The best thing about CISD for me, with the skills that you could learn, the tangible skills that I've talked to many people, they've used in their internships or their outside jobs, like learning how to write a speech or how to do a radio interview, how to negotiate, how to represent themselves and be confident. CISD is, I think it's very honest and handed and we realize that we're very lucky, but there is a world outside the classroom and I think the point of us going through this rigorous year is to be prepared for that. Because it's targeted at graduate students only, there is a sort of closer link to the real world. It's not just kind of come and do a master's and see there is a bit more geared towards helping people connect to organizations that they might want to work with. I'm working as a project manager for a company called DAI, which does contract work for DFID, the World Bank and the European Union and USAID. It's a fantastic job. There's really interesting projects that I work on and it's been able to really take the skills that I learnt at university and bring them into my job, so there's not that many people who get to do that sometimes. As a banker, it's allowed me to actually learn a lot more about the politics behind finance and that was very useful during the Euro crisis. It was also very useful in my job, which is emerging markets. We deal with that all the time. Today I work as a program officer with the UN Joint Programme on HIV and AIDS in Zimbabwe. It's also known as UN AIDS. I love my position and I think I can safely say that I wouldn't have applied for the UN had I not been confident enough in my knowledge base and the skill sets and the practical skills that I gained during my time at CISD. So as a unique university within London, it's fun, it's diverse, it's colourful, it's radical and there's lots of things there. And CISD within that, as I said, it's a bit more geared towards a professional sector. So you kind of get both the slightly more corporate development side but then also all the brilliant, wonderful things about SOAS that make it a really progressive and thoughtful university where anything kind of goes. So I like that combination because I don't think you want too much of one or the other.


So, good afternoon everybody and particular greetings to Dear Kraemer remotely for today. I would like to present a talk on classical gravity at high precision. And you see it, this is work together with different people. With Andreas Meyer, with Peter Marquardt from Daisy and with Gerhard Schaefer from Jena. Now, why I'm talking on gravity, okay, this is certainly a recent work of mine. But there's also a connection to Dirk, and he has published several papers on this field. And one is a remark on quantum gravity, I remember, 2011. I think we should go back to the other. I want to hear this. I'm sorry. I think I think there was just a mistake that somebody had their mic on at the wrong time. Okay, not worry. Okay, good. I will continue. And then there was a very interesting development that it was the paper not so non renormalizable gravity. I had the chance to listen to several lectures by Dirk at a gathering at the clay Institute during summer 2008. And that is definitely an interesting topic in getting say a new avenue towards this old problem. And that is the context of gravity. Einstein gravity can be renormalized. Now, Dirk is, of course, regularly contributing to basic conferences and that's already over decades. Let me just mention loops and legs and here there is a conference photograph of a conference special conference and QCD in Berlin 2009. And you see him here in the, in the Gaffering and this is an high valued conference being you see Nobel laureates actually two of them the third was still in the airplane. You see the CERN director general and then now the new science director of CERN from January so this is administratively and scientifically quite a lot of people came sometime to Berlin and of course notably Dirk. And you see Francis Brown here in 2008 this 2009 back. Dirk did something very important in Berlin, namely creating the colleague for Mathematica and Physique, the KMPB, and this has been initiated by him and this is an important platform for scientific exchange and we had quite some conferences during the years, and we we met at Boston, Linz, and during several workshops at Lisuzion to also build what he organized, and often after that, topical review books were created to cover the achievements made. So let me say we are very happy, Dirk, that we have you at Berlin and we hope this will be the case for a longer time and that this is very important for the scientific scene in Berlin. So let me say once again happy birthday and of course, many happy returns. Now let me talk now about the topic in closer terms. Let me move this here. And the motion of two gravitating masses. So what one has for this relatively simple motion is a so called conservative part and during the rotation, the masses of the masses each around the other. This is also a rotation part because gravitational waves are emitted. So we are going to consider the case of relatively low velocities. This is also the case for like all inspiring that their velocities are small against the velocity of light. The form of the orbit, of course, becomes more and more complicated when we go to higher and higher orders. And the lowest order is Newtonian level the usual elliptic motion which you learn at high school. And then it starts already at one PN the movement of the perihelion this which was first observed by Mercury in the case of Mercury. And we go several orders and the state of the art is now the fifth post Newtonian orders for first results already on the six post Newtonian order. Certainly, there are some rigorous results, namely the Schwarzschild solution. This is basically the case when the test body surrounds a very heavy mass that is known to all orders, but also there is in the next term. This is the so-called order new term that a reduced mass is considered to be in the next order for the two particles. And there is a formalism the self force formalism. And that has calculated these corrections to the 21st and a half post Newtonian order. We will take, of course, a profit of these two aspects a little bit later. And I have to say that we will not consider radiation but the radiation free case for the moment and of course one can also consider radiation but this is not the topic of this talk. And we will study in this way the inspiring face so the face when the two massive objects that are not yet coalescing but far enough away of each other and rotate around that this is the scope of what I've under considered. And the whole dynamics is important, of course for the description of the gravitational wave signals because these parts are just a part of that and they can be measured. And the goal is at the moment to derive the Hamiltonian dynamics. It is fifth post Newtonian order. Now I show you here some pictures of the LIGO Virgo data. And most of them show this gravitational wave signals you see for the case of Blackwell merges and tear down. We have also a picture on how it looks in these detectors. And two neutron stars would, would merge. The process is as follows you see first of all in starting oscillation here. This is the inspiring face then you come to the merger when these heavy objects become pretty close. And then unite into one object. This is a so called ring down and this is this part of the signal. So this is not what I'm going to describe at the end of the talk but this is the classical process, how it would be seen in the detectors. There are different ways to calculate things in in perturbative gravity. There is the post Newtonian expansion. So you have here a diagram measuring are in unit in certain units as a dimensionless quantity and the mass ratio of these two masses. So if you go to the one, then this is of course the equal mass case, and then you can go to extreme masses. This is what you do here. And here, this is the radius measured in the Newton constant times, the master can can can measures So the post Newtonian approach. This is what I'm talking about. Then by effective one body methods I will talk to talk about shortly, you can make a link towards numerical relativity. This is send a non perturbative solution. And then if you go to extreme, extremely small masses say towards the test body. And with respect to an heavy mass, you can do the cell force formalism and also get results. So but we will do the post Newtonian expansion in the following. Right after gravity was found. And we by Einstein, and partly also by Hilbert and Lawrence and trust in 1917 calculated the first post Newtonian correction. And that was then also repeated some 20 years later by Einstein infield and Hoffman this is famous result. And then the, around the end of the 60s, Chandra Secker and others have made the second, second post Newtonian correction and then there were of course also these radiation terms here. And then we had then the third post Newtonian was fully understood around 2000 and 2014 in the years after this was then the time and during which the first post Newtonian level has been fully understood. Part which is completely finished. And not only for the unpolarized case but also the spin effects and radiation and many more very particular things. So we will do non relativistic effective field theory this has been in gravity initiated by Goldberg Rothstein and we will follow work by Cole and small can a little bit later. And I will guide you from path integrals to generate Feynman diagrams of course in that case to the post Newtonian Hamiltonians and observables by methods of quantum from quantum field theory. It's not necessary to perform these calculations with these methods. It's only one way and it's not been the first way. Which has been used to will see this on a later slide. You see, most of these works have been done totally differently and achieved much earlier than this effective field theory methods and it's even now that effective field theory methods are a little bit behind of what can be achieved but it's it's just one method which is helpful in arriving say deriving these results and one has to see how efficient this is in the future. Now, the do go a little bit more into technical details. We consider point like objects and will not consider spin and finite size effects in the following. Then of course we have to work in some gauge. So this is here the harmonic gauge in the following. We have a singularity problems. Therefore, we have to choose as in quantum field theory, the dimensional regularization. We do this in in three months to epsilon dimensions and then the action has three contributions. The Einstein Hilbert action you see here which is Kayla, then a cage fixing term which is tied up to the Christopher symbol. And we see the the particle term. This is the the kinetic term of the black hole with the two masses here. This is the third term of the action. So why can quantum field theory methods be of help here and that is understandable of course any dynamical physical theory can be traced back to Lagrange formalism and can be derived from the first principle of the least action this is where all the physics comes from. And in the near to the non relativistic limit Einstein gravity possesses an expansion the Newton's constant so we can perform an effective field theory. And we will do this using the path integral because we need a good tool to generate all the the Feynman rules for the individual in the diagrams. And that's the way we go. So this will lead to an associated effective field theory representation, which is not necessarily build on flat space gravitons. But we will describe the the gravitation by effective fields and more and more complicated vertices which I will show you a little bit later. And so order by order new interaction vertices as known for effective fields in general will potentially at least appear. So this approach is systematic and is perturbative and will still represent full Einstein gravity. The key issue is to reduce all this enormous amount of terms we will need to calculate to master integrals which is of course not so many. And then one has to calculate the master integrals and finally is getting to the result. So the current level are five loop integrals and they partly range into from the physics side, the six post Newtonian level. This effective field theory was of course earlier namely as back in 1985, Caswell and LaPage already used in QCD and so you see this action will be transmitted into an effective action. And this is done in representing the gravitons in terms of so-called potential gravitons where the their component K zero is just proportional to the ratio of the velocity over our and the spatial component. So we have like one over R and radiation gravitons have that is this behavior. And so is quanta are gathered together with what we call potential terms and then we have in the tail terms, we have this radiation gravitons in the Feynman rules, but I will detail this a little bit later. The expansion of the action has to take place. And for that sake, we have to go to the metric and the metric tensor and this was a parameterization by cold and small can some 10 years ago, you have in total 10 fields. This is a scalar field five, three vector fields and six tensor fields sigma ij, which couple in this way with the velocity to the masses, which are in the game. Now, the first thing what we want to do is to calculate the potential. So we write down the potential interaction. This is minus IV here between the two big masses and then this decomposes of course into exchange of these different effective fields here. And then one has to observe what is the behavior of the temporal and the spatial modes which I said already before, and one has to expand to the enormous step, whatever you have to go at the corresponding propagators. Now we want to calculate a potential. So this is not just a scattering process but is a logarithm of a scattering process and that is that that is done in this way. And this is certainly so that we generate much to many Feynman diagrams, which will not contribute on the classical level. There is no pure graviton loops are allowed because they would be on the quantum level, so they would appear with the Planck's constant, then there should not be single source corrections. The self energies here would dress the black holes and they can be absorbed, of course, and they will not change these sources very much actually in an eclipsable manner. So this is also not considered and we will not consider source reducible diagrams. So we have to investigate things which lead usually in time ordering to certain combinatorial factors. Now, all together, we have for instance these two diagrams and then this can be covered to that diagram and if you put everything together it's actually the square of this single exchange here. So those things can be nicely algorithmized in computer programs and that's the usual way you extract potentials from scattering cross sections and amplitudes and this is the way you have to do that. This is the final thing and then you see you get then, if you take go to the potential you get then this is as the first term and then the whole the whole line of course up is just representing the potential disc graph. Now, I said already that most of the time it was so that the older times actually the results were known derived by totally different techniques and you see this here that only in 2004 the one PN was done this way. Then 2008 we had two PN and then three PN was 2011 11 years later than the the original, at least more than 11 years maybe. And then there were the calculation of the static contribution to four PN. There was performed in this paper and there was a little thing to be corrected by Damor and Jaroszki and it took until 2019 until everything about four PN was understood and in 2014 already the results was a better front better front techniques. Now what will be new and this is this came within two days. Actually the submission to the archive is five hours different only and by two different approaches, one by Fofa Mastrolias, Durrani, Sturman, Torus, Bobadilla and one by our group, and we had this calculation up in Itzio as I described and these the other authors. We had a combinatorial argument which is possible at odd PN so it was possible at five PN and we didn't know about this but this was very nice and the results have fully agreed. But the static contribution is of course not everything this is only the beginning of something and still I want to want to dwell on it a little bit because one can explain things very nicely in this context. More generally, when we want to go to five PN, we have to generate by a generator of Feynman diagrams, the diagrams and if you do that, you will get an enormous amount nearly one million Feynman diagrams. Then there is all kind of Lorentz algebra you have to do and or maybe Galilean algebra if you want because it's not relativistic. This is done by form. And then one has to reduce the master integral so many more things are done by form but not only these the Lorentz algebra, but the reduction to master integrals is done by a reduction program which is called Crusher by Mark Watt and Seidel. And then we have to throw away before a lot of diagrams because they don't contribute and that's about 200,000 diagrams. And then you see a handful of master integrals have to be known and they were known already in the static process and of course calculated several times. And one can then solve the problem. This is this way, at least what the potential terms are concerned. Now, let me show you a little bit more details. The what the diagrams are you see these five loop diagrams. This is the the the scalar interaction than you have. We have tensor interactions here. And actually, there is no vector interactions in the static part. They only will contribute in when we have velocity corrections. So the word on the Feynman rules. So we have here the different propagators the tensor the scalar and then you have all kind of vertices.  And then it becomes gradually more complicated for the four point verdicts and then you have three point vertices and so on. And then if you go higher and higher you get more and more. And then the end only the computer knows about the consistent set of Feynman rules. And of course, this is foolproof setup. So you you will not have a horse over there. This is all directly computed. Now the next thing is you you get apologies and we have of course kind of self energies to calculate. This is the master. There's a master's propagators which we we have propagators. You see here these topologies and you have to think of all these fields. And then you do the reduction to master in the cross. And the IPP reduction will then lead to only a handful of tracks where you master integrals you do the wrong series and then you get the poles and you get the constant terms and so on. The poles you get is only a first order to this order in the post Newtonian expansion and you get it in the potential terms and what we will discuss a little bit later also in the tail terms. And so you have some easier parts where the calculation is done by inserting things and this is basically you have to know the beta function for that and then there is a more complicated thing. But this is also known and the standard technologies allow to calculate those diagrams for instance. So in a nutshell, I collect these things are often beta function type solutions here several products of beta functions and then you have one which is not not so easy but you see you can also calculate this and you can if it would be needed you can go even higher. But at the moment it's not needed because all the poles are only one over epsilon so you have to go to this term. And that is it you see logarithm of two here, but this is intermediate in the moment and then we will see what is happening for the static potential so you start out with Newton. Then you get the static potential by the first post Newtonian thing. And if you go to in the in the harmonic age of a particular gauge to five pn you get this and you don't see any log two you don't see any CETA here and this. But we will see the pi squared or CETA to a little bit later when it comes to the velocity corrections. Now, let me explain you the general case a little bit. This is of course tied up with extremely long formulae, and it would be difficult to swallow the details here so but I will list for the beginning first of all the principle steps of the calculation. So the goal is at the end and Hamiltonian of course this is not what we start with, we start with the action and therefore we get first a Lagrangian, and then one has to perform a Legendre transformation to the Hamiltonian before one is able to do that one has to remove accelerations, the time derivatives of accelerations of higher order and so on. There are particular methods where one has to be extremely careful with to build this down but this is known in the literature how to do that in the early literature. And what I was mainly explaining here is the so called potential term, but there is also in the, this is a near zone description of the demotion, and there is a far starting from 4 pn also a far zone description. And so a subset of these terms are the so called at the end of the day, the non local contributions. And there is also some local contributions in the tail terms, but most of the local contributions come from the potential term. So, we will use both pictures and it's actually needed to use them for technical, at least if you're well I mean there's lots of reasons why one should use both pictures, but one will turn out to be a technical point so we will use for that sake, the separation in both pictures. Now what it turns out is both the potential corrections and the tail corrections are singular and so they have poles in one over epsilon. And the ones of course to remove these things and see whether there is a singularity free situation. But of course this is not uncommon in quantum field theory we have much, much higher singularities in the Lagrangian and the Hamiltonians and here. And the, we calculate the potential terms in d dimensions as a reason why we have to call to calculate, we at least have to calculate both of these quantities in d dimensions. So then we want to see what happens to the singularities and we will cover. First of all, we have a look on to the singular and logarithmic contributions to the tail term and add them to the potential term and then see what what is happening. And then actually the singularities will not go away and this has to do with the harmonic gauge we use that we have to apply another canonical transformation and then we will have a Hamiltonian which is Paul free. And then we can also arrange the, the canonical transformation for the logarithmic term such that we meet the non-logal terms which have been nicely worked out before us by Bini Damour and Gerallico at 5 pn. And that's the, that's the way we go to have a comparison. And then calculating age, the contribution to age tail we use because of this effective field theory method, the method of expansion by region, which has been introduced by Benekir and Smirnov, and later described by Janssen. We have shown that 5 pn there are no overlap terms, and one can actually organize this in a very, very nice manner. And we, we will get as a result, as I said already, the non-logal Hamiltonian, the canonical transformation makes finally the Hamiltonian Paul free, which is sent in slightly different coordinates, but the harmonic coordinates. And the formulae are still very large, so I won't show them here, but continue with the discussion, at least for the couple of minutes. And so what we, what we could do is that we, we wanted to look on the potential contributions first. And then we notice that from the tail terms we get in this, this mass ratio, a, at the first order and the second order contributions, so we, if you want to make a discussion without the tail terms we have to restrict the discussion to new to the zero and the powers new to the three up to new to the five. And indeed, we could show between the result derived by Damouret, the HEOB, physical equivalence by a canonical transformation. And we should notice that not even the simplest case, namely the Schwarzschild contribution is easily seen in these Hamiltonians, or in the going back in the in the Feynman diagrams. So they are basically everywhere and only you see it only in the result. And that gives you, first of all, a very good check to the to the whole calculation. And one is, of course, all this happy if all these checks work out and there's different other checks you can perform also. Now, the, the, there's also another being the methods been there. There was a discussion on the results by burn on the third post Minkowski and the approximation which is slightly different but post Newtonian and you can go to six pn we did this and here. So this is quite a part of the all the terms to six pn, of course, not the hardest part of the beginning. And this has been also confirmed by be neither more and Geralico. And that means that, of course, five pn is covered that we have also here in a very essential test. And it turns out that in the measure regularization to get the order new terms is not so easy, but we have a couple of days ago found a special treatment and now we can say more than our last preprint that we have all the order new terms right. So, there is still a series of more local tail terms which contribute order new squared, which have to be dealt with and this is still work in progress. And I should mention sets the nonloader contract versions of the tail terms in four pn and five pn have been calculated and we have agreement. We need a more and Geralico. This is not just the same calculation. This calculation was done in dimensional regularization and in the docs, the digital local terms are by product of that. And then in course of this we have of course also achieved that we get pull free Hamiltonians. Now, let me go right away not to any Hamiltonian but show observables. Because the different approaches will lead to different Hamiltonians and then you have to do canonical transformations to the map and that for that you have to have local representation. And as the non-local contributions to all these observables are known to five pn by now and agreeing. I can now discuss the local contribution to Perry Astron once, and this is the general case here. And what you what you see is we have actually all the terms, but the new square terms. So they are not yet listed in this list of the device bear contributions are listed. So they are they are known and they also agree with the work by by the more and collaborators and we work at the moment on the the new square terms, which are just rational in this case and to see what this will come. I can't tell you the final result on this now from the general motion you can of course go to the circular motion. And in the the the non-local terms were calculated for the circular situation. And we can add them in this is this term and the other term and that this is this one for Perry Astron and once you find them in our paper this is not not a very long expression but I have left them open. And here you see, we have two terms which we could not yet determine this is we work on that at the moment, but the associated terms here by square terms are there. And from what you saw on the last two slides. We can now go a step further, but what the more it all had already obtained and they call their method, the 2D 40 method, because it combines a lot of knowledge on this post Newtonian expansion. And also post Minkowski and expansion to different calculation and methods to fix the different parameters and this is very many of the Hamiltonian. There were two constants not yet determined now we could determine the pie square contributions already and we have all over agreement with this other group. And our calculation is up initial so we don't use any of these constraints. Our calculation is just based on effective field zero methods to get there. Now, certainly this is not so easy part and we have to see what the outcome of that is and but I can't tell you more details at the moment just that we work very hard on this calculation. Let me show you to the force post Newtonian all this also some phenomenon logical result and this is a bending energy normalized here over the reduced mass and then you see that this is the Newtonian limit, then you get one p and two p and three p and four p and this is the test particle limit here. And this would be the range in which play. So you get a range in which black holes merges is a bit wider and the smaller range where Newton starts and Newton starts would merge this is basically here, and the for the black holes you need a bit more and that is the Schwarzschild solution and we expect in somewhere here in the middle, the five p and the result but this is going to come. And then we can make a similar statement for the peri austral advance you see here this. It is Newton star Newton star motion and then this all of a range is black hole black hole, but the current sensitivity is and then you see the whole row and this is also here. Very singular and this is singular at this parameter x one over six this goes to infinity that is the Schwarzschild limit and then you see these corrections and we expect and the five p and result somewhere here. And you see that the convergence is not so nice. If you go to the higher values of x, and that will then invoke resumption and things which are already known in the literature and which the more and collaborators have used in the past already to lower orders to to get, say, a more stable result. So this brings me now to my conclusions and the. So, the inspirational phase of compact binary systems is very well described by the post Newton in expansion. So you have velocities which are of that order but still normalized to the light velocity of light is smaller against one effective field theory and calculation methods from quantum field theory are very effective for high post Newtonian orders always provided one is using intense computer algebra and suitably large computers but that is what people do in QCD anyway so this is not anything new. Then we have already some one and a half years ago calculated a static gravitational potential to five loops. And then following with different other papers we approached the five p and Hamiltonian and it has been determined up to a small set of rational terms, which is of order new squared of this order parameter in the mass ratio. And these results are obtained performing a five loop calculation of nearly 200,000 five and diagrams with partly very complicated vertices and the calculation has been performed up in it's your black we do that in QCD also. So, higher order corrections extend the area perturbatively accessible towards the region were presently only pure numerical measures methods are applied but to bridge between them this is still, of course, another issue I don't want to go into. And then it is also something else happening I didn't talk about. This is simply the so called possible in golf skin approach where other people are very active for instance we burn in this group, then Mr. Pardo and his group and then this was also, of course, initiated by people that more as so many other things and the, there is also very interesting work by him under very recently and, but from the full calculations, we talk about to look more difficult. And to do and the debate to five loops is still open but it's technically, of course, more ambitious. So thank you very much for your attendance. Thank you if you have questions, please feel free to raise your hand or just unmute yourself so we have a question from David, I think. Yes, I was rather surprised by the fact that your number of master integrals was less at five loops and four loops something funny going on that. You may have to do the table is for five loops. I mean there's another table for four loops. This is the four loops in the five in the five pn seeds this way. Thank you. It's only the static saying what is adding and then this is don't don't worry about this. Thank you. That's a very elementary question. Could you explain what the Perry Astrone advanced means. What is it that is. Yeah that this is when you know what the motion of the periodion of the Macquarie uses right. Normally you have an elliptic normally you have this elliptic motion, but these ellipse will in its in its pole will will move along with that due to due to one due to one pn corrections. And now we talk about even even higher order corrections. And, but you can this motion can be measured in by astronomical observations if you want. And therefore this is an observable and this observable that you can link I did not, did not write down the, the relation to the Hamiltonian. But like the energy did bending energy, you can relate this. This quantity to the Hamiltonian by a derivative of one of the Delany variables so one Delany variable is the angular momentum. You have another quantity so it depends on two of these Delany variables and introduced in the in the 19th century. And basically it is something where you derive the Hamiltonian, if the first derivative of the Hamiltonian with respect to these quantities. And you get an observable description which an astronomer code measure. And that's the very point I mean the, the, you have to define an observable to get rid of all these gauge degrees of freedom, you know, and that's that's why we choose this we could have chosen also something something else. Thank you very much. So please let's thank Johannes again for his very nice talk.


Today, I want to talk about how we can solve exponential equations without using logarithms. So if we don't want to solve with logarithms, we can solve exponential equations using the uniqueness property. And what that means is what we can do is write the exponential equations as two exponentials each having the same base. So this property only works in certain cases, but it helps us just to refresh some of our exponent properties and also practice using the uniqueness property. So we'll start with a very basic example, 144 equals 12 to the x. This method, our goal is to rewrite 144 as 12 to some power. So 144 is 12 squared. And so what this says is since the bases are the same, those bases can cancel out. And now we can just set the exponents equal to each other. And so the solution is that x equals 2. Now that's the most basic of an example that we can get. So let's try one that is slightly more difficult. For this next example, our goal will be again to write each of these bases. So one fourth and 64 as a base and an exponent that are the same. So what I would think of right away, I don't like dealing with fractions as bases. So I would rewrite one fourth as four to the negative one. And then we'll keep the two x outside. And then 64, if you think about that, that is going to be four to the third. And if four hadn't worked with 64, we would have had to just try again with a different base. But here it works. And so once the bases are the same, those fours can cancel out. And so here in the exponent, remember when you have a power raised to a power, you'll multiply so that would become negative 2x equals 3. And to solve for x, we'll just divide by negative 2. And so x is equal to negative 1.5. All right, one more example of this method. If you want to pause the video and see if you can come up with a way to rewrite both 27 and 9 as a base and an exponent with the same base. I look at the 27 and 9, and I immediately know the base I want to use is 3. Because 27 is 3 cubed and 9 is 3 squared. So just like the previous example, the 3s now can cancel. And when you have a power raised to a power, you're going to multiply those two together. So on the left, we have 3 times 2x plus 4. And on the right, we have 2 times 4x, which we can just multiply together. On the left, we'll have to distribute the 3, so it becomes 6x plus 12 equals 8x. And then if we move the 6x to the other side, we get 12 equals 2x divided by 2, and x is equal to 6. So those are just a few examples of solving exponential equations using the uniqueness property.


Welcome to my office. I live and work full-time from a tiny 16-foot airstream trailer and to do that I learned that I had to figure out four things so I didn't drive myself absolutely nuts. So today I'm going to tell you what I did so that if you want to work full-time or part-time from the road You can do it without beating your head against a wall. Happy Sunday birdwatchers. I hope you're all doing well out there It's Robin with creativity RV as you can see I'm about to start my work day except for me That's out here in the national forest and check out the view outside my window That's one of the benefits of getting to be a full-time working RV digital nomad now I can work from anywhere because I'm a content creator and a writer But you can too there are hundreds Of other jobs that I could be doing if I wasn't doing this And I know because I wrote the book work from home while you roam the ultimate guide to jobs that can be done from anywhere It takes you through all your financial considerations all the way down to a mega list of jobs with hundreds of resources and in the last 10 years the opportunities for people to have an adventure and live and work On the road before retirement has just Exploded because of the work that I do I need to have a really good computer Which means I also need to have power and I need to have internet and I need to have a dedicated Workspace when I first started on the road. I had a b-plus van with a Murphy bed That was a dumb move for me as a writer because I had to put the bed up and down and work on a lat pillow By the time I got to my third rig, which was a fifth wheel I was ready to have a big dedicated workspace during covid some friends And I literally circled our wagons out in the desert for a few months So I took that time to renovate the inside of the fifth wheel I got rid of all of that dark brown wood that they put in our v's and I lightened it up with paint And repainted the cabinets and the most important thing for me Was that I got rid of the big couch that was at the end of the fifth wheel And instead my friend and I installed a massive Dedicated desk where I could put my big computer and have space to spread out If I wanted to write on one side and paint on the other I could do that Well when I downsized to this airstream what was really important to me Was trying to find a good way to do that again just on a smaller scale And I finally figured it out the thing about having a dedicated workspace is that You get to leave work and go to a different area of the house to chill out I don't know if some of you experienced this during covid, but if you're working At your kitchen table, it's like the work never ends the emails never end And so for me I get to come over here and do my work in this nice big area with this big window And then go chill out and that was possible because I renovated my dinette The first thing I did was I got a trunk organizer To go on the other side of the dinette because I'm solo on the road So there wasn't anybody sitting over there and it was just wasted space Now I have this great organizer that closes up and hides all of my supplies And not only that I found the exact right size so that I don't have to secure it when I'm going down the road It just sits in there then on this side of the dinette you can see that I actually removed the bench It was so easy and it made the biggest difference inside of my rig Now on that side of the dinette I couldn't do that if I wanted to because underneath the dinette is the water tank and a lot of my electronics But on this side of the dinette there was nothing here But the bench with a storage drawer underneath it on a rail So all I had to do was take off the cushions Take out the bench which was drilled down into the floor and get an office chair Removing the right side of that dinette and putting in an office chair has been great I have a dedicated workspace and more storage But after that I had to figure out what to do with the back half of my RV and the bed Because the bed that came with my RV was super thin and uncomfortable There was a topper on it, but that barely helped at all mattresses that come in RVs are not great They're thin and they're uncomfortable You might think that they're great when you first go into the dealership and sit on one and you think oh, this is really nice But after a couple of weeks on one You find that they just kind of lose their shape and if you're going to full time Or even part time In an RV you have to make sure that your bed is comfortable I have switched out my mattress in every single RV I've had in the beginning I just tried to do toppers but that does not get the job done For me in an airstream. I needed to get an odd shaped mattress because there's that curve in the back Luckily, I found a great mattress by Brooklyn bedding's RV mattress line If you're not familiar Brooklyn bedding has a killer RV mattress line that is full of all of the weird funky non-standard sizes that you need to find when you're in an RV the people at RV mattress suggested I try the signature hybrid in a Twin full size because it would poof out into the curve in the airstream and it did They shipped these big boxes with the mattress for free from their factory in Arizona So they sent me mine and I opened up the box with my friend and took off the plastic And watched the new bed poof up. It just put the other mattress to shame Really, it was very princess in the pee and so comfortable and somehow Brooklyn bedding RV mattress makes the mattress firm, but also cushy. I don't know how they do it. It's magic But I love it putting in a new mattress was a game changer in here Now when I'm not working, I have this great chill space back there I put a bunch of pillows on the bed and made it into kind of a day bed area for the day and then at night It's like my little nest and you would think that it would feel small in a 16 foot trailer. It doesn't It feels huge back there and soft and comfortable And I get the best night sleep when you live in a tiny space like this every inch has to work The work area has to work the storage has to work And really the bed has to work because if you have a bad bed in your RV You're going to be a cranky camper Brooklyn bedding RV mattress has been nice enough to give our viewers a 25 off cuban I'll pin it at the top of comments below And check them out because they have all the different sizes you might be looking for different firmness different weights if you're worried about your gvwr and They have 120 day money back guarantee And a 10 year warranty now I have a dedicated workspace and I have a dedicated chill space But none of that matters when you're a full-time working RV digital nomad Unless you have access to the internet having internet is key and when I was first on the road It would take me 12 hours to upload a video and then it would time out in the middle And you know you park behind a rock and you don't have a signal and it just drives you nuts I don't have time for that. I don't know who has time for that. So what I do is I have starlink I also have an unlimited AT&T travel router, which is right here attached to my ceiling And I have Verizon on my phone with a hotspot in case I need that It took me a while to noodle this one out you guys Before I did this I was carrying the starlink dish in the back of my Jeep On top of its little mount which is huge and it took up a ton of room And then I had to run the cables through the window So bugs got in because an airstream doesn't have any slides to run the cables in now Starlink has a really funky proprietary cable So they don't make it easy to figure out a way to mount it and run it inside to the router If you're not a subscriber to this channel already and you want to know how I did that Please subscribe and hit the little bell Because next week I'm going to tell you how I run the starlink cables in here And how I got the unlimited AT&T service that I have on this router But for today, I'm going to tell you how I mount the antenna because that was a really key renovation for me Before I had this I had to pull the starlink on its little mount out of the back of the car Find a signal on the ground somewhere if I was lucky. I don't have to do that anymore So now when I set up camp I get the starlink router out of the back of the car still But I was able to ditch that stupid tripod mount that it came with and put it on a pole I pulled both of those things out and I mounted directly to the a-frame on my trailer Using an upside down flagpole mount that's meant to go on a picnic table I cannot tell you how long it took me to figure that one out So I put on this clamp that's really meant to go on a picnic table. I put it upside down Got it on there really tight and now I just need to unhook it right here To loosen up this pole and get it off This is the first time I've actually had to use a wrench Because uh, it's been windy And I think it got it a little tighter than usual I pull out that pole. I put it on the mount. I screw it in Plug in the cable, which I'll show you next week And I'm done and then I have connectivity and can get back here and get back to work Both my computer and my starlink have to be plugged into a regular household outlet Well, those outlets don't automatically have power in an RV unless you have an inverter. So One of the most important renovations I made in here was getting a power system installed From battleborn and dragonfly energy when I'm here working at my desk With my computer and the starlink going it takes a lot of power Luckily, I have two battleborn lithium batteries that I put in the back in a storage compartment Along with that 2000 watt inverter and lithium Is so much nicer than having a gm. I've had both but a gm. You cannot run down past 50 percent They don't have as much capacity as the lithium does and because the victron 2000 watt inverter is a sine wave inverter I can run my sensitive electronics off of it and I don't have to worry about that So all day long I'm charging my solar system with some external panels that I hook right into the side of the RV And when I'm going down the road I charge those lithium batteries twice as fast as I normally would because I had a dc to dc charger installed Which goes directly from the alternator in the car back to the lithium batteries I really don't worry about power that much anymore Especially when it's sunny because I can go for days without even having to look at my phone To see what my charge controller says in the newer airstreams The refrigerators have to work off of electric. There's no propane option I don't have a generator in here and before I put this system in I could barely keep the refrigerator going Now I don't think about power that often I go out a couple times a day and I move the solar panels So I'm getting the best charge but unless it's rainy and cloudy for three days. I'm good to go I really don't think about it when I first went on the road It never even occurred to me. I could renovate an RV I thought that there was some kind of magic sauce in the walls, you know Where the wiring and the plumbing was and I was scared to do anything but a command hook Not anymore. It is amazing what you can do in these spaces RVs can be modified and People out there are doing the coolest things inside of their rigs I always think it's funny when people look at this trailer and they go. Oh my god. How can you do that? I could not live in something that tiny Well, to me now that I've made these modifications It doesn't even feel Like a tiny trailer to me.  I've got my dedicated workspace. I've got a great chill area I have power. I have internet and so I can get up every day and do my job just like everybody else Except for I can do it anywhere I want. I don't have to be tethered to a location dependent job with these modifications In my airstream, there's a whole world out here You don't have to go from your job to your house to your job to your house and wait to retire someday to see the world If you want to do it now, you can You just have to put a little thought into making your space a workable digital nomad space for you I hope this has helped you do that Please comment like the video share it with your friends and I'll see you guys next week with that starling video until then Everybody out there have happy travels and be free


Okay, a number of years ago Jack Asgiff, he and Bill Bernstein could have an informal non-political chat as part of the agenda, and we all know that what Jack wants Jack gets has become a regular part of our conference agenda ever since, and it's now affectionately known as the Farside Chat. Jack's companion for this Farside Chat is a retired neurologist who helped co-found efficient frontier advisors. He's written a number of best-selling titles on both finance and economic history. He holds both a PhD in chemistry and an MD. Please welcome one of the smartest guys I know, Dr. Bill Bernstein, and the disclaimer that I always have to say, Jack and Bill, the bowheads community is a politics-free group, and we respectfully request that you honor that and refrain from discussing anything political. Other than that, the floor is all yours. Take it away, Bill. Okay. Well, thanks. I guess I mumble so badly that I get two microphones. The first thing I wanted to bring up is just a segue from your comments, Jack, about Fidelity's zero expense ratio funds. When I first read about them, the thing that came immediately to my mind was one of the most notorious tech funds of the late 90s, a company called eMachines, and their business model was giving away computers for free so they could advertise and make money on the advertising, and it seems to me that's what Fidelity is doing as well. And the question is, how do you really think that's going to play out for Fidelity? Well, I think it's going to draw a lot of business. The advertising is pretty blunt, and it's pretty clear who they're taking aim at. When we see our name, and when we see Vanguard and big capital letters, both face, you can't have any doubt about the name of the game they're playing, and it's a tough game.  And that's a perfectly good question, and the answer is a little complex. I mean, I'm not sure, I have no idea actually, what Vanguard is going to do in response. I have some things that I would think would be well done in response, working on larger accounts, but we are in a, as I think everybody understands, we are in kind of a box because if we did our index funds at no cost, which is an option always available to us, they will be obviously subsidized by the Welling and Fund shareholders and the prime capital and shareholders. The shareholders of all our active managed funds, and the shareholders of all our other index funds, if we did just the S&P 500, and they don't actually, Fidelity's fund is not an S&P 500 fund, the big one they're working on. And I think the reason for that is that if they use an S&P 500, S&P gets away with murder and would probably be charging one basis point just for using their name. And when you want to be a zero, one basis point, it's a killer. But there is an issue of implementation, what do we really got here? They have their own indexes, will it do better than the S&P? I have no idea, I'm not saying it won't, might do better sometime, worse others, that's the most likely scenario. So I would just regard it as very tough competition, and as I think I said in my remarks earlier, it's what I would do if I were Fidelity. They're out of the game, get in the game with a bang and become one of the big four and now the big three. And that's their goal, although one wonders a little bit why it's their goal. I mean that kind of immensely profitable company doing everything else, and I think it's just to preserve their mutual fund business, which is probably, I'm guessing here, 25% of their total revenues, I'm not sure exactly. And I'm not sure exactly, I don't really just venturing a total of gas. So they're doing it, I hope nobody is in retrospect, moves $3 million over and tells me that they're saving $10,000 a year or $6,000 a year, something like that. And then gets their tax bill for selling the Vanguard fund at $3 million and paying $200,000, well I don't know what it would be, a couple hundred thousand dollars anyway, of taxes, which would eat up that income. But we feel it now. I mean I don't have the data for you, but we see it in our own data that Fidelity is making a pretty big splash here. And we'll have more, they just did this in August I think. And so we have the August data and the data I showed you, but we'll have September, which will be very revealing, there'll be a trend there, there'll be October, and the data will come in. Vanguard has the data for Vanguard for all these periods, I do not, and that's fine. I don't need it, just reporting what it is, and we will find that out. But you never know where the next competitive threat is going to come from. And everybody, we know who everybody is shooting at. Everybody in this business is shooting at it. And they're all, all of you here in this room, they're shooting at the Bogleheads, that's who. And the big Bogle themselves. And at least some of the time. So I don't see that there's a good competitive, a really good competitive response. I don't think there's a winning competitive response. There may be an ameliorating competitive response, and I think there is, but that's up to Vanguard. I think that it might be who Vanguard, to point out to members in the fourth estate, how generous the owners of Fidelity's active funds are for subsidizing the zero-expense funds. Well, there's a lot of that going on, subsidization. And actually, I tell this story, it's one of the landmarks in my book, and it made it possible for us to be a competitor in this business seven or eight years ago, 1993, I think it was actually more than that 15 years ago. Because we had a very proscribed formula, set up series of formulas telling us in our original service agreement that established Vanguard how to allocate expenses between all the funds in the group. And it was very formal, like number of shareholders, number of transactions, executive time, that would be something you just allocate and direct and indirect expenses, classic, for doing that. And I could see that we were in a box because we were starting to have price competition. We had cost competition. We knew what the costs were. And so I put in a proxy, we put in a proxy, giving us the right to match competition in our pricing for the funds to use that as another indication. We kept the original standards, cost allocation standards, so we could also consider committing competition, committing competitive prices. So that's enabled us to do what we've done. But I don't think anybody is going to want to, I hope not, by the way, anybody is going to want to go to zero on new investments in our funds because it would be so apparent somebody else was doing just what you say, subsidizing the fund. And there's going to be a little bit of that no matter what you do. And you never know who's subsidizing it, who. We do the best job on that, we can, and are still able to compete. Okay. Well, I want to shift gears now and talk about the much bigger picture. We try to stay away from macroeconomics because speculating about it doesn't really do the average investor much good. But there's some things that are out there that I think that are of great concern. The federal, because of the recent tax cuts, the federal deficit is going to approach about a trillion dollars, and there's already almost 22 trillion in outstanding treasury debt out there on which the interest, the current servicing costs, are only $276 billion a year. If you do the math, that means that Uncle Sam is financing his debt at 1.3 percent. That is going to be changing very rapidly. The good news is that the term of that is about six years or so, the average term of that debt. So it's going to take a while for the Ottoman to hit the fan. But the bad news is that when it does, it's not going to be very pretty if servicing costs go up to the historical range of 6 percent treasury debt, which is a six-year treasury debt, which is around 5 percent. That puts the servicing costs at a trillion dollars a year out of federal tax receipts of about 3.4 trillion a year. So do you think that's of concern? And that's even before we get to the issue of corporate debt, which is also becoming very frothy and very covenant light out of control as well. So during the next downturn, corporations are not going to have a walk in the park either servicing their debt. So do you worry at all? Do you think that's of concern to the people in this audience? We used to say, people used to ask me, what keeps you awake at night? And my answer would be the same now, Bill, as it has always been. Nothing. If staying awake all night would help solve the problem, by God, I'll stay awake all night. Okay. But let me use that question as much more serious than that. I believe we're going to have a trillion dollar deficit this fiscal year. That would be the 2019 fiscal year, a trillion dollar deficit. And I won't get into politics, I hope this isn't politics. But let me just say that giving a ten trillion dollar, I think it is over time, a tax cut to businesses and a five trillion dollar, I can't remember the numbers, but say a hundred billion tax cuts to corporations and a five billion dollar tax increase to individuals, which is what's happening over time, say next decade, burges on economic instability. And I'm tempted to say in political brilliance, but I won't say that. So I look at it as, let me go back a little further, and say almost every bubble that we've had in the history of the world has been brought about by debt. And our debt in the United States is out of control. It is, I mean, it's in control, but nobody pays any attention to it. And I don't want to get into politics, but it is amusing to think the Republicans of fiscal hawks have been the ones responsible for this. That's not necessarily for or against it, but it is interesting to see that they're total in the face of political reality, given away on economic reality. So we have high consumer debt. We have not particularly high automobile debt, high credit card debt, and the whole new, you probably know this, the biggest single piece of debt in this country, by far, is student loans. And can they all be paid off? How can they possibly be paid off? I mean, it was a bad deal in the beginning to suggest, particularly from the private colleges, that you go here and you'll be able to make so much money that we can charge you a lot and you'll go out in the world and make a lot of money. It isn't that easy. There are only so many good jobs in America, good high paying jobs. And so you put a lot of debt together. There's still a lot of mortgage debt. There's still home equity debt. There's debt sort of everywhere. And I think that is where the next crisis, if it comes, and it probably will, I have no idea when, is going to be the basis for that. Too much borrowing. Well, that segues into another subject, which is you mentioned the B word bubble. And debt quite, quite accurately identified that as the source throughout history. There over the past several centuries of bubbles is what has me, there's the negative signs, which is the underlying condition, the amount of debt that's eventually going to have to be liquidated. Do you see any positive signs of bubbles out there, any behavioral signs of bubbles that worry you at all? I mean, Bitcoin, for example, Bitcoin, there's no question that there were the behavioral signs. Do you see any behavioral issues out there among investors that point to a bubble? Well, that's really an interesting point. And I can't avoid a political, I guess it's an economic comment, but also a political comment. Everything that is happening today is great for the short term and terrible for the low term. And I'm not only talking about the fiscal situation, but I'm talking about, and these issues are really important, the gap between the incredible gap between the wealthiest fraction, wealthiest 1% of America and everybody else, and particularly the lowest 15%, and I'm talking about an attenuation, acceleration of the gap between white and black, which is clearly there. Immigration built this country, and if you don't believe that, look in your own family trees, my traceability laws, I've got parents, grandparents, great grandparents, come off the road from Scotland in 1866. So I'm a child of immigrants or grandchild, and to stamp on immigration when it's been such a force for good in the country, all these things, and they're less tangible. It doesn't matter a heck of a lot on any of those issues, those broad social issues, but in the long run, it makes all the difference in the world. So what does that say? We have Bill, a market focused on the short term with a prayer that everything will be all right. And I haven't even gotten into climate change. I got here in Philadelphia, every day we're 10 degrees above normal, and this is only one season. And I read that the administration is not a political comment, happily. The administration predicts that the temperature of the world by 20, 20, by 2100 will be 10 degrees higher than it is today. No, I'm sorry, seven degrees higher than it is today. Just imagine what that's going to do to everything that we think about and do. And leave aside the upheaval in the climate that we're getting even now, the bigger hurricanes, the bigger rainstorms, and all that. So we're really on dangerous ground, and yet the market goes blindly along. And I do, in a sense, worry about that. As I tell people, I've been for quite a few years around 50, 50 stocks and bonds. And I spent half of my time wondering why the heck I have so much in stocks. And the other half wondering about why I have so little. This is the investor's dilemma. But by the way, that's one of the metrics I use to identify a proper stock bond allocation, is if you spend an equal amount of time regretting having too much or too little, you've got the perfect allocation. Let the record show that I'm really doing my best here to stay away from politics. On to another subject, which is completely non-political. Over the past 40 or 50 years ago, the percent of GDP being paid to workers as salary has decreased from 52% to 42%, which is huge. Where is that extra income going? Well, it's going to us in this room. And it's being on the other side of the balance, is that it's not going to people who are working for us. And so the question is, is that something that you worry about simply as an equity holder? Concerned about. Nothing keeps me awake. But of course, that's a problem. It's fine to say that we should avoid political problems or political issues, but there's no divorcing political issues from economic issues and from social issues. They're all part of what constitutes the United States of America and her role in the world. And you can see that shrinking. You can see China rising. Not sure what that means, but it doesn't mean anything good. When they start taking over islands in the sea of China, so-called, and the sea of the Philippines, and building little tiny reefs in the huge airports, let's take a lot of sand to do that. Competition in the world, America's place in the world, is threatened. It doesn't have to be given up. But what we're doing now is taking the nation away from its, what's the phrase they use, American tradition or the uniqueness of America. And that's been our biggest asset. Where does everybody want to go in the world when they're not in the US? They want to go to the US. That's a good sign. And I recognize you can't take as many immigrants as you might like to take. But they're all bound up, I think, Bill, and one part covered by your question and the part goes even beyond that.  And I want it to be a better country than it is. And I think it was a better country than it is. And I tell people, this is a political statement that falls both ways. I consider myself an extreme conservative. I love the country. I love our institutions. I love our entrepreneurship. I love our ability to do what we want, liberty, if you want to call it that. And I want to keep those things as much as we can. But I all of a sudden become a liberal to say that to keep those things, we have to make sure that the people in America who are not here in this room and get well taken care of. The underclass of America is large, average income $15,000 a year, I think. Imagine that, anyone in the room. Imagine that. So I guess the phrase I was searching for before was American exceptionalism. We're starting to lose that. And so I become so conservative that I want to be liberal enough to handle all of those who are not in the most favored places in America. Well, I don't think there's any way of spinning this next question politically, so I'll ask it. Which is that if you look at the number of publicly traded companies in the United States, around 1970 or 8,000 publicly traded companies, now there's 4,000. And so that raises several issues. Number one is why do you think that it's happening? Is it all the fault of Sarbanes-Oxley? Is it the rise of private capital as a source of funding? You don't need public capital anymore. Are there other reasons? And then the second part of the question is what does that mean for the people in this room? If you, you know, the number of publicly traded companies that we can invest in is slowly shrinking. Well, that's the first aspect of the data. I think the data is somewhat worse than you say, because I think the number of public companies remaining is more like 2,800 or 3,000 is compared to 4,000. But I'd also note that that 8,000 was probably, I don't have the data firmly in mind, was probably at a very high point. When we got into late 2000s, an awful lot of new companies came in. And probably the fairest comparison is we used to have an index called the Wilshire 5,000. So we're now, I would say, the best baseline is 5,000. And we're now down to 3,000, let me say. So the shrinkage is large, but not quite as large as it's billed to be. Second, if you look at the data, almost all the companies that are leaving are very small companies, small and very small. And some of my guests don't like to have to register with it or file information with the government. I think that's a very small part of it. Some of them just didn't make it. You know, in these boom years, led up to the market peak in 2000, the companies blossomed and then went away. A lot of tech companies. So I don't think it's as serious an issue as you say, but I do think it's a very serious issue. And I kind of wonder when I see one more damn merger, darn merger after another. And I think when we see a lot of that, I wonder, why are we doing this? Why does national policy allow all these mergers?  And he's my classic Republican. If that's, I hope that's not a political comment. He'd been dead a long time now. And so I worry, I'm concerned about it. But more than that, the underlying reasons that we allow companies to get bigger and bigger and bigger as a matter of fair international policy is I think the wrong way to be going. I think we ought to be much different antitrust, much different in everything we do to make these things and much stricter even bill, much stricter in accounting.  You know, you can do whatever you want. When you read pro forma, 99.5% of the time, not all the time, when you read pro forma, boy, put your hand over your wallet. Somebody's playing games with the numbers. And that's an important part of all this.  We're going to make it up with synergies. Those synergies are always talked about and almost never realized. This is savings because you don't need two chief financial officers, blah, blah, blah. And they just don't seem to materialize. So I'm unhappy with it. I hope it won't go any further. And there must be some limit because you may only have to own one stock to have the S&P 500, which I would think would be very bad. Okay. Well, it's, you know, it's 2018. So you have to ask the decadal question. I can remember almost 10 years ago to the date we were all together and we were in San Diego. And you were talking about the collapse of lame. And I remember that your voice rose about two or three octaves when you simply said the word. And do you think we're in a better place, a worse place now? I think I know what the answer is, but I want to hear what you think. Well, I think we're in a better place now than we were in 2008 because the particular debt was financial debt and mortgage debt. And then the creation of these, idiotic to the one of a better word, mortgage certificates, mortgage back certificates, which mortgages, which had no value, made money for the people that gave them the money, made money for the people that were buying houses. They gave them the best deals possible, even more than the value of the house. And then they sell them, and then they sell them to somebody else and they're put into a certificate. And everybody forgot that there were people at the bottom of the pile that could not possibly pay their mortgage debt. And that is not happening now. Well, I'm not saying there's none of it, but that is not the excessive thing and not the junk thing. So I do think we're in a better place now, but not a lot better place. And the market is telling us we're in a lot better place. I think that's right. I think that in some ways we're in a worse place because we had relatively high interest rates and five big banks that couldn't fail. Now we've got much lower interest rates to start from and we've got four big banks that are too big to fail, that are managing a higher percentage of financial assets. But on the other hand, as you point out, the epicenter of the crisis in 2008 was real estate. If the value of stocks falls by half, that's owned by maybe 10% of rich people and their net value, their net worth goes down by 50%. It's not that big of a deal in terms of the overall economy. But if 25% of the population owns an underwater house, that really does affect spending. And I think that's why what happened back then was so catastrophic and isn't likely to happen now. All right, well, one last question. I don't think that it's political to observe that there's been a decrease in the comedy of public discourse in this country. It would be political to try and blame someone. I wouldn't dare ever do that. And so the question is, what do you think are the limited implications for investors? And do you think that it's a problem, and the larger political sense of our country that is going to heal itself and mend itself at some point? And answer this in non-political terms. Yes, absolutely, yes, yes. So I certainly won't talk about fake news. No, no, no, no, no, no. The, I think it's tragic the way the power of the press has been more or less subverted to a certain number of people anyway. And it's told you don't need to pay any attention to them. You know, just listen to me, listen to the Internet you would think with the Russian interference, obviously interference in the last election campaign. People would now become aware that the Internet is talking about the medium for fake news. I mean, it's an outrage and the loss of our privacy is an outrage. And, but particularly the idea that what you're seeing there on your little computer, if you do these all, I don't do this stuff.  Cashmark, cashmark. I don't even know what it means, but I think it says, I think it says, you better get over here quick. And, but so I don't do that. But the press in the United States has been singularly responsible. You know, not always, not all newspapers. And now they're vilified. And the people that believe they're vilified cadre that believe they're vilified is large.  They've had editors going over. They have fact checkers. My God, you wouldn't believe the fact checkers. Find us little things in the world. And they're giving us what I believe is the straight story of America today. And a disomat gives us a feeling that all is well. And I would say all is not well. You know, there's so much going on that's important to the country.  And I won't get into the Supreme Court today. I mean, the implications of that are, of course, much more than trivia. A person on the Supreme Court was conservative leading. But the issue, you know, will resolve these issues eventually. But only if we can wake up people to vote, number one, to vote, because the absentee voting, the voters that don't show up, registered voters who don't vote, is shocking. And the whole underlying strength of democracy is to have everybody vote. And believe me, if everybody votes, we have a very different kind of America. So, and I worry about, by the way, building the money involved in the electoral process. The fact these, I saw Sheldon Adelson devoted $100 million to the coming campaign. He's a big Las Vegas, something, Macau. He owns gambling joints. I'm sorry, gambling establishments. Well, over the world. And he's my idea of a fraud. You know, God knows how many people got paid off to get a franchise in Macau or even for that matter in Las Vegas. And yet he's regarded by Forbes as a great businessman. I'm sorry to be in his company, by the way, they regarded me that way. I may not be much, but I'm more of a businessman than he is. Talk about damning with fake praise. So, no, these are big issues and soft issues and divisive issues. And, you know, I don't know how, I'm a little bit reminded that DeSanne Cdota is in the book, in a section called Presidents. I talk about the presidents that I've met briefly, mostly. And the one I talk a little bit more about is that I was invited to dinner at the White House in May of 1970. And the stock market was falling apart. And some genius in the White House, PR staff, decides that it would help investor confidence if they asked about 25 or 30 people like me, heads of financial institutions, which I was then. And I guess, no, I'm not still. But to the White House for dinner. And I got off the train in Washington, dial up 40 percent on, I'm sorry, 400 points or 40 points or something big for that day on news of meeting. The fact that these people like me are, by the way, a pretty ordinary crowd had anything to do with getting the stock market up. I don't know. So we went to dinner with the president. And it was in the state dining room in this little square table. And right across from me is that brooding portrait of Abraham Lincoln. And right below him is Richard Nixon. And so he gets up and he had all the joint chiefs of staff, council of economics, blah, blah, blah, all those people talk to us. And then he said, are there any questions? Nobody stood up. Not one person in that room. And I thought, after a moment's hesitation, they held with it. So I stood up. And this is very, this part of the question is very relevant for today. I said, Mr. President, you've reassured us all about our military strength and how well we're doing in Vietnam, how well we're doing in Vietnam. He did reassure us in that. And how the Federal Reserve will be Phil's usual role of lender at last resort. And all these, the economy is doing well and so on. But you haven't touched on the issue that I think is really the responsible for what is dividing America today. In view of your campaign pledge to bring us all together, what are you going to do about it? The silence could be cut with a knife. And he looked first angry and first astonished that this investment group would even think, be thinking about bringing us all together. I think annoyed that that was the first and it turned out to be almost the only question he got. And something he didn't really want to deal with.  Somebody did try and answer. He'd got point Chancellor Hurd of Vanderbilt to head a commission on looking at the divisions in the schools, things of that nature. And so he gave a kind of a fumbling answer. But he clearly was not happy with it. Well, he was there and I was here. So when you go out the door that's there, have you figured it out yet? We're going to be in the same place. So I can walk out there right next to President Nixon. And I said, you know, I hope you didn't think my question was rude. Oh, no, no, no. He said, that was exactly the right question. And that's why I'm doing what I'm doing or something like that. So I'm very lukewarm. But the divisions in this country, we should be united on so many things. And we are not united today. And so I think we have to face up to that fact and do what we can as citizens. And when we sit in this room and we'll be like, I wrote about the universe, what I wrote about the universe. You know, it's so big and we're so small, but that doesn't mean that one person doesn't make a difference. So I think we have to try and do better as individuals. And I've tried to do better not as an individual, but in a corporate sense, try to contribute something to the world and something to make America better. Spread stock ownership among people who get a fair shake. This is not, this is a crusade. And it was so easy because they were getting such a lousy shake before. Uh, so that's too much rambling. And I think you've heard quite enough from me today. Okay, well that was, that was fun. I think we better give it back to Mel before his hair catches my fire. Well, thank you, Jack and Bill. We're gonna take a...


OK, to the previous speaker, thanks a lot for that talk. That was interesting. It looks like we don't have questions in the room. I don't think it was for lack of interest. It was just a very good explanation. Thank you. So I'm a little early with these closing remarks, but I'm just going to go for it anyway. So in terms of upcoming events, the Linux Foundation has open-source summit North America coming up in late June in Austin, Texas. And there will be a Kubernetes on edge day North America coming soon. But the Linux Foundation hasn't surfaced the CFP site or registration yet. I believe that that's destined to go to Detroit either before during KubeCon, which I think is in October. There are a few other embedded system conferences held by the Linux Foundation. The one I'm aware of for sure is embedded the open-source summit with Automotive Linux, which is in December in Tokyo. And I think they have one of those before that in South America and perhaps one in Europe that if I'm not mistaken was in Ireland. But the Linux Foundation site should have references to those things. If you're interested in this IoT Edge and Kubernetes topic, there has been a Kubernetes IoT Edge working group operating for years over under the Kubernetes project. So it has a Slack channel. It has Zoom meetings that have been every two weeks, although half the meetings are for Asia. So they're in uncomfortable time zones potentially unless you're in Asia and half for North America. This group is in transition. So what happened was that a lot of the discussions coming up in this working group went beyond Kubernetes. I mean, there were even the heresy talks of, is Kubernetes really suited for Edge? And the Kubernetes project decided that maybe this is a better fit for being under the CNCF, because we've got a lot of CNCF projects like Kube Edge came and talked to us. Some of the WebAssembly stuff is over under the CNCF GitHub. And it's been decided that this group is destined to move, so that rather than being hosted under Kubernetes, it will still exist, but be underneath the CNCF. And that move is going to mean that perhaps the Slack channel will change the place we have a GitHub repository where we've published some white papers and collateral information. But I think somewhere between one month from now and October when KubeCon North America hits, this group is going to move. We'll leave the legacy things where they are now, the Slack channel and everything, but we'll probably leave a parting remark in the Slack channel saying go over here into this other channel on CNCF Slack and it's possible that we'll move the meeting times, but that hasn't been determined yet. But anyway, there is this group. We're very much open for users to come, listen and learn with often the meetings have pretty open topics. We've had recently demos of tools like Portainer, the Red Hat version of Red Hat has that micro shift and we had a presentation on that. And we're open if anybody in the audience works on these projects. Our rule is that we don't want presentations that are just commercial sales pitch. If you've got some product that's closed source and you're trying to sell it, don't come to this meeting to expect us to be a platform where you'll put on your sales pitch. But certainly if it's open source and it's okay if it's open source under a CNCF approved license and you sell a commercial version with support besides that's fine. Something like Portainer for example has given presentations at the group. So if you're either associated with an open source project or even a vendor that has a free community addition that's open source, you're welcome to just put yourself on the agenda for a presentation at the list. It's not very formal, you can, we share a document with the agenda and you just become a member, you get edit rights and put yourself on the agenda. So that's how that works and you might be interested in joining the group. So to wrap this up, I just want to make a comment that in tech, things are rarely these overnight successes that go from inception to universal adoption like instantly like the drop of water captured in a high speed camera or even within 24 hours. The process involved here is kind of more along the lines of pursuing a college degree. When you get down to it, these open source projects get built but it might take up to four years before they build up enough momentum, stability, things like this to get adoption. And along the way during that four year process, the ones that turn out healthy and get adoption are ones that get exposed in venues like this where users hear about them but freely exchange information, give feedback as to gee, I have this use case, it's not quite right but what could I do to accomplish this? And maybe the people behind the project learned to adapt it like the speaker before me talking about web assembly is an example of that where that's really a rapidly moving thing that people, it was originally done for web browser but the act of moving that kind of stuff over to be suitable for being something Docker-like for Edge but Docker-like in the context that it's packaged up, not Docker-like in the sense that gee, the web assembly might be smaller, have much reduced startup latency, maybe be more portable but these kinds of new things are the kind of subject matter both for that group I talked about conferences like this and what I'd like to encourage is that we're about to break for a happy hour and I know it's been a long day, it's tempting to go back to your hotel room but I've seen some pretty interesting conversations break out in the so-called hallway tracks so I'd encourage people to just hang around and have these conversations about the cool new technology you saw today or even cool new technology that you're aware of that you didn't see today and let's get these conversations going and learn from each other so please stick around for that happy hour, it's, I've been told that you go out the door, turn right and it's going to be near the front door somewhere, you've got one of these green cards that gets you a cocktail and you might as well at least hang around long enough to burn your green card before you head back to the hotel so that's due to start in 12 minutes, we still have a little more, I wanna just rapidly go through the list of people to thank these are the CNCF organizers of this event, a few of them were outside in the hallway and they were the ones who managed this thing so thank them if you see them also I wanna thank all the speakers, I'm not gonna read all the names because to be honest, I'd probably butcher two or three of the names but if you were here, you saw them and they said their own names and we'll just go through them but there's a lot of work in giving these talks, people rehearse them, they don't get paid for this and I wanna shout out some appreciation for the act of doing this, it's a lot like the act these days of writing a book in the computer industry, you might think that's glamorous and lucrative but nobody makes any money at that and I don't think anybody makes money at speaking at these conferences, they just do it to share their ideas and I wanna thank these speakers and then finally this event had a program committee and these are the people who reviewed the CFPs I'm on this list but there's a number of other people, this is also a fair amount of work you know we get over a hundred submissions and go through these and pick the best candidates, try to avoid duplications, one of the odd things about this and I already talked to somebody in the audience on a break about this who was interested in speaking so definitely at that happy hour if you're interested in speaking, come and chat with me as I can give you some advice having reviewed these both for this edge day but I also am a reviewer for the KubeCon conference itself and have been reviewing for KubeCon for three years. Often what happens is people put in a really good proposal but it turns out six people put in a proposal on exactly that same topic so there are certain things that are competitive, it's hard to really predict how that is gonna turn out if you did put them in in the past if you're in that scenario where you were one of six and very close you shouldn't get discouraged, you might be able to just submit it to the next one that comes along and do just fine. The other thing is with the CNCF and Linux Foundation I don't know the people are aware of it because they rarely do this but if you get rejected you can just email the people and ask them why and the people on these review committees normally give reviews in writing and I know for myself I never write up a review that I'm not willing to share with the author but you won't automatically get that but if you ask for it you will and you might learn you were in one of these scenarios where it was just a lot of competition and you could maybe leave it almost unchanged and just try again and just get it in at a different location or in other cases if this is the first time you're doing it maybe you're just not aware of the sorts of things that would get your speaking proposal accepted. A lot of this is just clear explanations of where you intend to go with this. Once again I'd be happy to chat about this and give people tips for getting those accepted or even you know a lot of times there's different tracks at these things too and you're gonna be far more likely to get accepted in one track versus another there's sometimes crossovers where at edge you could have it submitted under edge or maybe it has networking aspects and you'd be better off to submit it to a networking track. You're almost never better off to submit it to multiple because they will, in fact I think KubeCon recently prohibited multiple submits from one speaker so you couldn't do it if you wanted to but in the old days it watered down your vote and made it actually tougher to get an accept if you put in multiple. You're just better to put all your efforts into one talk, make it as good as you can and put it in there. So moving on, the final thank yous are to our sponsors who help pay for the event, the food and that's it, thank you for coming but like I said, please take advantage of the opportunity to continue the conversation at the reception which is supposed to start in seven minutes so maybe by the time you gather your stuff walk down to the entrance they should be pouring drinks so hope to see you there, thank you.


This video will explain to you the intuition behind a new game-theoretic solution concept called correlated equilibrium. Let's think again about the battle of the sexes game, and let's think about its Nash equilibria. Remember there's a Nash equilibrium where both players play B, there's a Nash equilibrium where both players play F, and there's another Nash equilibrium where both players randomize according to these probabilities, and that means that all four of the outcomes can happen. So both of these outcomes can happen, but these ones can happen as well. Now let's think about intuitively what makes the most sense to us about the battle of the sexes. It's really that this outcome would happen half the time and this outcome would happen half the time. If you and your partner really did have different preferences about what to do and you wanted to be together, you would work it out where you each win half the time. And something that might have struck you about battle of the sex is it doesn't give us a way to say that that's a stable outcome. And the reason why we don't say it's stable is that if both of these things can happen, then both players have to be playing mixed strategies with full support, and that means the miscoordination actions have to be possible as well. Well here's another example that we can think about that will give us some intuition for what's really going on here and how we can do something about it. So this is the traffic game. So this models the situation where two cars are coming together to an intersection and they have to decide whether to wait for the other person to go through first or whether to just go through. Well if one of them goes and the other one waits, then the one that goes gets the most utility and the one that waits gets a bit less utility. If they both wait, they're both strictly less happy because they both waited and they still have to decide what to do. If they both go, the worst of all things happens because they crash into each other. So in total we have two pure strategy equilibria that are again asymmetric, kind of like in battle of the sexes, and of course it's also possible to have a mixed strategy equilibrium here. But let's think about what would really happen in the world when we have this kind of situation where we have an intersection and there's the possibility that cars might collide. What we really do is we have a traffic light, and let's think about what a traffic light means game theoretically. It's a fair randomizing device that recommends actions to the agents. It tells one of them to go, it tells the other one to wait, and it's fair in the sense that at different times it makes different recommendations. Well the benefits here are that the negative payoff outcomes are completely avoided. We can achieve something fair and in general, although not in this example, it's possible to end up with a sum of social welfare that exceeds that that can be achieved in any Nash equilibrium. Well we can use the same idea to achieve the fair outcome in the battle of the sexes game. So we could have a situation where the husband and wife flip a coin and depending on how the coin comes up they go together either to the ballet or to the football. Well this is essentially the idea of a correlated equilibrium. A correlated equilibrium is a randomized assignment of action recommendations to the agents such that everybody wants to follow the action recommendations. So we have some randomizing device that tells me B some of the time and F some of the time and in a correlated way, potentially correlated way, tells you B some of the time and tells you F some of the time. So flipping a coin where if it's heads we both get the recommendation B, if it's tails we both get the recommendation F is a randomizing device like this although it's possible for it to be more complicated. And in principle if it comes up heads and we understand that to mean that we're both getting the recommendation B, this doesn't compel us both to go to the ballet. We still get to freely decide how to interpret that recommendation but it's a correlated equilibrium if neither of us would want to deviate from the recommendation. And you can see in this example with Battle of the Sexes that indeed neither of us would want to deviate because if the other one is following the recommendation and I deviate then I'm just going to get a payoff of zero instead of getting a positive payoff. So a correlated equilibrium is any such randomized assignment of these possibly correlated action recommendations that leaves nobody wanting to deviate. It's a generalization of the idea of Nash equilibrium because if these action recommendations are not correlated at all then we just get back to mixed strategies like we had before so we can capture any Nash equilibrium this way. But we can also get new things like we've just seen so it's this strict kind of weakening of the concept of Nash equilibrium it includes more things and it can get us these kinds of nice fair outcomes.


Too often, many people let their mental health issues go unheard and untreated, waiting until they're drowning in it before seeking help. According to the National Alliance on Mental Illness, around 10 million people in America suffer from a mental illness that severely interferes with major life activities. Sadly, more than half of these mental illnesses go untreated. Sometimes you might feel like it's easier to sweep your issues under the rug because you don't have enough time to deal with them. I mean, we are humans and lead lives that can be scattered and consuming at times. But not dealing with your mental health only works to prevent you from living your life. Even though it might seem like the best route is to just ignore it, this is oftentimes a recipe for a world of emotional distress later on. By dealing with your mental health issues sooner than later, you can ensure that you are on the path to recovery. You might be showing signs that your mental health has been left untreated and you don't even realize it. So keep watching to find out some signs that you are not taking care of your mental health. Number one, you feel like taking risks. Have you been feeling extra rebellious lately? You might be feeling more impulsive and spontaneous and find yourself doing things you would never normally do. Many who are stuck in their lives and are dealing with mental health issues will often seek ways to numb their pain or take their minds off of it. This leads them to take these sorts of risks, which will grant them a momentary reprieve. Licensed psychotherapist Jonathan Schnapp states, Sometimes people find themselves contemplating taking risks or doing things impulsively that put whatever stability they've built at risk. They know it's self-destructive, but find themselves throwing caution to the wind, doing something they rationally know will not bring them any lasting joy.  Number two, you're spending more time on social media. The online world has become a prominent part of today's society. It seems like everything revolves around Instagram and TikTok and other social media platforms. These apps have become a kind of escape for people, a place where we can pay attention to the lives of others rather than our own. According to Carolyn Robestow, a licensed professional counselor, an increase in numbing activities, anything from scrolling through Instagram to increased exercise can indicate an increase in stress. We tend to disguise these as healthy or self-care, but ignore the fact that we're using them to ignore uncomfortable feelings. In reality, you're just avoiding your true feelings with notions of self-care. And this can be harmful because instead of facing your situation and dealing with your problems, you're running away from it and seeking the comfort of other people through a screen. Number three, you're losing your passions. Have you found that you don't really get excited to do the things you love anymore? You might love reading, painting, or gardening, but now those tasks that used to bring you so much joy do not. Of course, everyone has bad days and it's normal to feel down and unmotivated sometimes. Despite this, if you find that you feel unmotivated and lost regularly, this might be a sign of a decline in your mental health. You might feel out of touch with the things that used to calm you down, and this can potentially put you into a cycle that can be hard to get out of. Since you've lost interest in the things you love, you might also put your relationships in career at risk because you're not putting as much effort into it. The fact that you're apathetic to what you love might be a sign that you're losing touch with yourself and that your mental health issues are surfacing. Four, your sleep schedule has become out of balance.  Maybe you have trouble falling asleep or you can't stay asleep all night. Dr. Jillian Louise Adams, a medical physician with a focus on mental health, says that frequent oversleeping could be a sign as well, demonstrating that your body is fatigued to the point of burnout. Your mind might be constantly turning, thinking of the next thing you have to do or other worries, making it hard for your mind to rest and relax. Along with this, a lack of sleep can have negative effects on your waking life too, leading to mood swings and lethargy, which can cause strains in other parts of your life. Although everyone has times when sleep just doesn't come easily, if it happens routinely for you, this is a sign that you might be struggling and that your mental health issues are going unnoticed. And five, you're experiencing unpredictable mood swings regularly. If you feel like your emotions are all over the place recently, like one minute you're feeling anger, then happiness and sadness, this is a sign that you're not taking care of your mental health. It's normal to have days when you feel off balance with your emotions, though it can be signifying when it's a daily occurrence. You might feel scattered, like you don't know how to feel or react to certain things. Depression and anxiety can make it tough to regulate and control your thoughts and feelings, which is why you might be feeling a lot more and all at once.  If you are noticing these signs in yourself or appear, it is likely that there might be mental issues that have been untreated.