This lecture is part of an online graduate course on Galois theory, and will be about the algebraic closure of a field. So last lecture we saw that if we've got a field k and a polynomial p with coefficients in k, we can find a splitting field of p where this is generated by the roots of p and p factorizes into linear factors over L. We can obviously do the same thing with a finite number of polynomials p. We just multiply the polynomials together and take the splitting field of the product. Now what we can do is we can do the same for all polynomials in k of x. So what we're going to do is to extend k to a field k bar such that first of all, any polynomial in k of x factors into linear factors over the field k bar. And secondly we want k bar to be generated by roots of polynomials in with coefficients in k. So this is just like the definition of a splitting field except instead of doing it with one polynomial, we do it with all polynomials. And when we do that this field is called the algebraic closure of k. Now the construction of the algebraic closure is very similar to the construction of a splitting field except you do it infinitely many times. So the construction might be something like this. Let's first suppose the field k is countable. Then we all we do is we list the polynomials in k of x. So we might get p1, p2, p3. And there are only a countable number of polynomials so we can just list them all in a row. And then we take a field k equals k0. We extend it to k1, which is a splitting field of p1. And then we extend it to k2, which as you can probably guess is a splitting field for p2. And we carry on like this and we put a k bar to be the union. And you can easily see that that's just a field and contains a root of any polynomial in k of x. So any polynomial in k of x factorizes into linear factors. And what if k is not countable? Suppose k is uncountable. It's similar. But we well order the polynomials pi using the axiom of choice and then do something similar. Okay, well, if you don't know about well-ordering you probably don't care very much about uncountable fields either so we won't worry about it too much. But if you go to a set theory course, they tell you all about how to well-order things. And if you well order the polynomials, you can just sort of copy this proof and you get an uncountable well-ordered chain there. Anyway, a field is called algebraically closed. So field L is called algebraically closed if all polynomials in L of x have roots in L. In particular, that means all polynomials factorize into linear factors. And the algebraic closure of k that we've constructed is algebraically closed. Well, wait a minute. I seem to be kind of getting away with something because all I've proved is that any polynomial with coefficients in k has a root in k bar. But in order to claim that k bar is algebraically closed, I need to show that a polynomial with coefficients in k bar is algebraically closed. So I seem to be have slipped up a bit. So what we have shown, so we know that any polynomial in k of x has a root in k bar by construction. We want that any polynomial in k bar of x, and let me just put the bar in fluorescent pink so you notice it, has a root. Well, actually, this is not too difficult to show. If every polynomial in k of x has a root in k bar, then we can show that any polynomial in k bar of x has a root. So suppose that p of x is in k bar of x, and it might have coefficients might be say a naught, a one, a two, and so on. It might be x to the n plus a n minus one x to the n minus one plus a naught, where all the a i are in k bar. And now all we do is we look at the field of extensions. We take k and then we look at k with all these elements a naught, a one, a n minus one are joined. And then this is also contained in some field with k a naught up to a n minus one alpha, where alpha is going to be a root of the polynomial p. So we can just adjoin a root of p to k if we want. So this field k is certainly contained in k bar. And what we want to do is to show that we can also, if we want, pick alpha to be in k bar. Well that's quite easy because we notice that this extension here is finite because all the a i are algebraic over k. And this extension here is finite because alpha satisfies a polynomial with coefficients in these. So this extension here is finite. So alpha is algebraic over k. And what this means is that alpha is a root of a polynomial with coefficients in k. And we've shown that any such polynomial factors into linear factors in k bar. So we may as well assume that alpha is in k bar. So this shows that the algebraic closure of a field is algebraically closed which is really rather fortunate because it would be kind of stupid if it wasn't. So we can see that any field has, let's call this k, has an algebraic closure. So actually we only sort of really prove this for countable fields and mumbled something about set theory for uncountable ones but never mind. We can also sometimes ask about a weaker property or a weaker construction. Suppose instead of asking for all polynomials to have roots. Let's have the problem of find a field l with k contained in l so that all elements of l have a square root in l. So an algebraic closure would certainly have this property but what we want to construct is a smaller field that's only closed under taking square roots. And we would like the smallest possible field so we only want l to be generated by the operations of repeatedly taking square roots and field operations. Well we can construct a field like this. We could take k equals k0 and we can embed it in a bigger field k1 where with k1 you would join all square roots of elements of k0. So this is just like what we did for an algebraic closure exception. Instead of taking all polynomials we're only taking polynomials of the form x squared minus a0. Now it's certainly not true that k1 is necessarily closed under taking square roots but that doesn't matter. We can extend it to a bigger field where we adjoin square roots of elements of k1 and you can continue this an infinite number of times and let's put l to be the union of all these fields. Then you can see that l is closed undertaking square roots and secondly l is generated from k by the usual field operations plus minus times divide and taking square roots. Now you see if we were really lazy we could have used a similar argument for the algebraic closure. So we could have said well k1 is going to be generated by all roots of polynomials with coefficients in k0 and then k2 is going to be generated by all roots of polynomials with coefficients in k1 and we sort of continue and construct the algebraic closure to be l. And that would save having to prove that k1 is algebraically closed. In fact we showed that k1 is in fact equal to k2 but if we were too lazy to do that we could just use this argument instead which would be kind of a bit sloppy. So this is a fairly common construction mathematics. If you want to construct an algebraic object closed under some operation you can quite often get it by just iterating a countable number of times and taking the union. By the way if you wonder why anybody should care about fields closed under taking square roots that's related to the old problem of doing things like squaring a circle or trisecting an angle because the numbers you can construct using a ruler and compass turn out to be exactly the numbers you can construct from the rational numbers using the field operations and taking square roots. So a number can be constructed by ruler and compass if and only if it's contained in the field you get like this by starting with the rationals and taking its closure under square roots. These are sometimes called Euclidean numbers. So let's have some examples of algebraically closed fields. Well the example that everybody knows is you take k to be the field of real numbers and then the algebraic closure is the field of complex numbers. So this is sometimes called the fundamental theorem of algebra which says that the complex numbers is algebraically closed. In fact this is a particularly easy example because we only need to take a degree 2 extension of r whereas in general the algebraic closure of a field would be a huge infinite extension. And how do we prove complex numbers are algebraically closed? Well we'll be giving an algebraic proof of it later on in the course and if you've been to a complex analysis course you've probably seen a proof of it using Louisville's theorem. What I'm going to give now is a very short topological proof. So I suppose p of x equals x to the n plus a n minus 1 x to the n minus 1 and so on plus a naught is a polynomial with coefficients in the complex numbers. We want to show that p has a root and what you notice is that if x is large say x is equal to r sufficiently large then this bit here x to the n is bigger than this bit here so it has bigger absolute value than a n minus 1 x to the n minus 1 plus a naught and so on. In fact you can assume it's much bigger and that's pretty much all we need to know to show if it's algebraically closed.  Well as I said x to the n you remember from complex analysis goes around the origin n times but it's perturbed slightly by this but since this is very small the perturbation isn't going to be very big so if x is doing this p of x will sort of wiggle a bit and it will sort of go around the origin n times so this is what p of x does and now imagine making this circle smaller and smaller so instead of looking at radius r I might look at some smaller radius and then what's going to happen well it's going to go I don't know this bit will no longer be smaller than this bit so we can't really assume it goes goes roughly around n times and if I make it smaller still so I just get a yellow spot there then what happens to p of x is it will just look like this actually that's not terribly legible let me do it in green instead so I'll put a green spot there so and now let's look at what happens so here this pink circle goes around n times anti-clockwise where n is equal to the degree of the polynomial p on the other hand this yellow or possibly green spot goes around the origin zero times so as you imagine contracting this circle here its image starts off going around the origin n times and ends up going around the origin zero times and you know if you sort of imagine this this thing going around as being a loop of string or something what we've got is this loop of string kind of going around the origin three times or n times like that and you're trying to move it around so it ends up going around the origin nought times but if you imagine the origin as a sort of post there it's sort of caught on the post and you you can't move it to going around the origin nought times without at some intermediate point passing through the origin so there must be some intermediate circle between this big circle in the origin such that if your if x goes around that circle it must actually pass through the origin the the number of times you go around the origin is sometimes called the winding number so what we're saying is the winding number starts off being the degree of the polynomial here and goes down to zero there what i said sorry the winding number of the image goes down from n to zero so at some point it must change and the only way it can change is if if the curve passes through the origin so what we have shown in fact is that anything of the form x to the n plus f of x has zero if f of x is less than x to the n for x having absolute value r for some fixed value of r that's because if f of x is less than x to the n then x to the n plus f of x will have winding number n because it's this is sort of forced to stay roughly in the same direction as x to the n so it's the same winding number as x to the n um so this doesn't need to be a polynomial at all it can be any continuous function um so um so that gives the complex numbers as a fairly natural example of an algebraically closed field so let's have some natural examples of algebraically closed fields um there are lots of examples you can get just by taking the algebraic closure of a field but the problem is is not very natural they're rather hard to write down explicitly i mean our construction said you know you had to write down this infinite sequence of polynomials and keep adding roots and you know actually doing that would be a horrendous bookkeeping operation so let's see some natural examples well first of all we have the complex numbers secondly we've got things like the algebraic closure of q bar inside the complex numbers that so these are the so-called algebraic numbers which are the elements of c that are algebraic over the rational numbers and um since the complex numbers are algebraically closed it's fairly easy to check that all the elements that are algebraic over the rational numbers are also algebraically closed so this is called the field of algebraic numbers and there's an entire subject called algebraic number theory devoted to studying just this field um apart from this it's really quite hard to write down natural examples the the only really natural one i know of is is the field of preser series um these were actually invented by isaac newton but there are too many things named after newton so some of newton's inventions are named after other things so you remember the lorant series or rather formal lorant series are just the power series or formal power series over the complex numbers except you're allowed to have a finite number of inverse powers so for example we might have x to the minus 3 e to the x would be a lorant series x to the minus 3 plus x to the minus 2 plus x to the minus 1 over 2 factorial and so on um now preser series are a slight variation of this so what we do is we take the union over all n of greater than or equal to one of lorant series in x to the 1 over n so we take x to the 1 over n and then we're allowed to um invert so it's so you might have a series like x to the minus a half plus 2 plus 3 x to the half plus 4 x and so on that would be a typical preser series and newton more or less showed that preser series are algebraically closed i mean he didn't actually state that because algebraic closed algebraically closed fields hadn't been defined and wouldn't be defined for several hundred years but in spite of the fact that they hadn't been defined newton still more or less managed to show that the the field of preser series is algebraically closed he sort of proved a theorem equivalent to that um well we showed existence of algebraic closures um now we should discuss uniqueness of algebraic closures and here we run into the same sort of rather funny problem that we had for um splitting fields so any two algebraic closures of k are isomorphic and the proof is much the same as the splitting fields except you have to repeat things an infinite number of times instead of a finite number of times so i'm not going to bother doing that but the trouble is this isomorphism is not unique and in general there's no way of making it sort of canonical and this runs into a it's not really a serious problem but it's a sort of rather irritating bookkeeping problem in that you can't really speak of the algebraic closure of a field because you know if two people come up with algebraic closures of the field they may be isomorphic but there may be no good way to agree on what the isomorphism between them is um for instance you get a problem like this if you're a category theorist and you try and make um suppose you take a field and you ask is taking the algebraic closure is this a functor so you remember from category theory that to make it a functor you've got to say if you've if you've got a field k and a map from k to l and you take an algebraic closure of l is there a natural map from the algebraic closure of k to the algebraic closure of l and if you think about it a bit it's really not easy to to make this into a functor because you know which which isomorphism you're going to take and I mean I think if you work very hard and using the use the action of choice a lot you might be able to sort of push through something but it's really rather a mess and there's a sort of analogous very similar problem to this in algebraic topology so what I want to explain is that is the problem of uniqueness of the algebraic closure is related to the problem of defining the fundamental group of a topological space x so um you know if you've got a topological space say a surface with genus 2 surface then you can define a fundamental group whose elements are roughly loops started on this surface so so a typical loop might go around there and then background there and if you've got two loops you can sort of try and compose them and you can try and make that into a group well you've got to be a little bit careful because if you've got two loops it's not quite clear how you compose them what you've really got to choose is choose a base point and instead of looking at arbitrary loops you should just look at loops that start at this base point and go round and then if you've got a loop that starts at that base point and if you've got another loop that starts at that base point and goes around there say then you can compose them and get a loop that goes like that so you've um by it's not too difficult to make to make these loops into a group if they're taken up to home a topic and the problem is so you've got this fundamental group is usually denoted by pi 1 so you might say well you've got a fundamental group pi 1 of x well it seems to depend on the choice of base point well it doesn't really because if you pick another base point then um for any loop here um you can turn it into a loop at this base point by going along a fixed line between these base points then round that loop and then round there and from this it's not too difficult to see that pi 1 of x doesn't depend up to isomorphism on the choice of base point however if you try doing that you run into some rather nasty problems that the problem is that the isomorphism between these groups for these two different choices of base point depends on the line you've chosen between these two points so we've got the same problem that we had for algebraic closures of fields what we should do is not define the fundamental group of a space x but define the fundamental group of x with respect to a fixed base point x zero and this map here is not a functor if you've got a map between topological spaces you don't get a well-defined map between this whatever it is however you do get a well-defined map for these things so this is a functor and now i want to show that same sort of problem happens for algebraic closure so if you've got a field k we can um embedded in an algebraically closed field k bar and we can define an absolute Galois group Galois group and i'm going to just define this to be the automorphism group of k bar that fixes all elements of k so it's just a group of symmetries of k bar and you should think of the absolute Galois group of a field k as being analogous to the fundamental group of a topological space x in fact as i mentioned a few lectures ago growth and dick had a had a formalism in which it more or less is the fundamental group of something if you're willing to use et al topology and the problem is that the fundamental group of a space x isn't a functor if you don't pick a base point and similar the absolute Galois group of a field k is well it's not really a functor in other words if you've got a map from k to a space k one and you embed this in an algebraic closure k and embed this in an algebraic closure k bar then if you look at the automorphism group of k bar there's no natural map from this automorphism group to this automorphism group well what you can do however is you can define an absolute Galois group if you pick an algebraic closure k bar now picking an algebraic closure k bar turns out to be very similar to picking a base point x zero so if we pick a base point x zero then we have a nice fundamental group which which is doesn't depend on all these funny ambiguities similarly if you want to define the absolute Galois group of a field we really have to pick an algebraic closure even though all algebraic closures are isomorphic if we don't pick one we run into nasty problems about this thing not being a functor so most of the time it's harmless to talk about the algebraic closure of a field and you don't need to worry about this ambiguity but sometimes you do by the way if you do need to worry about this ambiguity that there's a construction called a groupoid that i just quickly mentioned that sort of gives a neat solution to this problem so groupoid is a category such that all elements such that sorry all morphisms are isomorphisms and now in these two cases we can construct a fundamental groupoid that doesn't depend on a base point and we can construct an absolute Galois groupoid that doesn't depend on the algebraic closure and we do this as follows the category here has objects points of the space x and the morphisms from a point x naught to x one are the same as homotopy classes of paths from x to x one sorry from x zero to x one in the space when i say paths i mean homotopy classes of paths but there's not enough space to write out homotopy here now this groupoid i'm going to define a category whose points are algebraic closures k bar of k so i said there's really no canonical choice of an algebraic closure although they're all isomorphic so you just take all of them and the morphisms sorry that's not points it's objects and the morphisms from one algebraic closure k to another algebraic closure k are just going to be isomorphisms of fields from the first one to the second so if you're bothered by this lack of uniqueness of the algebraic closure you need to go and find out what a groupoid is and work with the absolute Galois groupoid rather than absolute Galois group but as i said most of the time you can sort of get away with the absolute Galois group and not worry about this this this rather complicated nonsense okay next lecture we're going to give another application of the splitting field of a field which is to construct the finite fields or galois fields


Kaima Pujin. Kwaia Puli, Komore, Komore, Komore, Nikini, na. Nikini, na. Na. Sofa, so good. I think we are enjoying and we praised the Lord that this was a success. Jp wa maiku ua, it was awesome. Very nice, good weather, and I've enjoyed it all the way. And I'm happy that I'm still feeling strong and I'm going to go a long distance. We made it 10 kilometers, actually we are among the top 10. How was your experience brother? This was a test, but it was a test of our self sacrifice. It was a test of our perseverance, of our consistency. This was a test that we have won and what we have won is not a run. What we have won is our friends who are in the streets who we want to help. That is what this run has been about. Because it was all about creating awareness about drugs. This is good for you men. You know to stay cool it will have a sober mind. If you mind it no sober you can't say you are cool. So let's keep our mind sober by not going the drugs way and the Lord shall bless us. Keep cool. My experience was good. I had to pull some people like faster, but it was a good experience. It was excellent. I had a fantastic time. How many kilometers have you done? A whole full. We've done 10 kilometers. You sure? Ya ya ya. It was quite a race. We loved. There was no competition. Thank you very much. This was a very good experience. I hope we would actually do this more often. Probably once a month. That would be fine. Thanks. We've done 10 kilometers. Miguel and Amani and the rest. Oh it was nice. At least now we are relieved. But I think we should be doing this more often. How often in a year? Like 5 times. And then the rest we can't be doing ourselves. It was a fun work. I wish we would be doing this often. To keep us healthy. Once a quarter. A lot of fun. 10 kilometers. 10 kilometers. Was fun. How often will you want us to organize this? Often as you can, when possible. And we also realize that when you go as a team, you are able to endure easily. Thank you. We are glad to join this campaign of drug awareness. And I would recommend if the church would consider that we have it either quarterly or monthly. I have run the race like Peter. I have completed the race. It was very nice. In fact, we have run and we had drug awareness. People were asking why are you guys running? What is this about? I think the church will make this monthly if not quarterly event. I met a lot of people. It was a lot of fun. And it was healthy. I walked for 5 kilometers. I went for the 10 kilometer run. Fantastic. I did not even walk for a centimeter. I ran the whole race. From the start to the end? Drug awareness is an important aspect of our society. It's affecting every family and every estate. So it's good that we bring it out to light so that people know that drug, we are combating this problem of drugs. We went for a walk today. And we are here with the Maxwell Academy group. This is our principal Mr. Dander. My name is Larry Rusinescu. We had a really good time. 5k a walk. Rather relaxed but still enough to build up a sweat. So we're so happy we could support the project. And drug awareness is a really important thing. We have come to join the SDH church in the drug walk. Or health walk this day. As you are aware, it's our mandate to coordinate the campaign against alcohol and drug abuse in the country. Do you do one-on-one cancelling? One-on-one? Yes, we do one-on-one cancelling. We have professional counsellors at our station. We have a toll free number which is 1192. So from your telecom line, you can call freely, get to meet with our professional counsellors and they'll get to advise you not only on alcohol and drugs, but also in other issues that are affecting us as human beings. The experience was wonderful. In fact, I didn't do 20 according to my counter. It's 24.7 kilometers. It is the work of the church to identify the needs of the people who are around them and find a way of meeting their needs. And by meeting their physical or mental needs or challenges, we will be able to reach them spiritually and prepare them as we prepare ourselves for the second coming of Christ. The experience was quite interesting. I enjoyed seeing the children, mothers working and running with their children. I was happy to see the youth turning up in good number. And the church was full and the roads were full and this is quite an impact. I am sure everyone who saw the group were impacted and they know as a church we are standing against the drugs and we are saying no to the drugs. So I enjoyed it and I would like to see more and more of this. If it is organized, I'll participate.


Today I want to do a little review on the Backfire Hammer. I'm never going to buy a first generation board again. Didn't even sell it anymore. They have the Hammer Sledge.  It was by far the best board I've ever ridden.  I have no idea why anybody ever rides in them. Literally for me, if I go on a long ride and it's at night, one time my tire is flat. That's why I liked about the G2 and the G3 was that they just were so well-rounded, you know? They're just easy to use, enough speed, enough battery. You didn't really feel gypsum in any area.


Dwi'n golygu Iam Trafflun i London o'r Llongterfyniad ym Gwyllt yma i gwybod i'ch ganddo i gael eu dynion yma. Ac oedd oherwydd dyma'n hanes. Dyna'r ddiwedd yma'r ochr dyma, mae'r amser yn dymian gyda'r 60r hynny ac yn gweithio i'r ddweud o'r cyffredinol. Felly iddw i'r gweithio i Llanddol yma, mae'r newid gyda'r PXG store. Mae'n gweithio i'r gweithio i ddim yn ei wneud, I'm also really excited to get my hands on their apparel line for the first time so it could be an expensive trip. But there's a surprise in store and it's not for me we've made this journey for. It's, as I said, for my good friend and he's about to be in for a little bit of a surprise. Right now Damien is in the room next door. He's getting a camera set up on a tripod because he thinks he's come on this journey to help me film which is a generous offer from him. But what he's about to find out is that I'm not the one getting custom fit. It is him. You've never been custom fit before. It's his 60th birthday. It's a bit of a surprise and I'll bring the news to him. Well, you look as though you know what you're doing there. I don't mate. You're making a good impression. Is it the little bottle on the right? Listen, forget the little bottle on the right. I've got a surprise for you. You're not behind the camera.  It's your 60th birthday. I've arranged for you to be custom fit and I'll do the filming. You do the inner golf balls. You've got 10 minutes to get warmed up. Mate. Thanks. Are you ready? Just launching a fraction of how you may be bought. Yeah, really good. Carlos just put me straight away. Really, really supportive. Really helpful. No, he's been absolutely brilliant. So knowledgeable, so patient. I'm really enjoying it. Damian is well and truly into that custom fit and there seems to be enjoying it. I'm going to leave him to it and let him get settled in and we'll check in later as to how that is progressing. But for now, I'm going to go back into the new London South Store and have a little news round of this apparel. I've got a feeling, like I said, this could cost me a few quid. It's so nice to have a dedicated store in the UK and if PXG do something, well then you can be guaranteed they do it well. Having a store in the UK provides golfers who are perhaps less confident about buying online the opportunity to visit in store and the opportunity to go through the custom fit process in a high-end facility and also find out what this apparel is all about. Big texture effects on that. That's a seven and two. Would you say, would you miss being left more so than with the audience? Yeah, overturning one. Is it? Yeah, yeah. When you've left, some girls are still 150, 140, 152. I think that's the change in technology, the biggest change. It's that forgiveness element, isn't it? Midway point, obviously, at your starting position with his M2 irons. How was he getting with them first of all? Numbers were really good. Strike was brilliant, good launch. Damian plays a lot of links golf, so he wants to keep his launch down a fraction. One place where we could definitely gain was just with ball speed and tighten the dispersion up a little bit. So we put him into the Gen 6 XP head, gained about 10% in carry distance and 10% ball speed, which was great. But the shaft we put in, it was a zealous eight, quite similar to what he's using now. Great numbers, but it was just launching a little bit too high and he, as he plays a lot of links golf, he wants to keep that launch low. So we think we're going to try and get him into something similar to what he's hitting now because the numbers are great, but just to keep that launch down a fraction. Right, 10 minute break. From what I'm watching, it seems to be going well, but how does it go from your perspective? Really, really informative hand. Can't believe the difference. Already, in terms of launch angle consistency, dispersion, also landing angle. So obviously in terms of landing on the green. Stopping. So I haven't explored all the different set of options which we're going to go on in a minute. I've just spoke to Conrad and he says obviously there's some changes he's now going to make and he's getting another set up for you. And the process of custom fit, having not done it before, initial thoughts? It's a must. It really is. The difference it makes is significant to me. Just the data alone. Even just using my existing ions. And just to add clarity on what the launch angle was. Distance and everything else. But when I'm hitting targets and I'm already seeing significant improvements, for sure it's the right thing to do. Right, well good luck. Thanks mate. Any more surprises for me? Not just yet. Okay. Drill this one in. Great strike. Really good mate. Really interesting. White is yours. Blue we've just done which we don't really want. This was just one of the earlier ones. But if you see where we are now, it's a lot more consistent. It's a lot further. Other kind of important numbers to look at. Spin now is not much more. About 100 rpm more. We've had a lot more of spin in the p-head if we went for that. We really want our ball because of the links got off. Ball speed one or two. 111.6 now. So 10% further. Average. Carrying 158. Compared to 141. I mean again, left-right you were very consistent as is. So on average now 7 feet left. Compared to 10 feet left. That's what performance is on dispersion as well. It's just mind-blowing really. I'm just disappointed I haven't done it before. Yeah it makes a big difference doesn't it? Right then all you're all done. How are you feeling physically? Hold on knackered. Yeah I think 95 shots. Did you really? It's thorough isn't it? It is. That's one of the most impressive things. Every time I kept coming back you were changing weight. You were changing shaft. So that was good to see. But you've pretty much come in. You've got this MMT shaft. 80 gram. Stiff. XP head. Happy? Absolutely. In terms of consistency. In terms of results. In terms of data. It was the best by far. Now what I noticed is the MMT shaft is black. But you've got a dilemma now. You've got to choose what head to go with. There's black on black now. I think it's chrome on chrome. What are you thinking? I'm going to go for the DLC. Which is the black. Right. DLC is the coating isn't it? Yeah. The black. Which is a great address. Feels great address. Still by having the confidence isn't it? Yeah absolutely. They look superb with the black shaft as well. Yeah I looked at the double silver ones. But I prefer the black. Yeah. So more results. Results? I'm jealous to be fair. I'm just going out and playing now. Congrats. Happy birthday. What a lovely surprise.


So, we're going to be doing a lot with Sam bam files over the next couple of days. And it's kind of useful to dig into them a little bit and have some familiarity with what they are so I think for a lot of people bam files like really a black box right like they get a bam file, maybe they feed it to another piece of software. But they don't necessarily understand like how to read it or what's inside it. So that can be useful for things like just basic to see or as soon as you need to do something that the like next tool doesn't quite do, there may be a time when you need to actually kind of like interact directly with the bam file and understand how it works. So there is a specification we link there. I talked about how Sam is just uncompressed version of the bam file. Bam files are usually indexed so we keep hearing about indexing, you build an index to go along with your bam file so that it can be read in by like things like IGV. This is what a bam file looks like. It has two parts. It has a header section that has information about from like the sample that was aligned and the program that aligned it. And then it has the alignment section where each row of the file basically has information about a read and how it was aligned. It's a little bit hard to make out but you have like a read name that's very similar to what you saw when you were looking at your FASTU files. There's a flag. We're going to talk about what that means. Next up is like the position in the reference or the reference record that you're aligning to. So this is chromosome one and the position in chromosome one. Then I think this is a mapping quality cigar string. Then the reference sequence in the mate pair. So when there's an equal just equal sign it means it's the same so that in this case the mate pair is also mapping to chromosome one. And then here's its position. And I think this is the length or size of the fragment. And then the actual sequence itself and then the quality string. So that's just for memory. We'll look at in a minute, see if I'm right about the order of things that are in there. This is just reminding you about the header section. So the header has things like the short order of the alignment. So sometimes it can be useful to just look at a band file and look at the header. So if you're trying to understand like what is this data where did it come from, you can find information, like in the regroup area about the library or the sample. You can see what program was run on it sometimes this will give you information about like the type of a liner that was run, or the reference genome that you were aligning against might be specified here. It can be really useful sometimes to to dig into the sandbam header section. This happens to us all the time like especially if someone gives you data or you like download alignment data in BAM format. There's like a kind of a paper trail in here like a record of how we got to this BAM file. And you might look at it and decide like oh I don't really like the way they did this I want to get the fast queue and like redo the alignments or something. Let's see. We already talked about this how it's divided into two sections. This is just kind of looking at some example data in an example header section so here you've got things like the regroup ID so you're getting like like sample ID and sample name and here's like an example of a program record where it shows you if the WA was run and it can actually have like details of the specific command that was run, which can be helpful. And then this is just a bit of a zoom in on the alignment section which I should have used when I was pointing out all of the parts to it. But that's just those an example of what 10 alignments look like. And we're going to break some of these sections down. So this is the order of those entries so each is separated by a tab, and then these are the 10 or 11 things that are in each row each alignment record. So again you have the query name so this is the name of your read usually. There's this flag which will talk about the reference name, the position of your alignment, the mapping quality score. And then the gar string which we'll talk about, and then information about the read pair where where it aligns the length, the sequence and the quality. And these are just examples of what those look like. So any questions about like the contents of a band file on the records. It's an attempt to kind of like demystify because I think when most people see this they're like what is this gobbledygook right. But if you like break it into its parts it's actually not that scary it's not that much more complicated than a FASQ file you've got your, your read name, where it's aligning to where it's made is aligning to the actual sequences there so that can be helpful if you need to like work your way backwards like you can actually revert from this back to a FASQ file if you need to. And that's possible because the sequence and the quality string are still there they're still in the alignments right. So you can get back to like a simpler version of your data if you, for example want to like realign it but you don't have the raw FASQ data that happens to us all the time too. And a lot of places actually don't keep the FASQ files they just keep found files because they know that they can revert to the FASQ file from the band file. So just to save on disk. Okay, so we talked about this. There's just two elements of this that we're going to talk about a little bit more so there's this thing called the flag, and there's this thing called the cigar string. So this flag is basically a way to encode a whole bunch of information in a really efficient way. So this is a series of so called bitwise flags represented as a single number. So you're essentially storing a binary string of, and this keeps changing over time as they add more but I think it's still currently 12. What you're doing is you're, you're representing a binary state of 12 questions with the value zero or one. So zero you can think of as no one you can think of as yes, and then each value in the string of zeros or ones represents a property. So for example, is the is the alignment representative of a duplicate. That's represented by this second last value here. If it's a zero it's not a duplicate. If it's a one, it is a duplicate. Okay, so it turns out that there are two to the 12 possible combinations right you've got zero zero zero zero zero zero, you've got one zero zero zero zero zero one one zero you got what I'm saying right so there's 12 which is 4096 possible combinations. So that means you can represent all of this information that the status of whether it's a duplicate or not whether it's a supplementary alignment or not with a single number between zero and 490 4096. That's what is in that field of the band file. So if we go back to like one of our examples. This particular flag is 99. So 99 corresponds to one set of values. And there's a handy tool which we're going to play around with in the practical where you can go to this website and just enter the number 99 and it'll tell you which of those properties that particular alignment has so it'll just like go through the, the permutations yes this know that and so forth. Any questions about these so called bitwise flags. This is important because if you want to filter your band file for some reason like let's say someone asks you. I don't know how many reads were there in your example that were properly paired duplicates or something like that you can like figure out you can go to this website you can check those boxes for the properties you care about. It'll tell you that number and you can run a single command that says, give me all the alignments with this value. And that will give you all the alignments that have the properties that you're looking for. So the other kind of simple is are going to like play around with it later and hopefully get more of a sense of it. The other kind of confusing thing is the cigar string. So cigar string is one of those other columns of information. And this is basically another space saving innovation, which is a really efficient way to describe an alignment. So the string of, or it's the cigar string is a sequence of base lengths and operations, indicating which base is aligned to the reference, either, and it doesn't distinguish actually between match or mismatch, necessarily. And so it can represent deletions insertions introns. There's all these different kinds of operators like the most common or obvious one is match so there's a series of positions that match the reference. There can be insertions relative to reference there can be deletions that you can represent soft clipping and so on. And the easiest way to understand this is with an example. So this is an example cigar string 81 m 859 n, and then 19 m. What this is describing in a pretty efficient way is 100 base pair read consisting of 81 bases that match the alignment matches 859 bases that are skipped, and then another 19 that are matched. So it can represent us kind of split read exactly like the ones we looked at in the last lecture right where you've got part of the read aligning to the next on, then there's an intro on and then the rest of the line it picks up in the next on. So it's kind of like if you've ever done like a blast search.  So that's a nice visual way to look at an alignment but it takes like a lot of characters right it's like, you know fills pages. This is like a really efficient way to convey that same idea. And so software programs can like look through the BAM file and use that information in various ways. So just really quickly cram files we've talked about BAM files cram files are just that sort of next innovation and compression that give you even smaller files, so something like 30 to 60% smaller than the BAM file. The BAM files basically like a G zip SAM file like it's just using like regular text compression technologies. The BAM file is using knowledge of the reference genome. So you actually, when you create a cram file you supply reference genome and by kind of knowing the reference genome you can, you can basically compress that alignment, even more, because you can do things like it's almost like the cigar string you can say this hundred base pair read this hundred base pair span matches like position here to here. It's a really efficient way of just storing what that alignment is much more efficient than, or it's with I guess storing even what the sequence is you need to say like the sequence we're talking about here is the hundred base pair reference sequence from position a to position B, you can represent that much more efficiently than actually storing the sequence itself in a file, even when you compress that sequence. Yeah. Yes. And there's a couple different things so one is that I think some of these compression standards involve compressing the quality string the quality representation to a simpler format so you can lose some specificities of the quality depending on the settings. And then, in a sense you can lose things if you lose the reference that you use so this actually happens where you like, download cram files from SRA, but you, they did not properly document the reference file they used to compress the cram file. And then you have a problem where you can't uncompress it, or you're kind of guessing how to correctly uncompress it because maybe they use like some janky custom version of the reference that they use in house it's not obvious or available. I think like now SRA is much better about making sure that when you submit cram files that you properly, you actually submit like the reference you used, but there's still a bit of like faith that I don't know if they like actually like go through a full decompress and recompress like want to make sure it works you know. Yeah. So that's a good question. So this basically kind of stores like a diff from the reference genome which allows it to be really efficient. I think you guys have seen bed format so far no maybe. The bed format is just another commonly used file format it's much simpler than the band format. It's just a tab separated plain text file that has minimally the chromosome name to start in the end, and then other optional columns. So there's a number of different flavors colloquially referred to as like bed three bed four bed six bed eight. It always starts with just chromosome start stop like this from some start stop, but then it can have up to nine additional fields, including a name, a score, the strand, and then these thick start thick end and so far. Columns that you use if you're planning to upload your bed file to a tool like the UCSC genome browser, and you want to stipulate how the features in your bed file look so like are they the thick bars in UCSC or they like thick and then thin and different colors and so far. But the most common is just actually like the first three or maybe the first five or six. And then, I think now I've already introduced you to tools like bed tools which you can use and manipulate bed files. Similarly, there seems like Sam tools bam tools to card. We are going to use these extensively especially Sam tools and the card to manipulate our BAM files and Sam files. And common sources of confusion. These come up in basically all genome related bioinformatics. The most common source of confusion is the coordinate system so have you guys heard of like one based and zero based coordinate systems before. So it turns out that like the bioinformatics and genomics world could never agree on whether you should represent your genome coordinates with zero base for a one base system. So what does that mean, basically one basis where you count the basis directly so if this is comes a one and this is literally the first nucleotide in your chromosome and it happens to be a T, you would number that T one and so forth. It seems logical right like the first, the second, the third. I feel like this is maybe the more human interpretable or intuitive. But it turns out that for various like mathematical and computational reasons there's a lot of efficiencies to actually numbering it starting with zero. In which case you numbered the positions between the basis so like zero is like the position before the first base and one is position between the first and the second and so on. And these two systems have their pluses and minuses but they just their consequences that like representing something like a single nucleotide looks slightly different depending on whether you're using a one based or a zero based system. And then the whole world as I said is kind of split evenly between them so certain file formats are one base like Sam, and some file formats are zero based like bam. Which is kind of funny. And bed is like kind of maybe the most famous zero based file format. So that's just something to be aware of it's just a super common gotcha you just have to deal with it. Genome builds, just make sure you're using the right genome build this will probably happen at some point in the course that will go to load some data in IGV that was aligned with hg 38 but we've selected hg 37. And the data doesn't make sense. That's because your data is like mismatching with your reference genome. And then there's this idea of variant shifting and parsimony. I think this is the last one, we don't do a lot with variants in this course I won't spend a lot of time on this but the idea is that there's more than one way to represent a variant so in this case we have a deletion of a CA. So if you look at this reference sequence which is GGG CA CA CA GG, and there's a CA missing. Normally unless you do some very complicated molecular biology, you really have no way of knowing which CA was deleted, right, like, you know the reference has five CAs, you know your sequence as for, but it could have been any of those five CAs that was deleted, and for the you really don't care, right, it's going to have the same consequence on the protein. But the problem is, we can't all agree again on like, which way we should represent it. So they're like various different ways these are all valid or like correct in a sense ways to represent this. But some of them are longer, some of them are shorter, some of them have the variant at the right some of them have the variant at the left. And so if you're getting into variant representation there are certain like formats or standards and conventions that say like you should left shift like have your variant be as close to the left as possible. You should have it be parsimonious which is the variant should the leels of the variant should be as short as possible as long as they're greater than zero. So, long story short like this bottom one is a good representation because it is short, and it is, I guess, as far to the left, as possible. So that would be, I guess a more standard way of representing it. Before I sort my BAM file, we're going to come across this you before you index a BAM file or use it, you often need to sort it. The most common thing to do is sort by position. So we're going to sort, I think, in this course, mostly it's not always by position, but occasionally you may find that you need to sort your BAM file by read name. And usually done when we need to easily identify both reads of a pair. So like one common example is fusion detection where you're trying to compare like you're really focusing on where the two needs are in relation to each other. And so you might sort by read name to be more efficient for that kind of an application. So those are the lectures, and we're going to start with practical tomorrow on alignments. Thank you guys.


how can we sort of shrink the economic sphere, much like we shrunk the agricultural sphere? It's not like when we went from the agrarian age to the industrial age. It's not like agriculture disappeared. It's just that it went from consuming 80 plus percent of human attention to like sub-5 percent in a developed country today. And I think we need to do the same with the economic sector. We need to go from the sector where everything is based on prices, where everything is explicitly incentivized, that now occupies the vast bulk of people's lives. And we need to shrink that down to make room for all these non-economic things. Because a lot of stuff that we need to work on can't have prices. I'm here today with Albert Finger. He's a partner at Union Square Ventures here in New York City. I'm excited to talk about his new book, The World After Capital. We come to this meeting at a time when the world is both excited by the possibility of technology and terrified of the disruptiveness of technology. And I think he can help us sort ourselves out. Albert, thanks for joining me here today. Pleasure to be here. What inspired you to write this book? You've been a practitioner and a visionary. I've followed your blog. But all of a sudden you went to the book. Yeah. What's going on? Well, as a VC, I sort of feel like I have this front row seat to innovation, to kind of what's coming down the pike. And even before becoming a VC, as a both undergraduate and graduate student had studied computer science and economics, and eventually came to realize how computers are going to have a much, much bigger impact on the world than most people tend to believe. Like way bigger. And I was seeing it in the kind of things we were investing in. I was seeing it in what was happening in the world. And I was starting to give these talks. And I was sort of trying to get at this idea that somehow this is a big shift. It's a big transition. And I remember I was walking down, I think, Market Street in San Francisco. And it kind of snapped for me, because I had this insight that this is as profound a transition as when we went from the agrarian, from the forage age to the agrarian age, and then from the agrarian age to the industrial age. And that really is what the book is about. The book is about why is digital technology so disruptive? Why is it causing such a transition? And then how should we be thinking about this transition into a new age, which in the book I call the knowledge age? Understanding not only the technology as the possibility for efficiency or whatever, but understanding it in its context with a sustainable society is a very important dimension. I think that's absolutely crucial, right? Because if we think about what happened in the transition from the agrarian age to the industrial age, it took us quite a while to find something that works, right? I mean, at the early industrial age, people lived in squalor in the cities. Working conditions were terrible. There was child labor and so forth. It took quite a while. And really, we had sort of a golden age of, at least in the US and several other sort of developed countries post World War II. We're seeing it massive rise again and kind of sort of people being depressed, people taking drugs, even suicide is climbing significantly. And a lot of this is related to this transition and the shift that we're in. And I think one of the key points is that politicians have been treating this shift as if it were some increment on the industrial age. And people are like, yeah, you keep saying that. You keep saying that retraining which you mentioned or something else is going to work. But all I see from where I sit is the elites and the cities are getting wealthier and where I am, it's sort of devastation and opioids. And so I think because we've been unwilling to acknowledge that we need to invent a new age, we've been caught up in incrementalism. And that incrementalism has opened the door for people like Trump. Because Trump sort of says, well, look, what they're telling you is not working. I'm going to take you into the future, the future in this case being actually an imagined past. It's a return to the past. So he doesn't actually have a forward-facing agenda. But this rise of populism that we're seeing in many parts of the world is again the same transition that's happening. And so in the book, I make this point that why are these transitions happening? It's because some fundamental shift in technology. So the forward-shorter agrarian transition was the invention of agriculture. So from hunter-gatherer to systematic agriculture. And that was roughly 10,000 years ago. And as a result, we changed everything. We went from being migratory to being sedentary. We went from very flat tribal societies to extremely hierarchical agrarian societies. We went from basically being promiscuous to being monogamous ish. And we went from having these animistic religions where every animal, every tree had a spirit in it to the theistic religions. And then only a couple of hundred years ago, we had the Enlightenment. And with the Enlightenment, we had all sorts of scientific breakthroughs, chemistry and electricity and mining and so forth. And that again brought us this huge change. It shifted us from living in the countryside to living in the city, from living in large extended family to living in nuclear family and no family. From having lots of commons to basically private property being everywhere. From kind of a great chain of being theology where religion says, look, you're a farmer, and I'm going to tell you how to be the best possible farmer, but you'll never be a noble person because you weren't born as one. We went from that to the products that work ethic. You work harder, you make more money, and wealth is good, and maybe even greed is good. And so we had these two huge transitions. And the sort of insight that I had when I was working down the street in San Francisco was the reason what happens is when you make a big technological leap is you shift the binding constraint.  How much food can you find? Once you invent agriculture, your binding constraint is land, arable land. How much arable land do you have? And once you have industry, it shifts to capital. Who can build machines and railroads and infrastructure? And the reason the book is called The World After Capital is because I basically say, look, we have sufficient capital, and I have a definition of sufficient that we can talk about in a second. But what the scarcity now is, is attention. What is it that we as humans are paying attention to? It's this huge crisis of attention effectively. And that's sort of the central idea of the book. Interesting. Now I've seen some, which you might call smoke signals of concern, like the movie, The Social Dilemma and various about how this is affecting the human brain. Somebody gave me a book this weekend. It was about, what was it called? Something about personal mythology. They said, you used to have the church, the gods, the parables, and everybody thought of those as the myths, kind of the Joseph Campbell catalog. But now there's so much hitting you all the time that in your own psychology, what becomes your myth is almost a personal thing, rather than a collective thing that we all adhere to, like Easter Sunday over Moses or something like that. And I think that breakdown is related to this technological shift also, not just in the fact that we have social media and so forth, which we can come back to in a second, but also because when we went into the industrial age, we made the narrative of purpose. One about your purpose is to find a job, do well in the job, and then also consume and maybe donate a little to the community. And that was held on its purpose for people. But as it's getting harder and harder for many people to find meaningful jobs, jobs that are interesting, jobs that pay a living wage, that narrative has broken down. And we have not substituted any kind of new narrative of purpose. And so, yes, when you have this breakdown of an existing purpose, like the automotive workers when their plants were shut down or coal miners when the mines shut down, when you have that breakdown, when you don't have an alternative narrative, and then you have this infinity of opinions online where you can read anything and everything, that's a perfect storm for a huge crisis of mental health, for a huge crisis of purpose, for a huge crisis of democracy. Experts are now on the out and out. It used to be, professor at NYU or Oxford or University of South Carolina or something, and there was an aura about that. And now people say, experts, oh, they're just bag men for power. People like Richard Edelman, who does a lot of work for the World Economic Forum, has shown that confidence in expertise, confidence in academic leaders or Nobel laureates, are all plummeting. Yeah, the Edelman Trust Survey shows the lowest levels of trust that we've had in a long time. Martin Gouri has a good book about this called The Revolt of the Masses. And in my book, what I attempt to do is to sort of say, there is a narrative that we can provide people with. And there is a new source of purposes, a way of thinking about purpose in an age that's post the industrial age. And I call it the knowledge age, because I think, basically, we need to substitute. We have this, what I call the job loop. And the job loop is, you have a job, you make some money, you spend the money on goods and services that other people produce who also have a job. That loop was very successful for us. But the loop that we need to really be spending time on is this sort of knowledge loop. And the knowledge loop is where you create a piece of knowledge, knowledge, by the way, I use very broadly the books, including art, music, etc. And then somebody else can, you share that, somebody else can basically consume that piece of knowledge and they can then create a new piece of knowledge on the basis of that. And that knowledge loop, of course, has been at work for a long time. But we really need to accelerate it now, because we have these big unsolved problems, like the climate crisis, infectious disease. And so one place to find purpose is in the knowledge loop or in basically supporting things that are non economic. So a lot of the things that I think we've lost sight of are non economic things, you know, taking care of your friends, taking care of your family, taking care of animals, the environment, things that are not economically incentivized. And a big goal of what I write about in the book is how can we sort of shrink the economic sphere, much like we shrunk the agricultural sphere. It's not like when we went from the agrarian age to the industrial age, it's not like agriculture disappeared. It's just that it went from consuming 80 plus percent of human attention to like sub five percent in a developed country today. And I think we need to do the same with the economic sector. We need to go from the sector where everything is based on prices, where everything is explicitly incentivized that now occupies the vast bulk of people's lives. And we need to shrink that down to make room for all these non economic things, because a lot of stuff that we need to work on can't have prices. Right. So I don't know whether you saw it, don't look up. Oh, sure. David Sarota, the co writer with Adam McKay is one of my best friends. Oh, fantastic. We don't have enough people today looking out for big objects from space. Why? Because there's no price mechanism to incentivize that society as a whole has to decide this is an important thing. And there can't be a price for it because these events happen every few million years. There's no market for it. And so in the book, I write that there's lots and lots of things that don't have prices and can't have prices. And so the goal of this transition, in my mind, the goal of the power of digital technology and the way we should be using digital technology is to shrink the economic sector and let the non economic sector grow. And how do you see how do you see the arts in that realm? Is that part of the non economic sector? Oh, absolutely. Absolutely. And I think, you know, with the internet, we have seen a flourishing of the arts in a really marvelous way, right? Because let's say you write a song in the pre-unit world, you kind of had to find a label to put out your song and get it on the radio and so forth. Today, you just put it on your SoundCloud or your website or wherever YouTube and millions of people can hear it. And so I think we have, in fact, blown the door wide open on arts. I think we have a huge explosion of beautiful, new graphical art being generated. And I do think that's something we're already seeing. We just need to create a society where more people find that's how all I need to do and I can live. We're still attached to the idea. No, no, no, no. If you want to live, you have to have a job. It's the only way you get to live. You have to have a job. You have to pay for yourself. Otherwise, you don't get to live. But we have all this automation and we can make more automation. So why should we be attached to this idea that everyone needs to have a job? And you can connect to large scales of people, what I might call audience, because of this technology. So instead of playing in a bar for 12 people sitting at the counter, maybe 2,000 or more can be watching. And it doesn't preclude you from playing in the bar. That's right. I mean, these are. You can do both simultaneously. Yes. Exactly. Exactly. There's a danger here, which is in the middle of a transition, in the disruption when the fear is rampant, a counter reaction could, which might call, stop, stomp out the potential and turn us away from something that could ultimately be a much better life. Oh, absolutely. But I think the step one is politicians, leaders of all parts of society need to first accept that we are in the middle of a transition that is as profound as these prior transitions. And so it means we have to change everything. That means we have to change how we think about the education system, how the healthcare system works. In the book, I talk about what I call three freedoms. I talk about economic freedom, informational freedom, and psychological freedom. So economic freedom is some form of universal basic income. Just give people enough money. So if you don't want to work, you don't have to work. If you want to just do art all day, play the guitar, fine, do only fine. Informational freedom is about who controls computation. Is it controlled by a few large corporations in the government? Or is computation accessible to anybody and everybody? And psychological freedom is about how do we let go of all these things that culture has now told us for several hundreds of years of where your worth comes from, where your value comes from? And how do we live in a world where I can access anybody else's information all the time? How do I create the psychological freedom that I don't constantly react by saying, oh, this person is awful, and this is terrible, and I'm in this constant state of agitation. So those are the three freedoms I talk about in the book. And to me, they complement each other, and they are necessary to handle this transition well.  When we went from the hunter-gatherer age to the agrarian age, the hunter-gatherer societies basically wiped out, the agrarian societies basically wiped out the hunter-gatherer society. And then how did we get from the agrarian age to the industrial age?  I mean, we talked previously about Thomas Piketty earlier and capital in the 21st century, where he documents how the old power which was land-based capital wasn't really removed until the end of World War II when industrial capital became the new power. A lot of people believe that the hunter-gatherer age was this incredibly violent age that people didn't live very well. But actually, what we know is that hunter-gatherers worked only a few hours a day and lived pretty happy lives. And things really went sideways on us when we went to the agrarian societies because we were bad at agriculture at first, so we didn't produce enough upload, so people starved. We lived close to animals, so we introduced all these diseases from the animals. And so actually, that transition was a very bad transition not just for the hunter-gatherers whom we wiped out for the most part, but it was also bad transition for the agrarians. And some people interpret the story of the fall from Eden as going from the hunter-gatherer life to now having to till the soil and live by the sweat of your work. That's one possible interpretation. My personal preferred interpretation is that once we started creating knowledge, knowledge started creating new problems for us. So we created the knowledge of agriculture, and that created problems like infectious diseases for us and starvation, and so we needed to figure out how to store things, we needed to figure out how to refrigerate things. And then more recently, we invented fossil fuels and how to burn them to make power and electricity and transportation, and that's created the climate crisis. So I tend to think of the fruit of knowledge and eating from the forbidden tree of the fruit of knowledge as getting on this treadmill off. We invent something, and the thing that we've invented has these consequences that we now need to live with and deal with. So a big part of the thinking in the book is how do we free up more human attention, get it out of that job loop, and get it into the knowledge loop so we can work on these big problems, and also big opportunities, frankly. It's not just about problems, it's also opportunities. We've made huge breakthroughs in decoding the genome and understanding how cells work. We're making huge material science breakthroughs. We're making breakthroughs in building rockets. So there's also all this upside. I agree with you, though, that if there isn't a narrative that describes a future that makes sense, not just technological sense, but also societal sense, if we leave this vacuum, then people like Trump will come in with a very crude narrative, and it will resonate with people because we haven't given them an alternative. And that really, you asked me at the beginning why I read the book, that's really the thrust of the book is to start to create a narrative that people can be excited about. There's another dimension to this that economists often worry about. They had this old, what I'll call metaphor, called the Treaty of West Failure, the nation-state, and they were installing a government that governed those things. In the world of globalism, with the technology, nanosecond transfer of money or other things, many people are scared that with those efficiencies, powerful can escape governance and, how would I say, people are very much more vulnerable and at risk. And it felt to me like in the beginning of globalization, say when I was in college and people liked Dick Cave's or people, I can remember the book Global Reach and various people at Harvard, MIT were talking about, there was so much enthusiasm for globalization and now it almost feels like, as you say, the Trumpians have picked up and it's all at house. You know, there's definitely a backlash against it and I think one can easily understand why. I mean, we've taken a lot of manufacturing and shifted it from the U.S. to other places and people have lost jobs. We talked about this earlier and we had told people your job, that's kind of your purpose. And so absolutely it's really easy to understand why people are discontent with globalization. However, I would say with the technological progress we're making, that's no longer the sort of question, right, because Nike today can make a shoe without a human touching it from beginning to end. So it doesn't matter what the price of labor is.  And so while I think there are good arguments to be made why globalization was maybe not handled always in the smartest of ways, I think that's sort of undoing that and thinking that when you reshore manufacturing, you're going to create a lot of manufacturing jobs, I think it's equally wrong. So if we reshore manufacturing, it's going to get reshored in a very, very, very low labor. I was going to say, you just put the robots on a different continent and assemble that way. We've gone through a pandemic, a tremendous distress and crisis. I saw some interesting upsides. I have two little daughters. And so my daughters at the start of the pandemic were in second and fifth grade. My second grader became what you might call virtuous, a virtuoso in the realm of using a laptop computer and transferring things, stuff I didn't learn how to do until I went to college. So I think at some level, what you might call the silver lining of the stress of homeschooling and so forth, allowed some of these children to get on the pathway to that world that you're envisioning. So we homeschooled our children all the way through high school. We now have two graduating college seniors wanted Wesleyan and wanted UPenn and we have a sophomore at Cornell. So we embraced homeschooling long before it became popular. And in part because the education system we have today is strictly an industrial system. We created and scaled it. We treat children by manufacturing date. Sir Ken Robinson talks about this in great detail. And so because I believe we're past industrial age, that's the whole point of the book, I wasn't going to suggest that our kids go through an industrial age system. And so we had this beautiful setup. They spend a couple hours a day with tutors and the rest of the day they could kind of do whatever they felt like. And sometimes that was making a movie, sometimes that was cooking, sometimes that was learning how to make fashion. There's a very sort of wide variety of interests. But the interests are what propelled the curiosity. So much of the school system is about stamping out curiosity. And to the extent that we want this knowledge loop to work, we want more rather than less curiosity. My older of those two young daughters who's now almost 13 in seventh grade said, you know dad, being in remote school for a year, I'm not sure how much I think going to school is a good thing anymore. And she started looking online and found a Stanford online high school and said, I may want to apply to that. I said, well, what are you going to do with your time? She said, paint, draw and play the piano. And maybe you'll let me borrow your guitar. So she was right in that space. So I do think the pandemic accelerated certain things that were already happening. So there was homeschooling was growing and it's grown much more as a result of some micro schools, just alternatives to the existing school system. Remote work was already a trend has grown tremendously in our portfolio. We have 125 active portfolio companies, a third are roughly are entirely remote now. They don't have an office anymore. So that's a trend that got accelerated. But I also think coming back to something you said earlier, the crisis also showed how fragmented society is today. I mean, at every step along the way, is there a virus? Is there not a virus? Did it come from China from a lab? Does it matter? Should we mask? Should we not mask? I mean, every single thing became super polarized. Everything became a reason for people to yell at each other as opposed to try and work with each other. And that is the result of this sort of social media landscape that we find ourselves in, which we basically haven't, you know, we haven't learned how to be good citizens and nobody's taught us how to be good citizens in that world of this sort of multi just anybody gets to say whatever they want at any time. Now, I think that's a good world ultimately. I just think we need to figure out how to live in it. And that's going to take us some time. And again, that requires some level of creation. You said it earlier, you need to have some level of creation, some level of values that you all subscribe to, something that you sort of say that all makes us, you know, want to sort of be together first, and then we can disagree about certain things. That's fine. But we need this base layer where we sort of say here's some level of solidarity. I love the quote that you have coming in, right, which talks about that it's not just for ourselves, not just for our family, but for all of us. And so that's really a big part of the sort of book is to sort of say, how can we create this narrative? How can we in a way bring back some form of humanism, some form of sort of talking about, you know, human solidarity amongst ourselves as the first and foremost thing before we get into whatever our differences on any policy on any particular issue might be. But right now we don't have that because it used to be provided by religion, not being provided by religion anymore. Purpose used to be provided by work, for many people not being provided by work anymore. So we have these things that have broken down. The Edelman Service Show Trust has broken down massively. So we, we badly, badly need to reinvest in this base layer of what is it that when we get together makes us each other as humans as wanting to work with each other, not against each other. Healthcare with the pandemic and all the technology, are you seeing an evolution of healthcare and healthcare systems in a way that's hopeful? Yeah, I mean, we've made a number of investments in digital health. And I think as a first step, just giving people more and better access to information is really, really important. So for instance, we're investors in a company called Clue that makes an app for women where women can track the cycle and can really sort of empower women to understand their reproductive situation. That's easily accessible. Anybody with a smartphone can just download that app, right? You don't need to go to a doctor, you don't need a prescription, you just go get the app. We've made an investment in a company called NURX that if you want birth control, for example, you used to have to go to a doctor and get a prescription in many states. With NURX, you just do it over text, text back and forth with the doctor, get a birth control prescription. So I do think broadening access is something that's happening through digital technology. But we still are very much in this problem where we have created a setup in healthcare where so much is about making profits off drugs, making profits for healthcare systems. And I think when you're trying to provide this kind of service, you need structures that allow not just profit optimization, but also saying we need to serve the community, whether that's by mandate or because we simply embrace that as who we are. It doesn't matter how it comes about, but it needs to be there. And I think we've lost sight of that. I mean, I think a lot of that descent into sort of the maniacal focus on profit starts around the Milton Friedman, you know, a company's sole responsibility is to burn the profit up in the New York Times. And so we need to come back from that. And again, the basic idea here is if we create more room for non-economic activity, so non-economic activity includes a lot of basic research, and a lot of health is actually still very poorly understood. Like try to read up on nutrition and see how incredibly poorly nutrition is understood. By the way, you earlier said we have this lack of trust into academics. Well, one reason we have this lack of trust in academics is because, for example, if you look at nutrition, the whole thing about carbohydrates versus fats, that came out of a Harvard study that was paid for by the carbohydrate industry. And so it's no wonder why people all don't trust things, because when you sort of peel back the cover, all of a sudden, like, wait, we've been told this thing is bad when in fact this other thing is bad, largely because of a study done by some prestigious academics who were paid off by the sugar industry. Yeah. There's a book, Amanda Collin Campbell, I believe it had been at Cleveland Clinic and Cornell called The China Study. And it was about the transformation of people from agriculture to the coastline industries and how their diet changed in the onset of things like Alzheimer's disease and heart disease and so forth. And when Campbell created that book, he came back and he was invited to be on boards of many health charities. He took so much heat from industry people who he then, I think a second or third edition of the book, wrote a final chapter about the political economy of inhabiting foundations to stop them from recommending healthy things to preserve the profits. And it was really, really hard reading. I mean, my father was a physician and I was like, wow, I can't believe how tense this has become. And then I look at my friends, Democratic Party friends, Republican Party friends, concerned about fiscal discipline. And I showed them World Health Organization, United States ranking 38th, OECD numbers on the cost of healthcare per capita. We are double the OECD average. And I believe all but one OECD country ranks above us in performance.  But why aren't we creating, with all of our technological wizardry and so forth and innovativeness and the way we talk about our society's vitality, why aren't we producing twice as good for half the price instead of 38th best for twice the price? And one of the arguments I make is because we're caught up in this job loop thinking and because we're caught up in this thinking of the way to do things is through market prices. And I'm a VC. I love markets. I love valuable tool. But there are lots of things that they can't solve. And we have gotten to this point of sort of market maximalism where we're like, oh, well, the way to solve this is by privatizing it. And the way to solve this is, in fact, at the same time, we've allowed many markets to become highly concentrated. I have a chapter on why concentration is being driven further by digital technology. Digital technology drives concentration massively because of basically what happens when you have data and then you have a little more data and then you have a little more data and you see this in Google and Facebook. But you will also see the manufacturing. You will also see the CPG. And you've seen it. You've seen the financial services. So we're sort of this strange combination where we have this market maximalism where we believe we can solve everything from markets. At the same time, we're very poorly functioning markets because they are highly concentrated with lots of market power. And then we wonder why we have bad outcomes. So in my mind, we just need to really kind of hit the reset button in a big way and make this big transition where we let more and more people opt out of that system. Once we let people opt out of that system, interesting things will happen. Like as long as we keep people trapped in this job loop, if you're working for a pharmaceutical company, if that's how you make your living and that's how you pay for your house, for your children's education and so forth, of course, you're going to push this drug, even if you know that it's the wrong thing, even if you know that it makes people addicted. It's hard to get off that thing once you're inside of it. I once attended a lecture at the Union Theological Seminary. And the individual, the speaker that night, gave a talk about why we have deified markets. And he said, because looking at it, he's a theologian. At face value, it's a tool. It's an instrument as a means to our end. But he talked about how at the end of the feudal period, he was talking about Scotland and Adam Smith going from the theory of moral sentiments to wealth of nations. And he said, they realized that using moral and ethical discourse as a civil servant made you look like you were affiliated with the corrupt feudal lords because the church had co-opted. So you went to this antiseptic scientific value-free discourse, which carried on. And then when the communist nations, Russia and China, adopted this central planning on scientific basis, a lot of people didn't want to use that antiseptic language anymore. And so they deified the market. The market became the thing that solved all our problems. And I think it's fair to say, and I say it in the book, I think it's fair to say that markets actually worked incredibly well for the creation of capital. So the capital in the title of the book is not financial capital, it's physical capital. It's the thing, you know, we don't drive around in gold bars, you need cars, you don't close yourself in dollar bills, you need clothing. So markets actually were incredibly good at giving us a lot of capital. It's the question now, what do we point all those resources at? And this is the moment where we need to recognize that there are these vast swaths of problems and opportunities that cannot be addressed by the market system. In effect, one way of saying, and I say it in the book, is that it's because markets have been so successful that the problems that are kind of left over are the problems that markets, and especially markets of the variety that we have today, cannot and will not solve. And so this goes back to the same idea that when we went from the agrarian age to the industrial age, we shrunk the agricultural sector relative to human activity. And now we need to do the same with the economic sector, with the one where everything is explicitly incentivized through an income, through profit, through stock options. We need to shrink that relative to human activity and really let the human activity that's based solely on, I'm doing this because I want to do it because I want to help my friend because I want to spend time with my daughter and my parents because I want to take care of animals, whatever the case may be, to really create room for that. And we have the technology because of digital technology. Because of automation, we have the ability to do this. But we have to create a society where this becomes possible and desirable for people, where you don't look at somebody and say, well, that person's a bum, they just play the guitar all day, they don't have a job, where you go, oh, well, it's beautiful that they can play the guitar. And now I kind of like that song. That mindset shift is dramatic. And it requires us to change everything exactly the same way we changed everything in those two big priorities. And we just don't seem to have the will or the desire to embrace this. Instead, we're just clawing on as hard as we can to the industrial age, which is no longer working.


Always remember, folks, whatever you think about, you bring about whatever. You focus on growth, super events, having a great day, safe day. Let's make it a great night, folks. To master love, you have to practice love. The art of relationship is a whole mastery, and the only way to reach mastery is with practice. To master a relationship is, therefore, about taking action, not about attaining knowledge. Knock it off! Let's take a look at it out here. We have the Dow Industries right now trading up $5.37, NASDAQ is up $3.44, S&P's up $7.76, Gold. Gold contract down $5.20, starting at $17.89 notes. We have Silver up $0.22, $0.22, $0.50 an ounce, Light Sweet Crew. Where are you? Light Sweet Crew? Yeah, caught a bit. Up $2.76 trading, $7.137, notes and bonds. The 10-year note down $7.16 trading, $1.30-20, the 30-year offer full point at $1.60-30 and $Kingdala. $Kingdala right now down $68, TICS trading out at $96.483, the euro is at $1.12-82, the yen is at $1.14-09, and the British pound is at $1.32-63. Our phone number is<PHONE_NUMBER>, give us a call, folks. I know what's going on in your world, and the world of the S&Ps, let's take a look at them. What do you have? This is going to be a nice setup, man. We at a trader's market here, folks, and so what we had out here is this, yesterday rejected lower price, had light of volume as you went against the swing, okay? So what do you have here? We had the swing that's laying out here at $137 million, $132 million, and $127 million. So we committed that yesterday with $107, the rejected lower price. Now, what do we do today? You got a nice bounce going, okay? Look at the contraction of volume, monster, man. You're over 49 million. So my take is that we are going to go right back top side again. We'll see whether we test the lows of the highs. The spy, I'm figuring, you know, we're dealing with about 467. Right now, you're 462. The high is 473. I don't think we'll hit the high. Most times when this happens, folks, what you get is this.  You have another contraction of volume. Let's see, Tuesday, Wednesday, this is setting up really nice, man. So let's pitch. After a big day like today, okay, you can pitch more than likely what will end up happening is that you might go a little sideways tomorrow, they'll jam it. So tomorrow is Wednesday. Yeah, perfect. Thursday you jam it higher. We go away for the Christmas holiday. We come back next week, go sideways, tries to mess around with the top here, and then January, whatever day we come back to work. I suspect that we're going to have that had brought us, we're at the top of the range and I suspect coming January, we're going to go right back downtown. We go take a look at the NDX100, what do we have with the NDX100? You have the exact same setup inside the NDX. The NDX right now, we're at 388. Bottom line is that this can get up to 400. That's how this is shaken out. Thursday is a full day. Yeah, because the markets are closed Friday. This week, next week, we don't get anything. Gold, gold contract out here. We take a look at the gold contract. Gold contract traded down to 1785, we're at 1789 right now. Bottom line, we'll see how this baby shakes out. It might take us, we're going a lot higher, but it's a struggle. There's no two ways about it, man. This thing's just been messing around and this has no doubt to the US dollar because the dollar folks is hanging at highs and looks that this high can be basically blown away. Right now, you're at 96, 478, and we've been up here for three weeks thus far, three trading weeks. So it's pretty wild, man, and we'll see if in fact it wants to break out or break down. Let's go take a look at some of the higher volume equities out here. Okay, so you got Apple up 290, Convales up 169, Micron, big number up, that would come up with numbers. They come up, they're up 812, you have Nvidia up 12 bucks, Uber Technologies up 2, Tesla's up 34, Microsoft's up 7. Well, what's intriguing is that, here, watch this, AARK, I had asked Dave Mazder about this yesterday and he didn't answer the question because this was a competitor, I guess. Well, anyway, Cathy Wood, bottom line, they just came out with a new statement. I'm sure that her compliance department said, hey, man, you can't tell people that you're going to compound 40% a year to try to collect money. So the bottom line is that, let's see, that's the one in deep value, isn't it? No, this is the one from yesterday. Right before I get on the air, I'm going to find this, oh, here it is, yeah. She just came out with, well, actually 11.30 this morning. She came out with a new statement and the new statement is revising the statement that she thinks that AARK was going to go up 40% compounded per year for five years. So let's see, please note that AARK revised the statement from its original version to clarify any misconception in the marketplace. The footnote says, adding that the statement is based on AARK's research, current views, assumptions, and is not a guarantee of future results. Forecasts are inherently limited and cannot be relied upon. And even after the clarification, Wood still predicts 30% to 40% annual rate of return during the next five years for AARK strategies. Now, when you go to the bottom of this, right, this is pretty wild, man. OK, so she has nine funds, six are actively managed, three to track indices, and there's only one fund this year, which is the 3D printing ETF that's currently in the post-impositing results. So that's pretty intense, folks, OK? Because of the fact that, of course, you know, the market's up, and so folks that are definitely investing in that are going to be saying, OK, what is the problem here, man, if the market's up and we don't have a way down? And it has it, let's put it this way, on her main fund, that's really what I was really looking at, the AARK, she still has net positive cash coming in it, you know? And that's crucial, and so she can buy more of the same stocks. Dow, Dow Industries right now trading up $5.56, you get the magic up $3.35, S&P's up $7.6, stay right there, folks, we'll come right back.


At 35 years old, Daniel Naboa is Ecuador's youngest elected president, and an heir to his father's banana business. He has promised to rebuild the South American country, which is struggling with a weak economy and rising crime.