“Yellow Peril, Z-Mouse and Spray Can” – Rudolf Seising

Rudolph Seising:
Thank you very much for this kind introduction, thank you very much for the invitation and I’m sure my English is as bad as your German. If you don’t hear me it’s because of my cold in this room, if you don’t understand me it’s because of the language. My title you’ll see here from the yellow para to the Mouse and spray can, Wiener Cybernetics and that is Fuzzy Set Theory.

What I want to do today is show you a link from Cybernetics or from Vena’s work to Lotfi Zadeh’s [inaudible 00:00:29] Fuzzy Set Theory and I think people from NAFIPS, of course, know that story already, but people who are not in NAFIPS maybe it’s something new for you. Is this working? It’s switched on but it is not working.

Speaker 2:
Space bar, [inaudible 00:00:51].

Okay, I want to start with the book maybe you don’t know so much. It’s a book before Wiener’s Cybernetics, is a book what was called The Yellow Peril, because it was yellow and peril because most of the engineers didn’t understand what was written in because it was so much mathematics.

It was written during the war and you see what Norbert Wiener did in this book it was much more mathematically as in cybernetics but he did the same things in a higher level maybe, you can say that. He wanted to unify communication engineering with the field of statistical time series. He wanted to do that in theory and practice and the relevant method for this purpose included filtering, in addition to extrapolation and prediction.

Moreover he fused his methods into what is a quotation, into a common technique which in the opinion of the author is more effective than other existing technique alone. Predicting a time series he said, “Or message could not certainly not simply consist of its constant continuation. This would instead be a matter of statistical prediction, estimating the continuation of the time series or communication. In most probably future pattern while minimizing random error as Vena’s described the program in greater detail.”

Here’s the quotation, “We have a message which is a time series and a noise which is a time series also, if we seek that which we know concerning the message which is not bound to a specific origin in time. We shall see that such information will generally be of a statistical nature. This will likewise be true of our information of the same sort concerning the noise alone, or the noise and the message jointly.” The quotation goes on, “While this statistical information will in fact never be complete as our information does not run indefinitely far back into the past. It is a legitimate simplification of the facts to assume that the available information runs back much further into the past than we are called upon to predict the future.”

“The usual electrical wave filter attempts to reproduce a message in its purity when the input is the sum of a message and a noise.” What he did now is he said, “Okay, this is mathematical stuff and I have to go to a colleague of mine, and this colleague was Ernst Guillemin or Ernie Guillemin.” He wrote that he have to go to this book, Guillemin said, and here you see the quotations, “A problem of realization takes one into the theory of [inaudible 00:03:53] networks as developed by Guillemin and others.”

First of all who was Ernie Guillemin? Here’s a biography of this man, he was born you see in Wisconsin, he studied electrical engineering in medicine and then he became teaching assistant. Then he came to Munich and that’s the reason I was familiar with this person, he was a PhD student of Reinhold Sommerfeldt who was one of the most famous quantum mechanical researchers in that time in Munich. He wrote his PhD thesis in German, then he returned to the MIT, then he has a career as a professor in electrical engineering.

You will see the dates of his professorships and what he did then he wrote a lot of books and he was very famous as a teacher in electrical engineering. Here you see the books he wrote and you see a photograph, and yesterday, in the photo show I saw a picture of Ernie Guillemin. I would be very glad to get this photograph is anyone has a relation for that please tell me.

What is interesting, Ernst Guillemin wrote the first book on communication networks. Volume One and Two in the 30’s already, it’s the first book with that title, and you see other books and one interesting book also, is in 1953 Introductory Circuit Theory. I will give you a quotation of this book later. First of all, what was communication theory in that time, of course, it was not internet, it was not world wide web. Communications here in that time was telegraphy and telephony and Ernst Guillemin did a lot of research work, of course, mathematical research work as people who have been mentioned yesterday to.

You see Karl Ferdinand [Braun 00:05:38] is a German researcher and Kempel was mentioned yesterday already, and William [Cower 00:05:45] who was a German one and he came to the United States. He had a relation with the stuff of Kempel. What you see here … Maybe that is working, yeah. What you see here is these electrical filters mentioned already by Vena, and you see what is a filter doing. A filter is doing, is blocking frequencies and some frequencies are going through and you see different forms of these filters, they are blocking these frequencies or these frequencies and the other frequencies are going through.

You see there is a different between theory and practice. What you see here is what the filter is doing, and here you see what he should do in theory, so there’s the difference. This difference is very interesting and I want to quote you something from the book of Ernst Guillemin, Introductory Circuitry, it is from the preface of this book and it’s some sentences, “One final point, the teaching of this subject I regard it as important to remind the student frequency that network theory has a dual character. It is a Dr Jekyll and Mr Hyde sort of thing, it is two faced if you please, there are two aspects to this subject.”

“The physical and the theoretical, the physical aspects are represented by Mr Hyde a smooth character who isn’t what he seems to be and can’t be trusted. The mathematical aspects are represented by Dr Jekyll, a dependable extremely precise individual who always responds according to established custom. Dr Jekyll is a network theory that we work with on paper, Mr Hyde involving only pure elements and only the ones specifically included. Mr Hyde is a network theory we need in the laboratory or in the field.”

“He is always hiding parasitic elements under his jacket and pulling them out to spoil our fun at the wrong time. We can learn all about Dr Jekyll’s orderly habits in a reasonable period, but Mr Hyde will continue to fool and confound us until the end of time. In order to be able to tackle him at all you must first become well acquainted with Dr Jekyll and his orderly ways. This book is almost wholly concerned the letter, I’m content to leave Mr Hyde to the boys of the laboratory. “

This is the end of this introduction of this book and you see what he did. He said, “Okay, there’s a lot of stuff in the laboratory but I, Ernst Guillemin, I am working in mathematical electrical engineering. Here is what a student of him wrote when I interviewed him, and this student, of course, is the founder of the Fuzzy Set. He said to me, “Everything was idealized, resistors, inductors, they all were perfect elements. For even at that point I had some discussions with Guillemin.” I said, “This is unrealistic, the real world is not like that. I mean resistors are not pure resistors, capacitors are not pure capacitors [insofar 00:08:53].”

I said, “I told him that I think that at some point in the future circuits will be designed and analyzed using computers even when I was a student at MIT.” He summarized in his interview, he said, “Guillemin was happy with that world. He constructed the world by himself, it was a perfect world, everything was perfect in that world. He was happy and so never considered noise, he never considered non linearity, he never considered imprecation. He never considered those things so it was an idealized world, a world he was happy.”

That was a student of Guillemin and, of course a student of Vena too, and this was Lotfi Zadeh, and here is the biography of Lotfi Zadeh, you’ll see he was born Baku in Azerbaijan, he is because he’s still alive, he’s 93 now. He studied electrical engineering in Tehran, then he worked with the US army forces in Iran. He immigrated to the US in 1944, he studied with Ernst Guillemin at the MIT and then he wrote his Master’s thesis with Sir Robert Fano who was a student of Guillemin in that time.

Then he changed, and in my interview he said, to that time, “I came to the United States in 1944 to pursue graduate studies in electrical engineering at MIT. At that time with the end of the war not far away MIT did not have many graduate students, just the same it was an exciting place towering as a center of instruction and research among all other institutions of higher learning in science and technology. Lectures and writings by Vena, Guillemin, McCulloch, Pitts and others opened a window to the world of communications control, computers, and cybernetics. The cold winds of the cold war were beginning to blow but the future of science and technology looked right and full of promise.”

Then I said already, he changed, he changed to Columbia University and here’s the letter of Guillemin who said to the Dean of Columbia University at that time, to electrical engineering in Columbia University, that he’s very sorry that Lotfi Zadeh will change the Universities. He went to the Columbia University, this is a picture of Lotfi Zadeh with, maybe they are FBI people, maybe they are students I don’t know. You see, I have no idea which year it was, it’s a gift of Lotfi Zadeh to me, but I don’t know the date of this photograph. He started research at Columbia, he wrote some papers, he wrote the paper in the Journal Electronics, here you’ll see what is the topic, More Hardly Law, so it is in the beginning of communication engineering, communication science and I don’t want to go into details. I will give you the second slide of his biography.

He wrote his Master of Science, I said already at Columbia University, he wrote his PhD thesis, his supervisor was John R Ragazzini, you see frequency and annul of this variable networks. It’s the Vena stuff still, and the Guillemin stuff, and then he wrote in 1950 a paper, An Extension of Vena Theory of Prediction, together with Ragazzini is written in brackets because he wrote, of course, the paper and the supervisor was the second author. In 1952 he changed to information theory and system theory, I will go to some details later. Then he changed in 1959 to the University of Berkeley and then he started with his work in Fuzzy Set Theory.

Somewhere is my clock, I don’t know the time. This is the memo of this paper I showed you already with Ragazzini, An Extension of Vena Theory of Prediction and this is what he said in this paper, “He generalized Vena theory in two ways, the first, the single component of a given time series was separated into two parts of which the first is a non random function in time which that can be represented as a polynomial. While the other part functions as a stationary and statistic random function represented by a given correlation function. In Vena theory by contrast, a non random portion of the signal occurred only when it consisted of a known function in time.”

That was the first, and the second was, “The response behavior of the prediction time, or the waiting function used to make the prediction should disappear outside of finite time interval. In Vena theory on the other hand this time interval was assumed to be infinitely long.” These were the two generalizations, I will not go into details here, I only want to show that this was a continuation of Vena’s work with Lotfi Zadeh in that time. Here is the paper, and here you see two authors Lotfi Zadeh and John R Ragazzini that appeared in 1950.

Of course he was influenced by Norbert Wiener, he told me he went to his lectures and, of course, he was influenced by his book Cybernetics, you all know what is the content of the book of cybernetics so I don’t have to read what is written here. Of course, he was also influenced by [Shannon 00:14:33], you see this book or paper, first it was a paper in the Journal on Mathematical Theory of Communication, and we already mentioned Warren Weaver today, was of course, the author of the introduction that was first in the Scientific American and then later as an introduction of the book that they published together.

What is interesting in this theory of Shannon, and what is interesting for the continuation of this history is that Shannon wrote in the introduction, this sentence, “The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Either exactly or approximately and we will see in Fuzzy Set Theory we do it approximately.” Here is what Lotfi Zadeh wrote, or he gave a talk for the New York Academy of Science in 1952, and here is what he wrote in the paper that was published later. The title of the talk is Some Basic Problems in Communication of Information, and he gave a lot of remarks to these problems.

Here are two of his problems, the first problem is that actually a set of signals, an arbitrary selected member of the set say, X of T, is transmitted through a noisy channel gamma and it is received as Y of T. Your sender signal and your receiver signal at the different point and the question is, is it the same signal? As the result of the noise and distortion introduced by gamma the received signal Y is in general different from X. Nevertheless, he says, “Under certain conditions it is possible to recover X or rather a time delayed replica of it from the received signal.”

You have operator gamma and it’s very easy in theory but what he said is, “Of course, it’s only easy in theory, in practice in the laboratory it’s very difficult to have this operator gamma, you have to build a collection of circuits for that.” The special case is the reception process, let X consist of a finite number of discrete signals which play the roles of symbols, or sequences of symbols. The replica’s of all these signals are assumed to be available at the receiving end of the system, suppose that the transmitter signal XK is received as Y. To recover the transmittal signal from Y the receiver evaluates a distance between Y and all possible transmitted signals by the use of a suitable distance function.

Then selects the signal which is nearest to Y in a term of this distance function. Then he gives some examples, what is a distance function? These are mathematical terms for distance functions and he showed these distance functions in this paper. Then, and that is more important, he wrote this, first you see the distance function, and the distance function between XK and Y is smaller than the distance function between XI and Y. He says, “Okay, we take the nearest one.” In many practical situations he wrote, it is inconvenient or even impossible to define a quantitative measure such as a distance function of the disparity between two signals. In such cases we may use instead the concept of neighborhood which is basic to the theory of topological spaces.

What he did here is, that maybe we need a new theory, he said, “Maybe we need a new theory.” He didn’t say what kind of theory. He said, “Maybe it should use a concept like neighborhood.” What he had in mind is something like topology. The second problem he showed is multiplex transmission of two or more signals, X is the set of signals X of T, and Y is a set of signals Y of T, and then he said, “You are sending these two signals but what you get at the end is a sum of both signals.” Now the job is to extract X and Y from the sum, and again he says, “In theory it’s very easy to have the operators.” Here he called them filters, you have filter N1 and filter N2 and they are operating to the sum and the output if X or Y.

You can see that here, I am sorry for that. Here’s a picture of his paper for the Academy of Science in that time, and he was developing now a kind of algebra of electrical filters, geometrical representations of nonlinear filters and of linear filters. It’s still a continuation of Vena’s work in electrical filters, and here you see pictures from his papers in the 50’s, so he wanted to establish an algebra of filters. Here’s a paper hand written from Zadeh where he started to consider stochastic filters, and stochastic operators. He saw okay it is not enough to have an algebra we have to go very deep into mathematics, and he used operative theory that he knew from quantum mechanics.

Then you see that he gave talks on filter theory, he became a member of the Editorial Board of Information and Controls so he came in the area of control theory. Here you see one of the first examples of the Journal IRE Transactions of Information Theory, it was started in the 50’s and he became a member of the Editorial Board of these Transactions to. What is interesting with this journal is that in the editorial board of this journal there were Shannon and [Wiener 00:20:38]. Both of them wrote an editorial in the 50’s to the readers of this journal, and Shannon wrote an editorial in March 1956 and the title was, The Band Wagon. You see in June the next issue Norbert Wiener wrote an editorial and that title was, What is information Theory?

What Shannon did in his editorial was he said, “I’m very proud, I’m the founder of information theory.” He didn’t say that Wiener is a founder of information theory to, of course, he didn’t say that. He said, “I’m very proud of the information theory, everybody’s using my concept, everybody is using information, everybody is using the concept of [entropy 00:21:17], also in philosophy, also in sociology, also in psychology. Now stop it.” He said. Indeed the hard core of information theory is essentially a branch of mathematics a strictly deductive system which research rather exposition is the key note, and our critical threshold should be raised. He said, “Stop this using information theory in other fields, I don’t want it.”

You know Norbert Wiener is the opposite, in his view was different, so three months later he wrote an editorial and here’s written what he said, “I’m pleading in this editorial that information theory go back of its slogans and return to the point of view from which it originated, that of the general statistical concept of communication. I hope that these transactions may encourage this integrated view of communication theory by extending its hospitality to papers which while they be on communication theory cross its boundaries and have a scope covering the related statistical theories. In my opinion we are in a dangerous age of over specialization.” It’s the opposite and people in electrical engineering and information science after this had to decide will I go to the Shannon camp or will I go to the Wiener camp?

Here you see some people, I show this not because of this, you see they are doing communications theory and they’re doing statistics. Richard [Bellman 00:22:50] was a close friend of Lotfi Zadeh and that’s the reason why I show you this picture. People started working in these areas. Here’s an editorial Lotfi Zadeh wrote in the same journal some years later, you see 1958, and his title of his editorial was What is Optima. What he did in this editorial is he said, “We have to say what is an optimal communication system?” He said, “It’s not very easy to say that because you have to say in which view is it optimal?”

He gave examples, I only can show you a survey. He said, “They are different criteria and because of different criteria optimality is not a scalar function but maybe we have to use a backdoor to use this word of optimality.” You see Lotfi Zadeh was very deep in this areas of system theory and information theory, and then we have this. It was the first journal paper I found in 1965 that mentions Fuzzy Sets, this is a journal New Scientist, April 1965 and this is the editorial of the editor. I think it was Nigel Calder in that time, and what he wrote here I want to read here, “Some of us have been looking anxiously for more powerful way of dealing with complex ill defined features of the real world. Including much of human affairs which at present alludes the grip of objective analysis. Obvious examples raise from the variability of legible handwriting to the waiting of factors in political decision making. Now I think I know who has the most promising line of attack.”

“At Berkeley California, Professor Lotfi A Zadeh, has for some months past been developing a theory of Fuzzy Sets, it is a mathematical tool. Closely analogies to ordinary [inaudible 00:24:49] but instead of specifying that an element falls clearly in or out of the given set, one can say that it is partly in. Ascribing to its membership some appropriate weight between zero and one. When Zadeh’s work becomes more widely know many people, engineers, psychologist and strategists among them will seize on it eagerly. For my money it’s implications are immense and it has a straight forwardness characteristic of a big idea.”

This was first mentioning Zadeh’s Fuzzy Sets, and what I’ve found in his house and in his office is many of these programs of conferences where he gave talks on his Fuzzy Set Theory. Then there appeared a paper, Fuzzy Sets and Systems, I go to this paper later. First I want to show this, another talk Lotfi Zadeh gave on Fuzzy Sets in Stanford in 1965. I want to show you what is a Fuzzy Set, okay people from NAFIPS know that already. You all know what is a set, here you see a set like you have given it in school, and this is a Fuzzy Set, so it’s very easy. Boundaries are un-sharp, you don’t know where ends are set, where starts the compliment of the set.

Here is maybe a more nice to say what is a set, [Gail Cantor 00:26:32] a German logician and mathematician said, “We need something like sets, the set of animals, there are cats, there are dogs, there are horses, they are elements of the set of animals. Of course, Otto Lilienthal, a telephone, a canon, and some water is not an animal, so it’s very clear what is an element of a set and what is not. Lotfi Zadeh said, “We can do that, we have a set of animals, and we have a set of non animals.” In that time in 65′ he said, “What is with starfishes, what is with bacteria? Are they elements of a set of animals or not?” He mentioned this motivation in his first paper, he was a electrical engineer and this was only motivation.

I think in that time in the 60’s nobody knew is a bacteria an animal or not. This is more mathematically the definition of [Gail Cantor 00:27:24] for a set, a set is a collection into whole M of definite and separate objects, small M of our intuition or our thoughts. You see all objects have a value, zero or one, if the object is an element of the set then it has a value one, otherwise it has a value of zero. Here is the definition of Lotfi Zadeh for a Fuzzy Set, a Fuzzy Set A in X is characterized by a membership function or a characteristic function. UA of X which associates with each point and acts a real number in an interval zero one, with the value of UA of X at X representing the grade of membership of X and A.

You see every object can take a value between zero and one, that is a small idea and it was a small theory, and it developed to many applications. In usual sets [inaudible 00:28:21] you have to combine sets, and you can do the same with Fuzzy Sets, that of course has to be, he defined what is an empty set, an empty Fuzzy Set. Membership value is zero, equal Fuzzy Set means membership values are equal, compliment this one minus membership function, and containment means that membership function of A is smaller that the membership function of B at every point.

That is easy, and what is interesting is how he defines union and intersection of Fuzzy Sets, and here he said, “The membership function of the union of two Fuzzy Sets A and B is a maximum of the membership values. The intersection is the minimum.” That is a very interesting definition, I will say you later how it comes from. Interesting because, of course, if you have only zero and one, then the maximum is one and the minimum is zero. If you have more than zero and one but all the numbers between this is more, this is an extension of user sensory.

In 2005 we had 40 years of Fuzzy Sets, this is a paper he wrote, in 1965 and you see in next year we have 50 years of Fuzzy Sets and I think there will be celebrations like 10 years ago. This was 40 years in Beijing, they celebrated this theory. I wrote my book on the history of this theory in 2005, it appeared in German and in 2007 it appeared in English, what I say today here is most of it is written in this book so I don’t have to go into details here. You see I have a different view, I’ve started with a prehistory, I couldn’t do that in that talk.

Then the genius of the theory of Fuzzy Set in the 60’s then some applications, I don’t know whether I can go to this part here in this talk. Then there was an enforcement of the theory of the Fuzzy Set as a scientific paradigm, and since the 90’s I think Fuzzy Set theory is usual and normal and it is going to be in every text book.

What I wanted to say in this talk is that there are three scientific concepts that acted as origins of the theory of Fuzzy Sets and one is Information Theory that is related to Norbert Wiener. Thinking machines that is related to Norbert Wiener, and System Theory maybe that is related to Norbert Wiener too. I want to start in the last 15 minutes with information, with thinking machines. You all know thinking machines, history of computers started after the World War II and this is the first big computer is ENIAC and it was the first machine that was called thinking machines.

Here you see some headlines in that time after the World War, people didn’t know that there are computers, and journals, and newspapers said, “We have these machines and these machines are like brains.” They said, “These are wonder brains, these are electrical brains, these are mechanical brains.” They said, “They are acting like brains.” That of course is a very difficult question to say, I think they do not, but in that time they popularized computers as thinking machines. Here you see some books by Edmund C Berkeley, Giant Brains, or Machines that Think, that is the title of the book, so again they said, “These machines are thinking machines.”

Here you see some comic, the problem is too difficult for one man, I will ask my electronic brain. This is what was said in the 40’s and 50’s. Of course, we have the paper of Alan Turing, Computing Machinery and Intelligence, and Alan Turing asks in this paper, Can Machines Think? We have a paper by Lotfi Zadeh in the same year, he wrote a paper for Columbia Engine and Quarterly, a journal for students in electrical engineering in Columbia University and the title was, Thinking Machines a New Field in Electrical Engineering.

He said to the students of electrical engineering, “This is the area where you will work, this computers is your area and you have to study how these thinking machines work.” What he said is, “A thinking machine is a system, it has an input and an output but there is something in. It’s a processor, it’s a computer, it’s a storage.” What is very important for Lotfi Zadeh it’s a decision maker, for him thinking machines are only thinking machines if they can decide. I cannot go into details in this point, it’s very interesting in that time that this decision maker is very important for Lotfi Zadeh.

What he wrote in this paper is, “The type of machines [cached 00:33:20] above can be made as a crude, or as elaborate as it maybe desired. It is not as fantastic as it may appear, in fact such machines may be common place in anywhere from 10 or 20 years hence.” That was in 1950, and he wrote, “Furthermore it is absolutely certain that thinking machines will play a major role in any armed conflict that may arise in the future.” He was right, of course, he didn’t know what will happen in that time. In one of my interviews he said, “In 1960 I wrote a paper entitled, Thinking Machines a New Field in Electrical Engineering, which as published in Columbia Engineering Quarterly, like others I had greatly underestimated the difficulty of designing machines that can approximate to the remarkable human ability to reason and make decisions in an environment of uncertainty and imprecision.”

That’s the reason why he developed Fuzzy Set Theory, I want to go to that to, but first I want to show you this another journal article he wrote four years later, and the title was, Systems Theory, and what he said, “Dear students of electrical engineering at Columbia University, you have to study systems theory and systems theory is very easy, because systems theory is only this.” This definition was from Webster’s Dictionary, a system is an aggregation or [inaudible 00:34:49] of objects united by some form of interaction or interdependence.

He gave examples, a set particles, a group human beings, a complex of interrelated industries, an electrical network or a computer. What he said is, “System theory is very easy, because the output is a function of the input, that’s all.” Here’s a black box picture he showed, there are inputs, there are outputs and we are not interested what is in, that was in 1952. Then he became a protagonist of system theory in the United States, he wrote books on system theory, he wrote a book, Linear System Theory, together with Charles Desoer. He wrote a volume with [Elliot Pollack 00:35:31], both are colleagues from Berkeley and both books you can find in the book stores today.

He was very famous for systems theory and if he would have never established Fuzzy Set theory he would be famous for that. Of course, then he became Dean at Electrical Engineer in Berkeley and then there was an interesting symposium. This is the proceedings, it’s a symposium on use on general systems theory and that was a little idea like this conference is because they invited people who are doing research on systems theory from electrical engineering, but also from sociology, and psychology, and biology, and economy. They thought they all are doing systems theory, and let’s bring them together they have to discuss. It was a great disaster, they couldn’t communicate, that is what the editor wrote in his preface, was not very successful but it is interesting because there was Kenneth Boulding, the famous Kenneth Boulding who attended to this conference.

He wrote a poem to every talk he heard and this poem was printed on the page of the beginning of the talk in the proceedings. Here is the poem of Kenneth Boulding to the talk of the Lotfi Zadeh, A system … I cannot read it but I know it by brain. A system is a big black box, of which we can’t unlock the locks and all we can find out about, is what goes in and what goes out, perceiving input output pairs related by perimeters permits us sometimes to relate an input output, and a state. If this relations good and stable then to predict we maybe able but if it fails us, heaven forbid we’ll be compelled to force the lid.

That was the poem, Kenneth Boulding a lot what Zadeh did in this talk because it was the first time Lotfi Zadeh, or anybody in electrical engineering said, “We need more than only input and output. What we need is a concept of state and here we need U as an input and Y as the output, and S as the state. It’s the third variable, and because of that you need two equations for systems theory for identifying systems. This was a generalization of systems theory by Lotfi Zadeh, it was the first generalization, and then to come to the end of this development.

In 1962 he wrote a paper from Circuit Theory to System Theory, it was an advisory of the IIE and what he wrote here, don’t read it all, the important sentence is the red one. What he said in this paper is that we are system theorists and we are doing identifying systems, and the most complex systems we can identify. We cannot identify them all, and the most important systems we have to identify is biological systems, and we have not the mathematical tools to do that. Then he said, “We need a radically different kind of mathematics. The mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions.

Here’s the first time he said, “We need a new theory.” He said, “Maybe cloudy or fuzzy is a concept I will use.” Three years later he will establish this theory, at that time he does not know what kind of theory he will establish. Can I have five minutes more, three? He gave a talk in 1964 in Ohio, it was a military air base, I asked him, “What was the title of the talk, is there a paper of this talk?” He said, “No, I know what I say.” I think it was a kind of secret maybe because he’s 93 now he doesn’t know what, but I think he doesn’t want to say what kind of talk he gave.

He traveled to Ohio from Berkeley, and he a stop in New York and he wanted to meet his parents. They were in New York at that time too, and they wanted to have dinner together and that dinner was cancelled. The myth of the establishment of Fuzzy Set Theory is he was at the airport and he asked, “When will the next flight go?” Then the man said, “It will be maybe at, that time.” Then he thought, okay that is very fuzzy and let’s establish fuzzy set theory. I think that’s not true, but many people write that in their books. I thought what did he do in that time, there is a paper, I show you what kind paper and then I will stop.

There’s this problem, you know I said he gave a talk in pattern recognition, he was not an expert in pattern recognition, he never did pattern recognition. Pattern recognition was a subject in that time, computers should do pattern recognition that was the time of the perception, so it was a thing to give a talk. He was invited to give a talk and his idea was, we have the pattern there with this square or whatever it is, name is X and you have to decide or the machine has to decide is it an O or is it a D? The machine can say, “Yes, it is an O or yes it is a D.” Maybe it is better, it’s his idea to say, “It’s an O with a membership degree, new O between zero and one and it’s a D with a membership degree, new D between zero and one.”

That was his small idea, and you see the text he wrote this here, and it’s interesting where this text comes from. This text comes from this memo, it’s written in 1964, it’s a Rand memo, it’s close to a government organization, it’s a kind of research organization that was secret. This memo was not free available in that time, of course, then you see the authors are Richard Bellman, Robert [Caliber 00:41:56] and Lotfi Zadeh. Lotfi Zadeh is the third because we was not with Rand he was at Berkeley University, but Richard Bellman was with Rand and he was his close friend. They published the paper written by Lotfi Zadeh under these three names.

I’m sure about that because in September of the same year we have this letter from Bellman who was Editor of the Journal of Mathematical Analysis and Applications to Lotfi Zadeh. He writes, “Dear Lotfi, I think that the paper is extremely interesting and I would like to publish it in this journal.” It was not his paper it was the paper of Lotfi Zadeh, and in 1966 this paper appeared Abstraction and Pattern Classification in the title you don’t see that it’s the Fuzzy Set Theory, but the content is an introduction into Fuzzy Set Theory. This paper I showed you already in 1965 is the famous first journal paper Fuzzy Set and here he is showing all the definitions of Fuzzy Set Theory. You can find today in all the books.

I am sorry I have to stop here, if you have questions, I can talk for another half an hour, but I will stop here. Thank you very much.