Good evening friends, I welcome you all to the Hindu Uniscape Analysis brought to you by the Shankar Reyes Academy. Today's date is 22nd December 2023. Before entering our discussion, I have an important announcement to make. Guys, marks your calendar for an unmissable opportunity. Are you gearing up for the UPSC preliminary 2024? Well, we have got the workshop just only for you. Join us from December 23 to December 30 for an exclusive and free UPSC preliminary workshop. Whether you are in Anandagar or connected virtually from any branches, this workshop is tailor-made to propel your preparation to the next level. Or Agenta, it is packed with insights and strategies that you need to crack the preliminary examination. From subject-specific tips and tricks to dissecting the previous equation papers and analyzing the trends, this workshop has it all. If you are worrying about handling unknown areas, fear not. We have got you covered. 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On Thursday, Kerala announced that it is having around 87% of active COVID cases in the country. According to the Union Ministry of Health and Family Welfare, there were approximately 300 new infections and three deaths in the last 24 hours. See, this is the crux of the news article. So in this context, let us quickly revise about the basics of COVID-19. Firstly, let us see about the basics of COVID-19 disease. See, COVID-19 is an infectious zoonotic disease caused by SARS-CoV-2 coronavirus. See, it is an RNA-based virus with ribonucleic acid or RNA as its genetic material instead of DNA. What does it mean? It means the virus can blend with the DNA of the host and can mutate rapidly. So due to this property of rapid mutation, it has become deadly in nature. Moreover, know that it is a member of the coronavirus family, which includes various other viruses which are being responsible for severe acute respiratory syndromes or SARS and Middle East respiratory syndrome or MERS infections. The interesting feature of the coronavirus is that it has many regularly arranged protrusions on its surfaces because of which the entire virus particle looks like an emperor's crown. That is how it got its name coronavirus. Now, let us see about the transmission of this virus. See, the virus primarily spreads through respiratory droplets when an infected person coughs, sneezes, talks or breathes. It can also spread by touching the surfaces which are contaminated with the virus and thereby touching the face, particularly the mouth, nose or eyes of a person. Now, let us see the symptoms of the virus. The common symptoms include fever, cough, shortness of breath, fatigue, muscle or body ache, loss of taste or smell, sore throat, congestion, etc. Symptoms may range from mild to severe and can appear 2 to 14 days after the exposure to the virus. Now, let us see the major tests to detect the COVID-19 virus. Firstly, let us see the molecular test. See, the molecular test commonly known as RT-PCR test. It is used to directly detect the presence of the virus in the sample. See, this test detects the virus RNA that is the genetic material of the virus. A nasal or throat swab sample is generally being taken for this test. Secondly, let us see the antigen test. A COVID-19 antigen refers to any foreign material or viral proteins in the body which will trigger an immune response. This test helps to identify the antigens which are related to COVID-19 viruses. This test is also called as rapid antigen test and it gives the results which are faster than the molecular tests. But here also, nasal or throat swab is taken. But there is a drawback. Antigen tests have a high chance of missing the active infection. Thirdly, let us see the antibody test. See, it is also called as serology test and it screens for the COVID-19 antibodies in the blood. It tells if a patient is previously infected with COVID-19 viruses. The antibody test does not look for the active viruses but it checks whether one's immune system has responded to the infection. This test also needs blood samples. See, these are the three major type of tests for COVID-19 infection. See, this is all about the discussion. In our discussion, we saw about the basics of COVID-19 virus and in the second part we saw about the three major tests for the COVID-19 viruses. With this learned points, let us conclude this discussion and take up the next news article for our analysis. Look at this editorial article. This editorial is basically a criticism on the union government. This article mainly criticizes the government regarding the use of prevention of money laundering act 2002. Moreover, it also talks about the frequent use of enforcement directorate to arrest the legislators in the opposition ruled states. This article also states that union government uses the PMLA act against various judgments of the Supreme Court. Lastly, it also criticizes the activity of the government by saying that it goes against the federalism which is one of the basic structures of the Indian constitution. See, this is about the editorial article. The article may look so cynical but we as an aspirant who want to enter civil services should develop the virtue of political neutrality and impartiality. So, from this kind of article, we can just take criticism points regarding PMLA and use it in our critical analysis. With this basics, let us get into discussion. So, in our discussion today, let us try to answer a main question about PMLA 2002. Look at the question, what is money laundering and how it is a lifeline to the organized crime operations around the world. Moreover, critically analyze the effectiveness of the PMLA in preventing the money laundering in India. See, the question demands three things. First, we have to write about money laundering. Then, we have to write about the relationship between money laundering and organized crimes. And finally, we have to write about the criticism surrounding the PMLA. In the last part, we must mainly focus on the effectiveness of the PMLA in preventing money laundering in our country. This is a skeleton of how our answers should be. This question can be asked in the GS Paper 3 under the subtopic of challenges to internal security through communication networks, role of media, social networking site in internal security challenges, and thereof. We saw the question and the relevant syllabus. Now, let us start answering the question. In the introduction part, you can define money laundering and add some data regarding the phenomenon. Money laundering is the act by which the proceeds of a crime are made to appear legitimate. According to UN Convention against the Transnational Organized Crime, money laundering involves knowingly converting the money or moving property which is obtained from a crime to hide its illegal origin or to assist someone in the original crime to avoid punishment. Money laundering involves a series of steps to disguise the origin of illicit funds. The prime focus of money laundering, as I already mentioned, is to disguise the origins of illicit funds as if it came from the legitimate sources. This typically includes three stages. Placement, that is, introducing illegal funds into the financial system. Layering, creating complex transactions to obscure the money trail. Finally, integration, making the funds appear to be legitimate. See, the Enforcement Directorate is India's primary agency for combating financial crimes. Annually, it publishes the report detailing the value of the proceeds of crimes which were attached and confiscated under the PMLA. Let us see the data. In 2021-22 financial year, the ED attached a POC worth over 55,000 crores related to money laundering. See, this figure, however, only represents a portion of the total laundered money activity which was detected and it does not reflect the broader economic input. For instance, let us see a data. A 2012 report by the Central Bureau of Investigation estimates that India loses around $50 billion annually through tax evasion which is associated with money laundering. See, I have given you an elaborate introduction. You can precise it and use it in a concise manner. Okay, this is about the introduction. Now, let us get into the body part of the answer. Here, we have to write about the money laundering and its link to organized crimes. See, money laundering often has a strong connection to organized crimes. Firstly, the organized crime groups engage in various illegal activities like drug trafficking, human trafficking, arms smuggling, extortion, fraud, etc.  Since these criminal organizations cannot use these illegal funds openly due to their illegitimate origin to make this money appear legitimate and usable, they employ money laundering techniques. After laundering the money, these organized crime groups integrate the laundered money into the legitimate economy. See, money laundering allows the criminal organizations to sustain their illegal activity by reinvesting the laundered fund. See, reinvesting the laundered fund ensures a continuous cycle of generating illegal profit, laundering them and furthering criminal operations. In addition to this, the organized crime groups use the laundered money without drawing attention from law enforcement or financial regulators. They also use the laundered money to bribe officials and fund the other criminal ventures without any suspicion. This is why money laundering is considered as a backbone of organized crime. See, let me explain the linkage between money laundering and organized crime with a simple example. Let us take a fictional character. Let us name it as One Punch Bhavani. Here, One Punch Bhavani is a drug lord. Bhavani makes money by selling narcotics. In fact, he makes a lot of money by selling narcotics. But can Bhavani actually spend this money? The answer is no. Let us say, Bhavani tries to buy a Toyota Fortuner with this dirty money. If he pays the entire sum in cash, the showroom people will not accept it or they will ask for Pancor details. Bhavani cannot provide his Pancor details as the money he is providing is unaccounted one. So, for Mr. One Punch Bhavani to use his drug money, he must launder it first. So, without money laundering, organized crime will not be very lucrative. Here, moreover, I want to quote a dialogue from one of the greatest TV shows, The Wire. The Wire is about a political investigation into crime in the city of Baltimore. While investigating the drug trade, one of the detectives in the show, which is played by Lester Freeman, mentions that if you follow drugs, you get drug addicts and drug dealers. But if you start to follow the money, you don't know where it is going to take you. See, this statement basically sums up the relationship between organized crime and money laundering. We have addressed the first part of the question quite in a elaborate manner. Let us move on to the second part of the question. Here, we have to analyze the role of PMLA in curbing the money laundering. To deal with the dangerous money laundering activity, India enacted the PMLA in 2002. Despite the act being enacted in 2002, it came into force only from 2005. The main objective of PMLA is to prevent and control the money laundering and to confiscate and seize the property which is obtained from laundered money. But is the PMLA effective in achieving the stated objective? The answer is complicated. This is because even though PMLA is a well-intentioned act, it has many issues in it. The first issue is the narrow focus. The PMLA primarily addresses specific crimes associated with money laundering. For example, the Supreme Court in Vijay Madanlal Chaudhary and others versus Union of India case limited the PMLA's application to the wrongful and illegal gain of property which is a result of the criminal activity which is related to scheduled offenses. Here, scheduled offenses are included in Part A, B and C of the PMLA Act. Due to the narrow focus, it excludes several other financial crimes such as tax evasion, corruption, etc. The second issue is the complex legal process. The legal procedures mentioned in the PMLA are very time consuming. These complexities often result in delayed justice and protracted trails. This discourages the law enforcement authorities from pursuing accidents against the various individuals who involve in money laundering. The third issue is lack of collaboration. Insufficient collaboration among the enforcement agencies who are investigating this phenomenon often leads to the duplication of effort and wasteful of resources. The absence of effective collaboration reduces the collective impact in combating money laundering. The next issue is the lack of adequate resources. There is an issue of resource shortage including insufficient personal and outdated technology. This resource deficiency acts as a hurdle to the collective combating of money laundering activities. The next issue is the use of PMLA and ED as a political tool. See, the union government has been using these acts and their authorities to stifle the opposition by mainly targeting the legislators from the opposition states. This goes against the spirit of federalism. Lastly, there is an issue of political intervention. This potentially hinders the PMLA's efficacy in holding those people accountable before law. Such interferences might compromise and the integrity of the legal process. See, these are all some of the issues of PMLA 2002. But on the other hand, PMLA also has some positive aspects. See, the first positive is the burden of proof. According to section 24 of the PMLA, the burden of proof is on the accused to prove his innocence. Normally, in most of the cases a burden of proof must be provided by the government to prove that the accused is guilty. But in PMLA cases the accused is considered guilty and the accused must prove that he is not guilty and innocent. This acts as effective deterrence against the money laundering activities. Secondly, according to section 45 all cases are cognizable and non-bailable. So, ED can arrest an individual without any warrant subject to certain conditions. See, this also provides effective deterrence against corruption. Thirdly, to increase the effectiveness of PMLA certain provisions of the act were amended in 2019. One of the important changes brought by 2019 amendment was regarding section 2. See, section 2 of the acts was amended to expand the scope of proceeds of crime or POC. See, in this juncture, we are to know what does proceeds of crime means. Let me give you an example. Let us consider a person named Sandaram. His profession is dealing drugs, which is an illegal activity. What Sandaram does? He launders the money he makes by selling drugs and he buys a prime real estate in Ananagar, Chennai. This real estate now comes under proceeds of crime. By 2019 amendment, which I had told that it expanded the scope of POC or proceeds of crime. With the expansion of the scope, the enforcement directorate can take action against those property which may directly or indirectly be derived or obtained as a result of any criminal activity related to scheduled offence. This expanded scope of PMLA in turn will effectively curb the money laundering activity. See, these are all some of the positive aspects of PMLA. So, the PMLA has both positives and negative. This is why I earlier mentioned that the answer to the question is PMLA effective is complicated. Now that we have analysed the effectiveness of PMLA in curbing money laundering, we can move on to the conclusion part of the answer. See, you can end your answer on a positive note. You can mention some data to highlight the PMLA in action. You can mention that according to data from FIU or financial intelligence unit, approximately 14,000 suspicious transaction reports and over 1,000 PMLA cases are submitted in 2020. This shows that PMLA is effective but to make it even more effective the ingrained issues of PMLA have to be addressed. See, this can be your balanced conclusion. See, this is all regarding this discussion. In our discussion we have elaborately saw the various provisions of the PMLA and we have discussed about the issues and the positives of this act. So, with this learned points, let us conclude this discussion and take up the next news article for our analysis. With this news article, Namdappa flying squirrel has been found again in Arunachal Pradesh. Know that it went missing for nearly 42 years. It was last seen in 1981 based on a single individual which was found in Namdappa Tiger Reserve in Arunachal Pradesh. See, this is the crux of the news article. In our context, let us know some key facts about Namdappa flying squirrel and also let us see about zoological survey of India. See, the Namdappa flying squirrel is a rare and elusive species of flying squirrel found in the northeastern Arunachal Pradesh. This squirrel was discovered in 1981 in the Narunthappa National Park. So, that is how it got its name. This flying squirrel has distant physical features including a membrane called Pata GM that allows it to fly between the trees. Now, let us look at the habitat and distribution of this species. See, it primarily inhabits the high altitude forests of Namdappa National Park. It specifically occurs in the area with dense vegetation and tree cover. Know that it is an endemic species meaning that it is found exclusively in the Namdappa National Park region. Now, let us see about the conservation status. See, it is considered as a critically endangered species under IUCN Red List. If you are conserving it means you should have had threats now. So, let us see what are the threats faced by them. Firstly, with respect to poaching of animals for food. Secondly, with respect to habitat loss and degradation. Thirdly, various geophysicals, phenomenon like landslides and flooding results in the habitat loss of this species. Now, let us see the notable behavior of this squirrel. See, Namdappa species is a nocturnal like most flying squirrels. It means they are active only during the night for feeding and other movements. It diet primarily consists of fruit, nuts, seeds and possibly insects. This is all we need to know about the Namdappa flying squirrel. Now, we shall see about the second topic, Zoological Survey of India. See, Zoological Survey of India is a subordinate organization of the Ministry of Environment, Forest and Climate Change. Note that it is not a statutory body. It is a national center for the survey of animals and the exploration of the resources leading to the advancement of knowledge. See, ZSI or Zoological Survey of India was established in 1916. It has its headquarter set, Kolkata and moreover it had 16 regional stations which is located in different geographical locations of the country. See, Zoological Survey of India has been declared as a designated repository for the National Zoological Collections as per the National Biodiversity Act 2002. Moreover, ZSI publishes the red data book on Indian animals. See, it was first published in 1983 and is similar to red data book which was published by IUCN. That is all about the discussion. In our discussion, we saw about two environment topics which are Namdappa Flying Squirrel and Zoological Survey of India. So, with this learned points, let us conclude this discussion and take up the next news article for our analysis. Look at this news article. Anshuman Patnaik has been chosen by the competition commission of India to lead its investigation unit. See, he has an experience in overseeing the various investigations and cases which involved various big companies. Notably, Mr. Patnaik has been involved in examining the various actions of alphabets, inks, gull and other similar companies. See, this is the crux of the news article. So, in this context, let us see about competition commission of India from our example perspective. To see this, we need to go for a flashback. See, in 1960s and 70s, there was an act called Monopolies and Restrictive Trade Practices Act 1969, that is MRTP Act. See, the aim of the act is to control the monopolies and prohibit the monopolistic and restrictive trade practices. He has rolled on and this act was replaced and repealed by the competition act 2002. See, this was replaced based on the recommendation of Raghavan committee. So, in a nutshell, the competition commission of India is a statutory body established under competition act 2002. And moreover, this competition act was further amended by competition amendment act 2007. Now, let us see what is the purpose of this commission. Its main goal is to create and sustain the fair competition in the economy which will provide a level playing field to the producers and to make the markets work for the welfare of the customers. That is it is working for both producers and customers in a market. So, the act prohibits various illegal practices like anti-competitive agreements abuse of domestic position with enterprises etc. Moreover, it will also regulate accusations which cause or likely to cause adverse effect on the competitions within India. Now, let us see the composition. It consists of chairperson and six members which are appointed by the central government. On talking about their qualification the chairperson and every other member should be a person of special knowledge and should have a professional experience of not less than 15 years in areas like economics, law, finance, accountancy and management etc. Let us see the appointment process. See, both chairperson and other members will be appointed by the central government based on the recommendation of a selection committee. See, this committee is headed by the justice of India or his nominee. The other members include the secretary in the ministry of corporate affairs and the secretary in law ministry and justice. Apart from them, there will be also two experts who possess special knowledge and professional experience will also be a part of this committee. Now, let us see what is the tenure of the members. Note that the chairperson and every other member of the team will hold office for a term of five years provided they have not attained the age of 65. Note that they are also eligible for re-appointment. In case of vacancy caused by the resignation or removal of chairperson or any other member, then such position shall be filled by the fresh appointment based on the set committee recommendation. And in case of vacancies in the chairperson's office, the senior most member shall act as a chairperson until the new person is chosen. This is all about the news discussion. In our analysis, we saw about the structural part of the important economic organization called Competition Commission here. With this learned points, let us conclude this discussion and take up the next news article for our analysis. Look at this news article. Recently, both the Lok Sabha and Rajya Sabha have passed the post the bill 2023. The bill is now waiting the ascent of the president. Note that the bill aims to replace the Indian Post Office Act 1898. This text and context article 10 here is regarding this bill only. The article covers the important provisions of the bill and the criticism around the bill. So in conclusion, let us cover them in a brief. Let us start with the important futures of the bill. The first major change which is brought by the bill is regarding the exclusive privilege of the central government. The 1898 act provides that wherever the central government establishes the post, it will have the exclusive privilege of conveying the letters by the post. But this bill does not provide for such privileges. The bill also states that India Post will have the exclusive privilege over issuing of the postage stamps. The next future is regarding the appointment of Director General of Postal Services. See, this act provides for the appointment of such authority. Moreover, it provides that the Director General may make regulations regarding the charges for services and supply and sale of the postal stamps and postal stationaries. The third and the most contentious provision is regarding the powers to intercept the postal articles. See, the bill allows for the interception of the postal articles on various grounds. The grounds being the security of the states, friendly relations with foreign states, public order, emergency, public safety or contraventions of the provisions of the bill or any other law. The bill also states that central government may empower an officer of India Post to deliver the postal article to the customs authority or any other specified authority. The said authority will deal with the item in the question. The next important future is regarding the function of liability. See, the post office exempted from the liabilities related to its services. The bill also states that the officers are not liable unless they act fraudulently or cause, loss, delay or misdelivery in a deliberate manner. The last change is regarding the offenses and penalties. See, the bill removed the various offenses and the penalties which are provided under 1898 Act. The bill only provides punishment for amounts not received by the user. These are all various provisions of the bill. Having seen the provisions, let us see the criticism surrounding the bill. The first criticism is regarding the violation of the right to privacy. Critics argue that the bill violates the fundamental rights to privacy. It enables the state surveillance without adequate safeguards which is potentially compromising the privacy of the citizens. The second criticism is regarding the lack of clarity and guidelines. See, there are various issues due to the vague ground for the interception, absence of clear definitions for the terms like emergency and the absence of guidelines for the interception. Critics feel that this vagueness will lead to misinterpretation thereby cuddling the rights of the citizens. The last issue is regarding the absence of a grievance redressal mechanism. The bill lacks a grievance redressal mechanism for citizens who might be subjected to interception. This prevents them from rising concerns about such actions by saying that these are all some of the issues with the Post Office Bill 2023. See, this TNC article quotes two important Supreme Court judgments regarding the right to privacy which you can directly quote in your main censor. Now, let us see the judgments in a brief. The first judgment is regarding the People Union of Civil Liberty versus Union of India case 1996. In this case, the Supreme Court stresses the importance of having protections in place to prevent unfair or random use of surveillance by the government. Basically, the Supreme Court said that there must be no room for vagueness in the guidelines regarding wherever the government can undertake surveillance. The next important judgment is regarding the Justice case Putta Swami versus Union of India case 2017. In this case, the court declared that the right to privacy is a fundamental right. The Supreme Court also stated that any action by the government which is affecting the privacy must meet certain criteria. The criteria being it must be full, it should have a valid purpose, it should be appropriate and necessary and it should not excessively restrict the rights and it must include measures to prevent the potential misuse. See, this judgment underlines the significance of safeguarding the privacy and emphasizing the need for clear cut legislations. This is all regarding this news discussion. In our DNC discussion, we saw about the important provisions of post office bill 2023. In a second part, we discussed about the criticism and the various judgments regarding the right to privacy by the Supreme Court of India. This is all regarding this discussion. With this learned points, let us conclude this and take up the next news article for our analysis. Look at this news article. Yesterday, the Rajasabha passed three new bills which after becoming law, will administer the criminal justice system of India. They are Bharatiya Nyaya 2nd Samhita Bill, the Bharatiya Nagarik Suraksha 2nd Samhita Bill and the Bharatiya Sakshya 2nd Bill. See, these three bills are set to replace the existing criminal laws such as Indian Penal Code 1860, Code of Criminal Procedure CRPC 1973 and Indian Evidence Act 1872 respectively. As the bills were now passed by Rajasabha, they will be sent to the president for ascent and soon they are going to become laws. See, this is the crux of the news article. In our discussion, we will understand the key provisions of the three bills. Now, first let us take Bharatiya Nyaya 2nd Samhita Bill 2023. See, this bill seeks to replace the Indian Penal Code 1860. The bill aims to repeal nearly 22 provisions of the IPC. Know that the bill also proposes changes to the 175 existing provisions of IPC. Additionally, the bill introduces 8 new sections to the Indian Penal Code. Now, first let us understand the changes to the existing provisions of our IPC. Firstly, the punishment for all types of gang rape under IPC will be enhanced.  Secondly, the punishment for the rape of a minor under the IPC will also be enhanced. As per the bill, a person who involved in raping a minor will get death penalty. Moreover, note that for the first time the bill introduces capital punishments for the offence of mob lynching. The bill states that the offence of mob lynching would be punishable with seven years of imprisonment or life imprisonment also. Fourthly, the bill proposes to omit the provisions under the offences of adultery. See, this is in line with the Supreme Court's ruling under Joseph Schein v. Union of India case. See, this case declared that section 497 of the IPC was unconstitutional. Note that 497 of the IPC dealt with the criminalisation of adultery. See, these are some of the important changes brought to IPC under the Bharathi and Nyaya Sanhedra Bill 2023. Now, moving on to see about the new sections that are being included in the IPC. Firstly, the bill introduces section 109. See, this new section will deal with the organised crimes like drug trafficking and smuggling so on. Secondly, the bill introduces section 110. This section will deal with a petty organised crime like automobile or jewellery theft. Then, the third section is section 111. See, this is an important section which deals with the offences related to terrorist acts. Fourthly, with respect to section 302. See, this section will deal with the issues. And finally, section 150. See, this section will deal with the acts of a person which will endanger the sovereignty, unity and integrity of India. Section 150 says that if any person commits an act that injures the sovereignty or unity of India, then such person shall be punished with imprisonment and he is also liable to pay fine. Note that this section 150 has been introduced to deal with the sedition. This new bill will replace the section 124A of the IPC which shares trial dealt with the sedition. Ironically, the bill retains the sedition in another form by introducing a new section called section 150. See, this is all about the Bharatiya Nyaya Sanjitha Bill 2023. Now, let us move on to see about Bharatiya Nagarik Suraksha 2nd Sanjitha Bill 2023. See, this bill will replace the criminal procedure code of 1973. The bill seeks to repeal 9 provisions of the CRPC. The bill also proposes changes to 160 provisions of the CRPC. In addition to this, the bill also introduces 9 provisions to the CRPC. Now, let us see some important provisions related to our exam. Firstly, the bill seeks to introduce a new section called section 230. This section mandates that a copy of FIR should be available to the accused and the victim at free of cost. Note that it further states that the FIR shall be made available within 14 days from the date of production or appearance of the accused. This provision ensures transparency in the investigation procedures of the police. Secondly, the bill permits the filing of zero FIR from any part of the country. Now, we have to know about what is the concept of zero FIR. See, when a police station receives a complaint regarding an alleged offense committed in the jurisdiction of another police station, zero FIR mandates that the initial police stations which received the complaint now, it has to register the FIR. And later, it has to transfer the FIR to the relevant police station for further investigation. See, this is what the concept of zero FIR. So, it eases or it permits the filing of zero FIR from any part of the country. Thirdly, the bill allows for the examination of the accused persons through electronic means like videoconferencing. It will help to expedite the investigation process. See, this is all about the Bharathi and Nagarik Surakshasanthi Bill 2023. Now, finally, let us see Bharathi's Shakshya 2nd Bill 2023. See, this bill will replace the Indian Evidence Act of 1872. The new bill proposes changes to 23 provisions of the Indian Evidence Act. It also introduces one provisions to the act. Now, let us see some important provisions in this bill. Firstly, the bill permits the use of electronic or digital records as evidence. As per the bill, the electronic or digital record will have a legal validity as a documentary evidence. So, it can be used as an evidence. Secondly, the bill expands the ambit of secondary evidence. For example, the copies which were made from the original evidence by a mechanical process can also be considered as the secondary evidence. Like this, the bill expands the ambit of secondary evidence. See, this is all about the Bharathi Shakshya Bill 2023. See, this is all about this discussion. In our discussion, we saw about the three new bills regarding our criminal justice system. This is all regarding the discussion. Now, let us move on to the next part of our video, that is to discuss the preliminary practice questions. Today, we are having four questions. Let us solve them one by one. See the first question which of the following symptoms is commonly associated with COVID-19 and distinguishes it from the other respiratory illnesses. See, out of four options, A, C, D are very generic and will be common to all other respiratory illnesses. So, eliminating all of them, the correct option would be option B. See the second question, which of the following about Namdappa Flying Squirrel is correct? See the first statement, it is endemic to India, Nepal and Bhutan. See, from our discussion, we saw that it is endemic only to Arunachal Pradesh, India. So, the statement A is wrong. See the second statement, it is listed as the least concern by IUCN. See, from our analysis, we saw that it is listed as a critically endangered species under IUCN. So, it is also wrong. Third one, it primarily inhibits wetlands and lakes. See, from our discussion, we saw that the Namdappa flying squirrel is commonly found in the high altitude forest of the Namdappa National Park. So, this is also wrong. See, the final statement, it is a nocturnal species known for its ability to glide between the trees. See, this statement is correct. So, the correct option is option D. See, the third question of the day, consider the following statements about Competition Commission of India. First statement, it was established under Monopolis and Restrictive Trade Practices Act 1969. See, it is incorrect, because CCA or Competition Commission of India is established under Competition Act 2002. See, this act replaces the MRTP Act. Let us see the second statement. CCA consists of chairperson and maximum of four members. See, from our discussion, we can easily say that it consists of maximum six members. See, the third statement, the decisions of the CCA can be appealed only to Supreme Court of India. See, this is incorrect, because the appeals from the Competition Commission of India can be made in National Company Law or NCLAT. So, eliminating all of them, the correct option is option D. See, the final question of the day, the Post Office Bill 2023 allows for the interception of the postal articles on various grounds. How many of the below mentioned grounds are stated in the bill? First statement, security of the state. Second one, friendly relations with foreign states. Third one, public order. Fourth one, emergency. Fifth one, public safety. See, from our commentational perspective, we can say that all these five situations will come as a ground for any exception. So, all of them are correct. So, the correct option is option D. See, the main question based on today's analysis is listed here. Interested participants can write and post it in the comment section. If you like today's video, you can like, comment and share it with your friends. For more updates regarding civil service preparation, subscribe to Shankar IAS Academy. Thank you.


Hi, everyone, Joe for Jasper's casebreaks.com coming at you with 2021 Panini National Treasures Collegiate Football. This is FOTL, first off the line edition. So if you're not familiar with that, they release this, you know, first, before, I think, direct to consumers instead of through the distribution process, blah, blah, blah, blah. Anyway, comes out first, exclusive parallels, usually pretty loaded, fingers crossed, let's see what we got in the box that we're going to do, which is actually coming from a fresh case. Big thanks to this group right here for making it happen. Thanks to the people who bought their spots straight up and congrats again to the winners of spots in those two, the two fillers out. We did remember I accidentally wrote filler 25 twice in the title, but in the skew number in your order confirmations, it will say 26 on it. Next pack will be, we'll skip to 27 and we'll post another one of these one box breaks as well. So that's where those numbers look a little weird. All 32 teams are in. Let's roll it, let's randomize it. Two out of four, six times for names and teams. One, two, three, four, five, and six in the final time. Kevin, down to Aaron.  Six times in column A, two out of four, six times for the teams. One, two, three, four, five, and sixth in final time. After six times we got the Pat Riots down to the Eagles. I'll give you a little trade window here too. All right, Kevin with the Patriots, Aaron with the Steelers, Bradley with the Seahawks, Aaron with the Rams, Nicholas with the Broncos, Aaron with the Ravens and Saints. Brandon, you got the Chargers, Jeff with the Texans, Brandon with the Packers, Dale with the Chiefs.  Let's sort alphabetically by team. And while you're considering a trade, let me flip screens really quick. Here's the fresh sealed case, FOTL first off the Line 2021 NT Collegiate Football. I'm sure that's the right one. Let's pop this guy open. Let's pop this side open. If you want to run this back, I'd be more than happy to do so. Just use casebreaks.com. Alright, so from top to bottom, we'll go one, two, three, four on the dice roll. And if I roll a five or a six, I'll just roll again. One, top box. So we'll put a few X's right there so we know these are from the same case. Alright, any trades? No, not even a whisper of a trade. So let's just roll. TWC trade window closed. And let's just print and rip. Alright, good luck gang. Another one box rake will be loaded up. So if you want to run this back, I'm more than happy to do so. And we'll do the same process. We'll sell 12 spots outright and we'll do two of those fillers. If those full spots move more quickly, a lot of times we'll, you know, reserve the right to cancel a filler, add some full spots back in just to try to follow along with the momentum as closely as possible. Remember, we're going by that group rake checklist that I dropped into the chat if you're watching live. We always default to a checklist first from that particular year. So that 11 out of 99 to Sean Watts will go to Houston. And that'll be for Jeff with the Texans. And we have one out of 25 DeAndre Swift. It'll be a lion in this set. And that will be for Alan in Detroit. It's a cool looking... That's part of the 7 looks like, right? It's got to be. That looks cool. We've got Kyle Pitts, 15 out of 75. For Aaron and the ATL. Got a redemption. Oh no, sorry. We have college silhouette signatures. That's Rashad Bateman. Has he played today? No. He's probably not playing this preseason game, right? Yeah. No targets, no nothing, so maybe not. But no more Keys Brown. So Aaron Miller with the Ravens. That's a possibility that he may see some of those targets. Apologies to the Vikings. Amir Smith, Marseille tumbling over here. But we do have these soft mats right there to prevent anything. Significant. I don't know what he's been doing in the preseason. But that'll still go off to Ryan Hines in Minnesota. We've got 21 out of 99. Anthony Schwartz, that will be for Cleveland. Aaron Miller. Cleveland, this is for you. All right, we've got a 3 out of 8. T-Law, Trevor Lawrence, two-color jersey, and on-card autograph. That's some great penmanship there too. Jeff Henn got randomized the Jaguars from a spot he won in the filler and gets the T-Law RPA. I feel like it's one of the best autographs I've seen of his. That's very nice, Jeff. I hope he has a huge season this year. All right. And the book is going to be Alabama's Jalen Waddell, 20 out of 32. Dual Relic and Autograph for Miami. That is awesome. And there you have it, boys and girls. A nice quick break. An empty box right there. Nice quick break of 2021. National Treasures, Panini National Treasures Collegiate Football. One box, first off the line edition, Random Team Break number one. There's a few more boxes. We haven't seen any cool bowl patches yet. All these rookies that we're going to see in their second year this year, it's going to be great to see. It's going to be a lot of fun. So let's do another box. I'm Joe. I'll see you next time for the next first off the line break, jaspyscasebreaks.com.


Okay, sorry. I'll say it again. Doing the problem of estimating a covariance matrix, or more generally, estimating a matrix C that's been corrupted by a multiplicative noise so I have the w is some noise matrix. You can think of it as a white wish art which it is in the case of it for the sample covariance matrix, but more generally, it can be any multiplicative rotation invariant noise. It's easy to normalize it so as mean one. Okay, and then I argue that if you don't if you don't have a prior on your matrix C if you don't have a, if you don't have a prior on the eigenvectors of C, if your prior on C is rotation invariant, then you'll follow your estimator has to be in the case of rotation invariant estimators and a rotation invariant estimator, since the only eigenvectors in the problems are those of the matrix E, it must be in the same basis. So if E is diagonal. So you diagonalize E, you get eigenvalues lambda k and eigenvectors vk, your estimator of C will be in the same basis, but you can change a coefficient. For example, you have a tremendous dimensional reduction, you go from estimating and square coefficient to estimating just and coefficient, and the other merit miracle is that you can all do that in the large and limit, but the two miracles are related, because initially, you have sort of n square data and you're trying to estimate n square, the object of size n square, and that's very very hard to do to do a good job. Now, I only want to estimate and coefficient. So, there'll be, I still have a sort of factor and it goes to infinity. So I can have a concentration. If you want to talk about medical term but you have things that will actually converge to the right answer. By the way, this is a hopeless problem. It's impossible to recover C, exactly. You'll just get the best estimate of C. C is, I mean it would be extremely unlikely that C is in the base of E. Okay, so, so, so, so in typical meaning in every case, your estimator will be, will not be a perfect you can't find you can't have perfect estimation the only case where you have perfect estimation is this is parameter q, which is also super important here, and over T, if q, if q goes to zero, then then you recover perfect estimation. Okay, but, but, and, and, but, I guess in the general case I don't need this, this, this concept of q because I have a general noise. And what will matter is the S transform of this noise. Okay, so. The estimators in this form, we can ask the question what's the best we could do. So the best we could do is called the oracle. So suppose I, I'm looking for an estimator in this class. Okay, but I actually no C. So, okay, so it's kind of a strange question but it's kind of gives you a bound on how. So if you stay in this class, and you, and then the best you could do is the estimator, the best estimate of that class knowing see. Okay, so this is called the oracle, it's cheating. But it's useful to compute. And if you, and so the oracle would be. Okay, so I would say, let me just write the equation, what I want, I want to minimize I want the, I want the argument over the side K of, like a VK, K transpose minus C, and then I take maybe a I can take the trace of this. Okay, so if, if I know the matrix C, then I'd like to fix the coefficient. So, so it's going to come with the problem I have some some basis which is not the basis of C, but it's a basis. The basis I have, what are the best coefficient. Okay, so this is the best estimate of C in the least per sense. Okay, and it's fairly easy to do to do I'll just give you the answer is to the side K. So and this is an oracle or to normal basis. Okay, the VK or norm, their, their, their, their, their normalized eigenvectors so they're orthogonal and, and normalized. And then you get that the coefficient or just VK transpose C VK. Okay, so the intuition. Again, here, I'm sort of using the language of finance. C is kind of a risk matrix that I'm trying to estimate. These are, you can think of them as portfolios their vectors of weights on stocks. So the best risk that you should apply to each of these portfolio. Well, in this case, it's kind of, it's kind of pseudo. Well, it is the, it is the eigenvalue of the matrix. Chi. And what I can value you should use is the realized risk the real risk of these portfolio. So if that that finance analogy is something. Okay, but you can just do this in two line computation. Okay, so the question is, can we estimate something like this. So, obviously to compute this I need the knowledge of C. And so as I said, then the the there's a miracle that happens in the large end limit that you can actually achieve this without knowing C. Okay, so the, the, and if it will be the argument as follows, this is the best. So I'm stuck in this, I'm stuck with this class of estimator. And in this class of estimator the best I can do is this. If I achieve this on average, then I have the best of this class of estimator and this class of estimator is the, the best I can do in this problem. So, and this shows that the estimator that will build is optimal. And, and, but of course, I need to do this without the knowledge of the matrix C. But I will you see I'll be using these kind of properties, especially the one at the bottom that where well actually I'll specialize it to the problem that that that I'm looking at, I'll be using the T transform of E. I'm going over W. And I'll have. So I'll have something like this for, for my problem where I have the free product of C and a matrix W. I'll be using an expression like this, which relates to me. So this matrix in the basis of E and a matrix in the basis of C. And from this I can compute, I can have a relationship between the eigenvectors of E and the eigenvectors of C. And this will, and it's essentially this is a sandwich between the eigenvectors of C and so these are the eigenvectors of E and, and the matrix C some. This is the kind of thing I'm going to try to do. I'm going to try to do this. Well remember, well. Yeah, so remember the G matrix. This is maybe more useful I won't use this one but remember, I said this many times that it's, it's a projector vk okay let me, this is E. But it's true for any matrix. So, so the idea to try to get something like this I wouldn't I would like to. So to know psi of K, I just need to. I need to, to, to, to take GE and Z matrix C take the trace. If I do this I will have. Yeah this I can also write as trace of this is a this is a scalar this is a number, you can write as trace of vk transpose c vk. And then you can use the cyclical property of the trace. It's also the trace of C, vk, vk transpose. If I can take the trace of the matrix C with a projector on the on the eigenvector. I have the quantity that I want. And remember, the resolvent at this format the resolvent matrix as a projector on each eigenvector with a pole at the eigenvalue. So, for the, but I want to be using the T matrix because for the product the T matrix as as this beautiful property. So for the T matrix is very similar for T matrix I have that it's equal there's just an extra matrix here, which shows up here as sum over K of lambda K, vk, vk transpose in the same pole is the minus lambda K. Okay. So basically what I want what I morally would like to do which I could do in finite and so at finite and these objects of actual poles. Okay, so at finite and what I really wanted to do is trace of C, T, E of Z. So this would give me sum over K of lambda K, vk, vk transpose C, I take the trace, let me pull out the lambda K, and then I take a trace here traces linear, I can, and then Z minus lambda K. So this trace I'm interested in, I could just take the residue, so I can compute this function. And I take the residue at, at, so if I want side K if I want side 27. I just take the residue at the pole Z minus lambda 27. And I will get, I will get this object that I want.  The problem here, when we do the continuous limit is that these functions, when there's a lot of eigenvalues, they don't, well, if you want on the real axis they stay, they stay random, and near the axis, they behave as the, all these random eigenvalues behave as a branch cut. So, taking a residue at the branch cut won't work. Doesn't make sense, but nevertheless this is never, this is the right object that I want to compute. So, let me just call this object. Let me just call this H of Z. Okay. And, and, and really this quantity. Here, I've written it, this is side K. So the quality I'm interested in is side K, so side K is in this equation so let me rewrite it. So, above H of Z, I said, it is equal, I'm not sure I can compute it but it is, it's true at finite N and it will be equal to lambda K, side K, Z minus lambda K. So, I have this T transform of the matrix E. I trace it with the matrix C that I don't know but later in the computation I'll manage to get rid of the matrix C, but so I can define this unknown function H of Z. And at finite N, it has this pole structure. It has the coefficients I want. The coefficients are residues of poles of for, and then lambda K's are the eigenvalues of E. Okay. And, but now I want to take the large N limit of this equation. And then the large N limit, if everything is nice and smooth. These all go to continuous function. If I'm evaluating this function not on the real axis but anywhere else in the complex plane, I claim that this will become integral from lambda minus to lambda plus the assuming that the spectrum of my matrix E in the continuum limit will have a density of a row of lambda I could have poles as well but a direct masses but let's assume it converges to a, to a nice density without direct masses. And, and this density is defined is bounded so it's defined between line and the minus and lambda plus, and then I have lambda side becomes a function of lambda. So I have lambda minus lambda d lambda. Okay, so what I'm saying is that this sum in a continuous, evaluate at a Z that's outside the real axis converges to an object like this one. And the object I'm trying to, to get is psi of lambda. So what is client lambda.  But I can write it as psi of lambda k v k v k. I'm also estimate I'm also making assumption which is justified that that this coefficient converged to a smooth function of K, and K becomes a continuous index, and instead of labeling it from from zero to one. So in increasing order of eigenvalues it's it's easier to to label it by the corresponding eigenvalue and. Okay, so, so psi of care now right it's psi of lambda k, and I said it psi of lambda k behaves as a nice smooth function that I'm trying to estimate. So this is, this is why I'm saying that this lambda of course. This is lambda. I have a sum over K but I'm switching to an integral over lambda so I need the density. Okay, and just remind just the parallel, which you which you should all know is G of Z, for instance, which was some over K, the classical function just transform Z minus lambda k. It converges to an integral row of lambda Z minus lambda. Okay, so it's really the same type of of continuum limit. And again this is only true for an argument Z elsewhere in the complex plane on on the real axis. These are random functions with poles and they they're violent and they don't converge anything nice. So if you look away from the real axis, these converge tonight functions. Yes. Yes. Yes, yes, yes, where happened to my one over and so here definitely there's a one over and here there's a one over and, and I lost a one over and somewhere. It's in the trace. Yes, here it's a. Okay, I'm sorry. This is. This was a towel. So let me put a trace. Yes, really it was a towel. So this is a towel and towel is really trace one over and. Okay. So H of Z is towel of CT using. And then, then I need a one over and here. Okay. So I'm almost done. I'm not, not almost done but by the way, I know if we, when do we end. Okay, so what can I erase I'll start over here. Okay, fine. And then this. Basically, I'm going to use again the plan. Sorry, I never in the Plemish formula. So you know the Plemish formula for, for, for, for G is that once I have the continuous version of Z. You shouldn't all know that pi times the imaginary part of G of lambda minus I epsilon, when I take the limit of Ada, Ada times those two zero plus this equals. It's one of the fire. So fire row of lambda. Okay, so. So this. And this is not specific to the function row. I mean this is true for any such integral. So in my case I have, I have the what's on the numerator is not row but row times lambda times this function psi of lambda. So the claim is if I know this function H of Z, I can recover so that the imaginary part of H of lambda minus I Ada will converge to pi row of lambda times lambda time this function I'm interested. Okay. So, if I have my function, I just need to, to compute this H and take the specific limit. Look at H on the real axis because really, okay, maybe just practically this step back a little bit. What are we trying to do. We have a sample covariance matrix E. And we know it's not a good estimate. Okay, so yeah. We're going to pause to pause anyway here to try to remember what are we what are we trying to achieve. We have a sample covariance matrix E. And we know that for instance it's eigenvalue distribution is too wide. Okay, so maybe the truth see somewhere here. And, and so in a sense, we'll need to shrink the eigenvalues because we, we know from the direct problem that the matrix E is wider has a larger variance. And so, so what we'll like to do is build an estimator chi, which which I write again as psi of lambda k so basically I go from. What I want to do is take the eigenvalue so lambda case or the eigenvalues of the matrix observed, and I want to modify them by a function. So I'm trying to find this function, the optimal function to shrink the eigenvalues. So to think of this function. This is as a function of lambda. Well this function is really only defined from lambda minus to lambda plus. I really don't care where the function does outside. But actually, it's not true it even tells you something if you have a few outliers, the function can tell you how to treat also the outliers because this is really a theory of the bulk, but it also works. There's a word by Auntie Knowles on the fact that that this also works for outliers. Okay, but anyway, let's focus on the bulk. No size is the replacement function this is this is the continuous version of side cake. So, what I want to say is that. So if I don't do anything if I don't clean my data. There is the. So this is the Y equals X line. Okay, so this is not doing anything. Okay, so I, so if you think psi of lambda, if I say, if I say psi of lambda equals lambda for instance maybe right this way, psi of lambda equals lambda is the, I don't do anything function. I said this is equivalent to say my estimator is just a sample covariance matrix. Okay, but I know that the small eigenvalues are too small, and the large eigenvalues are too big. And that's one reason and also the fact that I don't know precisely the eigenvector also forces you to do even more shrinkage. What you end up doing is some thing where these guys you definitely want to move up these guys you want to move down and you want to do something in the middle. Well, it's actually, it's actually monotonous. Okay, so your function you want is a function that, and actually, yeah, so, so this, this is lambda and this is psi of lambda. So if I say that shrinks, I mean I should use a different color although I don't think the colors show very well in the screen but so have a function here might be like this and I have different shape depending on on the noise and. Okay, but I want to it's a shrinkage function, it tells you I see an eigenvalue lambda that's small, I give it a bigger value, and then I see a big one I give her a smaller value, and I do this in a sort of way, and typical eigenvalues are one, and so an ideal value one I typically, I might move it a little bit but but but one is not exactly a fixed point but an approximate fixed point of this problem. And so, okay, so this is the, so this is the function we're trying to get. And I argue that in the continuous limit on the nice circumstance, it converges to a smooth function of lambda. And it's actually monotonous, I'm not sure with the I think we finally proved that it's monotonous but but I intuitively has to be monotonous it'd be very strange. If, if this function is not in monotonous the increasing. So if I was small I can value, I do something with it, but I'll. Okay, so this is how I build my estimator. Okay, and this is the function here. So in a, it's just. So I have a this function of a complex variable H of z. So, again, H of z is going to be the normalized trace of T, E of Z, I'm seeing, so I haven't computed this function yet. By the way, it's very similar to the, the object that I encountered yesterday in the, the phase retrieval problem. So there was a function that I didn't compute in the phase retrieval problem, also called H of z, but it was a slightly different version of this but it's again, a phase of some noisy matrix and, and, and the original matrix, except that in the other case, the, the, with the Wishart matrix and the noise were sort of inverted but anyway. So, so I haven't told you how to compute this and I really hope I can do this in 15 minutes. But if I know this function, then I'm done, because on the relaxes where they're where their eigenvalues, this thing will have a branch cut. I can look at the value of the branch cut which is really this process of taking the imaginary part very, very close to the relaxes. The branch cut of this function will give me my this function kind of lambda time stuff that I know I know pi and a row row this is the sample, the sample, I can measure the sample density. So the sample density I know I know pi I know the lambdas themselves. And so I, from this, the branch cut of this function H, I can estimate this function, at least in theory. Okay. And so, and this function as I said it's something it's just some of her shrinkage function that will take for, for, for noise that definitely, it will be some sort of monotonic function of lambda. Okay, and, and there's some sort of limit when there's no noise, you get the identity function, when there's infinite noise, you just get a flat, you can estimate everything, anything. So, so the other extreme limit would be psi always one, this would be the sky like kind of the infinite noise limit. So the no noise limit you get, you get cycles lambda, the infinite noise you get cycles one and for in, in normal case you get something in between. Okay, now, how do we estimate this and this is where these formulas become in handy. Okay, because you see, I need to compute the normalized trace of a tea operator. This is the matrix of a noisy matrix and trace with with C. And if I look at this relation that I've specialized. So, the expectation value over the noise of the team matrix that I'm interested in is related to the team the team matrix of C. The expectation value of the matrix of C is super simple. It's an object like this is C data identity minus C. Okay, so let's let's let's see what we can do with that. And then just a little bit of simple algebra to recover something useful. And see the clock is running. Keep this. Is that I can take this expression, multiply this is a matrix expression, but I can multiply by C on the left and on the right and take the normalized trace. Okay, and so I get that my function H of Z will be given by the normalized trace of C. And then let me specialize exactly.  Capital Z. So, so, and maybe I'll use a lowercase z or data. So, so capital Z will be what's in the, the argument and the argument is is well little Z as transform of the noise evaluated at the T transform of the sample covariance matrix. Okay, so this is just this argument here that I give it a letter to be able to to do the algebra more quickly. Okay. Yes. Yes, but it's a normalization convention I don't actually need it. I don't know. It's just a clean way of normalizing things so that the typical eigenvalue is one, and so on. If trace of C were seven, then the typical eigenvalue would be seven, and etc. So a clean way maybe it doesn't cost anything to normalize in that way and it's easier to when I plot things that one is the value where where I expect most eigenvalues to lie or the average eigenvalue etc. Okay, so I just define this this this variable Z is the argument, and then. You know, just like T of C is C evaluated some data is data identity minus C inverse, but here this and I need this evaluated at this big Z. So I have C, another C, not going to write C square, because I'm going to expand this, and then big. So it's just that I'm evaluating this. Yeah, I'm evaluating the, the, the, the, the T matrix at this argument. Okay, this argument is a bit messy. So I'll just leave it here. Okay. And now I want to do some very simple algebra. I have C of two C's and basically what I would like to do is, is, is relayed back to, to another to the original T transform. If you want the one thing that I also have this other expression that T of E. The value of Z is T C, even a big Z. Okay, so if I can. And T C is really the normalized trace of C evaluated a big Z. So what I'm trying to do is recover an expression like this, except that here I have two C's I have C squares. Okay, but instead of writing C squared C times C, and you see that by adding and subtracting this identity matrix times Z. I can use the fact that that this is the inverse of what I will, I will build something that will cancel this term. And so I actually did this way I'm going to get rid of one of the C's. Okay, so let me do this. Let's say that this is the same as tau of C, C plus C minus big Z identity plus big Z identity so I haven't really done anything, and then I have big Z identity minus C inverse. Okay. So if I look at this term here. The inverse of this term with a minus sign. Okay, and this is just a constant. I mean, in the matrix sense. Okay, so what I get I get. Well, let me tell of minus C. This is the identity minus C. And then I have this term here which is the identity matrix that can pull out of the trace, plus Z tau of C. This is the identity minus C inverse. Okay, well this is just the T transform of C evaluated in capital Z, and the T transform of C value in capital Z is just the T transform of E evaluated in the normal Z. So this is just plus Z. E of Z. I should put smaller Z's like this. So you don't don't confuse.  Okay. And here. The the this this has disappeared. Sorry. This is this here. This is the inverse of that. So it becomes the identity matrix. So I get minus tau of C plus minus because this is the minus the inverse of that. Okay, so this is my major H my matrix H of Z. It's very simple. It has a term that depends on the trace of C, but actually, I don't even care about this because it's this is real. This is real. And the only thing I really care about every race it's here is imaginary part. So this doesn't even contribute to the imaginary part. Okay, so that's, and then. And then I have the, the T transfer and you see. It's like miracle it's gone. See is gone. Well, here, what's left is a trace of C but, but it's real anyway so I don't care. And I've managed to express everything back into quantities that I could have principle observe the T transform of the sample covariance matrix. And this object here, which has the S transform of the noise, but evaluated the T transform of the sample covariance matrix. This is the sort of the large and miracle that essentially because everything converges to limits that I can compute. I could actually compute this only using objects that are that depend on E. Okay, so I put all the pieces together. And then you're going to have to trust me on some simple algebra with imaginary parts and so basically what I need to do. I'm really interested in in psi. So psi is really H imaginary part of H divided by row. This is itself. So row lambda actually row lambda is the imaginary part of the T transform. So I can write it as a ratio of two imaginary parts. So, this is what I'm going to do. And then the factor of pies cancel out so I get psi of lambda will be equal to some ratio. Initially, let me put the limits but actually it could be the same limit to ratio of two limits of imaginary part. So I have the imaginary part of I really erased it, but it was to do to what was it. Use my notes because I don't want to say something silly. Yeah, it's. T of E. Evaluate that lambda minus I eta times S transform of the noise evaluated the same T transform divided by. Okay, so it's a ratio of the imaginary part of the T transform. Except that on the numerator, the T transform is multiplied by the S transform of the noise. So if the noise is one. If there's no noise. If there's no noise the S transform of the noise is just the one. And then I get the ratio of something divided by something but the same thing. So, and there was a lambda that disappeared. What happened to my land anyway.  Okay, so. So, so if the noise is zero, then if there's no noise, no multiple, no multiplicative noise means multiplying by one, the S transform of the identity matrix is one. So I get the ratio of two quantities, exactly the same. So I get that the, the, the, the shrinkage function is lambda itself. Okay, then I can do a few things that I don't have time to do, but I can specialize. And then I go back now I say okay well what really just mean we're sample covariance matrices. So if I say the sample of the noise is one over one plus qt. Then I can write explicit equations that a bit more explicit than this. I promise that if C is an inverse we chart, then actually you have explicit formulas for T e. Okay, so, so, so he becomes the product the free product of which are an inverse we chart that that's that all of this is very explicit, and you can actually write the formula, and you get, you get linear shrinkage. And what is linear shrinkage is you get something very simple you get a side of lambda is essentially alpha times the identity. Or maybe I'll write it as alpha times your matrix plus one minus alpha times the identity, and alpha is some sort of signal to noise ratio. I think alpha is is p over p plus q. The variance of the signal divided by the variance of the signal plus the variance of the noise. Okay, this is typical shrinkage. Oh, yes, this is also okay you can write it here lambda. But this translates directly onto a matrix. The matrix chi is alpha identity plus one minus alpha identity. So here's the number one. Yeah. So, so basically, you have a shrinkage function on the eigenvalues but because it's a linear function of the eigenvalues. It's a linear function of the matrices themselves. So this is the only the only super simple case. Okay, and as I said, this is even true in finite dimension this was done by statisticians. In finite dimension, you can you you don't do you don't use this you use a Bayesian approach, and the fact that C is an inverse wishart you say you put an inverse wishart prior on the matrix. And, and you get this formula, but in this context what it means is that. That these formulas, you do you do recover the Bayesian what I want to say is that you do recover the Bayesian approach you do see that this is a shrinkage, and a shrinkage is always a signal to noise parameter. So, q is the noise in the in the sample covariance matrix P is the amount of signal that you have in the original matrix. So this is kind of a signal to noise ratio.  These are all continuous functions on branch cuts. And in real data, you have finite and then you have polls. And so I haven't told you how to deal with that, but but the simple trick. One trick that works. It's not the best thing you could do but it, but it's, it's the first thing you can do is to just take an imaginary part. An imaginary part that's not too big or not too small. So, imaginary part of order one of a root and then you can apply this.  But so, and in a way in a way to a way to but you can you could just make take this limit and not go to completely zero. You basically say, Okay, I'm going to use eight I got one of our square root event and use the equation as is, and this is a pretty good answer. You can do better, but you need to work more and to play with data and. And I'm done. Sorry, for being a bit late. Thank you for one question. Isn't it a mixed up in the notation and a bit confused for a minute or two, like you end up with HZ at the top, which is some of our care of lambda k psi k Z minus lambda k. Yes, yeah, and below you, the H of Z is the tau of T e time C. Yes. The lambda case are the eigenvalues of E. Okay, this is role. This is role of E. Okay, then it's fine. Yeah, I actually never use in this derivation. I've never actually give you a symbol for the eigenvalues of C. C appeared as a trace C appears in the trace. I never actually use an eigenvalue decomposition. So nowhere in the computations do I needed to tell you what the eigenvectors or the eigenvalues of C is. There's another way to do it is that Jean-Philippe Bouchot prefers because it's to define the overlap between the matrices, and then, and it's even more intuitive in a sense. But I find it's a bit cumbersome. I find it more cumbersome, but he prefers this formulation and then this is what I prefer. So, so you can define, you can say that C as eigenvalues mu's and eigenvectors use, and then you ask yourself, if you have a ul and a vk, what's the overlap, and you can define the overlap function. And the overlap function will depend on lambda and mu. The problem with that is the continuous limit, the continuous limit of that is a bit tricky. And so you need to be a bit fuzzy about what you're, but I guess you can make it more rigorous, but I find that this is closer to being rigorous. It's very far from being rigorous, but it's slightly closer to being rigorous and then introducing this matrix of, so basically it's a function of two parameters, lambda and mu, so it's a function of, which tells you how an eigenvector associated with lambda of E, what's the typical overlap with an eigenvector of eigenvalue mu for the matrix C, and you can do the sole derivation by introducing this function, which actually useful because this function can be used in other computation as well. I don't know what you do in your paper actually, but in the book you do that kind of question instead. I think we do both, yeah. Okay. Yeah, we first introduce this big five of new and lambda. But then, then I think we go straight to this. Yep. All right. If not, then thank you very much. Thanks.


Good morning, John. Last month I had a big Twitter thread and then a Vlogbrothers video about the temperature of the surface of the North Atlantic Ocean and how it seemed to have increased, at least in part, because we mandated low-sulfur fuel and cargo ships and the sulfur had been reflecting light and seeding clouds, which decreased the sunlight hitting the ocean. And how, in effect, we had been, like, accidentally doing geoengineering and maybe accidentally doing it would be useful in figuring out how to intentionally and thoughtfully do. And some people got pretty mad, some of them for good reasons. Mad enough that Radiolab called me and was like, hey, do you want to talk about how that day went for you as a way of exploring geoengineering? And we did that, and that episode is out, and it's great, and I'd love it if you listened to it. But look, I knew that people were going to get mad, I just didn't know how mad they were going to get. Some people, like, felt betrayed by me, because the reality is, geoengineering is the most controversial idea in climate science by far. Some people think that it is criminal, that we are not doing it right now. Some people think that we should ban even doing research on it. But I haven't been in that space professionally for a long time, so I had some catching up to do. Luckily, a couple of climate scientists who have YouTube channels agreed to talk to me in a video on Hank's channel that I have just uploaded. Adam of Climate Adam and Miriam of Zenturo talked me through a lot of the global warming conversation, and you should definitely check that video out. And also, their channels are amazing, and if you follow both of them, you will be among, like, the 99.9% most informed people on climate change, so you should definitely do that. It's low-lift, the content is super accessible, and great. But I wanted to make a video here that's just sort of, like, quick and dirty intro to why geoengineering is interesting and also so controversial, and why I think the fact that most climate scientists are opposed to geoengineering is, in fact, very good news. First, let's define the term. What is geoengineering? The definition is controversial. But broadly, it's any time you take an action to intentionally change the systems of planet Earth. More specifically, these days, when we talk about geoengineering, we're almost always talking about the amount of heat in the system. There is other geoengineering, like, if you wanted to restart an ocean current, if you wanted to change ocean acidity, if you wanted to decrease the amount of storms, all those things would be geoengineering.  We would have been engineering the planet to get warmer. But it wasn't engineered. It was accidental. We did it for other reasons. So it's not geoengineering. It's just an oopsie. It was initially an oopsie. It's not really an oopsie anymore. Now it's like, uh, stop hitting yourself, kind of situation. So these days, we're mostly talking about intentional actions taken to decrease the amount of heat in the planet Earth system. And importantly, there are lots of different ways to do that. We talk about geoengineering as if it is one thing, and it is not. Like, already we are doing some geoengineering. We paint roofs white, and that is like a main benefit of decreasing the air conditioning bills for those buildings, which also decreases energy consumption. But additionally, it does reflect some amount of energy back to space. Not a measurable amount, but that's part of the reason why we do it. So painting roofs white is geoengineering. But heading up the ladder of complexity and impact and controversiality, here's an incomplete list of other geoengineering things. High albedo crops, like crop plants that are more reflective and lighter colors, could make the planet more reflective. Ocean mirrors could reflect sunlight back to space. Marine cloud brightening would seed clouds over the ocean, reflecting more light up. High altitude cloud thinning would thin the wispy cirrus clouds that actually do a better job of trapping heat in the system than reflecting it back to space. And finally, stratospheric sulfur injection would be putting a ton of sulfur dioxide into the stratosphere because those sulfur particles are good at reflecting light and they'd stay up there for a long time. Each one of these has advantages and disadvantages. And as we went down that list, we got more impactful and scary. Like high albedo crops would have a small and mostly local and temporary reversible effect, whereas stratospheric sulfur injection would have a large and global and long-term effect. Now the argument in favor of doing these things, and each one of them is a solar radiation management technique. That's the term we use for managing the amount of the sun's energy that gets trapped in the system. The reason why we do that is because the heat is a big part of the problem. It's not the only part of the problem, like ocean acidification would not be helped by any of these things, and that's also a big problem. But the amount of heat in the system already is making life harder on the planet and that's just gonna keep getting worse decade by decade for a while. And honestly, we don't know exactly how much worse it's gonna get. And in fact, that is another vote in favor of doing geoengineering research. It could be that things get worse than we expect faster than we expect and it would be nice to have a tool in our back pocket just in case we need it, even if we don't wanna use it, even if we're not sure if it's gonna work or we don't understand all the harms it's gonna do. The arguments against are many and they are varied and I have sort of different feelings about them personally. And I'm gonna give them to you as I understand them and this is gonna be biased. First is this is gonna be good for fossil fuel companies because they're gonna do a lot of this work, whether it's like moving carbon around or it's doing all the chemistry that's necessary to do geoengineering. I don't care, look, I wanna be on the record.   If I knew for sure he could fix this problem. I would hate it. I would hate, I'm thinking of who it is. I would hate giving him all that money, but I do it. I might even say nice things about him afterward. Maybe, that would be harder, honestly. But, relatedly, number two, this would be good for fossil fuel companies because we just keep burning fossil fuels forever if we didn't have to worry about the heat. If we could manage the heat, then we'd just keep burning. This doesn't worry me that much because I just think it's wrong. I recognize that there are people who are like this who are like, we should just spend the money to do the geoengineering and not change anything. But, ultimately, renewables are just better. I would be more worried about this if the cost of solar and wind and batteries hadn't gone down by like a thousand times since I graduated from college. But they have, and already in most ways, they are better than fossil fuel infrastructure. And I think 10, 20 years from now, they will be way better than fossil fuel infrastructure. And we just won't use fossil fuels because they're worse. Now, onto the things I find more compelling. Number one, this is going to be by definition a trolley problem. What do I mean by that? I mean that if you're trying to do something that's gonna help the whole planet, there will be areas of the planet that are harmed. The scientists I've talked to are quite uncomfortable with this. They understandably do not like the idea that they might be put into a position where they'd be asked to advise on whether we should take an action that will like save a million lives but actually cause the deaths of thousands of people. And this is like not abstract. Now, for clarity, we already do this with accidental release of carbon dioxide all the time. Not accidental, incidental. We make decisions here in America to produce carbon dioxide and that's gonna have a negative impact on the world and it will result in death and suffering. It's not a comfortable idea, but it's a real idea. But we're not doing it on purpose. We're doing it so that we can go visit our family in Indiana. It matters when you're doing it on purpose and part of me thinks it shouldn't matter, but it does. So say like low level example, you just do some marine cloud brightening.  But maybe the water that's forming clouds there now would have formed clouds over land and fallen as rain and you're creating a different rain pattern and those people's crops fail. So they don't have the income they expected. They don't have the food that they expected and there's a fan. So yeah, trolley problem uncomfortable. Now we do that nationally all the time. Like when we say we're gonna shut down a coal-fired power plant or we don't want as many coal-fired power plants that has negative impacts on people. But we do it because it has positive impacts on more people. But that's very different when that's one country making decisions for itself than if it's one country making decisions for another country which leads me to the second thing that is a good thing to point out. Actively doing geoengineering could cause war. So say one country is taking actions that's making it better for the people in that country but it's resulting in less rain falling or flowing into another country and that country has instability because of that.  And I'm trying to get comfortable with the idea that the way that it feels matters because the way that it feels matters. Third, if we did it for a while and then suddenly stopped, that's very scary. So basically if we're doing this radiation management the amount of heat that would be in the system if we weren't is going up and up and up but we're getting that heat out of the system through radiation management. If one day through an accident or a policy decision or the fact that like one country was doing it in the other countries were like, you need to stop. If suddenly it all stopped after having done it for a while climate models don't like that. That could result in like a very chaotic series of events for the planetary system. There's even a term for it. It's called termination shock. That's scary both practically and because the term. That's just a scary term. That's a good one. Neil Stevenson. Next on the list, Miriam really drove this point home to me and helped me understand it. This isn't a thing that should be done unilaterally but it is a thing that could be done unilaterally. It's inexpensive enough to do some pretty large scale geoengineering that a single country and not even a big one could start doing. Also is totally possible that the countries doing that would be the ones who created the problems and might be doing it without regard for local impacts that would have. So you wanna do this in a way that involves ideally all of the countries kind of coming together and reaching some sort of agreement. And in a complicated system like the earth and complicated idea like geoengineering that sounds very hard and almost like it literally couldn't happen but maybe it could like we've done diplomacy on big hard things before. Next, and this is the second most compelling of all of these arguments to me. We actually don't understand this stuff that well yet. Miriam was talking about how like of all the variables and climate models, the things that like increase the error bar the most is actually aerosols. So like the effect of particles in the air reflecting light back to space. That's a lot of what we're talking about in geoengineering and we don't understand yet very well the mechanism of how that works and how much it does what it does. And this isn't just about like energy out, energy in. If it was just energy out, energy in then we'd understand it. But what it's also about is how it's going to affect the climate system as a whole. If we do stratospheric sulfur dioxide injection and it decreases the temperature of the planet by a degree that would be amazing. But what if it also dried up the monsoon season in Southeast Asia and then hundreds of millions of people are now food insecure when they were not before. If that's a thing that might happen you don't wanna do that which leads me to the last most important thing on the list of reasons to be very cautious about geoengineering which is we just got one planet. This is the only one. We're already messing with it and that's really scary. And to solve the messing with it problem by messing with it is understandably terrifying. And I'm like okay so we gotta understand it better and Adam makes a great point which is that in order to do an experiment that actually will tell you about the potential impacts of geoengineering you kinda already have to be geoengineering. When I made that original video what was so compelling to me about this marine cloud brightening that had been unintentionally happening reflecting extra energy to space cooling the North Atlantic is that we'd been doing it and it wasn't controversial while we were doing it because we were doing it on accident. And so to me like keeping doing it doesn't seem that scary but maybe it is because like we keep doing it in a different way. It might seem like blowing a bunch of sea water into the air so that salt crystals, seed clouds would be a pretty benign way of doing things but maybe it's not.  Maybe the salt that seeded those clouds would be a significant amount of salt falling on crop lands and thus making that crop less productive over time as the salt content builds up. None of this is simple.  And both of those things are very important things to consider when taking really big actions like trying to intentionally affect the systems of the planet. But the most hopeful thing I got out of this was that for the most part climate scientists don't think that we need to be doing geoengineering yet because we're not in that situation yet. And what I hear a lot on social media and from friends is that we are in the most dire of circumstances but when you look at what's possible it does still feel possible to solve this problem without resorting to geoengineering which might very well be a last resort. Which leads me to what I think is a fascinating question. Is taking carbon dioxide out of the air solar radiation management? Cause like yes it is. It would have been solar radiation management to put it in there in the first place if we'd done it with that goal. There is a kind of geoengineering that everyone is in favor of which is reducing the amount of methane and carbon dioxide that is released into the atmosphere and then reducing the amount that is currently in the atmosphere. And just like with geoengineering there's a long list of ways to do that that range from controversial to non-controversial. But if there is less carbon dioxide and methane in the atmosphere there will be less heat in the system. We know this and we are doing things as individuals in societies to act upon that knowledge. We are not doing it as fast as I would like. There will be tremendous negative consequences to not doing it faster. At least about this thing. Everybody who knows what they're talking about on this topic agrees on that. And that's a nice thing to have. I've put the link to the conversation that I had with Miriam and Adam on Hank's channel in the description, along with Adam's video that he made about my video which is very good. And also a link to both of their channels because as I said, if you follow both of them you will be among the most educated people on climate science in the world. And their content is so good. It's not complicated. It's very accessible and they know what they're talking about. And right now at Pizzamist.com there's a special bundle. Today's special is false to suggest bundle. It is false to suggest as some recently have that the Pizzamist hot sauce should be used on your cheats at John. In fact, this is a collaboration between two products that can only be shipped within the US which enables us to provide an excellent deal for all who celebrate Pizzamist.  That would be an absolutely wild thing to suggest. Totally irresponsible. Just get these two cool items for a deal. That's all. John, I'll see you tomorrow.


We youngsters nowadays have less control over our emotions. So how to react in situations where our beloved or close ones betray us? This girl is already heartbroken, eh? See, somebody can betray you or you can think they will betray you only because you have unrealistic expectations of them. Well, if they do what they want to do, why do you think they have betrayed you? They're doing what they want to do, you must respect it. If you say, they love it to me, I love them. If you love a person, should you let them do what they want to do or should they do what you want them to do? For most people, love means you must do what I want. No, no, love means they can do what they want and we will love them, isn't it? You have this thing that if I love you, you must listen to me. Oh no, if I love you, I want you to do what brings joy to you, isn't it? You understand the concept of your beloved? Water, our loved ones are going there in a way that's not good for them and we want to correct them. And that's why we are telling them. Then you should have been the mother. Because I'm not saying that it is never true that somebody may be going off track and you try to do something for them. I'm not saying it's never true, but you don't take this position that somebody is wrong and you're going to fix them. They're doing what they want to do, isn't it? What they want to do right now may not be beneficial for them, possible. But you must look at it sincerely. Are you complaining because it's not beneficial for them or you're complaining because it's not beneficial for you? Most of the time it's this, genuinely look at it. It's not beneficial for you, but it's good for them, please let them do it. But they are damaging themselves. Yes, then you have a right to intervene and try to do your best. But not always, not always can you enter somebody's life and do something for them. If I have to enter your life and do something for you, I have to earn it, isn't it? I have to earn a relationship where I can intervene in your life. If you don't earn that, you cannot intervene. So if you are unable to intervene, you must just understand you have not earned that. Closeness.