Massachusetts, Virginia, Tennessee, Mississippi, Montana, Utah, Oklahoma, District of Columbia, Puerto Rico, Shrek and Samoa, Northern US, Virgin Islands, state, flags, order, arms, and now we invite you to join the staff of the group, in welcoming the graduating divisions of your applause as they enter midway to Shermoneu drill hall and are announced in the following order. State flag color code 902 provides the recruit wire and drill team in band for today's ceremony. Ladies and gentlemen, you may be seated. Thank you.  For the remainder of the review, no one will be permitted to pass in front of the review stand. And we ask this as a courtesy to our reviewing officer. Photography is certainly encouraged, but we ask that you remain seated and off the drill deck. The photographers you will see on deck throughout the review are the official photographers of recruit training commanding, recruit commanders. Ladies and gentlemen, good morning. I'm Lieutenant John Godfrey, recruit training commander of ceremonies. I'd like to welcome you to today's past review. Today, you will see eight divisions comprised of 723 sailors participating in their graduation ceremony and soon to join the most powerful navy in the world. Please draw your attention to the unit position at center deck. There is the review commander and staff. The review commander is responsible for conducting the graduation ceremony. Today's review commander is Seaman Recruit Kendall Jarvis from Los Gatos, California. Let's give him a hand, folks. Performing today is the staff unit on their eighth week of training, the triple threats and state flags unit on their 10th and final week of training. These units are comprised entirely of recruits. During their night of arrival, recruits are placed in the divisions of 88 personnel and assigned division commanders. Recruit division commanders from the backbone of recruit training and our key individuals in the life of every recruit. Division commanders must serve as counselors, disciplinarians, administrators, and military leaders. Above all, they must show themselves as outstanding examples of military pairing, appearance, attitude, and behavior. Each division also has a recruit chief peddler officer. This senior recruit supervises the divisional staff positions and leads the division in the absence of their division commanders. Now, ladies and gentlemen, it's my pleasure to introduce the graduating divisions, their division commanders, and recruit chief peddler officers. As I introduce each division, they will raise competitive flags they have earned throughout their training. As I introduce each recruit chief peddler officer, the flag representing their home state will also be raised. Please hold your applause until all introductions have been completed. I will be starting from their right. Division zero, zero, one. Commanded by chief peddler officer, Summer Cates. Peddler officer, first class, Brady Chang. Peddler officer, first class, Bao Vu. And their recruit chief peddler officer, Seaman Apprentice, Devin Davis from San Antonio, Texas. Division zero, zero, two. Banded by chief peddler officer, Leiland Kuhn. Officer, first class, Anthony Douglas. Officer, first class, Christy Jones. Their recruit chief peddler officer, Fireman Austin Rinky from Milwaukee, Wisconsin. Division zero, zero, three. Peddler officer, Mary Nnamati. Peddler officer, second class, Gino Bono. Peddler officer, second class, Thomas Lopez. Their recruit chief peddler officer, Airman Apprentice Marcella Torres from Topeka, Kansas. Division zero, zero, four. Peddler officer, Antonio Olmos. Peddler officer, first class, Lucas Kiley. Peddler officer, second class, Kathy Garcia. Their recruit chief peddler officer, Seaman Apprentice Julia Vega-Meyers from Marietta, Georgia. Division zero, zero, five. Peddler officer, Jason Brownlee. Peddler officer, first class, Lamarcus Seabury. Peddler officer, first class, Alexander Iono. And their recruit chief peddler officer, Airman Voldemar Hernandez from Drozby, Texas. Division zero, zero, six. Officer, Salteria Robinson. Peddler officer, first class, Benjamin Page. Peddler officer, first class, Raul Garcia-Vecencio. And their recruit chief peddler officer, Seaman Apprentice Marcos Martinez from Oxnard, California. Division nine, zero, one. Chief peddler officer, Tim Yaca-Mission. Peddler officer, first class, Andrew Reese. Peddler officer, second class, Alma Gallegos. Their recruit chief peddler officer, Seaman Apprentice Andrew Murray from Townsend, Massachusetts. Division nine, zero, two. And then five. Chief peddler officer, Lazarus Bullock. Peddler officer, first class, Cody Gaines. Officer, second class, Jennifer Andouard. Recruit chief peddler officer, Seaman Gladys Garcia from Laredo, Texas. Demanding officer and staff for recruit training command, we congratulate these division commanders and recruit chief peddler officers on a job well done. You will see the ceremonial sideways boats in a nanoguard take their places for arrival orders. This time on our tradition is our formal greeting to this morning's reviewing officer. When requested by the announcer, please stand for the arrival honors, marching out of the colors, the national anthem, and the invocation. As a reminder, military guests shall remain covered throughout the entire graduation ceremony. And ladies and gentlemen, one final note. As befitting the importance of this occasion, our ceremony is conducted in a formal manner. However, we do encourage you to participate in today's graduation ceremony by letting your applause show these sailors just how proud of them you are. Once again, welcome aboard. Will the guests please rise and remain standing for the arrival of the official party, recruit training command. The guests may be seated. Please rise, present this morning's invocation. Let us pray. Almighty God, creator of all that is, we thank you that we have the opportunity to come before you today to celebrate the great accomplishment of our new as United States Navy sailors. Thank you for the successful completion of boot camp here at recruit training command. We thank you for their families, friends, and mentors who have encouraged and inspired them to get to this moment. We also thank you for the RDCs, the instructors, facilitators, and staff who have sacrificed greatly and forged each single one of their lives for the past several weeks. These sailors have been tested and tried, and yet through the pressure they have been transformed into warriors. Now these warriors, these mighty sailors, stand here today with the awesome responsibility on their shoulders, that future freedom is dependent on them, and they have the great responsibility to their families, their country, those who have served before them, to the constitution they swore to defend, the leadership, the world, and future generations. We pray, we pray they won't fall to the weight that rests upon them, but they will rise for the tasks that are set before them. And we pray that they would be men, women, and great characters who are confident and tough and always ready to get the mission accomplished as they defend freedom and democracy around the world. So then, as our new sailors go around the world, who are now be forged by the great sea, may they always be a beacon of hope and light, and Lord, may you always grant them immeasurable courage, unwavering strength, sound guidance, and godly wisdom, but most of all you remain their spiritual anchors of faith, hope, and love, and may their lives always reflect the core values and core actions and everything that they do. In the most holy name we pray, amen. At this point, the commanding officer will issue orders and instructions to the unit commanders, then the unit commanders will be faced about and relay the information to their divisions. Today's events show how orders are passed through the chain of command. Divisions, report, sir. Very well, I present the graduating division. Request permission to make sure of you. Very well, make sure of you. Aye, aye, sir. Good morning. I'm Commander Rick Jarco, Executive Officer of the Crew Training Command. On behalf of the commanding officer, Captain Kurtrick Brooks, I'm pleased to welcome our families and friends to our graduation ceremony, and we look forward to sharing this momentous occasion with you. I have the pleasure today of introducing and recognizing one of the finest Americans that I've had the opportunity to serve with in the United States Navy. And I'd like to recognize him today because this is his last graduation as the Command Master Chief of the Crew Training Command.  So I'd like to ask him to stand up before he heads off to be the Command Master Chief of the USS George H.W. Bush, an aircraft carrier currently on deployment where he will lead sailors doing real-world Navy work right now. I'd like to ask him to stand up and recognize him with me with a round of applause. He had the opportunity to lead 75,000 new recruits, new sailors headed out to the fleet, many of which he will lead again on the warship to our J.W. Bush. So thank you, Master Chief, for your service here at Recruit Training Command. Also with us today is our reviewing officer, Captain Omar Martinez, Commander's Action Group Naval Service Training Command. I cannot thank all of our visitors enough for your continued support, and I'm sure your sailors are grateful for your encouragement throughout their training at Recruit Training Command. I would also like to welcome all the veterans in our audience and thank them for their service to our country. Would all of our veterans please stand up and let's give them a round of applause. Divisions 901 and 902 graduate today. Division 901 is the state flag unit providing the 50 state flags, District of Columbia and U.S. territory flags, drum corps, and color guard. Division 902 is the triple threat unit providing recruit choir, drill team, and band. Please join me in giving them the six other graduating divisions here today a round of applause for their outstanding performance This is where our Navy heritage meets the future and where these young men and women enter the profession of arms. The staff of Recruit Training Command is dedicated to providing the United States Navy with basically trained, physically fit, and smartly disciplined sailors such as those standing here this morning. These sailors have successfully completed 10 weeks of demanding recruit training. They have earned the right to wear the uniform recognized throughout the world as a symbol of freedom They and others like them serve as the bedrock of our naval forces. They will join other sailors around the world to give our Navy its combat edge and enable us to keep this nation secure. This training group is ready to graduate and serve in the world's most powerful Navy. Ladies and gentlemen, I present to you 723 of the newest and sharpest sailors in the United States Navy. Recruit Training Command's competitive system among individual recruits and divisions promotes teamwork, attention to detail, and pride and accomplishment. Divisions performing above standards throughout their training are awarded recognition flags in the five mission areas. Academic achievement, military drill, compartment readiness, applications, and physical fitness. These flags are carried as a visible symbol of the division's success. Each flag indicates that your sailors individually and as teams met performing standards in one or more mission areas. A division that excels in every phase of training qualifies for the battle efficiency honor division recognition and is awarded the battle honor flag for this exemplary achievement. Division zero, zero, five has earned this honor today. And we congratulate Captain Martinez who will now present this week's individual awards and he will be joined on the drill deck by our Executive Officer, Commander Jargold, and Recruit Training Command's Command Master Chief Wallace, and the General Academic Seaman Stephanie Lee, Division zero, zero, four from Dana Point, California, has earned the Academic Excellence Award which is sponsored by the Lake Defiance Chapter of the Illinois Society of the Sons of American Revolution. Seaman Lee receives a letter of commendation from the commanding officer. Well done, Seaman. For having displayed extraordinary qualities, best expressed by the American Spirit of Honor Initiative and Loyalty. Seaman and Jeremiah Samples, Division zero, zero, five from Newark, Ohio, is awarded the Navy League Award which is sponsored by the Navy League of the United States. Seaman Samples is presented with a commemorative flag and a letter of commendation from the commanding officer. Well done, Seaman. Seaman Apprentice, Andrew Murrow, Division nine, zero, one from Townsend, Massachusetts, is the winner of the United Service Organization Award for best exemplifying the spirit and intent of the word shipping. Seaman Apprentice Murrow is presented with a commemorative flag from the United Service Organization. Well done, Seaman. Seaman Gladys Garcia, Division nine, zero, two from Laredo, Texas, is the recipient of the Military Order of the World Wars Award of Merit. This award was presented for meritorious performance during recruit training. Seaman Garcia is presented with a commemorative flag from the Military Order of the World Wars. Well done, Seaman. The Military Officers Association's Leadership Award is presented to Fireman Sonny Gray, Division zero, zero, three from Pocatello, Idaho for demonstrating exceptional tenacity and professionalism. Fireman Gray is awarded with a letter of commendation from our commanding officer. Well done, Seaman. Seaman Apprentice, Morgan Jenner, Division nine, zero, one from Valley City, North Dakota is the recipient of the Navy Club of the United States of America Military Excellence Award and the qualities of enthusiasm devotion to duty, military bearing and teamwork. This award places her at the pinnacle of today's newest sailors. She is awarded a flag letter of commendation Seaman Apprentice Jenner, the staff of recruit training command salutes you as the finest of this group of graduates. Well done, Sailor. Division It is appropriate to recognize such outstanding individual accomplishments by these sailors with a round of three cheaters. The episode will lead all graduating divisions to three cheers for this morning's award winners. I had the distinct pleasure this morning of introducing our reviewing officer, Captain Omar Martinez, Commander's Attractor Naval Service Training Commander. A native of Cedar Rapids, Iowa he elicited the United States Navy in 1986 and was commissioned in the limited duty officer program in 2000. Among Captain Martinez's operational and sea duty assignments are USS Carl Vinson where he served as Executive Department Head and Avanosher. Avanosher on board USS Montgomery-Sharp. And personnel officer, Avanosher and Executive Department Head on board USS Constellation. Prior to his current assignment, he served as Chief of Staff for the Chief of Naval Personnel, Executive Officer of Naval Station Great Lakes, Assistant Chief of Staff of U.S. Third Fleet for Commander Naval Forces U.S. Pacific Fleet. Ladies and gentlemen, please join me in a warm recruit training command welcome to Captain Martinez. Good morning. And welcome to all our distinguished guests and most importantly the family and friends these sailors and ranks today. It is a great privilege to join you today to welcome these men and women as the newest sailors in the United States Navy. To all the sailors standing now before me, congratulations on your accomplishments and on your new forms of magnificent and I want to personally congratulate and thank each and every one of you that has earned the title of United States Sailor League. In 1986, over 36 years ago I put on a Navy uniform and like you, I made the choice to enter the profession of arms and of service to our Great Lakes. Each of you has selflessly answered the call to do to serve a cause greater than yourselves. You have passed every test trying over every challenge improving yourselves worthy of wearing a uniform that symbolizes freedom throughout the world the uniform of the United States Navy. Whether you stay for four years or for 30 years you have joined an exclusive organization of those who have chosen the path of service I call the greatest Navy in the world. To all the families and friends of these sailors you have played a vital role in helping to shape them into a person who chose to serve their country and to understand the Navy's core values of honor, courage, and commitment. You have supported your sailor over the past 10 weeks and in a few minutes from now you'll see your sailor that embodies the Navy ethos and demonstrates a cordial toughness. Your sailor will continue to lie with love and support wherever the Navy takes us. We also now welcome you into the Navy family. Welcome aboard. To the leadership at recruit training command from the ship's officers to the recruit division commanders to the civilian staff, thank you. Thank you for your continued commitment and gratitude by training and sending the absolute best most qualified sailors to the fleet. Please join me in a special round of applause for the staff of recruit training command. Sailors, I can tell you from experience that you are about to embark on one of the most challenging adventures of your life. But I can also tell you that if you serve with honor and keep faith with your fellowship needs commitment and strive for excellence and what you do it will also be one of the most important. You've chosen to serve your country at a time when you are most needed. When America must show strong presence throughout the world on the seas, on the ground and in the skies. And when you leave this drill hall please know that your journey will continue and you will continue to grow as a United States sailor that the only thing you'll leave behind at Great Lakes is a little bit of your heart. Yes, that's correct. Each and every one of you will leave a little bit of your heart here at Great Lakes and if you're lucky as me you could come back and you could relive some of the moments that you lived here when you graduated from camp today. You will realize how powerful it is to serve in our country. In closing I would like to be the first to say to you thank you for your service. I'm proud of you. I'm proud of you. And I will cheer you. Congratulations.  Executive Officer, Commander Jargo, please remain seated until your graduates have been placed on liberty. Sexual interiors, fall out and retrieve out of gardens. And without further delay now hear this, now hear this. Liberty goes!


So, now we have seen that each of these factors contributes x minus lambda i to the power di to the characteristic polynomial and x minus lambda i to the fi to the monic polynomial. But we do not yet know about the comparison between the numbers di and fi these positive integers which one is greater which one is lesser and so on right. Let us look at a ii minus lambda ii and define this as ni. What do you think is the monic polynomial for ni? Remember lambda i is now given fixed number the ith eigenvalue exactly. What do you think is the monic polynomial for ni? Let us make it simple. What do you think are possible eigenvalues for ni? What kind of a property does this have ni? I am now going to claim that this ni is a nilpotent matrix. What is a nilpotent matrix? A matrix which when raised to higher and higher powers eventually at some level it becomes a 0 matrix. So, the claim is that ni is a nilpotent matrix. It is not that difficult to see you see. Why? Because what is the minimal polynomial for aii? It is x minus lambda i to the fi right. So, mu aii is equal to x minus lambda i to the fi. So, the eigenvalues of aii are what? Only lambda i. So, what are the eigenvalues of ni? So, this implies eigenvalues of aii is equal to lambda i and nothing else right. We have just seen that because it is minimal polynomial of that form. So, that can be it is only eigenvalue. So, what are eigenvalues of ni? For any eigenvalue lambda i of aii and some eigenvector you must have aii minus lambda iii times v is equal to 0. That means, ni v is equal to 0. So, the only eigenvalues that this fellow can have are 0's 0 you agree? The eigenvalues of ni are 0. Then minimal polynomial of ni can be some x raise to some power some arbitrary power. What power exactly do you think it is? Let us now get into that question even. Can this be a power more than di? What is the size of ni? It is di cross di. So, consider the set with any vector. So, for any vector v in v i v n i v ni square v until ni to the power di v. This is not v I am sorry. This is actually in f to the di right.  So, they must be linearly dependent and that linear dependence is exactly how we cook up minimal polynomials. But here we already know a priori that the minimal polynomial can be of some hi let us just say. Actually it is going to be just fi. We will see that hi is equal to fi. Nonetheless therefore, one of these fellows in fact the linear independence in this case is lost in a very special manner. Why? Because if this is the structure of the minimal polynomial at some stage you will have exactly 0. So, does not matter what vector v you choose you do not have to go up to powers as high as di at most rather higher than di. As high as di is the maximum it gets. So, ni raised to some power less than or equal to di must vanish. Please follow the stream of reasoning again I will repeat. What am I saying? First we saw that this fellow has a minimal polynomial like so. Therefore, the eigenvalues of ai are nothing but lambda i's. If the eigenvalues of ai is nothing but lambda i then the eigenvalue of ni defined like so has to be only 0. If all the eigenvalues of ni are 0 then its minimal polynomial must have a form like this some hi right. So, the minimal polynomial has a form like this we want to find out what this form must be what this number must be. So, now we see that this number cannot be any greater than di because no matter what vector you take how do we find the minimal polynomial just go back to the construction choose any basis for every element of the basis you keep hitting it until you arrive at a linearly dependent set. Now here at the linear dependence will be very special kind you do not actually need multiple fellows because the minimal polynomial has a specific form here. So, it means that it will be ni raised to some power acting on that particular fellow is 0. So, you take the highest power among all the fellows in the basis set. So, first let it act on v 1 then on v 2 then on v 3 then till v di and look at the highest power to which ni has to be raised until it loses linear independence which is when it becomes 0 exactly that is why it is a nilpotent operator right. So, now can this number hi be any more than di it cannot right. So, this means that this hi is less than or equal to di, but what is this hi? Hi is nothing, but this fi right fi is the original monic polynomials factor right original minimal polynomials factor. Now, we have constructed this ni if this hi is any different from fi then we will have a contradiction it means that ni has ni when raised to this power hi vanishes and now before does it vanish yeah that means x minus lambda i yeah for ai i this would have also vanished at that same hi yeah. So, I did just use this as an artifice, but really what we have is hi must equal fi. So, essentially what we have is fi is less than or equal to di is this part clear it is very important if not I will repeat what am I saying that when we transferred the argument from ai i to ni I just said for argument sake let us take another variable hi, but really this hi cannot be anything other than fi because ni is related to ai i after all look at this the moment you raise this fellow to some power you are basically raising ni to that same power because they are equal. So, if hi were different from fi then you had better replace fi with hi there instead right do you see that I just chose hi on the on the go like that randomly about because I did not want to prolong the argument at that point, but the point is hi must be equal to fi if hi must be equal to fi and hi cannot be bigger than the algebraic multiplicity therefore, fi also cannot be bigger than the algebraic multiplicity which means what exactly in the context of this whatever power you have raised every factor x minus lambda i in the characteristic polynomial that is the algebraic multiplicity you need not raise it to a power greater than that in the minimal polynomial that means the minimal polynomial definitely divides the characteristic polynomial yeah so let me erase this part now. So, the minimal polynomial divides the characteristic polynomial which leads us to the celebrated Cayley Hamilton theorem that is the characteristic polynomial definitely belongs to the annihilating ideal of a. So, this must be 0 in fact the role of the minimal polynomial is not highlighted much because it takes a lot more work as you see of linear algebra to understand how to even get the minimal polynomial characteristic polynomial is rather easy because you know how to find a determinant like an algorithm, but it suffices you see. So, for example, some of the applications people say of the characteristic polynomial is in finding or the Cayley Hamilton theorem. So, this is so I am not written out step by step, but I have argued why the Cayley Hamilton theorem must be true this is exactly nothing but right this is exactly the Cayley Hamilton theorem the utility of this one of the utilities is if a matrix is invertible you can just find the inverse of the matrix without those determinant and all those computations why because you have okay let me now erase this because we know that the Cayley Hamilton theorem is true suppose you have a to the n plus alpha 1 a to the n minus 1 plus alpha 2 a to the n minus 2 plus so on till alpha not oh sorry alpha n rate yeah i is equal to 0. If the matrix has an inverse which is to say that it is not singular that means it has no zero eigen value if it has a zero eigen value it cannot be inverted. So, if it has indeed got an inverse then you will have a inverse a to the n plus alpha 1 a inverse a to the n minus 2 plus dot dot dot till alpha n a inverse is equal to 0 and now you have a inverse is equal to 1 by alpha n rate times summation alpha i a to the n minus i minus this is n minus 1 yeah sorry yeah that is right yeah yeah n minus i minus 1 right i going from 1 okay the last fellow will actually remain plus so there has to be a minus sign here plus a to the n minus 1 so the last fellow will be what 1 through n rate yeah no what should be the number oh the a inverse will go right so n minus 1 yeah that should be it so i is equal to 1 is what but we have this constant 1 here right so it's a monic polynomial so it's this one I'd rather keep as free from this so is this right yeah so this is without doing any determinants or anything provided the matrix is invertible if it's not invertible there's nothing you can do even with determinants right but if it's invertible then just keep multiplying the matrix and you can get an inverse for the matrix by dint of the kelly hamilton theorem right so now you might say okay there's been enough work done on this we've got it down to its smallest possible ingredients so we've achieved quite a lot apparently right because we've started with an n cross n matrix we looked at these a invariant subspaces constructed through co prime factorizations of the minimal polynomial along the way we saw how to cook up the minimal polynomial as well right so once you have these co prime factors you can actually have we prove the kelly hamilton theorem without using determinants yeah and we've also seen that any matrix can be brought down to this block diagonal structure each block diagonal sizes di cross di where di happens to be the algebraic multiplicity of lambda i where the lambda i's are the distinct eigenvalues of the particular matrix right so why are we still not satisfied what do we want to look for further you see what is sitting inside each individual block diagonal what if each individual block diagonal doesn't look very nice so we are talking about say a 100 cross 100 matrix in which suppose one eigenvalue is repeated 10 times then you still have a 10 cross 10 block diagonal matrix and there's a lot of coupling between these 10 variables and that may not be to our liking we might still want to disintegrate this down so hereafter what we are going to look at is the following we will zoom in on that matrix so let's we forget the original representation we have gotten up to this far a 11 a 22 a kk where a ii is of size f di cross di and there's nothing further we can do to this overall thing here so this is what a looks like yeah subject to the choice of basis based on the kernels of those irreducible or co-prime factors of the minimal polynomial now we want to take a closer look at each individual a ii and we've already seen certain things what have we seen we have seen that the minimal polynomial of a ii is going to be of the form x to the power fi sorry x minus lambda i to the power fi while the characteristic polynomial of a ii is of the form x minus lambda i to the power di the question is can we do something more about this we know that ni defined as so these are some of the observations we've made already a minus lambda i or sorry a ii minus lambda ii and ni to the power fi is 0 and ni to the power um let's say k is not equal to 0 for k less than fi that is to say that the minimal polynomial of ni is x to the power fi we've seen all this this is a summary of what we have seen so far based on this we now want to get further down deep down into the structure of a 11 and see if we can get it down to a nice looking form yeah you consider that an endeavor worthy of certain merit right worth our while why because again obviously if the di is pretty large in itself then we may not have achieved too much we still have to solve a large size system okay so let us get down to the business of studying these ni like objects so now from here on we will completely focus our attention on mil potent matrices whose minimal polynomials happen to be of the form x to the x raised to some power is equal to 0 and therefore of course the characteristic polynomials also happen to be x raised to some other power probably is equal to 0 yeah so that is our attention because if we study this we can then fit this back in here like a puzzle so this is already a basis now for this now based on this can we also choose some smart choice make some smart choice of basis after this to transform this further yeah and that will lead us to the so-called Jordan canonical form okay so what I will do is in whatever time we have left I will just first give you a statement of the Jordan canonical form all right and maybe we will not have time for the proof but we will try to understand the implications of Jordan canonical form and if again if time permits we will see some applications of the Jordan canonical form okay maybe in the next module when we have time or the next lecture when we have time we are going to a detailed proof because the proof takes quite a while okay but at least that is the reason for us to avoid the statement of the theorem and some of its interesting implications so here is the statement of the Jordan canonical form so now our basic vector space is of size di but we will really consider that our entire space is now n dimensional and the n dimensional these are all of size n cross and I mean when we are fitting it in here these are of surely of size d1 cross d1 but if this is all that we are interested in there is no point in carrying the subscript and all of this right which is to say that suppose okay let us give a numerical example to motivate this better suppose you have this matrix 0 1 0 0 0 1 minus 1 minus 3 minus 3 okay what do you think is its characteristic polynomial this could be by the way one small little matrix sitting here but for me now this is nothing but my entire vector space so I might better as well consider this to be my three dimensional vector space so I shall be using n to denote the vector space so in fact you can check that this one is x my x plus 1 whole cubed you can just check so therefore its eigenvalue is minus 1 so its minimal polynomial must look like either x plus 1 or x plus 1 squared or x plus 1 cubed nothing more surely yeah because we have already proved Kelly Hamilton theorem and in that proof already we saw that the degree to which every factor gets raised in the minimal polynomial is at most equal to the algebraic multiplicity and no more you don't need to raise it to any higher degree than that so we can also check this here so you take a plus i what does that look like 1 1 0 0 1 0 minus 1 minus 3 minus 2 surely this is not 0 so x plus 1 is ruled out but try a plus i squared is that 0 well the first check itself tells you it's not 0 the 1 1 entry this multiplied with this leaves you with a 1 so this is also not equal to the 0 operator and now of course there's no magic in it you can just go ahead and check that a plus i cubed must be 0 that's essentially nothing but the Kelly Hamilton theorem yeah so just check this as an exercise so my point behind trying out this exercise is to now tell you that forget about this di fi and all this i dependence and all this business look at our basic operators to only belong to that one kind which is operators of repeated eigenvalues operators with repeated eigenvalues because if they are not repeated we exactly know what to do with them we are now zooming in on each individual block so with this motivation we will not forget about all these index terms and the subscripts and superscripts and we will only consider operators a such that it maps from v to v chi of a is equal to x minus lambda to the to the n where the dimension of v is n and mu of a is x minus lambda to what power exactly let's give it's just some name shall we let's call it f well of course f is less than or equal to n so we are only going to look at this kind of operators now okay so with this in mind define n is equal to what do you think n is a minus lambda i yeah so surely this is nilpotent right in fact when you raise it to the power f it becomes just a zero operator right and all its eigenvalues must be zero right just as a has all its eigenvalues at lambda n has all its eigenvalues at zero so then here is the with this setting here is the statement of jordan canonical form there exist v1 v2 until vk belonging to v such that n raised to the power m v1 v1 n raised to the power m v1 minus 1 v1 n v1 v1 that ends the story with v1 next starts the story with v2 m v2 v2 n raised to the power m v2 minus 1 v2 n v2 v2 dot dot dot until n raised to the power m vk vk okay n raised to the power m vk minus 1 vk n vk vk is a basis for v with raised to the power m v i plus 1 is equal to okay I have just chosen v i so this i can be any number from 1 through k what do you think this is just a guess yeah so should it be just this or should I you know take this acting on the corresponding v i is equal to 0 which tells me what exactly that is look at these last fellows or the first fellows in these what do you think they are a basis for if I hit these fellows according to this premise if I hit these fellows with another n they get taken to zero so these fellows that I am starting each of these blocks from they form a basis for the kernel isn't it kernel of n yeah that is n to the power m m v1 v1 until n to the power m vk vk is a basis for kernel n okay it's almost like magical what does it say it says that you'll be able to find a certain number of vectors inside this vector space such that if you keep hitting them with n repeatedly until a point arises where it devolves to zero and then stack them up like this you'll end up with exactly n number of vectors of course how to choose those v1 through vk in a special manner may not be very obvious at this point but it says that there does exist and the proof of this so this is actually the statement of the existence of Jordan canonical form for any operator with repeated eigenvalues okay all its eigenvalues are repeated so if it's not diagonalizable at least you can get it down to the Jordan form okay and if you can get it down to the Jordan form then a basis that takes you to this Jordan form looks exactly like this okay so this n by the way need not look like any special nilpotent matrix just that matrix I had chosen right a plus i that was a nilpotent matrix for that a 0 1 0 0 0 1 minus 1 minus 3 minus 3 that matrix that I chose and then I took a plus i right so that's a nilpotent matrix this n could be just that nilpotent matrix so the only question that remains is of course the proof remains a big question we will not have time to address that in this module but the more important question is suppose you believe this is true how to choose these v's it turns out that this choice of v is critical to our ability to get this down okay so we will see that in the next module


Sandballs possess dermal armor, which is a type of bony plate that provides protection against predators. These plates are unique to the sand boa family, ericity, and have not been observed in any other snake species. Additionally, these plates are believed to be derived from ancestors of the sandballs, suggesting that they may have evolved more than once within the group. Furthermore, the presence of these plates suggests that sandballs may have benefited from increased protection when faced with predation. This article was authored by Petra Freidlova, Veronica Janovska, Jana Mrilkova, and others.


to do helicopter experiments. All right so we got three different sizes right? Helicopters? And I'm going to have these on a link in the description where you could download the templates so you can make your own. Okay so what we're going to do is predict when we drop them from the stairs we'll make them in just a second. Which one do you think will take longer to come all the way down at the top of the stairs? Maybe the small one? Okay we're gonna do a small one so let's go ahead and we'll make them and then we'll go test them. So if we look at this first we're gonna take A and C we cut here. Oops let me do it again. They got A and C we cut right on the dark dark lines and we're gonna fold the dotted lines in. So you go ahead and fold that right along the dotted line. Hey it's rocket science right? Or helicopter science? It's not easy otherwise everyone would be a helicopter pilot. Okay so perfect nice and straight there and then you're gonna take the other one and fold it that way. Yep one folds. Yep exactly perfect.  So we're gonna do the other two the same way. Nice fold there. These are all pre-cut so you're gonna have to cut these on the lines and fold on the dotted lines. I'll have the directions in the description if you want to make your own. I'm sure we're gonna make a couple of our own after this. This is just the templates we're using. And then one more looks like a nice helicopter and that's the prediction that's gonna take the longest. Why do you predict the smallest is gonna be the longest? Because it's smaller and less heavier. Okay perfect good guess good guess. I already kind of know so I'm not gonna guess. Fold there around the dotted line and flip it over. Before you did it what one did you guess? I'll tell you after we do it all right. Perfect that's good that's good so let's go ahead we're gonna take these and we'll go in the other room. Alright so we got three helicopters on top and Grace predicted the smallest helicopter to take the longest to come down. We're starting with the largest one first. Here we go. It took about six seconds I think. Wait you threw that. There we go. We have an audience here. Alright last one. Whoa. Crashing bird. Let's do that one again. I think the small one worked. Okay medium one worked the best. Yeah I think so too. Alright so we'll try we'll try to make one ourself in the design first.  So what I did is I doubled these two so make a bigger wing. Yeah two there and then two there and we're gonna cut it right less than the full length and then here I did the same I kind of cut it and it's like same design except these are bigger and that's shorter. Okay let's go cut it. You want to cut it out? Yeah. So you're gonna cut straight down here and then cut it right there. Yep. It's already flying. Cutting corners is really hard. I'll show you a trick. Cut straight here all the way go straight all the way across. See how you can go straight up right? Then you don't have to do corners. Do this part. Okay perfect. Now fold it up right? Wait I have to cut that. Oh you're gonna cut those all the way. And I have to cut that? Just to that dot right? Not all the way just to the yeah right there and you gotta cut the middle you're right. I kind of forgot since that we were all pre-cut last time right otherwise it's just one big wing if we don't cut it. Stop right before it right about there. That's good. That's good. That's good. That's good. Yeah let's get a little space. All right here goes the test. Okay now let's go upstairs. All right. Test number two with Gracie's design. Here we go. Oh it's good good. Woo! All right. It was going really good at first. Good design. Nice. So that was Gracie's design right here with the bigger wings kind of made it longer down about halfway until it decided to crash and blow up. All right. Test results is Gracie's design one with a 4.4 seconds in the air with the smallest one going 2.2 seconds. Let us know what you did and what your results are in the comments below.


I will say that this is one of my favorite talks to give at Mises U. I've given a variant on this talk for some years. I've had family members in the medical profession, and my earliest interest in economics was partly about the monetary issues, but partly about healthcare policy. So, I've enjoyed over the years being able to follow what's happened in medical care, but I have not enjoyed the trend toward greater government involvement in medical care. I think that that's been damaging to health. I think it's been damaging to our economy, and I hope to show you a few reasons why I think that here in this short talk. I want to say a few things first about statistics. There is a common caricature of Austrian economists that we don't like statistics or that we don't like numbers, that we've got some kind of aversion to looking at data. And I'd like to dispel that, that's not the case. We do use data, numerical data, quantitative data, but we're very careful about it, and we are cognizant of the limitations of statistics. There are plenty of Austrian economists who without becoming heretics or something have used statistical information, but we're aware that there are some problems, especially when you start aggregating, and then if you're not very careful with what you're doing when you're aggregating, you can lead your readers to some pretty bad conclusions. So, I'd like to give you an example of this, I'll use something that came up in a talk that I heard earlier this year at my college, at Woffin College. This is something you may have seen in one form or another yourself. There's a common criticism of American medical care that our infant mortality rates are high compared to other countries and our life expectancies are low compared to other countries that are of a similar economic stratum. So you'll see information like this here. These are some OECD countries, more or less in our economic neighborhood, and you can see the life expectancy at birth in 2013 in the left-hand column and then infant mortality per thousand live births. They're in the middle column and then the percentage of the population over 65 in the right-hand column. So what you see here is life expectancy is 78.8 in the United States. That is the lowest life expectancy in this list, lower by about two and a half years than the OECD median life expectancy. The infant mortality rate per thousand live births in 2013 was 6.1. OECD median is 3.5 and I think we are in this list the highest rate of infant mortality. We can't explain this life expectancy problem by looking at the age of the population is not like we've got an unusually elderly population. In fact we've got compared to many of these other countries we've got a fairly low population over 65. So critics of the market approach to medical care will say, we'll see here we've got this relatively free market American medical care system and it's failing us. So we've got a high level of infant mortality, we've got a low life expectancy and therefore compared to some other countries that have more single-payer systems or have more government involvement than we do in the United States we're not doing well. So let's think about this one kind of disclaimer I want to make here. First of all is I am not going to make the argument that the United States is some sort of free market medical care system. It is not. It is far from it and has been for a long time. This is not just a product of the Affordable Care Act. This is a long time involvement of government in medical care picking up significantly in the 1960s but we've seen some steps in that direction since that time as well. So I'm not trying to paint some sort of here's the free market American medical care system versus all those socialist people in other countries that have their single-payer systems and so forth. That's not what we're looking at. But let's think about these statistics here and I think this will give you an idea of some of the problems we face in trying to do some research on this kind of issue. Let's suppose we were to look at the rate of survival of patients of a highly skilled and experienced, highly reputed surgeon in some field. What would you expect the survival rate for patients of that highly regarded surgeon to be compared to other surgeons? Lower? Why? If they take the harder patients, more difficult cases, that would tend to make their survival rates lower, not higher. So you can't assume that the highly skilled surgeon is seeing the exact same sort of cases that a fresh graduate out of medical school is going to see or out of some surgery residency is going to see. The person who has the reputation for higher skill is probably going to be the person to whom people take their more difficult cases. So looking at the survival rate of patients of a very skilled surgeon would not be the only thing you would want to look at when trying to determine whether that surgeon is a good surgeon or not. It would be one thing you'd look at, but not the only thing. I think a similar problem is happening here when we look at infant mortality statistics. Are we counting the same things? Are American hospitals more likely to treat a premature baby, for example? So in a 2008 study, Joy Lawn estimated that a full three-fourths of the world's neonatal deaths are counted only through highly unreliable five-yearly retrospective household surveys instead of being reported at the time by hospitals and health care professionals as in the United States. Moreover, the most premature babies, those with the highest likelihood of dying, are the least likely to be recorded in infant and neonatal mortality statistics in other countries. Compounding that difficulty in other countries, the underreporting is greatest for deaths that occur very soon after birth. Since the earliest deaths make up 75% of all neonatal deaths, underreporting by other countries often misclassifying what were really live births as fetal demise or stillbirths would falsely exclude most neonatal deaths. This is Scott Atlas now, not Joy Lawn. Any assumption that the practice of underreporting is confined to less developed nations is incorrect. In fact, a number of published peer-reviewed studies show that underreporting of early neonatal deaths has varied between 10% and 30% in highly developed Western European and Asian countries. The United States strictly adheres to the World Health Organization definition of live birth and uses a strictly implemented linked birth and infant death data set. Many other nations, including highly developed countries in Western Europe, use far less strict definitions, all of which underreport the live births of more fragile infants who soon die. As a consequence, they falsely report more favorable neonatal and infant mortality rates. And I would go on, you can read more about this elsewhere if you want more information on this. But this has generated a kind of apples and oranges problem in looking at something as critical as infant mortality rates. Infant mortality rates are very important for life expectancy numbers because if you have an infant death, you're essentially adding a zero into your average. So if someone dies at three days old, you're losing 80-something years perhaps of life expectancy. If someone dies at age 75, you're losing whatever life expectancy is. It's not exactly the average amount of 75 because a person aged 75 has a longer life expectancy because they've already survived a lot of the things that'll kill you when you're younger. But you're not losing as many life years, expected life years. I know this can be taken as kind of a morbid discussion here, but I hope you understand the importance of getting our numbers right and comparing the right thing. If you're comparing the U.S. infant mortality numbers to a country in Western Europe that has a more straightforwardly socialist medical system, we have to be sure that we're counting the same things. And in fact, we are not. The United States also is more aggressive about resuscitating very premature infants, meaning that very premature infants are even more likely to be categorized as live births in the United States even though they have a small chance of surviving. There are some other factors, population heterogeneity in the United States that really don't have anything to do with the medical care system or how much government is involved in the medical care system. It has a lot to do with who we try to save and what the demographics are. If you use National Center for Health Statistics and European Perinatal Health Report data, even if you don't count the population differences, demographic differences, risk factor differences that tend to weigh against the United States, we have in the United States superior infant mortality statistics or rates, rather, for premature and low birth weight babies. So I start this presentation and devote a few minutes to this because it's important to understand that when we are having a discussion about medical care and someone who favors more government involvement in medical care says to you, well, just look at the numbers. We're not doing very well in the United States. Our system is broken. It seems to work better in France or pick some other country. Why don't we move towards something like what France is doing? And I think there are some real problems with that. And you need to be aware that those numbers are not telling a straightforward story. So when we're looking at statistics, we need to be careful of what we're actually measuring. When I went to this talk, I got interested in this, again, kind of a renewal of concern about this issue. And I looked at some other factors that maybe this is something else that might affect our life expectancy statistics in the United States. So, for example, suicide rates, suicide tends to be a cause of mortality that disproportionately affects younger people and therefore, again, takes more potential years of life out of your average. Our rates are, it appears, slightly higher than the average. If you look at 2014 data, which I have here for countries that, again, are roughly in our economic neighborhood, we see that the United States rate is slightly higher than average. It's not some kind of below average number that would reduce our life expectancy statistics. This is probably not a big reason for that gap that you see between the United States and the OECD median for life expectancy. This one might be, though. Motor vehicle crash deaths tend to affect younger people more than older people. And the United States has a pretty high motor vehicle crash death rate compared to many countries that are in our economic neighborhood. Part of this may be that we drive more miles on the highway. But this is not something that can be laid entirely at the feet of the medical care system. And if we have a larger proportion of Americans who are getting hurt and killed in car accidents, we can't say, well, you know, that's because we have markets that are relatively more influential in our medical care system in the United States. Now, we do have a very high cost. And this is another kind of leg of that argument that is commonly advanced against the market as a mechanism for providing medical care. There are a couple of reasons that we might see this sort of high expenditure. One is maybe we're getting better medical care. Maybe we're getting more out of this. And I think there is an argument to be made that some of that medical expenditure is, in fact, purchasing better medical care. On the other hand, perhaps we're seeing elevated costs for other reasons that are not so beneficial to American health. Vijay Boyapati points out four reasons for rising medical costs in the United States. One is, he says, employer provided health insurance, which came as a result of high tax rates during World War II and the effort of employers to provide employees with a non-taxable benefit. And courts ruled in the 1940s that if an employer provides medical care or medical insurance to an employee, that is not a taxable benefit. So that means that in order to avoid taxes, employers have an incentive to provide a lot of health insurance. This is a third-party payer, and we'll get back to that later. If you have someone else paying your medical bills, how careful are you going to be about costs? Answer, not very. A second reason is medical licensure. We'll talk about that as well. Third, the obesity epidemic. And fourth, he says intellectual property, that is patents on drugs and other medical equipment and devices. If you look at some of the arguments about health care cost growth, many of them have to do with a kind of a moral hazard problem. And that is if someone else is paying your bills, either government or an insurance company or a charity, then you are not going to be as careful about your medical costs. For example, a number of years ago I was having some back trouble, went to a doctor about it. The doctor said, I'd like you to get an MRI, and so I said okay. And I called either that day or the next day and scheduled an MRI within a day or two. Try that in some countries. And I got an MRI. I didn't ask what the cost was going to be. I looked at my bill later and it was several thousand dollars for the MRI. My out-of-pocket cost was maybe a hundred or something. It was trivial compared to the total cost. I didn't know about the cost of the MRI. If I'd had to pay even a slightly higher out-of-pocket cost for that diagnostic procedure, then I might have said hey doc, can you get by with an X-ray? You really have to have the MRI. My back pain is, my back is bothering me that it's not crippling. Maybe you can get by with an X-ray instead. But I didn't really pay attention to the price because I had very little incentive to. So if medical insurance, private medical insurance or something like Medicaid or Medicare picks up the tab, then that means you've got patients that really don't care very much about the cost. But there's another kind of problem here which is that sometimes you can spend more money on medical care and not get an improved outcome. This might be because a lot of our expenditures in medical care are going to things that really don't generate much impact. Could be because you've got a lobbying organization that has pushed for widespread medical, early medical testing for some disease. And so you get piles of money flowing into this diagnostic procedure that really aren't generating very much in the way of improvements in health. So this has been referred to as flat of the curve medicine where you're spending more on medical care but the additional gains from that spending are very low or nonexistent. There's a famous experiment conducted about five years ago in Oregon where they randomly assigned increased medical benefits, Medicaid benefits, to 10,000 individuals. Kind of a lottery. If your name gets drawn, then you get the extra medical benefits. If your name doesn't get drawn, you don't. And then they looked at the differences in medical or health outcomes between those two groups. And they found that in fact the expanded Medicaid coverage generated no significant improvements in health outcomes in the first two years, despite increased use of prescription drugs, office visits, preventive care services including mammograms and annual spending per individual in excess of $1,100. So it's possible to spend more money and not get much of a result. The answer to health problems is not necessarily to go to the doctor. Sometimes health care is, or health is achievable through other means. And whenever you throw more money at medical care, you're inevitably taking it away from something else that might actually be more beneficial to you as a person. So increased medical spending is not necessarily welfare enhancing. I'm skipping over some of this in the interest of time, but we can end up kind of spinning our wheels with buying new technology and making doctor visits more available to people and not getting something that is helpful. Fundamentally, we could end up spending a lot of money on insurance that causes people to go visit the doctor more often or take advantage of diagnostic techniques and end up not really improving our health. But I think a key part of understanding the medical cost increases in the United States is our third-party medical care system. And again, we've seen this since the 1940s, expanded in the 1960s with the advent of Medicare and Medicaid, which puts an intermediary, either the government or an insurance company, in between the patient and the care provider. So the care providers, doctors, nurses, whoever else is trying to help is perhaps paying more attention, or at least is incentivized to pay more attention to the bureaucrat or the representative of the third-party payer than to the patient. The bureaucrat is maybe a thousand miles away and gets a summary of the interaction between the patient and the doctor. So you go to the doctor, the doctor writes a few things down, or more often now is typing them down into a form. And that form with the stripped-down information about the patient and the symptoms and the proposed treatment ends up going off to this office somewhere where somebody far removed from actually laying eyes on the patient and hearing exactly what the doctor hears and all the nonverbal communications going on. That bureaucrat is then going to look at this very abridged record of that visit and then make a determination about whether the doctor did the right thing. This is one of the reasons that doctors do not appreciate in many cases electronic medical records. It's not that they are opposed to technology per se, it's that very often electronic medical records, for which there's been a really big push in recent years, are aggravating this kind of illusion that the bureaucrat has enough information to make this kind of decision about whether the doctor did the right thing or not and made the correct diagnosis, suggested the right treatment and so on. So that's a real problem when you've got a care provider who can be ultimately prosecuted and maybe have a license removed for doing something that makes sense when you consider the full range of information that the doctor has when talking to the patient, but that's not really reflected in the stripped down medical record provided to Medicaid or provided to an insurance company. So as a result of this, we've seen, well partly as a result of this, we've seen an increase in medical care costs and this is a diagram that's getting a little bit out of date because it goes only as far as 2012, but you can see at least over a 20 year period medical care costs have increased at a far more rapid pace than inflation in general. Inflation being measured by something like consumer price index, which we understand there are problems with that too, but medical care increases at a rapid rate. Now tomorrow I'm giving a talk on the crises in higher education and I'm going to point out something very similar with higher education and actually the reasons are connected. Who's been funding more and more of the cost of higher education? Government. So third parties are paying, government's paying the bill, you don't care as much about the cost. Now toward the bottom of this is a purple line indicating cosmetic services. This is not Mary Kay, this is cosmetic surgery and that sort of thing. And you notice there that cosmetic services, that subset of medical services has increased at a rate about half that of inflation overall. Why would that be? Why would we see such a low rate of increase in the cost of cosmetic services as opposed to medical care in general or physician services in general? And perhaps that it has something to do with the fact that insurance companies, Medicaid, Medicare, etc. do not pay for elective cosmetic procedures. So you are on your own, you're paying out of your own pocket for those kinds of things, which makes you a better shopper or a more careful shopper. It means that you're going to avoid unnecessarily expensive procedures. There's some other things going on here too, maybe some technology has improved in that area compared to some other parts of medical care. But if you look at cosmetic services, that has, that I think reflects the benefits of direct pay. I've talked a bit about the competing standards in medical care. The patient is in this mix with a lot of other institutions. The employer is selecting an insurance plan. The insurance company is providing some direction, for better or worse, to the medical provider. And it's also lobbying the government. It would be great if an insurance company could get the government to mandate its services, wouldn't it? Wouldn't that be fantastic if you're an insurance company, you can get the government to require people to buy what you have to offer? So then the government regulates the care provider and regulates and regulates and regulates, as well as regulating the insurance companies. Insurance companies, in exchange for getting their product mandated, also are required to provide different bundles of insurance than was perhaps once the case. So the patient gets kind of lost in this, and especially once you consider where the money is coming from.  But it's clear that the majority of the money that's going to a doctor or hospital or other medical provider is not coming directly from the patient. And so when the doctor or hospital is paying attention to where the dollars are coming from, that rarely includes the patient. The patient is unfortunately sometimes lost in this process. And then we have the Affordable Care Act. And this is, I had this original diagram and then I started drawing all these other things on there to try to show how this works.  And so the federal government mandates patients to get medical insurance. And if they don't get it through an employer or privately, they go through a state exchange or a federal exchange. There have been a few changes in how this has administered over the last year or so, but states can't be required to expand their Medicaid eligibility and so forth. But the end of the process is this moral hazard problem. The mandate that was supposed to ensure that more Americans get medical insurance, which is not the same as medical care, that mandate has resulted in some increases in costs of insurance. And we'll look at some of the reasons for that in a minute. So this is all kind of boiling down to a moral hazard problem, which is that the insured person is going to behave differently than the insured person would behave if paying out of pocket. I have insurance on my car. I know that if my car is damaged, I will only pay whatever my deductible is, which I think is $500 or something I don't remember. And if the car is totally destroyed, I still only pay $500. I might see an increase in my future premiums, but the vast majority of that cost would be absorbed by my insurance company. So I'm more likely to leave my car parked on the street where it's more likely to get sideswiped by another vehicle. I'm more likely to leave my car parked in the driveway instead of the garage where hail could damage my car, which in fact did happen. And I'm more likely to leave it unlocked with the increased potential that it could get stolen. I'm careful about it, but I'm not as careful as I would be if I didn't have insurance. Now there are some market-oriented ways to avoid this problem. Insurance, conventional medical insurance as we've known it in the United States for a long time, is a kind of a use it or lose it proposition, which means if you don't use the benefit that your insurance company would pay for, you don't get anything. If you pay out-of-pocket for the majority of medical services, then anything that you don't spend, you keep. So that's why your incentives are different with out-of-pocket pay. But of course, we know that out-of-pocket pay could get very expensive very fast if something serious happens. So we do have certain risks that we would want to have insurance for. And that's where a health savings account is helpful. I read yesterday that Congress is considering an expansion of the availability of health care savings accounts. I'm not familiar with all the details. This is all very much in flux right now. I just read a few sentences yesterday in a brief news story on this. But apparently this is coming up for discussion as something that we might expand. I would regard that as a good thing because that puts more control in the hands of the patient. It makes the patient a typically better shopper because the patient is the person who is able to keep whatever is not spent on medical care. I pay an insurance premium. I'm never going to see that money again unless I get sick. If I contribute to a health care savings account and I don't get sick, I keep the money, essentially. So there are some advantages to this. I won't go into all the details here. But there is still a role for insurance, but it's not that very low deductible insurance that we typically see in the U.S. where your deductible is $300 or $500 or something like that, which means that the trigger on filing a claim is very low. It doesn't take very many pounds of pressure to get that insurance company involved. If you have a high deductible on insurance, say $2,500 or something, then if something really bad happens to you, insurance picks up the tab. But for the vast majority of your run-of-the-mill medical services that you demand every year, that would come out of this health care savings account. You contribute to that sort of like you do with an insurance premium, except that, again, if you don't use it, you get to keep it. And that makes people better shoppers. It removes that third-party payer somewhat from the decision process. Let me just say a couple of things more on the medical costs and whether they're worthwhile. So there was a study in health affairs several years ago by Phillips and Eber at all, about seven authors there. But what they say, and here's the abstract for their study, they say the United States spends more on health care than other developed countries, but some argue that U.S. patients do not derive sufficient benefit from this extra spending. We studied whether higher U.S. cancer care costs, compared with those of 10 European countries, were worth it by looking at the survival differences for cancer patients in those countries compared to the relative cost of cancer care. We found that U.S. cancer patients experienced greater survival gains than their European counterparts. Even after considering higher U.S. costs, this investment generated about $600 billion of additional value for U.S. patients. The value was highest for prostate cancer patients, breast cancer patients, and they do not seem to have been driven solely by earlier diagnosis. So this is one indication that perhaps, at least in some parts of medical care, the costs that we are paying have been worthwhile. If you look at the added years of life, added quality of life, perhaps we may see some gains. The survival benefits are worth something. So it might sound like I'm contradicting myself here. So in some places, in parts of my talk, I've been saying that medical expenses are triggered by an over-reliance on third-party payers, and perhaps in some cases they're not generating the kind of medical outcomes or health outcomes that we would like. There's the Argon experiment, which shows that you can give people better insurance or more insurance, and they're not necessarily going to get healthier. And then on the other hand, I've got this study here that's indicating that if you spend the extra money, you do get better outcomes. You get greater survival rates and so forth. So what's going on? Okay, this is a huge topic, and the healthcare is wide-ranging from Botox to open-heart surgery, and some of our technology, some of our interventions, medical interventions, have been useful in extending life. Others have not, and others are simply high-risk. You spend a lot of money per year of life saved. Doesn't mean we shouldn't try them, but it does mean that when we look at those statistics on life expectancy, that aggregate statistic is concealing a lot of detail that is quite important in this area. I always like to quote from Yuri Maltsev's article on Soviet medicine. Yuri Maltsev, for those of you that don't know, is an Austrian economist who teaches, I think, in Wisconsin now, and he defected from the Soviet Union in the 1980s and came to the United States and has been a strong advocate of markets ever since. And he pointed out that if you're looking at medical care in the United States versus some other countries like Great Britain, which is a common comparison country for us or Canada, in fact, we do pretty well. He said in his article, which is linked there, if you want the presentation, I can send that to you later, so you can have all these links. He says, the Brookings Institution found that every year 7,000 Britons in need of hip replacements between 4,000 and 20,000 in need of coronary bypass surgery and some 10,000 to 15,000 in need of cancer chemotherapy are denied medical attention in Britain. In Canada, the population is divided into three age groups in terms of their access to health care. Below 45, 45 to 65 and over 65. And he said, needless to say, the first group enjoys priority treatment. The American Medical Association in a report on insurance and denial of insurance claims found that Medicare denied nearly 7% of its claims higher than any private insurer. We see in some countries greater access to medical technology like MRIs. Sometimes that's good. Sometimes it just, again, spins our wheels with more expense for not much additional health. But that's another benefit of having a relatively free market medical care system. If you look at cost containment, how does Medicare and Medicaid stack up compared to every other kind of medical provision? Medicare and Medicaid patients end up paying more than other patients. So if you want to contain medical costs, expansion of existing government programs or creation of new ones may not be the way to go. Here's some more up-to-date numbers. Maltseff's numbers were a few years old, but if you look at availability of diagnostic technology like MRI machines or CT scanners or PET scanners, we see that in, again, nations in our economic neighborhood, we have typically far greater availability of these diagnostic procedures in the United States while I was able to call a few years ago an MRI place and get an MRI within a couple of days at low cost to me. So if you look at CT exams per thousand people, we have 240 compared to the OECD median of 136. If you look at mammography machines, this is a very politicized kind of industry, so I'm not trying to say that this is some sort of unadulterated endorsement of markets as an expander of medical technology. The whole breast cancer industry has been heavily politicized, but you can see that in the United States, which is on the far right of that diagram there right next to Korea, the diamond there is the total number of mammography machines per million inhabitants. These are 2015 numbers. And so we've got the technology. Sometimes, again, we're spending the money on the technology without huge gains in health, but it is the high medical costs that we're spending are buying us greater access, at least to diagnostic technology and some other things. It's also buying us shorter wait times. You can pay in dollars or you can pay in your wait time. And if you've got a very serious medical condition, you know that wait times can be literally painful and also lead to an exacerbation or aggravation of your condition. So if you have to wait a long time to see a specialist, that is definitely not to your advantage. You might be cheaper, but if you have to wait and your condition becomes more serious, you might have wished that you could have paid more and gotten seen faster. I am out of time. I had 45 minutes, but thank you very much for attending and I'll be happy to answer.


Hey guys, what's up? On today's video, you will learn what reuse content is and how to keep your channel safe and monetize. Hey, what's up guys? My name is Nolden, welcome to Freedom Quick Tips, where we discuss important topics such as channel's best practices, YouTube policies, and whether we think that National Puppy Day should be a thing. Yes, a thousand times, yes. Now, something less cute, but no less important in reuse content. What is it and why should you care? Well, if you'd like to keep or want a piece of that sweet, sweet YouTube ad revenue, you should care since reuse content is part of YouTube's channel monetization policies. That means that if you want to stay or get in the YouTube Partner Program, your channel should avoid reuse content. Now that we've established the why, let's address the what. YouTube says that reuse content refers to channels that repurpose someone else's content without adding significant original commentary or educational value. Sounds simple enough, right? Plainly put, that means taking any content that you didn't create yourself and using it in your video without adding anything to it like your own voice commentary or changing it in any significant way. But Freedom, what about the content that I have license for? I hear you asking. Great question.  At least, not as far as the YouTube Partner Program is concerned. An important side note, reuse content is separate from YouTube's copyright policy, which means that you need to make sure your channel is compliant with both. Right then, but as anybody who spent any time on YouTube would know, there are tons of channels that use content that isn't their own in their videos. You've got movie review channels, reaction channels, news channels and so on. Surely they're not all just uploading videos for our entertainment purely out of the goodness of their hearts. Well, the key to using third-party content in your videos in a way that can be monetized isn't adding something uniquely of your own, which again can be your own original commentary like what we're doing right now. Such that the resulting video is different enough that it cannot be mistaken for the original and that people would want to watch it because of what you've added. A great example of this is the channel history buffs. Nick reviews historical movies and provides his original insights in the form of voice commentary, riveting stuff if I do say so myself. Channel links are in the descriptions below. While you could probably find clips of the movie, he reviews it in other parts of YouTube or the movie itself in YouTube movies. You would have to watch his videos to get his own unique take. If you're wondering, here are some quick examples of reuse content that is not allowed by YouTube for monetization. Number one clips of moments from your favorite show edited together with little or no narrative whatsoever. Number two short videos you compiled from other social media websites. Number three collection of songs from different artists. Even if you have their permission. Number four content uploaded many times with other content creators. Number five promotion of other people's content even if you have permission. So guys just to recap, reuse content means using someone else's content without changing it enough with your own material that it becomes its own unique thing and should be avoided if you want your channel to be or remain monetized. Hope that helps. Please don't forget guys to like, subscribe, and hit that notification bell icon. Ask any questions you may have in the comment section below and let us know as well if you like puppies as much as we do. Once again guys my name is Nolten. This has been Freedom. Quick tips. See you guys all in the next video. Bye guys.


This is higher term of activity and engagement with you that is happening in all these countries, Pakistan, India, and then other places in the world. The recipient of the answer international award will happen in Al-Qaeda Congress in a house in Brazil and will receive at least residency along the way to create a new work in June and financial and financial support to present this new work. And the engagement will also occur along New York. And it's now, but I have the honor to announce the first recipient of the answer international award and the award goes to Lude Samba in the United States and from Al-Qaeda. Lude Samba, we are right now in a small convovo that is in the Pacific floating jungle, and the African house which will be created by the S&O lab. So we are going to try to switch Lude Samba to Samba. When you call them, they are waiting for us. Right now? Yes, please. The power of the S&O or the community after being there. Sometimes deeply wrong. I don't know. Shouldn't be. Now you can connect with them. Now you can connect with them. Can you hear the applause? Can you hear the applause? Yes, I can hear your applause. We are the first winners of the answer international award. And thank you for coming in line. Can you hear? Yes, what happened? Quite difficult situation, technical, but here we are. You cannot do that. You cannot deny it. Our light is more designed in front of the room because we are having problems with the light. S&O lab, S&O lab. And we knew this three days, three years ago when we first began to come here and work with this community that has suffered violence for many years. So we came with our theater. We have the motorcycle light. Are you sure? Yes. That is wonderful. Think about the award.  And what's your project going to be? I think it's wonderful. It's a prolongation of Ellen Stewart's spirit. This is the first thing. This situation we're living here, this difficulty, this fight to make things happen and continue. This, I think, was the spirit that I learned from Ellen Stewart. So it's really alive. Yes. We are working casually with the Afro-Colombian antique tradition. And I think it's a very nice homage, how do you call it? Yes. That we want to give to Ellen, working with this woman, that one of the characteristics of this population is that they don't have opportunities and they have incredible talent. And this is our fight to try to help people that have incredible talent and they cannot show it to the world. So this is why we are here. And I think this is the spirit of Ellen Stewart. Your work has been partly in Colombia, but also partly in Italy, where you have been working with refugees and victims of torture and violence. And the work that you have proposed for the residency actually is more connected to this group of people in Italy. Do you want to mention something about that? Yes. For us, it's like a step forward of the 10 years of work we have done with the victims of torture. Because we have worked for six months, intense work with a group. Then we make a performance and this group goes and we have a new group. But now you are giving us the opportunity and the Spoleto Festival to make a step forward in the sense that we are going to choose the best, not so many because we have not the possibility, but the best talent that we have seen in these 10 years and we will put them together to make a performance. So it's an opportunity you are giving to us. Thank you. Do you want to remind us a little bit about the performance? Yes. I want to, no base here, but for all our work we have done it together and she will explain a little bit about the performance in Spanish or in Italian. Is it possible? Of course, of course. Can you speak Italian and I will translate you? Thank you, thank you. So the idea is that we want to create a show that talks about the journey. The journey of people who in these last months, in the last years, have also risked their lives to find a way to save themselves from very, very difficult situations. Wait a minute, I will translate you. I will translate you. Sorry, I can't hear you. I will translate what you said so far, ok? Yes. The performance they are proposing for the Spoleto Festival is based on the idea of a journey and the journey that many of the immigrants have been living and going through in the last months and last years and based on the tragedies that are happening in the Mediterranean area in the last years. So the idea is to tell the journey, but to tell it through personal stories, personal experiences, so to make it human. This journey that we know so far, especially through statistics, that is the anonymity of the numbers, so to make this humanity alive, so the way is to tell this journey through the personal stories of the people. Right now we only hear the numbers and the statistics of this tragedy and through the performance they want to give a more human presence to the story of the journey. They imagine it like a biblical journey, ok? As a starting point, they will use a text of a Sufi poet which is entitled The Words of the Birds and this will be taking place on a boat which is imagined to be in the middle of the Mediterranean Sea. Ok, grazie. Yes, so thank you, there are people who are asking who is behind you? So here behind us are the most beautiful women that are the singers of the alabaos that they are in, we can call them, they are the ghosts of the jungle. We want to give homage to Ellen Stewart and I think the best way and the most beautiful way is that they will sing for her and for you all the alabaos songs. It's like a gospel, kind of gospel of the Pacific coast in Colombia. Thank you. We will make them sing. Thank you. Thank you so much, it's amazing, beautiful voices. I think now you can understand why we do what we do. Yes, definitely, definitely. So we really thank you so much and we will be in contact shortly in the next weeks and we wish you all the best for this production for the Bogota Festival. Thank you very much and really we have no words to thank you all. Actually Bernardo and Nube and all the women, you don't have wine with you but we have prepared wine for the people that are here and we want to make a toast for you. Thank you very much. To you, to your performance and your work, a toast and thank you so much. Thank you. Salute. Ciao. Ciao. Wow, that was amazing. A lot of people took a lot of time and effort to put this all together but there's probably one of us who really coordinated all the rest of us and made sure we got everything done on time. I want to give a special thank you to Adriana Garbagnati for all the amazing work she's done with us. She's in the kitchen because she also cooked the meal that you're about to enjoy. Adriana Garbagnati. So now you will get a program for tonight which talks a little bit more about Nube and Bernardo's work. We're very excited to see what they will be bringing to Spoleto this summer. I want to take a couple of minutes to explain a little bit about what's going on for the rest of this week and on into La Mama Umbria 2016. So we have upcoming this week La Mama Umbria play readings. These are plays that were written by playwrights last summer under the facilitation of Brandon Jacobs Jenkins. There's a bunch of playwrights here. Raise your hand, you guys. We have playwrights from last summer in the house and we're so happy that you're here. We're looking forward to hearing all the plays that you guys have written inspired by your time in La Mama Umbria. You have a complete schedule of the plays in the program plus so you can also find that online. They're free to come and attend. They'll be here in this room and we encourage you. They start on Friday and they go all through Friday, Friday evening, Saturday, Saturday evening. So please come and enjoy the plays. Now as for La Mama Umbria 2016, we're going to have some things we've had before and some new programming. So first of all will be the director symposium which will go from July 11th to August 10th and the teaching artists who will be part of that program this year include Lee Brewer and Juan Mitchell of Mabu Mines. The award-winning puppeteer Basil Twist, Sanjoy Ganguly from Yana Sanskriti in India who was also one of the finalists here for this award. Yoshiko Chuma from Japan. Marianne Weems, you're in the house. Marianne, where are you? Marianne Weems is going to join us this summer from Builders. Thank you so much for being here. Ilya K. Schneider, Enrique Vargas and Tian Mancha from China. So we encourage you to look at the website and encourage directors to sign up for those workshops. They're going to be amazing. Starting on August 12th, we have the Playwright Retreat and that will be facilitated this year by Mack Wellman. Yay, Mack. He's an extraordinary teacher and artist. I have a new program after that called Next Generation New Performance Development Incubator. This will happen between August 25th and September 4th. We need your help in getting the word out to all the people that could come to this program. This program is for artists under 35 years old who are going to be able to use the residents of Lamama Umbria as a retreat to create new pieces. New work. It's an incubator. You can work on things. You can develop projects there. And there will be Lamama artists there during the entire time for feedback. It will be more like the Sundance Institute process where people watch each other in rehearsal. They give feedback to each other when they want it. But it's really an incubator for new work by young artists. Something that we're very, very excited about. And you can find out information about that online with an application form. That program, because it's supported by the local Umbrian grant and government, is free. So people who get accepted to the program don't have to pay for anything except for the room and board at Lamama Umbria. And the program itself, though, is without charge. So we're very excited to be able to offer that. In addition, for those of you who are interested in the Spoleto Festival of Two Worlds, we're offering a Spoleto Festival Tour, July 2nd to July 12th, two nights in Rome, and then a week at the Spoleto Festival with tickets to four or more productions that are happening during the festival. And that tour will be led by the extraordinary Frank Carucci, who's right here. And to finish up, as we have in the past years, we're going to be participating in Lamama Spoleto Open, which are performances in the Festival of Two Worlds, the Spoleto Festival of Two Worlds that we produce, both at the Contiere O'Birdon, which is our little theater in Spoleto, at Lamama Umbria, and sometimes at various other spaces around Spoleto. One of those productions will be the production that Nube and Bernardo are working on, and that will become part of this festival. So lots of exciting things to look forward to. I hope you'll all spread the word and join us. And thank you very much. And now I want to reintroduce Mia. I was going to say some concluding comments, and she's preparing food. Well, I could... Okay, Mia would be saying. Please join us now for a meal prepared by our Italian colleagues who have joined us specifically for this occasion. So Adriana, who you met, and her sister Maria, and several other of our Italian colleagues are here. And we're pleased that we want to announce the donations of some of the items you'll be having from Urbani Truffles, Truffle Company, Jerry's Market in New Jersey, Monini Olive Oil, and Mutti Tomato Sauce Company. So thank you to all those sponsors. We appreciate that very much. We also want to thank Culture Hub and for their work in live streaming this event and in bringing us the video you saw earlier from Columbia. We are going to have some music coming up, so we want to extend our thanks to Claudio Scarpottini and Yukio Suji, who will be playing music for you as you enjoy the rest of your evening. So thanks for being here. Take care.