that change has affected you your preparation Things like that It's changed my life doing these remote, but it's also made me much more optimistic about the American economy So I was convinced that doing them remote would be terrible like oh you can't do them remote And it turns out we had to do them remote and I've asked a number of people And basically they can't tell the difference as listeners whether or not it's remote They can tell by the fact that they're seeing the two separate little boxes on youtube But they seem to me just as fine So I think you have to wonder how much of our economy Can we in fact do remote and people like me have been saying no we can't do this remote Uh, and we can so I think having been forced into that new mode There are in fact big productivity gains on their way that said We do hope to return to doing a lot of them face to face as soon as we can We'll see when that is but I for one will not be hesitating to get my vaccine Oh, you know what the biggest change has been from the the pandemic is not having proper access to the library So a lot of people it's hard to prepare for them because you'd have to get all these books So I even said I was like, oh, you know, Jeff and Dallas We need to pick some economists Because to prepare for economists, you don't really need to read books Is that like a little bit of an insult? But anyway, we did a bunch of economists I thought they turned out great and that was because of the pandemic And that was a bigger change than going from face to face to remote my reading habits To jump to a listener question then What kind of split do you think?  Well, I just like meeting the people right above all so that in a sense is my wage for doing things So we want to do Lydia Davis up in Albany. I suspect she would do remote I'm not doing it because I want to meet her But I suspect it's the other side of the market that will constrain us They'll be like, well, you know, you don't have to come up like we're willing to do it remote and actually they're terrified That I didn't really get a vaccine after all or the vaccines don't work or Maybe you are carrying tuberculosis by then or I don't know. I don't think it's going to be up to us for quite some time So we'll I'll just take what reality sends me. We have a backdrop of remote It works fine. We'll see what we can do past that We'll get into predictions at the very end on some of this stuff The do you think so you mentioned we we shifted composition To people you don't have to do as much research on because it's harder to do that Or online research, right? It's not that there's no research But I don't need the books of the library right In terms of the composition of guests otherwise, you know, we didn't really do a lot of Of covid programming. Um, in fact, I'd say we did more counter programming to covid Uh, we did a few notably paul romer and glenn weill In terms of the guests or episodes How do you think the composition other than the obvious was affected? By our switch. Do you think we got different guests than we normally would? You know relative, you know, holding the kind of research side Constant do you think our composition of guests switched? I don't think so much, you know, we're well enough known now that say people with the new book out They they simply want to do us whether we deserve them or not So that's good so, uh You know, maybe doing something like flying to london to ducan house guard I would have tried something like that again. I'm not sure with whom like Fly to italy and yell out alana for auntie's name and hope she appears with a tape recorder But something like that would have happened and it didn't we had three covet episodes I'm glad we had three but covet has been covered very heavily by me on marginal revolution And I think whatever I have to say people get there and it changes so quickly. So I'm happy with the three we did and Probably it's going to stay at that yeah We this was a year of repeat guests. We actually So we had fuchsia dunlop last year, but it was kind of a bonus episode. It wasn't um, it wasn't her featured again But this year we had ezra kline for the second time promoting a book Ross dalton promoting a book as you mentioned and then russ roberts says the bonus episode as a third Do you expect we'll do more uh repeats and and paul romer? I forgot paul romer So we did him a second time as well. Do you anticipate doing more repeats in the coming year? Well, I guess my new view is they're all bonus episodes, right? Uh, I don't want to say we're going to do more repeats because it might get some people soaps up Uh, but in fact the repeats were really good. So how many of these have we done jeff? Do you know? In total or this year in total? Uh, in total let me get a real-time fact check from dalis, but I think we're at maybe 110 Okay, so well over 100 so counting this episode, which would be the last of the year. It'll be 112 So that's a lot of people to be you know dredging up from the ranks and if someone's really good They have more than an hour to say right even if someone isn't really good. They have more than an hour to say so, uh Maybe we'll do some more repeats right depends what people are up to Yeah We did have one one guest who sadly we will not have a chance to ever interview Uh, last year we had a confirmed time to interview clayton christensen Um, unfortunately, he had to postpone because his health took a turn for the worse and then sadly He passed away at the very beginning of the year Um, so we'll never get to hear that interview. What were you hoping to learn from clayton christensen? How he thinks disruption really works how to improve the case study method at harvard business school Uh, how his Mormon upbringing and faith has influenced his ideas on management. What's his favorite movie? Uh, there's plenty we would have had to talk about with clay. He was a fan of what we were doing Very sad that probably will never happen. Yeah Um, all right. Well, let's let's go a little bit into the numbers, uh of c wt this year. We'll talk about The most popular episode picks for A most most underrated episode this year And then we'll get into some name that production function our favorite segment on the easier interview episodes so first by the numbers we did counting this one. This will be our 29th episode of the year So that's pretty typical for the past few years. That's once every other week plus a few bonus Any idea what the most downloaded episode was of this year? I don't know at all, but my guess would be matt yaglacias You are you are correct. Wow great matt broke broke the record uh for first week downloads um because because there is a bias that we do get Growing listenership over time so earlier episodes will do slightly worse than later episodes in the year. So if you look in the first six months Adam twos was the record breaker, which was a big surprise actually to me I had no idea how ardent the adam twos fan base was but he was also on macro musings david becker's podcast that we produce here at mercatus And uh, it did very well over there too. So adam twos is Very popular and it was a good episode adam and madder indicating twitter really matters For your podcast audience, right? Yeah, that that is very true. Um, and much discussed on twitter and um And of course matt aglacias shortly thereafter Making moves um and and striking out on his own and also recently announcing that he's becoming a senior fellow over in this gammon. That's right That surprised me That's good Good for them good for him All right, uh Now underrated what are your picks for underrated? I'm not necessarily equating this with listens, but listens does factor into it Well, I don't even know how any of them are rated I thought the alex ross episode was really good. I suspect vogner fans rate it pretty highly But there aren't so many of them. So that's one of my picks for underrated jimmy wales I'm not sure it's underrated, but I think precisely because he's been Successful and moderate and reasonable Uh twitter doesn't go crazy over him one way or another So my guess is that will do very well in the long run But in the short run it was not like a super social media driven thing because he is not insane So I would name that as underrated Those would be the two picks that come to mind right away, but maybe you can tell me Yeah, I think if you if you look at who underperformed You clearly see a bit of a you might call it a liberal arts bias when we're we have guests that are less known a and be that they're talking about music or Fiction and they're not well known again. That's when you tend to see a dip. So Emily st. John Mandel Ed would edwidge dandy cat. They all They all did slightly worse and then I would say weirdly the episode performed decently, but John McWhorter as I was looking through the stats I was surprised. Um, I would say he underperformed. I would say to the extent that that tells you something about Performance and how people rated it then I would say John McWhorter underrated But here's what I suspect went on there He is so available in the podcast forum That you don't need to come to us and until very recently Adam twos was quite underexposed in the podcast forum That's being remedied for the better We were the go-to Adam twos place All right, let's jump into Um a round of name that production function So we'll do two rounds of this and as a reminder to you I've gone through and picked some of my favorite answers from Uh responses to your inquiries about a guest production function I picked some of my favorites. So I'm going to read you a quote and you guess who it is I'll be lucky to get one of these because I treat the segment As telling me what not to do not like something I should remember to do Yeah, and you uh, but some of these are really easy.  All right. So number one I have a lot of projects on the go and switch between them Kierkegaard called it crap rotation You work on something you put it to one side and then you pick something else up Um, I gave a TED talk on this. I called it slow motion multitasking I think it's striking how many very successful people practice this and have these multiple projects on the go They provide relief when you're stuck on something you just do something else and don't get stressed about it because you've got something else productive to do I have no memory But it sounds like tim harford. So that's my guess You are correct. That is good. Thank you tim for doing so much and reminding me of your productivity Tim tim in the early, you know, I think we recorded him late last year and he released early this year Um, so it it does feel in some ways like a lifetime ago All right, number two I mostly did what I wanted to do that this person's talking about going to school Like high school I mostly did what I wanted to do and not what I was told to do if I wasn't interested in a subject I did very little on it if I liked something I would read 12 other books that no one told us to read on the topic I remember when in the college application, they had you list all the books he'd read in the last year I wrote down a list and I was so terrified They would think I was a liar that I ended up cutting that list in half less. They think I was making things up That sounds like a rich person. So can I guess read Hoffman? But again, I don't remember I like that. I like that your intuition was it's a rich person Um, I don't know how rich he is, but it wasn't read Hoffman. This is an academic and he any second guess An academic recorded very early Hmm Who would that be An academic I didn't did we record any academics very early? I don't even other than garrick jones Uh jason firman Oh, that's right. Yes. Yes, of course And he does read so much And of course the story with jason firman from a production standpoint is that we recorded him I think before the holidays and he was scheduled to release in the first few months of the year and we bumped him because We did have I think a more Kind of pressing covet episode And then we just couldn't find a natural place to slot him in and so he kept getting bumped and bumped and bumped and only released in the end of In the end of the summer sometime. So he's actually our Last release that was recorded in person But was I still feel bad about that like we somehow I didn't do him proper justice, but he's not an academic That's what what threw me. Yeah, his episode performed really well. I mean, there were There were some, uh, I don't know c wt true. There was a thought we had some agenda between From holding it as as long as we did I can assure everyone it was for banal production reasons, but his episode performed well. So um, no concerns there And the part where he announced 2 q is right? I mean that just took off like wildfire Yes, it was is our most viral Our most viral episode for that reason. No, actually, I would I will have to say if I think of the Of a revelation in an episode that I think went underappreciated tyler It's that you revealed in the ashley mires episode that you have a peloton bike and you at least at the time were using What a peloton bike was your main form of exercise? Is that still the case? It is whenever the weather is bad, which is fairly often where I live It's peloton every day. So And you have the full kind of you do the classes and everything or just the bike. I don't The bike the software confuses me I can't can't figure it out, but the bike is great Very happy to have it This is consistent with tyler. I know exactly. Thank you Well, I'm glad to hear the peloton is still working out for you And we'll especially now right this is late december. So of course i'm using it all the time. Yeah um, all right, uh finishing on our first segment on production function Uh, this is kind of a negative production function in the sense that it's kind of something this person realized they they weren't good at Okay, here it goes, but it turns out it is challenging to manage it involves real skills It's stressed me out. I don't think I did a great job of it You get a good appreciation for the idea of even though it might be hard to measure or see externally There is real skill being deployed in middle management Hmm I don't know if i'm going to have Any idea but middle management. I don't know nicholas bloom worked at mckinsey Again, that's a guess not memory, but how's that? That's a that's a good guess But wrong but wrong wrong totally wrong This person was referenced earlier and uh hint. They are not managing anyone decidedly now. They've made a recent change Not managing anyone decidedly now everyone's managing someone I think uh, they've struck out on a solo venture So matt of course that must be matt. Yes. Yes. So matt uh in the early days of vox matt was in more of a managerial position And he realized it wasn't for him. And of course Maybe take him had a step further with the solo venture on sub stack. Yeah. Okay next one You will get this one because i'm not going to try to remove the uh, I'm not going to try to remove the clues If you pack if you wrap it up in some software, I promise I won't I think Yes, that if if you're getting too many of these that'll be my that'll be my tech I think music critics need to have a command of neighboring cultural areas because music is not just separate from the rest of culture From the rest of our world when you're writing about opera you're writing about literature as well as music You're writing about staging theater ideas. So every music critic can't be a pure specialist That has to be a alexa ross, right? Correct. All right last one in this segment I think almost part of it depends on how you look at the world Do you look at things and then try to think okay? How can I simplify this? How can I take something that's incredibly complex and narrow on a specific dimension and really understand that in a Way that can shed light on the world and then along with that also being humble about the fact But that doesn't mean you've understood everything you've looked at one dimension It sheds lights on things it sheds light on things, but you need to really know what you don't know That was somebody's answer It was I have no idea. No idea whatsoever. This way this one's hard. It's um I'm trying to think if I can give you a a good clue They're speaking in a way that would make sense given their academic work. Um, so this person I gained notoriety for exploiting a certain econometric technique And has used that to write a number of really good papers and economics. That's melissa dalban That's correct. Okay. So I think I think her answer was very in keeping with the fact that Her papers can tell you a lot about a very specific thing But she was very careful about saying that you know It only gives you part of the story and you have to be really careful about what you don't know Sure I'm looking for tips on like how to use my vacuum cleaner so I can You know write more blog posts in the evening Well, you you know what you don't know about vacuum cleaners, I think So that that gives us a good excuse to turn into some twitter questions. All right. Well, how about we go first to a question from conversation with tyler producer dallas floor She has a couple good ones, but the first was what's your go-to quarantine snack these days Well at the beginning it was pickles But I got sick of pickles I I believe you said in your post that pickles were great because you They're always delicious, but you don't overeat them, but you I was I was half right. You don't overeat them, right?  It is somewhat filling.  Is that so the case? Yes, but less than I had been then Because there's been outdoor not right now, but there's been outdoor dining for most of the year But there wasn't that when I was speaking to us, which was I think early to mid-march Yeah, um, so here's another question from twitter then um at porosi 1980 says Food question delivery and takeout during lockdown. Is it a temporary blip or a permanent change to eating out? Permanent change to some extent. I think maybe a third of that shift will stick I don't myself like, uh Takeout, I think the food tastes much worse I would just do whatever's possible to make it fresh Served at the right moment at the right temperature and if that means I cook it So be it if that means eat outside when it's called so be it But eat food properly, but I know the world does not agree with me I've had a small number of dining in episodes But I'm always going at 11 a.m when no one else is there And there's only a small number of places. I'll do even that Show up at 11 order Uh, no one else is there leave by 11 20 That works in like two or three places I go to Uh Jared Sylvester from twitter asks what is the post-pandemic outlook for ethnic restaurants and are any of your heuristics Are any of your heuristics for finding good ones different now? At least where I live northern virginia. I've been surprised I might even say shocked at how few of them have closed So they must in some way be more thickly capitalized than I had thought So you know, we can debate exactly when how many people will take the vaccine and so on But it seems most of them are sustainable or they would have closed by now Uh, DC's a different story a lot have closed or they're just like weirdly boarded up Uh, but where I live I haven't lost a single favorite that I'm aware of And uh, that's very heartening So heuristics haven't really changed because Hasn't changed but I would say this while the pandemic is still on the value of comfort food is higher The value of complicated dishes is lower They're harder to pull off under current circumstances. There are issues with kitchen crowding staff can be lower The good side is you often have the best person in the kitchen cooking for you The downside is complex production is harder But order simpler dishes and they will taste better And that would be like a new rule pandemic dining order simpler dishes and comfort food It will taste better and you will enjoy it more. Yeah, I'm actually kind of ashamed to think I haven't thought about that when I'm ordering takeout Is I'm not really ordering what I think will actually travel well or hold up well I still order what I want to taste What I think will be delicious as if I were in the restaurant. So That's a helpful heuristic for me. So thank you I don't think buffets will come back post vaccine I think they will eventually but we'll have to lose the collective memory if being afraid of them Okay, let's switch to another big Another big area that started the year and was sort of eerily I don't know prescience the wrong word for it, but uh A couple of listeners indicated they really wanted to hear your thoughts on State capacity libertarianism given that you started the year with this big post, you know outlining this Sort of trying to name a new strand of libertarianism and and indeed arguing that it was the future of libertarianism Um, and then we have this major global issue that At least in my mind directly relates to some of the key Points of tension or Even just gaping fishers now in Uh, a broader libertarian ideology about the proper role of government and what restrictions we might take short or long term In order to let the government step in and handle certain problems. So I'm assuming I looked in the first The first post a marginal revolution that I found that referenced coronavirus was until january 23rd And I think you were actually linking to a bloomberg column. That's correct So I don't even think you know this You've obviously written about pandemic in preparation before Years ago, but when you wrote this state capacity libertarianism column Or post on marginal revolution, you weren't really thinking at all about the fact that you know, there was something brewing in Wuhan Correct. I had read the Wuhan reports and I was concerned But events of concern come out of china fairly often with flu viruses and the like and I didn't then think this one was it Uh, I did mention it to some people on whatsapp. So I was following it, but uh I think right now libertarians are at a kind of war with each other I'm not sure a state capacity Libertarianism is the future of libertarianism, but it's the future or present of my libertarianism I just think you millen Friedman said this too. He said one of the public goods you need government for is to control contagious diseases This is that When it happens, you will best secure liberty by beating back the virus That does mean say subsidies for vaccines and government taking an active role and trying to support testing We did a better job with vaccines than testing And uh, that's the case when you really want your government to have its act together And you can see a big difference between countries where the government did a good job and countries where government did a bad job And it has long run implications for their liberty What surprised me is how many libertarians moved into a kind of denialism Like oh, this isn't so bad. It's only the old people. It only kills whatever percent uh Sort of older more more macho libertarians would have said oh This virus is terrible. I mean we need to let the market rip to crush it And if we would let the market do whatever, you know, that that would be so great and the market would crush the virus better than the government I don't think that's quite true as stated, but it would have been a very libertarian response Uh, but instead I think there's been a lot of people Who've gone down different rabbit holes that haven't really been that truthful or have involved very off predictions Like oh all this thing will be over with by you know the fall or something You know when I read that post now It seems to me a pretty clear distinction. You're talking about sort of the Old emphasis on As you say like there might be the thing of like well, we just need to let the market go And so the argument is not this isn't a risk. It's that the best way to solve it is to have the strong market response Um, do you see that as the do you see that as being a clean line here? When you were writing that post and you're thinking the kinds of people who are emphasizing state capacity more and what it can do to empower Individual action or whatever are exactly the kind of people who are now arguing within each other in the libertarian community in that response I think who ended up where is 80 85 percent Uh predictable, you know, I would stress. I'm not a big fan of lockdowns. I did think in march We did the right thing by closing so many things so quickly because we knew so little And had to prepare hospitals and just figure out that like you can do things outside and if you're Modestly careful, it's probably fine almost all of the time Uh, but since then I don't think lockdowns have been a good idea. So, uh, I think really Lockdowns are just shifting exposure through time What you want to do is get to the point where you are winning the war against the virus And that you will do better with vaccines and testing Even tracing I've mixed feelings about uh, clearly there are countries that have done it well But i'm not sure I ever thought that that would be possible in the united states We are not a trace kind of country Uh and same with england It's just not something we're going to be very good at we're too big. We're too complicated. We're too messy We don't even have an integrated system of national id which i'm fine with by the way that we don't But given that we don't have systematic electronic medical records compatible across all systems So odds are trace was never going to work here in my view So, uh childhood friend and listener of the show paul mats go On the state capacity libertarianism question says He suggested the framing and i'll just provide it to you Based on the events of 2020 What are the best cases you what are the best cases you can make for or against state capacity libertarianism? So let's do the pro case. What is the pandemic? um How does the how does the pandemic bolster the case for state capacity libertarianism? Well, our best program in the united states operation warped speed Will have ended up making an enormous difference Getting us vaccines sooner and a broader choice of vaccines And if some of those in the pipeline had failed the fact that we invested in this portfolio of seven Would have turned out to have been very important Uh As i'm speaking we're not completely sure how important that will be but ex ante that was a brilliant decision And arguably we should have done more so That's the good side. I think the downside of state capacity libertarianism Is simply realizing there are some very nice features to not being surveilled all the time As they do in china when I said a moment ago that the united states Is not very good at trace though. It's good at innovating If you had stronger state capacity Presumably you should worry more about state surveillance than I do So that to me is the best case against state capacity libertarianism as I envision it Even though having a good trace regime would have been fine in this instance. I'm not sure it would have been a good precedent Yeah, one thinks about the fact that I think it's still the case that germany germany can't do a census because they're just such a cultural Resistance to a census a national census because of the way it was misused in the past And it's interesting how these cultural attitudes affect The ability the government to respond and set long term have these longer term effects But korea south korea did a remarkable trace Well, you know one person would get something and they Trace that person to hundreds of others and then test them Just as a logistics operation just incredible what they did Yes, my mother-in-law is korean and went back to korea over the summer and Uh her experience traveling there and the procedures and It probably was your ideal version of state capacity because it was very much empowering you to live your life But you were required to take a number of steps including downloading I think three different tracing apps and getting a lot of notifications about exposures and everything else But she was able to actually have a holiday while she was taking care of some family business, so But here's the thing. I did not get on to a plane And fly to korea now. I would have had to have quarantined. I think there it was for two weeks I don't recall but whatever the period was I could have done that. So I actually preferred to stay here Uh, but socially overall they did quite a good job Revisiting your conversation with russ and I think it's instructive just for all of us to go back and Examine what our attitudes were in middle march when things were starting to shut down and how long we thought things would last and so on You know, it seemed like If you look if you kind of read between the lines of what you all were saying I think the worst case scenario that you outlined was that You know, we'll still be in a situation like we are now maybe through august Maybe later. Thank you open it up to being a little bit later um, if we had known in march that it would be say a year Before life would resume to normal in some form of normal Where people can interact more freely in person And I know a lot of this is endogenous, but If we had known that we were in it for a year in march How do you think things would change? Would it have made things worse or better? I'm not sure it would have mattered because many people have been acting with very short time horizons I think overall my predictions in that episode are are quite good. I reread it recently And the biggest thing I got wrong was I thought unemployment would stay higher for longer than it did And the general underlying mistake in my forecast Was I thought people would stay terrified for longer than they did uh And they have resumed in many parts of the country in numerous ways And that has led Transmission to last longer in many cases Uh, it's also helped the job market come back. So that's what I was off on But I think I even said in that dialogue. Well, we'll probably have vaccines by march Of 2021 and at the time that was a very bizarre prediction that was not being widely made Uh, and it turns out, you know, it'll have been very very close to correct Yes, and uh, we can jump back into Twitter questions then Um, I'm also wondering when you're going to mention the biggest single event in cwt of the whole year And I wonder if we even agree on what it is but continue Oh my gosh now the the tables have turned now. I'm scrambling to figure what that could be Um, well, let me ask you a recent episode. You may not have even heard it yet But anyway, go on. Okay. Well, I think I think I know what you're talking about now But let's let's go back to Twitter and then we'll see Actually, uh Well, let's not change there. We'll we'll go to Twitter and we'll stay we'll stay somewhat along COVID lines Uh Brandon Tice on Twitter asks what are your tips for planning safe but still enjoyable local road trips? Do you think trips are still advisable with a Emerging wave I know you had spoken earlier about you went and visited new york at a time when after their wave had ceased and it was actually Arguably safer to go there than to stay in northern virginia at the time. Um How how would your outlook on trips change? Do you have anything planned for the winter months? I'm reluctant to tell people they should go because many of them shouldn't They might be more vulnerable than I am or just less disciplined as travelers So when I went to new york for one thing I drove up Which I typically never do And I was not even willing to use like the restrooms on the new jersey turnpike Which are ghastly in the best of times But I'm just like I'm going to pull over the car and do my business right here And that of course is extremely safe And new york then had about one tenth the covet load than northern virginia did when I went So I saw more people but it was all outside And at one tenth the load I was pretty sure I was not boosting my net risk and the trip itself seemed safe But again, most people will set out to do something like that and I'm not sure If they'll all pull it off So, you know right now I'm hanging around waiting for my vaccine figuring out how I will get one And uh, I don't have a trip planned, but I don't need to plan to do a trip So we're just going to see how everything goes Very well uh another question for twitter from Sisyphus What policy not sisyphus sisyphus? It's okay What policy consequences if any can we draw from the rapid development of vaccines in response to the pandemic? Is there any way to accelerate innovation in other areas similarly? And I'll just add on to this. I thought it was interesting that In your conversation with russ, you know, you would already This is true to form for you, but you had mentioned the notion of big prizes as a way to try to spur innovation and then In some ways you could see almost the seeds for fast grants Being discussed in that conversation though. I know it came separately But maybe this is a chance for you to talk a little bit about fast grants But then other ideas that you see based on the success of the rapid development of vaccines Including fast grants, but not only the world has seen It can address critical problems much more quickly than it had thought So the use of the internet to spread science was a big factor Philanthropists stepping up My own effort fast grants the idea that you would get grants to top researchers Within a number of days And make these submission forms super easy not the people had to worry about what kind of font was being used on the submission Not that they would have to wait six months for an answer But they would hear back in a few days and get the money, you know a day or two later We showed that can work and we did that to a scale of about 43 million dollars and Could have done more and it had a pretty substantial impact so Not just that but everyone sees when you put your mind to it You can be a lot better and do things more quickly and I hope we keep that lesson Emotionally internalized and don't just do it for the stuff that feels pressing now But do it for many more things take dengue right always with us It's not a new thing doesn't command the headlines It's a very high number of people each year can ruin their lives We should do more we can do more I think the pessimistic case would be One reason we were able to act so quickly on covid is because it became this clear focal point Where that was the thing to do is to figure out this problem And once we figure out this problem That energy will dissipate Um In ways that will prevent the kind of speed that we saw do you agree with that take or disagree It's certainly true that is a big advantage But I think as people expand the size and scope of their mental models They will see you can carve out sub sectors Of academia of philanthropy of government of private sector That take other maladies very seriously and they're not going to quite have the same urgency I mean one big advantage if you would call it that not advantage, but Other labs were closed unless you were doing covid work. So at least for a while There was a big substitution into covid work And uh, that's not going to be very common, right? But I also think the other tasks will benefit a lot from the work done on covid So the notion of a semi universal vaccine a testing to find other viruses Using mRNA vaccine platforms to combat other things All those will be offshoots of the covid triumphs. I believe I hope I think And uh, we need to see those through and not just give up on them Yeah All right, let's jump into the second round of name that production function These are all related to writing And I think I think these are a little bit easier, but let's see. All right All right, so first one From engineering I learned to start with an outline and decide what I wanted to say and then write all the sections to meet my outline Justice Breyer taught me just write all my paragraphs and then work backwards to figure out what I had to say after the fact Engineering Justice Breyer, who do we have on these shows? What I'm what I'm learning is that our recollection of these episodes. I mean, this is true of me as well is that A lot of these past episodes just feel A long time ago. I can distinctly remember doing this episode last year And the episodes felt very fresh to me But this year it feels like long periods of time have passed since we've recorded some of these But this person studied engineering at mit and then became a lawyer I don't know who we said That is rachel harman Who you spoke to about policing because she's done a lot of scholarship on oh, of course You know, I I don't have her. I brought a little cheat sheet list And you gave me a cheat sheet list and I made the mistake of looking at mine Rather than yours and her name wasn't on it. That's why I wrote all of these episodes It was a good episode. Yeah, it is a good episode and And yeah, I think we're three visiting but Yeah, studied MIT engineering at MIT and then Became a lawyer and talked about how those two kind of ways of viewing the world has been useful. Yeah, not just in writing Okay Second one on writing In college I would munch on a box of Dunkin Donuts to get some of these Second one on writing In college I would munch on a box of Dunkin Donuts to get through a term paper now. I find whatever cookies my kids have I always have some sweet junk food. This is probably not really great advice for anybody, but it's just my habit Is that emily st. John mandel? No, this is uh ashley mears. Okay And that very good episode one of the best of the year I thought Yes, ashley mears. Uh, and I think uh performed perform. Well, I think people did give that I was worried people wouldn't give it a chance, but from the numbers people Seemed to have given it a chance and I think uh those who've listened to it really enjoyed it All right next one I haven't always found writing easy at all I've been to a lot of therapy of various types to stabilize myself emotionally and psychologically I still do it's very important for me in handling the stresses that arise in writing And one of the things I realized in the course of that is actually rather than thinking it was something terrifying That I had to steal myself to do the best way to think about it was something I do every day So it's like exercise if I have the chance. I like to exercise. It's a puzzling activity I just treated almost like a game Rearranging the words trying to fix things Now is that emily st. John mandel? No, no Who is it?  It's just something like brushing your teeth. It's just Okay, last one My parents My parents really loved books. We always had a ton of books in the house We went to the library every week. I had an enormous time to read There was a period of time when one of the requirements to curriculum was that I had to write something every day That's what got me writing in the first place. I might have had a completely different life If I hadn't had so much time to spend reading in such a focus on books I mean, I guess emily st. John mandel again third time's the charm. You're correct That one was emily st. John mandel. Thank you for playing name that production function I uh, I is it just me or did you not explicitly ask it this much this year? Um, I was reviewing the conversations and I I did leave some out for for this segment, but Um, it also didn't seem to come up as explicitly as a segment If it came up, it was a little more Organic, yeah I just think you have to vary somewhat and not become too formulaic And even if something is good or people like it better to leave them wanting More than they just know it's coming all the time. So That's part of my production function Yeah Okay, so why don't we uh, so you've mentioned that I haven't brought up the big highlight of the year So what what is it Tyler?  Well, you tell me what you think it is From context clues, I'm guessing it's your interview with John Brennan. Is that right? That's correct And one of my questions in particular I'm reluctant to speak for him because the exact wording is very important and careful So I urge you all to check the transcript, but I asked him about UFOs And I pushed him on it And as I understood his answer again with this caveat, please read and listen to his words Don't take my word for it, but I took him to be saying That the single most likely explanation Was in some way alien beings now. He wasn't saying that's higher than 50 percent But simply that of all the explanations. He didn't see a better one than that And he was head of the cia for what four years Now he wasn't pretending to know he's he's not like, oh, I've got the little green men, you know hidden under the ground somewhere and in Langley Just after having thought about it long and hard He thought we needed to seriously entertain that possibility. But again, please check his words One of the crazy things about 2020 has has been this sort of under sort of under discussed acceptance of what you just described that That it has become more mainstream is the wrong word but more accepted among smart people that We may be seeing actual signs of alien life or it may not be likely But it's becoming the most likely explanation And there's you know, even if it is which I give, you know, five percent I've been saying it's almost certainly drones not that the proverb be a little green men are inside but It should be a big big thing And it isn't And that to me is so startling uh So brennan can say what he said It won't be on the front page of the new york time. Some number of people will talk about it uh To me that's more remarkable than the phenomenon itself It's the lack of interest. Oh fair me paradox. Well, it turns out, you know, they've been here. Oh, whatever. Okay, forget about that one I yes, and I I think that relates back to covet too because in any kind of dramatization of a pandemic It is so focal to people's it is the thing that everyone is thinking about all the time And that has not been the case Across the country for Even, you know, for someone like me, I mean, there are certainly days when You know, I'm not I'm not, you know, driving through quarantine checkpoints I'm living my life in my house and trying to keep to myself and similarly There have been a number of stories that have come out in 2020 that That if you were experiencing the movie version of this It would be a huge thing that the characters would be listening to on the radio and it would be everyone would be buzzing about it And they've just gone totally unnoticed. I've never seen a year like this, right? yeah, um in some ways it's kind of You you think about how the history books will be written about it Because we think it'll be all coveted But it might be all these crazy discoveries that we made in 2020 that some of which had something to do with covet But many of which didn't space acts and protein folding a lot happened this year that arguably is getting us out of the great stagnation Yeah Okay, some more questions for twitter and then then we'll wrap it up Um Paul tilly on twitter asks what industries or groups surprised you in their response to covet good or bad? Well that the nba just shut down all games as early as it did in march Was brilliant and prescient And that that they would have the guts to pull the button on that Rather than dragging it out.  I've always liked the nba, but uh For that they deserve a prize On the downside You know, I don't think you should blame small businesses or businesses for wanting to reopen Even if it's bad for society, maybe you should blame the people who go uh but just The ease at which people have Considered going to these very large scale events like college football games In a way that to me just doesn't make any sense So I believe an intertemporal substitution If you can don't do it for a year, but next year go to twice as many games And how hard people find that to do Uh is really striking and we actually need to incorporate into our economic models So I can travel less this year and next year vaccinated. I might take more trips, right? If the world will let me Uh do more face-to-face CWT's and so on Hang out with lydia davis, whatever But uh people don't think that way It's more a utility function of habit formation than intertemporal substitution than I would have thought And I already knew the behavioral evidence on that So it's not that I'm completely in the dark that people aren't entirely rational But even then I've revised my priors yeah Another question from nickel mulani Any big changes to your production? To your production function in 2020 that you think will stick around for the future Oh, we'll stick while doing these by zoom will partially stick. I suspect I think I wake up slightly later In the morning Not by much just like by 10 15 minutes. I wonder if that will stick uh Cooking more. No, that's not gonna stick Uh So mostly I'll go back. I hope I you know again It's when the world lets me is the binding constraint and I think it will You mentioned in your conversation with rest that you thought, you know That there would be kind of an average is over aspect to the return to face-to-face that More would happen Over zoom or remotely because we've gotten better at it and then the face-to-face would You would require more of it that you would you would savor it and Maybe even Save it for special occasions or just yeah try to get more out of it. Do you Do you that there might be some exuberant return to face-to-face? Do you think do you think that's going to happen vaccine rollout? I used more explicit language than that if you recall It may happen before vaccine rollout Uh, but I think that will be the case There'll be a certain amount of people going crazy and that might just mean a lot of strips to the shopping mall It might mean Other things that won't mention on a family podcast But a lot of people have just returned to normal routines already So again, that's a big part of what surprised me But certainly not say in california or new york. You haven't really been able to I have you thought at all about the How it might be determined by locality I mean living in dc one of the things that you get a viewpoint in is I was living in dc Um, I could see what was happening in maryland. I could see what was happening in dc I could easily see what was happening in virginia Um, and then for anyone who's done any kind of interstate travel by car It's striking the degree to which you can just sense the different response Just passing through And so in a place like dc or say la which is still very You know, you have to wear a mask in public versus other places where it's uh, well, it's indoors and if you know It's a little more laissez-faire even if they have Restrictions on the books. I wonder if that will linger if there will be the kind of you go to dc and playground etiquette Will be different than playground etiquette, you know in north carolina or whatever I think it will we've been cut off from each other People don't quite know how other places are what they're doing how they feel I've been to maryland chesapeake west virginia southern, ohio New jersey new york city new york state northern virginia, of course The part of maryland near dc And each and every one of those areas has been quite different Uh, and again, i'm not sure that's something I would have expected It's a kind of counter to these globalization homogenization arguments And I do think much of that will stick Yeah Um, all right last question for twitter from craig paulson, uh ev fellow He asked when we're gonna get the book with daniel gross on talent. This is your next book. I believe any update on timeline there We have a draft of about 80 000 words if I recall it is not finished, but it is well along And the when depends exactly on the publisher Of course, we're recording this Before it is being presented to all you listeners. I expect that by the time you're hearing this I will know when but at the moment I don't quite know exactly when but it's well along It's not like a figment dream in our heads. It exists It needs to be better needs to be finished But it will come out and not you know five years from now All right, so let's switch to thinking about the year ahead. So I'm gonna Ask you to channel your I don't know your super forecasting abilities First question. Will you be moving to substack in the coming year? No I write for free on marginal revolution I'm fully aware that people who do substack can earn a lot of money But I'd actually rather have the bigger audience and as you all know conversations with tyler is free There's no ads. It's fully open And I just think that to have audiences like this is a privilege Greater than the money. I know that's weird, but No, I think I think we're in a I very much enjoy producing a podcast that we don't Have to worry about monetizing it explicitly By running ads as much as I would enjoy having tyler Read ad copy every episode. I think I think that would get old quickly In what month do you think we will record the first in-person cwt? Oh, I think that's pretty random, you know, it could be quite soon if it's outdoors There's that homeless man, you know, we want to record. It could just be someone I know and trust Uh, I'm not sure where I'll be in priority line for vaccines But I'll say february All right, february. Yeah, we have talked about uh And it depends on you and alice and other people. I mean if you all don't want to do it You know, we're not going to do it. So someone has to be there to make it work And uh, you know, it is unanimity rule. It's not my say so Yeah, I think the big the big issue has been Um Travel and if you have to travel then it's harder to do it safely Um, but certainly if if the people are local, um, that's something we can certainly accommodate Um Will we hold a live event for cwt? live recording in 2021 calendar 2021 I'll predict yes Uh, but not in the spring Yeah, I think so too. Again, maybe with the caveat that we've we in the warmer months It's not necessarily that everyone has gotten the vaccine but um, but we here's the thing the auditorium is not booked, right? That's a big head start That's right. Um Not related to cdt and will you when will you watch a movie in a theater with people you don't know? Oh last week Oh, you've done it Natasha. Well, you rent out the theater privately And natasha invited two of her russian friends In a theater that like seats 150 And i'm like, I don't know these people. Do you trust them? And she does and she gave me really very convincing evidence that they're Even like past the point of optimal safety and to sit in opposite corners of a huge theater Uh, I've been running out theaters a few times. It's not as much as you think And uh, I hope the price doesn't go up. It's a great thing to do Uh, so Yeah, you got out of that question on a technicality So you were with people you don't know but I was thinking specifically of a scenario in which You're buying a ticket and you don't have control of the theater. When do you think that'll happen for you? Well, the second vaccine dose is two or three weeks after the first so that day No, you need some time for immunity to to kick in so Uh, that's probably another two weeks That's when is that an answer to the question of what's The first thing is you're going to be doing as soon as that that Absolutely I mean, it depends what's showing right? But that's the first thing I want to do How important is the theater? What speaks to you about the theater experience? Do you care about the technical specs of projection and sound? Is it everything? It's everything It's the greatest art form of the 20th century And I was born in the 20th century and I'm going to stick with that form as long as I can And see what it does for me. It's not always good. I'm very willing to walk out Uh, but I want to be in the theater again seeing a new release and not having to pay a hundred bucks to rent out the whole thing But in the meantime, I will pay up. Yes Well, I hope that you will be able to enjoy A theater and enjoy going to see movies with other people I hope that we will be able to see each other face to face because I don't think we've even seen each other face to face since Maybe april when I recorded the tenlock episode remotely And we were very concerned with like disinfecting the microphone and wearing gloves But masks were not a thing yet, but we did it in a socially distanced way But I am looking forward to a resumption of some face to face With conversations with tyler in the next year And before I go, I want to thank everyone on the team who has helped make our switch this year There's been a lot of work done behind the scenes To prep guests and to equip them with equipment They need to keep the quality of the conversations high. So let me give a shout out to everyone who helped out this year That's dallas floor graven laura katelyn schmidt kate brown kate delinoy mycopper slone shearman karen plant christina b Hailey larson animic vade carter willey ashley schiller Thank you all very much And we look forward to another year of production You remember that list better than I remember people's production functions But I would second and third that wholeheartedly and thanks to you all for listening and or reading A great pleasure to have you as an audience And you yourself jeff obviously should be on the list. Thank you


my life in college is also such it's up to now it's the most inspiring and the most variable life period that I have. But the good thing is I had a good result because I become more independent, I become more like an adult, I gain more skills that I need. I think this is the time when I really depend on my own because my family are not in America. I only depend on myself, my community here, my peers, my friends. So it's such a precious life period where when I kind of reshape and not reshape but reshape by reform and improve myself to become a better person that I personally like and I personally feel proud of. Yeah I think it's memorable and I don't regret that I made the choice of studying abroad. It's so precious even though there are so many stresses. It's still rewarding and I'm glad that I made the right choice.


means that h tilde n k l minus 1 x is actually equal to minus the sum y equals x0. OK, sorry about this long equations. There's not much I can do about it. But you see, because you have this difference and you know that it's 0 on the boundary, you can just sum from the boundary to your point and you get your function. That's easy enough. What that means is that if this thing, yeah, l minus 1. So if this thing is a polynomial of degree k minus l, then this thing's a polynomial of degree k minus l plus 1. OK. And at k, it's obvious the thing is a polynomial of degree 0 of degree 1, 0 of degree 0, right? So they just increase by degree each time you go back, which is exactly what was asked. OK, so their polynomial, that proves 2. So now we have to prove 1. So this is a really fun. If sum over z, sorry, and I think I should be at k. Oh, by the way, I said it proves, I'm sorry, I said it proves 2, but it proves that this guy is a polynomial of the right degree. But then this is just a convolution with shifts of the thing. So of course, that becomes a polynomial of the same degree. That's easy to see. OK, so that proves that these guys are actually polynomials of the right degree. This thing, not enough room on these boards to write these formulas. So hk, this is a continuation of it. That's a product. OK, so I just wrote it out. You get this sum, OK? But now you've got RT, you've got this sum, and you could put the sum first on the z's. If you do the sum on the z's, there's RT, RT inverse. So that just becomes an identity. And that means that z1 is equal to z2. So this thing is equal to the sum over z of q to the minus l z x0 n minus l hk n 0 z. But that's actually just a way of writing q star minus l acting on h, OK? But what does q star do to h? It shifts it around in the l's. So this is hk n of l, and then you just evaluate at x0 n minus l. And lo and behold, it's told you to evaluate it on the curve x0 at l, but that's only equal to 1 when l is k. So now we found the phi's, and that's always true. Now you can see why to get a closed-form formula for this might be a little bit tricky. You see, if you want a formula for something, you have to be able to calculate the hidden probability of a geometric walk to that curve if you want an exact formula. If the curve is just linear, particle, hole, hole, particle, hole, hole, then it just goes up like that. And we all know how to calculate the probability of a Brownian motion to a line. And it works also for geometric random walks. Same tricks. These are actually beautiful because you jump over because of the memoryless property of geometrics. It just forgets that. So it's just perfect. So you can calculate probabilities to two lines. But this thing would ask you to calculate the probability that you go hit a staircase. So it's obviously not going to be a nice formula. So let me just write out the conclusion. kTn, this is the one point. That's all we needed, is RT, this funny RT on the sides, q to the minus n, g0n inverse, where g0n equals probability where tau0n is just the first time you hit the curve between minus 1 and n minus 1. I'm sorry, it comes out slightly awkward enough. But this isn't actually true. This is only true for below the curve. Above the curve, it's some sort of analytic extension of that. I want to write it a slightly different way. So this formula actually only holds below the curve. But I want to write it everywhere. And when you try to write it everywhere, you find out it's this. Things start to look familiar, where I should actually call this sort of script s, because it's not the same s as before. It's the microscopic s. So this script s is equal to e to the minus t over 2. This r, I'm just writing it out, and this is q. And q bar is an analytic extension of q. If you like, these things are given by contour integrals. But perhaps I won't write the contour integral down. And epi, s bar epi x0, is just the expectation. Now these are geometric walks instead of Brownian motions of this s bar. So now it has to hit before time end. And so that's the solution of Tasep. So the theorem is sort of written in different pieces here. This holds with that kernel for any right finite initial data. OK? One can also write formulas for not right finite initial data, but they're a little bit more cumbersome. It wants to be written like this, I'm not sure why. And of course, if you've got some special case where you can compute the hitting time to a curve, for example, the periodic, you just compute it. You can calculate the s epi explicitly. And it's just exactly the formulas they had before. OK? Yeah. That's easy. Well, because you're trying to hit the curve x0. So particle, whole, whole, particle, whole, whole, that just means that x0 is minus 3i. So you're trying to hit the curve minus, I can't draw anything for the life of me, you're trying to hit the curve minus 3i. Of course, it's just the other one is a little staircase. So it's not surprising you don't have exact formula. But of course, everything we do is soft, so of course the staircase gets proved by just linking it to the other guys. So for example, for the staircase, you will not have a completely explicit formula here. It'll be mildly inexplicit in terms of hitting times of the staircase. When you pass to the KPZ limit, it doesn't care if you had a little staircase or if you had a straight guy. They're all flat. OK? Does it make sense? I should just add a word because I want to show you, I have 15 minutes, so I want to show you a little bit of the scaling. I said I would do the 1, 2, 3 scaling today, so I'll try to do that. While this is true, it's not actually true that these Ks in this case are trace class operators, but there is a conjugation to make them trace class operators. And that's enough to make the sense of the Fred Holm Determine because the Fred Holm Determine is invariant under conjugations. So if you can conjugate to a trace class operator, that's fine. It means that the space may actually not be exactly L2, but it's something a little bit different. And this R is a typo. Of course, that's Z. OK, so now we want to take the 1, 2, 3 scaling limit of this thing. I just want to show you how remarkably easy it is. Once things are written in this form, so we'll take the density is about a half. And then we know that we should restail h epsilon tx. We know from the first lecture epsilon to 1 half h2 epsilon to the minus 3 halves t epsilon to the minus 2 epsilon to the minus 1 x plus epsilon to the minus 3 halves t. And this thing is supposed to go to the KBZ fixed point as long as initially the functions converge to some function. So you set things up so that h epsilon 0x, this is you take your Tasep height profile and you produce h epsilon. And you set it up initial condition so that h epsilon 0x converges to some upper semi-continuous function in the Hausdorff topology I talked about. OK? Now, hT z, as I said before, is basically just the inverse of xT minus 1 z minus 1 minus x0 inverse x1 minus z. So it's basically the same thing as the inverse of x0. And so the probability that this function is less than or equal to something just gets translated into the probability that x0 of, OK, it's a little bit complicated, but it's not anything difficult. So it'll just take me a second to write.  And that tells you the probability that h was less than these ai's at the appropriate points. OK? You wanted to know that hT xi is less than or equal to ai and it just translates into this. OK, so we can call this number n. And we just have to do some rescaling of our formula. OK? Here's the formula. Let's take, for example, this guy here. We want to rescale him. So when you untranslate through this whole thing, you want to take a limit. So you're trying to take a limit. So you just take a limit of this and a limit of this, right? I'm basically going to show you how to take a limit of this. And then you'll see the rest. OK. So when you translate, you get epsilon minus 1 half s minus epsilon to the minus 3 halves t. This is the microscopic s.  Takes a while to get them straight. OK? So that's the new t and that's the new n. And I think I dropped a, but it doesn't matter. You'll see that it's not here. Of course, you can just write x plus epsilon to the 1 half a. OK. Now the s has variables. And of course, when you take a limit of friend-holder determinants, you may have to shift the variables. You may have to do conjugations to get the thing to come out right. And here you have to do a little shift. So we have to evaluate, first of all, that the lattice size is this. But actually, you have to shift 2 epsilon minus 1 x plus epsilon to the minus 1 half u. And that's allowed because of conjugation. OK. All right, so we want to take a limit of this. And you may think this looks very imposing. But actually, the limit is like butter. Because this is just this. And q inverse, I have a fourth of a fourth. So this is just e to the minus epsilon to the minus 3 halves t over 2 times minus 1 half grad minus plus. OK, now the q to the minus 1. q to the minus 1 was 1 plus 2 grad plus. And I said it has a kernel. But that kernel is actually not an L2. So you don't have to worry about that. So I'm just going to write that as e to the log. And you might think, well, that's not quite allowed because grad plus is an operator bounded by 1. But we're on a lattice of size epsilon. So actually, grad plus is size epsilon to the, lattice of size epsilon to the 1 half. So we're, so grad plus is an operator of size epsilon to the 1 half. So that's OK. So plus 1 quarter log 1 plus 2 grad plus. So just remember, that's the order of epsilon 1 half. And then, OK, so we've got that. And then actually, I want to separate out the epsilon to the minus 1 x here and write this as q star epsilon to the minus 1 x. OK, that's what you get. And I didn't write inside the variables. Fair enough? Now this guy here, this guy's being evaluated at this point here. And that's actually the mean of this random walk q star. So you won't be very surprised to know that this thing goes to e to the x d squared. That's OK if x is positive. If x is negative, then you have to pull some more stuff into the other guy and then pay for it later. That's OK. So this is actually very easy. That is just the standard convergence of random walks properly resented to Brownian motions. But what about this thing? So here's the black magic. Minus 1 half grad minus. And now I'll just expand the log. And remember, we're on a lattice of size epsilon 1 half. So grads are size epsilon 1 half. That's 2 grad. This is just expansion of the log plus. And now the next term is going to be order epsilon 1 half to the fourth. So this is order epsilon squared. That's what's inside here. Fair enough? Now this thing is completely amazing. Got minus grad minus plus the same 1 half grad plus. So that's a Laplacian. Does anyone see that? That's a discrete Laplace operator.  Sorry. There's a plus. Sorry. Plus minus 1 quarter times 1 half of 2 grad plus squared. And then this thing is like cubed. Sorry. I just want to see if that's correct. It really matters. OK, good. Sorry. OK, now it's correct. I hope you can all expand the log for me and just tell me if I made a mistake here. I'm pretty sure this is correct. OK. So this and this is a Laplacian. A standard centered Laplace operator. But if you take grad plus squared, it's actually a Laplace operator also, but it's shifted by 1. Because it evaluates at 2 minus 2 times 1 plus. So you get this Laplace operator minus this Laplace operator, which is a difference of Laplace operators, which is a third derivative. Plus a third derivative. So the whole thing after a little bit of computation, and you've got this epsilon to the minus 3 halves times the size epsilon 1 half, this thing is e to the t over 3 d cubed. Why would the third derivative come up in a probability problem? I have no idea. So you see the S is just converged to this S operators, which I wrote out there erased. The S is just converged in a few seconds to the S operators in the continuum. And now the epi operator, well, the epi operator is just evaluating random walk paths of these S's. And it's not too hard to imagine that the random walks are just converging to Brownian motions, hitting the rescaled x0 path, which just turns out to be minus the height function, because x0 is the inverse of h.  And so that gives you the K-P-Z fixed point formula. So let me just try that. Maybe I'll just say it. So what you check is that the limiting guys also under a conjugation are chase class. And the map from initial data in UC, remember UC is upper semi-continuous functions with this local Hausdorff topology. And it turns out they have to be bounded by linear infinity. And G in LC, which is just minus UC to these operators, K is a operator K-hypof minus 2 over 2 K epi G 2 over 2. Or it might have a minus sign on it, it doesn't matter. That this map is actually a continuous map in trace class. And that means you can pass to the limit. So in other words, if you've set up your initial data so that h0x converges in UC to a later profile, then at time t later, the whole thing converges. Again, to the kpz fixed point. OK? So it's that soft. There's one little twist to this, which I haven't gotten to, and I'll just explain in words. We started with right finite initial data. So when we get to the kpz fixed point, we had a kpz fixed point, which the initial data has to be minus infinity after a certain point to the right. So everything I've written is only proved so far for initial data for the kpz fixed point, which is minus infinity to the right of, well, 0, but it doesn't matter because of translation invariance. So it just has to be to the right of some point. Does that make sense? But now you can check, because you have exact formulas, you can check how much it matters out there. There's a worst case scenario, which is you just start with something which is growing linearly at infinity. And then there's the other worst case scenario, which is you have minus infinity to infinity. And you can check that the difference, if you're at minus l and you cut off, is actually like e to the minus l cubed uniformly in the limit as you take the casep under the 1, 2, 3 scaling to the kpz fixed point. So that means it's very easy to remove that, and you get the convergence for anything. And so that's the difference. I'll stop there.


I've talked about pick-up-and-play games, meaning games that have a simple display with simple controls that just about anyone can get the hang of, and I've talked about pick-up-and-die games, meaning really difficult games where you pretty much just have to die many, many times to get any progress in the game. Then there's games that developer Rare makes for the NES, some of which fall into a different category, being pick-up and what the hell even is this? Marble Madness falls into this category, and Solar Jetman as well. Both of those games have very particular controls that are tough to even approach, let alone get used to, but both of those are still good games. Rare also developed Captain's Skyhawk, and it also falls into that pick-up and what even is this category as well, but I'm not totally sure it's a good game. On the surface, it looks awesome, as most Rare NES games do, but it is tough to get into, and this time not just because of the controls and the unconventional display, but also the difficulty. You play as a fighter jet, getting five lives and three continues to get through nine levels with no saves or passwords, with some levels featuring unique objectives like dropping off supplies in these holes here, picking up passengers, or docking with your space station once your mission is complete. The trouble here is with the controls, they feature the now-traditional pilot controls, where to climb you press down and to dive you press up, but it's a bit rough around the edges to say the least. The controls are just a bit drifty and slow to respond, I guess you can get used to them eventually, but I sure as hell had a hard time doing that. It was just tough for my primitive brain to predict when my fighter jet would stop drifting once I let go of left or right on the D-pad. You can also hold select while pressing left or right, and you do a barrel roll! Sorry, just fulfilling my obligations. Another major issue here is with the very first level, it's kind of a Zaxxon style, only you're flying straight ahead, but you're still skimming the ground and shooting stuff as you go. The problem is that there's so much debris when you blow something up, it can be tough to determine between what are the smoldering remains of your enemies, and what's an enemy projectile coming at you. I swear I died like 20 times on this first level alone. It doesn't help that in many cases you get so caught up in dodging projectiles that you end up crashing into the terrain. It took a long while, but I finally got the rhythm down and I was able to better recognize enemy projectiles while not crashing into stuff, but yeah, some of you out there may not have that kind of patience. You do get rewarded for your patience though, in the form of these stages here. It's essentially the NES doing its version of Afterburner, and it's pretty dang good. The controls feel a bit more forgiving since you have a little more space to work with, and it's simple, seek and destroy enemy fighters. I should mention that you collect credits from each enemy you destroy, and if you're able to successfully dock with your space station, you can use those to upgrade your default weapon or to buy bonus weapons, and there's three extra to choose from. Intercept missiles, air-to-ground missiles, and Hawk bombs, but the game kind of holds your hand here a bit and only makes bombs available on certain levels where they're, you know, actually useful. There is a story here, but it's nothing you can't guess or even make up yourself. Aliens have invaded Earth and have built four bases across the planet designed to drain Earth's energy somehow, in order to feed their own space station thing, I guess. You, as Captain Skyhawk, have been chosen to fly a fighter jet designed to buy scientists, so sayeth the instruction manual. Shouldn't engineers be designing those instead of scientists? Anyway, you fly the F-14 VTS to make stuff go boom until there's no more stuff to go boom. Anyway, Captain Skyhawk gets plenty of points for looking really cool, but the Drifty controls and the difficulty here means that you have to be really patient to get into this one. I will say, when you die, the checkpoints are pretty forgiving, since you start reasonably close to where you died, but that's not gonna make up for the game's flaws. If you really want to play a shooter similar to this, I'd roll with the aforementioned Zaxxon or Afterburner, even on the Sega Master System. They're just much more approachable than this one. If you do approach Captain Skyhawk on the NES, be prepared for a lot of frustration. Yeah, there's some good stuff here, but you gotta put the work in to get to it. Alright, I want to thank you for watching, and I hope you have a great rest of your day.


This is stock number 2-1 J2-1. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used Jeep and Jeep Wrangler headquarters. Today we are checking out this brand new 2021 Jeep Wrangler Unlimited Rubicon. This one has the award-winning 3.6 liter Pentastar V6 motor which gives you 285 horsepower 260-foot pounds of torque. It is matched up with the 8-speed automatic transmission and it is in black clear coat. We shoot all of our videos in 1080p 60 frames per second so if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is definitely your best way to check out the quality and condition of the vehicle before seeing it in person and in this case on a brand new vehicle the looks and styling. So obviously this one has the LED light group. Get the Rubicon badging on the side and if you'd like to check out all the photos on this Jeep in the upper right hand part of your screen as a link to our website click that and check us out there. This one comes with these special 17-inch painted and polished aluminum lipped rims and it has BF Goodrich All Terrain LT 285 70R 17 tires. Definitely an all-terrain tread pattern to those tires. You get the Granite Crystal Jeep and Trail Rated logo with the red outline. Then you get the black letters with the red outline on the hood. The Sport hood on there. The LED lighting group gives you the LED running lights, the LED headlamps and the LED halo lights there. You also get LED fog lights and the red toe hooks on the front of the vehicle. This one does have the plastic bumpers. You can get the metal bumpers on these as an option. A couple little Easter eggs here.  You also get T-50 on the side that tells you which Torx wrench to use to get those door hinge bolts out. You get the rock rail standard with the Wrangler Rubicon. It has the enter and go system so if you have the keys in your hand or your pocket you just have to put your hand in the door handle and it'll automatically unlock. Here's a look at the original window sticker. I'm not going to go through everything so feel free to pause this at any time. Everything on the left there is your standard equipment and then the optional equipment starts at the bottom there. Black clear coat paints 245 leather trimmed bucket seats are $15.95. Cold weather group gives you heated seats and remote start. That's $9.95. LED lighting group is $12.95 which is everything you just looked at. Daypoint 4 radio and premium audio group is $18.95 so that gives you the Alpine premium sound system with the subwoofer in the back. Also has the navigation system, the serious guardian for a year and travel ink and traffic plus for five years which is really a nice setup if you think about it for $18.95. Dual top group is $23.95 so you get the soft top included. 8-speed automatic transmission and the V6 are $3,000 combined. You get the keyless enter and go system which is $5.45 and then that color match hard top is $13.95 or I'm sorry $13.00 and then the color match vendors are $6.95. Those special rims are $9.95 total MSRP is $58.665 and if you'd like to get your summit price in the upper right-hand part your screen is a link to our website check that out there to get all the rebates and incentives on this Jeep. Three year 36 bumper to bumper and five year 60 powertrain. They're your miles per gallon 24 highway at 19 city and 21 average for a full-size Jeep that's pretty amazing and then you get your four star front crash test radio and roll over it's all rated before. You do get four-wheel disc brakes on this vehicle and I believe on the Rubicon they're heavy-duty. On the back here notice you get the LED tail lamps as well. You get your HD backup camera get a better look at that tire tread there. You also get LED lights for your license plate lights and red tow hooks on the back as well. Not much to see back here since we have the box for the soft top back here. I did want to point out you can still take these hard tops off you got three bolts on each side two on the top for a total of four and then two quick disconnects for your electrical and windshield washer fluid. Those bars are now painted to match the vehicle. They made these back doors a lot lighter you also get the badge back here for the two door four-door wheelbase and overall length as well as water-forting and that's some pretty cool stuff there. Shuts nice and solidly and a lot smoother than the old JKs used to. I don't think I'd get a Wrangler without the color match top it's always really good looking. You do get the heated mirrors on here. Inside the leather trimmed seat package gives you the black leather seats with the red stitching. You also get the red Rubicon stitching up there and they now come with side airbags right there. This is your lumbar and driver's seat height adjuster. Comes with factory formats auto headlamps and tilt and telescopic steering wheel. As we hop inside the vehicle here you can see at this one only has 22 miles because it is brand new and you get these 7 inch LCD display. Check out the animation that goes across there pretty cool. You get a digital spinometer you get the compass then you'll get a time or miles to empty or you can change those to whatever you want totally customizable. Has the heated leather wrap steering wheel cruise controls on the right bluetooth and information center controls on the left and then audio controls on the back of the steering wheel. You get the 8.4 with the premium audio group and navigation system. Has AM, FM and Sirius XM radio capabilities. You can do your climate controls here as well. I think we have to have the next accessory on to do that. You got dual climate controls you can control where the air is blowing. You also have your heated seats and heated steering wheel buttons and you can check out that backup camera. You can see just how crystal clear that is. It's definitely an HD backup camera. Those grid lines are dynamic meaning that they're going to turn as you turn that steering wheel and if you were to ever put a receiver hitch on this this line right here would line right up with that so you could get hooked up to your boat or camper or whatever you were hauling first time every time. So then you also have the apps on here so you have the off-road pages and the projection manager so the projection manager is where you can project your cell phone via Android Auto or Apple CarPlay to the screen and if you have a different navigation system say Waze or Google Maps you can project that to the screen and use it right on the screen also works for media and songs and stuff like that. We actually did a demo on Android Auto if you want to check that out it's in the upper right hand part of the screen. Works very similar for Apple CarPlay but we did a demo so check out that video and then you get your off-road pages which are pretty cool. They do take a second to load so while they're loading I can say that you can do all your climate controls and everything down here as well as volume and tune controls. You get the little animation on there as well. You can see it has the pitch and roll. You can see we're nice and flat in our brand new picture studio. You got latitude, longitude and altitude and I think because we're inside the building here we can't get a really good read from the satellite so that's why it says zero for the altitude. You got coolant oil, coolant temp, oil temp, battery voltage, trans temp and oil pressure and then you have your drivetrain here so with the Rubicon you also obviously get the sway bar disconnect or connected front axle if it's locked and rear axle if it's locked or not tells you all that stuff as well as your steering angle so you turn that and you can see that those angles change which are pretty cool and then yeah just a lot of cool stuff that you can do with this radio in addition to the serious traveling and traffic plus that they give you as well. You get down here you got a media center AUG's USB USB-C and then this is what makes a Rubicon a Rubicon if you can lock that you can lock your front and rear axles or just the rear axle and then you have the sway bar disconnect right there and then you have an off-road plus mode too. 4x4 shifter on the floor and then the 8-speed automatic transmission you get the little wrangler on the top there or I should say the Jeep on the top there and then you get the switch blade key which is pretty sweet and you get remote start on there as well so Jeep on the back it's definitely heavy-duty well put together definitely a solid key fob so you know which key fobs in your pocket. You get that red dash finish on this one you also get the red stitching on the dash up there has the auto dimming mirror SOS and assist buttons the front hardtop pieces come off very similar to the old JKs the only thing you don't have is those screw-ins in the middle there and then you do get the latches up here and I don't know if I said it but home link so you can do your garage doors and everything. We'll do one more walk around here I'll leave the lights on for you so that you can check out all those LED lights. The other thing that they do on the Rubicons is they put this 3M tape on the back of the front fenders so that you don't get these all rock chipped up bigger tires tend to throw rocks up a little bit more so it's nice that they're protecting your investment you can see you get the LED tail lamps there and I would personally like to thank you for checking out the video today and hopefully from this HD video you will have gotten a really good idea of the overall styling and options on this particular Wrangler check out those LED lights there seven slotted grille and to see more pictures of this Jeep or one of our other 450 new and used cars trucks SUVs minivans Wranglers you name it we got it go to our website www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summitauto.com and if you like to check out more HD videos you can go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos that you see there in fact in a second you'll see link to subscribe to our YouTube channel on your left a link to more Jeep Wrangler videos like this one on your right if you have not been to our website on the bottom link to this vehicle on our website click those check us out and we're super excited to be offering the 2021 Jeep Wrangler Rubicon in black clear coat with the color match fenders and hard top thanks again for checking out the video


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