"Could you give me some idea of what your work involves?" "Do you think of yourself as having a job?" "It is rather difficult to explain the mathematician's notion of work" "Some people are obviously involved in teaching and teaching is a job" "A difficult job" "And then there are people who do research" "And research is a job too but the work is very irregular and uncertain" "What I meant was that I assume you are paid wages so I was wondering what you provide in return" "Well, it is rather difficult to define it exactly" "Why is it difficult?" "Because I'm in a rather exceptional situation" "I'm in a research institute here" "And most of my colleagues would tell you that people in such situation don't do anything very much" "And it's quite true..." "Well, you didn't draw those signs on the board there but your eyes saw them and understood them and they could have drawn some somewhere" "So if you agree we'll take that as a point in your work" "Would we try to isolate this point and see what it is made up of?" "That is simply an attempt to understand one of the basic formulae of quantum mechanics that I didn't undertsand properly and that I probably still don't undertsand properly" "And I got a colleague to explain it to me who taught me some formulae" "As I always do in that case" "What's a formula?" "It's like "Hello, how are you?"?" "More like E=mc² as Einstein says!" "How would you describe to a child what a formula is?" "For most people, and even for many physicists, a formula is something magic" "like a magic formula which produces the rabbit from a hat" "It allows you to make completely undreamed of connections" "Could you give us an example of the kind of formula that produces a connection?" "A moment ago I mentioned Einstein's formula E=ms² which is typical of the kind of thing I mean" "The energy contained in a body which has a mass m is eaqual to m multiplied by the square of the speed of the light" "It's a typical example because it allows you to link concepts which have no a priori connection" "Could it be applied to yourself?" "No, no" "Why?" "Because you haven't a mass m?" "Oh, I've obviously got a mass m" "Quite an imposing one in fact!" "But my mass doesn't play a part in my life" "Here we are talking about a corld completely separated from the everyday world we live in" "You could say there are 2 kinds of world: the world of physics and the everyday world" "The world of physics is characterised by mathematical concepts whereas the everyday world is characterised by everyday language ...so he asked the servant to bring him some ragout for lunch" "And she got it wrong and thought he said rat" "So she brought the count some rats" "René Thom:" "Whereas it's the world of physics that is more or less fictitious" "And then she asked what he wanted for his next course" "And the count said jacket potatoes" "So the servant sent back to the kitchen and she said "jacket potatoes?" "but I've no jacket!"" "So she went back to the dining room..." "As soon as one recognises the possibility of acquiring knowledge outside the domain of science," "then one is already moving away from the beaten track" "Naturally enough, scientists, as a general rule, will always say that salvation can't be found outside science" "It's a prejudice of the profession" "Could you describe for us one of the things which you write?" "I could draw the surface of a catastrophe, if you like..." "That's the surface that averone knows there" "This dotted line can't be seen" "And this is all projected onto a plane" "Here the projection and here the singularity" "And there you've got the graph of the visible outline" "This diagram is one of the basic figure we encounter in this kind of catastrophe theory" "You've just written something but you don't think of yourself as a writer" "There's something interesting in maths books, I think, because whereas writers generally use letters, mathematicians use both letters and figures, mixed up" "So why do you write both figures and letters and...?" "As a matter of fact, apart from the zero..." "There's a three" "Or the Dr. Cosine" "There's a three, a four, a two, and a lot of letters..." "Yes, it's true that there are a few small natural entities" "But what are important are the algebra symbols i.e. the plus sign, the equals sign, ans so on which are not in themselves letters in the linguistic sense of the word" "So you would write x where Zola wrote "plus bread" or "minus money" or whatever" "Is there a relation between both?" "That's right" "There's certainly a relation between the plus symbolised by a cross and the plus in ordinary language" "Certainly" "But the relationship tends to be forgotten in algebra" "And you have to work very hard to resurrect it" "You've drawn a curved surface there and underneath there's a sort of sheet, or a square of some kind" "And you're claiming that it's a kind" " I don't remember the name - of catastrophe" "Yes, there's a fold at that point made up of two folds which peter out together" "Can you make out the two folds?" "The word catastrophe is a word that is very..." "You could easily make this into a model with a sheet of paper" "You make a fold there and another one there, like that" "And there you've made the same thing in paper with fixed blocks that is with a completely straight outline" "You have to place it at an angle like that for the situation to correspond to the one I've drawn" "The situation?" "Yes, it's a situation" "Algebra, in fact, is used to define situations" "So it is very closely related to everyday life?" "Oh yes, absolutely" "But that was my hope in developing this theory" "I wanted to show that a large number of everyday situations are governed or informed by algebrais structures" "It's a surprising fact" "Supposing... two lovers split up and one of them is very unhappy because the other one has found someone else" "So he feels he's been struck by some sort of catastrophe" "Do you think that this situation could be described like this?" "Certainly it could" "You could express it formally like this" "Can you predict such a situation with this model?" "Ah, that's a much more difficult area" "Prediction... isn't usually possible" "You see, this theory is a theory of classification, a taxonomic theory as our biologist colleagues would say" "So it's not theory of prediction" "Mind you, I was a wild success when I went to Japan to talk about my theory because everyone thought that it would be able to predict earthquakes" "And obviously we can never do that" "Or rather, it probably is possible to predict earthquakes to some extent, but using methods completely different from this one" "Well, if it can't be used for predictions, can it help create new ways of thinking which might prepare people for such moments?" "You don't even know that you can't predict things if you haven't first tried looking at them in new ways" "Possibly" "What I do think is that this method allows us to think in a different way and to see things in a new light" "It allows us to take our distance from an object and no longer to conceive it as an object but to see it as a geometric form" "And when something becomes unfamiliar it also becomes easier to manipulate graphy metry geo" "We find it easier to escape from the attractions of semantics" "What is semantics?" "Semantics is the science of meaning, of the sense of words ge oh graphy ge oh metry" "There's a lot of sense in those diagrams" "There are arrows getting at all kinds of things" "Yes, of course" "But I meants sense in the sense of the general theory of language, do you see?" "Language is a series of signs which signify something" "And what they signify is what semantics is about" "Could you tell us a bit more about this model?" "A moment ago you mentioned that you were going to draw us the most basic of the diagrams..." "For this model?" "Yes" "This model is particularaly suited to providing a geometrical reprenstation of the notion of capture and its abpproximate opposite, the notion of emission" "When you say a sentence like "The cat eats the mouse"" "in the phenomenon which "the cat eats the mouse" describes, we have two actants as they say in linguistics, the cat and the mouse, which are separate in space" "Could you say two actors?" "Yes, two actors if you prefer that term" "Actants is the convertional term but you could say actors..." "And at the end of the process when the cat has eaten the mouse, only one remains which is the cat the cat has overcome catastrophe and that's why it's the subject of the sentence" "But Mao Zedong would have said that the mouse had been transformed into a part of the cat" "Yes, you could also say that there has been some merging of object and subject" "But the merger cannot be reversed and is therefore a catastrophe" "Who finds it catastrophic?" "The mouse obviously" "But the cat too" "Because the very process of capturing something is one that the cat cannot reverse either" "This idea could be developed quite considerably" "However, if you want to represent capture here, it has to be done in this plane, within this small segment..." "Then you must imagine that from this point, let's call it alpha, you have a vertical which bisects the surface at 3 points, and if you take the corresponding function v which is a function that has 2 minima," "rape and let us suppose that the minima represent the two actors in the catastrophe, in the story" "Here we have a deep actant, the cat, and a slightly less deep actant, the mouse" "And when we move across this small segment here, we eventually meet the curve of bifurcation K which is equivalent to this point here, let us say," "and so at that point on the curve of potentials we have th cat here and all the mouse has is a little pocket left, sticking out like that" "But when we go beyond there, the pocket wich belongs to the mouse is completely captured by the one of the cat" "So that's how you express the idea of capture in geometrical terms" "And in some ways it's the most simple geometrical expression of a general dynamic interpretation of the process" "You talk of capture and you talked of information..." "No, we might have talked of information a little while ago but it was a much more general notion than capture" "What was it you said after the capture?" "What was the word I used?" "I can't remember" "Oh yes, I mentioned emission" "Well, emission is what you would get if you reversed the arrow of time" "If you reverse the process, you start out with a single actant who creates around himself a second actant" "So you would have to reverse this series of transformation in such a way that you would have the cat emitting a mouse" "Only that doesn't generally happen, for obvious reasons" "But emission processes do exist" "Moreover, there is a very interesting question which I always put to the technicians:" "when you draw a process of capture symbolically you can draw it like that, two actants becoming one, whereas the process of emission involves one actant becoming two" "Could a kiss between two lovers be a process of emission?" "No, it would be a process of transfer or, prossibly, the creation of an intermediate actant between the two of them" "Now, if you want to create an intermediate actant, you have to imagine a slightly more complex catastrophe" "You have to take it to the power of five if you want to create an intermediate actant" "What gave you the idea of using the word 'catastrophe'?" "It's a word that writers use, isn't it?" "Do writers really use it?" "I mean, people whose job is to write" "Why this word rather than 'crisis' say?" "No, 'crisis' wasn't right" "There's a term which is much more mathematically correct, 'discontinuity'" "But I wanted connotations of dynamism" "I wanted to show that discontinuity was produced by an overall dynamic situation" "And that's why I rejected the term discontinuity which is somewhat flat" "There was also the word mutation, but that wasn't very suitable either because it is already used in biology in a technical sense..." "It's quite extraordinary that the people who have translated the Taoist book the I Ching" " you know that the Chinese of the Lao Tsu period constructed a general theory of changes or mutations in the world which are transcribed in the I Ching..." "Like the Chinese today..." "Maybe" "Yes, you could say that the 1 which becomes 2 and the 2 which becomes 1 are mutations which you can find in the Masters' book" "And the people who translated the i Ching into French called it the book of changes, the book of mutations" "And Brecht called it the book of reversals" "Really?" "At all events, I had to fall back on the word 'catastrophe' partly because it was already used in physics" "I have to admit that I may have succumbed to a somehwat facile temptation to use the evocation power of a word" "And from my point of view it is rather unfortunate since I believe that catastrophes are necessary and beneficial as well as disastrous" "I think that our lives depend on the continuous use of catastrophes" "How do you mean?" "The most simple kind is the way the heart beats" "The contraction of the heart is simply a series of catastrophic transformations within the cardiac muscle" "And it's quite normal" "All life is based on reflex processes of regulation which involve abrupt changes of rhythm or discontinuities" "So from that point of view it ceases to be surprising that the word catastrophe is used in a sense which is rather different from its usual one" "What we see there is an abstract representation of a concrete form, is that right?" "That's it" "It's an abstraction or a diagram representing a concrete situation" "For example, when two things meet and merge, the meeting can be represented by a diagram of this kind" "Obviously the mouse's horrible fate is a slightly 'far-fetched' interpretation of it" "but it still remains a fundamental one" "What about a war?" "Or rising inflation?" "or a fit of jealousy?" "Could these be?" "Yes, indeed" "And as far as war is concerned, such an interpretation is obvious since this theory is totally dependent on the idea of conflict" "It's the old Heraclitean idea that conflict engenders everything, that all morphogenesis derives from conflict" "Morphogenesis?" "Any generation of forms, the appearance of new forms" "Would human beings count as the appearance of new forms?" "Of course, because they result from a conflict" "What conflict?" "The conflict by which the fertilized egg is separated from the mother's body" "And you would describe that as a kind of military war?" "No, I wouldn't describe it as a war, but I would describe it as a conflict in a slightly more abstract sense" "I know that Heraclites use the word 'war', 'polemos' to describe the universality of the conflict" "But it's certain that war as we know it among human beings is one of the manifestations of conflict, a social manifestation of it, you might say" "Why do you prefer to illustrate your ideas by looking at a drop of rain, for instance, or the curve of a leaf," "or the way a swallow's wing folds back, rahter than using social conflicts as a source of images?" "I think that the phenomenon is much purer and much easier to see in geometric form or morphological form" "Whereas in social phenomena you always find some interpretation involved" "However, if we looked at war as we have experienced it over the last few decades, they are all disgreements about space" "Could you indicate where space and time are on the diagram?" "There's no fixed position for time" "As I explained a little while ago, the same section reversed could describe capture and emission processes indifferently" "So I can put time where I want to in this diagram" "It depends on the requirements of the particular situation" "Space, on the other hand, is always this basic space here" "That's where morphology taked place" "And what generally happens is that inside each of these folds there are two stable areas" "I draw those in blue, whereas the maxima are in red" "Inside this fold here there are two stable areas which compete each other" "And they will divide up the territory they govern" "Supposing it was a baby and his mother?" "Yes..." "In that case, there would be a movement across in this direction" "But the division generally takes place in such a way as to create a sort of shock wave in the middle of this fold, and below the shock wave you have the lower attractor which is shown by the lower strip of the surface," "and on the other side of the shock wave, you've got the upper attractor" "Those are the ordinary situations in this catastrophe fold" "In fact, it means you can't believe in any idea of progress, doesn't it?" "All progress is a set of catastrophes" "That's how we'd have to describe it, isn't it?" "If, indeed, this theory were completely accepted... if we extrapolated from it to evolution for instance, then it would go rather against the idea of progress..." "As we have been taught it" "As we normally think of it" "But I have to confess that personally some common ideas need to be revised, such as for example the idea that man is superior to the beasts because of language" "I don't believe that the invention of language is nearly as remarkable as people sometimes say" "And this is to some extent borne out by recent experiments with apes when it was shown to be possible to teach an ape how to use a fairly large number of symbols" "And they seem to be able to use them almost spontaneously and to create their own grammar" "So from that point of view I think that man's invention of language isn't as remarkable as all that" "Thus there are two fork-shaped diagrams" "One representing capture in which we believe that time moves from left to right" "And on representing emission, in which an actant emits an object, a descendant which becomes separate from it" "So there are two typical morphologies which are not even equivalent from a thermodynamic point of view" "Thermodynamic?" "Yes, from the point of view of probability of occurence in nature" "I would be tempted to say that the morphology of capture is infinitely more natural than the morphology of emission" "What examples would be more natural?" "For instance, it's much more natural for 2 raindrops to join to make 1 than 1 raindropt to split into 2" "It happens much more often" "And I think that's one of the things which explains arrow symbols" "Why is the arrow always used to symbolise two things which join to make one, rather than one becoming two?" "I think that the Chinese would have put it the other way round" "I don't know but..." "The great principle of Maoism is that two are in one and they've hanged people for thinking that two merged into one" "It's part of their great attack against Confucius" "I don't know" "Didn't Mao say somewhere that one is transformed into two and two into one?" "I don't know whether this doctrine has a privileged way" "But I would still imagine that of the 2 transformations, 2 making 1 is more natural than one making 2" "Which reminds me, since we're talking about the Chinese, that in Ancient Chinese there's an ideogram which has approximately this structure and it's still to be found in the symbols in current use to mean entry," "and it's always shown as goind from bottom to top" "Coming back to what you said about emission broadcasting on tv, emissions of sperm, issuing banknotes, all these kinds of emission..." "That's it" "These are all operations which in one way or another require a certain potential to be lost" "No emission takes place without there also being come loss of potential energy which previously existed" "Whereas capture is generally beneficial as far as energy and entropy are concerned" "Entropy?" "That's yet another idea" "It would take too long to explain in detail but all I wanted to say was that if we want to express time this is the standard way of doing so, with the arrow pointing in this direction whereas if it pointed in the other direction it would seem unnatural" "Is this a universal or merely a cultural convention?" "Is it important to know whether or not it's a universal" "Yes, for me it is an extremely interesting question" "Why do mathematicians or physicists always want to know whether or not something is a universal?" "Mind you in this case the problem isn't..." "It's as if there were only one truth and not many truths..." "The problem isn't a problem in mathematics" "It has more to do with gestalt theory or general psychology or anthropology" "It's not a mathematics or a physics problem, although it has implications for physics" "In this arrow which points in one direction and not the other," "there are two forms which become one" "That's right" "Why do you think two forms becoming one has to do with information?" "It has to do with direction, since we talk of the direction in which the time arrow is pointing, which therefore gives it a certain sense" "And it is more natural to say that the sense is understood from left to right rather the reverse" "And I don't think this is linked to societies which use the arrow" "One could obviously say that societies which use the arrow tend to draw the arrow in the direction which it moves and to define the movement of the arrow by the direction in which it points" "That's quite true but I'm convinced that the same kind of symbolism exists even in societies where the arrow is not used" "Why did you, when you were talking about heat a little while ago..." "Would you talk about this in a different way so that we could regnise things more easily?" "What was it that disturbed you in theories of heat?" "In my sense, all you're talking about is information..." "What a disaster the word 'information' is!" "It's used at every conceivable opportunity..." "You referred to forms, to morphogenesis..." "I think we should try to be more epistemologically precise and replace the word 'information' by 'form'" "So could we talk of things being broadcast, being transmitted in this context?" "But it's quite different with capture and emission" "There you have morphologies which are precisely defined and whose form can be clearly described, whereas people imply all kinds of things, mostly extremely vague, by the notion of information" "So Shannon's theory is not a theory of information" "It's a theory of transmission which is something quite different" "When you mentioned transmission a few minutes ago, you mentioned a descendant, which made me think about legacies and so about transmission" "That's it exactly" "But the basic graph of communication..." "Could it be placed on the square there?" "On top" "The graph looks like this" "Here you've got the source or the transmitter" "There you've got the target" "Here the receiver" "Here the message of the gift" "So for instance in the sentence "Eve gives Adam the apple" you have a completely typical morphology" "The apple is the message" "Yes, the apple is the message" "You can see that from the morphological point of view, if you break this in two, you have an emission catastrophe here and a reception catastrophe here" "So it unites two basic catastrophes which are inverted in relation to time" "And that means that there are some elements of reversibility" "This is a catastrophe which obvioulsy cannot be reversed and whose direction is very clear" "But in fact when you change the targets, if you reverse the time arrow you still have the same morphology" "In such a way that you can cancel out the effect of time in a communications operation" "But shannon's theory essentially concers the phenomenon of transmission" "That is to say it has to do with what is here, what is called the channel" "And the transmitter transmits a fairly complex morphology which passes along the channel and at the exit of the channel, there is another morphology" "What Shannon's theory studies is the connection between these two morphologies" "But that's the problem of transmission" "Does transmission play a part in the creation of form?" "Between the source and what's there, the message, is that the apple?" "What is true is that the message has in general a very clearly defined morphology" "What is true is that the message has in general a very clearly defined morphology" "Could we define all forms as moments in a process of transmission" "All natural forms..." "Or extra-natural..." "That's a very old idea" "It's exactly what Heraclites said" "The master whose oracle is at Delphi neither speaks nor conceals, but betokens" "That is to say that all natural forms are like messages which it is our job to decipher, whose meaning we have to unravel" "So you could well look at it like that you could say that there is a sort of universal donor which broadcasts messages that we receive and which we have to interpret" "But that's a very poetic or very theological way of looking at things" "But instead of thinking of ourselves as transmitters or receivers, couldn't we think of ourselves as messages" "Messages between what and what?" "Between you and others, for instance" "Thinking of ourselves more as machines" "It's perfectly true that, given what you do, you could well think of yourself as a channel between me and other people" "I hope the channel won't distort things too much!" "Could one think of a woman as a channel between the father and child?" "That too" "But there is a small difference because the woman already exists whereas the typical channel derives from the source and it is the product of an explosion at the source" "So you believe that the channel is something secondary?" "Yes." "In fact, in my table of basic morphologies, I've placed the messenger catastrophe where something of the following kind occurs a messenger comes up to the transmitter which gives him a message and message and messenger go back to join the receiver" "And in a case like that you can indeed say that the messenger already exists and is the physical embidiment of the chennel" "Thus the channel already exists" "And there are actualy many situations like that" "Can the message create the means, the medium?" "Certainly" "At least in biology that is certainly the case in many situations" "But we've come right back to Lamarck now, with the function creating the organ" "Not always" "I think it does, because I'm a disciple of Lamarck" "But if my biologist colleagues heard that they'd blow their tops!" "What is certain is that societies organs are determined by functions" "And I think it's also the case in biology" "So, we wera talking about information" "And I was saying that in many cases the word 'information' ought to be replaced by the word 'form' which is a word that imposes far fewer restrictions" "This is very definitely not a piece of information" "But in fact the use of little diagrams, like the ones here, can to a great extent explain the ways in which the notion of information is misused" "Fundamentally, for information to exist, there must be both someone who needs it, that is to say a person who suffers from a lack of something such as for instance, someone in a strange town who wants to go and see a friend" "he knows the address but doesn't know where the road is and he asks a passer-by where such and suach a road, or such and such a number is" "And the passer-by gives him the necessary information i.e. a description of the route to be followed in order to find the road" "So in that kind of situation there is the person who is in difficulties and who sends a request to the donor" "The donor gives the information" "which is then captured by the demander and once it has been captured it leads to action, to the carrying out of the desired action" "All that is to be found in the word 'information', in my opinion" "Putting that into a diagram would be extremely complicated" "You can see that for most of the verbs whoch describe spatio-temporal interactions, the diagram showing the whole interaction between the actors, the actants, is usually much less complicated" "The most complicated is the one showing the messenger, and even there some things have been cut out and some things linked together" "But with that exception, the operations described by verbs are always very simple" "So this diagram contains a sort of dialogue with the addition of an action that is beneficial for the person in need" "It is something that is very complicated, and our minds always tend to suppress a certain number of the elements it contains so as to make the situation simple enough to be taken in at a glance" "And the misuse of the notion of information derives in fact from the suppression of certain things in this diagram" "For example, you could suppress the person who is in need" "In a judicial proceeding, when an enquiry is begun, , that's the society that plays the part of the person in need against" "And society tries to extract certain information from the person under suspicion" "TV against people" "Sometimes this can be arried as far as a veritable excision catastrophe such as violence of torture" "The judicial sense of the word 'information' is a very special one because it has some use for the social group which hopes to benefit from it" "But there is an even more dubious use of the word information, where there is no one asking for it" "And that is in the one which concerns journalism and advertising" "When the word is used in journalism, the journalist supposes the existence of a demand and he sometimes even creates demand by artificial means" "And in advertising what typically happens is that the action which the information wishes to provoke will be beneficial not the person who receives the information, but to the person who puts it out" "And that is quite contrary to the notions which underly information" "Do you have an example in mind?" "Yes." "You were talking about ***** and it was a piece of information which could interest the firm ***** but which in general doesn't interest the man watching tv" "I might want to wash my shirt" "Providing you've got a shirt to wash, obviously" "Mathematics might therefore involve the temptation to limit what is possible, without being aware of it" "They give an account, they are the visual expression for limiting the possible" "Mathematicians have huge temptations like children who always want to have things both ways and who always want more of everything... an expression of the human being's desire to get bigger..." "I'd be inclined to say that mathematics are rather the opposite" "That is a sort of regulated failure in which we try to accomplish all possible moves but only on condition that these moves are completely ineffective" "In other words, in order to work out an algebraic structure integrally, passing from natural entities to infinity, if you want to go for an endless walk, you can't accomplish it" "I can accomplish it because there are an infinite number of situations because I feel as though I am a fraction and not a whole number" "Ah, but that's different" "If the whole corresponds to a movement of the body and if you carry out his movement an infinite number of times, you go beyond your capacity and you die" "So if we want to fully represent beings in mathematics by material action, we must suppose that these actions are useless" "The mathematician's vision contains, from the outset, a definite choice which is to suppose that things have no use so as to be able to make them as many times as wanted" "So mathematics are interesting not because they help us accomplish what we've dreamed of, but because they help us dream of what is real" "No, I think that..." "Guerini used to say: "you have to dream as well"" "and he's a materialist" "So saying that dreams are necessary is a materialist idea" "Mathematics can help us to do that perhaps..." "Certainly" "But in order to define the limits of what's possible, you have to, in some sense, dream of what is impossible" "DIRECTING BY"