Collaboration anyone can I hear anyone? Oh, hold on. I need to unmute people. Okay I'm mute. I'm unmuting Ivan. I'm unmuting Con VB Okay, I think I am muting David The one guy I know hold on it looks like we can do it ourselves Sorry Okay, so yeah, I'm new to this. This is but I wonder why my videos not showing All right. Hey everybody. All right Whoever's here. Let's talk. I'm open. Hello. Who's here? Who's not muted? Who's here? I'm here Hello Yeah, who's this? It's con Ivan Hello, I See yeah, I see con okay Okay, I guess people mute and unmute themselves. Okay, this is my first attempt at this So my idea was if this works, I will do more in the future But I thought this would be like, you know an attempt. So any suggestions comments? Whatever I'm open Someone say something ask a question Can I ask a question? Sure I was reading through the citations of one of your articles how we come to own ourselves and In the citations there was an English translation of one of Hoppe's writings things called property anarchy in the state But it said it was an informal translation. I wanted to know Where if you had that translation and I have a follow-up question if you Well, we could talk fairly informally here To be honest, this is a strange coincidence. I just talked to Hans hoppa Five minutes ago. We were talking on the phone We were friends we talk all the time I'm not sure which Which that which audit which which Publication that is Could you could you tell me more because I don't remember any kind of anything about that It's it's in German. It's good I can really read it but I can to anarchy and Start and it's in your article how we come to our own ourselves It says there was an informal English translation of it But I couldn't find I couldn't find it on the internet if it is on the internet. So I Think if I remember what happened was Hans told me yes, I thought of this before but it's not been translated and so I looked into it And I think Gido Holtzman or Hans. I can't remember which one at this point helped me translate a few passages But as far as I know that particular piece is not in Translated from German into English or other languages I Would like to but all I have is the Translations of a few passages that I got out of Gido Holtzman and in Hans The reason I asked this is because I'm currently trying to write something on children rights and The in the in your article you talked about that a lot And I wanted to ask if you still hold the belief that we have positive obligations for children. We need to Satisfy Yeah, my view is not changed I think that if you You know Create a life that is arguably rights-bearing then yes, you have some positive obligations to take care of that life just the normal, you know Conservative traditionalist view of of living I Don't think is that controversial How you format why you have this obligation is a libertarian thing But yeah, sure. Yeah, I don't disagree that you have an obligate the problem is saying you have an obligation Doesn't mean too much because if you don't have a statist apparatus to enforce it What does it really mean? Right? I mean If you have a 14 year old child who's being abused and neglected They're basically better off to run away and find a new life or a new home or a new set of parents or whatever then to try to Sue their parents for support. Yeah, excuse me, sir Sure, you allow my friends to join. I'm trying right now. Hold on a second. Hold on a second. Okay Any questions comments discussions anything I mean, I'm open to anything I'm just doing this as an experiment to see what what might work in the teacher Could I ask a question? Mr. Kinsella? Sure You can you hear me properly? I hear you Okay Mr. Kinsella, I Wanted to know I'm a lawyer based in Paris. My name is Viraj Bidi and I know that you have worked a little bit on questions of International investment law and things like that. I think you also written a book which was published by Oxford of Quite of quite of a quite a while back. Is that is that correct? Yes, although the second edition just came out last month, so it's actually pretty recent 2020 Okay, so I had a Just as a matter of discussion, I had a two-part brief questions both are very brief the first was More more legal the first question was do you really think that? That an idea like states giving consent to To arbitration under all these I'm sorry investors giving consent to arbitration under all these treaties In the light of the current crisis could kind of put the state's feet to the fire and use that and you be used as a signaling mechanism Even to try and control the amount of madness that these states are going to do in the name of this crisis That was my first question and more generally do you think that? Investment treaty arbitration even though we have always been against investment treaties in principle Is that the lesser of two evils compared to not having anything as a protection for foreign investment? These are my two questions. Thank you. Well, why don't we just talk about it because I'm not sure that we're against investment treaties. I mean, what do you mean by that? Well, I was looking at this I was looking at a lot of articles on these two to try and see the kind of position that was taken and for example Robert was never a big fan of any any investment it is because Finally, it was I mean he said that it was just finally special interest coming in and and getting what they wanted in those It was all the protectionism all over again, and it didn't really change anything And so I think that the default position would be unilateral free trade, right? Okay, so if you have a reference to what you're talking about with Rothbard, please send it to me because I'd be interested in it Type it in the link. I mean, you had a very famous article on NAFTA, for example Which I can which I can find for you. I'll type it in the in the chat and we can pursue of some time Right and so now we get into the way some lawyers look at things I Don't think of Free trade as the same as I think of investment issues Okay, so let me let me explain free trade just means that between regions or nations or states That they trade with each other with very low impediments to trade basically low tariffs Okay, so free trade has to do with Nations trading with each other Services or goods, okay, okay investment agreements Have to do more with Citizens or investors of one country From another Jurisdiction investing in and establishing a business unit and a factory or something like that in another country Okay, and so that that issue Usually has to do with investment agreements which are called bilateral Investment treaties BITs or multilateral But they have to do with protecting property rights in the local regime Okay, okay free trade Honestly has almost nothing to do as far as I can see with With protecting property rights free trade just means how much of a tariff Will you impose on the flow of goods and services between borders Right, and then immigration is yet another issue of the free trade or the free flow. Sorry of Human being bodies like between so you have free immigration issues How much immigration can there be you have free trade which is just trade between people in different countries And then you have foreign investment issues and those are all distinct And people confuse these issues and they usually confuse them because they don't understand the difference or because They want to push one policy over the other and so for example Intellectual property is a big big issue from the West and from the US Like Hollywood and the pharmaceutical companies. They want American style or Western style intellectual property pushed onto the other countries now How do they do that? How do you push it onto another country well you could make it a condition of a Agreement right and the agreement could be an international trade agreement or it can be a immigration agreement Or it could be a all all these kinds of things the you know the The monetary organizations that you the United Nations a human rights organizations so But the the bottom line is that There's a confusion because most people are very naive about these issues and the people that are experts in them And they're usually academic or governmental experts for What five ten fifteen years of their career? They understand the system very well right so They can manipulate it because most people don't understand what they're talking about So for example, they will say that well if I mean Donald Trump does this In the intuitive way like he says well China is ripping us off or stealing our IP so therefore So he uses that to manipulate the the trade deals with them Right, but okay, if you understand the way that law works and property rights work and IP works You'll see that Intellectual property protection has almost nothing to do with Free trade between countries right So of course they use this they they use it as an excuse so it's like Donald Trump will say well we can Impose tariffs on China and use it as a bargaining chip because they're stealing our IP But IP theft even if it's really theft is a local issue. It's like a foreign investment Issue it's not a trade issue. It's a foreign investment issue And that's an issue that every country agrees that every other country has the right to make a decision upon like the United States can decide Which foreign country nationals can invest in the US? Europeans French Chinese Whatever they can make a decision about who can invest in their country Singapore Hong Kong, whatever So that's in it. That's a local investment issue, right? That's a property rights issue And so all these things are mingled together for political reasons I don't know if I answered your question, but I think that So if we could if we could really separate the investment aspect of these treaties and just have that that would be perfectly legitimate As long as nation states are still around Well, so my view is that it would be purely a protection of property on the international plane between nation states and there is no there is no There is no fancy stuff that goes that goes beyond just the protection of property That would be perfectly Is that I mean So so my personal view is that By and large by and large over the last 70 years the Slow movement of the world trading system towards more trade of goods and services between nations has been a good thing, okay? I Don't as a libertarian. I don't think it should have been managed Right. It shouldn't have been like. Oh We can have this much and there should be these conditions But still there's been a gradual movement towards free trade of services and goods And there's also at the same time been a gradual movement towards Opening of regimes towards for an event if we call it FDI foreign direct investment I think these are all good things But I think they should not be completed So It's in the interest of Western powers and developed nations and developing nations and The southern nations as we call them. It's all in their interest to have open Free trade right to basically lower tariffs But it's also in their interest to lower barriers to foreign direct investment That is investment from outsiders who want to open factories or invest in their countries But the problem is that they always almost always impose conditions upon this So for just for example this There is essentially my point because they impose conditions Would we be better off without any of these investment treaties or is that still a lesser evil? Compared to having nothing and being at the mercy of the state in which you're investing That that's a that's a that's an interesting question I don't know if I am competent to answer that my my my my intuition my feeling is that Over the last 70 years Basically, even though I'm opposed to managed trade and the way the government has done it Things have gradually Opened up and they've made the world more interconnected and I think that's a good thing And in fact, this might be the only thing that prevents us from going into Crazy times right now, right because we're so interdependent I mean you have the Americans saying that oh, we're dependent upon Chinese supply chains for Apple products or whatever and Maybe a company would diversify or whatever, but on the other hand, it's good that we have this interconnection so that You know, we don't want to nuke each other. We don't want to have war with each other We know that that would result in chaos. No one is self-sufficient. No one is independent and The division of labor and the specialization of laborers has been spread and I think that's Been a roughly a good thing, but it's been accompanied by this idea that the government Manages it right and so that's the big problem the government manages it and So at one hand it makes us richer on the other hand It makes us more dependent upon the idea that the government has to be in control So I can't I can't say which one I think is predominant What do you think? Thank you very much Thank you very much. I would probably leave the floor for other people to ask you questions I just wanted to make a brief comment We could very well have ended up with a very very centralized international investment regime Because we had things like the Havana Charter in the 1950s, which thankfully failed So I personally think that the way it is right now in a very decentralized manner where decisions they decide for themselves and you have many Variations of investment rate is I think that's a good thing I mean it still it would have been better if the states didn't manage it as you said But it's better than a centralized management that we could have got Under things like the international trade organization and and Havana Charter, but thank you for answers Stefan.  All right Can you hear me? I do All right, cool. So my question has to do with It's a more of a theoretical question. It has to do with You know the foundations of Austrian economics and praxeology Now I've known for a while that there's been a controversy within the Austrian school Regarding the concept of time preference and how you know traditional pure time preference theory is justified You know recently I heard Bob Murphy talk on the Tom Wood Show about this and I went back and just went over his Arguments where I can find them on the internet Now it appears to me that The opposition to the idea of pure time preference stems from a misunderstanding Not not simply of the ideas of you know Goods and ends and means and things like that But also possibly of the nature of time itself from a praxeological standpoint So I just wanted to first ask you Whether you've kept up with this debate within the Austrian school and what your view is in my hunch is that you probably agree with the the traditional view of Time preference the pure time preference theory of interest, but I'd love to hear your take on this hmm Well, I Sure, I don't hold myself out as an expert on certain topics I Follow this and I have followed it The particular thing you're talking about it sounds familiar, but I'm not sure if I'm up on it If you want to update me more I'm up to it. I do have some thoughts on To me it's about the nature of the distinction between Economic analysis right fundamental primordial economic concepts and Normative concepts with people and legal which people conflate together and Then so so then we get to this issue of scarcity and then time and so to me time is one of the most Fascinating concepts that Affects all of this And I have a feeling there are people that have written on this and scattered ways that I am not Sufficiently familiar with that I could be but on the other hand, I feel like everyone that writes on it Disappoints me so my view on time is that time is Time is not so I like I would personally And again, you asked me a question. So I'm answering time is not a fourth dimension in physics Okay, it's not another dimension and in economics. It I don't think time is a scarce resource. I Just think time is a concept that we develop that Explains the flow of events the fact that things happen after each other in other words the fact that there is causation or causality and so I Don't think that time Is a thing that exists in The way that the other resources exist that we Categorize in economic terms and that we Protect by legal Regimes right like scarce resources or property rights So to me time is just a concept we use to explain The flow the succession of events So I think that you're in danger of The fallacy of reification right where you like you Conceptualize something that helps you explain some phenomena, but then you think of it as a real existing physical thing So I don't But again, I'm not a physicist. I'm not an expert. I don't think time Is the fourth dimensional thing that exists? Or a resource that you can own If that's what you're asking Yeah, yeah, that makes sense. I mean the I guess the What this turns on? Is whether the concept of time preference is something that logically follows from the action axiom If I understand correctly Bob Murphy denies this and there are others. I mean, I think we don't hold has also written on this and What I've heard from Bob Murphy and what I understand of his view is that he says if there's such a thing as Time preference that is that people Prefer things sooner rather than later. Why not construct a Concept of proximity preference and say that people prefer things that are closer to them rather things that are far away You know, so, yeah I'll give you my my thoughts on it So fact of acting means that you act at a certain point in time, right and so You could say that it in the luxury really demonstrates that you prefer the present over the future But in a way that's unavoidable because some things have to be in the future or some are in the present So I'm not sure if that's actually true like It's like I think maybe if you read Hoppe's article like explaining why in difference analysis like is flawed Like you could like the whole Baridians ass thing But like the mule that like it's looking at a bail of hay on the left and the right everything's the same And he doesn't choose so that shows he's demonstrating indifference Like Hoppe's argument is that like no you can never demonstrate indifference I Think maybe an extension of that argument Hoppe's analysis of it of indifference analysis could be applied to time preference theory because You could never You could you can only act for what is available at the present, right? So interest rates and things like that arise from the fact that you defer your consumption based upon your vision of the future Right in the way you structure production and things like that But you can never really demonstrate that you're acting right now for something 10 years from now I mean it might happen, but you can how can you demonstrate that in the current? Time so I'm I mean I'm I'm just personally really skeptical of this whole idea of time Like I had a I was just revisiting a lecture I had with Jeff Tucker and Stefan Mollin knew some other guys Here in Texas about seven eight nine years ago It's called Liberty on the pines and we were talking about I mean Whether time is a scarce resource and I made the comment that well time is scarce because As far as we know we only have so much of it in our lives. So it's got aspects of scarcity and Tucker said Stefan I thought you said that you don't think time is a scarce resource and I said well, you're right I don't think it's a scarce resource per se. In other words Time is gonna go on no matter what you do. It's just gonna flow. It's a flow of events I mean if you want to be scientific about it and be a physicist or a faux physicist you could say oh, it's a second law of thermodynamics or whatever but really from a from a human action practical logical point of view what we know is that We envision the future and we act now to try to make a causal change that will have an effect in the future That's the basic structure, right? So to me time has to be based upon that practical logical structure So to me time just means The fact that some things happen after the other or there's some things cause the other Right, so I'm not that deep on this to be honest So I admit that other people pretend to be deeper, but that's my my perspective I do not think of time as another dimension or as a scarce resource that you can own Okay, well that makes sense. I I don't want to take up too much time because I know there's probably others. No take your time. Go ahead. Just Well, I just wanted to just Give my my take on this because to me It appears that there is a like a fundamental misunderstanding amongst a Lot of Austrian economists regarding what time actually is because I I Think I've read Hans Hermann Hoppe as well Mentioned that time is a factor of production. It's one of the means That's used in the production of goods and I think that in man economy and state Murray Rothbard It says something, you know to this effect that time is I Forget the term that he used. I believe he says that time is a nonspecific Factor of production to me it just appears that That While time is Something that goes into production. It's not that time is a means that's separate from other Goods that we use in the production of any good It's just that we have certain time units of goods which we use in the Production of any good which is unavoidable.  That's However, you want to divide that up in terms of time. That's 70 year units of that person's life Or you know if if a college kid was doing his homework and that took two hours and it required certain resources primarily his own body Then we can say that that production process takes two body units or pardon me to our body units In order to complete that process so I think that This is an important thing for people who are using the practical method to be clear on and I know I'm not articulating this the best way, but I think that the Conception of time and what it means when we when we talk about time something that we need to be very clear on in order to Avoid a lot of these misunderstandings and misconceptions And confusions, you know as as we just go about praxeology, um I can't disagree. I actually Agree that more work needs to be done on clarifying these concepts and like so Austrians and other economists will use Interchangeable somewhat interchangeable terms and concepts like like you said factor or asset or good and I do think that so When you say time is a factor. Yeah, it's not clear what that means like so they they lump together factors of production Things that are scarce things that you have to To assemble to make your final product happen According to the way that you want it to happen productively, right? And so that could be a certain amount of So you could say it's a certain amount of time because you envision that okay, this would take me 2.5 years to do so you could say that time is a factor and We also have to have 10 and tungsten and labor and resources and energy and time and Whatever But to me, it's just like a verbal description from the entrepreneur's point of view of how he envisions accomplishing his task doesn't mean that it's scientifically Excuse me or economically accurate as An outside description of what he did to accomplish his goals. I mean basically from praxeology You us you you manipulate scarce resources you you employ your means To achieve your ends like we know that is true because that's the structure of human action But does that mean that time is one of the The means really just because we say that there's a difference between what we call super abundant and Merely abundant or less abundant resources Right a cataclysm difference like so for example information is called super abundant because anyone who gets the information or a pattern or Recipe or knowledge about how to use a certain factor that information could be used forever In a way, it's super abundant, right? Compared to the use of a resource like a location on the earth like a factory or the amount of Ten or lead or gold or or oil or whatever resource we're talking about, right? Those are scarce by physical nature and by subjective human appraisement Right, and so we have to distinguish all these things And when we lump them together because we notice a commonality like Okay, as an entrepreneur as a fact as an investor as an employer I have to take into account of the scarcity of time and The uncertainty of the future and I have to take into account My supply of ten and lead and Meat or whatever whatever whatever it is and my my factory You you do all these things practically to make To yield an achievement right to yield an end but just because an entrepreneur does that and has to do that to Have a successful result Doesn't mean that time is a scarce resource just because you know, he has to do it now rather than later. I Mean if you don't do it now, when are you gonna do it? You got to do it at some point in time so this concept of time Factors in and it factors into interest rates and the conception that we have is living human beings like we have we have We have parents. We have grandparents. We have ancestors. We have children We have grandchildren. We have future progeny that we all think about that formats the way we live our lives That's fine time formats our thinking process Anyway, that's all I have to say about this for a second That that makes sense. I hold a similar view. Thanks. Thanks again stuff. You're welcome. Thank you for talking anyone else Can I ask a question? Sure Actually, it's not mine have it here in the chat. So I just read it What do you think about risk in relation to viruses Would you agree with Mike humorous argument that a significant risk of contagion is enough to qualify as aggression? So I guess this is the danger of saying ask anything, right? Look, there's lots of things that are hard for lots of us to know I have my own opinions and I'll spill them out in a second Look, if you read Robert Nozick His entire argument for the state is based upon this idea of risk like at a certain point If you don't join the the dominant crowd you pose too much of a risk and we can force you to join our club And then the state arises from that excuse me the minimal state to be sure but the state Now to me humor is like a modern He's a modern iteration of this idea He's got libertarian and anarchist sensibilities, but he has in empiricist utilitarian Unprincipled mindset, I would say So I like him personally. I like some of what he's written He's smart but I'm not a fan of his kind of 60s go-go approach like I mean at least Nozick did it a certain way So Humor I have lots of issues with the The consequentialist you utilitarian Like explicitly anti-principled approach of some of these these types like humor Like like for example, I've talked to him and I've read his stuff and Are you against intellectual property? I Don't know. I have no opinion. I mean, how can you write a book like this and and Speak out and pretend to have some knowledge and Have no opinion about patent and copyright law It can't just be a matter of like well, we'll figure it out someday It's like saying Okay, well Jewish extermination concentration camps dropping nuclear bombs over Japan Yeah, you can debate every one of those things. Okay. Well, you can debate anything or how about? shadow slavery, how about black slavery in the u.s. Well, I Well, okay, maybe blacks were inferior. Maybe who's gonna pick the cotton? I mean you can come up with any kind of argument for these kind of things So at a certain point, I think you need to Figure out what your principles are and my principles as a libertarian and as an Austrian are Individual rights property rights First use principle that kind of thing You know, you can have lots of edge cases gray areas difficult issues I don't doubt that but that doesn't mean that everything is up to this utilitarian gravely analysis where we just sort of like Never never ever ever settle on any principle view of anything at all like, I don't know maybe a kill be maybe Maybe a had a right to Kobe or maybe had a reason to kill B You never know There's a billion You know things that could come into play So I don't know I probably got distracted by your question, but go ahead Well, okay, thanks. Oh Stefan Hello Nice to talk with you again. Have you been all is good. Who's this? It's Nate the volunteers. Oh, I interviewed you back in January All right, that sounds that sounds right. I'm sorry for not recognizing your voice No, it's all good. It's all good. So, um, I do have a question in regards to quite a bit of Several arguments that I've had with both libertarians and anarchists in regards to the left-right paradigm which I believe that Any libertarian if they have connected any of the dots should reject in its entirety I've always argued that Libertarianism is neither left nor right and the left the left and right are two wings of the same bird of prey and the libertarians should Get off of that paradigm and run away from that bird of prey as fast as they can before it eats basically eats you alive Do you think that it is a huge misconception to Frame libertarianism as either left or right. Hmm. Well, what do you think? I think so Well, I mean I've been a libertarian for 30 years and what attracted me to it from the beginning was this Orthogonal breaking out of the left-right spectrum boundaries, right the The conventional wisdom that like oh your left or right. I think the left-right thing is total total BS and Yeah, so I think that libertarians who insist on Framing everything and well everything everyone else insists on framing it left-right terms and libertarian shouldn't go along with that I mean our whole our whole purpose is to say that the left-right spectrum is not the right way to look at Politics and interpersonal relationships Right, I Mean the no one chart and the these two these 2d attempts to sort of break out of the left-right spectrum in the 70s or 80s whenever they came about They were trying to say that we're not The spectrum is not correct. And in fact, I think that the spectrum Helps both sides of the mainstream like because they can they can stick to their sides You know the left and the right and they can try to say that they're distinct from each other, but our whole MO is libertarians say that Dude, I if I'm talking to a conservative, I am way more conservative than you are in terms of say economic rights And if I talk to a lefty, I Am way more liberal than you are in terms of liberal values civil liberties things like that So you can as a libertarian you can outdo either one of these now. Why is that? it's not because I mean you couldn't put us on the left-right spectrum How can you be more left than a lefty and we're right than a righty? Unless it the circle closes back on itself in which case it's not linear and you know So yeah, I reject the whole spectrum. I think it's mostly nonsense. I Mean you could come up with two three four five seven dimensions of Ways that you want to categorize people and they might all be conceptually Legitimate But it wouldn't just be left and right. That's just two of the of the dozen For the libertarian the main spectrum that matters is aggression versus non-aggression Respect for private property rights in an institutional way versus Versus lack of respect and so You could you could map these things on each other and multidimensional Analyses and that's interesting It's not always tactically useful because Left and right people want to see the world in their terms, right? Anyway, that's my rambling thoughts. Thanks. Thanks for What do you think? I mean you could talk to I mean I'm not the only you could what do you think Nate? Oh Yeah well, I've always framed libertarianism as Just respect for self-ownership property rights non-aggression and To tie it all in together as freedom of association Course I Often get into of course. I usually when I define it that way I I I often, you know run into those Who say they are libertarians and then? Once I once I shared that definition to them you know, they often reveal themselves as status in some sort of way and There's a few a few a few people that I've run into have basically admitted that They're not really for individual Individualism or individual rights if I'm if I'm framing it correctly that is But I've always But I I guess what I'm trying to say is I've always viewed libertarianism as the as the right of The right of the individual above all Essentially and I think and I've read your article on Mises called what is a libertarian and That that was pretty much what my grasp on the whole thing was in regards to how you Define libertarianism or how you advocate it Because whenever I'm because whenever I am talking about libertarianism in general I Kind of take inspiration from Say Eric July Larkin Rose or blood of the brave You know who blood of the bravest No, I know the others but not that one.  He's a hip-hop rapper So I've interviewed him as well You know when I'm when I'm talking like those three I just I Just keep it real and not try to muddle down the whole concept of libertarianism to try to try to appeal to others or What do you call it Eric July mentioned this several times. So what what is it called again? It's not it's not virtue Signoing it's counter signaling. There we go. So I don't try to counter signal. I don't try to muddle stuff down. I just Advocate for what it really is And I and I seem to see quite an epidemic of it within libertarian circles Whether it's anarchist or not. I hear you. I hear you Well, so today's This is an experiment to see how it would go and if people are interested I might do this on a repeated basis I don't know if you guys have any opinions Open to them. Well, this is great actually it's great to Get to talk to you up to now. I really only you know read your work or heard you speak when you're interviewed On various podcasts, but I actually I would love If you were to make this a regular thing that would be wonderful I may do that. Thanks for the feedback Yeah, I would I would love to have a Lot of conversations with you because I always learn something new whenever I read your Columns and Watch your interviews. All right. Well, thanks. Do you think? Midday or do you think nighttime? What it's the best time to do something like this probably midday US time. I Think this time is good since other European people it might be late for European people that's and Play it for US people. So maybe even a little earlier like 10 or 11 a.m. US time so that it's You know, I think this was a good time. Okay. Yeah, I think I think this was a good time, too Okay All right. Well, I'm gonna let it go a couple hours earlier like you said All right, I'll think about it Maybe fun we all need to get out and talk and next time everyone else can chat and I'll try to figure out the zoom thing and get everyone to Collaborate more Appreciate it Hi, Stefan. Can you hear me? I? I do Yeah, so thank you for the stalk. I wanted to comment about zoom so I suggest you try Jitzi. It's an open source and more secure alternative to zoom which is proprietary and it's not very good So you might want to look into that Why don't you send me a link and I'll take a look I Sent a link in the reply to your tweet where you announced the stream Okay, perfect. Thank you and There is also a question if you care to answer Sure, so In the beginning of the talk you somebody asked you about Moral obligations towards children where the parents have this obligation So I wondered what you think of anti-natalism So it's essentially a position that it's immoral to create life because you doom a person to suffer inevitably and It's most commonly argued by David Beneter. He is an analytical philosopher. Maybe I know of him. I Mean, I never I've never heard that view although. I'm not surprised that it exists anti anti bent. What is it anti-benetalism? It's anti-natalism anti-natalism Um, I wonder if it's anti-natalism anti-natalism. Yes, maybe I'm not Yeah, um, I mean the problem with that view is that Every action that we humans take and from so from my point of view every action that we take Can have unforeseen consequences, right and can cause things to happen And if you Strictly link your actions to causes to responsibility then Everything you do you're responsible for Which is the strict liability view which I actually disagree with in the law, right? Like if you own a dog and the dog Runs a mile and bites someone on the arm. Oh Is your you own the dog so you're responsible for what the dog does Now in a sense, I agree with an aspect of this Philosophy in that I do believe that if you create a child Which some of us do as parents and the child is a dependent being initially and has needs Yeah, so I think that the parents have an Positive obligation to take care of the child now I guess you could argue that because the world is uncertain and the future is uncertain You could never guarantee that you could even do that even if you live alone in the prairie and You have three children and you have you know a farm You never know. Maybe they're a plague would come and or more rotters would come and You couldn't take care of your children. Um, I don't I just I'm not persuaded by that view I don't think that there's anything Metaphysically wrong with creating a life in the world That sparks a new life Because that's no different than saying that you take an action that causes something to happen Things change because of your actions So in the end, I think you can only take responsibility for a certain small Locusts of actions around your direct Action which is legally what the idea of proximate causes about like what are you approximately like? Approximately means closeness or distance or like what do you cause to happen? so if Steve Jobs creates the iPhone and 17 years later some child dies because You know a mother was distracted checking her Her cell phone messages on her iPhone while driving And ran over a child or whatever Yeah, you could say That's what we call a cause in fact like with a but for cause like without Steve Jobs creating the iPhone this wouldn't have happened Although you can't really even say that because maybe someone else would created it But I think that's too far. I just I think that at a certain point We all live among each other in society and living in General has risks because we live among people that have free will and they can choose to do whatever they want and They're their behavior is therefore unpredictable and the future is also uncertain and unpredictable So everything that every human ever does every actor ever does always has a risk of Affecting the future harming other people So that that mere risk can't be enough to say that we shouldn't act Because It would just mean that we have to all commit suicide Which to me is like pointless and unrealistic and fights the proposition in the first place because If our lives don't matter Why do the lives of our future progeny that we might endanger matter like the whole thing is a Risk game So I guess I'm not persuaded by this although I haven't heard of this particular sect Thank you for your play So I'd say that it doesn't essentially argue about Consequences of your actions as you said the view that Benatar takes for example is about a symmetry between play a pain and pleasure in which he essentially argues that the state of non-existence is always better because the absence of pain is good even if good is not enjoyed by anyone and The absence of pleasure is not bad unless there is somebody for whom this absence is the deprivation and on the other hand It's a presence of pain is bad and if you create life you necessarily expose Whoever you create to the possibility of pain well So it's like a comparison between two states as a state of non-existence and Existence and you always choose Not to create people.  I don't know Right. So like the idea of eternal punishment never made sense to me So but but the idea that you could create a being that Had to choose whether to be good or bad now the Christians will say oh well, you have a choice You have a chance. You're given you're given a helping hand whatever but the point is For the guy that chose the worst life of all right to be a murderer to be a bad father To go to hell at the end of his life He would have been better off never having been created So how could a good God create a guy like that? Like what's the point? So my argument initially as a as a as a smart-ass 19 year old was oh Well, that means that everyone that you think is bad is really a Robot like that's a God robot like like God never creates really bad people like all the people you think are bad or just Robots God made that give us a fake choice But then if you figure that out then you're in danger of the God mafia make the whole thing makes no sense I mean it devolves into You could maybe make a movie out of it or something but So I kind of sense the feeling of this idea. I just I don't think that Having a baby in today's real world is a horrific crime Like it would be to create a new soul Who is doomed to hell forever? Because you know it because you're omnipotent like we're not actually God like God Should know better. He does know better. He's omnipotent. He's omniscient He makes a soul that he knows is doomed to hell forever and To me that's in a way. I Could see an argument that that's unforgivable But but that doesn't apply to our actions as non-gods because we're not gods Right. All we do is estimate the future. No, go ahead. Sorry.  I mean like in a sense as far as we know all life comes into being at a certain point and expires at a certain point and The if there's a conscious Life form behind that That type of life like humans then they will experience a consciousness and they will experience certain Pleasures and pains if you want to simplify it and That's that's inevitable I mean it's it's it's I don't see how that could be Be avoided In avoidable part of what it means to be alive if you're conscious So any conscious being will always have a finite lifespan and will experience certain Good things and bad things and some will be better or worse than others by certain Human metrics and so that's just an Inessential an essential part of life So if you're opposed to any suffering, let's say or creating a new being that has suffering then You're opposed to life per se and again Ultimately that leads to nihilism or some kind of What like the the hemp to movement the what is my friend Nina pale is part of this the Voluntary human extinction movement or something like just yeah, it exists But I don't argue on the same grounds and then there are some radical environmental group So the reasoning is quite different from the academic philosophy Interesting, I don't I don't know much about it. I all I know is what I just said to be honest Well, thanks for that anyway Thank you Could I just say something very quickly regarding this? sure Now I don't presume to be an expert on Antinatalism or what you know the basic argument is from what I understand. It's the idea that It's unethical to bring a human life into existence for whatever reason and it just seems to me that the problem with that argument Is one that has to do with the philosophy of human language more than it has to do with metaphysics because In order for Something to be unjust to a being it would have to have been done to that being But the problem is that a being does not exist before they're brought into existence So before I was born I didn't actually exist so My coming into existence was not something that was done to me by my parents because you know, I didn't exist for them To do anything to me before I was born So it's only after somebody is born that I think you can talk about even justices or injustices So the actual act of creating a being cannot be just for unjust It has to be treated as an amoral action is what I think I mean a lot of you know philosophers a lot of philosophers have Especially I think Wittgenstein have attacked metaphysics as basically being nonsense, which just arises out of the imprecise and careless use of language, and so I think it's it's something that Needs to be taken seriously and this is why I you know initially brought up the The concept of time because I'm becoming more and more sensitive as I think more about Not just praxeology and Austrian economics, but also libertarianism and the foundational ideas of Morality and I have a keen interest in argumentation ethics as well, and I think that a lot of the Problems that seem to be Irresolvable I Think we can make quite a bit of progress if we see these as problems arising from our use of language Rather than problems as such. So that's just my two cents interesting anyone else because I think if not I'll end this shortly and think about the best way to Maybe repeat this or restart this in a few days or next week or something like that But I welcome any feedback or comments on what might be a good idea to do this We'll see the chat box the chat People are typing up commons. I see it now. Yeah, I can see it Okay But I wasn't looking at it during the thing. Yeah If I'm good, I ask one more question Sure If you had the opportunity and this is actually something that I am probably going to do in the coming week week or weeks If you had the opportunity to talk to our decision maker, it's a political decision maker or other decision maker About libertarianism and Austrian economics Somebody who has absolutely no idea of what this is and you had maybe an hour or two hours to give a presentation to him about libertarianism and Austrian economics For the purposes of decision-making. I mean, this is somebody maybe let's say who's was actually controlling the lives of others But what would you where would you start and how would you structure it? I know that that's that could be a bit complicated. I need to think about it myself But we would you have any any starting points on your in the way you think Well, and I'm open to anyone else's views, but I'll tell you quickly. First of all, I'm I'm not persuaded that Like so, I think there's there's an entrenched state which you can call the deep state Right. It's not the the politicians are not always the ones that are the ones that matter The state will persist in most countries. There's a government even if there's no government You know what I mean? There's a state even if the government fails So there's a bureaucracy. There's a permanent class of workers that maintain the state I tend to think that the current politicians like the congressman The president these guys are just figureheads that are temporary. They come in and out So I'm not sure who am I talking to am I talking to these guys? Or am I talking to the guys that are in the deep state? I think the guys in the deep state don't care because they Want to maintain their power and their and their and their and their their salary basically to be honest If I talk to an opinion maker so-called like a Donald Trump or a Congressman I Mean as a libertarian I would choose the things that either or the highest value or the ones that I thought could have the most effect Now for me personally, I Would focus on patent and copyright because I think that they are the two intellectual property basically even though everyone knows oh can sell us all up on this It's not I'm not up on this because I happen to know about it. It's the other way around I mean it really is one of the most dangerous things Me yeah, I could talk to Rand Paul about the drug war, but he pretty much already knows right I Could talk to Donald Trump. Okay, you should legalize marijuana and if you legalize marijuana you probably will win the next election But if you don't you're gonna lose to zombie Joe Biden So there are simple issues right To me it's it's really all about intellectual property, but I'm under no illusions that We can make these intellectual arguments to enough of the populace to make a difference, but Ultimately I do think that like okay, so we have the drug war we have public education We have real war. We have the military. We have welfare. We have the central bank at the Federal Reserve All these things are so entrenched. It's so despairing to think of how you can talk these people Out of it who have it an interest in maintaining it right because they're basically Employed by it or supported by it So it's difficult. I mean you can't talk a public teacher out of supporting public schools Government teacher, you know, you can't talk a you know and so The same thing is true, but so for me it would be Let's just scale back patent and copyright law and let innovation work its magic and help the free market Overcome the obstacles that you guys are putting on us and your other laws taxes regulations, whatever So to me it would be patent and copyright To give a Predictable can sell I answer sorry Okay, thank you very much. I was thinking more about going on the lines of monetary policy because that's something that I understand better So I guess I guess we always go go and talk about what we understand and and I think that the central bankings Is is One of the biggest problems because it helps the state finance its activities, right? and it causes inflation and it a dominates the entire the entire culture and I think there's a great essay which any of you if you haven't read it It's it's it's by oh who's the he's one of our Austrian fellow travelers the literature guy who wrote the the It's about Paul Cantor Paul Cantor and Thomas Mann and inflation Thomas Mann and hyperinflation And not just that some of the stuff by Gito Hozman, but it's about how this inflation mentality Corrupts our entire culture It sounds like a throwaway thing, but I think it really does have a big influence on How the entire society acts and reacts and why we save and we don't save and why In a in us in a co vid thing like we have right now. Everyone is unprepared for like no one has two weeks four weeks three months of savings Because everyone's living hand to mouth because of inflation so hyperinflation or inflation like we have now I Think has a significant impact on society So in a way, I would say yeah, you know if I could reform one thing it might be this Federal Reserve. I Don't know. It's hard to say Patent law Federal Reserve public education income tax War the drug war They're also horrible It's hard to say which one Tactically you should reform first if you had that You know that wizard wand choice. I was thinking more on the lines of Playing their own game in the sense giving them the the sort of points that they would like to win in a popularity contest And then trying to find points in That in that week, I think most of us would be persuaded to do anything that would have any positive effect I think it's it's all pretty hopeless to be honest not to be pessimistic Anyway, all right guys, I'm gonna I'm gonna go now, but we'll do this again soon if If it makes sense Thanks, everybody Thanks for doing this stuff. Thank you guys


Hi, thank you for inviting me here. It's a great group of people. And I'd like to say got it, I guess. And I'd like to tell you something in the interface of dynamics and number theory. So I'll basically start with number theory. And then gradually you'll see more and more dynamical stuff. So what, what I should say here is that it is the main result is joined with Andreas Strombergson and Xu Cheng Yu. Time allows I'll also talk about results with an aura grow. Some extensions. Maybe somewhere then. And let me explain. So there are many strange words. Why do I have shrinking targets. Which you mentioned in the spaces and also what is the last year. So let me start with the last year in the front end approximation. This is the number. Well, basically that's that's the theorem. What I'm doing here is taking the supreme norm. Why is the matrix Q is a vector. Actually, I think this is not correct. Q is the end. And, and then you can approximate so this theorem says that you can basically approximate integer values of the system of linear forms with integers with a good precision and they like to raise norms to approximate to appropriate powers and then the formulas are look very, very nice. So, for example, if you specialize to just approximation of real numbers, you have the familiar inequality y minus p or q less than one over t q and q is less than t, or maybe maybe you can just write like this. It's simpler q y minus p. Okay, so that's that's what you want to solve and you can always do this. And there is a corollary also proved by Dirichlet that you can compare the discrepancy with the denominator itself so this is just familiar inequality. So this is y minus p over q, so it's in one over q squared. Okay, and then, and then so called metric number theory deals with various improvements enhancements, and so on of these inequalities what can be approximated better what can be done. And in particular, the main question is what happens if in this inequality systems one and two the right hand side is replaced by a faster decreasing function of T so I'm talking about this right hand side here, or this right hand side here. What happens for typical in particular typical with respect to the bed measure. So, most of what I'm talking about will be about results for typical wise, although it's not. There are other things that can be said. And oops, doesn't work for me here. Okay, and what I what I was trying to say is that it is actually quite well studied in the setting of number two, so called asymptotic approximation, but not so well for one so the so the setting improving. This setting is basically some new stuff and people were paying attention to it recently much more. And I'll talk about the history as well. Okay, so let me first talk about the setting to quickly. So, I want to take the function, some decreasing function which I'll call the approximating function psi. And then w mn of psi will be the set of psi approximately matrices so those wise for which you have infinitely many solutions of this inequality. So now instead of one over Q to the n, you have this function and then there is King hinge and Sierra. And the advantage of having this powers here is that the condition and hinges serum is uniform and doesn't depend on the dimensions which is what they really really like. Okay, so you have this convergence or divergence. And, in fact, monotonicity of psi is only needed when in dimension one, and the rest is true anyway. So this is related to differential injection. And also, what did what you can see is that the condition is stable with respect to replace psi by constant right so this series converges if you multiply by two still converges and so on. And, for example, I want to pay attention to this. So the specific function one over T and call it psi one. So that from directly follows that functions that matrices are proximal with with this function is the whole thing. And then by hinge and serum if you multiply it by C it will still have full measure. And by the way, the complement to the union of all these guys is a set of badly approximate matrices. So, so this is what so what I'm trying to say is that the complement is still in some sense big, but it has measure zero. And one other remark that the theory comes from the fact that it is a limb soup said what we're talking about so in fact why it belongs to this set if and only if this system has a non trivial integer solution for infinitely many natural numbers T. Okay, so, and this system is rather easy right so it's basically some kind of so we're talking about unions of neighborhoods of affine subspaces. Okay, so we can we can write to write something right in such a way. Again, if we restrict and then equal to one then we're talking about various intervals, taking the unions of intervals. And then to prove something like this you need to have some kind of quasi independence estimates for these unions and various methods to do this coming from geometry or arithmetic. So, it turned out to be not such a difficult problem. And then, let me switch to improving number one. And, well, to basically to improve the original degree of theorem, not its corollary, I need to consider not leave soup set but limit set. So this is my main definition. For today, I'll define the set dmn of psi to be the set of psi directly improvable matrices. What does it mean. It means that instead of T here, I have some right hand side, sorry, instead of one over T. So, before we had psi one of T which is one over T. And, well, then it's clear that you, it's too good to be true to wanted for all T but I want to demand that this has a solution for all large enough values of T. So the theorem says that if you put psi one here you have everything. Okay, so why is it an interesting setup. So the interest comes from the paper of them important Schmidt in 1969, who showed this very surprising sharp drop well at least for me when I first learned about it it was very surprising. You replace, you replace it by 0.99 over T and suddenly the set of solutions. The set of why is for which you can solve this has has measure zero. So in other words, what they proved. Well, again, let me maybe write it in the case in one dimensional case. So if C is less than one. And for almost every Y real numbers, real number exists sequence to K going to infinity, such that you write the Y Q minus P less than C over T K and then Q is less than T K. No, non zero integer solution. Okay, so if you put one things are very different, but just a little bit less than one. Suddenly everything changes. Okay, so this sounds rather, rather strange and I'll try to explain why this is happening. So but first let me pose some questions. So now that this we have this result, you can just see and try to find the right condition for this psi. So, and this will be kind of between one over T. And C over T where C is less than one. So maybe there is some kind of log factor or some other power, which distinguishes measure zero from full measure so that that's a natural question and I think we first tried to. So it is actually answered for M and then equal to one in my paper with Nick Wadley 2018 and the method was using continued fractions. So you can express in one dimension is things in continued fractions and figure it out and then if minimum of M and then is bigger than one, it's still not done. What I'll talk about is some partial result, which is quite close to full result but still not full result. So, so this seems to be much more difficult and much more sensitive problem. So I ask, why is it the case, because there should be some duality between lip soup and limit sets right so I was before I was talking about some kind of a case which were unions of neighborhoods of a fine subspaces. We end up talking about Lim soup set of their complements and this complements are much more complicated basically. So there are complements of those neighborhoods and what to do with this is not, is not clear so okay so there is a, there's a question about continued fractions maybe I'll answer later if you don't mind so I can actually just trained respond to chat because I happen to see it so so so you can write that why belongs to the set. The man. Si, if and only if some conditional continued fractions happens. Okay, and this is and. Yeah, and what, what is an efficient condition I'll also tell later because I'll try to state the general theorem, where I'll have this condition plus something else and this is something else will not need so I'll answer this question. A bit later. Okay, so now let me try to get to the main result. So, so the crucial critical case for this to have zero measure notice when when this happens when. So your function psi is one over team minus something right and this something. Now this something has to go to zero, because if it doesn't go to zero that I am in in very important Schmidt situation. Okay, so, so you can we can work with psi, or sometimes it makes more sense to work with this fight, which you can of course express in terms of psi. And so my condition will be involving this function fine. And what I, what I want to do is I want to assume both these functions to be non increasing. Okay, it's some kind of technical condition maybe it's not so important. But let me do it like this. And the case of the function having positive limit corresponds to the world for Schmidt situation with C less than one let me shut the door and I'll be right there. Okay, now it's quieter. So, so here's a theorem, and it will answer the question I got in chat it's kind of very long. But at least it has the condition. So it's joined with Andreas and should change. Take arbitrary and then you take this function psi and this phi gives you the discrepancy the difference from one over T. And I, we have two constants, capital D and lambda D, which depend quadratic from on D where D is M plus M. And now we have certain convergence divergence condition. So if this series converges. Well, I am also calling it one, even though now this one means different thing maybe, maybe I should call it a red one. Something like this. If this series converges then this set is a fully back measure. So we have phi to this power times log one or a fine to some other power. And we want to want this condition to be optimal. And then where it comes from. And then it diverges. Unfortunately, we're not able to prove that the measure is zero. We need a very strange condition, which is very hard to read so I'm not even going to read it. The limit of certain ratios will, if the limit for certain ratios is going to zero, then the divergence case can be can be can be treated. Well, we really believe that this condition shouldn't be here but for now it is here so let me give some examples. So this condition will be called to in the red square. And by the way, our result involving continued fractions was gave exactly exactly this condition. And of course, we have that lambda two is equal to. Okay, so, so, so, so easy D is equal to two. Right, so, so we have side D. We have a D is equal to one. Lambda D is also equal to one. Okay, and, and the condition was just the sum. Okay, so let me show some examples. For example, what if you have this log discrepancy we have one over T minus C times log T to some power over T and then you can check that the critical exponent is one over capital D. Critical exponent tau, and there is no problem with condition to it is always satisfied. Okay, so the conclusion is that you have for this family of functions, you have full measure if tau is bigger than one over ID, in one dimensional case it was bigger than one, and of zero measure otherwise. And if you want to fine tune this a little bit for example, you keep this critical exponent one over ID, and then you put log log T to some factor, then your situation becomes trickier. So the divergence of this one is equivalent to saying that tau is less than lambda D plus one over ID, but sometimes we do the we get this to sometimes and sometimes we don't. So we can only prove that that this condition grantees full measure and this condition grantees zero. Okay, so it's a bit annoying, but at least I'll I'll try to really say why where this anonymous comes from. Okay, so anyway, so the bottom line is that we have this series that decides what happens in this in this problem. So fine tuning of. All right, so now, I guess it's time to explain why dynamics is involved so usually the history of using dynamics and number theory is not great. Sometimes it's great but more often than not you do something by dynamics and then number theories come and say well all right it's very easy you just do this and that and you can also be fine. So as far as this problem is goes goes I, I don't really see how to do it yet. So it's, it is one of the domains where you can do something using dynamics and classical methods. I don't show anything close but anyway, let me go through the dynamical approach which actually can be extracted from them important Schmidt because the way they proved it can be translated to dynamical terms. There was a correspondence between approximation dynamics was spelled by Danny, and it goes. Now it, I mean, usually goes by the name Danny correspondence, which we was the term we invented in the paper with Margulis in 1998 and then with what labor adapted it to the directly improvement situation and also I should mention my work with Barack wise 2008 where we also utilize this correspondence. So, so let me try to. So what I want to do today is try to explain how dynamics enters the picture, and I want to take the easier case. I want to take the easier explanation so my function for now will be constant times psi one so it is and see is less than one so this is the Davenport Schmidt situation. And I want to see what happens after we translate the setup into the language of flaws in the space of lattices. So why let us as well. So if let me fix the C fix the matrix why and then you have this definitely different improvement condition. So let me write it down. For all large enough tea. This system has a non trivial integer solution. Okay, that's, that's basically, basically the definition and let me draw a picture corresponding to this definition it means that you have this R M here. And then you have a very long and thin rectangle, which so one side is C over T and other side is T. And then you have this objects, which are the vectors with coordinates, why Q minus P and Q. Maybe it's something like this for all integer Q and somehow there must be an integer point here. Okay, so that's what what this condition says. Okay, and then you can tweak it a little bit and the way you tweak it is that you take this rectangle and turn it into a box. So, equivalently with some with a little bit of computation you can do the following again you have these two axis. And now you just squeeze this rectangle so that it's area is still the same. No area this D dimensional volume. Okay. Well, so you have M coordinates with okay so. So the way the way this exponents are worked out guarantees that see the T cancels, and you and you only have this constant term here, and you can make it to be the same now you have a cube and what you are doing. So this is to is multiply the first value by something big and the second value by something small. So you're applying a diagonal matrix. And again, you have some kind of So now you're talking about applying this diagonal matrix to this and again, you want an integer vector here. That's the condition. Yeah, so we are. And so basically I moved from this setup to so called geometry of numbers studying ledges. And let me give this notation so so lambda sub y will be exactly this latest. So this is the set of all vectors of this form will be. I'll call lambda sub y. Okay, and a sub s will be this diagonal matrix. And then what what we showed is the following that you have this directly approval condition, even only for all large enough as this lattice as a non zero vector in the bowl. With radius C and power m over D. Okay, so this ball with respect to the supreme norm. Okay, and you can restate it as follows. It means that AS lambda y is not in certain set K sub see the power m over D, where I'm using this notation case of our to denote the set of lattices which have trivial intersection with a ball of radials are. Okay, and here we are in the situation of certain certain nice compact subsets in the space of lattices. So I can maybe draw a picture of this space XD. It's actually SLDR module SL. The space of any module lattices. And then you have certain set case of our right here. And then you start with lambda y. Maybe it's somewhere here. So, apply a sub s. And then you don't want to enter this KR for large enough as so this area is forbidden completely. Okay, that's, that's a dynamical interpretation of the improvement which is essentially between the lines of them and put Smith. It's important to remark that if R is less than one, this sets actually have none empty interior. And if also if, if R is bigger than one, then this KR is empty. Okay, so R equal to one is some kind of critical parameter. Okay, because what happens with K equal to one is this cube of radials one. And then by Minkowski's lemma where you absolutely must have intersection of any unimoderal lattice with this cube but if you replace if you remove, if you decrease the radials then it's not going to sometimes happen and it's not going to happen for all lattices and you have some set of lattices for which it doesn't happen. This is the green set case of part. Okay. So, any questions. Maybe I should stop and ask if I do something here. Anyway, so now, the conclusion is that this explains how David Palsch meets theorem can actually be derived from the rigidity of the action of this group as, and this is a case of fixed targets. My topic is shrinking targets but for now I'm not drinking anything I'm just keeping the same target. Let's figure it out. Okay, so we have this improvement property with the function given by C times psi one, and this happens if and only if the trajectory eventually avoid some neighborhoods of this set. Okay, so case of one, I mean what is case of one case of one is the set of lattices with this property that have vectors on the boundary of this cube but no vectors inside. So this is the set, and this set is called the critical locus of the supreme norm so these lattices are called critical and what picture again again this this will be the space xd I'm drawing it like this because it's not compact, but it has finite measure so this part which goes to infinity the cusp is kind of thin, I mean it's thick but in terms of the measure is thin. And then somewhere you have this set case of one, and here you have k sub r. Okay, and again if your starting point is in such a way that the trajectory does not reach it this set at all so this is not allowed. And then, then we have this directly improvement business with this function C one and this is very strange if you believe that this trajectory is connected should actually go anywhere so you have the notion of organicity of this action, and organicity tells you that almost every why will actually not have this property. Okay, and by the way, this set k one plays an important role in our proof. So the structure of the set is given by the theorem of higher, it was actually conjectured by minkowski and proved by higher. So this set is what you think it is. Namely, you have, maybe I should draw a picture here let's let me take D equal to two D is equal to two. Of course you have the latest Z two which belongs to K one right it's in the interior, but also you can share it's in the vertical direction and also share in horizontal direction separately. Okay, and so what you what you'll see is the union of the orbits of this upper triangle and lower triangular groups. So, in the space of ledges. You can. This is space X two space X two. Then this, this guy is the union of two close to her cycles. This is K one, or maybe number theorists prefer to understand this space as a union tension bundle to the modular surface. This is also great. Because here you have this her cycle one her cycle consists of vectors pointing upwards and another consists of vectors pointing downwards. Okay, so that's, that's, but topologically, it is just the union of these two circles and for for the bigger than two. It's kind of a mess you have a lot of so so when D is equal, let's say D equal to equal to three. You have a lot of three dimensional dry, which six of them actually which are somehow glued together in a very strange way and that's, this is the, this is this is the set. Okay, and this is, again, this is K one. And if you want to have K sub R when R is less than one unit to have some kind of a neighborhood with this set, but not just the absolute neighborhood. Very complicated neighborhood. Okay, but anyway, for the purpose of proving them and put Smith's theorem and doesn't matter we just have some open set and every almost every orbit should enter. And then, then you derive everything. So, now the argument goes similarly for functions which decay. I guess I have to speed up a little bit. So, so it is. And then, if, if the fun, if this five goes to zero, it turns out that you actually talking about targets which shrink. So you have this K one, which is somewhere here. And then you have R of s here K R of s which becomes sure smaller and smaller. And you need to have this condition. This is not in case so it's about the rate of shrinking rate of approximating this set, you said, K, K one. Okay, so, so that's, that's how this strictly improvement is reduced to shrinking targets theory in dynamical system that's basically what we did with Nick Wadley. And then you can make it even nicer if you discretize. So, you have this yellow set and you make a say Brown set out of it by moving it in the AS direction by time one, and then you have this discrete condition. A j, j is a natural number. And this becomes this set becomes a big J. And for large enough, J, you don't want to get there. Okay, so, in other words, take here this should be a compliment. So why isn't the compliment if and only if a J applied to lambda y belongs to this be J from it into many J. Okay, so, so we're reduced it to basically to some kind of barrel can tell you and, and of course, but I'll come to the limit says that the right condition and the sum of measures of the J's is if the sum of measures is finite if almost surely have finally many solutions, if the sum of measures is infinite and something else, then the number of solutions is infinite. And this something else, basically some kind of quasi independence properties of this family. Okay, so now I have to rush a little bit. I guess, at least what is left are several steps. We need to come come come up with a with a measure I mean what is really the measure of this set. And new is now the hard measure SLDR invariant probability measure on the space of lattices. So we need to come to compute it or to estimate for small enough are not sorry for our are close to one. And then you want to also have this BJ, which is this brown set, which you get from KR by extending it in in one direction. Actually, I have to say that I put this equivalence in quotation marks, because it's kind of, it's a little bit approximate you need to squeeze it between two sets. And in this approximation actually using the monotonicity property of the function. Okay, so, so then, then you need to estimate this, this measure. And then, you need to establish some kind of quasi dependence of pre images. And also, another step is to go from almost every lattice lambda to almost every lambda of the form. So, so again, for the first part. Remember that in the D is equal to two, we are talking about a set of the form, some kind of neighborhood of these two circles, and it's even more complicated in high dimensions. And now you need to move it a little bit in the transfer so the action and also do some work. So this, this is actually the bulk of the paper. Okay, so this one is work is done is done here. And so let me show you the main measure estimate. Remember that we had this exponents capital D and lambda D. And then the measure of K sub R is a SR goes to one is approximately one minus R to some power times log of one minus R to some other power. So, with Schuchin you actually did the case D equal to two before. Okay. So, and then as a corollary we can actually look at this shifts the cylinder and the only difference is that we go from this power to this power. Okay, so just simply because you lose one dimension so so it's, but it also requires requires a lot of work. And then for parts three and four. Here is where dynamics is important. So before we only had the geometry, and basically, I want to use the fact that you start with this set of so I want to do three and four, the same time, because it makes sense. Alternatively, you can take care of three. So remember that three was some kind of quasi independence conditions. And then you have a affiliated version but in fact, modern technique allows you to have the affiliated version right away. So what you what you do is, is the following. Let me try to draw a picture don't have much time so maybe I'll just use pictures. So, let me start with some kind of the set of the form, let us solve the problem with some why. When you apply a some s and the way it is set up shows you that in fact you get.  In the sense that if you fix some, some open set you, then the proportion will be approximately the measure of you. Okay, and in fact, there is an exponential rate of mixing and this gives rise to exponential rate of equity distribution with some error bounds so we first spelled it out. Well, the first was spelled out in the thesis of Margulis about genetic flows and also flows, but then we did it for flows of this type, driving from the exponential mixing of the action. And in fact, we need the refined version so called effective double equity distribution which is the paper of Michael Bjorkland and Alex Rodnik. So, so there are some strong dynamical, dynamical results, which make it possible to try at least to extract this was independence conditions, but the bad news is that these results. So applicable to smooth functions. And so to apply this machinery, this sets BJ, which you start with, need to be approximated by smooth functions and the coefficients and the mixing estimates depend on the size of their derivatives and the size blows up as J goes to infinity because they this sets become thinner and thinner. Well, I don't have time to convince you that if you take care of this factor, appearing of big derivatives you actually end up having this very strange technical condition which I don't even want to mention I'll mention it anyway. It's somewhere somewhere here. The point is that if you, in addition, assume this, this convergence you get, you are able to use this mixing mixing technique. Okay. So, I guess, I have to stop now let me, let me just mention. So I left this page blank just in case I have one minute so maybe I'll have one minute to mention the extensions and one is so called approximation with weights. Again, I don't want to spend much time on it but weights basically means that you treat various components of Q and various linear forms differently. So you have a vector alpha and vector beta, and then you do absolutely the same but your dynamical system is now as depends on this alpha and beta and this is just e to minus alpha one s up to e to minus alpha m s and here you have beta one s beta m s. Okay, so all these guys were the same. But in fact, you can make them a little bit different and still prove more or less the same result because this Bjerkel and Gerdnik condition actually takes care of even this, this type of expansion. Okay, and finally, you can also use other norms. Okay, so everything I did was for the supremum norm, and then we ended up having this very strange critical laws. You can choose another norm, you can still save, you can still state the number theoretical problem. For example, you can take Euclidean norm, and then you have a different setup and you can still ask the same questions about the improvements of the theorem and this is work I did with an aura grow that I don't really have time to mention. For example, when the norm is Euclidean and when m and then are equal to one, we have a necessary and sufficient condition for this set to have measured zero full measure without any extra technical assumptions. And here we're lucky to be able to derive it from some dynamical systems results from some current. Okay, anyway, I guess I'm over time already so let me stop here and write a big thank you for your attention and invitation.


The Great Search, where every single week Lady Aida uses her powers of engineering to help you find things you need on digikey.com, we're going to make a lot of a part shortage so this particular segment that we do each week on the desk of Lady Aida is even more useful. Lady Aida, what is the Great Search this week? Okay, this week's Great Search is actually a continuation of last week's Great Search because when you're out of a part, you'll do anything to get an alternative. So we're not like a super shortage, we're having a little bit of a shortage for the AP 2-on-1-2, which is our go-to regulator. We love the 3.3 volt regulator, it has 600 milliamps out. It's got a very low drop out, it's stable with ceramic capacitors, it's just an all-around great little regulator and we use it in so many of our boards, like almost every board and feather uses it. It's also very inexpensive, it's about 10 cents in quantity and so we have a bunch on order and we're going to get some more, but while we're waiting for some to come in, I want to be able to stretch out that supply and also I'm thinking like, I take advice from Mr. Lady Aida and Mr. Lady Aida, I used to say, never let a crisis go to waste. Now we say let every third crisis go to waste, but try to not let two out of three crises go to waste. Yeah, when five crises come up, it's okay to say never let a crisis go to waste but maybe a fifth one, that one can kind of go to waste. It's on us. It's not a yogurt hardware, if you get five crisis stamps you get a free crisis. It's okay. So seeing that there's other parts we've had to find alternatives for like MOSFETs and crystals, those are much easier to replace, but a regulator, what's interesting about that is because we have this kind of favorite regulator and it's using so many things. Not being able to get it is more of a supply shock than just not being able to get a microcontroller. If we can't get a microcontroller, which we can't, only those boards that use that chip go out, but if you have something that literally 70% of your boards are using, you can't get it, it's a little bit more stressful. And so last week what we did is we did a great search where I showed how to find an alternative for a lot of our breakout boards that don't need as high current. They can get away with 150 milliamp regulator. I still want that ultra low dropout. Of course I want it to be pin compatible, not require bypass cap, fairly low quiescent current, fairly low noise and we found a couple of good alternatives. This week I want to future proof myself. I want to say look, we found alternative for the breakout boards, for the feathers and the dev boards, we still want to have a high current output regulator. So let's quickly go to the overhead and I'll just show what I mean. Since this is the QDPot ESP32, this has an ESP32 dual core 240 megahertz microcontroller with Wi-Fi, it uses a lot of current. When you turn that Wi-Fi on and start blasting or connecting to the SSID, the power ramps up and you can easily use 300 milliamps and so I definitely can't use 150 milliamp regulator. It wants something that is stable and good for 500, 600 milliamps. That's ideal because you can also power your peripherals from the same LDO. And so you'll see here, this is the LDO, I'm using the AP2112K, again I love it. Another alternative that is drop-in replaceable for that same current is the RT9080. We covered that in a previous great search when I showed looking for a much lower quiescent current. Only thing is that that regulator is also impossible to get and both of these have pretty intense lead time. So let's go to Digikey, let's go see what we can find. This is the part, again I can't get lead time stretching out into 80 weeks. I feel like I'm a weather lady now and I'm stretching out into the weekend and it's going to be hot. It's going to be 80 weeks of lead time. But what I do like about this is again it's got that high current output. So before what we did is we focused on pin compatibility. Let's find something that has the same SOT23 or TSOT235. This time I'm going to look for a fixed regulator that's about the same size or maybe smaller. Maybe I can make a version of my PCBs going forward that can use two different packages because that flip-flop design can really save you when you can use two alternatives. So we're still going to go with the surface mount parts. I definitely need to have an enable feature but the problem is sometimes the features have more stuff. So I'm actually going to leave that unchecked. I'm just going to look for something around 0.4V at the max 600mA dropout. Current output is 600mA but I can go higher so I'm not going to check that either. And then I'm going to check I do want one fixed positive 3.3V output and I want it to be active. So we've got a couple of similar parts. You'll see there are a lot of SOT23 looking things but there are also some weird SMT parts. Also of course since I didn't filter by package I'm getting SOT223s. So now let's look at what's really important to me which is the current output. Again, I need something that's like at least 500mA. I'll go up to like an amp. I think anything more than that's going to be a pretty big package. It's not going to be something really tiny so I'm going to apply that. Let's look at quiescent current. I definitely want something that has like 100mA or less because the AP2112 is about like 80mA. It's actually a little bit less maybe 40mA and I definitely don't want high quiescent current so I'll apply that. Alright now we're doing pretty good. So let's look at what we've got as some options. So I do care about pricing. I can't really afford to put a dollar regulator on every feather if I'm going to sell the feather for about $10 retail. So let's put in the view price at $10k pieces. Okay now we've got some good options. So first up there is this pin compatible runic regulator. There's also this one which actually looks pretty nice but it's not in stock. There's some other packages. There's this 6DFN which might fit but what I really like to look of is after I got past the SOP223s is a couple of on semi-NCP parts. These are really tiny. These are 1mm by 1mm SMT but they do come in a couple different configurations and they have ones. There's a few BGAs. I'm going to skip those. It looks like other companies are also using that same triangular DFN style. So what I'm going to do is, oh first I'm going to look at maybe dropout and maybe filter on that. So let's look. So max dropout remember the previous AP2112 had a dropout of about .4 volts over 600 milliamps. I don't want anything much higher than that. So let's filter for about half a volt. I think that's still quite high but better than nothing. And then voltage input max is fine 5 volts. So yeah I think we've got a couple good options here. The B33s I really liked.  The NCPs are, oh interesting I didn't select the right dropout max, huh, okay, not sure what I did. But I did like the look of these NCPs. I'll say that one thing, once I saw this little DFN package I was interested in it. And when I looked at the datasheet there's one thing to watch out for. There's an A series and a B series and the A, so you have to be careful.  This regulator has an option if you look here there's a, when you disable it it doesn't just float the output, it actually pulls the output low, which I don't want. Like I don't, sometimes I have like a feather that is disabled but you can still provide like an external 3.3 volt somehow. I don't have a pulled down 3.3 volt and I don't really like that in the regulator although I can see why somebody would want it in some cases. So you do want to make sure you get the B type for this. So when I looked through these I saw that there was the NCV8177B and then the NCP176 also available in the 6DFN. And then I think I also looked at what was actually in stock right now which is like very few things. Let's see if I can find the part again. No, oh you know what because I bought them. But I was like I have to buy them before the show. So I ended up looking at the NCP167 and B which came in at BGA and DFN. And the reason I liked this one is it's, first off they had some stock which I purchased. I left some in. It's 700 milliamps output and very very low dropout only a third of a volt at 700 milliamps. And again it's got this very tiny XDFN shape. And it seemed like NCP that on-semi this NCP series they had a lot of different alternatives. You know the 6DFN version that I showed like there was also a 6DFN version it doesn't fit within a SOP235 like you can't have both share the same package. But I did find that you know I downloaded from DigiKey they have a service where you can get like the CAD model. So I went here and I downloaded the footprint directly and imported it into Eagle and then I just tweaked a little bit to pass my DRC and then you can see here this part here I haven't situated within the SOP235 and so you know for my next board that I run I'm going you know because it's like it's so tiny it is small it does fit into a 6x6 rule. If you need 7x7 or 8x8 it's going to be tougher I mean this is a very small part I'll show it on the overhead as well. But because it does fit inside that package what I might do is the next few boards I run is have this sort of flip-flop design where you can use either or it doesn't take up any more space and then you can see you know the pads you have to kind of route them like it's not the order of the pins is not exactly the same so you have to kind of like the V and pin kind of has to go around a little bit. But I think I can have a you know a PCB that has either and have the stencil have either and then you know whichever I can get if I can't get the SOP23 I can go with the DFN or vice versa because they seem like they're very equivalent regulators. So let me show this on the overhead. So I did pick up some of these the NCP167B and let me see I mean these are so small I just got this package today so we're gonna look I don't see I already lost a bunch okay so these it's like they're really tiny I mean you definitely can't hand solder them yeah I mean you can barely see it but it it does have a little triangular center ground pad and it has a little I mean like yeah you can't really see it but it's shining on the tip of my finger it does have the four pads again it's a little bit of a scary small package but it seems to be quite popular it'll fit inside the package of the I mean I prefer the SOP235 but I think the next prototype I make I'm gonna try to have this as an alternative and you know if this it's a little bit more expensive but I will say if I'm making you know a QV pie this is a lot smaller I could save some space it's only like you know 25 cents instead of 10 cents it's a lot smaller and maybe I can fit you know an extra if I need a couple extra traces on the top this will give me some clearance so I'm gonna try this you know as an alternative I think even though I don't need to use it yet knowing that this part shortage is only gonna extend I'm a little bit more wary now of having this dependence on a part where if I can't get any it's like I can't really manufacture anything so thankfully you know I'm finding ways around it but do yourself a favor because I think this part shortage is gonna be another year and a half or two years so you'll thank yourself later for adding multiple package options to your design today it's gonna be a long winter spring summer it's ground on day in far shortage land all right that's the research all right thanks everybody