Right. Hello. I'm Brett Halpern, the Scientific Director of AI Horizons Network, and this is our weekly AIH in Semihar series. Today, we have Jungo Tassai from our University of Washington talking about low-resonance, low-resource, deep entity resolution with transfer and active learning. Sorry about that. Jungo is a PhD student in CSU University of Washington, advised by Noah Smith, and he works in natural language processing, machine learning, and this is from ACL 2019. So Jungo, take it away. Okay. Thank you for the introduction. All right. So I'm presenting low-resource, deep entity resolution with transfer and active learning today. I originally presented this work at ACL 2019 in Florence, and I conducted this research while I was an intern at IBM Research Alamedin last summer, and this is showing work with Kun, Sairam, Yunyao, and Zushin from the IBM Research Alamedin. Okay. So here's the contribution of our work. We propose a deep learning-based entity resolution model that allows for easy transfer learning from high-resource to low-resource scenarios, and we also establish an active learning algorithm to further adapt the transfer model to the target scenario. And lastly, we provide extensive empirical evaluations over benchmark data sets and demonstrate that our system achieves state-of-the-art performance while using only an order of magnitude for your labels. Okay. So first, background and introduction about entity resolution. So roughly speaking, entity resolution or ER is the task of identifying different presentations of the same real-world entities across different databases. So for example, we have citation records in the ACM database, and we also have citation records in the Semantic Scholar database, and we're going to find which record in the ACM corresponds to which record in the Semantic Scholar. Now, here's another example. We have Twitter users and Facebook accounts in the world, and we want to know which Twitter user corresponds to which Facebook user, and why do we want to do this? Applications of entity resolution include knowledge-based creation, text mining, social media analysis, and also ironically, entity resolution or ER is also called in many different ways in literature, such as record linkage, merge curves, and entity matching. But the fundamental problem behind these problems is pretty much the same. Okay. So, well, you might think ER can be simply done by just looking at string similarities. However, it turns out the world is very complicated. There are many traditional challenges. Well, several challenges in entity resolution. First, we have name ambiguity, such as Michael Jordan in the basketball and Michael Jordan in machine learning. And this is very challenging. For example, when you disambiguate Chinese names in science papers, because there's many overlaps. There are other problems like data entry errors, missing values, and abbreviations. And we have to know, for example, ACL stands for association for computational linguistics when we deal with scientific papers, not Boston city limits, etc.  We always get these different entities like the music festival and the soccer league. And we have yet to solve this problem when such a solution when we do entity lookups. Okay, so in literature, there are two major strands of models when solution. One is rule based systems. And the other one is learning based models. And in the rule based systems, we define similarity functions between strings to make matching decisions of entity representation. And on the other hand, learning based methods train statistical models on the training data, such as SBM and decision tree and apply it to any evaluation data you want to use your answer solution models for. Okay, so in this work, we focus on the machine learning based approaches. In particular, we focus on recent deep learning based solutions. So these models have the benefit of avoiding the need for defining features for every single answer solution scenario, unlike other machine learning based methods, because we use distributed representations instead of feature engineering. However, deep learning based models require many labeled examples to perform outperform other learning algorithms, such as SVM and naive base. As you can see in this plot, only after we get enough labels does the deep learning based method plotted in blue here. I'll perform the others. So to address this issue of data hungryness. This work establishes a novel framework for lawyers so statement solution. So now before discussing approaches, we formalize the problem of answer solution. So given two sets of their recollections from two databases. The one and the two, we classify each pair, you want to need to in the Cartesian part of the one cross the two into matches and no matches. Ford, you want to need to is represented as a tuple with attributes as, as you can see in this table. So in the, in the case of citations, we have several attributes, such as author title and year and using these inputs. We want to identify the same entities across databases. And those two databases even be to can be the same single database in which case we have the special case of answer solution, which is called duplicate detection within a single database. Now, conventionally, we solve this problem for solution by two steps. The first step is called blocking where we reduce the Cartesian product by filtering out obvious mismatches. Because the Cartesian products is too huge. And we want to make it track double. And for example, we can eliminate tuple pairs of papers that have different year attributes. And the second step is called matching where we classify the remaining pairs in the candidate set after blocking to identify actual matches. And our work focuses on this matching step and fix the blocking strategy in each ER scenario, regardless of the methods we use to. So this ensures that we make fair comparisons across different matching methods because we use the same blocking strategy regardless of the method. Now, a framework for low resource deep and solution consists of two overall approaches. The first one is transfer learning, where we develop a deep learning model that allows for transfer learning from a source scenario to a target scenario that has no labeled data. We can simply train a deep learning and solution model on the source data set and then use the same network parameters for the target scenario. And active learning target scenario, a small number of informative, informative samples. Now we first present our transfer learning. So we take a similar deep learning architecture to Moodleville and others 2018 to compare a pair in the candidate set after blocking. So for example, tuple A comes from DBLP and tuple B comes from Google Scholar. And we want to compare those tuples across these two databases, DBLP and Google Scholar. So for each attribute, such as the author attribute, we construct vector representations by using bidirectional GRUs on top of the FASTX pre-sharing vectors. And the FASTX vectors are obtained from subword representations, which is particularly important to address the problem of out of vocabulary problem that appears frequently in databases such as proper nouns and technical terms in these databases. So for instance, we get vector representations for allenturing for tuple A and we also get a vector representation for tuple M for tuple B by the same bidirectional GRUs. And these representations are reflective of subword information. So we can make sure that these words are, even if they are out of vocabulary, we get proper vector representations. Now once we get attribute vectors, we compare the two tuples by taking the absolute difference between these two vectors. We make these comparisons across all attributes, not just the author, such as title and year in the example of citation genera. And once we get those vectors, we add those similarity vectors to represent the overall similarity between the two tuples. And this addition operation is critical because it ensures that dimension, the final dimension is the same regardless of the number of attributes that we have in the scenario. And this allows us to transfer the network parameters between scenarios that have different numbers of attributes. So for example, Google Scholar has full attributes while the Quora scenario has a attribute such as the publisher name in addition to author names and year. But we can still transfer all network and readers between these two scenarios without any modifications in terms of the architecture. So finally, we pass this similarity vector to the feed for the matching classifier and predict a match or no match. And we can train this network by simply maximizing the log likelihood of the label training there. Now we can apply the domain adaptation technique for transfer learning from computer vision literature in addition to these simple building blocks. So in particular, in addition to the matching classifier, we pass this vector to the feed for domain classifier as well. And importantly, we create a gradient reversal layer between the domain. And this ensures that the domain classifier is trying to distinguish the source and the target scenarios while the rest of the network is trying to fool the classifier, meaning that it is encouraged to develop domain-dependent representations which are useful for transfer purposes because they don't distinguish between different scenarios. Can I ask a question? Yeah, sure. In the previous slide, you assume that the attributes in the two databases have been already matched in the previous one? Yes, that's right. Yeah. Okay. So in every scenario, you have to do sort of schema matching, right? You're right. But the target scenario could have different schema results, right? Yeah. Like I said. Okay. So, right. So, good. So now we present our transfer learning results. Here, we assume we have no target labels. So we can see that by adding the domain adaptation technique, we generally improve transfer learning performance on the target databases, DBL, PACM, DBLP Scholar, and Quora. However, there's still a huge gap between the transfer learning results and the results we get by training the network with all target labels. Okay. So remember that the transfer learning results, we don't assume any target labels. Now, this motivates us to explore active learning as a method to further refine the transfer model to close the gap between these, well, the high resource scenario and the low resource scenario. So we present active learning. Again, active learning further refined the transfer model by iteratively labeling informative examples from the target. But there are two major issues to achieve this goal. The first problem is that we need substantial labeled examples to tune the transfer deep learning model without overfitting to the subset of the labels. Now, the second problem is specific to the problem with entry resolution, which is since the distribution of entry resolution labels is skewed toward a negative or no matches. It is hard to find false negatives and to improve the recall of the system. Because of course we have way more no matches than matches when you compare different databases, even after blocking. And in order to address these issues, we propose an entity, well entropy based sampling method. So let H of X be the entropy of the prediction on input X given by the current model. Then on certain examples of size K can be defined as the set of pairs with top K entropy. We can manually label those uncertain and therefore informative examples for the model. And we can tune the current model to these new examples and repeat this process iteratively. So this is sort of the most naive way of doing active learning for entry resolution. However, the two problems we just mentioned still remain. So again, we need substantial labeled examples to the transfer to the transfer network parameters that manual labeling does not scale. And this tuning method will suffer a recall because of the nature of entry resolution labels. Now, in contrast to uncertain examples, we can also define high confidence samples as the set of pairs with bottom K entropy. And we can manually label uncertain and therefore implement examples while automatically label those high confidence samples by model prediction as a proxy. Now we can then tune the model to these examples and this repeat this process iteratively. So this solves the problem, the first problem we just discussed by adding high confidence examples with labels as, with automatic labels as a proxy. We can avoid overfitting only to manually labeled examples. But again, problem two supersists such tuning will lead to a model with lower resource or lower recall because the entry resolution examples are skewed toward a negative or no matches. So in order to solve this problem, we further have to divide high confidence and uncertain examples by the current model predictions. So in particular, we define high confidence positives, high confidence negatives and certain positives and uncertain negatives using entropy and the current model predictions. So these four classes respond to likely true positives, likely true negatives and likely false positives and likely false negatives. For example, pairs that have high entropy and are classified as positive by the current model are likely false positives. So we sample these four classes of pairs we just defined equally and tune our model to the sample of examples. So we later show that this sampling strategy with partitioning with respect to the four classes actually helps our active learning substantially. So now we present our results. We focus on the citation genre here because we have expensive benchmark data sets. So the X axis here indicates the number of examples we manually label. And the Y axis indicates the F1 score of the system on the same evaluation data. Now we see that deep entry resolution model we transfer an active learning, which is plotted in blue here, achieves the best performance with faster conversions as compared to the other machine learning based methods. And also the vanilla deep learning method auditing red here. And again, we see that deep learning model is better hungry and under performs SVM under this low resource setting where we only have 1000 labeled examples for the target. However, by adding active learning, we significantly outperform SVM. And in particular, the combination of transfer and active learning. The active learning alone already eos performance better than SVM and other machine learning algorithms we tried in the paper. But when you when we combine transfer and active learning together, this eos the best performance. Now you might say that SVM can also perform much better than this by incorporating some sort of active learning. Well, there are many active learning methods in literature for SVM. But our results show that deep intersolution with transfer and active learning even outperforms SVM with full training data. So this suggests that deep intersolution model with transfer and active learning is strictly better than the performance. Well, better than the SVM performance since the performance with a full bit labeled training data can serve as not sort of an upper bound. So the same patterns hold for other scenarios such as the core citation data set and we see a significant performance gain by transfer and active learning. We also test some models on other generalized incitations in the restaurant genre. We again see that transfer learning alone doesn't suffice eos a reliable system but when combined with active learning we get better performance. Now in the software software genre we again see that deep learning with active learning plotted in blue here achieves the best the best performance in a low resource setting. And we can see you can see more results in other genres in our paper. So now we want to give an analysis on our approach. We presented several approaches and we want to know whether how effective these approaches were. So the question is how important was our sampling strategy in active learning. So we compare different sampling strategies here. And the first strategy is to just to take top K entropy pairs and annotated them each iteration manually and tune the model to these manually labeled examples. So if we partition these manually labeled uncertain examples into likely post positives and likely post negatives. And instead of just sampling them we can equally sample them from these two classes right and then by doing this partitioning we get a performance boost. So specifically we see that recall improves dramatically while keeping the high precision. So by combining both partitioning and high confidence sampling or high confidence automatic labeling we just discussed we get the best performance both in terms of precision and recall. And this means that in addition to the partition mechanism we just introduced the automatic labeling also have to deep learning model to tune better without overfitting. So we can also look at the actual breakdown of the manual manually labeled samples using the goal labels. So when we do experiments we don't assume any goal labels but when we look at when we give an analysis we can use the goal labels. The partition indeed helps us find more balance samples here. But interestingly we sample more true positives. So ideally we want to find we want to find the force negatives and post positives here. But here by doing this partitioning mechanism we sample more true positives because we aggressively choose likely post negatives. But again these post negatives are generally challenged to find because of the nature of inter-resolution where the labels are skewed toward a negative or mismatches. So in conclusion our deep inter-resolution model EOS competitive performance to state of the art while using an order magnitude fewer labels. We also saw that transfer learning alone that is suffice to construct a reliable inter-resolution system. But when combined with active learning we get stable and high performance. And this work provides for the support for the claim that deep learning can provide a unified integration method even in lowest of settings without the need for future engineering for every single year scenario we have. And for future work we are interested in applying our methods to more complicated scenarios, genres and also knowing which languages. And we are also interested in applying the transfer and active learning frameworks to more problems than the answer solution. So lastly we thank Sid Muttagal, Vamsi Mendri and PbMoleCare for their help with this work. And I'm happy to take questions. Thank you. Thank you Joseph. Thank you very much. If you want to ask a question, please unmute yourself. This little red microphone icon at the bottom of your screen. And I see Hamid's already unmuted. So Hamid, you want to start? Yeah, yeah. So do you have, so can you use also this active learning method for fusing the entities? So so far you connected them, matched them, but then now I have to fuse them, right? You know, to take like attributes from different places that are similar and combine them. And that's a manual process that's very, very expensive. So can you use the active learning with your sampling to reduce the cost there? Can I use sampling of active learning to do sort of schema matching your question? No, no, the fusion part. So all you did was the linking, right? But at the end, I have to combine the attribute values from different places. And they're similar as well. And they combine them into one result. Yes, yes. They're connected. Got it. So in this work, we haven't tried it. We used the benchmark data sets that already have already done like the fusion process you just mentioned. But in principle, yeah, we should be able to do active learning or not just the linking part, but also the future part. Yes. But in reality, it's sometimes challenging because there's different types. So you have to tune the model well. But yeah, that's an interesting question. We've done it. We have done it. Yes. Yeah. Any, any other questions, please unmute yourself. Okay, I have one. So you were, you were matching across to publication databases.  Relatively similar data sources. If you did publications and resumes, I mean, the same information is there. Is it just going to be, is it going to be just like two publication databases or is the heterogeneity going to maybe. Yeah. Yeah, that's a good question. So one of the actual advantages of the deep learning methods is you don't have to do a feature and during. Well, you have to do, you have to tune the model, but we'll hyper, you know, tune the hyper parameters. But you don't have to find different features for different scenarios. So we hope that this method will work better when it comes to sort of more textual data. So actually, there's some cry work that showed that deep learning methods of a form other learning based methods substantially. When they work on some textual data. So instead of having these. Relatively strict sort of relatively structured data like titles and year and authors, we can have more textual data like product descriptions that can be a little that can be messy, that can be a messier. And we think that this method would work scale better to these highly textual data that relatively unstructured data. But that's sort of future future work and we are sort of lacking. Nice sort of empirical, well, benchmark dances right now, but it would be great if we can try on sort of even private data. If we can try that. So I got another question for you. Yep. Okay, so did you consider any kind of confidence is full as a few of the sources. So for example, say Google scholar confidence is a data person. So did I use confidence course to do for active learning or I don't know for the matching part for the matching part. So we didn't, I see. So we only, yeah, we train this model on the negative log likelihood. So that's sort of the only place where the probability came in. In the matching part in the active learning part we also looked at the confidence levels and certain examples. We are not making use on this course. Yeah, so in active learning part that influence of your sampling or, or you say, the expert on a look at, you know, high confidence versus the confidence and just disappear. Right, right. No, is it like automated or automated right so we use these. So, we have this transfer model and the transfer model gives you the scores. On the label, sorry, on the pairs that we don't have any labels for. So it's automatic. It's completely automatic. Now we can also look at the correlation between actual human human annotations. So humans can also give some confidence scores and we can also compare that with model predictions that would be interesting. Maybe in some cases it's very easy for them for the deep learning model, but it's very hard for humans or something like that. But we haven't done it. Okay, any other questions. If not jungle. Thank you very much for the, for the very cool presentation and the good slides. There will not be a seminar next week because we have the horizons. AI horizons network is part of a research week in Cambridge. We hope to continue the week after that. We're going to try to include also talks about data sets and tools that can be shared with our colleagues in the universities. So, stay tuned and we'll have an announcement out hopefully soon for the next seminar. Thank you. Thank you.


Welcome back to our lecture series math 1050 college algebra for students at Southern Utah University. As usual I'll be your professor today Dr. Andrew Misseldine. Lecture 14 is a direct continuation of lecture 13 for which last time we were solving systems of linear equations by reducing the associated augmented matrix via the some type of combination of three elementary row operations and we would use these operations to transform the augmented matrix into an equivalent matrix which was an echelon form. When the matrix is an echelon form it was a whole lot easier to solve perhaps using the methods of back substitution and in this lecture 14 we want to continue doing that but instead of being so mysterious about it like we were in lecture 13 we want to be very precise about how we make the decisions we do and thus presenting the so-called Gauss-Jordan elimination algorithm here. Related to this is known as the Gauss elimination technique sometimes called Gaussian elimination. Some people use those two terms interchangeably Gaussian elimination versus Gauss-Jordan elimination. For the purpose of this class I'm not going to enforce a strict adherence to one term or the other there is a slight difference in technique and I'll point it out when we get there but honestly whichever approach you would take isn't going to make much of a difference for you as you work with this method to solve systems of linear equations. So let's talk about the Gauss-Jordan elimination technique. So the idea is that we use this technique to solve systems of linear equations and we first do that by translating a augmented matrix excuse me we first start by translating a linear system into an augmented matrix like we did in the previous lesson. So for the sake of example consider the following augmented matrix. So we'll have entries three zero three negative six augment with 18 that's the first row the second row will be three negative seven sixteen negative five and then lastly we have three negative nine twelve and negative nine. So this is just an example matrix and associated to this would be a system of linear equations. The first equation would be three y minus six z is equal to 18 the second equation would be three x minus seven y plus 16 z is equal to negative five and then the last equation would be three x minus nine y plus 12 z is equal to negative nine. Remember each of the columns inside the matrix in the side the coefficient side of the matrix is associated to a variable the right side this augmented column is associated to the right hand side of those equations and this vertical line is exactly where the equal signs would be. So we've just encoded the linear system as a matrix. So this is what we learned about in lesson 13 and we're going to utilize this to help us to solve some linear systems much more efficiently. So the first step of Gaussian elimination is once you have your augmented matrix here you're going to begin with the leftmost non-zero column. This is what's going to become the current pivot column and the pivot column will be at the very top of this column. All right so when you look at this matrix right here you don't see any zero columns a zero column would be like zero zero zero it has only zeros inside of it. Okay since we don't have anything like that the left column is the leftmost non-zero column that's typically going to be the case. So this right here is what we refer to as our pivot column and it gets the name pivot because the rest of the calculations the row operations we're going to do in in short order here is going to be pivoting around the pivot position we're now going to introduce in two sides of the matrix. Now given our pivot column we're going to put the pivot position in the topmost spot that we can do. Right now that's the very top of the column but as we start to move to the right in our matrix your next pivot position can't be higher than the previous pivot position because we're trying to put a matrix initial on form so you take the top most spot that the pivot position can be in for the very first column that's non-zero that's going to be the very top. Now it's okay that there's a zero in that position you just can't you don't have a pivot in a zero column but the pivot position could have a zero inside of it that's okay that actually leads to the second step in Gaussian elimination here so the second step is that you're going to select a non-zero entry in the pivot column and you're going to move it into the pivot position and you will want to use your interchange operation to do that okay so looking at our matrix here there is in fact a zero in the pivot column we don't in the pivot position excuse me we don't want a zero in the pivot position ideally we would love a one but honestly any non-zero number will work for us so we have to put something non-zero in the pivot position and we can do that by interchange and how we do that exactly it doesn't really matter as long as you grab some non-zero entry and put it in the pivot position because it's a non-zero column there is at least some number in that column that's non-zero make that interchange and it doesn't really matter which one you do for the sake of this example I'm going to interchange the first and third rows so interchanging row one and three which I will typically denote using this arrow here just connecting the rows that we're swapping here and so if we interchange those rows we'll get something like the following the third row now becomes the first row three minus nine sorry three negative nine twelve negative nine again then the second row we didn't do anything to it so three negative seven sixteen negative five and then the first rows down at the bottom zero three negative six eighteen so we interchange the two rows but be aware that the pivot position is still one one the top left position there and the pivot position didn't move but everything moves around the pivot position as we were explaining just a moment ago okay now with your pivot position it's really nice if you have a one in the pivot position there like so that's what I was just saying earlier now it's not necessary to have a one but it's super super nice the proper gauss-jordan elimination technique would actually postpone this step until later but if we can get a one in here that's really really nice why might you postpone it well there's a lot of possible reasons like if you took like for example if we had interchanged rows one and two so what have we put this row actually in the first spot in order to get a one in the pivot position you have to scale the entire row by three which is does perfectly great right here you get a one but here you would get a negative seven thirds here you get a sixteen thirds here you're going to get a negative five thirds fractions are a nightmare to most college algebra students and so dividing by three just to get a one isn't necessarily the best thing to do we can actually talk about that in a later video in this lecture here we'll stick with this one for now the reason I actually grabbed the third row as opposed to the second row is I noticed that in the third row which was originally the third row it's now the first row everyone in the first row is divisible by three so if I were to divide row one by three I could get a one in my pivot position which is extremely ideal but I also don't get any fractions because everyone was divisible by three so if you divide the first row by three we get one negative three four and negative three now again getting the entire row divisible by a factor is not always the simplest thing sometimes you have to accept fractions the good news is that you can usually procrastinate fractions so that's another thing you know we don't like fractions sometimes we like to procrastinate in which case in this situation we do both and it makes us all happy that's perfectly great so now we get a one in this position that's ideal not necessary step three sort of like an optional step when it comes to Gaussian elimination if you don't do it now you can do it later many of us like to do it now but certainly not at the price of introducing fractions into this thing okay so then we look at step four once we have a non-zero entry in a pivot position ideally a one we can start using row replacement to zero out all of the zeros above or below the pivot position right so with this matrix there is a three below the pivot position we want to get rid of that this one's already a zero so we don't have to do anything with it the nice thing about having a one in this pivot position is that in order to get rid of this number you're just going to look at that number and pick its additive inverse that is in order to get rid of the three we're going to replace row two with row two minus three times row one okay now if this number is not a one you're gonna have to probably use fractions to make this thing work so again this is the procrastination of the fractions here if we can we like to avoid the fractions as much as possible having a one in your pivot position is super nice in that regard okay so in that the next step now we're going to do replacement we've done interchange we've done scaling now we're going to do replacement so we're going to take row one and times everything by negative three for convenience i like to take this entire row we times everything by negative three and i'm going to write a little superscript up here so for the first column one times negative three is negative three for the next one negative three times negative three is positive nine the next one four times negative three is negative 12 and then for the last one negative three times three is again a positive nine like so and so then i just write these little superscripts because i don't want to do too much in my head the more i do in my head the more difficult this can get but at the same time i don't want to write endlessly lines of matrices right here so these little superscripts have been a useful tool to help us do our math with fewer mistakes i'm not changing anything in the first row so we're going to get one negative three four and negative three nothing in the third row changed either zero three negative six and 18 there it's the second row that changes again i'm going to add these superscripts here three minus three is zero i get a zero below the one which is what i was looking for negative seven plus nine is a positive two 16 minus 12 is a positive four and then nine minus five is a positive four as well and so at this point let's see we use row replacement to create zeros and all of the positions above and below the pivot in the first situation you didn't have a pivot you didn't have anything above the pivot so we just did everything below and so next what we're going to do is we're going to focus our attention because with this pivot column we've now finished it we have a one in the pivot position we have zeros everywhere else that's exactly what we want to do next we're going to switch our attention to this sub matrix um looking at the sub matrix here where is the first we're going to start repeating we're going to start repeating the operations here so we now look at the sub matrix and we identify so let's read step five here i didn't do that yet consider the sub matrix by ignoring any rows or columns containing a previously used pivot position so we're going to remove this row remove this column so we get a sub matrix so then we're going to start step one again which remember because you can't see it on the screen right now with step one we're going to look for the leftmost non-zero column which is going to be this one right here and then we're going to put a pivot in the very top now it's important you look at the sub matrix because even though that this number here is non-zero I only care about these right here if both of those numbers were zero we'd actually have to move over to the next column to look for the leftmost non-zero column even if this one is non-zero it's only in the sub matrix the rows and columns that contain pivots we're ignoring as we go through this algorithm so this is going to be our new pivot position so let's put it right here and then we we're going to repeat steps two through five that is we repeat this whole process until we finish so I'm going to move to another screen so I have a little bit more space to work this thing out here if I copy down the matrix we had just a moment ago because it's now gone the first column was now reduced row reduced so we had the one zero zero the next row currently looks like excuse me next column currently looks like negative three two and three uh then four four negative six and then negative three four and 18 like so okay our pivot position now is going to move to the two two spot and some people like to write all the pivot pivot positions that we've used so far like I might keep a box in the one one spot now and focusing on the two two spot and I want to start row reducing the matrix there all right so I have a two in the pivot position I would love it if there was a one a quick examination it's like oh wow everything in the second row is divisible by two so I could actually divide by two and then row reduce the matrix in that way oftentimes as you see these problems we're going to connect matrices together with this little twiddle symbol here the idea is these matrices are not equal to each other because as you change the numbers that changes the matrix and a matrix is only equal if all of the numbers inside of the matrix are equal to each other but it is row equivalent as in we do row operations to change the matrix and that's how they're the same they're not equal matrices they're row equivalent matrices are just equivalent matrices for short and so thus we don't use an equal sign we use a little twiddle to suggest the equivalence there so this gives me a one in the pivot position and the next thing I'm going to do is I'm now going to use row replacement I didn't have to interchange anything this time because I had a non-zero entry in my pivot and I actually like that one because I could get a one there very nicely so next what we're going to do is we're going to get rid of the zeros above and below the pivot so I want to get rid of this negative three right here so I'm going to take row one plus three times row two so what this means is I'm going to take one times three it goes right here two times three gives me a six and then two times three gives me another six if I add those together it's going to get rid of the negative three but I'm going to back to that in just a second I also want to get rid of this three right here and to do that I'm going to take row three and replace it with row three minus three times row two so this gives me a three sorry a minus three a minus six and a minus six right feel free to use lots of paper here because these matrices can get big but this I promise you is a very efficient way of writing these things down so I kind of can't see that matrix there let's do try this again so I didn't do anything to the first pivot column you never that's never going to change for the rest of the problem next we're going to get negative three plus three which is zero four plus six which is ten and then the augmented column there six minus three is equal to three the second row doesn't change this time zero one two and two and then for the third row we have the zero then we're going to have three minus three which is zero and then we're going to get negative six minus six be careful on that one it's not zero that's a negative 12 and then you're going to get 18 minus six which is 12 like so so now if you look at the first column it's completely row reduced to one in the pivot position zeroes everywhere else then you look at the second pivot column there's a one in the pivot position and there's zeros everywhere else it's completely row reduced so with that now done we move to the next column over and look for a non-zero number in rows that don't already have pivots so that means our next pivot position is going to be this one right here three three and then we continue to row reduce this thing I would level one to be there so if I would divide everything by negative 12 so take row three and divide everything by negative 12 fortunately again there's no fractions here I did choose this example so that in the end fractions were never needed because I know many of us are deathly afraid of those fractions so if you divide negative 12 by negative 12 you're going to get a one if you divide positive 12 by negative 12 you're going to get a negative one like so and so again we still have our pivots in particular it's this final pivot that we're interested in but for the sake of illustration I like to put all of the pivot boxes there now that we have a one in the pivot position we got rid of all the zeros in the column other than that one which means we got rid of this 10 right here we can do that by replacing row one with row one minus 10 times row three so we're going to get a negative 10 right here we're going to get a positive 10 right there now for the second row we want to get rid of this two right here to accomplish that we're going to replace row two with row two minus two times row three so we have one times negative two which is negative two we take negative one times negative two that gives us a positive two and then we're going to add these things together and our matrix to then be row reduced at that moment so looking at the first row you're going to go one zero zero ten minus ten is zero then you get three plus ten which is 13 then for the next row you're going to get zero one zero because again two minus two is zero then you're going to get two plus two which is four and then lastly you get zero zero one and then we didn't do anything to negative one that time so looking at the coefficient matrix we now have it row reduced this matrix now is in row reduced echelon form that is the coefficient matrix right here and then once it's in row reduced echelon form this right here should be in fact our solution then fact that the solution to this equation to the system of linear equations you have three variables x y and z for which x should equal 13 y should equal 4 and z should equal 1 that solves the that solves the problem the system of linear equations we accomplish this using this method of gaussian jordan elimination so the idea of gaussian jordan elimination is that you use repeated uses of scaling replacement and interchange to row reduce the coefficient matrix until you obtain the row reduced echelon form and once this once the coefficient matrix has been row reduced to its r re f then the augmented column should bear the solution to this system of linear equations we'll demonstrate how to do this in a few more examples but this at least explains the gaussian jordan elimination technique how we can use it to row reduce matrices and solve systems of linear equations


This is Richard Rogers, who is a metals conservator. He's done some fabulous work for us with our astrolabe, which is going online to the Metropolitan in New York. So what have you done with the astrolabe? Well, we've generally cleaned it. As you know, there was a number on the back, which we identified the number, which we removed from there as a bit of disfiguring and put onto the bottom edge so it's a bit more discreet. And then there was some third-degree corrosion around the main ring there, which we cleaned off and treated. And also the black that was in the depth of the detail there, which was hiding the nice sort of scroll design going round the edge. Looks so nice. And then there's just a wax to sort of present it better and remove the blocks of paint that were round the edge. I think what's lovely about it is it looks like it's had some conservation of something, but it doesn't look overly clean. So it looks like an object. Yeah, I've kept it. Where its edges sort of didn't really work. Yeah, we haven't tried to posit it or anything like that. That's fabulous. Thank you for that. Okay, thank you.


Hi everyone Joe for jazby's case rakes.com coming at you with 2023 tops pristine baseball eight box pick your team number nine here on Tuesday two Tuesday the fifth tops pristine baseball eight box pick your team number nine Bryant last spot mojo if you got blaster five next to your name that means you won those spots in the in that blaster box filler so congrats the winners and thanks everyone else for grabbing your spot straight up I appreciate it all right and settle in ladies know this full case is going to take a minute or two big thanks to all who helped fill this break sort of an awkward pull to drag the camera back a little bit myself a little extra room here I mean listen Duncan that audit will still be there but there may be things you've never seen before in a group break that's why every break has the potential to see something brand new empty case doesn't seem like a lot of boxes and it's not only eight boxes but with the number of the sheer number of packs here that's what makes this break a little on the longer side but that's okay I don't think anything sold out after this so we can take our time got the sounds of us open tennis on in the background like it's on a couple Americans battling here got Tiafoe and Ben Shelton he's the young star I guess Tiafoe is not that old either but but technically Ben's the youngster he's the kid would be 149 mile per hour serves he's also up two sets to one we got another pick your team in the store ladies don't want to check that out you want to get your teams and remember keep the mind the promo tonight so you're eyeing a team in the next pristine don't wait to stack those cards are on top there don't wait grab your team to be part of the promo tonight so these cards right here that I'm sliding up and placing on top are the ones where the parallels are and this final pack that I'll rip in a second those are just the base cards although that's where the personal endorsements autographs can be if any cards back there and you there's a relic auto right down there too yeah hundred I don't I don't know actually don't know if those serve a return though but I don't know what the average serve is on on tour from for them for the men probably in 120s I 120s 130s maybe low 130s maybe you get to 140s I think he got up to 140 in this set got a Nolan aeronaut oh snap die cut those can be numbered and sometimes they can be autographed if they are autographed they're in those encased cards there's Michael Stefanik to 75 you can tell these are refractors now Xander Bogarts to 99 and Buddy Kennedy to 99 and behind Byron Buxton is your relic autograph and that's gonna be Jersey and auto Dylan Cease around the diamond Jersey and auto 54 out of 99 and that'll be for the Chicago White Sox Sal one that in the filler oh Shelton's up one nil one love in the fourth set all right you're in case cards Clayton Kershaw Dodgers that's gonna be for Ryan Larry Walker Larry Walker Cardinals edition going at 10 out of 50 that will be for the Cardinals Larry Walker played for the Cardinals yeah he played two seasons or season the half with the Cardinals at the end of his career all right well there you go Stephen Carney Cardinals our autograph is Shay Langaliers A's that's gonna be Brian to 99 there's Aaron Judge for the Yankees that'll be for James Mark Appel Orange for the Phillies John 25 out of 25 and Vaughan Grissom Justin Braves Eric Houston needs a little expose oh no wait Sal has the Nationalist in this one oh I'm sorry you were talking about Larry Walker oh yeah you did start with Montreal let's forget about that all right next box Rex it's officially chilly season rex saying because he's building a chilly display are you a bean or no bean chilly guy isn't chilly supposed to have beans in it is it chilly there's no beans I can't admit I eat a lot of chili so I don't know if I don't really know you love to eat a lot of chili if it's there I eat it it's fine not so we're not not chilies but like the chili dish where they that they haven't cook off where it's like a like a shoot with a crock pot with beans and ground meat and other flavors and stuff like that you put all that in there yeah I don't know if I just chili like I think Wendy's has chili by a cup of that and I don't know for that Jan what's up you found out that junior Bridgeman used to be a Louisville Cardinal and his ex MBA is second behind George Michael run as the wealthiest as second as the wealthiest what and Bridgeman has opened 260 fast food and other businesses I'm assuming wealthiest ex MBA player second wealth is easy really I can't be right for source Jan one of the Kobe Bryant guess he's not with us anymore but it wouldn't the Kobe Bryant estate probably be second wealthiest behind second wealthiest behind Michael Jordan it's a former NBA player Grizzleby thought it was Iverson I don't know everything has been a little loose with his money hasn't he was going to get like a $50 million payment or something for a shoe deal right right showing up at fanatic live events at the national yeah someone someone fact check Jan on that Jan and Rex and two guys that you need to you know fan check fact checked often they'll come up with some stuff and you're like wait what that doesn't make sense and it turned out nope not true I'll never never forget that there was a Corbin Carroll yeah what is this Jan you still have you still not said what list what what's what what your source is he's still Iverson stuff to Fort LeBron is second but you just said former NBA you know what what I don't know what Jan is trying to say no yeah you had to be there all right Johnny your refractor Johnny Benchin 99 for the Reds Christopher Morrell Cubs 25 Jordan Walker rookie refractor and a Greg Soto to 50 that's for the Tigers all right Devin Williams for the Brewers reveals a New York met around the diamond relic and autographs darling marté piece of lumber and auto going to going to Howard and the Mets there you are these here I guess I'll just leave these out here I'm gonna do a recap at some point all right you're in case cards at Stave Winfield Padres that'll be for John G we got Ian half what's the haps that's the 15 4 out of 15 Keith with the Cubs and more Cubs this time an autograph Nelson Nelson of Alaska is for Keith and we got a clay Holmes for the Yankees that'll be for James a Gunner Henderson blue nice 60 out of 75 for the O's that's for David and another Nelson Velazquez for for Keith and the Cubs I guess Keith you're starting your Nelson Velazquez PC whether you intended to or not all right another box Jason I think Taufel's gonna lose showings up 3 3 1 probably the racket come on man so much for him being the future of American tennis American men's tennis yeah I know it's gonna be Belton Ben Sheldon now sorry Taufel yeah no he's been playing well second round but then last two were the last quarterfinals at US Open in Wimbledon US Open quarterfinals obviously like right now and then Australia oh okay he's ranked currently number 80 yeah the French Open's kind of we clay's always weird none of these guys to have that much experience on it yeah there's a there's eight boxes in this figure team come on come on Taufel yeah just consistently and it's the wrong side he kind of looks a little like his like his smile kind of looks to look looks a little like Nadal doesn't it yeah I was just showing that swag he's like 20 on Florida he's feeling himself he's worried he's like Nadal's hot sleeveless shirt next box you got a Julio Rodriguez oh snap die cut and that was huge Taufel 3 2 rex thinks that maybe he needs to be a golfer where the name like T off oh ha ha oh can say go to 99 that's Devil Ray's edition that's gonna go to Tampa that's for James Brandon Woodruff Brewer since it's a 75 and gold Santiago Espinal for the Blue Jays to 50 and behind Jock Peterson is your relic auto and that will be that will be for the Blue Jays Jersey and auto Matt Chapman Toronto Stephen Carney with the Blue Jays 85 out of 99 and you're in case cards that'll be John Carlo Stanton Yankees that'll be for James Starley Marta blue for the Mets Howard to 75 the autograph is Jermaine Palacios that's for Detroit Francis with the Tigers will count T mojo and J J Bladay for the A's Brian K Mookie Betts 35 out of 75 Dodgers Ryan Gansby and Zach Thompson is your autograph that's gonna be for Stephen and the Cardinals alright another box so fan nation has a story about Bridgeman is off course success according to this article that I'm looking at here on a wealthy gorilla calm richest NBA players in the world this is a recent article September 2023 bridgeman is third on the list Michael Jordan magic Johnson junior Bridgeman then LeBron I think Jan got the numbers a little mixed up but the gist of his point is still there I wouldn't have known I would have known that it's net worth almost 600 million dollars started with a Lakers enjoyed a sexual career as a player his impressive net worth came following retirement from the sport and career as a business man setting a bridgeman foods in 2016 he serves all serves on the PGA board of directors as well as the board of governors to the Natesmouth basketball Hall of Fame since 2010 yeah oh does this guy he is 69 years old yeah he's on his fourth on the list in his 30s yeah wait till he starts doing business stuff yeah right and that basketball those basketball teams like are like a billion dollars now so I don't know about Brady Rex where that's just a bad basketball list but Brady's Brady's got to be one of the top I mean in reality it's actually random soccer players that are probably gonna be tops talked on that list Christiano Messi David Beckham you know guys like them are at the top the sheer number of endorsements global endorsements that they have is kind of crazy alright during this is a junior bridgeman old basketball purpose from the 70s early 80s to late 80s actually during the off seasons of his playing career Bridgeman worked and learned the business model of Wendy's fast food restaurant franchise then after retired he invested in the franchise and eventually owned 100 Wendy's and Chili's restaurants before selling them in 2016 as president and CEO of Bridgman Foods Incorporated in 2017 Bridgman became a bottler for the Coca-Cola Company in 2018 signed a letter of intent to buy bottling operations in Canada in December 2020 he bought Ebony and Jet those magazines are 14 million dollars at the magazine's declared bankruptcy and then in March May of 2022 an investment firm co-founded by Bridgman now it's the firm partnered with Ball Corp. construction operate the legendary operating integrated secondary alumina aluminum mill in Los Luna, New Mexico he's all over the place in 2018-2022 Alabama Governor K. I've announced that man a capital partner to the guy that firm that he co-founded would invest in a bottling facility to be located in Hope Hall Alabama owned and operated by the affiliate of man of beverages and ventures all right next box Bryce Harper oh snap Sheldon's up 5-2 now yeah yeah I just blinked and it was just yeah it was just 3-2 and all of a sudden it became 4 and then 5 just like that Buster Posey to 75 going going gone insert that will be for Francis and the Giants oh the winner of this is playing no that would be right that would be like the changing of the guard right there yeah we got a gold Kyle Stowers to 50 that'll be for David and the Orioles the wizard Ozzie Smith to 99 for the Cardinals and Freddy Freddy 1975 the 1975 will color match with the blue for my boys and blue Gamsby relic and autograph is Tony Gonsolin get well soon Tony's been having some arm issues some elbow issues that's gonna be for for Gamsby go bounce back you know like most of the time pictures for an all-star one you don't drop off that but off a cliff like that not at his age so there's a cool wit Maryfield that will be for the blue birds that's gonna go to Stephen Carney Hosell two bays red one out of five for the Astros Howard all aboard the Big Hit Express on a two Tuesday then we've got going going gone big boppy David Ortiz that's for Michael P won that spot in the filler as to 75 we got Pudge for the Marlin Stephen Carney brand Crawford gold 39 out of 50 for the Giants that's gonna be for Francis and Christopher Morel orange 23 out of 25 for Keith in the Cubs right halfway through the break four more box to go another what 30 minutes to go Dodgers played an early game today actually not looked at any of the other scores it looks like the Philly shut out or the Padres set out the Phillies Padres three hit the Phillies they were they were hot too for an attest crushes crush the Homer in this one blue jays beat the A71 Springer singles in two extending the blue jays lead Rockies beat the Dimebacks 3 2 Kyle Freeland throwing six solid innings in that victory he improves to 6 and 14 Astros beat the pounded on the Rangers 14 1 in a key divisional matchup the Rangers were super hot look like they went super cold Royals beat the White Sox 7 to 6 it was a Boc off a Boc off for second time this season opposing pitcher Bocs in the run that's a thicker card there was that a one I don't know we're gonna find out okay ahead of ourselves show Cardinals beat the Braves 10 to 6 Nolan Gorman hitting well met beat the Nationals 11 to 5 Peter Lanzo with his 42nd homer of the season Yankees beat the Tigers 5 to 1 Giancarlo Stanton hits his 400th Reds beat the Menor 7 6 and that was on a walkoff as well Dodgers fell to the Marlins Brian Delacruz breaking the tie with a home run Ryan Yarbrough taking that loss in extras raised beat the Red Sox 8 to 6 Renlau hooks a three run walkoff homer for the raise in the 11th that's that's always a rough one Brewers beat the Pirate 7 to 3 Carl Santana Mar canna cap off a six run fifth for the Brewers twins be the Guardians 8 to 3 Donovan Solano breaks the game open with the bases clearing triple and the only game in progress right now is Orioles at Angels 4 to 3 it's the bottom of the ninth and those are gonna try to walk it off as well Nolan Aronato oh snap die cut and there it is Ben Cheldon beats Francis 10 seed unseeded Ben Cheldon beats 10 seed Francis Tiaffo who graduates him good good guy Tiaffo done Cheldon moves on all right we got Steve Garvey orange to 25 Greg Maddox purple for Justin to 99 and there's Calricken Jr the Iron Man is 75 for David do I think the Braves will win the World Series specifically the Braves we've got a great shot at it they're a very good team but it'll be plows kind of a crap shoot so you don't know it's a super fractor ladies and gentlemen and it's Aaron judge all rise James who got who won a spot in the blaster break one of one the Yankees from that blaster break and gets the one-of-one Aaron judge patch auto that is hot the popular demand three-color patch on card auto one of one man that is nice James all aboard the big hit express that is nice Austin Riley Braves everyone's just stunned into silence no one's saying anything in the chat Jonathan India blue that's for the red that's gonna go to Jake that's the 75 got Kyle Stowers rookie auto for the O's that's gonna be for David there's Reggie Jackson for the A's that'll be for Brian Kay there's Corey Lee Astros 18 out of 50 for Howard and Cleveland this is for you Jose Ramirez 43 out of 50 Guardians no reactions from this huh very quiet in the chat right up there I guess everyone's just stunned into silence that is nice all right three a box is to go are you not entertained maybe everyone's asleep it's my mic working Mike check Mike check the chat's broken maybe the Aaron judge broke the chat oh now David's there all right there you go I was gonna say can't believe there's no reaction to it I'm assuming everyone's either asleep or stunned into silence my bench Felton's gonna face and face a Novak yoga they're just gonna be a tough match up in the semifinals fractures and numbers it's gonna be Ronald Acuna Jr. orange 25 also had that Adley Rushman refractor Jason Alexander 99 purple for the Brewers and Marco Pell blue for the Phillies David Belcher is gonna get that Adley Rushman the relic in auto is gonna be Alec Manoa for the Bluebirds Jersey and autograph going out to Steven Carney you're in case that's Ronald Acuna Jr. for Justin and the Braves Saniel Contara to 75 for the fish Steven George Kirby is your autograph that's for Seattle that'll be for West Alejandro Kirk blue jays you see the card and slid onto the side over there it's gonna be Steven in the blue jays we got gold Corey Seeger 37 out of 50 for the Rangers John G and Sandiel Contara autograph this time for Miami that's for Steven Carney nice how awesome is that hit over there look tied it up guess we have that on local television here it's like the Orioles are changing pitchers Brandon Jury popped out for Anguipo then doubles Moustakis pops out Ohapi walks then Mickey Moniac singles the center scoring Ren Gifo and tying the game so Moniac sets first Ohapi's at second pitching change looks like Randall Dreechick and finish the game walk it off with the angels we got an orange going going gone Francisco Alvarez 21 out of 25 nice one for Howard in the Mets it's the relic autograph he got Josh Naylor blue to 75 he's pissed popped it up Alejandro Kirk blue jays to 50 and we got a nice Anthony Volpe purple seven out of 99 for the Yankees that's gonna be for James alright and behind Gunnar Henderson is Andrew Jones piece of the bat and autograph that's gonna be for Justin and the Braves number to 30 out of 99 that's right Duncan your guy Alejandro Kirk there's Nolan Ryan for the California Angels I would be for Travis got Nolan Jones red two out of five for the rocks that's gonna be for Jake Jake out of fives and under train was on a two Tuesday all aboard the big hit Express Cory Lee Houston that's gonna be for Howard and the Astros Cory Lee again for Howard and the Astros this autograph and that's the uncirculated we got Jose Ramirez blue to 75 you're welcome Jake that's for Cleveland that's gonna go to Adam and oh snap that's Byron Bucks and oh snap die cut and autograph that's gonna be for Joe and the twins alright final box coming up ladies and gentlemen and good luck we can pull some nice stuff out of this pristine lately so get into it boys and girls get your spots and don't forget to get your spots before 1030 Pacific so plenty of time 45 minutes but get a spot for a chance to win some boxes details on jasky's case breaks calm it's 10 box Tuesday let's see if Gunnar Henderson's gonna do something here that's good for the hobby he's one for four double in the sixth top of the 10th runner on second here's an Otani going going gone insert I think he did not play today no I think he's carrying like some sort of side injury or something like that kind of tweak something of batting practice oh snap for Nana Tatees junior die cut Gunnar Henderson move the runner over set of encased cards good luck at ladies and gentlemen we got gold Joe Maurer to 50 Jordan Westburn see what he can do one for four the double and the fourth Brandon Crawford 30 out of 99 Tim Anderson purple to 99 all right so there's in Westburn gets the fielder's choice another up 5-4 we got Volpe rookie refractor for the Yankees and we got a gold jersey in auto that's gonna be it's mad like turpentine and look like India ink I held my nose I closed my eyes I took a sip I didn't know if it was day all night John the India jersey and auto India 45 out of 50 that's gonna go to Jake and the Red Legs yeah Gansby James won the Yankees in the filler and got the judge a one-of-one judge we got Brian Bale Michael Pied and the Red Sox got a gold Pudge Ivan Rodriguez 33 out of 50 Florida Marlins that's for Stephen Carney Orioles Kyle Stowers for the Orioles we're up 5-4 in the Angels now Aaron Hicks up to bat it's gonna go to David Belcher Gunner Henderson is gonna go to you as well David got a Julio Rodriguez gold for Seattle six out of 50 that'll be for West and the last one is jazz Chisholm I think he had a home run off my Dodgers earlier today Stephen Carney with the fish and there you go ladies don't that's your break pristine pick your team nine in the books so here were your relic autographs and other notable cards like that purple Volpe the orange Alvarez Corbyn Carroll base and the Dylan Cease you're in case cards the die-cut Byron Buxon was really cool we got the out-of-five Nolan Jones train whistle Kirby pose your mirrors gold autograph morel orange David Ortiz going going gone auto to 75 Al Tube was to five Zach Thompson Mookie blue Palacios Gunner blue the laska's Ian half to 15 Kershaw and of course the Aaron judge popular demand patch and auto the popular demand obviously as you've seen in the review the recap not very common nice stuff there ladies and gentlemen there you have it I'm Joe for jazzy's case breaks calm thanks for watching thanks for breaking with us I'll see you next time for the next break bye bye


This is the first time I've done this lecture, and I think it's the first time we've had this lecture at Mises University. You know, this was a very dry almost inconsequential topic when I was in graduate school and for Austrians it's even more sort of not that important because income distribution is just a result of the processes that we study and theorize about all the time and it's only recently become an important really critical topic politically and ideologically over the last ten years. I think the promoters of this concept economic inequality and equity those sorts of issues have been working on the issue for well since we first realized more globally that Mises was right about socialism and communism that's when the socialists sort of shifted gears and one thing they shifted to very early on this has already been mentioned by Gene Epstein is that they were going to drop the idea of national socialism and nationalized industries and central planning in favor of things like economic inequality. So politically it's become very very important. We see articles and reports and studies about how bad income distribution has become that the high incomes now earn 40 or 60 or a hundred times what low-income people have or that corporate CEOs make a hundred or two hundred or a thousand times what their average worker makes and things of that nature that's more or less propaganda than it is statistics and facts and figures as I'm going to show Now as an introduction, I'd like to point out that Austrians love economic inequality in the sense of the natural inequalities that human beings have in so many different respects and how the market can turn these unequal statuses into great things for all parties considered. The second thing that's going to bog down the lecture a little bit is just laying out on the table all of the different types of equality and inequality. The third thing and most important I think is that the socialist voice opposition to economic inequality. They see an unequal distribution of income or an equal distribution of wealth or any of the precursors to those achievements as being fundamentally flawed, evil, unethical, immoral and of the greatest concern for government to come in and change. But their voice I argue is basically filled with lies, distortions and the unseen. What goes on in the economy that we don't actually see and of course we do see incomes reported to the IRS unfortunately and we do see various forms of welfare benefits going out to help the poor and the low income. But what we're going to find out is that a lot of this socialist voice is based on a house of intentionally bad cards. And I would suggest that reality to the extent that we can find it out there these days is a good guide to understanding the issues and to dealing with the socialist voice. Now I'm going to begin with a statement by Murray Rothbard about the natural inequality that exists in humanity. And so this is basically reality. If men were like ants there would be no interest in human freedom. If individual men like ants were uniform, interchangeable, devoid of specific personality traits of their own, then who would care whether they were free or not? Who indeed would care if they lived or died? The glory of the human race is the uniqueness of each individual. The fact that every person, though similar in many ways to others, possesses a completely individuated personality of his own. It is the fact of each person's uniqueness, the fact that no two people can be wholly interchangeable that makes each and every man irreplaceable and that makes us care whether he lives or dies. Whether he is happy or oppressed. And finally, it is a fact that these unique personalities need freedom for their full development that constitutes one of the major arguments for a free society. So that's just an observation of reality on Rothbard's part and a reflection upon what brings forth the greatest results from this reality. You know, I was thinking about this and in many many cases, it's not the fact that we are similar to one another or just like one another that really allows us to reach our full potential as students, as workers, as collaborators, as artists, as entrepreneurs and business people. Very often, it's the case that when we associate with people who are very much different than ourselves, is when we very often find the greatest rewards. Aspects of human inequality, and this is just a very crude list of some of the ways in which we differ from one another when we start with a physical and biological. We go to our individual tastes and preferences for good services, art, music, food, and so forth. Then there are issue related, job issue related differences in intelligence, talents, education, training, and experience. Some of the basic economic characteristics of individual humans are our tastes, such as labor versus leisure. Some of us are quote-unquote hard working, and others of us are lazier and more laid back, and there's really nothing wrong with differences in tastes, in the marketplace. Some of us excel, we're go-getters, we are people who get things done, and there's other people who sit back and study and contemplate things are not really active. They don't look active. So if you go down the hall and you look at me in my office, I'm going to look like I'm not very active, but I'm really doing some important contemplating about the future of things to come, and the next brand new economic theory. Very important here is time preference. Whether we're now intensive, where we're only concerned about the now, we want to consume everything right now. And there are others, people who are more future-oriented. They're not interested in the here and now. They don't spend all of their money, you know, going out and having great food at the restaurants and wonderful clothes and so on and so forth. And then there are other people who, you know, eat peanut butter and jelly and wear old clothes and save their money. And then there is risk-taking preferences. Some people are risk-oriented and they might be inclined to become entrepreneurs, where other people are less interested in the risk. We're afraid of risk. We're afraid of uncertainty and most humans are actually of this sort. Where we don't really want to be out there, we don't want to be under the spotlight, we don't want to be taking risks. And like most other things, the market simply takes this as an objective state of reality and allows us to take advantage of those differences. The Law of Comparative Advantage, which has been talked about in the lecture on labor, so this is an extension in part about that. The Law of Comparative Advantage basically tells us that we all have a comparative advantage or comparative advantages that might need developing but certainly are available to us. So we all have a place in this marketplace or this market society. Then there are dubious types of equality in markets. So the previous slide we looked at differences in people and this is a slide where we look at wrong-headed types of equality in markets. There's the inequality at birth, the equality by birth, the equality of opportunity, and the equality of results. None of these things are actually equal in the world. They're not really possible in the world. Our births are, you know, a happy coincidence of people, circumstances, genetic codes, and all the rest, and so we come out unique into this world and we can be an important part of this market society and everything that comes from that. And we obviously don't have equality by birth, no place under no set of circumstances or any kind of system is that the case. And obviously people have different opportunities in this world. Some people are born into dire circumstances. They're born into difficult situations. They run into all sorts of negative consequences, whether they're born into a communist state or born into a war-torn area of the world. There's obviously negatives as well as positives and there's no real conceivable way, no realistic way outside of some kind of academic game that that could actually be brought into some sort of equality for all. Equality of results is obviously wrong in every attempt to create equality of results is going to fail. And in the limit, Mises says, found and demonstrated that the attempt at equalization will destroy civilization. So there's a lot at stake here, but we also recognize the reality of the benefits that come from all this inequality from the genetic level all the way up through everything, including our individual experience. Now we can look at the issue of inequality and various types of systems where we look not just at the individual, but we look at the system in which we find them. And there are some basic types of system, natural law, which is sort of pre-society on up to the present, and the rule of law, which developed in a market setting and is still with us in bits and pieces, obviously. And those systems find that in various specific terms, we are in fact equal and we can, at least in theory, exist in a just system. Now the political systems, theocracy, monarchy, democracy, dictatorship, socialism, whether it's the Russian style socialism or American progressivism, all of those systems are in some sense caste systems, where you are born into a position into the system. And that position is different from the person sitting next to you and the person sitting behind you and the person on the stage. I used to have democracy as a rotating caste system long ago, where we voted and, you know, it could be you running the system, one election and you running it the next one, and then that person all the way in the back sleeping is could be running the system the next round. Of course, then the Bushes came along and the Clintons came along and I realized that it really didn't rotate throughout the entire system, but just amongst a couple of well-placed aggressive families. Capitalism in the sense of anarcho-capitalism or anarcho-capitalism with law is a system that is at least based on equality of opportunity and and of law and it's a system of justice. And I'm not going to get into any philosophical disquisitions about any of this. I'm just laying out all of the terms that you might come across in debates and discussions with your friends or your teachers and that sort of thing. You know, they're the socialists are very shifty and they could easily switch from one form of equality to another or one form of inequality to another and there are many different ways to define those terms. Now once we have the basic conditions of reality and we look at this reality in terms of nature and specifically in terms of the market society or even the mostly market society we see the path towards human economic development and actually it's it's not just basic economic development it's development in all of its many in assorted forms. So we begin with reality Mises says quote the diversity of nature which does not repeat itself but creates the universe in infinite inexhaustible varieties okay sort of restating what I opened the lecture with in terms of Rothbard's disquisition on reality okay the reality is is that we're not little fixed creatures were very unique and were subject to change. Okay human economic development requires freedom and despotism of every sort stymies human development and economic development. In development here is defined as the movement from subsistence to a more or less advanced economy. The best example of this is the industrial revolution. Okay the best example of this is the industrial revolution when human beings went from almost an entirely subsistence existence ruled by a bunch of men on horses with long spears and told what to do to a position of being independent relatively independent actors who were able to consume earn and consume more than subsistence more than just staying alive. Okay so that in the 19th century for example and really the first half of the 19th century the income and standard of living in England which was the first one of the first countries to develop economically income rose noticeably and even dramatically above subsistence.  So then we have this process of economic growth involving savings, capitalists, entrepreneurs you know doing their various roles in society. Workers saving depositing money with banks capitalist accumulating savings investing in companies and entrepreneurs increasing productivity so on and so forth all managed by entrepreneurs at risk and every one of those roles in societies is harder than it looks. What the socialist will point out is examples of people like oh you know that person you know twiddled his fingers and all of a sudden he was a billionaire and he didn't do anything and now he's buying a giant boat and you know or whatever that's what that's how the socialists want you to condemn civilization on anecdotes that really don't reflect any of the underlying reality. This is a very hard system that has developed over hundreds of years the global division of labor and our standard of living that increases not just incomes but population life expectancy even equality is much better under in a market society than it is in other types of totalitarian or despot societies. Capitalists of course have to deprive themselves from consumption in order to have savings to lend to entrepreneurs and they're still subject to all sorts of risks they might not get paid the money back okay that happens all the time and yet they earn and quote unquote unearned income widely vilified. Entrepreneurs bear uncertainty and we see the extreme success stories but never the 100 or 1000 entrepreneurs who failed or who barely survived their journey of entrepreneurship and even labor you know if labor wants to earn more they've got to work more or they've got to invest in their quote unquote human capital through education or training or experience and that's not easy that's difficult it's expensive college is expensive okay and you have to give up something it's an opportunity cost if you're in college chances are you're not working a full-time job that you could qualify for uh with your current education experience background resume etc so i started by looking at what socialists have done and they've turned away from the efficiency standard they marks and his followers said you know communism socialism is going to be much more efficient we're not going to need 17 different types of toothpaste we're only going to need one it's not going to have to be advertised it's you know we're going to just produce so much of that stuff that everybody's going to have way more toothpaste than they could ever possible use and that's going to be true for everything and we're going to be able to you know work in the minds and learn the trumpet and you know play soccer and all sorts of things so they had this sort of efficiency productivity issue that fell apart with the downfall downfall of socialism and they've turned to equity the redistribution of income and wealth and of course they've also turned to ecology global warming climate change and so forth and both of those things involve technocratic expert driven solutions to issues where science really is detached from the situation like with covidia or the kovid crisis and vaccines and all that stuff nobody knows enough to break through all the proclamations of government scientists um in any substantial way so we're you know the the general population is a bunch of sheep when it comes to income distribution or global warming or covid science so that's where we are today and i want to bring up an example of this misinformation as it relates to income distribution and this is well first of all the the biasing of the debate is important in terms of income distribution the actual distribution statistics that you're familiar with and have been exposed to do not count all of the money american taxpayers provide for low income families and by low income i mean below the median income household uh does not count all of the tax dollars taken away from people who actually earn income so it understates welfare and it understates taxation and it also doesn't do things like consider all of the business failures So the top one percent. Oh, yeah, that's great. I wish I was in the top one percent but you know 99 out of 100 people failed completely in their pursuit of achieving that one percent and then it doesn't consider all of the economic potential that mises demanded that we pay attention to specifically the fact that some people earn abnormally high incomes and stymie competitors at the same time it doesn't consider the fact that welfare recipients are capable of working more than they currently are and it doesn't consider that taxpayers are widely discouraged from maximizing their free market incomes in other words I'm going to show you the sort of lie beneath American economic income statistics in a different way than gene epstein did But there's a lot here that's left unsaid Okay, there's a lot left on the table We could have more total income The economic pie could be much bigger if we didn't have the system of high taxes and generous welfare benefits This is from a forthcoming book by Graham Eaklin in early it's called the myth of American inequality how government biases policy debate and basically what they did was they took all forms of welfare benefits that are missing from the statistics Okay, so the statistics count like a dozen different welfare type of payments there's actually over 100 different welfare programs and they do get smaller and smaller and smaller but collectively they're very large They also include all forms of taxation especially at the federal level and what they do in great detail is on this graph here and this is income distribution for households broken into quintiles so you have the bottom 20% of household incomes the middle 20% of household incomes and the top quintiles so there's five quintiles representing 20% of households each and the dashed line here is the household earned income when they went out and got a job or got dividends something that they actually earned of their own accord and so that graph starts at near zero down here at the bottom quintile and it goes up to $350,000 per year per household for the top quintile that's the average so within the top quintile there are people earning $220,000 there are people who are earning $22 million of income but the average is about $300,000 per household per year now when we start adjusting that for transfers or welfare and taxes what we find is that the bottom two quintiles actually get a big boost in income from welfare and other transfer payments so that even in the lowest quintile their ability to consume is almost $50,000 per household where if they had to go on their own accord without welfare with their current work effort they'd be down here $10,000, $2,000, $12,000 per household but actually they're able to consume about $50,000 which is just slightly less than the second quintile which is not much less than the third quintile so these bottom three quintiles with the help of big welfare payments and taxes over here have been kind of equalized in terms of their consumption possibilities and then as we move to the fourth quintile we see that taxes become a greater burden and there's no net transfers in to that 60 to 80 percentile range and then finally in the fifth quintile the high income quintile it's nothing but net taxation and it can be rather extreme the highest income categories essentially pay all the net federal taxes and the bottom quintiles pay no net federal taxes but receive very substantial welfare payments as a result so we go from a this is the United States we go from a distribution here where people are not working or hardly working at all to people who are probably working a lot you know if you run into somebody who's making a big young person who's making a big salary chances are they're working all the time and as I said as you go to the top 1% this figure rises very dramatically once you break it out of 20 household 20 household groups so if you you know if you looked at just earned income the people in the bottom 20% earn say $2,000 and relative to that in the upper income groups it's like 120 so the relative income from the top to the bottom is 60 to 1 the US government when they make their adjustments the ratio goes to 16.7 to 1 reflecting some taxes and some welfare benefits and if you look at this graph where you take all welfare and all taxes into consideration the top quintile household on average only consumes potentially consumes four times what the bottom household consumes or is able to consume so it's a big distortion it goes from 60 to 1 down to 4 to 1 in terms of poverty this is the official poverty rate from after world war 2 to the COVID period and after world war 2 35% of Americans were in poverty and that gradually declined well actually dramatically declined to less than 10% in the mid 60s and then in the mid 60s legislation was passed to enact the war on poverty and as a result the official poverty rate according to the way they measured things sort of cycled around that 10 to 15% ratio ever since so right now if you look at the past if you went back and look at the stories from 2021 you'd find out well you know the poverty rates fall and it's great you know we're in a bubble who cares the poverty rate the official poverty rate did fall okay and now as we go further into 2022 and 2023 the poverty the official poverty rate is going to escalate quite a bit because it does so according to the business cycle but if you look at the trend in the poverty rate as measured by Graham, Eakland and Early when you take into consideration all the welfare benefits and all the taxes the poverty rate has actually come down to 2.7% in 2017 and it almost follows that historic trajectory before we had the war on poverty established in 1965 so the the war on poverty actually froze the poverty rate that had been declining very very rapidly so those are just two examples of misrepresentation and distortion of the data because the academics the media the politicians they want to use poverty and income distribution essentially to take more money from taxpayers that's big that's basically it they want to raise taxes they want a wealth tax they want a profits tax they want to increase the tax on high incomes everything and anything they just want more going into the government they don't ever say that we want this money going to low income people but they definitely want your money okay that's clear and it's only clear once we understand these statistical distortions that you know you would think that the government bureaucrats would want to correct their statistics or politicians would want more accurate statistical data or social sciences but this has been going on incorrectly for decades and I was really surprised when I read their results okay so our takeaways here are the you and everybody else are being misled by those that are inclined to socialism which includes the government the media the political parties Thomas Piketty in particular as from the academic side of things they've been more or less intentionally misleading you and in Piketty's case if you read his books which I don't recommend actually because it's fantasy you know and it's so much fantasy that these people and many others believe in you know the romantic writings of Charles Dickens and Ebenezer Scrooge and all of that they think that that somehow history and Piketty and his book capital actually does say that he said you know all these romantic writers they were talking about this obscene poverty and you know they just didn't make it up well yeah fiction writers make things up that's what they're that's how they make money is they make things up okay most important is that inequality is something it's kind of like the raw material the raw fuel of the market economy and then economic development it means that everybody certainly can do much much better they can survive and do much much better in a market economy no matter what their inherent disadvantages are they can always do much much better it's part and parcel of the market and it's why Austrians have a tendency a strong tendency to value freedom and economic freedom in particular third is that policies designed to equalize economic results are disastrous okay Mises showed that you know perfect socialism and perfect equality of results will break down society into economic chaos but that any movement towards equality does the same sort of thing so as Americans are taxing high incomes and rewarding people who don't earn income who aren't working essentially we're reducing the our economic pie we're stifling the people in the low income categories and we're stifling the people in the high income categories and we're stifling the people in the middle income categories which means that if we reduce those burdens taxation and welfare the economic pie would grow and there would be even more that would come out into the distribution and economic freedom also results in greater economic equality some of the inequality in our current system is not the result of a pure market process it's the result of government monopolies and favoritisms all the things that Frederick Bastiat argued against that we shouldn't protect that we shouldn't advantage any single individual or group of individuals we shouldn't give them preference we shouldn't give them protection in America and some of those really unbelievable stories of income and wealth are fueled by government privilege so or some combination of the two so that's another action item that Austrians advocate it's not just reducing taxes reducing welfare but it's also reducing privilege reducing intervention in the economy all interventions create some privilege some protection somewhere and the less we have of it the better thank you very much