This morning, the anti-corruption commission visited his property and my property. We are neighbors. I had no idea that the anti-corruption commission had also visited Honolibo Harikalaba. The major contention we have and will just discuss briefly is that this is an act of harassment on Honolibo Harikalaba. That's why I have taken it. I know it's a clear case of harassment even for you because I know even for your property that you are talking about. It's a matter that the SEC has even tried, the previous government has tried to harass you over. Accept my commiserations. But you know it's not a big deal because as you rightly put it the property which is in question is the property that was built using the gratuity in 2016. I got another gratuity after I resigned and we tried to finish and went ahead to try and see if we can get a loan from the bank. We have laid our lives and I say we myself and my wife and family have laid a life that is very transparent. If the anti-corruption commission wants to go and visit our property, we still ask them to go. If they want to visit other property in Woodlands, we still tell them. Because these are things that we can account for. I'm only shocked myself that they can begin playing such games. But you see, I think this is where President Akanda HLM is losing it. And if this is the way he's going to be fighting corruption, then he's going to decimate the fight against corruption completely. Because even those that should be held captive will run away. And it will be looked like it is witch hunt simply because everybody is being put in the net. I have known you myself, but I have known you. And I know what you are getting when you were a diplomat at the Ministry of Foreign Affairs. Diplomats get a lot of money. No, zambians don't know that. Diplomats get a lot of money. That's why they run to go into foreign service. Let me speak to that. When you have 38 missions, so at that time you only have about 38 ambassadors and some consular general. So it's a high privilege. I always thank President Galungu appointed me as ambassador, high commissioner to South Africa and to Ethiopia. So what we get as an ambassador is almost $10,000 depending on the station. It depends. If you are in Washington, you get about $21,000. So if I'm in Washington, I'll get $21,000. That's $400,000 kwa cha a man. Muma na kutawakwa ta manu, te tukure kwa maflats. And I was ambassador. Tamu noa imwefena ishiba? Mkwa. Tamu pepa? Aona kadiwa. Namoranges insha ishiba. So you are getting $10,000 for colleagues that were, for example, in Washington because of the high cost of living, would get $21,000. We'll say you can't save a $5,000 to $10,000 a month. And that's a lot of money in kwa cha times. This is a lot of money. So I was surprised that they are attempting to criminalize. And for me, I worked under Dr. Chubaisa construction office for a period of 10 years. When I was separated, I served as a deputy permanent secretary for 10 years. 2003 to 2011. I was given a gratuity because when you are appointed as permanent secretary, they have to retire you. The position of permanent secretary, you have to be put on a contract. So they retire you from your position of civil service. They even pay you. And then you have this contract. And if the contract is cut short, you are still paid a lot of money. So like you have had three huge gratuities. And for the last seven years I've been earning a large sum. And I'd always tell my diplomats that you never live a life of kings while you are away. Because you are going back home one day. So build. And I used to demonstrate by myself. You are saying that you've come to my place here. I have lived here from 2008. Just as a civil servant, this has been home. Even when I was minister of foreign affairs, when I was land minister, we have always lived our lives modestly. I know, you might not want to make it public, but I know you also run businesses on this side. Yes. Very successful business. You supported the newspaper, which was probably lost making for a long time. For many years. So for them to attempt. But it comes very clearly. The president is using the law enforcement agencies to shock voices that are critical. To shock voices that are criticizing. You've been very critical of him. And by coincidence, just the other day, you raised a matter against a state house official and you called on the president for that official's position to be regularised. And you made a mistake. I supported you. I was shocked because the gentleman in question is not even the one I was referring to. How do you just come because you are trying that position? I mean, it's for the president to respond. We were talking about illegality. Yes, and even article 92. It's not one to be looked at in abeyance. And in isolation. That is an article which will only work if it is used within a certain channel. The president's powers as you like putting it are not cut a blanch. No, no, no. It can happen already. They are regulated and they are guided. But it must be guided. So if a person has not been sworn in, if a person has not been has not received the authority for the position, then the position becomes irregular. Regardless of who makes it, that's why you find that presidents after the end of their offices, they are brought to book. Why? It's not because they didn't have the powers. They could have had the powers. Either they have used the powers or they didn't use the powers appropriately. And that's the challenge that we have. So that's the coincidence we have for people that follow these matters is that we criticize an official at state house who we think that the president should regularize his position. He should because the structure of government has been 7 for the last 20 years. And I know how, for example, if a person is created, there is a division called public service management division. Public service management division? Yeah, before... And there is public service commission? Yeah. Then there is management development division? Division, yes, exactly. Yes. These three bodies of the civil service work in tandem. In tandem, yes. The public service commission basically is the one which puts up jobs. Yeah. They are the ones who demand jobs. So first before that... The public service management division then gives responsibilities. No, before that. The public service management division MDD comes to assess if you need that position. Or not? Yes, or not. Exactly. Do you need to create a department? Do you need to create a ministry? Or do you need to create a single position? Yes. And then they create job descriptions? Then they create qualifications required for that position? Yeah. And then it goes to PSMD? Yes. Who then has to seek authority? Yes. Because the minister of finance has to fund that office? He has to find money holding the votes? Yes, yes. And if it's not there, sometimes many times they are deferred to the following years. Yes. Because the budget has been done, you know, you don't want budget overruns and so people think that appointing one is just that simple. No, even if you are a president, for as long as you bring something which is outside the establishment, the law requires that you follow the procedures. That you follow the procedures. MDD has to come in, public service commission has to come in and then finally PSMD has to come in. If that is not done, that is irregular. And so I was surprised that Ennovis at the civil service would want to school me. Who started your career as a civil servant? And rose in the ranks. But the time you are becoming a MP in 2011, people don't realize that you have been a civil servant for a long time. So these harassment, ambassador and court for president, they cannot succeed if he continues doing that. As you say, for me, the same property in question is talking about has been a subject of investigation before. We have had the DEC at my residence before when I resigned as minister. You are aware. We have had our vehicles seized at some point after I resigned. So these are not new things. But this will not deter us from making sure that we speak for the people of Zambia. I think this will not stop us from making sure that the people of Zambia are well represented and will continue talking for them for as long as what is right is right. And what is wrong if indeed the Harikawa has gotten offence, nothing will be punished. So what? No, it's clear that the SEC and that's why they are having difficulties to gana support for the fight against corruption. No matter how eloquent the president speaks about it, no matter how he appears to sincerely speak to this. It doesn't have support because of things like this where you use under abuse law enforcement agencies you use them as tools of oppression. If you and I were quiet, the SEC would not have been here. How would they even be here? They are only here because they want silence. But let them put restriction orders as much as they want. Job in the scripture says naked I came, naked I shall return. I was not born with everything. If I engage them once, it can even get all of them. It doesn't matter. But he must know that we hold him accountable. We must call that lawlessness to order. No, but that lawlessness to be fought. We have a right to own a property. Of course, we are going to high hot. The fundamental right for you to own a property legitimately end cannot be taken away because one is president. No. Or because I'm speaking against him or because I'm criticizing him. So he hopes that then he will inconvenience. To not happen. No, it would not happen. It's a wrong method but it's a good trial. It's a good attempt but it will not work. It's far from it. It cannot work. That's for lesser men. For some of us, we are excellency, we are resolved. Resolved to a point of giving up even in zero positions for as long as it will take us to represent. Thank you, excellence. For as long as it takes us to say what is true, what is right, it doesn't matter. And we are ready for the ramifications. It's a pity that people that want to show that they are good at governors can begin playing such kind of shenanigans to want to distract the public. I think people are interested in the high cost of millimail. People are interested in the high cost of fuel. People are interested in the dollar stabilizing. People are interested in these issues and you want to distract them by bringing restrictions notices to Ambassador Muamba and Harika Lavawa in our neighbors. I think it doesn't work that way. I think I've been around myself here. Everybody in the neighborhood knows. Yeah, you are among the earlier shot came here. Yes. We were found here. No headband. I'm a headband. Okay. For the social media audience, we will do something very formal. We've got a media organization that has joined us. So we will speak formally to that media. And thank you colleagues for coming. This morning, this morning, we received officers from the Antcorruption Commission who saved myself, Ambassador Manio Muamba, with a restriction notice over my property here in Baumoro, Makeni. And unknown to me, Honu Boharika had also received a similar restriction over his property again here in Makeni, Baumoro. We have condemned this action against by the SEC. For me, what I've stated is the law should not be used or abused in the manner that it is being abused. I've called on the SEC should have first called me to establish my sources of income. Exactly. If they became aware of a property that they thought could not commensurate with my income. That's procedure. They should have called me, interviewed me, asked me to submit records and details of my income that built that property. But just to come and save me for the first time with a restriction notice, we've taken it as an act of harassment, an act to silence the opposition, an act to silence critics of the president. Thank you very much your excellency. In the same vein as Zambatheda Mwamba has said it in 2017 when I resigned as a foreign affairs minister, the anti-corruption commission had salmoned me of a property here, the same property and I think they tried to be very professional at that time because they called me and asked me how I managed to build the flats in question and I explained to them but look, I have been member of parliament two times and I used my gratuity and you can go and verify this. I also verified the loan I had within the Zambia Bank and they were satisfied that there was nothing wrong that I had done. The same happened because they came they even got vehicles that had gotten from parliament and they discovered that those vehicles were legitimately gotten from the national assembly then as a member of parliament. Now for president I can in the HLM again to begin a going round circles when he said you see what will happen this month how people are going to be prosecuted and if this is the way he is fighting corruption then the fight again is corruption is done. It's completely lost because even it's stolen from the public some of us resigned as a result of abuse of office if people will be allowed to go scot free as a result of playing games like this you are now shielding the real people that should be facing the law because everybody if you are going to put them in this kind of an umbrella because of politics then you are going to miss it and this is why when we say president that in the HLM is basically doing job on training these are the things that are talking about and he doesn't have a clue of how this fight should have been he should have allowed the anti-corruption commission to be autonomous and give them the political will rather than putting them under his office as a result of that he has lost the fight and because he has lost the fight he also lost the elections in 2026 because there is nothing that he is standing for and if you will be harassing people he's been telling you ambassador and that was foreign affairs minister by the way I know how much an ambassador ends as minister of foreign affairs I know that when you go to a place like London an ambassador does not end less than 15,000 pounds a month when you go to Washington an ambassador doesn't end less than 20,000 dollars a month when you go to at Sababa an ambassador ends an average of about 10,000 dollars a month and so when you look at the money that they end and then you begin doing that it's a lack of research on the part of the president and he's acting out of lack of understanding of how the system works when you pursue a person that has been very conservative like myself like I said I've been in this place myself for a very long time I even refused to move out of my residence because I wanted to be comfortable with with where I am modestly like this and even what we have done has been very modest we have relied on banks ourselves to finish our projects and that's how we do it so for someone to come without even giving you an opportunity to behave and just give you a restriction and notice that now don't sell this property until we finish investigations it's an abuse of the law and it's unacceptable in a democratic dispensation such as ours we will not allow it there's a matter of concern regarding the president's address on Saturday where when he made reference to the creation of the economic and financial crimes caught he says everything is in place and will ensure that this this process people go to jail in the next 90 days now that's extremely dangerous the judicial is independent the judicial has a chief justice who responds to the constitution the executive cannot give directives of how long court cases should take and what period those cases should be implemented the president is exerting unnecessary pressure to the judicial to convict persons wether they are guilty or not I think just not to cut you short I think he must speak a leaf from his colleague Lady Manawasa he might not have liked President Chiluga both of their souls rest in peace but he was sure that he allowed the due process of the law to take place without putting a cap on it it is not in his space the president it is not in his space to begin saying this is how long the judiciary should go that is why basic civics which I know the president started would tell you that the independence of the three organs of government the legislature which is parliament the executive which is his cabinet and the judicial which is headed by chief justice what is his name again Mumba Marila state council yes, state council these three independent wings of government must be allowed to operate independently why not make an announcement on behalf of another wing in parliament he announced 90 days people will go to jail that the process has to complete in 90 days I think it's important for the judiciary to acquit themselves from those directives they should remind the president that they obey the constitution and the constitution assumes that you have a right to innocence that you cannot be deemed guilty in the manner that the executive is dealing there is a lot of governance issues that must be screwed on and I hope that his analysts I don't know what's happening at cabinet office because what we used to do ourselves in the civil service when ministers come we used to call it an orientation for ministers to know the do's and don'ts and it is incumbent upon the sector of the cabinet and the office of the president to sit down with the president and tell him how his powers work in what ways his powers should work but it looks to me that that kind of thing never happened with what we are seeing now in an August house and announce that now it will take 90 days Yes, I've set up the economic and financial plan You don't do that We thought it was a chief justice So it appears the chief justice is the mayor cover It was set up by himself You can't do that You can't do that You can't do that You can't do that You can't do that


Okay, so good afternoon and let's begin. Just to recap the last time we saw some other consequences of the Gershkorin disk theorem and then we started discussing about perturbation location and perturbation of eigenvalues namely that eigenvalues of a matrix change when the matrix is perturbed. And so the starting point is that we are given a matrix A of size n cross n and it has eigenvalues lambda 1, lambda 2 up to lambda n and this matrix A is getting perturbed by a matrix E to get the matrix A plus E and suppose we compute the eigenvalues lambda hat 1 up to lambda hat n or in particular if some eigenvalue is lambda hat what can we say about how close lambda hat will be to one of the eigenvalues of the matrix A that is can we say something about lambda hat minus lambda I modulus value for some I that is will this value be small for some one of the eigenvalues of A and the various ways to answer this question first of all if A happens to be a diagonal matrix if A happens to be a diagonal matrix then we can simply directly use the Gershkorin disk theorem to say that this difference between lambda hat and one of the eigenvalues is at most the L infinity norm of E this is what we saw the last time and the other case is when lambda is a simple eigenvalue of A meaning that it has an algebraic multiplicity equal to 1 then if we denote X to be the right eigenvector corresponding to lambda that is A X equals lambda X and Y to be a left eigenvector corresponding to lambda that is Y Hermitian A equals lambda Y Hermitian then if E is a perturbation matrix such that its spectral norm equals 1 then if we denote A of t to be A plus t times E then we can study what happens to the how sensitive the eigenvalues of A by looking at the modulus of the derivative of the eigenvalue at t equals 0 so we showed that this is less than or equal to 1 over S of lambda where S of lambda is defined to be the magnitude of Y Hermitian X and S of lambda we called it the condition number or the condition of the eigenvalue lambda so this is for simple eigenvalues okay so it's an eigenvalue of A with algebraic multiplicity equal to 1 then we looked at the case where A is a diagonalizable matrix and E can be anything that means A can be written as S lambda S inverse for some invertible matrix S and a diagonal matrix lambda then we showed that lambda hat minus lambda I is at most K of S times the norm of E for some I where this norm is any matrix norm such that the norm of a diagonal matrix is the maximum magnitude diagonal entry in the matrix and K of S here is the condition number of this matrix S with respect to this norm used here of course the condition number is greater than or equal to 1 and it is equal to 1 when S is unitary so if the matrix is unitary diagonalizable then we have that lambda hat minus lambda I is less than or equal to norm of E itself so this K of S is equal to 1 and so then normal matrices are unitary diagonalizable so as a consequence if A is a normal matrix and E is arbitrary then we have that lambda hat minus lambda I is at most the here taken the spectral norm of E for some eigenvalue lambda I of A the next one is that suppose A and E are both Hermitian symmetric matrices then if we denote lambda 1 to lambda n to be the ordered eigenvalues of A and lambda hat 1 through lambda hat n to be the ordered eigenvalues of A plus E then we can lower bound lambda hat k minus lambda k so this is taking the kth largest eigenvalue of A plus E and subtracting the kth largest eigenvalue of A itself and that is at least equal to lambda 1 of E and at most equal to lambda n of E and further this magnitude of this difference is at most the spectral radius of E okay so this is where we stopped the last time now we consider one more case where A and A plus E are both normal matrices what that means is that we can write A as U lambda U Hermitian and A plus E as V lambda V Hermitian where U and V are both unitary matrices because normal matrices can be unitary diagonalized now if we look at the Frobenius norm square E2 square then that is the Frobenius norm square of A plus E minus A which I can write as U lambda hat U Hermitian just substituting for A plus E and minus U lambda U Hermitian just substituting for A Frobenius norm square and what I can do is since the Frobenius norm square of a unitary matrix is no yeah so I can pull out a U on the left and a U Hermitian on the right and since the since multiplication by left or right multiplication by a unitary matrix does not change the Frobenius norm of a matrix I can get rid of U and U Hermitian and write it as the norm of Z lambda hat Z Hermitian minus lambda square where Z which is equal to U Hermitian V is a unitary matrix okay so now this is a unitary matrix and this Frobenius norm square we know that it can be written as trace of so Frobenius norm squared of A is trace of A Hermitian so I just write that here so this is trace of Z lambda hat Z Hermitian minus lambda times the Hermitian of this which is Z Hermitian Hermitian is just Z lambda hat Hermitian Z Hermitian minus lambda Hermitian if I just expand this out this gives me this times this which is just the Frobenius norm of Z lambda hat Z Hermitian square and then this times this is just the Frobenius norm of lambda square minus 2 times trace of the inner product between this and this which is Z lambda hat Z Hermitian times lambda Hermitian. Now again this is multiplication by a unitary matrix so I can get rid of this Z on the left and Z Hermitian on the right and write this as lambda hat 2 square plus lambda 2 square minus 2 real part of trace of this matrix the same as the previous equation so what are we trying to do here we are trying to see how relate this E2 square to the eigenvalues of A and A plus E so that we can ultimately bound E2 square so for example here you can already see that this Frobenius norm squared this is just a diagonal matrix so it's just the sum of the diagonal entry squared this is also a diagonal matrix so it's just the sum of the diagonal entry square and then there's this term I'll come to that in a sec but the point is that on the right hand side I have terms that depend only on the eigenvalues of A and A plus E and if I can find an expression for for this quantity which only depends on the eigenvalues of A and A plus E then now I'll have an upper bound which connects eigenvalues of A and A plus E with the Frobenius norm squared of the error matrix or the perturbation matrix so that's the final goal is to find some expression for this quantity which depends only on lambda hat and lambda i now this quantity itself is something whatever it is but if I replace it with something bigger then I'm only making this whole expression smaller so I can say that it's greater than or equal to these two terms minus a quantity g star where I define g star to be the maximum that this can attain over all possible unitary matrices z so g star is the max of this thing two real trace of w lambda hat w Hermitian lambda Hermitian over all matrices w which are unitary now if I simply expand this out right and take into account the fact that lambda and lambda Hermitian are both diagonal matrices I can write this two real trace of w lambda hat w Hermitian lambda Hermitian as the summation over ij going from 1 to n of the modulus of w ij square times the real part of lambda i star times lambda j hat is there a question okay so this is like this now suppose we define a matrix c with entries c ij c ij is equal to this quantity this is this coefficient of this term here now what is this matrix c it has non-negative entries okay and if you take the sum of the rows the entries in any given row or the sum of the entries along any given column they all add up to 1 because w is a unitary matrix okay such a matrix is called a doubly stochastic matrix a matrix with non-negative entries where every column adds up to 1 and every row adds up to 1 is called a doubly stochastic matrix and so what we what we see is that whenever w is unitary then this matrix c will be a doubly stochastic matrix however the converse need not be true in the sense that if i take a c which is doubly stochastic it there may not exist at a unitary w such that mod wi squared is this doubly stochastic matrix so if i replace the maximization over w with maximization over all matrices c which are doubly stochastic then i'm only expanding my potentially expanding my space expanding the space over which i'm doing this optimization so this is further upper bounded by the maximum of 2 c i j so wi j squared is equal to c i j times this real part of lambda i star times lambda j hat over all possible doubly stochastic matrices now this objective function is linear in this matrix in the entries of this matrix c and further you know a linear function is both a convex and a concave function of these variables and so as a consequence this is this amounts to maximizing a convex function over the space of doubly stochastic matrices so in order to solve this optimization problem we need to know something about this constraint space what is the space of doubly stochastic matrices so let's precisely define that so suppose ds is the set of all doubly stochastic matrices okay it's a small exercise to show that ds is a convex set that is you take any two doubly stochastic matrices and if you take a convex combination of those two matrices you will get a doubly stochastic matrix so you can show this very easily so the set ds is actually convex okay now we we use one very very fundamental result from optimization that the maximum of a convex function over a convex set is always attained at what is called an extremal point of the convex set okay similarly if you want to minimize a concave function over a convex set the minimum will occur at an extremal point of the convex set so just to give you the idea suppose I have a convex function like this and if I have a convex set in on this real line which is an interval and if I want to in fact yeah if I want to maximize this convex function over this convex set then the maximum will occur at an extreme point this is also true if I take a convex function that looks like this for instance okay the maximum will be either at this point or this point depending on which one is higher the minimum could be at some point inside but the maximum will always be at an extreme point of the convex set okay so so then what is an extreme point it's like the end points of the convex set but the generalization is as follows so if d is a convex set on some defined on some vector space we say that x a point x in d is an extremal point or an extreme point of d if there is no lambda 1 lambda 2 greater than 0 which add up to 1 and x1 x2 belonging d such that lambda 1 x1 plus lambda 2 x2 is equal to x in other words you cannot find two points that are internal to the set d where if you take a convex combination of those two points you will get this point x okay so the so that you can see that from this interval also if I take either this point or this point I cannot write this as write this point or this point as a convex combination of two points that are internal to this convex set whereas if I take a point here I can write it as a convex combination of these two extreme points so this is not an extreme point so for example in two dimensions if I have a polygon like this then the corners of the polygon are all extreme points or if I have a circle in two dimensions like this the entire boundary of the circle is a are extreme points okay so the solution to this to this optimization problem okay will be at one of the extreme points of this convex set so all we need to do is to identify what are the extreme points of this convex set substitute those extreme points and then pick the best the highest value we can get so we need to understand what would be the extreme points of this particular convex set okay so the the extreme points of this convex set are actually given by a theorem which is known as Birkhoff theorem or the Birkhoff von Neumann theorem this is one of the this is a theorem I will not be proving in the class it's it's a it'll digress too much from what we want to do plus we are we don't have time to prove this theorem here but basically what it says is that the set ds okay is the convex hull don't worry about if you don't know what this convex hull means it's the convex hull of the set of n cross n perturbation permutation matrices okay and the extreme points of ds are precisely these permutation matrices okay that's the punch line the extreme points of ds are precisely the permutation matrices so basically if c is a doubly stochastic matrix then there exists an n less than infinity alpha 1 to alpha n non negative and adding up to 1 and permutation matrices p1 to pn such that you can write c to be alpha 1 p1 plus etc up to alpha n pn okay so any any doubly stochastic matrix can be written as a convex combination of permutation matrices that's the punch line and these permutation matrices are essentially vertices of this convex set ds in fact some side notes here are that there is another famous theorem called karath Yaldori's theorem which says that you can choose n to be at most n squared minus 2n plus 2 that is n minus 1 the whole squared plus 1 okay so while there exists n factorial permutation matrices of size n cross n we don't need to use all n factorial permutation matrices to decompose a given doubly stochastic matrices we can make do with at most n squared minus 2n plus 2 matrices and further this this decomposition is not unique there are the various ways in which you can decompose if I go back to this example here so if I take a point over here obviously you know I can write this as a convex combination of these extreme points in multiple ways for example I can take these three points and find the convex combination get me here or I can potentially take these three points and write it as a convex combination of these three points and so on so there's no unique way to do it but in this case you can see that for any point I can take a I can I can I can reach any point by taking a convex combination of three points so when n equals 2 what happens to n squared minus 2n plus 2 n squared is 4 minus 4 plus 2 in fact two points are enough that's what karat karatheadoris theorem says but this is not this this is not the convex set corresponding to permutation matrices so if you look at the 2 cross 2 doubly stochastic matrices you can write any 2 cross 2 doubly stochastic matrix as a convex combination of at most two permutation matrices okay so then what is a permutation matrix it's basically a square binary matrix with exactly one entry equal to one in every row and one one entry equal to one in every column and zeros everywhere else and we've also seen these matrices previously we know that p a permits the rows of a and a p permits the columns of a okay so now if we use this Birkoff's theorem then there exists a permutation matrix p that solves this optimization problem because these the solution to this optimization problem is an extreme point and the extreme points are all permutation matrices so for that permutation matrix we go back to the earlier way of writing this this expression and we write it as two times real part of trace of now p is a permutation matrix so p lambda hat p transpose because it's zeros and ones you don't need a Hermitian there times lambda Hermitian okay and now p lambda hat is a permutation of the columns p transpose lambda hat lambda hat Hermitian is a permutation of the rows of lambda Hermitian now so if p e i is equal to e or e of sigma of i so sigma of i represents the permutation so basically what it's saying is that the index i is getting mapped to index sigma of i that is what this permutation matrix is doing so there are different ways of writing out a permutation matrix one is to write it as a matrix and the other is to specify this sigma of i the permutation function which maps indices i equal to 1 to n to i equal to 1 to n okay so if we if we do this and then we substitute that into this expression you can actually simplify this formula to this expression here so we now see that what we are left with is just lambda i star times lambda hat of sigma of i okay so it's just products of permuted versions of lambda hat so thus what we have shown is that this e2 squared the l2 norm of e squared is lower bounded by the summation i equal to 1 to n lambda hat of sigma of i square so it was lambda hat i squared earlier but sigma of i is just a permutation so all the entries will get included if i use sigma sigma of i instead of i itself so this is also okay plus the summation i equal to 1 to n lambda i square minus 2 times the real part of sigma hat of lambda hat of sigma of i times lambda i star now this expression here is nothing but the modulus of lambda hat of sigma of i minus lambda i squared added up i equal to 1 to n so now this is beautiful because i am now shown that this quantity here which is the sum of the square differences of the eigenvalues of a and a plus e these are the eigenvalues of a these are the eigenvalues of a plus e but written in some other order sigma of i this sum is at most equal to the the Frobenius norm squared of e so what we have shown is what is it is known as the Hoffman Weyland theorem which says that if a and e are both n cross n matrices a and a plus e both being normal matrices and lambda 1 to lambda n and lambda hat 1 to lambda hat n are the eigenvalues of a and a plus e respectively and in some order then there exists a permutation sigma of i of the integers 1 to n such that summation i equal to 1 to n lambda hat of sigma of i minus lambda i square is at most the norm of e square okay so basically what this theorem does is to show that there is a strong global stability it's strong because it just depends on e2 square and it's global because it doesn't matter which e you pick even if you choose adversarily this thing is at most e2 square and these are stable to stability of the set of eigenvalues of a normal matrix okay so this is one more result that we have about the perturbation of eigenvalues of a matrix okay so if a is not diagonalizable we've seen that we can find a formula for perturbation of algebraically simple eigenvalues and we can also do one other thing which is that we can approximate um arbitrarily by a diagonalizable matrix so we can approximate this matrix a arbitrarily closely by a diagonalizable matrix and then everything we said about diagonalizable matrix is applicable and we can then say something about how the matrix a will get perturbed what we mean by we can approximate it arbitrarily closely by a diagonalizable matrix is something we've already seen before so I'll just state that to recall what we said so a is an n cross n matrix and uh so suppose this is any norm then given epsilon greater than 0 there exists a matrix a1 c to the n cross n such that a1 has n distinct eigenvalues and a minus a1 is actually less than or equal to epsilon in fact you can even make this okay is that most epsilon and corollary to this matrices is dense on okay so given a matrix a in c to the n cross n I can find a diagonalizable matrix which is arbitrarily close to uh this matrix a it's useful because one one useful way of approaching perturbation related problems is to first solve for diagonal matrices then solve for diagonalizable matrices and then use the approximation and some limiting process to say something about what happens in the non-diagonalizable case yeah


So welcome, Victor Strecker, and I'm really especially glad that we're having this conversation because we both think having a purpose in life is extremely important, vital. Yeah, and I have to say, you know, when you invited me on, I took a look at your background a bit just to see, you know, learn more about you and what you've been doing is so impressive as well. I kind of hope that we can kind of have a conversation and, you know, more than an interview as if we're just sharing coffee together or something at a little cafe. Where would the cafe be if we're hanging out? That's very kind. So I'll start with a question that is triggered by conversation I just had 30 minutes ago with one of my consolists because I do philosophical counseling. I help people find their purpose in life one on one. And I was saying, and this is something I often say, but in this case, I was living open the possibility of another answer, but I often say, they're not as many purposes as they are humans on earth, right? They're not 9 billion purposes, which, which creates a great opportunity also for a higher form of community, right? So what I would like to ask you is, do you agree with that? I find it a really interesting and unique question. I hadn't really thought about it before, but I am going to. I'd love to take a slight counter to that by saying, yes, if you ask people to write down their purpose, a lot of it looks like greeting cards. You know, I want to change the world. I want to do good things, whatever. And you can lump millions of purposes into something vague in general. But I believe that a purpose, a true authentic purpose is getting back to what Carl Jung called individuation that you're going back to something that's quite unique about you. And while there certainly could be some overlaps. I would say that there may well be, you know, you could probably get back to an individual purpose that is completely unique. That being said, I think that the values and identity features of that purpose may have elements that are very consistent with millions of other people around the world. Am I a giver? Am I a pleasure seeker? Am I a meaning seeker? Am I a guardian? Am I an activist? Am I an achiever? Those sorts of ideas and identities that people might have may certainly connect with many, many millions of other people. Does that kind of make sense? Right. So if people who start listening to us wonder about examples, right? Yeah. You have great examples that you give yourself in your TED Talk or in your books. Would you like to, what comes on top of your mind? Yeah, well, you know, my purpose, which is to help other people find purpose and direction in their lives. It's to also be a strong family person. It's also to be a good teacher and in fact to teach my students every one of them as if they're my own daughter, but also to get people out on the dance floor of life. I think, you know, I don't know if you had in Europe or did you grow up in Europe, Luis? Indeed, I did in Paris. Yeah.  You know, all these kids would go out and they'd take their shoes off in a gymnasium and they would start dancing to sometimes live music and whatever. You know, there were people called wall flowers and they were just, you know, stand along the wall and never dance. And they're always waiting for somebody asked them to dance or they're too shy to dance. And it is interesting word because wall, they're on the wall, but they're also flowers. They're beautiful. And to dance means, you know, a wall flower is waiting for someone else to bring them into life in a way.  And the other is people don't go out and dance because they think they'll make asses of themselves and other people will make fun of them. And one of the parts of having a purpose, I think is that a, you're willing to go out onto the dance floor and not wait for somebody to tell you what your purpose is. You know, I'll wait for the government or the church or my family or my community or media, social media, tell me, you know, what my purpose should be.  And I can't care all that much what other people are thinking about that dance. Those are parts of my purpose and you might see different domains of purpose in that. So I believe there are different domains. I don't want to turn purpose into something that is somehow ethereal and mystical. I think purpose is a self organizing set of life aims that you have. And, you know, I might have purpose at work, which is teaching my students as if they're my own daughter I have purpose at home to be a, you know, a strong husband and father and grandfather and son. I have purposes in my community. I have purposes in the world. I have personal purposes of having fun.  They help me organize that and they think help me think prospectively. And we found in our neuroscience work that there's when we ask people to think about their purposeful core values that more oxygen goes into this part of the brain called a ventral medial prefrontal cortex which is very human humans have much more of this and any other animal by weight. And so this part of the brain relates to prospective thinking. It relates to future orientation. What are my possible selves what are the people that I could be. And other other animals don't seem to have that my dog doesn't seem to have that a dolphin doesn't seem to and they don't change their behavior necessarily my dog isn't going to say, you know, I think I'm going to be a vegetarian now. But humans do. Is that making sense. Yes, I think I discovered that recently actually I was quite amazed about the was called the science of purpose right which seems to be like the miracle peel because it's it goes from, you know, aging to all sorts of mental and physical benefits. Now, I think what you're saying. If I understand correctly is that for you purposes more of verb than an object it's more the, the act of purposeful nefs of aspiring, rather than fetishizing a sort of all encompassing value right for which we would sacrifice. That's a great word fetishize. But yeah, here's a lot of this philosophical words sorry for sorry about that. However, someone may ask okay so how when does like if we speak of distance right if we think in terms of how far is the realization of the purpose right if I decide to make myself a coffee. It's going to take me five minutes if I have a coffee machine. If I decide to, you know, to, to be good to my neighbors okay that's maybe an everyday practice but that won't take me further away than you know one kilometer around. But now, if the purpose is justice for all. Then we we're much more distant right so someone might ask when is it of the same nature. You know the purpose of going to the supermarket in one hour and achieving justice for all. Is it just a continuum, or is there a moment where we have a qualitative jump. In that case, we would, we would try to, you know, know where if we are beyond that limit where it starts to be a real purpose or not. I love the question by the way this is exactly why I wanted to be on this podcast because you know you're such a bright thinker and your philosophical terms such as fetishism. It's great you fetishized purpose. And I think I'm enjoying this too so let's thank you. Yeah. You bring up a really, really important question and to some extent a slight disagreement among researchers of purpose. Some researchers of purpose regard purpose as a goal or set of goals that people strongly value. You know I might have a purpose of making coffee in the morning. That would not be a life purpose, but it is a purpose.  But most purpose researchers regard purpose as aspirational aspirations. So something that's much bigger if I'm going to teach every student as if they're my own daughter there are some elements of that that could be achieved. I suppose, but but really not it's it's more of a mindset I suppose where I'm thinking if I have a student who is in need. And I have a grant to write, you know a grant proposal for a sign in a national science foundation. I might go. Well, I should ignore that student and keep my door closed. But if that students my daughter, or if I'm the parent of that person, what would I want me to do. And I'd say, Okay, I better make some time for this student. And so it's it is more a general mindset of what I'm going to do in terms of all the conflicts that we face. And I think people don't talk enough about the fact that we face conflicts, all the time. I mean, every day we have little mini conflicts. Do I want that glass of wine or should I play with the children do I want this glass of water. Or do I want to have a big ham and egg breakfast or whatever you know there's all sorts of things that I can decide. And people with strong purpose actually have less conflict. I don't understand that direction. We do. We put people in the MRI magnetic resonance imaging who have strong purpose, and we put people in who have a weak purpose, and we give them messages that create conflict are intended to create conflict. And there's a part of the brain, the dorsal anterior cingulate which relates to conflict in the brain, and purposeful people don't have activation there when conflicted they know what to do. Right. What's interesting too is that that part of the brain the dorsal anterior cingulate is our pain center as well it's related to pain. So that I find fascinating. Very often conflict may create pain. And people, sure enough, who have strong purpose a strong sense of purpose in their lives are more resilient to pain they can put their arms in freezing cold ice water and hold it in longer. It's more vulnerable than people who don't who have a weaker purpose. I'm not sure that's answering your question but I see it a little more as this mindset as opposed to real specific goals. And I, but it does help you arrange those specific goals. It seems listening to you that the mindset is about unification of the self, isn't it. In the sense that a person that has a purpose is intentionally unified by a focus and therefore, as we know, whenever we are in focus that eliminates a lot of things from our attention or awareness. And therefore, a lot of possible conflicts are, are eliminated right. That's exactly right and you use an important word intentionality. I think people with strong purpose are more intentional. And we may be intentional for example I might wake up and the first thing I do is look at what the weather is going to be like and go okay I'm going to dress in a certain way based on that weather. What if you woke up and you said wow I have to give a talk today or I have to take tickets in a subway today or I have to do something I have to be kind to my mother today. Whatever those things are, if I start thinking a little more intentionally about even daily activities. Those things you'd go well what's important, and I'm going to now set my energy, my vitality, you know this limited resource I have toward those things that matter most. So, I believe that that's what purpose does it's not magic but it's, it's what what I find fascinating is that scientists have not taken this term seriously for decades and decades and yet we just published a paper literally this week in the Journal of Gerontology, showing that older people who have a strong purpose, have longer epigenetic clocks, your epigenome kind of is like the vinyl record on top of your hard drive of your DNA for the longest time and in fact in high school I was taught your DNA is your DNA and that's it that's all that's inherited, but there's this epigenome this vinyl record that ends up getting weathered sometimes or developed sometimes over years and parts of it may be even incredible. And that epigenome is can you can start looking at the epigenome and then creating a biological clock from that. And what we have found in our research is that people have longer biological clocks in other words our genes express more healthy proteins, like antivirals and fewer proteins that are negative like pro inflammatory cells you don't want inflammation, especially during a pandemic. So, those things seem to and people live longer, we found that our epigenetic clocks are longer people live longer if they have a strong purpose. Why doesn't science what isn't, you know, medical science take this seriously and so we need a purpose pill we need to figure out if this could help people live bigger, better, longer lives. Right. Because I think that's, that's what philosophy has been saying for centuries and 2000 years. I call it philosophical health. But I don't want to get too technical here but I think the epigenome is also sensitive to much more than the genome to mind some sort of mind action. You know, the final smart mind of a matter we don't want to get too spooky here, of course, but still, so we don't want to give the impression that it's, it's because of a vinyl or I cannot really record it. While there is some, I think, evidence that or at least claim that it is wrong to think that, of course, the mind has no power at all in the way we we live our lives in embodied situations. So now the question is, and I mean, this is, you know, we're talking about psychosomatics, we know that this is everywhere. For example, if, if you manifest some psychosomatic pain, right? So people usually think, oh, that's unhealthy. Oh, there's, there's a red spot or there's some pain that we cannot explain materially. But actually, one could argue, well, this is very healthy is, is that there is a good connection, good enough connection between the mind and the body such that the body can alert things that the mind might not be able to formulate. But here we're talking about precisely, we're talking about tensions and contradictions in our life, that because the life is not unified in, in some meaningful way creates this conflicts you were talking about. And now someone could ask you because you said in the beginning that you have several purposes. So how do this several purposes do not enter in conflict with each other. You can have purpose conflicts. Yes. I mean, if, if you follow at least my reasoning and I might be wrong, but if you follow my reasoning that you, if you think about life purpose, life is complex and you have different domains of life.  You know, I am to hear it. No, you're not here. You're not here present in your mind. So I, you know, people use this term work life balance, for example, to express the need to balance different domains of purpose. I don't like that because it seems like a zero sum game. If I work real hard, I can't live. If I live real hard, I can't work. I don't believe in that. I view it more as Venn diagrams. I view this as overlapping. Can I, for example, become a better human being personally and my personal goals that I have and my personal purpose through my work. Can my work in a way educate me to be a better human being? And maybe I am taking tickets in a subway, but maybe I could learn to be a better human being in doing that, helping people maybe have a better day, as opposed to just being, you know, acting like an automaton, which I've been hired to be essentially. So could I take that job and craft purpose from it? And there's a lot of research showing that indeed you can do that. And if you do that, you're much happier in your job, much happier in your life. That can also make you a better person. You could also, for example, if you care a lot about your family, you might say, well, what is our family purpose? And how is my relation, what's my relation to my family vis-a-vis that purpose? Is there some connection to a community purpose? So maybe our family decides to volunteer in the community or get into involved, excuse me, in some activity that involves community volunteerism. Those things may start connecting or in my work, I might say, yes, our workplace should volunteer and do certain things. I think that there are ways of reducing conflict. But I won't deny that there is sometimes conflict. I have a big purpose in my life in terms of my work. I want to help people become more purposeful. And sometimes that could interfere with my relationship with my wife, for example, just in terms of time. Right.  Right. And so that is, of course, something that you'll need to learn as we live, is that just the fact, I mean, being in the world of otherness with our fellow humans is both a gift and a curse. But he also said an interesting thing. He said, we know everything except how to live. And I think he said that in a time when we're discovering so many scientific advances in medicine and astronomy. We learn we're not, you know, we're not these giant things, learning more about the universe expanding. And, but I still don't think that we've learned how to live, which is why I appreciate you and what you've been doing, because I think that's what you're doing. You're saying there's, we need to figure that side of it out too, because we still haven't figured out how to actually live our lives. Right. And we're describing here, not answers, but maybe an understanding that our lives are complex and the conflict. And I think Sartre was growing up in a time when increasingly, you know, just like Nietzsche was growing up in a time where increasingly there were people were leaving their communities, you know, that they grew up in and moving to big cities and working in, you know, in, in industrial factories and killing themselves and, and, you know, just they're losing all sense of purpose and that was handed down to them. I think Sartre, you know, and his predecessor in a way, the proto existentialist Frigick Nietzsche said, you know, we have to now figure out our own purpose we have to create our own light. Is that making sense to you? That's right. I think that's what they have in common is that they pointed also with Kierkegaard, they point the vertigo and anxiety of realizing that meaning is not given as we thought before the death of God, right. Using quotes here. So, and then there is this rediscovery of, of a form of optimism and joy, which is the joy of realizing well then, if meaning is not given, let's let's try to to be sense givers. What's interesting is that you were talking about technology, you were talking about the influence of, of, of industrialization on this realization also of the absurdity sometimes of norms that are imposed upon us right purposes that are not our purpose, this is something we should also talk about right. There's no such thing as a human without a, a values or worldviews it's just that sometimes we are alienated to values that are not ours. So, we can't pretend that's very certain right, we can't pretend to live without values we can't be that person that says, I don't care about philosophy, I don't care about ideology, because that's we're made of this ideology so now, going back to that technology is of course in our lives. It's interesting because of course today everybody's talking about AI right, and even the, the big experts in AI and are saying well, the problem of AI is human is that we've never been exactly what you're saying, we've never been very good at defining our purposes. It's, you know, there's Stuart Russell's book Human Compatible, he quotes the famous myth of the genie and the three wishes usually in many cultures, we're giving three wishes and it doesn't end well right we get all confused and we ask for the wrong things. So, this moment of emerging technologies that seem to be giving some structure, some meaningful structure to our lives. I think it's more than ever a call to, to, you know, to sort of be responsible for the directions and the deep orientations that we give to our lives. But having said that, I think that someone might still ask, you know, someone might still say, well, this doesn't seem sufficient enough to have like a set of purposes that we hope won't be in conflict and basically which have to do to be with being a good person, right? Or you mentioned the example of dancing in your own dance, pre-organized, very normative activities, someone might say, I don't care about being a good person and we've seen that in history a lot. Sure.  And if we have to kill 1 million people to achieve that, we'll do it. So, how do we, where do we stop, right? Like, half an hour ago, we were asking, where does it start? Where does purpose start? And now I'm going to ask, where does it end? When do we know that we're not falling into some form of dogmatism? In fact, it's such a beautiful question. Years ago, I was invited to the city of Heidelberg, Germany, because Heidelberg wanted to become more purposeful. So, they invited, it was a great gig because we went out into the mountains into this, you know, 15th century convent, I believe it was, and we talked about it. And I remember there are all these people from the city of Heidelberg there, as I was talking about purpose, and I was talking especially about transcending purpose, purpose that would transcend oneself. And how that was healthy for you. And we've found, you know, some health benefits of a transcending purpose.  And it just struck me like, boom, I didn't really think about that, but Hitler had a transcending purpose. I'm sure, quite sure that Hitler was willing to die for his purpose. People in al-Qaeda or other organizations are willing to kill many people. And you could argue certain countries are as well, but, you know, we won't get into that debate, hopefully, or discussion. But you certainly know there are people thinking that they have a very transcending purpose. And I struggled with that actually. Honestly, there is, in Heidelberg, there's, there's a mountain there right at Heidelberg, and there's a pathway that goes up the mountain. It's called Philosopher's Way. And it's amazing because a lot of famous, I believe Gerta walked up this and so I decided, okay, I'm going to walk up here and try to find an answer. And I went up and I meditated actually for, I think about an hour or so and I started just, I literally sat up there for a long time and it's not that somehow an answer just came to me, but I started thinking about Nietzsche's terrible in the beginning of Thus Spoke Zarathustra, where it begins with a camel and the camel says, you know, load everything on me, load all the sorrows and the difficulties and the joys and love, load everything. In other words, educate me, completely educate me. And then the camel metamorphosizes into a lion. And there's this dragon on every scale has two words, thou shalt. In other words, you shall do what the government is saying, you shall do what the church is saying, you shall do what your parents said, blah, blah, blah. It's all, you know, this is what your purpose should be. The lion slays the dragon and then metamorphosizes one last time into a child, a child innocent of values. And the interesting you mentioned before, it's almost impossible not to have values and that's where I would say Nietzsche, I don't think Nietzsche had it right at the end. I don't think you can live without, I don't think you can somehow be reborn with no values and construct entirely your own values I think that's ridiculous personally but this idea of educating yourself is very important. So, I turn to my students and say, you're all camels, I'm a camel, I will always be a camel, but I am here always to learn, and I won't learn just from taking a class. I'll learn from going out into the real world and learning how real people live, learning how poor people live, learning how people die, learning how to make a canoe, learning how to be a bartender, learning how to be a nurse, learning the more experiences, real life experiences you can get the better educated you are, and that gives you a stronger transcending purpose that in, I don't know if philosophers must hate the word good but a good purpose, a purpose that somehow transcends and is helpful. There are people who, they may have PhDs but they can still be in a terrorist organization and believe in things that destroy a lot of humanity. And I don't believe they're real camels I don't think they've really educated themselves they might have been engineering, but not in the world. Is that making sense. I have struggled with that very issue. You're right. And many people, even in the history of philosophy struggle with that. It's the famous moral law of Kant right where he thought that if you, if you have a higher value you need to make sure that it can become universal. I see. Right. And so he always had this sense of it's not only about thinking for yourself, which is good. But it's also about thinking into the place of the other. What we might call empathy. Well, intellectual empathy because you know there is there is a we live in an over emotion list time and if you say empathy, a lot of people might think oh it's about feeling sorry for the other. It's right we agree that but what is interesting is that I mean in the philosophical health few sometimes people ask me okay so it's a new dogmatism you're going to tell. Who is philosophically healthy and who is not. But in fact, this doesn't apply because philosophy is not only philosophy as two legs. One leg is about trying to find indeed this overarching, you know explanation that will will give you so much purpose there is clarify everything right. The other leg it's it's the opposite is the questioning is the doubting is the capacity to to be able to think well, I think I might think this but someone else might think differently the curiosity for the other. And I think that philosophy is constantly trying to deal with these two aspects like the whole trying to give a big narrative to give a story that explains the whole the totality, but at the same time, care for the other with a big oh right the other. I love what you're saying and I'm learning something here that's that's really interesting that there are two sides of philosophy because I'm not a philosopher, but I'm, you know I enjoy reading philosophy and this idea of you know I think socrates said something like, you know, I know I don't know or something, you know related how important it is to admit that you don't know. There is that as but but he was always curious, always questioning always. And I think, keeping that open mind and that humility that we really don't know things but at the same time there may be things we can do in our lives that help organize our lives in a responsible way that make us happy. And this Aristotle's real question in Nicomachean ethics I believe what makes us happy. And, you know, one thing we found in our research very clearly is that hedonic goals do not necessarily make us happy in the long run. We've run into this hedonic treadmill where you know it's never enough it's never enough.  It's just, you know, it gets every time you engage in those things there's a diminishing return. And we have found that now, even in our physiology, when we look at our physiologic gene expression. So, I just, I love what you're saying about philosophical health. I wish people thought more about that I wish medicine thought more about it. Because I don't think we're, you know, I believe it was Marcus Aurelius who said don't live your life as if you're going to live 10,000 years, but the promise of medicine and public health is that will live 10,000 years that will live at least 100 years or 150 years, and all these new books about longevity and how we can live longer. What will we do in those years well we to me I think we're just stretching them out in a way and making each year thinner. It's kind of like if we have $10,000 versus $5 each dollar is worth more if you have $5 than if you have $10,000. So you kind of throw away those $10,000 each dollars hardly worth anything. And I think that's what we're doing increasingly we're throwing our dollars away on social media on what is Kim Kardashian wearing today. Who cares, you know, what these social influencers who have no necessary, not necessarily no skill sets, you know, to really learn from, and being a better human being. Like, why do I care what that influencer is doing. But we're spending more time on that. So that I think that's one of the motivations for what I do. I think this is very interesting because we know that evolutionary for a long time we will live 2035 years. And it could be that the amount of years we're given only makes us more superficial and and vein and anecdotic. I know that the resonates also with your personal history which you have not been hiding in your books. I don't know if we want to get into that but I don't mind. Right. This is up to you but before that I think that we have something really interesting there, which is the idea of reward right the idea of enjoyment. Some young people might think okay great looks cool. Having a purpose going to make me live longer and be successful let's have a purpose. And then, of course, they might go for something that makes them feel immediately good right. So, and you have I mean, at least in my consultations I have a lot of people who want shortcuts right the young people they seem to want shortcuts in a society that has you right I mean you mentioned this the fake celebrities. Society has this strong narrative of people who become extremely rich or notorious for doing nothing. Right, right. I think one of the first. I mean, I don't know but I remember when I was young was this Paris Hilton who was for being right. That's a perfect case. So, and so, of course, because we are in this democratic times everybody wants equality so everybody wants to claim some shortcut to a privileged state and, and sort of eliminate the effort it takes to to get in a place that really fulfills all the dimensions of who we are. And I think that there there is a sort of a thin line between of course, we're not advocating masochism right we're not advocating this like being for 30 years this hyper disciplined person who gets out because she or he have this big purpose but in fact, renunciates the every day here now for that. But we also don't want to advocate the cult of happiness in the sense that today people seem to think that happiness should or joy or enjoyment are the best measures of of us being on the right track, which goes right back to Nikomaki and ethics by Aristotle who said well there there is hedonism and Epicurus was one of the founders of that movement where pleasure is so important. And, but Aristotle said, that's fine. It's fine to seek pleasure. We all are pleasure seekers and that's good but if that's all we are and I think I'm quoting him said, then we're like grazing animals. And we all like to graze on good food or good wine or good sex or good travel or good whatever those things are good we all enjoy those things that's wonderful. But he also talked about euda monic well being euda monia being in touch with your inner daemon this godlike or true self that the Greeks thought we were born with. And if we can get in touch with that inner daemon, then we are more deeply happy. And that is that euda monia is what leads to happiness. That's, I think, where purpose is, you know, you can have different purposes. You can have Paris Hilton probably has some purposes or did. And, you know, she was more directed toward hedonic pleasure. And then she ran through probably, you know, I am guessing she probably went through some crises as a result of that because after a while, it becomes so thin, your life becomes so thin. So, but euda monia requires work as you're implying, not necessarily massacistic work, but certainly effort. I think, you know, philosophy is interesting. I wasn't at all philosophical in this way. And until my daughter passed away, 10 years, 13 years ago, which I can get to in a second, but I didn't really even think about these issues. And when I started thinking about purpose, and the more I read about it, the more I realized this is powerful stuff. This isn't just something that you can take a philosophy class. Okay, now I know what Aristotle said or whatever. It's powerful. It's also dangerous, even, you know, people can go down rabbit holes of philosophy and end up really becoming very depressed. Or they can, they can, you can turn your life around through philosophy and philosophical thinking for good or for for your own detriment, I believe. So it's a powerful thing I've learned that I didn't respect philosophy before. Now I have the utmost respect for what you do and what and how philosophy has worked in my life anyway. Right, and I can see you have you have read all the good references in. I think one of those good references, more contemporary is a wonderful book that you put you of course know by Anna aren't human condition, where she does come back to the idea. Very Aristotelian idea that what makes us really human is politics is entering into debate and action to make the world a better place. As opposed to the movement that she identifies since the 18th century, which she calls domestication really which echoes what you were saying about becoming animals again. So we domesticate ourselves because we have reversed this the priority and the domestic the family the house becomes the highest priority. The private sphere, but as she says very nicely the private sphere is a sphere there is deprived. It's deprived of community in the sense of action towards our ideals, which connects I think nicely to what you were saying about why also some people who feel attracted to philosophy end up being lonely or felt misunderstood or rejected. I fight for those people because I believe that in a way the our entire society today is is organized such to avoid. To that people think right so it's day it's a dangerous I think it's an errand to said philosophy is very dangerous as you as you also mentioned and that's we need to help when I was 20 when I or 18 when I decide to do philosophy. Everyone was against me including my parents very violently. The sense I had is okay so there's something wrong there must be something wrong with me.  I will be out of a job etc. And I think today people are realizing perhaps or maybe I'm being optimistic I don't know. I think that that aspiration to interrogate things do not take things for granted and also aspire for meaning aspire for a purpose that is not just something private and personal but that I think we all carry in us. This idea that we would like to get closer to paradise on earth. It's a dangerous idea. As you said yourself. Perhaps Hitler, I'm not sure but you know very bad people have thought about getting us closer to paradise on earth in ways that were wrong. But I think we have that it's in us. Because we live on this planet. We, we want, we have an intuition that can be very unconscious that can be very buried and all the norms that that we are, you know, a call to his past but I think we all are saying society doesn't want us to be philosophers in a way. I think so yeah and the way it's like you could even see the entire industry of entertainment or but also corporate work as a huge system that is targeted at preventing us from thinking.   And, and we play that game so we might end up being neutralized to. It's not true to. In fact, I thought long ago about what might be on my headstone and I started realizing it would be the number of journal articles that I wrote and the amount of National Institute of Health grant money that I brought in and my frequent flyer miles and I started realizing they're just asking myself the simple question is that what I want on my headstone is that what I want my legacy to be and I realized no I've got it I want to be doing much, much more than that and breaking out of that academic comfort zone. Which, which it does it's very, very comfortable being an academic and your students are, you know, so nice to you all the time of course, but breaking out of that and getting into the real world and trying to make change is a messy business and it can be sometimes painful, but it's so important to, I think, being for me, I think I believe I become a better professor, if I get out into the real world, and I try to help people in the real world, not just teach a course. I think I've become a better teacher, but anyway that's an aside. I love the fact that this really struck me that society really is against philosophy in a way society would much rather have you fall into certain tracks of clones of other people.  I want to question all of those things to go back and say, Well, we're here on this planet for this brief period of time. What are we doing? Are we just going to simply be automaton based on what society has dictated for us. So, yeah, society, philosophy is kind of a fight, isn't it? It's kind of a fight against that. I'm talking about how fragile and ephemeral life is. I mean, I have a daughter myself and I think your experience as you tell in your books is, correct me if I'm wrong, both one of a miracle and then, of course, on a fate, right? So your daughter was given the chance to live much more than you expected when she was born. She has this hard problem. But then at the same time, her life ended in her youth. And so that's not how people live, right? People live as if they were eternal. But you sort of were at the core of that mystery of being human, that in fact, we are floating above nothingness, right? And how does that connect to you insisting so much on people having a sense of purpose? Yeah, what a wonderful question. Yeah, just to put this into context, my daughter was born healthy. She caught a chickenpox virus when I was on sabbatical in Maastricht in the Netherlands. And she, this chickenpox virus attacked her heart. It destroyed her heart. And her only hope was to get a heart transplant. And she became one of the early children to get a heart transplant as a child. And we didn't know, you know, we knew her chance actually of becoming six years old was about 25%. And she made it through that. She needed another heart when she was 10, nine, I'm sorry. And then she died very suddenly and unexpectedly at the age of 19. I think you put it into such beautiful perspective that it was almost thrust on me, the fact that we are here briefly on this planet, whereas most people can kind of float through that. They don't have to think about those things. We were forced into thinking about it. So I don't claim any genius or any special intelligence in this. This is simply my environment being forced on me that changed how I think about things. And I started thinking about the existential nature of our, you know, of living. And I started thinking with her especially, well, we're going to make every day a special day for her. Not like we're going to go to Disney World every day and meet actors and things like that.  And we're going, and that kind of transferred to all of us. We started living bigger lives ourselves. It's almost like my life moved from black and white into Technicolor. And I started really enjoying my life more. I started moving outside of academia in the comfort zone of academia and started doing a lot more work outside of academics. And thoroughly enjoyed that. And so I started living a bigger, richer life.  And I was even under the illusion to some extent that there might have been some sort of force that was helping. And I'm not, I'm very agnostic religiously by the way, but I wondered whether there's some type of force that was keeping her going for some bigger reason that she had. And when she died, a lot of that kind of exploded or imploded. And so I did find myself in a kayak two miles out on Lake Michigan, which is a very large lake by the way, if you haven't been there, you can't see the other side, it's 87 miles. And, you know, I was thinking of continuing on to the other side of the lake, which of course I would have died. But I had, I don't know how else to say this, an epiphany experience when I was two miles out. And it related to, it was almost like there was a crossroads right there that came up that said, you can go this way and you'll die. And I was, this is just two months after she had died. And I had, I was so numb, I had no feeling whatsoever about feeling fear of dying. I thought this may be a really, really smart thing to do to die or to live. But I realized that if I was going to live, I'd really have to change my life rather significantly because I was starting to drink a lot of alcohol. I was watching television all the time as watching whatever Kim Kardashian was on, which I think is a sure sign you're getting ready to die. You know, it's just like my life was exploded and I didn't care about anything. There was something about that very experience where I thought, wait, I have agency here. I actually have, I can decide whether to die or not. And society has told us we should never even think about dying.  And that very agency that I started feeling kind of helped me.  So I went back and I started thinking more about that. I started reading philosophy actually. I started reading Seneca and Seneca's letter to, it's a famous letter, his letter to Marsha. Marsha, and this by the way is 2000 years old, but Marsha had lost her 16 year old son. And Seneca was kind of the, you know, the counselor, almost the newspaper counselor of her advisor to people. We have somebody in the US named Anne Landers and Anne Landers, you know, you'd write Anne Landers and go, oh, my husband left me or whatever. And Anne Landers would write something consoling what to do. So Seneca, I believe was kind of like that. He wrote this letter and I read this letter and it, and it moved me so much and it helped me so much in thinking about the fact that we're here for this brief time and we should really make the most of it. And now I regard my daughter's life as a gift to me.  I can learn from that and learn how to live a bigger life and then teach, hopefully help other people live bigger lives. Right.  Hopefully. Yeah, that's, that's my intention. Yes. And I think we, I think it's a good conclusion, at least for this first conversation, it sounds like we might have more. I've very much enjoyed it by the way, Louise. Equally, and I anticipated this. Perhaps I'll finish because this is connected. You have this beautiful image of the fortress of the ego that we carry around our head like a castle. And I think it's interesting because as you were saying when you were desperate and looking at celebrities on television, etc. At the same time, you were feeling sorry for yourself. No, I think that that's the thing with the ego is that, in fact, when you have too much of it, you, you don't have enough of it at the same time. And I think what purpose brings is that by identifying to something that is higher than yourself, that you admire, it lifts you up. Right. You say you transcend. Exactly. And you say that you were in the middle of that lake. You, you, I heard it. You said that you heard as if the voice of your daughter saying get over it. Meaning over, above, right. And I think we can conclude on that is that those people might now wonder, okay, so how do I, how do I get purpose? I have a lot of people contact me. They want philosophical consultations to try to define their purpose. And I always have them reflect on what they admire. For Descartes, let's finish with a philosopher that I think everybody knows. Actually, I thought everybody knows, but I see with students that people are forgotten about. I think therefore I am right that the famous motor from, from Descartes. He had this essay on emotions and he says that the primordial, the core emotion of all is admiration. And I think that's very unheard, but I do agree with that. The sense of admiration is what elevates us to what may become one day a sense of purpose. You know, it's so funny you say that I've been so many people come to me and say, okay, I understand how you formed a purpose, but I don't want a horrible thing happening to me in order to find a purpose. I get that totally. So how do I purpose without something awful happening? I often will suggest to people, look at individuals who you would like to emulate or some of the values or characteristics of people you would like to emulate alive or dead. And I think that's related to this.  In fact, he said, we shouldn't imitate other people, but we should try to emulate certain characteristics of people who we admired a lot. Is that kind of what you're saying? Completely. And I think that there is this element of deep engagement in real admiration that does magic. I mean, something starts to happen that indeed goes well beyond the laws of matter. That is fascinating. Shall we pause here our conversation and perhaps go for an episode two in a few months? I really would enjoy that very much. It's rare for me to be able to talk to somebody who has the depth of philosophical knowledge you have. I work with a lot of scientists, and even people in our own philosophy department at the University of Michigan, there are some wonderful people there. But in terms of their focus on what you're doing, I don't see that. And so it's a real pleasure to get to meet you and know you talk to you a little more. And I hope that sometime we can even meet in a real cafe sometime and have coffee together. Exactly. And I mean, I really admire the insistence you put on sense of purpose to be transparent. The reason why I contact you and discovered you is that I came up with this last year. I was doing a study with people who have been living for many years with a spinal cord injury as tetraplegic. 95% of their body is paralyzed. And yet these people that I interviewed, they really developed a very high sense of the possible and they reinvented themselves. And I was trying to understand why and if there were some element of philosophical health that helped them. And in doing so, I devised this method of dialogue, which I use also in my consultations with which goes through six steps. Start with the bodily sense. And then I moved to the sense of self asking you what do you feel about your heart you sense yourself. Then the sense of belonging. Then comes the sense of the possible, which for me it's very core to definition of health. We were talking about medicine. Well, if you have a high sense of the possible, you're healthy, even if you're paralyzed physically. And then after the sense of the possible, I ask about we talk about the sense of purpose. And then lastly, the philosophical sense. So I think we should even collaborate some some time more on this. I think there is a high likelihood that in through the idea of purpose, there can be a real bridge between the experimental sciences and the more qualitative approach that Very much. There's actually some research looking at purpose among people with spinal cord injuries. And I'd be happy to send some to you if you would like, but that's a fascinating area to me. I have another question too. As I think you might know, I have a app called purposeful. That's an application and within purposeful. I have a purpose cast that I do a podcast, not unlike this. And I'm wondering whether either I could interview you in the next one in that purpose cast or I could take this recording. And if it would be okay with you, we'd love to put it into purposeful because we have many thousands of people who listen to experts in this area and you're truly an expert. And I loved our conversation. That's great. And I'll put this on YouTube and I'll give you also the the sound if it's a podcast and of course you can reuse it. I think I'll stop the recording now thanking you again very much for this. And I think I'm going to continue reading also your more scientific papers because I think that there's really something that people should take also seriously researchers such that we move a little bit away from all the new wave. And every 10 years there's new wave of materialism right so now you're going to fix people with AI so every time we have to, you know, again to fight for for the soul of things. So thanks a lot. Thank you, Louise. Real pleasure.