In this talk we are going to be looking at a method that has come to be known as optimal interpolation. I would like to provide a quick historical perspective of this approach to prediction estimation based on a method that has come to be called optimal interpolation. During the 1960s and 70s operational centers in USA, Sweden, Japan and others routinely used iterative scheme like Bertoltz and Deuze or Krusman type that we talked about in the last lecture. These methods have also come to be known as successive error correction. You can see z minus h of xk in the iterative scheme which we can think of as innovation is also can be thought of as error and by iteratively performing the update we are trying to transfer the information from observation to from the observation network to the computational at work. So that method that class of methods Krusman type schemes have also come to be called successive error correction method. When this was going on in USA, Sweden, Japan and other countries in Soviet Union in 1960s a technique called optimal interpolation was championed by Gandine, Liv Gandine. Optimal interpolation was developed earlier independently by Norbert Wiener around 1914 in the USA and Kolmograf in the Soviet Union. The story goes that Norbert Wiener developed this method in the early 1940s but he did this work under a defence contract. So it was classified and by the time he could publish it it has to be unclassified. So it took several years before the first classification of Wiener ideas were known to the public. So the publication date the open publication date is around 1949 but he had also independently developed in the early 40s not knowing that Kolmograf was also working on similar problems. This goes to show big minds think similarly even though they have been working in geographically distinct locations. What is the basic idea of this method called optimal interpolation? I am going to illustrate this notion of optimal interpolation using a simple 2D grid problem. It can be extended to 3D grid as well. Here a 2 dimensional grid with nx times ny number of points, nx is the number of points along the x direction, ny is the number of points along the y direction, n is the total number of grid points. Let there be m observations inside this grid space. As an example I had nx is 4, ny is 4, so n is 16. I have a set of 5 observations z1, z2, z3, z4 and z5. We can think of these observations as scalar observation, temperature, pressure, humidity or concentration of some chemical whatever, quite different but essentially it is a scalar. So I am now going to consider 2 cases in our illustration. First let us assume the observations are perfect. Observations are perfect means there is no noise. Why do we do that? Even though we know observation generally are associated with noise I think it is good to get a grip on the idea by assuming that observations are perfect. So the field variable of interest as I said is a scalar field variable. It could be temperature, pressure, etc. Consider a time k, noon January 1st 2016 as an example. So k is a specific instant in time. There are m observational occasions. So at that time k there are m observations of the scalar field variable temperature pressure whatever and I have a m vector. The components of the vector are zk1, k2, km is a m dimensional vector at time k, zk. These are the observations that are available from the m observation stations. Now the observations that we are concerned with has a natural variability in itself. For example if you consider the temperature at the downtown Paris on December on January 1st of every year there is a natural variation the no 2 successive years will have the exactly the same temperature in downtown Paris at noon time on January 1st for the 100 years. So you can think of these scalar variables to be naturally varying. This natural variability is captured or is described as a random process. So given this natural variability we are going to consider zk as a random vector. So zk is random not because of the observation errors, zk is random because of the inherent natural variability due to the resulting from changes that are inherent to climate variables. It is assumed the observations are error free that is what perfect observations relate to. So the whole method of Wiener and Kolmograph which has come to be called optimal interpolation rests on the assumption that the properties of the random vector zk is stationary. What does it mean? The random process that describes the temperature time series is sorry has a stationary distribution. So what does it mean? z is a random vector every random vector has an associated probability distribution if that probability distribution is invariant in time that is called a stationary distribution. If that probability distribution changes in time is called a non-stationary distribution a fundamental assumption is that the temperature in downtown Paris at noon on January 1st of every year is drawn from a stationary distribution. The stationary distribution is the one that describes the underlying natural variability. So given the stationary distribution that is behind the realization of zk z bar is the mean of z z tilde is the anomaly z minus z bar expected value of z bar is 0 the covariance of z is given by expected value of z bar transpose and that I am going to call it c. So c is a m by m matrix c matrix talks about the covariance of the observations from different locations it is assumed that both the mean and the covariance of the observations are known. So let us go back in this case I have a grid with 16 points I have 5 observations I am now talking about observation vector. So let us fix the time so I do not have to worry about k let us fix the time k to be noon January 1st. So at noon January 1st I am getting 5 observations z is equal to z1 z2 up to z5 this will have a mean z bar this will have a covariance matrix c the covariance matrix c will consist of cij I runs from 1 to 5 j runs from 1 to 5 what is the meaning of cij cij is the correlation between the scalar variable at location i to the location j. So in order to be able so it is assumed that this correlation is known that is a key to the methodology. So the whole question is we assume the distribution stationary we may not be able to get a handle on the stationary distribution but what is that one can do I should be able to estimate z bar and c how would you estimate z bar and the covariance c. So let us look at the station so let us take let us take the time series of observations so z1 so if I now consider the time if I now consider the if I bring in the time now z becomes zk zk is equal to zk1 zk2 and zk5 therefore if I consider station 1 I am going to have a time series of that measurement over a long period of time. So we are for example I am trying to measure the temperature in downtown Paris at noon every day so that time series is known so once that time series is known so what is that we are going to assume I am going to fix the location downtown Paris I am going to fix a particular instance in time namely noon of a given day so every day in downtown Paris I am going to measure the temperature and there is a record of it and that time series is made available to me that time it is a long time series likewise so downtown Paris is only one observation station and I picked for an example in this illustration there are 5 such spatial observation towers or observation locations from each location at each instant of the day at each hour of the day there is going to be measurement of the scalar variable of interest so these sensors are going to spit out the values of the observed quantity and I am assuming I have already recorded so that is the fundamental assumption. So given a long time series of observation from each of these locations I can now compute the mean so I can say downtown Paris what is the mean so what is that I need to consider what is the mean temperature in downtown Paris on noon January 1st what is the mean temperature in downtown Paris on noon January 2nd so day by day by processing the data I should be able to compute the mean once I compute the mean if I have time series I should be able to compute an amelie once I compute the amelie I can compute the variance of the measurements at a given location this I can do for every location so I will have young locations for a given time I will have young means I will have young anomalies I have a time series of anomalies using the time series of anomalies I can also now compute the covariance so how do I compute the covariance let us say Cij Cij is equal to let us let us consider I am fixing the time right now so time k is fixed so I have an anomaly at station i I have a time series of that with respect to k so Zi tilde k is the anomaly at the kth instant in time at the IST station Zi tilde these are scalars I do not have to have even written like this I simply can square the anomaly once again I can I can square the anomaly sorry I can square the anomaly I can sum this anomaly over k is equal to 1 to n I can compute the by this and this will give me this is not ij this is ii so that is the variance at a given station now I would like to be able to compute the very the elements Cij this is essentially equal to Zi i tilde a time k Zi j k tilde the product of the anomalies at station i and j I am going to have to sum this up over k is equal to 1 to n over n so this is an estimate of the covariance between station i and station j this is the variance of the station i these two together decides the elements of the covariance matrix C so what is the fundamental assumption there are two key assumptions that are here I am assuming the scalar field variable of interest such as pressure temperature whatever it is has a natural variability this natural variability can be captured by a stationary distribution way stationarity in distribution analysis of non stationary stochastic processes are extremely difficult there are very few results in the analysis for the analysis and quantification of properties of non stationary stochastic processes the only thing we know is to be able to pin down analyze characterize the properties of stationary stochastic processes so in here Z k is the observation vector of time k is said to arise out of S under assumption is said to arise out of a stationary distribution stationarity is fundamental to anything that we can do computationally that is the fundamental key so it is the limitation that is that is imposed not because we wanted but because if it is not stationary there are not too many things we know how to do analytically so stationary assumption is fundamental in almost all of the time series analysis and likewise here I am assuming that I am having a parallel time series at each of the m locations one for each station from each of this parallel time series I can now compute the statistics the individual mean the mean vector the individual variances the covariances these two together summarize the vector Z bar and the matrix C and that can be done if you give me a long series of time series at various stations so we assume that we have availability of Z bar and C at m stations so that is what exactly is what I described is now reinforced in the slide let me quickly reinforce that so computation of the spatial covariance C is the computation of spatial covariance among m observation stations Z is the time series of the field variable Z bar is the vector of means so I am now doing instead of doing individual stations I am collectively doing for all stations Z k is a vector Z bar is a vector I am trying to take the average of capital T number of observations Z Z tilde k is the vector of an amelies earlier I talked about the individual an amelie now I can collect them in the vector it is a vector of an amelie if the vector of an amelie is known I can now compute the covariance matrix as Z tilde times Z tilde transpose the summation over k 1 over k this C is symmetric positive definite that is the assumption why if the number of samples is large if the number of samples has been collected over a long period of time I think one can readily see this C covariance the covariance is always symmetric if the number of data is small it may not be positive definite if the number of data is large that is the reason to believe that C so computed would indeed be symmetric and positive definite as well so I am going to make an assumption that C symmetric and positive definite given so what does C captures that is the important thing that is the fundamental idea of both Kolmogorov and Wiener and they propose this in nineteen early forty one forty two the matrix C captures the natural variation in the observation natural spatial variations please remember this is not related to the observation error covariance I should have said error here observational error covariance observational error covariance is R in this case R is 0 because we have assumed the observation are perfect so this is the this spatial covariance essentially captures the natural spatial variability of the field variable of interest in the region covered by the in the geographical region region covered by the YAM observation stations that is the fundamental idea that is the starting point now let me go back and talk about why are we interested in this correlation please understand our ultimate aim is to predict to predict I need to assimilate to predict there are only two kinds of things you can bank on to be able to generate a prediction one is causality another is correlation so if you are trying to use models to predict the models represent the causal relation that exists and that helps to describe the underlying physical process for example the dynamical system that relates to the motion of the earth around the sun the dynamical system that relates to the motion of the moon around the earth this combined dynamical system we have understood very well and using it we are able to predict the lunar and solar eclipses to very high degree of precision so this dynamical system essentially kept has captured the causality principle that underlie the motion of the moon around the earth and the earth around the sun so likewise every model be static be dynamic be deterministic be stochastic all models in some sense encapsulates some form of this causality principle momentum is concerned energy is concerned these are all causality principles in the case of time series I derive empirical models autoregressive moving average models they are empirical models these empirical models in time series are essentially derived out of correlation so what is that we do we look at a time series you compute this temporal correlation we see how the temporal correlation decays with time if it decays fast the process has less memory if it decays very slowly the process has long memory mathematicians have already analyzed properties of several different types of time series models and they have cataloged and they have created an album if you wish of correlation structures the various models so given a time series data you compute the correlation structure of the given time series and compare it against the album and look at which one looks closest it may not be one it could be a subset of 2 or 3 you narrow down the window and then try to use each one of these models to be able to distinguish which model is better so what is the underlying theme to be able to predict either you need causality or correlation this approach to optimal interpolation rush on an ability to predict based on correlation. So what does it mean if two quantities spatially separated is positively correlated means what if the variable in one of the stations increase there is a likelihood the other station will also increase because there is a positive correlation if there is a negative correlated if one increases other will decrease so I can infer from the increase or decrease of a particular quantity in a given station and knowing the correlation I should be able to predict what will happen at the other station that is the fundamental principle that underlie predictive science based on correlation so fundamentally ultimately the aim of data simulation is to predict data simulation essentially tries to help you to fit the model to data fitting model to data is essentially model calibration so the forecast generated from calibrated models are better than the one generated from uncalibrated model that is why we do data simulation the alternative to that is to be able to understand spatial and temporal correlation structure Venus theory applies both to temporal correlation analysis as involved in time series analysis as well as spatial correlation analysis as would be interest as would be of interest in any geophysical science. So the metric C captures the natural variability of the variable of interest in the chosen geographical domain now so I have please go back to my to my original picture here I have a grid I have an observation stations so the C is the covariance among the observation stations but my interest are in computational grid for example if I have established an observation network the observation network is going to be fixed in spatial distribution computational grid depending on the computing power I can change the computational grid at well if I have a larger computing power I can have a smaller grid size and a larger grid number if I have a smaller computing power I may have a coarse grid and a smaller number of total grid points so computational grid there is no fixed value for that it depends on what else I am interested what kind of processes I am interested in analysis and so on. So now what is that we would like to be able to do we would like to be able to transfer the knowledge from observation network to the computational network that has been the theme in the successive error correction that we have been talking about in the last lecture as well iterative methods so the theme is very similar except that this is this new idea is the rooted deeply in the correlation structure. So if I have values in the observation network please recall our ability to transfer information from observation network to the grid network this is Rm this is Rm this is this is Z this is H this is H transpose this is H transpose. So I can go from one network another network by this interpolation scheme. So what is that we have done from the observation stations we can also think of having think of having a time series of values at the good point using this interpolation. So if I have a time series so let us fix a particular time noon January 1st I have M stations I have a H matrix that can interpolate between the computational grid and the observation network yes you may say hey if you interpolate it is not the interpolation is going to incur error yes it may I am cognizant of that but I am I want to be I want the reader to appreciate that I have the ability to lift the information from one network to the other network through HM H transpose. So let us pretend now I have a corresponding time series of the same physical vary a field variable of interest at each one of the n grid points the time series the is the same in other words at noon I have an observation station I at noon I have interpolated value along the grid noon of today 2 o'clock of today 5 o'clock of today every day so by hour by hour I have a time series going over let us say 50 years of data I can do that. Again I want you to recognize while the observation network is fixed the computational grid may be changing so if I fix the computational grid and if the computational grid embeds the observation network there is one way to be able to lift it from the observation network the computational grid. So once I have the same time series at the computational grid I have a vector x from the vector z this vector x it belongs to Rn vector z belongs to Rm if I have a time series on the grid I have I can compute its expected value the proper then I can compute the anomaly the anomaly is such that it is mean is 0 now comes the important thing let D be a matrix that captures the cross correlation between the grid variable and the observation the grid and the observation network. So x tilde is a vector that is defined on the grid x tilde is a vector so x tilde is a vector belonging to Rn z tilde is a vector belonging to Rm so if I multiply x tilde by z tilde transpose you can think of this as this is the column that the row there is an outer product matrix this matrix is going to be Rnm if I took the expectation of this outer product matrix that is D so what is D? D is a n by m matrix that relates to the cross correlation between the grid variables and the observation variables so this is the cross covariance between grid values and the observation variables. So C and D are going to play a very major role in our analysis now please remember C may be fixed in time because observation network once we establish a network we cannot change but D can change in time I am sorry the computational grid can change in time n can change in time therefore D can change in time. So how do you get from observation to C to D is to be able to elevate interpolate from observation network to the grid network this interpolation scheme there are several such schemes I have already talked about a bilinear interpolation that interpolates between grid and the observation network so we can use one of minutes. So what is that we have I have access to C now I have access to D C is the covariance of the given field variable of interest at the observation location D is the cross covariance between the grid and the observation network so you have there is lot of statistical computation so if you have a time series over 100 years if you have a time series over 100 years hour by hour minute by minute your dataset may be very large from that set dataset you have to crunch the value of the matrix C you have to crunch the value of the matrix D that could be done very routine calculation it does not take too much time here I am just trying to describe formally the notion of computing the elements of the matrix I want to reinforce that again so let us quickly run through this calculations let XK be the state variable vector of the same field variable at the grid locations at time K we may have a time so if Z has a time series there is a corresponding time series for X once I have the time series I can compute the mean I can compute the anomaly I can compute the cross product which is D that is what so there we talked about a concept here we talk about algorithms so concepts algorithm concepts algorithms algorithm for C algorithm algorithm for D or given now what is the statement of the problem let I am sorry there is a spelling problem here there has to be a T let the observational covariance C and the cross covariance D be known matrix C and matrix D be known so what is C and D represent C and D represents the stationary values of the covariance between observations and covariance and the cross covariance between observations the grid because the underlying process of stationary C and D does not change in time especially C and D does not change in time if you consider a long time series and so what a stationary means I want to comment on that little bit if the regime of the climate has changed the underlying distribution would have changed so what does stationary assumption means in practice we are assuming the regime under which the climate is operating has not changed statistical that is the idea so how do you know the regime we are operating has changed or not that is a different question we should have a long time series you should break the time series into a different parts we should calculate different quantities in different times and see whether these statistical quantities have changed over 100 years first 100 years second 100 years third 100 years first 50 years second 50 years first 10 years second 10 years so the Kedel variation century variation annual variation so one can do statistical test for regime changes regime shifts if one has access to a reasonably long time series in other words one can test the hypothesis namely if the underlying statistics is invariant or change so we so it all it all depends on how much data you have if you do not have much data you cannot even do that testing if you do not have much data if you cannot do that testing just play the Lord and assume it stationary so that these these are some of the key things that one has to keep in one's mind now so what does CND refers in some sense they refers to the climatology and that is the important thing here CND refers to the underlying climatology the stationary aspects of the climatology suppose a new year dawns January 1st 2016 today I have computed CND over the past years a new observation from my observation network arises on this new day these the observations available only the observation network but I would like to optimally compute the values induced on the grid X so I hope you understand what I am talking to talking about CND are known CND are based on the past values they represent the climatology a new day dawns a new day brings a new observation Z the new observation C is confined to observation location M of them but I would like to be able to elevate that M to N good points how do you do that how do you do it optimally so that the statement of the problem given a new observation Z and the climatological information in embedded in CND how to optimally compute the induced grid value X from Z so I know Z bar what is Z bar Z bar is a long term average of Z because stationarity I assume Z bar has stabilized so Z bar is in varying in time so Z tilde is equal to Z minus Z bar there is an amelie of Z with respect to the long term average Z bar similarly let X tilde be X minus X bar I know X bar because I have computed D with it I do not know X X is the one I want to be able to determine but instead of computing X I am going to compute X tilde so if I compute so computing X is equal to computing X tilde because if I know X tilde I can add X tilde to X bar to get X so I am going to work with anomalies so that Z bar be the observation anomaly on a new day let X bar I am sorry Z tilde be the observation anomaly on a given new day let X tilde be the corresponding induced anomaly in the grid my job is to be able to optimally determine X tilde from Z tilde knowing C and D knowing C and D please understand the background X bar is known we can recover X once X tilde is computed so we are simply going to concentrate on computing the X tilde anomaly so what is the optimal interpolation approach please understand this is one of the earliest known methods in predictive science the basic idea of this of the optimal interpolation is to express the analysis increment what is the analysis increment X minus X bar so X tilde I what is X tilde I X tilde I is the new increment at the location at the grid point I that is to be gleaned from the new observation I am assuming I can express my X I tilde as a linear combinations of the observation increments Z tilde so let me let me I want to make sure my Z tilde is not that is right the Z tilde so Z tilde is the vector of observation increments I am going to compute location by location grid location by grid location I is the ith grid location X I tilde is what I want to compute now I have to concoct a model that relates the known to the unknowns X I tilde is not known Z I Z tilde is known so I am going to confine my attention to the class of recovery process to a class of estimators where X I tilde is expressed simply as a linear combinations of the elements of Z tilde so I want you to think about that that is it so what is that we are going to do if I am going to have a linear combination I need to have the weights so let W be the vector of weights that are going to be used in the linear combination W's are unknown weight vector so given this philosophy of connecting the known to the unknown let the unknown be the linear combination of the known so I could express this as W transpose Z tilde therefore under what condition X tilde I will be optimal it will be optimal under the optimal choice of W vector so the whole problem now reduces to finding an optimal vector optimal weight vector W optimal in what sense again we come back to these squares both Kolmogorov and Wiener independently in 1941 they were separated geographically they did not talk to each other but they had come up with very similar ideas so the mathematical problem now reduces to the following find a vector W belonging to RM that minimizes the mean square error between the value of the increment at the I at the grid from the linear combinations because underlying quantities are all naturally random I have to take the expected value so the objective function here is the mean of the square of the error so X I is the I at the component of the analysis increment vector at a given time so all these things are done at a given time if you are interested in various time I have to repeat it at a given time so with the loss of generality I am assume K is fixed K the time is fixed so Z tilde is the vector Z tilde I is the I at the component of the observation increment for convenience we have suppressed the time index because we have fixed the time this is an this is an analysis being done at a given time so if you have a sub routine that can do this I can repeatedly use this for various times I hope the formulation of the problem is clear now look at this now I am falling back to least squares but I am falling back to least squares not with respect to static model or dynamic model but based on correlation structure cross correlation structure stationarity assumption and so on F of W can be now written as this because it is like A minus B whole square expectation operator I can pull it into each of the term expectation of the sum is sum of the expectations the first term is the variance of Xi expected expectation of the square of Xi tilde is the variance expected value of expected value of Xi tilde Z tilde transpose it is essentially the I at the row of D so that is denoted by D I star please remember D is the cross covariance between the grid and the observation location so I know every grid point will be related to every observation locations so here I would like to talk about a particular difference between Cussman scheme and other scheme in Cussman scheme what is that we assume given point the number of observation station that I can affect the given grid point are those that are lying within the radius of influence D that came in 1950s mid 50s in Venus time in 1940s 4142 they did not restrict the influence of one and the other they assumed everybody is going to influence everybody but they were they were interested they were measuring the influence through correlation and cross correlation so I the I at the grid point has a cross correlation with every observation station and that is given by the I at row D I star so that this now becomes 2 times D I star W now I would like to go back to the W is a column vector I want you to understand W is a column vector D I star is a row vector so D I star W I am sorry D I star W that is an inner product it is a scalar because one is the row another is a column vector now that last term is essentially W transpose CW you remember C the correlation among observation locations now look at this equation 9 equation 9 relates to the Ith row vector of D the entire matrix C and the variance of the field variable at the Ith grid point all of them are known the what is the only thing that is not known W now please also realize this F of W in 9 is a quadratic form so what is that what is the mathematical problem pick W such that this quadratic form is a minimum how many times we have minimized quadratic forms in this class million times so one is a quadratic variable another is a linear variable another is a constant so computing the gradient of F of W in 9 I am not going to do the arithmetic I very strongly encourage you to apply the principles from multivariate calculus that we have talked about the gradient is given by 10 the Hessian is given by 2C we have already assumed C is SPD so Hessian is SPD say if I equate the gradient to 0 given that the Hessian is SPD it must be a minimum because the function quadratic function is a convex function is a unique minimum so the solution of 10 is given by 12 let us look at that now C is the matrix C is a m by m matrix W is a vector which is m by 1 vector that must be equal to D I star transpose please remember D I star transpose is the Ith row let us go back to now D D is a n by m matrix therefore in the matrix B if I consider the Ith row the Ith row is the m vector because this is m therefore D I star is the Ith row D I star transpose is the m column vector so this is of the form Ax is equal to b where a is an SPD now do you remember this is a linear system with symmetric passive different matrix I want to solve this how many different methods we have seen I can solve this by Cholesky I can solve this by qr I can solve this by SVD I can solve this by iterative scheme such as Gauss Seidel there are ever so many methods I can also solve this by gradient method I can also solve this by conjugate gradient method now you can see the power of the mathematical tools that we have already developed that is the key we are looking at the foundational aspects of algorithms to do data assimilation no matter what variety of assimilation process we are involved in please remember this idea is extremely different from any other ones we have already seen yet the tools we have developed are very helpful computing the quadratic form computing the gradient Hessian minimizing the quadratic form solving the resulting equation by matrix methods by direct optimization methods those are all tools in your toolbox in fact I would like to remind all of you that is the famous saying if hammer is the tool you hammer is the only tool you have every job looks like a nail I want all of you to write this down and put it in your study if you have only one tool and that tool happens to be hammer what is that you can do with the hammer you can only hit so the famous proverb is if hammer is the only tool you have every job looks like a nail you can only hit the nail so what you cannot do depends on what you do not know what you do not have so larger your toolbox better days now please understand our toolbox has been filled with tools rich tools that can be used in solving problems therefore 12 is a solution of a symmetric passive definite system I can solve this by one of several methods I would like the reader to indulge in this process and convince oneself that I can solve 12 by one of many methods but now by repeating this process for each eye we can obtain analysis increment over the entire grid but now look at this now if I want to solve this so for every eye the left hand side remains the same only the right hand side changes so we are going to have a collection of n linear system with the same matrix C but the right hand side is different what does it mean if you compute the Choloski factor for C once I can use it repeatedly for every solution for various grid points so that is a computational advantage so we can solve this efficiently by using Choloski decomposition of C once and repeatedly using the Choloski factor to solve the grid variables at each of the n locations this method has come to be called this method has come to be called optimal interpolation in the area of geophysics there is a method called Kriging I am sure many of you who are in geophysical sciences could have heard of that Kriging is a method essentially an optimal interpolation method. So, Wiener's method have been applied to many many different fields of activity it has been applied under the camouflage of very many different names Kriging is one such name that has been applied in geology and geophysics Kriging is if you look at the mathematics of it Kriging is essentially Wiener Kolmogorov's optimal interpolation the person who popularized the application of optimal interpolation especially in atmospheric as well as oceanographic sciences is the Russian scientist Liv Gandine Gandine has published a book that is totally devoted to application of OI to solve several different problems of interest in climatology oceanography atmospheric sciences and so on and I would strongly recommend the reader to take a look at this extremely good book by Liv Gandine. Now I am going to talk very quickly about the extensions case 2 noisy observations in practice observations are noisy noise is unavoidable therefore my observation Z is equal to Z bar is the mean Z tilde as the anomaly until now we had only Z is equal to Z bar plus Z tilde now we have a new guy coming into the table coming into the game that is V I am going to assume is Gaussian or is SPD I am also going to assume that the natural variability in Z and the observation noise are uncorrelated that makes sense the climate does not care for the instrument you used to measure so V essentially comes from the measuring measuring process the measuring process is not or it does not affect the natural variability of a climatic system. So the cross correlation between the natural variability of field variable interest and the observations are 0 in this case I can now compute the covariance of since we have discussed many of these things in data I am going to hit all the major points so Z bar is Z tilde is given by this so its covariance is Z tilde times Z tilde transpose there are 4 terms the cross terms vanish because there is no covariance between V and Z tilde so we are left with covariance of Z tilde is C plus R now look at this now what is the role of R R increases the covariance earlier R was 0 because there is no observation noise observations are perfect this is the only difference rest of it all the same so wherever there was C you replace C by C plus R solve the problem. So again it is reasonable to assume the analysis increment is correlated with the it is reasonable to assume the analysis increment is uncorrelated with observation noise sorry sorry sorry uncorrelated and that is described by this so I can define D D is given by the similar formula I have an FW which is the weight vector so the whole thing I am simply again assuming the grid analysis increment is the linear combination of the observation analysis increment. Now how good this is the linear assumption you can change that but to get the ball started Kolmogorov and Wiener assume that the given increment can be expressed as a linear combination of the observed one so you can probably in a given situation you can try other combinations of the dependence of X tilde and Z tilde and do the analysis but the trouble is if the instant you bring in nonlinearity that is going to be computational trouble. So you have to worry about is the trouble worth it if you take the trouble and spend more money to solve the nonlinear problem is it going to improve your prediction estimates so these are all open questions I am not going to indulge in all other possibilities it is simply to provide you a new way of thinking about prediction. So if you consider FFW and again I have given all the details I would leave this as an exercise so this is the quadratic form you compute the gradient you compute the Hessian you can see wherever there was C C is replaced by C plus R so except for that difference there is not much so the optimal W is now obtained as a solution of this if you set R is equal to 0 I get the previous equation. So knowing so what is the fundamental idea knowing the correlation structure of the field variable we can comma this is lower case we can easily lift the information from the observation network the computational grid that is the that is the essence of this discussion this module is contained in chapter 19 where we have discussed this at greater length book by Louis Lakshmi Rahandal 2006 with this I hope we have given you an opportunity to develop an appreciation for and another way of thinking about prediction, prediction creating analysis how to transfer the new information and combined with the old information I want to talk about that part that part a little bit Z the new observation that is the new information C and D old information so in some sense you can think C and D as an equivalent of prior Z has a new new information maybe base is creeping in very quickly here there are two pieces of information I am trying to combine them I am trying to combine them so as to minimize the error in the estimate least squares comes in creeps in secretly so base comes in secretly least squares comes in explicitly you can see the commonality between various techniques even though the basic assumptions with which these techniques are developed are totally different with that we conclude our discussion on the optimal interpolation techniques thank you.


Good morning everyone, my name is Noah Jessup, the founder of Proof Group, but before we dive in today I want to feel some of the energy in this room. All right, so I'm gonna say network and you say network, network, network. Okay now with that same energy I want you to give a thunderous round of applause and a huge warm welcome to my friend, the one and only. So we've got a little QR code which will be on screen for you to scan and this is your proof of attendance. Okay, if you want you can take a photo of it and then scan it later if you want to do that or just scan it now. And I'm going to give some opening remarks. You know there's a saying tell them what you're going to tell them then tell them then tell them what you told them. Okay, so we've got a bunch of speakers today, we're going to go lickety-split through the whole thing. It's going to be almost like TikTok style but in person, okay, very fast and hopefully really good. So that QR code is also there on the monitors if you missed it so it's in the back in the white box if you need it. Okay, so today's conference what's it about? So there's theory, there's practice and then there's a conference itself. Let's talk theory. So in terms of theory, our new country is even possible. We started new companies like Google, we started new communities like Facebook, we started new currencies like Bitcoin and Ethereum, could we start new countries? That's the concept of the network shape. And I wrote a book on this idea, you guys might have heard of it, it's available free at thenetworkstate.com, v1, I'm going to put out v2, the hard cover, make a movie and so on, maybe you guys will be in it. And so this is pretty cool theory and here's a visual of that theory, here's a visual of the concept, if Bitcoin's a decentralized currency, the network state is a decentralized country, right, where it's got the population of a country but it's all distributed around the world rather than concentrated in one place just like the nodes of Bitcoin are all around the world rather than in one place. And how do you build something like this? Well you can actually, there's a path to get to the cloud country to go from not just zero to one but one to one million. Here's an example, if there was a Satoshi in Japan living in a building by themselves, if they can build a community of let's say 17 people and then 172, they start getting rooms together, start renting together, eventually they have enough money to start crowdfunding buildings or floors, eventually they have enough money in scale at 17,000 to get maybe little cul-de-sacs or suburbs or what have you and going up another order of magnitude, they're actually at the scale of a very small UN listed country and one more at one million, 1029,314 people, it's a cloud country somewhere between Latvia and Bahrain, in terms of its size and scale in population and income and real estate footprint. So this is the concept, nothing here violates any laws of physics, it's just using Internet technologies we already have like crowdfunding and social networking and VR and Zoom and all this type of stuff. But this is the theory and that's cool, but how does it work in practice? And so that's what really today's conference is about, how do we turn that theory into practice? And if you talk about practice, I'm going to introduce a new concept today which is the parallel establishment. So imagine a thousand different startups, each of them replacing a different legacy institution. So for example at the top, there's San Francisco and we're replacing San Francisco both with things outside it like cul-de-sac in Arizona and Prospera in South America and Cabin which is in Texas but also around the world and the neighborhood SF is actually fixing San Francisco for within SF, right? So you can have the Satoshi strategy of going outside or the Satyana Della strategy of reforming within, either Satoshi or Satyana is fine, as long as you're not Steve who says it ain't even broke, Steve Bomber, okay. So San Francisco, replace San Francisco with these startup societies, then the middle is Harvard, right? We're going to take out Harvard and we have Parallel Education, that's that synthesis which is K through 12 but it's also AI tutoring, the Teal Fellowship Emergent Ventures you're going to hear from some of the founders of these today. And then the last row there's another example, we replace Media with Parallel Media, it's Twitter and X, it's Substack, you're going to hear from the author of The Great Lady Wing today and many other people doing Parallel Media, okay. And so this concept of the Parallel Establishment, if you take up all of these new institutional replacements on the right hand side together that's a Parallel Establishment, they exist alongside the legacy in Parallel, they're gaining strength, they're pulling away users until they become the new thing, okay. So this is how we turn that seemingly impossible thing of building a new country, break into a bunch of individual startups and then aggregate them together. There's two parts of the Parallel Establishment, there's a Parallel Societies, okay. And these are the physical societies, right. These are the first part of today's conference is about these to show that this is actually physical and real, okay. You're going to see about a dozen of these physical startup societies, there's cul-de-sac in Arizona, there's Prospera as I mentioned in South America, there's Cabinet in Texas, but these are actually decentralized, they plan to do nodes elsewhere, that's just their first nodes, okay. They're all kind of network cities or network societies that are setting up little nodes around the world. And so this is how we build internet-first physical infrastructure, we've got internet-first communities that are recruited from the internet, these are the kinds of places cul-de-sac, for example, is like a remote-optimized city, like if you built a normal city with roads for the daily commute, what would a remote-optimized city look like if it was built for remote workers?  So these are the parallel societies, and the other piece of the puzzle are the parallel institutions, okay, so you can almost think of it as like a vertical strategy of building a new city in place, and a horizontal strategy of replacing media and education and finance, okay, and those two are complementary, the vertical and the horizontal. So the second part of today's conference is about the parallel institutions, here, you know, these are the new New York Times' and Harvard's and new Supreme Courts and Wall Street's, it's Internet-first versions of medicine and law and media and education and finance and even science itself at DSI. This example on the right is for parallel education, so Replet has 20 million Replet developers just transforming computer science education worldwide, synthesis, AI tutoring, so you'll be able to scale tutoring, and the Teal Fellowship, you know, Teal's Unicorn Success is awkward for colleges, we have the Teal Fellowship, one of the co-founders right here is going to talk to you later today. So that's Ethereum practice and they come together in this conference, and I'm just going to briefly say, you know, who the speakers are and then you're going to hear from the speakers themselves. So we're going to begin with five physical parallel societies, okay, Cabin, the neighborhood SF, Nomad, Praxis, and cul-de-sac. In many ways, there are different ways of materializing cloud communities onto the land, okay, and again, some of them are outside of SF, some, you know, neighborhood SF is within SF, and you know, they're complementary strategies. Then we'll hear for four more physical societies from Prospera, from Fractal, from Vibecamp, and from Spectra, and these are by, you know, founders of already built cities who have already had large exits, very, very credible people who have either built or in the process of building. We're also going to hear from three builders of houses, towns, and cities. So Bill Cover is building like houses. Shervin Pishfar, first investor in Uber, has built a town, and then Saphon Zengerly of Casa Roscombe has actually built entire cities in Africa, and he's going to show you those, okay. So, and those, the reason is, the reason those complementary, those complementary is like just like in computer science, you might have innovation at the level of the database, but then the higher level at the innovation of the web server, innovation at the level of the house is complementary to innovation at the level of the town, then you can build new kinds of towns when your house is, okay. After that, the third part of part one, more parallel societies, these are different, these are more digital and emerging, they're more like dows, you know, and crypto stuff, and you start to see how this space is converging. So that's MetaCartel, Coordinate, Plumia, Yaim, and the Pronomos Fund by Patrick Freeman that invest in these new societies. We'll also hear from Vitalik on Zizalu, his pop-up, not network state, but what we're thinking of as a network school, maybe a competitor to Harvard and Stanford and what have you, because it's actually already got a strong research vibe. Then we're going to go to lunch, and after we come back from lunch, you're going to hear from Glenn Greenwald, Pulitzer winner, you know, when that was worth something maybe, and then also from Ashley Rinsberg in a law in Newhouse on how the media, the establishment are basically broken and how they're broken in great detail, and you kind of need that because that's the criticism part of constructive criticism, and then the second half is the constructive part where we're actually building something, right? So you need both. Criticism, why is it broken, constructive, how do we fix it? So Nas of Nasdaily, Naseri Seen, and Dan Romero will talk about building new media and new social media to replace the old. Next we have parallel education, so we have, as I mentioned, Synthesis, and Michael Gibson, a TL Fellowship founder. Tyler Kohn will talk to you about Emergent Ventures. Amjad will talk to you about Replet, and you'll see how education is being transformed. And then we're going to talk about parallel laws, okay? So essentially what a better system of laws look like? The laws are broken in San Francisco, they're broken for AI, they're broken for physical security, and for second citizenship, and we need to fix them for building entirely new cities. So we're going to talk about new legal systems and how we get there. Penultimately, we're going to talk about parallel biomedicine, which is a subset of both parallel regulation and parallel science and parallel medicine. You're going to hear about a new biotech-free zone, a longevity community, and Research Hub, a friend of mine, Brian Armstrong, and how they're doing decentralized science and trying to change the incentives for science. Last, you're going to hear about parallel finance. That's another way of thinking about crypto. That's why crypto people are interested in this, because parallel finance is a crucial subset, but it's a subset of the entire parallel establishment. And it totally will talk about how Solana has essentially built a parallel banking system, and Solana Breakpoint, by the way, is tomorrow and the day after and so on, in this exact venue, so you can, if you want to stay in Amsterdam, you can come to Breakpoint. And so that's the solution is a parallel banking system, and then you're going to hear about the problem, which the Winklevosses will talk about how the current system has failed on regulation, Cody Sanchez will talk about it's failed on Wall Street, and you'll also hear about how it's failing on currency and basically everything else. So in the beginning, let's get started.


So nine to five is your label.  All my first shows, the paper came from me working a job, all the early Martin, me working a job, and my pops working his job and putting his paper in. The homies working their jobs and putting their paper in.


A fiery horse with a street of light, a cloud of dust and a hearty high of silver, the long ranger. With his faithful Indian companion Totterl, the daring and resourceful masquerider of the planes led the fight for law and order in the early western United States. Nowhere in the pages of history can one find a greater champion of justice. Return with us now to those thrilling days of yesteryear. From out of the past come the thundering hoofbeats of the great horse Silver. The long ranger rides again. Al Starbuck undercover man for outlaw Miles Hobson had obtained the information he'd been ordered to get. He sneaked away from the loading area of the Overland stage and freight hauling company in Gateway City and met in the darkness with Chick Fallon, Hobson's right hand man. Chick? It's like Miles was told. There's a train of 50 to 60 freight wagons and about five passenger wagons leaving for California as soon as they can find drivers. Now the boss here will take any drivers he can get. Tell Miles if he'll send a few of his boys down here they'll get jobs. A few hours later in a hideout far from town Chick Fallon arrived with the news given to him by Al Starbuck. The door to the cabin was opened by Mallow, Miles Hobson's young and beautiful wife. A girl who married him only after the threat of death to herself if she didn't. She was blank-faced as she greeted Fallon. Miles and the boys are in the next room. They're waiting for you. Is Pete Shelton in here too? What do you mean by that? Do you think I'm blind, Mallow? I still don't know. Never mind. Forget what I said. I'm here to see Miles anyway. Miles Hobson, who had been playing cards with four of his men, rose as Chick entered the inside room. Chick? What's the word? Overland's sending 60 wagons to the coast including three wagon loads of guns and ammunition. There'll be no true best court until the wagon train reaches Fort Taylor. Listen, Miles, they need drivers for their train before they take off. By five or ten more, all things three of our men could get jobs. And if they did... Hold it right there. If they did. Ha-ha. They would have thought I had. What is this idea, boss? You poncho, you casco, and that's go-to. Go to the Overland outfit and get jobs as drivers. You handle those big wagons, don't you? See? And the mules, horses, anything. You do. I know you can. Well, we know that the Overland trains stop for the night at the entrance to the pass that goes through Sandstone Gulch. That's on the second day out. You're right about that, Miles. Al told me that. Everyone knows that. Well, if you three men could stampede the horses on the picket line, every man in camp would be chasing them. And meanwhile, you have the three wagons hitched up to the gun wagons and galloped away with them. See? See? That is a good one. It could be done. Sure it could. And you'll ride right to the end of the Gulch where Run and Wolfe and the Apaches would be waiting for you. Take the gun right to the Indians? Running Wolfe? Sure. We're going to steal the guns we sell to them. But if it's a 60 wagon train, we give them the guns for nothing. What? Nothing, Miles. But that's crazy. The money from so many guns would make us rich. The Indians wouldn't have enough gold to pay us. They'll pay us in another way. And they'll make us all rich by doing it. Oh. As soon as they get the guns, they'll ride back and use those guns to wipe out the wagon train. When that's done, we move in, pick up the gold that's on the train, and anything else that's small enough and rich enough to carry away. You'll kill everyone on the wagon train? Yeah. Why not, Pete? Only the Indians will do it. That's right. We can get away and get rid of any stuff we have to sell before the soldiers ever know about it. And I'll make sure that Run and Wolfe doesn't spoil our game. I may even talk them into fighting the soldiers. With guns like we'll give his people, they might wipe out the army, too. That'd be funny. Hey, boss. I think someone's listening at the door. Yeah, I see. And I know who it is. Wait here. When Miles Hobson walked into the outer room and closed the door behind him, he started to walk slowly and with a menacing air towards his beautiful young wife, Malo. I thought I warned you never to eavesdrop. I thought I warned you not to... Stand right there, Malo. Hey, what the... Don't move another step. Gun. Malo, where'd you get that gun? From inside the chimney where you'd hit it. Stop pointing it. If it goes off... Yeah.  And that may be the best thing that ever happened. Oh, you're crazy, Malo. Crazy.  But I'm not crazy now. Oh, now look, darling, I just... I can stay there.  Planning to have Run and Wolfe and his apaches slaughter out on how many people? Hundreds, perhaps. And you're planning to have them murdered because it'll help you get rich. Oh, come now, darling. You're all wrong. Really, you are. I'm not. Oh, but you are. Oh, nice work, Pancho. Grab her arms. How did you... How did you... Now, take that gun, darling. Don't struggle. You really fell for that old trick, didn't you? Don't. Don't you're hurting me. Help me. Someone help me. Don't worry about that, aren't you? Well, I'll show you a thing in miles. Come on, darling. Take that gun away from her, chick. Sure. Here, let me have it. There, that's it. Oh, my God. I'm sorry, my boy. Come back, Pete. All right. Pancho Acosta, grab her tire up. No. No. You come on. Please. Hold him.  Hey, what's this all about, Miles? What happened? It's not what happened. It's what might happen if I leave her here. What do you mean? She heard what we planned. She has a conscience, suddenly. I don't want to kill her, but I can't chance leaving her here. You mean she's coming with us? Yeah, with you, Pete, and me. We'll manage to keep an eye on her, see that she doesn't escape. The next morning, Casco Mead, Pancho, and Ascota prepared to leave for Gateway City where the Overland Stage and Freight Hauling Company was located. Hobson gave the men final instructions, concluding... And we'll be waiting for you two days after you leave at Rockpastry. Our Overland Wagon Train stopped there to prepare for the journey into the mountain country next morning. You'll take the wagons then. You have that straight? See you, Miles. And go ahead. Good luck now. Be careful. Pete. Yeah, boss. Get Miles Horses. Bring him here. Oh, yeah, boss, right away. Chick. Let's go inside and escort my wife out here. My loving, dutiful wife. You're not gonna keep her gagged? No, not while we're riding the back trails that I've planned taken to the Apache country. We'll be around her at all times. Three of us. There's no need to gag her to keep her tied either. There's no place she could go if she did escape. She doesn't know this part of the country at all. So we'll let her ride free and have nothing to worry about. A few minutes later, the three men, Hobson, Chick Fallon, and Pete Shelton, rode westward. Their horses formed a moving wedge around Molo Hobson as eyes straight ahead in lips firm. She moved with them. Whitey Kelso, hiring boss at the Overland Freight Company, was almost delirious with joy when he signed on Casco, Escoda, and Poncho as drivers for the great wagons. I've landed just three drivers in order to get this wagon crane started. Now that I have experienced men like you, we can set off in the morning. Bandy! Bandy! What is it, Bandy? Spread the word around. Tell passengers and drivers and guards we got the men we needed. We're taking off in the morning. The next morning, Miles Hobson and his men broke the camp where they had remained for the night. They continued their journey towards the Apache country. Once more, they formed a wedge around Molo Hobson as they rode. And at the same moment in Gateway City, the great wagon train of freight and passengers started toward the west and the gold California. And that evening, Miles to the west, Miles Hobson and his party camped for the night. It's a good spot. It's near the Apache camp. I'll see you running wool from the morning and get them ready for the attack. Chick, help Molo from her horse. We'll take turns guarding her while the others sleep. The next day, Miles Hobson met with Chief Running Wolf and laid down the terms for turning over three wagon loads of guns to the Apaches. Running Wolf gravely considered the matter and gave his answer. Uh, may agree. You give guns, we use guns. Catch them wagon trains. At Sandstone Gorge, we'll get the wagons to you there. We'll have engines. Many hundred engines wait there. When guns come, we take them. Kill people with wagon trains. That's the idea. And I'll tell you what else I have in mind. Pete Shelton was supposed to be watching over Molo Hobson as Miles Hobson and Chick Fallon ate that evening. When they weren't looking, he whispered, I'll be on the third watch. I'll take care of them. Be ready. And that night, on the third watch, Pete waited until he heard his two bosses asleep. He crawled to where they slept, his gun butt ready. He brought it down on their heads in rapid succession. Then Pete ran to Molo. It's all right. I did it. You didn't kill them. No, I stopped it killing, even for those who deserve it. It's so good of you, Pete. When I was alone with you today and asked you to help me, I was afraid... I'm frightened. The only reason I came along, ma'am, I wouldn't let myself have any part of helping Indians murder my own people. I've done a lot of things, but never that. I thought you might feel our way, Pete. But we haven't time to talk. Let's grab the horses and get out of here, this way. A few minutes later, Molo and Pete Shelton galloped away from the camp, heading eastward. But unknown to them, the man's anxiety to save the girl was to be his undoing. He had failed to tie the wrists and ankles of the two leaders, and the blows had only part of the effect he had expected. Within a short time, both Miles Hopson and Chick Fallon were on their feet, conscious. Miles, she's gone so speed. So the horses. And look, the hoof prints lead out here. You see? They're heading back east. Yeah, toward the main road. Miles, they're going to try and warn the wagon train. That's it. You're right. I should have been wise to be. He didn't go for this job at all. Go for Molo. He doesn't like the way you treat her. Don't look at me like that. I'm sure of it. Snake, I'll kill him.  But they're gone, Miles. They must have a few hours' lead on us. They've gone by the main trail. The only place they can be heading to can go by the prints, and that's what they do if they want to stop the train. Yeah, but I know this country. You see that rise over there to the east? Yeah. What about it? By riding hard over that rise, we'll reach the main road in a couple of hours. By staying on the trail that they took, it'll take them four to five hours more to reach the same point. You mean we'll be waiting for them? Yeah. And Chick, huh? We're going to kill both of them. The curtain falls on the first act of our lone ranger adventure. Before the next exciting scenes, please permit us to pause for just a few moments. It was dawn when Miles Hobson and Chick fell in after riding hard and fast over the ridge, came to the spot where they hoped to intercept the couple they were pursuing. An hour passed before Chick saw the riders coming from the west. Here they come, Miles. Yeah, I see them.  Yeah. We'll move in on them. Get up there. Get up there. He'd sheltered in riding in advance of Miles Hobson, saw the horsemen coming down from the ridge while they were still half a mile away. He recognized the horses and the men who rode them. They were sunk. They came to and got here before us. Oh, no. Yeah. Molo, turn around. Ride fast up into those hills. Do as fast as far as you can. I'll try and hold them off. You come with me. You can't stay here. I'm going to do it. I'll try to get them before they get me.  I can't know, but...  If I escape, I'll go after you. Only save yourself first now. I shouldn't, but good luck, Pete. I'll try to find help. Get up, Miles. Molo turned her horse, scalloped through the brush and set upward into the hills. Pete Shelton rode his horse among a group of trees and waited for him. A few minutes later, Chick and Miles Hopson came along the main road, riding cautiously. Miles, I think they saw us. They stopped. Yeah. And it'll be somewhere around here. Look. Over there in the trees. A horse. Let's go. Come on, get up there.  Oh, oh. Gonna make a fight of a chick. Yeah. It's no good, Pete. We'll take you, no matter what you do. Come on, big old man. Hey, that was close. Too close. We'll have to walk in on the Miles. Right over to this side of the road, behind the rock. Yeah. Get up there. Come on. Watch out.  We'll have to be careful. Start shooting, Tech. Hopson and Palin, fighting with Pete Shelton in the brush, were unaware that Molo had ridden away into the hills. She rode desperately without let up for hours. Hours in which every sound behind her seemed to be the one that would herald the approach of her murder-bent husband and his partner. Suddenly, her horse stopped, whinnied in a pitiful manner, and sunk to the ground in exhaustion.  The sight of the mask on the face of the first man, and the fact that the other rider was an Indian was too much. The nerve-wrought girl moaned and fainted beside the horse. The lone ranger dismounted and hurried to the girl. She fainted, Toto. Ah, and look, he must have been horse-all sweat. Yes, he seems to be exhausted. Perhaps the girl is lost. Do that, Toto. Now try to revive her and learn what it is that brings her up here. The lone ranger used the medical kit from his saddlebag to revive the girl quickly. She was in terror at first, but the soothing words and manner of the masked man soon calmed her. After a long period in which she said but little, her brain became alert once more, and she blurted out the story of her flight and the reasons behind it. The lone ranger tensed as she finished. The running wolf and his Indians are getting ready to attack the wagon train. Yeah. The train stops at the pass at the entrance to Sandstone Gardens. That's 20 miles from here. Puncho and Escoda and Cascore to stampede the horses during the night. Then they'll drop over the wagons and deliver them to run in wolf. We must do everything possible to stop that. I'll take you on my horse, Mrs. Hobson. We start the main road now, King of Sunny. At once, Tutto. Mrs. Hobson gave me a good idea where Hobson and Fallon caught up to her and Pete Shelton. They were right there first. The last rays of the sun revealed all the lone ranger had to know when he, Tutto and Mrs. Hobson reached the main road. Two men were in the field away from the road digging a hole in the ground. There was a body beside them. Oh, it's Pete. He's dead. Who are those two men? Not my husband, the chick-pallet. More scuffle, Fallon. Easy scuffle, easy Fallon. Tutto will help you to get down, Mrs. Hobson. Tutto and the lone ranger assisted Mallow from Silver's back to the ground. As the lone ranger dismounted and joined the Indian and the woman, the two men digging put their spades aside and raised their hands. I don't assume we have no guns. See, a man's dead. We have no guns. We're burying him.  This woman is a friend of the dead man. Look at him. They killed him. Kill him. Please try not to cry. There's too much to be done. Where did you men come from? With the Overland Wagon train. It passed here an hour ago.  We're supposed to go ahead and meet the train. At the pass to Sandstone Goche. There by now, it passed here an hour ago. Ah, soon it'll get real dark. You're right there at once, Tutto. You too, Mrs. Hobson. I'll help you on my horse. Thank you. Come, Tutto. There's not a moment to wait. TGC to be caught. TGC, Tutto. Come. TGC, Tutto. TGC, Tutto. Come. TGC, Tutto. Those are the most young old people. The lone ranger, Tutto and Mrs. Hobson arrived at the widely extended Wagon train camp early in the evening. Two men stepped out of the darkness and covered them with rifles. All right, Mr. Up with old men. New trains and raise them high. We have them high. Mr, where's the leader of the train? What are you, caretas? I have come on a matter of life and death. I must see your leader at once. Why? Apaches. They're planning a raid on your train. Thought that my Indian friend would bear me out here. He's going to raid. Well, don't just stand there. Come on. I'll take you to the man in charge right now, Whitey Kelso. Right this way. Whitey Kelso in charge of the drivers and the expedition was unbelieving at first. But he was a veteran of the West, and his memory was a storage place for names and the deeds of men. He recalled hearing of the lone ranger and Miles Hobson. Miles Hobson, huh? I thought he escaped in the Mexico years ago. Well, he's here now, not far away. And his men are in your camp, ready to work against you. The filthy varmints. That is, if what you say is the truth. Well, let's find out, Kelso. Let us stampede the horses after the camp is asleep. Why don't we hide at the picket line and see if they do? Well, that's a sensible thing. Get your men down there now and place them around in spots where they'll not be noticed. I'll do that, stranger. I want to be with you, because there's more to this than just the stampede of horses.  We've at least five hours before their attempts are moved, I imagine. Sure. Camp doesn't get quiet till after midnight. Fort Taylor is about 20 miles to the west of the gouch. Pa will ride around the gouch and go to the fort. He knows every path and shortcut. Let me get there, maybe four or five hours. Be back with soldiers by sunrise. Kelso, we must take every precaution to prevent injuries to your people. It was after two o'clock in the morning when the three crooks, Kasko, Poncho and the Scooter, made their move to the lines where horses and mews had been tied. As they neared the spot, they saw shadows everywhere, but none that moved like men. This is going to be easy, I think. It's not going to be easy until we get to the gouch for miles and running wool power. Watch out now. Kasko is right, Poncho. We have the gun wagons all hitched up without anyone seeing us. To get away, we must first ampead the horses. I don't think you're going to do that.  Ampead the horses. The lanterns were lighted and played on the three men. Look, all around is men with guns. Yeah, you didn't expect us, did you? If we did, we'd have used guns ourselves.  We ought to do that now. Not now, Kelso. There's a law to do that. And don't forget we have bigger game to look after now. Yeah, you're right. We still have to worry about those apaches whether they get the guns or not. They keep them waiting till daylight and riding those wagons as we plan. If we do things in the right way, I think we'll have no trouble. Miles Hobson and Chick Fallon on their horses beside Chief Running Wolf were getting anxious. The stolen wagon trains were hours overdue and they feared now that their plot had been thwarted. Chick talked across Running Wolf to Miles Hobson. We should have kept looking for Marlowe. Hey, look, here they come. You see, Chief, just like we promised, the three wagons. Well, now. And it's all right, too. See, Pontius driving the first one. And sure, that's Costco and Escorto and the other two. You see, Chief? May see. Now you go, lead wagons here with guns. Sure. Come on, Miles. Hit it, boy. Hit it. Chick Fallon was the first to reach the wagon driven by Pontius. Pontius, what kept you? Been waiting for hours. Everything all right? See, see, I think so. You and the boss go to the back of this wagon, please. Quick, please. Let's see what's back there, Chick.  Are the guns falling out, maybe? The bandit chiefs rolled to the back of the first wagon. Oh, oh, oh, there. Gasco, what's back here? We are, mister. Hey, what the... Hey, welcome.  Why, you... No, Miles! Hey, who shot him? Hey, did that? How'd you ask for the same tone? No, no, get your hands up. Forget about the guns. I'll get them up all right. Oh, my arm. Well, a nice trick. Look, the wagon's full of men with guns. The other way is our tool. We made your men drive us here so we could take the two of them. I'm laughing because there are a thousand Indians up there. They'll ride down after hearing those shots and killing... That is not so cheap. Don't push me with that gun, senor. I will not try to run. You see up on the hill, senor? Up where your Indian pals are hiding? Do those look like Indians to the up there now? Well, I'll be... Miles, look. Oh, my arm. It's soldiers up on the hill. And down on the road. We didn't move toward the place where you people were until Tonto told us the soldiers are ready to ride in on you and your Apache friends. Soldiers want you and Hobson for gun smuggling and murder. Stop it. This happened. Did... did Molo do this? Hobson's wife? No. She's back in our camp safe, though. She'll get a marriage annulment once she tells things to the court. But who did this to us? The masked man who shot your pal here. It was his friend Tonto, the Indian, who got the soldiers and told us they were ready to make the Apache throw down their guns. By golly, they did, too. Hear that? Means the Indians are giving up.  Well, let him tell you himself. He's gone, Whitey. He and the Indian rode off. Well, dog gone. Here he saved a few hundred lives, and he rides off before we can say thank you. And that's the way he's always been Whitey, I hear, tail. Yeah. And maybe, Fallon, you can figure for this time that we're talking about the Lone Ranger. This is a feature of the Lone Ranger Incorporated, created by George W. Trenville, produced by Trenville Campbell Muir Incorporated, directed by Charles D. Livingston, and edited by Fran Stryker. The part of the Lone Ranger is play...


Mulan, a film that came out in 1998, Jesus, I was of the five years old, a time before the beard. I remember Mulan releasing though. So I guess I was pretty active still and I was like, yeah, movies. And then the Disney nation attacked and started giving us modern covers of these movies. What was the first one? Was it Jungle Book? No. Cinderella? No, I'm pretty sure it was Jungle Book. Okay. Well, either way, I've avoided most of them. I think what about Snow White? That came first. Have they done? Yeah, I've done that yet. They probably will though. Yeah, I don't think. Do you think they're avoiding that one? Because isn't she saved by a kiss from a prince? Whatever. Oh, I have to change it to a family member again, like a sister. Oh, yeah, if it was a lesbian kiss, it'd be all right. Yeah, I'm not against it. So I always felt The Lion King was the end. I was like, right, you guys, that's it, you've gone too far. It's over. But then Mulan happened. And there's just all kinds of controversies with how this film was starting up, like people talking about it and different things happening. And then COVID happened. So it couldn't come out in theaters.  Isn't it like you couldn't get the streaming service on its own, but you have to pay extra to watch this one as well. Yes, 30 bucks, I think it was. Who the fuck's gonna do it? I don't know. Proconsumer, everyone. The thing about this is that we won't get the real numbers for how it's doing from these things. They don't release them, right? So we'll just have to go with whatever it said, but oh, it was great. It was successful.  You think like it would stop them? It's not gonna. Lion King was way too successful. It made like a bazillion dollars. So all the money will watch anything. I'm pretty convinced that your kids do. It's one of those things where they just they just think of the original while watching it. And they're like, this is great. Sounds like Star Wars. Speaking of that process, we're here today to watch Mulan 98 and then Mulan 2020, just to see how they compare 22 years apart. I wonder if anything's changed. Oh, I'm sure that as time goes on and we learn more about the craft, we can hone our skills and it's only getting better and better. Yay. Isn't it wonderful? We live in a world where most movies are great. Yes. Like wait a minute. Yeah, that's that's about it. Um, it's everybody got Mulan one. Derek, we can call them Mulan one. I've got Mulan one. Is it all ready to go? I am indeed. I have got the Mulan one. All right, go. How exciting. I'm very excited. Remember when China wasn't shit? I don't. Like aren't they restricted to like a two child household? I don't think that exists anymore. Yeah, I don't know. The incredibly benevolent, benevolent, tyrannical, totalitarian communist government are allowing you to have more kids now. Yay. Well, I guess you guys are not getting any Chinese sponsors anymore. Yeah, animations. I'm already thinking we need this in live action. What are you guys? Yeah, well, they're never going to build a real massive great wall of China. Wow, what a trick. That is an unhappy bit. He's like, thank god my man bun is still here. That's got a 20, 20 years up a rope bag. I was supposed to say like, huh, what a weird hook. Oh, at this point, you're like, okay, now it's time to go for knives. Oh, no, how'd you get in there? Where are your grappling hooks? Oh, there's that's boss man, right? This is, this is Alex Jones. Now all of China knows you're here. My children aren't going hungry.  That was a quick cut. Well, this is the thing that got no time to lose. This film is an hour and 27 minutes. Impossible. No one can get through the great wall. It's Batman's Uncle. Little brother. Oh man. How everything flows when it's all drawn. I miss it. Not only is this the beloved family pet, but this is China. So he's also emergency rations. Oh my God. No, he's just dead. And then the chicken. This would be seen as insulting the Chinese today, shitting all over their beliefs. The matchmaker is not a patient.  How recent. Oh man. Once Asian women hit, you know, 40 is just what happens, you know? Oh, this cricket under the water for five minutes to see if he's lucky. These are like the two evil arms from that James and the Giant Peach movie. There's three of them though. And then there's an old one. We don't talk about her. Wow, Mary Sue. So if there's anything wrong with your measurements, just let us know before you go on out. Be great.  Yeah. Okay. They're all this is the Twitch thought Academy. Is that a cricket on your ass? He looks like a Simpsons character. She's eaten several people. If you don't get a husband, then you become my dinner with Chinese. We'll eat anything. We cite that. Oh my God. Reminds me of Toy Story 4.    Oh, my God.  This way. I need you to wipe off my neck sweat. Remember to get in between the folds. Or else I'll just have to start again in two minutes. Oh my God. No, don't do it. Take that back. One moment. I just want to put a little lord in for you. Why you clumsy? She's like a Simpsons. Why you little? This is probably for the best. Oh, no. I think it's going well. Don't care. Everybody just standing outside. Put it out. Put it out.  You made it. Oh, that was the stock sound. You will never bring your family honor.  Coming from you. It's just the creature.  I think we need a sad song now.   It looks like a horse. You kids today with your new values. Okay. At this point, it'll be like, maybe you should pursue singing. Pretty good. Actually, everybody in town should do that. Yeah, you guys, not bad. Oh, two face. Wow, yellow face.  You gotta keep polished. I'm a really short people. You done with your song, honey? A lot of people would like to hear that. One man from every family must serve in the Imperial Army. He's like the Lee family and half the village steps forward. Report tomorrow to the Wu Xiang camp. Yes, sir. Report tomorrow to the Wu Xiang camp. Report tomorrow to the... His staff is tiny. I cut my finger. So when I was young, I thought that this was him pretending to die, like practicing on dying.  He tried to get out of service. Like, oh, I died. I was like, oh, yeah, that's right. He's an old buddy.   I know my place. It is time you learned yours. Wow. Yeah, Mulan.  What happens?    Oh no, not German. Anything but German. Don't touch me. You don't get it up anymore. Sorry, blame the Huns. Yeah, what am I supposed to do?   It's like some 80s montage music. I was gonna say, yeah. Music feels out of place, but at the same time, I'm cool with it. Will you replace your father in the army? No. Your hair has your power. Tie it back with the rain. God is gone. She has the force. Grandma's force sensitive. Grandma had you know it.  She's like Batwoman. Oh my God. Just like women. They're cleaned. Oh, this sort of proves my point. And sisters. Grandma looking spicy with that hair down. No, no, no, stop.  Yeah, best character.  Your great granddaughter had to be a cross-dresser! Oh my god! No! Your misguidance led Fartane to disaster Yeah, thanks a lot Oh my god Yo, Rocky! Wake up! You gotta go fetch Milan! I can't remember, does he accidentally kill it or something? Yeah I'm not even gonna pretend to know how that works Yeah But just so we're clear, that is murder there, right?  An all-cost mis-man Decides to take a little drag show on the road Oh no What do you mean a loser?  Me or you?    Please don't kill me, this is a kids movie Tell your emperor to send his strongest armies Yeah, but this is old Disney, they killed people I know, that's what I miss How many men does it take to deliver a message? Why? Oh, that guy looks like he's been having the meth Oh yeah, I think I've all been having the meth How have they been winning?   Hey Who's that They're gifts He brought us the complete DVD box That collection of friends To honor the fall family It's probably racist jokes and friends now It's cancelled Cheers No that too It's even older My lawn Does Mulad live here?  No Would you like to stay for dinner? No Would you like to stay for dinner? What? Mulan do you not see that? Oh it's the rabbit dog Oh no Well well The best thing you think we need a new vision of this Absolutely that was so bad To be fair if we did it again But without the things people like It'll be a hit The first thing we're moving The stupid annoying dragon character No one liked him That movie was so good I forgot how good it was It was a reminder of That Do we have to watch the bad movie? I mean Oh man I'm so tired I think I have a heart attack Ending credits music to the Chinese movie Need a saxophone solo I don't know Matthew Wilder did that Well it's Matthew Wilder too To be fair I'm really glad Stevie Wonder Didn't have to see the Mulan remake What fun Yeah that was awesome I expect the next one to be just as fun It probably will but in a different way It's 30 minutes longer So it's gonna have a lot more 30 minutes more fun Well I'm glad that's all we agreed to do today So So everyone ready?  They'll add in magic But they'll take out Mushu And add in that thing No it's great the way that it sits there like an object So far we're still missing All like six of the companions We'll see how we do it Is Mushu gonna be a girl?    But how can you fight it?


Okay, so our next presentation is going to be a reading from the books, three part series books called murder incorporated empire genocide and manifest destiny. I'm just going to read a little bit about them here. This is a internationally celebrated black writer and radio journalist author of six books and hundreds of columns and articles. He's an organizer organizer and inspiration for the prison prison lawyers movement, former member of the black Panther Party and supporter of his radical move organization. He spent the last 30 years in prison, almost all of it in solitary solid solitary confinement in Pennsylvania is death row. Millions of people in this country and around the world, believe moving it is innocent and of course I do. Stephen Victoria is a film director and producer is documentary films include long distance revolutionary. A jury was moving out of motion. What a great film and one bright shining moment the forgotten summer of George McGovern. He is also co-authored with moving up this new three parts series titled murder incorporated empire genocide and manifest destiny. Thank you. Thank you. And we have an endorsement from them and I'm going to read that and then introduce our reader. So, I'm Stephen Victoria says, mumia bull Jamal and I were honored to include two passage or passage from our murder incorporated book series. We're only reading one here will post the other one. The importance of the Cold War Truth Commission can be found in two places. First, right in their very name, truth, offering sanity to a truly insane chapter of history. Secondly, more truth found in the hearts of the folks who have undertaken this invaluable project. And our reader today will be Alexis Green. She is a California State University Chico alumna from Los Angeles. She is currently on a mission to write, illustrate and distribute educational coloring books. As the founder of AJG books, a graphic design and book publishing service. All right, can everyone can everyone hear me? Yes. Yes. So good afternoon or evening good evening everyone. So, as Miss Brunke said, my name is Alexis Green. I'll be reading an excerpt from Murder Incorporated Empire Genocide and Manifest Destiny by Mumia Abu Jamal and Stephen Victoria. A segment from book three perfecting tyranny chapter six stasi 2.0. Citizens commissioned to investigate the FBI on 8 March 1971 110 miles away from media Pennsylvania, a suburb of Philadelphia, Muhammad Ali and Joe Frazier were pummeling each other in Madison Square Garden. The eyes of the world were focused on the fight of the century. But that evening in media, a sleepy Hamlet residents call everyone's hometown, a daring break in was underway at a small FBI field office. More than 1000 classified break. Oh, sorry one 1000 more than 1000 classified documents were retrieved by a small group of passionate American citizens who were active in both the civil rights and anti war movements. Arden dissenters against the want the wanton murder in Southeast Asia, as well as a domestic terrorist actions under foot by US intelligence community hostile to the recently slain M okay civil rights black liberation as well as other groups fighting for justice. This tight group, known as the citizens commissioned to investigate the FBI knew it was time to do some to do more than protests. As Ali peppered smoke and Joe with the barrage of stinking jabs and Joe countered with the historic left hook that sent the Louisville lip crashing to the canvas.  Among the documents reports that democracy now was one that bore the mysterious word coin tell pro one of the activists slash burglars john rains acknowledges the group, the group consisted of whistleblowers before whistleblower had entered the lexicon. He also knew citizens had to do something bold, something intrepid. Yes, something intrepid because Hoover, besides being diabolical was also untouchable. He had presidents who are afraid of him rains explains. Nobody was holding him accountable and that meant somebody had to get objective evidence of what his FBI was doing, get their files and get what they're doing in their own handwriting. At the time Betty Medsker Medsker was a reporter for the Washington Post. Shortly after the break in she received the cash of documents from Liberty publications with a letter from the Citizens Commission to investigate the FBI, explaining when where when and why the stash of evidence was collected. Medsker was shocked and stunned by the trail of criminal behavior perpetrated by the Bureau, and it quickly became apparent to the reporter that Hoover's FBI was especially fond of conducting quote blanket surveillance of African American people unquote. The documents detailed surveillance programs in nearby Philadelphia as well as various national programs. The documents also revealed that the illicit spying and counselor intelligence was ubiquitous throughout the community. Churches classrooms stores down the street just everything. In fact the FBI was grooming informants in every walk of life, all of them targeting domestic dissenters. The revelations also expose the FBI is directive to, quote, enhance the paranoia, unquote, of anti war activists through harassment intimidation rumors lies and invent an installing agent provoc, provoc, provocators everywhere. The surveillance, quote, the surveillance was so enormous, unquote, explains Medsker that it led various people, the various people, rather sedate people in editorial offices and in Congress to compare it to the Stasi, the dreaded secret police of East Germany. The media whistleblowers protected their anonymity for more than 40 years, forcing the press and public to focus on the substantive content substantive, substantive content rather than the worn out and predictable debate over whether the burglars were treacherous will know treasonous or not. As was the case with Daniel Ellsberg, and the release of his Pentagon papers just three months later. On that fateful night, Frazier narrowly beat Ali, and while the two warriors nurse their wounds in a building anchored between 7th Avenue and 34th Street, each of eight other warriors set up shop in a Pennsylvania farmhouse and dropped a dime on the bruise ugly and illegal operation. The closure of Hoover's massive and secretive kelp pro coin tell pro hijinks, along with his iniquitous violations of civil civil liberties, helped pave a way for the notable church committee, headed by Senator Frank Church of Ohio. Idaho, that investigated the entire spectrum of us intelligence operations. In fact, the church committees damning report triggered various congressional intelligence oversight committees, including the House select committee on assassinations, as well as the defense surveillance court, or FISA, which as we've seen sort of kept us surveillance in check for a short time. As expected, control by FISA waned as the various agencies kicked back, and then the subsequent reform met reform measures, dramatically dried up with the election of Ronald Reagan. On the 9th of March in 1971 in the quiet suburbs, West of Philadelphia, eight courageous men and women with ice in their veins decided to hell with civil obedience and put everything on the line in an audacious move to alert their fellow citizens that treachery was under foot in a move that defines self sacrifice. These eight unexpected swashbuckling activists bring to mind the essence of William, counselors words when he spoke of the tragedy, courage and death at Kent State University. These were his words, the four who died here, the nine who were wounded here, they did more for their country than all the Nixon's and the Agnews Agnews, I believe, and the Reagan's could possibly do. End excerpt. Thank you, Alexis.


Some of you may be familiar with the US Institute of Peace Conflict Curve that you're seeing on the screen at the moment. Much of what we do in this course and much of our dialogue will have to do with what you see on the right hand descending part of that curve. The curve itself is kind of a heuristic device that is something we use as a good discussion springboard which may not in itself reflect reality. In fact, my friend and colleague Andre Bartoli has critiqued my use of it before by saying this thing is upside down. In fact, if you take this parabola and make it much more the way real conflict operates, it ought to illustrate that coming out of intense violent conflict what we have is a very uphill journey through peace enforcement, peace keeping, peace building, ultimately. What I want to do is to start at the apex of this and move down the right hand side and draw attention to some very, very discrete categories ultimately landing on the one which occupies the most of our time, strategic peace building. The first, peace enforcement has come to mean how we engage that process often without the will of the parties. That is that the violence has gotten so bad on the ground that an interposition of military force is often considered necessary. Peace keeping is the process of cooperating with the outcomes of a signed peace accord in which military forces or the forces of the combatants themselves have found ways to separate and create a new demilitarized space where the fighting is dramatically curtailed if not stopped. That's both an outcome of a political dialogue but also creates space for greater political and societal dialogue and potential success for peace building. Then lastly, as you come to the bottom of the curve, you see the conditions for strategic what we'll call peace building and that of course will occupy the bulk of our time.


5. Keywords to increase your confidence in the classroom as a teacher Many people choose teaching as a profession, but not all of them feel comfortable and confident in the classroom. Unfortunately, students notice this lack of confidence quickly and once they do, they lose their trust in the teacher. As teachers, we all want to have successful and engaging lessons which give us confidence. Thus we can say confidence and effective lessons are interrelated. Confidence breeds effective lessons and effective lessons boost our confidence. Anyhow, confidence is not gained immediately after a teacher enters a classroom. This may take time to build and for this one should be very hardworking and persistent because if after several lessons you feel your students are bored or you cannot achieve the lesson goals, there is no way you can feel confident. During my time teaching, I came to realize and single out 5 keywords to become more confident in the classroom as a teacher. This post was written by our ITTT graduate Anna Hitchie, Preparation. The first and perhaps the most important thing is how well you are prepared. A lot of teachers don't put enough effort into their lesson planning and end up feeling nervous about being asked questions from the students. This is one of the main causes for teachers to lack confidence in the classroom. Spend a decent amount of time preparing for your classes, especially in the beginning. This starts with setting up a detailed and organized lesson plan, including the student and teacher goals and things that could possibly go wrong plus suitable solutions. A TEFL certification course covers all of these aspects of lesson planning. Panic As the Greek proverb says when at a loss, as to how to go on, cough. Even if you are well prepared, your students' curiosity and creativity may lead to questions you aren't prepared for. This happens more than often and is no cause for panic. Simply pause for a minute and think about the question. Once I found myself in a similar situation when a student asked me to explain why the participants should choose to sell the company over taking a loan from the bank during a Business English class discussion. I just tried to explain my personal point of view because truly I did not know the answer to this question. Later, when I was doing my 50 hour course in teaching Business English, I learned that, in a Business English class, the teacher does not have to be knowledgeable about the field of business but should simply focus on teaching English. The truth is, there will often be questions you won't have an answer to as a teacher. And that is okay. You can admit that you don't know the answer to that question and promise to find out before the next class. Enthusiasm Interestingly, even when the objective of the lesson may not be that interesting to students, if the teacher shows enthusiasm, their energy catches the students and they become interested and attentive. For example, I taught a lesson once with a lot of enthusiasm and it was a successful class. The students were active and listened carefully. A little while later, I had a fever and felt terrible but had to deliver the same lesson to another class.  It's true what American psychologist Wilbur J. McKeechee noted. Probably no one thing is more important than the teacher's enthusiasm and energy. Feedback While it's usually the job of the teacher to give feedback to their students, it's also necessary to realize your own strengths and weaknesses every once in a while. There are many ways to obtain feedback about your lessons and teaching ability as a teacher that will help you improve and feel more confident in the classroom. At the end of a semester or English program, you may give your students a short feedback form to complete anonymously. You may also ask your co-workers and boss for feedback about your own teaching skills and ways to further improve. Never be afraid of negative feedback but take it and turn it into your strengths. You are surely also going to receive positive feedback which has a boosting effect on your confidence as well. Appearance Last but not least on my list is appearance. As we all know from our personal situations, you feel the most confident when you feel comfortable and satisfied with your appearance. Wearing neat clothes, a new hairdresser and new way of doing your makeup can be an instant confidence boost that works wonders. Are you ready to teach English abroad? All these keywords above help to improve the teacher's confidence in the classroom and lead to effective lessons with your students. Apply now for your TEFL TESOL certification course and start teaching in a matter of months. Speak with an ITTT advisor today to put together your personal plan for teaching English abroad. Send us an email or call us toll free at 1-800-490-0531 to speak with an ITTT advisor today.