Oral-History:Lennart Ljung
About Lennart Ljung
Lennart Ljung was born in 1946 in Malmö, Sweden. He attended Lund University and earned a B.A. in Russian Language and Mathematics in 1967, a M.S. in Engineering Physics in 1970, and a Ph.D. in Automatic Control in 1974. Ljung served on the academic staff at the Lund Institute of Technology from 1968 until 1976 when he became Professor of Automatic Control at Linköping University in Sweden. He served as the head of the Control division and Chairman of the Department of Electrical Engineering at Linköping Institute of Technology and Director of the NUTEK/VINNOVA Competence Center ISIS, and is currently Director of the Strategic Research Center MOVIII. Ljung’s research focuses on model building, system identification and adaptation, resulting in numerous degrees and awards, several publications and articles, and extensive contributions to the field of Control Theory.
In this interview, Ljung outlines his research in Control Theory and his contributions to the field. He discusses his career influences, his research methods, and his experiences. He reflects on the challenges and achievements throughout his career, such as the creation of the Linköping group, his development of the MATLAB system identification toolbox, and the publishing of his book System Identification: Theory for the User, as well as provides advice for young people interested in control theory.
About the Interview
LENART LJUNG: An Interview conducted by Graham Goodwin for the IEEE History Center, 25 March 2014.
Interview #649 for the IEEE History Center, the Institute of Electrical and Electronic Engineers, Inc.
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Lennart Ljung, an oral history conducted in 2014 by Graham Goodwin, IEEE History Center, Piscataway, NJ, USA.
Interview
INTERVIEWEE: Lennart Ljung
INTERVIEWER: Graham Goodwin
DATE: 25 March 2014
PLACE: Newcastle, Australia
Video
Introduction
Goodwin:
My name is Graham Goodwin and today I am talking to Lennart Ljung who is professor in Linköping in Sweden. So good morning Lennart.
Ljung:
Good morning, Graham. It is very nice to be in your office here sitting and have a nice chat with you.
Early Life and Education
Goodwin:
Indeed. I am looking forward to learning more about you. So I am going to just ask you a number of questions. And I am looking forward to hearing what you say about yourself and your views on the progress of our discipline. So maybe we should just start with some background. Lennart, where were you brought up and where did you begin your university studies?
Ljung:
Yes. I was born and raised in Malmö which is the third largest city in Sweden. It is very close to one of the classical university cities in Sweden, Lund University. Which is about 15 minutes away so it was very natural for me to go to Lund for my university studies. So that is where I start my studies...
Goodwin:
Okay. And why did you choose to do engineering?
Ljung:
Well, actually I did not choose to be an engineer. I couldn’t decide. I wasn’t sure whether I should be a mathematician and study mathematics at the university or I should be an engineer. So I did both to begin with. So I entered the school of engineering in Lund. At the same time I studied mathematics on the university level and followed that for some time for three semesters. And that is the level you get to at the university studies. At the end of the third semester at the final exam, I did not solve the last problem. I did pass very well, but I didn’t solve the last problem and that was a sign to me I am not going to be a mathematician. Mathematics is very one-dimensional and if you would give a contribution to that you have to be at the very top. So I decided to join engineering instead it is more broad, more safe.
Goodwin:
Oh, okay. That is interesting. So the experience issue --to say an undergraduate in Sweden, do you think they differ from the experiences of the students today?
Ljung:
Yes. I think we were less demanding. We had no text books in many studies. The topics were a bit defined by the lectures. And we had not very many electives. Not many choices. I choose programming as my only elective topic and imagine: in the end of 1960s, you could be an engineer without taking one single course in programming but I did one.
Goodwin:
That is amazing.
Ljung:
Fortran.
Goodwin:
Fortran. Yes. Indeed. Okay so when you finished your undergraduate program you went straight on to do a PhD. Is that correct?
Ljung:
Yes. I stayed on at Lund and joined the control department under Karl Åström’s leadership.
Goodwin:
All right. And do you want to say some things about the supervisor?
Ljung:
Yes. Already in 1970 as this was, Karl Åström was a legend at Lund University. So this group was very well organized and was like a company. As graduate students we had specific tasks. We had a well-kept Fortran program database that helped us in our PhD studies. It was a very energetic and very creative environment so I had a lot of fun there and I did a lot of things. Karl used to give me some papers to read: Read that - that is good for you or and he gave me the advice to study seriously the book by Kai Lai Chung on advanced probability. It was excellent advice it turned out later on. So that is how I was brought up into science. At the same time I could say if I count the number of hours that I sat down with Karl Åström in a formal supervision situation, they were not many over the four years, but this influence came another way, through ideas, what to read, suggestions and all that.
Goodwin:
All right. That is interesting. And what on earth persuaded you to work in the control area in the first place?
Ljung:
When I couldn’t be a mathematician, I decided to be a physicist so I did my Master thesis in physics, solid state physics, on alloys, spectra. And it didn’t catch on I didn’t really like physics so much after that. So this was 1970 and you know that there was a lot of talk about cybernetics at that time. And also although we did not all understand the full impact of computers we felt that somehow programming, will probably be important in the future so in that sense control, automatic control was a bit more futuristic than physics. So that is why I went into control.
Goodwin:
Really? Well, it is an interesting transition. And so you started doing control. What things excited you as you did your PhD? What are the things that really interested you as you did it?
Ljung:
What I think is, what I think still attracts the graduate students is this mixture of all, nice mathematics, interesting mathematics and some practical applicability around the corner so that was exciting stuff.
Goodwin:
Yes.
Ljung:
And Karl handed me a couple of books and papers by Yakov Tsypkin who was very well-known at that time for his work on learning systems as it was called. But actually it was another name for stochastic approximation it turned out. Very exciting things. You could learn things by just observing how they behaved. And as a result of that I went on a, I’d said, pre-Doc to Moscow to spend a half year with Tsypkin in his famous lab in the Institute of Control Sciences. And that was a very exciting time. Six months. Maybe mostly from a cultural point of view. You know in 1972 was at the height of the Brezjnev stagnation in Russia or Soviet Union and that was an interesting time to spend there. And of course scientifically I met all of the great well-known leaders at the institute and not the least Tsypkin himself was an excellent person to know, to work with.
Goodwin:
Were there differences between the ways that the Russians or the Soviet block researchers were undertaking research and what you were familiar with in Sweden?
Ljung:
Yes. The Institute of Control Sciences was a huge institute. 2000 people employed there mostly for life; they got their degree from a Moscow Institute. You had to be born in Moscow to live in Moscow. So they came from a Moscow institute and spent their whole life at this Control institute. Many were very good. Many were not so good but they still had their life time position there. So it was not the same kind of creativity and energetic feeling as I had in Lund as a PhD student. So very different in that sense.
Goodwin:
Interesting. So then you completed your PhD back in Lund.
Ljung:
Yes. 1974.
Post-Doc at Stanford
Goodwin:
In 1974. Okay. And then where did you go immediately after you completed your PhD?
Ljung:
More or less directly after I completed my PhD I went as a Post Doc at Stanford to spend some time, a year with Tom Kailath at ISL at Stanford. And that was also a very energetic and good environment to work in. Tom Kailath had a large staff of PhD students working for him and many great people I met at that time were exciting. Of course, Stanford is a fantastic place for a Swede anyway with the climate and the closeness to beaches and mountains and what have you.
Goodwin:
Yes. An intersection of two aspects--scientific excitement and worldly excitement.
Ljung:
So the years that I talked about from 1970 to 1975 were very formative for me. First of all, our two sons were born both in that period. I met Karl Åström, I met Yakov Tsypkin, I met Tom Kailath in the span of these five years. Three excellent mentors that have meant a lot to me in my scientific development clearly. All of them know mathematics very well. They know that mathematics is an important tool to work with in Control but they also know Control is not about mathematics primarily. So I got this feeling of what is important and what is good in control from three different people. And basically the same kind of view.
Goodwin:
It is interesting how these experiences shaped the rest of your life in terms of your own approach
Ljung:
Yes.
Teaching at Linköping
Goodwin:
So you completed this period at Stanford. And then what happened then? Did you take a permanent job somewhere? What was next?
Ljung:
Well, I have to tell you about the situation in Sweden in 1974-75. At that time a professor was a head of department. But there was only one professor per subject in a university in Sweden. So in 1974, there were four professors in Control in Sweden. In Stockholm, Gothenburg, Lund and Linköping. It so happened that the professor in Linköping, Jorma Rissanen, who was also my opponent by the way.
Goodwin:
Yes.
Ljung:
He decided to resign and move back to his position at IBM in San Jose. So somehow suddenly there was a position available. Otherwise I would have to wait for somebody to die or to retire to have an opportunity. So I applied for this position in 1975, actually early 75. And you know in these ancient times you had a committee to sort out who will be employed. They didn’t just look up your citation record.
Goodwin:
As we might use Scopus or Google today.
Ljung:
Yes. Not just Google citations. They actually read everything you had written. Amazing. So I was very lucky, since because of that I got this position in Linköping. So in 1976, when I was 29 years old, I made my first and final career step at the same time.
Goodwin:
That’s interesting!
Ljung:
And I have remained there ever since, working as a professor in Linköping .
Goodwin:
But doing different roles I guess running different organizations?
Ljung:
Yes. In a sense. I mean I have always been the head of the Control division in Linköping and that involved a lot of work to begin with to build up the undergraduate program and the graduate program. We could talk about that in more detail a little bit later perhaps.
I created some broader organizations to cooperate with other groups at the University. But for the first 15 years I basically was just a professor in a group. The group grew from one person to 25 around 1990 and, at the present time we have about 50 in the group.
Sabbaticals and Research Collaborations
Goodwin:
Yes. So you - - it is an amazing development from those beginnings. They obviously chose well. So you have worked in Linköping for a very long time. Have you visited other places for sabbaticals or for longer periods of leave that you would like to talk about.
Ljung:
Sure. I mean - - I liked Stanford very much so I returned to Stanford for a sabbatical in ’80, ’81 and then I went to MIT in ’85, ’86 on another sabbatical. And then as you know I also like Newcastle, Australia very much. I think this is my fifth kind of mini sabbatical here this time.
Goodwin:
That is also amazing. Your visits are always important for us.
Ljung:
Yes, I like it very much. Yes. So I have been to many places on different parts of my career But I have only have had one real job all the time, as a professor in Linköping.
Goodwin:
Okay. So during these leave periods and with the many opportunities you had, what about special collaborators, people who have influenced your work and who you enjoyed working with?
Ljung:
Yes. Of course I have had a large number of students. I worked a lot with my graduate students but if I looked into my publication lists I may have had more the 100 coauthors but I tend to not directly always co-publish with my students. Only when I have done say above and beyond my normal supervising duty, I choose to be co-author of the work they publish. But I have had other co-workers: I can point to Torsten Söderström for example who was a colleague of mine when I was a graduate student in Lund. We together did a lot of work in the early ‘70s on closed loop identification and on recursive identification. And that culminated in 1983 when we published our book on Recursive Identification... Since then I remain a good friend of Torsten and we keep in contact and I ask him whenever I have technical problems. I ask him for advice but we haven’t written anything since 1983.
Goodwin:
It is interesting that you put all of that intense work together into a book and you still talk to each other.
Ljung:
Yes.
Research Reflections
Goodwin:
That’s good. And so it must be a very special relationship. Do you see research as just a short-term or a long-term adventure? Where do you place it on the spectrum?
Ljung:
Well, things take time generally speaking. I think that is important to keep this in mind. And I am very worried actually right now with the current frenzy of bibliometrics where you give the impression that science and research is about writing a paper, count how many times it is cited in a short time span and that is what research is about. It is not! Research is about inventing and discovering new theories, new methodologies and having other people use and reuse those ideas, hopefully for a long time. And that is what research is about. Things take time!.
Goodwin:
I totally agree. Also do you sometimes return to things later and re-evaluate? In this case, the process of research can take many years where a topic is revisited and refined until finally you feel satisfied.
Ljung:
Exactly. Actually I can give an analogy, I don’t play tennis but I took tennis lessons at Stanford a couple of times and I learned that the Follow Through is a very important concept in tennis. That means basically that you should continue the racquet swing even after the ball has been hit and it is on its way. So that is follow through and I think that applies to many things in addition to tennis especially research. So think of research in the context of “follow through”. I often think of this analogy.
Control Systems Research and Applications
Goodwin:
Sounds good. Okay. So before you mentioned the thing that was exciting about control was the combination of theory and relevance. Can I just spend a couple of minutes talking about applications that you have worked on.
Ljung:
Sure.
Goodwin:
Are there applications or approaches to real problems that you would like to talk about to give some context to the applied side of your work?
Ljung:
During my first 15 years in Linköping I was basically just involved in toy applications. Like a Master’s thesis project of simple character often involving just applying identification techniques to some processes in industry in a relatively straightforward manner – Often useful, but straightforward. In the beginning of the ‘90s I thought that we should do a little bit more than that. Remember in the ‘90s, it was also a time, all over the world, when you created big and broad centres with our groups. So I had the idea that Control people should team up more with computer scientists, because we have something in common including the basic views on many things and we know that, in many universities around the world, there is a tension between EE and Computer Science. So I wanted to bridge that in a sense, so based on that I put together a center in 1995 that comprised groups from EE, mostly signals and systems and groups from Computer Science. And a dozen of big or semi-big companies in Sweden. And we started on a bigger project, a bigger center. And there have been a number of centers after our initial beginning in 1995. Still continuing, two of them are still running right now with five years of funding remaining. So that has been very, very useful and in that context I became much more involved in more serious applications.
Goodwin:
Is there anything you would like to tell us about how you approach these large-scale serious applications? Is there something that other people could benefit from in the way you do this? I mean from managerial or the way the problem is approached?
Ljung:
Yes, I think it is a matter of having an open mind to other groups and not imposing your views on what is science to them because they have another view. You know a model is one thing for us. It means a completely different thing for a Computer Scientist. So you have to really be humble and accept that and let things take time, also here. And do something together. A good thing is really to solve a practical problem together. Each group throws in their own tools and you show to each other that it all works together. I think that is the key to make it work.
Goodwin:
Very interesting. So could you take a minute to just mention some of the large number of companies that you worked with. Would you like to give us an example of one of those and tell us what it led to?
Ljung:
Yes. One good example is when we started our first center ISIS, back in 1995. We had the SAAB Aircraft company as one of our partners and they wanted to have help with their navigation systems. They of course used inertial navigation and the GPS systems and they wanted to have another leg to stand on.
Goodwin:
Yes.
Ljung:
And then they knew that they were measuring the altitude with the altitude meter from the airplane to the ground. At the same time they had maps of the ground available. Height maps.
Goodwin:
Yes.
Ljung:
So that by matching the altitude to the ground map, you could decide where you are. So as a compliment you would try to move around in an area and see how does the height profile change and compare with what is possible to experience on your map.
Goodwin:
Yes.
Ljung:
Globally. That was terrain navigation. well, navigation through terrain measurements.
Goodwin:
Yes.
Ljung:
And we solved it by attacking it by a simplistic probabilistic approach. So we were gridding up the ground into regions. And then computing the posterior probability of each point.
Goodwin:
Uh huh.
Ljung:
You then had an idea where you were located.
Goodwin:
Right.
Ljung:
As you made the grid fine and as you made it adaptive we came very close to what became known as particle filtering. Now particle filtering was not certainly not invented by us. But we were at the very forefront of when it came. So we had a head start. In particular my colleague, Fredrik Gustafsson, had a head start in particle filtering. He wrote some important contributions both on the theory and the application of “particle filtering” to navigation early on. And then that transitioned to more of a serious thing on Sensor Fusion, on SLAM etc.
Goodwin:
Yes.
Ljung:
And Autonomy. How can we autonomously decide where we are. So that became a big area for our Control group. Most of it led by Fredrik Gustafsson. So that was spin-off from a real application into something that was scientifically valid and compared very well to what was happening in science at the same time.
Goodwin:
I think that is a great story. It is fascinating to see the origins in a real world problem of a question to be solved and then how that thought process led alternately to tools that have general applicability today.
Ljung:
Exactly, I think it is a very nice example of that
MATLAB toolbox
Goodwin:
Yes. Okay. Thank you. All right. Now in terms of practical things your work has had huge influence beyond your immediate vicinity through your MATLAB toolbox. Do you want to talk about that for a minute? How that happened and how you view that piece of your life ?
Ljung:
It is a good example of how timing and luck play a big role in your life.
Goodwin:
Yes.
Ljung:
And that was when I was in sabbatical at MIT. ’85 - ’86 that I bought MATLAB to MIT in the fall of ’85. Actually I bought MATLAB to LIDS at MIT. So then I used MATLAB when I taught my graduate course on Identification in the Spring of ’86 by showing some code snippets in MATLAB how these ideas can be used in practice to my course participants. Then Jack Little, who is the owner of MathWorks called me up since he had heard about that. And he said “Why don’t you write a toolbox on identification for MATLAB.” I said, no, no. I can’t do that. I am not a sufficiently good programmer. But somehow I was persuaded and started to write this thing. After a month I had version 1.0 finished. But later on a lot more work was put into it. For the first 20 years I wrote every code line myself in the product that was sold. Nowadays for the last 10 years it is more of a teamwork where Mathworks has more direct influence of the final product, design of code. But I am heavily involved, I work like almost every day with issues in this tool box. And I don’t really view this as part of my scientific work, it is a matter of Follow Through actually.
Goodwin:
All right. So in what sense is this a follow through? Can you explain what you mean by that?
Ljung:
Yes. If you write a paper, maybe somebody will read it. You never know.
Goodwin:
Right.
Ljung:
If you write a textbook, well if it is adopted, you find you educate some students in your views.
Goodwin:
Yes.
Ljung:
But if you write the code...
Goodwin:
Yes.
Ljung:
...People use your ideas without knowing it, so it is a final, validation I think for this type of work. It is the final way to make the theories used in practice. And this toolbox has a lot of industrial users.
Goodwin:
Indeed. Absolutely true. Yes. And do industrial users give you feedback and say how it went and what things they like and so on. Is this part of the joy of having a toolbox?
Ljung:
Oh, yes. Oh, yes. I frequently get mail, in fact too many mails from people who have questions about this and that. Related to the toolbox syntax partly, but mostly related to the application to the real world of the identification problem. How could we use these properties?... how should we approach this?... what ideas can we use?... This has been very good to have kind of direct contact with a lot of people who I would never have met otherwise.
Career Influences
Goodwin:
Yes. No. That’s interesting. Okay. So let’s move away from these practical things and move back to people. Are there people you would like to talk about just briefly who you think have had the most influence on the way you think about problems in your career?
Ljung:
Yes. There is no doubt, I talked about my three mentors from early 1970s. There is no doubt that Karl Åström is the person who had most influence on my scientific career. He has always been a role model for me in basic things, how we run the department, how you approach research, how you relate to applications and how you disseminate what you have done.
Goodwin:
Yes.
Ljung:
So that had made the greatest influence, for sure.
Career Highlights
Goodwin:
Yes. That is interesting. So Karl is the person with the greatest influence. What about some highlights in your career. Are there things that really stand out, some exciting moments that you would like to tell us about?
Ljung:
Yes. If look back to what I have done... I can point to three things I am kind of proud of.
Goodwin:
Okay.
Ljung:
All right. One is I created this group in Linköping with now 50 people. We have graduated 75 PhD students over the years and as you know, your old PhD students are like your children. You follow them all the way through life and you feel joy when things are good for them. That is I think one of the best feelings you could have about what you have done for research.
Goodwin:
Yes.
Ljung:
The second thing I could point to is my book System Identification: Theory for the User, which somehow to my surprise and delight has been read by many more people than I thought to begin with. And the third item I could point to is, of course, the System Identification Toolbox which is the way we have put forward identification to many uses around the world in different areas, both in industry and in academia.
Career Challenges and Reflection
Goodwin:
Yes. I think everybody would agree this really great achievement and must be exciting for you. Can I ask you about challenges Lennart? Were there any challenges that you are prepared to tell us about?
Ljung:
Well, I think the biggest challenge I have had was when I started the bigger centres in the middle of the 90s to really make the computer scientists and AI people bring in the control picture and that required a lot of work. I wouldn’t say that I succeeded so well. I mean there is still much more things to be done. We have not really penetrated what can be done with our joint tools scientifically. But we have created, at least right now, several groups within our department and in cross couplings with other departments where we are actively using a broad view of automation, autonomy and control, based on the experience that we have had in this kind of development in the different centers. So this challenge only partly succeeded but I think it will turn out in the long run that it means something, that will mean something.
Goodwin:
All right. What about anecdotes of things you would like to say that maybe humorous or interesting that you feel would be interesting?
Ljung:
Yes. I can tell a story about mathematics, which you are partly involved in yourself.
Goodwin:
Okay.
Ljung:
When I was a graduate student I studied convergence of the Least Squares method. And I was pretty convinced that it will always converge if the smallest eigenvalue of the regression matrix tends to infinity. And I had many proofs of that. But alas, I found errors in all of them. So it delayed my thesis certainly for half a year at least. I wanted to have that theorem in my thesis because, as you realize, that would also have solved the convergence problem for the Self-tuning regulator.
Goodwin:
Yes.
Ljung:
Because that is essentially a least squares problem.
Goodwin:
Yes.
Ljung:
And finally I gave up. In my thesis I just published a minor result where I confined the model set to be only a finite number of models.
Goodwin:
All right.
Ljung:
And I was still convinced afterwards that I must be able to prove it. And many other people tried. I was reviewing maybe ten different papers. And I was an expert in finding the errors in the proofs because I had made so many myself.
Do you remember when I came to Newcastle in 1978 I talked about these problems in one of my seminars.
Goodwin:
Indeed.
Ljung:
Maybe it caught your attention because you proved something a few years later when you were on sabbatical at Harvard.
Goodwin:
Yes.
Ljung:
For the convergence of adative regulators.
Goodwin:
Yes.
Ljung:
But you realized that somehow you must link the rate of increase of the different eigenvalues to be able to prove the convergence.
Goodwin:
Yes.
Ljung:
And a few years even later TS Lai showed that my conjecture was wrong.
Goodwin:
Right!
Ljung:
You can give examples where the smallest eigenvalue tends to infinity but you still don’t have convergence and consistency. What is required is a link between how the fastest eigenvalue relates to the slowest eigenvalue value. I think it is this log thing or iterated log. So my conjecture was wrong. The point of my story is that it shows the strength of mathematics. If you can’t prove something even if you are convinced it is right. Maybe it is not right.
Goodwin:
Yes. I think it also shows your earlier point about research being a long-term adventure.
Ljung:
Yes.
Goodwin:
Because that went through many cycles before the question was ultimately resolved.
Ljung:
Exactly.
Evolution of Control Theory
Goodwin:
Yes. Your description is a very nice example of that. Okay. So you know we both still work in the control area, do you have any comments about the current status of Control and what is exciting and what is important?
Ljung:
Well, it is clear to many of us that we are now in the transition from automation to autonomy. And that requires also a broad view of what tools you need to go from automation to autonomy and I would advocate that we should more clearly embrace what the AI, Artificial Intelligence, has to offer in that respect. And I am, as I said, still involved in centers that have autonomy, autonomous vehicles for example as a big research area. And I am excited about what can be done in that. And I will be pleased to see how much the insights from Control will deliver for final solutions here. So that is one thing that I would like to follow. And another thing...
Goodwin:
Yes.
Ljung:
...Is that in my book on Identification I kind of view and describe a coherent structured view of system identification. Because the area was quite scattered in the beginning of the 70’s. Nowadays we have seen an onslaught of new techniques mostly from statistical learning theory from scarcity from convexity, say nuclear norms and what have you... atomic norms and so on, which right now look more like a new big bag of tricks for the area and we don’t really know where to use what and how, what are the properties. I would like to see what will happen when all these pieces fall together eventually in a big puzzle and see what is the picture of parameter estimation and system identification in that view with the new tools. What do they mean in the final analysis.
Goodwin:
Yes. I think this is a wonderful point and I remember very well how exciting it was to read your book on system identification because before your book the area was like a smorgasbord, but if one read your paper it all became somehow clear that all these pieces fitted together and there was one way to think about the problem. And all these things were somehow off shoots of a central thought so I think I resonate with your idea that doing that in some of the emerging fields now is would be exciting.
Ljung:
Yes. I am trying and, I hope I will live long enough to see what will happen with that.
Advice for Young People
Goodwin:
I am sure you will. Okay. So we are getting towards the end of our discussion, Lennart, if that is all right. I wondered if we could perhaps end with thinking about the next generation and the young people. Is there any advice that you would like to give them or words of wisdom in conclusion?
Ljung:
Yes. I would like to say that we should remember that we still have an exciting future in Control. I think the future is linked to a broader view of what other disciplines can bring into our field and, as I said before, autonomy will be around the corner. Very exciting to work on in coming years for a new generation. Also, remember "Things Take Time" and "Follow Through".
Goodwin:
Yes. Things take time and follow through. Yes. So Lennart, it was great to talk to you today. I learned a lot about you even though I have known you for many years.
Ljung:
For how many. 30 something years? We met first time in 1974, no 1976 on your way to Tbilisi.
Goodwin:
Indeed, indeed. That is right. So it has been a long journey for both of us but the talk with you today has been great. Thank you for all your time and effort in talking to me and sharing it with other people. Thank you.
Ljung:
Thank you Graham. Very nice. Thank you.
