Saturday, March 6, 2010

A SOCRATIC DIALOGUE ON MATHEMATICS - by Alfred Renyi

from
Dialogues on Mathematics,
Alfred Renyi, Holden Day Publishers, San Francisco, 1967

A SOCRATIC DIALOGUE ON MATHEMATICS

SOCRATES Are you looking for somebody, my dear Hippocrates?

HIPPOCRATES No, Socrates, because I have already found him, namely you. I have been looking for you everywhere. Somebody told me at the agora that he saw you walking here along the River Ilissos; so I came after you.

SOCRATES Well then, tell me why you came, and then I want to ask you something about our discussion with Protagoras. Do you still remember it?

HIPPOCRATES How can you ask? Since that time not a single day has passed without my thinking about it. I came today to ask your advice because that discussion was on mind.

SOCRATES It seems, my dear Hippocrates, that you want to talk to me about the very question I wish to discuss with you; thus the two subjects are one and the same. It seems that the mathematicians are mistaken in saying that two is never equal to one.

HIPPOCRATES As a matter of fact, Socrates, mathematics is just the topic I want to talk to you about.

SOCRATES Hippocrates, you certainly know that I am not a mathematician. Why did you not take your questions to the celebrated Theodoros?

HIPPOCRATES You are amazing, Socrates, you answer my questions even before I tell you what they are. I came to ask your opinion about my becoming a pupil of Theodoros. When I came to you the last time, with the intention of becoming a pupil of Protagoras, we went to him together and you directed the discussion so that it became quite clear that he did not know the subject he taught. Thus I changed my mind and did not follow him. This discussion helped me to see what I should not do, but did not show me what I should do. I am still wondering about this. I visit banquets and the palaestra with young men of my age, I dare say I have a pleasant time, but this does not satisfy me. It disturbs me to feel myself ignorant. More precisely, I feel that the knowledge I have is rather uncertain. During the discussion with Protagoras, I realized that my knowledge about familiar notions like virtue, justice and courage was far from satisfactory. Nevertheless, I think it is great progress that I now see clearly my own ignorance.

SOCRATES I am glad, my dear Hippocrates, that you understand me so well. I always tell myself quite frankly that I know nothing. The difference between me and most other people is that I do not imagine I know what in reality I do not know.

HIPPOCRATES This clearly shows your wisdom, Socrates. But such knowledge is not enough for me. I have a strong desire to obtain some certain and solid knowledge, and I shall not be happy until I do. I am constantly pondering what kind of knowledge I should try to acquire. Recently, Theaitetos told me that certainty exists only in mathematics and suggested that I learn mathematics from his master, Theodoros, who is the leading expert on numbers and geometry in Athens. Now, I should not want to make the same mistake I made when I wanted to be a pupil of Protagoras. Therefore tell me, Socrates, shall I find the kind of sound knowledge I seek if I learn mathematics from Theodoros?

SOCRATES If you want to study mathematics, O son of Apollodoros, then you certainly cannot do better than go to my highly esteemed friend Theodoros. But you must decide for yourself whether or not you really do want to study mathematics. Nobody can know your needs better than you yourself.

HIPPOCRATES Why do you refuse to help me, Socrates? Perhaps I offended you without knowing it?

SOCRATES You misunderstand me, my young friend. I am not angry; but you ask the impossible of me. Everybody must decide for himself what he wants to do. I can do no more than assist as a midwife at the birth of your decision.

HIPPOCRATES Please, my dear Socrates, do not refuse to help me, and if you are free now, let us start immediately.

SOCRATES Well, if you want to. Let us lie down in the shadow of that plane-tree and begin. But first tell me, are you ready to conduct the discussion in the manner I prefer? I shall ask the questions and you shall answer them. By this method you will come to see more clearly what you already know, for it brings into blossom the seeds of knowledge already in your soul. I hope you will not behave like King Darius who killed the master of his mines because he brought only copper out of amine the king thought 'contained gold. I hope you do not forget that a miner can find in a mine only what it contains.

HIPPOCRATES I swear that I shall make no reproaches, but, by Zeus, let us begin mining at once.

SOCRATES All right. Then tell me, do you know what mathematics is? I suppose you can define it since you want to study it.

HIPPOCRATES I think every child could do so. Mathematics is one of the sciences, and one of the finest.

SOCRATES I did not ask you to praise mathematics, but to describe its nature. For instance, if I asked you about the art of physicians, you would answer that this art deals with health and illness, and has the aim of healing the sick and preserving health. Am I right?

HIPPOCRATES Certainly.

SOCRATES Then answer me this: does the art of the physicians deal with something that exists or with something that does not exist? If there were no physicians, would illness still exist?

HIPPOCRATES Certainly, and even more than now.

SOCRATES Let us have a look at another art, say that of astronomy. Do you agree with me that astronomers study the motion of the stars?

HIPPOCRATES To be sure.

SOCRATES And if I ask you whether astronomy deals with something that exists, what is your answer?

HIPPOCRATES My answer is yes.

SOCRATES Would stars exist if there were no astronomers in the world?

HIPPOCRATES Of course. And if Zeus in his anger extinguished all mankind, the stars would still shine in the sky at night. But why do we discuss astronomy instead of mathematics?

SOCRATES Do not be impatient, my good friend. Let us consider a few other arts in order to compare them with mathematics. How would you describe the man who knows about all the creatures living in the woods or in the depths of the sea?

HIPPOCRATES He is a scientist studying living nature.

SOCRATES And do you agree that such a man studies things which exist?

HIPPOCRATES I agree.

SOCRATES And if I say that every art deals with something that exists, would you agree?

HIPPOCRATES Completely.

SOCRATES Now tell me, my young friend, what is the object of mathematics? What things does a mathematician study ?

HIPPOCRATES I have asked Theaitetos the same question. He answered that a mathematician studies numbers and geometrical forms.

SOCRATES Well, the answer is right, but would you say that these things exist?

HIPPOCRATES Of course. How can we speak of them if they do not exist?

SOCRATES Then tell me, if there were no mathematicians, would there be prime numbers, and if so, where would they be?

HIPPOCRATES I really do not know what to answer. Clearly, if mathematicians think about prime numbers, then they exist in their consciousness; but if there were no mathematicians, the prime numbers would not be anywhere.

SOCRATES Do you mean that we have to say mathematicians study non-existing things?

HIPPOCRATES Yes, I think we have to admit that.

SOCRATES Let us look at the question from another point of view. Here, I wrote on this wax tablet the number 37. Do you see it?

HIPPOCRATES Yes, I do.

SOCRATES And can you touch it with your hand?

HIPPOCRATES Certainly.

SOCRATES Then perhaps numbers do exist?

HIPPOCRATES O Socrates, you are mocking me. Look here, I have drawn on the same tablet a dragon with seven heads. Does it follow that such a dragon exists? I have never met anybody who has seen a dragon, and I am convinced that dragons do not exist at all except in fairy tales. But suppose I am mistaken, suppose somewhere beyond the pillars of Heracles dragons really do exist, that still has nothing to do with my drawing.

SOCRATES You speak the truth, Hippocrates, and I agree with you completely. But does this mean that even though we can speak about them, and write them down, numbers nevertheless do not exist in reality?

HIPPOCRATES Certainly.

SOCRATES Do not draw hasty conclusions. Let us make another trial. Am I right in saying that we can count the sheep here in the meadow or the ships in the harbor of Pireus?

HIPPOCRATES Yes, we can.

SOCRATES And the sheep and the ships exist?

HIPPOCRATES Clearly.

SOCRATES But if the sheep exist, their number must be something that exists, too?

HIPPOCRATES You are making fun of me, Socrates. Mathematicians do not count sheep; that is the business of shepherds.

SOCRATES Do you mean, what mathematicians study is not the number of sheep or ships, or of other existing things, but the number itself? And thus they are concerned with something that exists only in their minds?

HIPPOCRATES Yes, this is what I mean.

SOCRATES You told me that according to Theaitetos, mathematicians study numbers and geometrical forms. How about forms? If I ask you whether they exist, what is your answer?

HIPPOCRATES Certainly they exist. We can see the form of a beautiful vessel, for example, and feel it with our hands, too.

SOCRATES Yet I still have one difficulty. If you look at a vessel what do you see, the vessel or its form?

HIPPOCRATES I see both.

SOCRATES Is that the same thing as looking at a lamb? Do you see the lamb and also its hair?

HIPPOCRATES I find the simile very well chosen.

SOCRATES Well, I think it limps like Hephaestus. You can cut the hair off the Iamb and then you see the Iamb without its hair, and the hair without the lamb. Can you separate in a similar way the form of a vessel from the vessel itself?

HIPPOCRATES Certainly not, and I dare say nobody can.

SOCRATES And nevertheless you still believe that you can see a geometric form?

HIPPOCRATES I am beginning to doubt it.

SOCRATES Besides this, if mathematicians study the forms of vessels, shouldn't we call them potters?

HIPPOCRATES Certainly.

SOCRATES Then if Theodoros is the best mathematician would he not be the best potter, too? I have heard many people praising him, but nobody has told me that he understands anything about pottery. I doubt whether he could make even the simplest pot. Or perhaps mathematicians deal with the form of statues or buildings?

HIPPOCRATES If they did, they would be sculptors and architects.

SOCRATES Well, my friend, we have come to the conclusion that mathematicians when studying geometry are not concerned with the forms of existing objects such as vessels, but with forms which exist only in their thoughts. Do you agree?

HIPPOCRATES I have to agree.

SOCRATES Having established that mathematicians are concerned with things that do not exist in reality, but only in their thoughts, let us examine the statement of Theaitetos, which you mentioned, that mathematics gives us more reliable and more trustworthy knowledge than does any other branch of science. Tell me, did Theaitetos give you some examples?

HIPPOCRATES Yes, he said for instance that one cannot know exactly how far Athens is from Sparta. Of course, the people who travel that way agree on the number of days one has to walk, but it is impossible to know exactly how many feet the distance is. On the other hand, one can tell, by means of the theorem of Pythagoras, what the length of the diagonal of a square is Theaitetos also -said that it is impossible to give the exact number of people living in Hellas. If somebody tried to count all of them, he would never get the exact figure, because during the counting some old people would die and children would be born; thus the total number could be only approximately correct. But if you ask a mathematician how many edges a regular dodecahedron has, he will tell you that the dodecahedron is bounded by 12 faces, each having 5 edges. This makes 60, but as each edge belongs to two faces and thus has been counted twice, the number of edges of the dodecahedron is equal to 30, and this figure is beyond every doubt.

SOCRATES Did he mention any other examples?

HIPPOCRATES Quite a few, but I do not remember all of them. He said that in reality you never find two things which are exactly the same. No two eggs are exactly the same, even the pillars of Poseidon's temple are slightly different from each other; but one may be sure that the two diagonals of a rectangle are exactly equal. He quoted Heraclitus who said that everything which exists. is constantly changing, and that sure knowledge is only possible about things which never change, for instance, the odd and the even, the straight line and the circle.

SOCRATES That will do. These examples convince me that in .mathematics we can get knowledge which is beyond doubt, while in other sciences or in everyday life it is impossible. Let us try to summarize the results of our inquiry into the nature of mathematics. Am I right in saying we came to the conclusion that mathematics studies non-existing things and is able to find out the full truth about them?

HIPPOCRATES Yes, that is what we established.

SOCRATES But tell me, for Zeus's sake, my dear Hippocrates, is it not mysterious that one can know more about things which do not exist than about things which do exist?

HIPPOCRATES If you put it like that, it certainly is a mystery. I am sure there is some mistake in our arguments.

SOCRATES No, we proceeded with the utmost care and we controlled every step of the argument. There cannot be any mistake in our reasoning. But listen, I remember something which may help us to solve the riddle.

HIPPOCRATES Tell me quickly, because I am quite bewildered.

SOCRATES This morning I was in the hall of the second archon, where the wife of a carpenter from the village Pitthos was accused of betraying and, with the aid of her lover, murdering her husband. The woman protested and swore to Artemis and Aphrodite that she was innocent, that she never loved anyone but her husband, and that her husband was killed by pirates. Many people were called as witnesses. Some said that the woman was guilty, others said that she was innocent. It was impossible to find out what really happened.

HIPPOCRATES Are you mocking me again? First you confused me completely, and now instead of helping me to find the truth you tell me such stories.

SOCRATES Do not be angry, my friend, I have serious reasons for speaking about this woman whose guilt it was impossible to ascertain. But one thing is sure. The woman exists. I saw her with my own eyes, and of anyone who' was there, many of whom have never lied in their lives, you can ask the same question and you will receive the same answer.

HIPPOCRATES Your testimony is sufficient for me, my dear Socrates. Let it be granted that the woman exists. But what has this fact to do with mathematics?

SOCRATES More than you imagine. But tell me first, do you know the story about Agamemnon and Clytemnestra?

HIPPOCRATES Everybody knows the story. I saw the trilogy of Aeschylus at the theatre last year.

SOCRATES Then tell me the story in a few words.

HIPPOCRATES While Agamemnon, the king of Mycenae, fought under the walls of Troy, his wife, Clytemnestra, committed adultery with Aegisthus, the cousin of her husband. After the fall of Troy, when Agamemnon returned home, his wife and her lover murdered him.
SOCRATES Tell, me Hippocrates, is it quite sure that Clytemnestra was guilty?

HIPPOCRATES I not understand why you ask me such questions. There can be no doubt about the story. According to Homer, when Odysseus visited the underworld he met Agamemnon, who told Odysseus his sad fate.

SOCRATES But are you sure that Clytemnestra and Agamemnon and all the other characters of the story really existed?

HIPPOCRATES Perhaps I would be ostracized if I said this in public, but my opinion is that it is impossible either to prove or disprove today, after so many centuries; whether the stories of Homer are true or not. But this is quite irrelevant. When I told you that Clytemnestra was guilty, I did not speak about the real Clytemnestra - if such a person ever lived - but about the Clytemnestra of our Homeric tradition, about the Clytemnestra in the trilogy of Aeschylus.

SOCRATES May I say that we know nothing about the real Clytemnestra? Even her existence is uncertain, but as regards the Clytemnestra who is a character in the trilogy of Aeschylus, we are sure that she was guilty and murdered Agamemnon because that is what Aeschylus tells us.

HIPPOCRATES Yes, of course. But why do you insist on all this?

SOCRATES You will see in a moment. Let me summarize what we found out It is impossible in the case of the flesh and blood woman was tried today in Athens to establish whether she is guilty, ~while there can be no doubt about the guilt of Clytemnestra who is a character in a play and who probably never existed. Do you agree?

HIPPOCRATES Now I am beginning to understand what you want to say. But it would be better if you draw the conclusions yourself.

SOCRATES The conclusion is this: we have much more certain knowledge about persons who exist only in our imagination, for example: about characters in a play, than about living persons. If we say that Clytemnestra was guilty, it means only that this is how Aeschylus imagined her and presented her in his play. The situation is exactly the same in mathematics. We may be sure that the diagonals of a rectangle are equal because this follows from the definition of a rectangle given by mathematicians.

HIPPOCRATES Do you mean, Socrates, that our paradoxical result is really true and one can have a much more certain knowledge about non-existent things - for instance about the objects of mathematics - than about the real objects of nature? I think that now I also see the reason for this. The notions which we ourselves have created are by their very nature completely known to us, and we can find out the full truth about them because they have no other reality outside our imagination. However, the objects which exist in the real world are not identical with our picture of them, which is always incomplete and approximate; therefore our knowledge about these real things can never be complete or quite certain.

SOCRATES That is the truth, my young friend, and you stated it better than I could have.

HIPPOCRATES This is to your credit, Socrates, because you led me to understand these things. I see now not only that Theaitetos was quite right in telling me I must study mathematics if I want to obtain unfailing knowledge, but also why he was right. However, if you have guided with patience up to now, please do not abandon me yet because only of my questions, in fact the most important one, is still unanswered.

SOCRATES What is this question?

HIPPOCRATES Please remember Socrates that I came to ask your advice as to whether I should study mathematics. You helped me to realize that mathematics and only mathematics can give me the sort of sound knowledge I want. But what is the use of this knowledge? It is clear that if one obtains some knowledge about the existing world, even if this knowledge is incomplete and is not quite certain, it is nevertheless of value to the individual as well as to the state. Even if one gets some knowledge about things such as the stars, it may be useful, for instance in navigation at night. But what is the use of knowledge of non-existing things such as that which mathematics offers? Even if it is complete and beyond any doubt, what is the use of knowledge concerning things which do not exist in reality?

SOCRATES My dear friend, I am quite sure you know the answer, only you want to examine me.

HIPPOCRATES By Heracles, I do not know the answer. Please help me.

SOCRATES Well, let us try to find it. We have established that the notions of mathematics are created by the mathematician himself. Tell me, does this mean that the mathematician chooses his notions quite arbitrarily as it pleases him?

HIPPOCRATES As I told you, I do not yet know much about mathematics. But it seems to me that the mathematician is as free to choose the objects of his study as the poet is free to choose the characters of his play, and as the poet invests his characters with whatever traits please him, so can the mathematician endow his notions with such properties as he likes.

SOCRATES If this were so, there would be as many mathematical truths as there are mathematicians. How do you explain, then, that mathematicians study the same notions and problems? How do you explain that, as often happens, mathematicians living far from each other and having no contact independently discover the same truths? I never heard of two poets writing the same poem.

HIPPOCRATES Nor have I heard of such a thing. But I remember Theaitetos telling me about a very interesting theorem he discovered on incommensurable distances. He showed his results to his master, Theodoros, who produced a letter by Archytas in which the same theorem was contained almost word for word.

SOCRATES In poetry that would be impossible. Now you see that there is a problem. But let us continue. How do you explain that the mathematicians of different countries can usually agree about the truth, while about questions concerning the state, for example, the Persians and the Spartans have quite opposite views from ours in Athens, and, moreover, we here do not often agree with each other?

HIPPOCRATES I can answer that last question. In matters concerning the state everybody is personally interested, and these personal interests are often in contradiction. This is why it is difficult to come to an agreement. However, the mathematician is led purely by his desire to find the truth.

SOCRATES Do you mean to say that the mathematicians are trying to find a truth which is completely independent of their own person?

HIPPOCRATES Yes, I do.

SOCRATES But then we were mistaken in thinking that mathematicians choose the objects of their study at their own will. It seems that the object of their study has some sort of existence which is independent of their person. We have to solve this new riddle.

HIPPOCRATES I do not see how to start.

SOCRATES If you still have patience, let us try it together. Tell me, what is the difference between the sailor who finds an uninhabited island and the painter who finds a new color, one which no other painter has used before him?

HIPPOCRATES I think that the sailor may be called a discoverer, and the painter an inventor. The sailor discovers an island which existed before him, only it was unknown, while the painter invents a new color which before that did not exist at all.

SOCRATES Nobody could answer the question better. But tell me, the mathematician who finds a new truth, does he discover it or invent it? Is he a discoverer as the sailor or an inventor as the painter?

HIPPOCRATES It seems to me that the mathematician is more like a discoverer. He is a bold sailor who sails on the unknown sea of thought and explores its coasts, islands and whirlpools.

SOCRATES Well said, and I agree with you completely. I would add only that to a lesser extent the mathematician is an inventor too, especially when he invents new concepts. But every discoverer has to be, to a certain extent, an inventor too. For instance, if a sailor wants to get to places which other sailors before him were unable to reach, he has to build a ship that is better than the ships other sailors used. The new concepts invented by the mathematicians are like new ships which carry the discoverer farther on the great sea of thought.

HIPPOCRATES My dear Socrates, you helped me to find the answer to the question which seemed so difficult to me. The main aim of the mathematician is to explore the secrets and riddles of the sea of human thought. These exist independently of the person of the mathematician, though not from humanity as a whole. The mathematician has a certain freedom to invent new concepts as tools, and it seems that he could do this at his discretion. However, he is not quite free in doing this because the new concepts have to be useful for his work. The sailor also can build any sort of ship at his discretion, but, of course, he would be mad to build a ship which would be crushed to pieces by the first storm. Now I think that everything is clear.

SOCRATES If you see everything clearly, try again to answer the question: what is the object of mathematics?

HIPPOCRATES We came to the conclusion that besides the world in which we live, there exists another world, the world of human thought, and the mathematician is the fearless sailor who explores this world, not shrinking back from the troubles, dangers and adventures which await him.

SOCRATES My friend, your youthful vigor almost sweeps me off my feet, but I am afraid that in the ardor of your enthusiasm you overlook certain questions.

HIPPOCRATES What are these questions?

SOCRATES I do not want to disappoint you, but I feel that your main question has not yet been answered. We have not yet answered the question: what is the use of exploring the wonderful sea of human thought?

HIPPOCRATES You are right, my dear Socrates, as always. But won't you put aside your method this time and tell me the answer immediately?

SOCRATES No, my friend, even if I could, I would not do this, and it is for your sake. The knowledge somebody gets without work is almost worthless to him. We understand thoroughly only that which - perhaps with some outside help - we find out ourselves, just as a plant can use only the water which it sucks up from the soil through its own roots.

HIPPOCRATES All right, let us continue our search by the same method, but at least help me by a question.

SOCRATES Let us go back to the point where we established that the mathematician is not dealing with the number of sheep, ships or other existing things, but with the numbers themselves. Don't you think, however, that what the mathematicians discover to be true for pure numbers is true for the number of existing things too? For instance, the mathematician finds that 17 is a prime number. Therefore, is it not true that you cannot distribute 17 living sheep to a group of people, giving each the same number, unless there are 17 people?

HIPPOCRATES Of course, it is true.

SOCRATES Well, how about geometry? Can it not be applied in building houses, in making pots or in computing the amount of grain a ship can hold?

HIPPOCRATES Of course, it can be applied, though it seems to me that for these practical purposes of the craftsman not too much mathematics is needed. The simple rules known already by the clerks of the pharaohs in Egypt are sufficient for most such purposes, and the new discoveries about which Theaitetos spoke to me with overflowing fervor are neither used nor needed in practice.

SOCRATES Perhaps not at the moment, but they may be used in the future.

HIPPOCRATES I am interested in the present.

SOCRATES If you want to be a mathematician, you must realize you will be working mostly for the future. Now, let us return to the main question. We saw that knowledge about another world of thought, about things which do not exist in the usual sense of the word, can be used in everyday life to answer questions about the real world. Is this not surprising?
More than that, it is incomprehensible. It is really a miracle.

SOCRATES Perhaps it is not so mysterious at all, and if we open the shell of this question, we may find a real pearl.

HIPPOCRATES Please, my dear Socrates, do not speak in puzzles.

SOCRATES Tell me then, are you surprised when somebody who has traveled in distant countries, who has seen and experienced many things, returns to his city and uses his experience to give good advice to his fellow citizens?

HIPPOCRATES Not at all.

SOCRATES Even if the countries which the traveler has visited are very far away and are inhabited by quite a different sort of people, speaking another language, worshipping other gods?

HIPPOCRATES Not even in that case, because there is much that is common between different people.

SOCRATES Now tell me, if it turned out that the world of mathematics is, in spite of its peculiarities, in some sense similar to our the world in which we live, about the world of human thought, the question remained as to the use of this knowledge. Now we have found that the world of mathematics is nothing else but a reflection in our mind of the real world. This makes it clear that every discovery about the world of mathematics gives us some information about the real world. I am completely satisfied with this answer.

SOCRATES If I tell you the answer is not yet complete, I do so not because I want to confuse you, but because I am sure that sooner or later you will raise the question yourself and will reproach me for not having called your attention to it. You would say: "Tell me, Socrates, what is the sense of studying the reflected image if we can study the object itself?"

HIPPOCRATES You are perfectly right; it is an obvious question. You are a wizard, Socrates. You can totally confuse me by a few words, and you can knock down by an innocent looking question the whole edifice which we have built with so much trouble. I should, of course, answer that if we are able to have a look at the original thing, it makes no sense to look at the reflected image. But I am sure this shows only that our simile fails at this point. Certainly there is an answer, only I do not know how to find it.

SOCRATES Your guess is correct that the paradox arose because we kept too close to the simile of the reflected image. A simile is like a bow - if you stretch it too far, it snaps. Let us drop it and choose another one. You certainly know that travelers and sailors make good use of maps.

HIPPOCRATES I have experienced that myself. Do you mean that mathematics furnishes a map of the real world?

SOCRATES Yes. Can you now answer the question: what advantage would it be to look at the map instead of looking at the landscape?

HIPPOCRATES This is clear: using the map we can scan vast distances which could be covered only by traveling many weeks or months. The map shows us not every detail, but only the most important things. Therefore it is useful if we want to plan a long voyage.

SOCRATES Very well. But there is something else which occurred to me.

HIPPOCRATES What is it?

SOCRATES There is another reason why the study of the mathematical image of the world may be of use. If mathematicians discover some property of the circle, this at once gives us some information about any object of circular shape. Thus, the method of mathematics enables us to deal with different things at the same time.

HIPPOCRATES What about the following similes: If somebody looks at a city from the top of a nearby mountain, he gets a more comprehensive view than if he walks through its crooked streets; or if a general watches the movements of an enemy army from a hill, he gets a clearer picture of the situation than does the soldier in the front line who sees only those directly opposite him.

SOCRATES Well, you surpass me in inventing new similes, but as I do not want to fall behind, let me also add one parable. Recently I looked at a painting by Aristophon, the son of Aglaophon, and the painter warned me, "If you go too near the picture, Socrates, you will see only colored spots, but you will not see the whole picture."

HIPPOCRATES Of course, he was right, and so were you, when you did not let us finish our discussion before we got to the heart of the question. But I think it is time for us to return to the city because the shadows of night are falling and I am hungry and thirsty. If you still have some patience, I would like to ask you something while we walk.

SOCRATES All right, let us start and you may ask your question.

HIPPOCRATES Our discourse convinced me fully that I should start studying mathematics and I am very grateful to you for this. But tell me, why are you yourself not doing mathematics? Judging from your deep understanding of the real nature and importance of mathematics, it is my guess that you would surpass all other mathematicians of Hellas, were you to concentrate on it. I would be glad to follow you as your pupil in mathematics, if you accepted me.

SOCRATES No, my dear Hippocrates, this is not my business. Theodoros knows much more about mathematics than I do and you cannot find a better master than him. As to your question of why I myself am not a mathematician, I shall give you the reasons. I do not conceal my high opinion about mathematics. I think that we Hellenes have in no other art made such important progress as in mathematics, and this is only the beginning. If we do not extinguish each other in mad wars, we shall obtain wonderful results as discoverers as well as inventors. You asked me why I do not join the ranks of those who develop this great science. As a matter of fact, I am some sort of a mathematician, only of a different kind. An inner voice, you may call it an oracle, to which I always listen carefully, asked me many years ago, "What is the source of the great advances which the mathematicians have made in their noble science?" I answered, "I think the source of the success of mathematicians lies in their methods, the high standards Of their logic, their striving without the least compromise to the full truth, their habit of starting always from first principles, of defining every notion used exactly and of avoiding self-contradictions." My inner voice answered, "Very well, but why do you think, Socrates, that this method of thinking and arguing can be used only for the study of numbers and geometric forms? Why do you not try to convince your fellow citizens to apply the same high logical standards in every other field, for instance in philosophy and politics, in discussing the problems of everyday private and public life?" From that time on, this has been my goal. I have demonstrated (you remember, for instance, our discussion with Protagoras) that those who are thought to be wise men are mostly ignorant fools. All their arguing lacks solid foundation, since they use - contrary to mathematicians - undefined and only half-understood notions. By this activity I have succeeded in making almost everybody my enemy. This is not surprising because for all people who are sluggish in thinking and idly content to use obscure terms, I am a living reproach. People do not like those who constantly remind them of the faults which they are unable or unwilling to correct. The day will come when these people will fall upon me and exterminate me. But until that day comes, I shall continue to follow my calling you, however, go to Theodoros.


AUTHOR’S POSTSCRIPT

An optimistic author does not write a preface to his book, because he is confident that it will speak for itself and he is convinced that the readers will understand what he wants to say without any additional explanation. While I am an optimist, I felt that in the case of this book, if not a preface at least a postscript was needed on the aims of the author and on the considerations which led him to choose the literary form of the dialogue. I add these remarks in the form of a postscript because I really want them to be read after the dialogues.

The interest in mathematics and its applications is increasing year by year in every country among an increasing number of people. I have been asked several times to give popular talks on mathematics; on such occasions I noticed that many people were primarily interested in finding out what mathematics really was, what its specific method consisted of, what its relation to the sciences and humanities was and what it could offer to those working in different fields. I found also that those who attended such lectures on mathematics or who were ready to read books on mathematics written for non-specialists usually wanted simply to broaden their outlook rather than to acquire specific mathematical methods. Even those who actually needed a knowledge of mathematics for their work, before deciding to study seriously a particular part of mathematics, wanted to find out what they could expect from it, especially since the study of mathematics is not easy for those unused to it.

While talking about mathematics to non-mathematicians I encountered quite a number of prejudices, misunderstandings and misconceptions, not only among people whose main interests and activities are quite far from mathematics but also among those who through their profession have a certain knowledge in some part of the field. This is really not surprising as those people who have some knowledge but do not have sufficiently broad vision or sufficiently deep insight, are most inclined to make false generalizations. I found also that the principles of mathematics and of its applications are often disputed even among mathematicians and many questions in this field are subject to controversy.

These circumstances convinced me that there exists a real need for a discussion of the basic questions of mathematics and its applications in a manner which while comprehensible to non-specialists, , yet presents these problems in their full complexity .I realized that it would not be an easy task to make such questions understandable to the general public, therefore I searched for a special method to bring abstract problems nearer to the layman. This search led me to experiment with the Socratic form of a dialogue. The Socratic dialogue presents thoughts while they are being created and dramatizes ideas. By so doing it keeps the attention awake and facilitates understanding.

I chose as the central theme of the first dialogue the question "What in fact is mathematics?" I consider the discussion of this question especially important because the teaching of mathematics in elementary and high schools is still far from giving a clear-cut, correct and up-to-date answer.
In this dialogue I tried to follow as closely as possible the method and even the language of the original Socratic dialogues. Socrates himself is the main actor and the discussion takes place in the period when mathematics, in the sense that it has been understood ever since, was born; thus mathematics is presented to the reader "in statu nascendi." In the dialogue Socrates applies his peculiar method of discussion: by the phrasing of his questions he leads his partner to understand the issue. Thus a Socratic dialogue is not the clash of two points of view; rather the participants try to find out the truth together. By a logical analysis of the concepts involved they arrive at an answer to the questions step-by-step. During the discussion the participants often make statements - sometimes in a quite categorical form - which they later realize to be false. Thus a Socratic dialogue is an organic whole and its real meaning can be understood only if one reads it from beginning to end, if possible without interruption. All these features make a Socratic dialogue lively and vivid, and so I found this form particularly suitable to my aims.
I had still another reason for choosing this form: it is my firm belief that the Socratic method is basically cognate with the mathematical method. In this belief I was very much strengthened by the recent fundamental research work of Arpad Szab, which has thrown quite a new light on the origin of Ancient Greek mathematics.

The first dialogue was published in Hungarian1 in 1962. In 1963 a French translation appeared in Les Cahiers Rationalistes.2 In 1963 I presented this dialogue as an after-dinner talk to the meeting of American Physicists in Edmonton, and an English version was published both in the Canadian Mathematical Bulletin3 and in Physics Today4 and was reprinted by the journal Simon Stevin5 too. Since then it has also appeared both in German6 and Portuguese7 translations.
The favorable reception of the first dialogue both among mathematicians and among non-mathematicians encouraged me to continue experimenting with this genre. A second dialogue was first presented at the University of Toronto in 1964 and appeared in English in the Ontario Mathematics Gazette8 and later in Simon Stevin9.

Since in the first dialogue I had discussed the relation of mathematics to reality only in a general philosophical sense, in the second I wanted to make central a more detailed discussion of the applications of mathematics. It was logical to choose Archimedes as the chief character of such a dialogue as his name even in ancient times was inseparably connected with such applications. The historical frame of the second dialogue, however, did not allow me to say all that I wanted about this controversial topic.

Thus I felt I had to write a third dialogue, the chief character of which was Galileo, the first thinker in modem times who fully realized the central importance of the mathematical method in discovering the laws of nature, and who propagated his conviction with great force. The second and third dialogues thus complement each other, and also the first. They are, however, essentially different from the first in form and style. Archimedes and Galileo do not, of course, use the method of Socrates: instead of guiding their partner to guess their thoughts, they express them themselves. Thus I had to dispense with the main source of inner tension which the Socratic dialogue provides. I tried to compensate for this loss by putting these dialogues in extremely decisive historical situations, the dynamics of which were inseparably connected with the issues of the dialogues and would thus amplify their tension.

Featuring Archimedes and Galileo made it possible to touch in these dialogues on much more specialized mathematical topics than were discussed in the first one, especially on such ideas which originated with Archimedes and Galileo themselves; I tried to incorporate in some form or other most of their famous achievements.

In this connection I must say a few words about how I dealt with historical facts. In all three dialogues I tried hard to avoid every sort of anachronism. I was careful not to attribute to my characters any such knowledge of mathematics as well as of other things) which they could not possibly possess at that time. However as both Archimedes and Galileo were pioneers whose ideas and way of thinking were not only far ahead of their time but also are modern even when measured by present day standards, I was not prevented from including in these dialogues everything I deemed important to say. Of course, in order to avoid anachronism I had to restrict myself mainly to examples from elementary mathematics; I could thus go into infinitesimal mathematics but only as far as Archimedes and Galileo did themselves. This restriction, however, had certain advantages because it forced me to avoid examples which would have been too difficult for the non-mathematician.

I did not, however, interpret the requirement of historical faithfulness so rigidly as to attribute to my characters only such views and ideas which they certainly possessed; I felt free to attribute to them views and ideas at which they may have arrived, particularly if these were logical developments of such ideas with which they were definitely familiar. In cases, however, where it is known they had erroneous beliefs, I felt compelled not to hide the fact. Thus, for instance, it is known that Galileo thought that the planets move in circles around the Sun and he did not understand the role of gravitation; so Galileo speaks about these questions accordingly. On the other hand, I thought it admissible to make such bold conjectures as, for instance, that Archimedes arrived at certain ideas which are nowadays classified under cybernetics and that he planned a machine for sieving primes.10 I cannot support such conjectures by any document, and of course do not consider them as well founded; the only thing I claim is that it is not unthinkable that these conjectures are true and, furthermore, that the facts at our disposal are as insufficient to disprove these conjectures as to prove them. I thought that "poetic license" entitled me to use such hypotheses as these.

As for the historical background of the second and third dialogues, I kept to the facts in every essential point. The only exception, where I departed consciously from the facts, is in the second dialogue where King Hieron is directing the defense of Syracuse in the siege of the year 212 B.C., while in reality he died three years earlier. However, both dialogues contain the description of hypothetical events about which we have no definite knowledge, but which are not contradicted by known facts. This is the case, for instance, with the plan of helping Galileo to escape: we do not know whether Torricelli and his friends really had such a plan, but it is not at all impossible.
The essential content (though usually not the wording) of some sentences in the dialogues is either directly attributable to my characters or attributed to them by their contemporaries. This is the case, for example, when Socrates talks about himself11, Archimedes about his method12 and Galileo about the language of the book of nature.13 Such sentences (and only these) are printed in italics.

I have tried to present the personalities of my characters as faithfully as possible. In the case of the third dialogue, the drama of L. Nemeth influenced me greatly: I took from it, among other things, the idea of presenting Torricelli and Signora Niccolini.
For those who want to study the historical background of these dialogues, a selected bibliography is added which does not aim at completeness; it contains only such books I found particularly useful in the collection of my material.

I hope this postscript makes clear what my aims were in writing these dialogues. It is up to the reader to judge how far I was able to realize my intentions.

ALFRED RENYI

1 Dialogus a matematikarol, Valosag, 3, 1-19, 1962.
2 On dialogue, Les Cahiers Rationalistes, 33, NO.208-209. Janvier- Fevrier, 1963.
3 A Socratic dialogue on mathematics, Canadian Mathematical Bulletin, 7, 441-462, 1964.
4 A Socratic dialogue on mathematics, Physics Today, December, 1964, pp. 1-36.
5 A Socratic dialogue on mathematics, Simon Stevin, 38, 125-144, 1964-1965.
6 Sokratischer Dialog, Neue Sammlung, 6, 284-304, 1966.
7 A matematica – Un Dialogo Socratico, Gazeta de Matemtitica, 7.6, No. 100, Julho-Dezembro 1965, pp. 59-71.
8 A dialogue on the applications of mathematics, Ontario Mathematics Gazette, 3, No.2, 28-40, 1964.
9 A dialogue on the applications of mathematics, Simon Stevin, 39, 3-17, 1965.
10 Such an apparatus was first described by D. H. Lehmer (A photoelectric number sieve, American Mathematical Monthly, 4°, 401-406, 1933).
11 See for example "The Apology of Socrates" (Great Dialogues of Plato, translation by W. H. D. Rouse, edited by Eric H. Warmington and Philip G. Rouse, Mentor Books, 8th printing, New York, 423-446, 1962).
12 See the letter of Archimedes to Eratosthenes (The works of Archimedes, with the method of Archimedes, edited by T. L. Heath, Dover, New York, 1960 ) .See particularly the following sentences on page 13:
"Certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards, because their investigation by the said method did not furnish an actual demonstration. But it is of course easier when we have previously acquired by the method, some knowledge of the question, to supply the proof than it is to find it without any previ- ous knowledge."
13 See particularly in the letter of Galileo called "The Assayer" (Discoveries and opinions of Galileo, translated with an introduction and notes by Stillman Drake, Doubleday Anchor Books, New York, 237-238, 1957), the following sentences:
"Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics.”
SELECTED BIBLIOGRAPHY
A Socratic Dialogue on Mathematics
Rouse, W. H. D. (trans.), Great Dialogues of Plato (Mentor Books, New York, 1962).
Szabo, A., Wie ist die Mathematik zu einer deduktiven Wissenschaft geworden, Acta Antiqua Acad. Sci. Hung., 4, 109-152, 1956.
• Die Grundlagen der fri.ihgriechischen Mathematik, Studi Italiani di Filologia Classica, 3°, 1-51, 1958.
• The transformation of mathematics into deductive science and the beginnings of its foundation on definition and axioms, Scripta Mathematica, 27, 27-48, 1960.
• Anfange des Euklidischen Axiomensystems, Archive for History Of Exact Sciences, 1, 37-106, 1960.
• Der alteste Versuch einer definitorisch-axiomatischen Grundlegung der Mathematik, Osiris, 14, 308-369, 1962.
A Dialogue on the Applications of Mathematics
Clagett, M., Greek science in antiquity (Collier, New York, 1955). Heath, T. L., The works Of Archimedes with the method Of Archimedes (Dover, New York, 1960).
• A manual of Greek mathematics (Dover, New York, 1963).
A Dialogue on the Language of the Book of Nature
Annitage, A., The world of Copernicus (Signet Science Library, New York, 1947).
Drake, S., Discoveries and opinions of Galileo (Doubleday, New York, 1957).
Fenni, L. and G. Bernardini, Galileo and the scientific revolution (Fawcett World Library, New York, 1965).
Galilei, G., Dialogues concerning two new sciences (Dover, New York, 1914).
• Dialogue concerning the two chief systems-Ptolemaic and Copernican (translated by Stillman Drake, foreword by Albert Einstein. University of California Press, Berkeley and Los Angeles, 1962).
Geymonat, L., Galileo Galilei (Einaudi, Rome, 1957).
Santillana, G. de, The crime of Galileo (Mercury, London, 1961).

A note from an article on the net:

Alfred Renyi was a famous probabilist and number theorist, co-creator with Paul Erdos of the subject random graphs, and for many years director of the Institute of Mathematics in Budapest. This is a most inviting, charming and thought-provoking tour de force and jeu d’esprit. It poses the basic problem, and answers it in a way that invites further questioning and deeper development. Apparently Prof. Renyi used to give live performances of this work, assisted by his daughter Zsuzsanna, to whom he dedicated the book Dialogues on Mathematics (1967).

A Socratic Dialogue on Art and Beauty - By Trevor Coffrin

[The following is a Socratic dialogue I have written to help get at the meaning of the word beauty. All characters are fictional, except of couse, for Socrates]. Atreus is the director of the Art Gallery of Athens, and has to determine which of two paintings will be displayed in the main foyer of the gallery during the grand opening next week. Unfortunately, the foyer can only accommodate one of the paintings, and since it will be this painting that will receive the most attention and make the strongest impression with the gallery visitors, Atreus wants to ensure he places the more beautiful of the two paintings there. Finally Atreus decides which of the two paintings is more beautiful and hangs it in the foyer.

The next day, Atreus spots his old friend Socrates walking by the gallery, and asks Socrates what he thinks of the painting in the main foyer. Socrates exclaims that the painting is exquisite. Atreus then goes on to tell Socrates of the difficulty he had in trying to decide which of two paintings was to be hung in the foyer. Atreus explains that after much difficulty, he finally determined which of the two paintings was more beautiful. Upon hearing this, Socrates has the following conversation with Atreus.

SOCRATES: Atreus, I envy you greatly. If I was curator of this gallery, I would have spent a lifetime deciding which of two paintings were more beautiful, yet it only took you a single day.

ATREUS: Surely Socrates you do not give yourself enough credit. You are one of Athens most intellectually gifted citizens. You would have no difficulty in determining which of two things were more beautiful.

SOCRATES: No Atreus, you give me too much credit. I would never be so foolish as to claim that I could determine which of two things were more beautiful, for I do not even know what beauty is.

ATREUS: Surely you must know what beauty is. The notion of beauty comes so naturally to us that to claim not to know is simply foolish. Even a child knows what beauty is. Are you just putting me on, Socrates?

SOCRATES: Not at all Atreus, I am only asking what beauty is out of complete and utter sincerity. Please won’t you lend me a moment of your precious time and impart on me your knowledge in this particular area?

ATREUS: Very well Socrates. Beauty is that which we find physically attractive, things that are pretty, things that look good, are pleasant to look at, pleasing to the eye and so forth. Surely you would agree?

SOCRATES: So Atreus, beauty is simply that which pleases the eye?

ATREUS: Of course, Socrates. It is as simple as that. You see, the notion of beauty is not a difficult concept to grasp; you understand it already.

SOCRATES: My dear Atreus, I am troubled by one thing. What are we to make of music that people speak of as beautiful? Are we to say that they are mistaken in their thinking and that only that which is physically appealing is beautiful?

ATREUS: No, Socrates, of course not, music too can be beautiful.

SOCRATES: But I thought beauty was that which is pretty, pleasing to the eye, things that look good, etc. Are you now saying that your definition of beauty was inadequate? If so Atreus, please try again to tell me what beauty is and be as exact as you can in your explanation this time.

ATREUS: We will simply adjust our definition of beauty to include those things that also sound beautiful. Will that do?

SOCRATES: I am not sure, Atreus. We’ll have to investigate this new definition further to see if our understanding of beauty is adequate. Let me ask you this Atreus, is our dear old friend Cronus beautiful? (Here I imagine the fictional character Chronus to be a withered unattractive old man).

ATREUS: Surely Socrates, most would not think so. Cronus is of such an old age that any beauty that once was with him has now left.

SOCRATES: But Atreus, our friend Cronus has given all his wealth to charity, has worked a lifetime as a volunteer, and is widely considered a virtuous person by all who have met him. Would it be wrong to say that Cronus’ character has moral beauty?

ATREUS: No, I suppose it would not be wrong to say that Socrates. I would agree that Cronus’ character is morally beautiful.

SOCRATES: Therefore I am left to conclude that beauty is not only that which is appealing visually and audibly, but there can also be beauty in character, is this correct Atreus?

ATREUS: Yes this is so Socrates.

SOCRATES: And what is it about Cronus’ moral character that makes him beautiful?

ATREUS: Cronus’ moral character is considered beautiful because the acts he performs are morally praiseworthy; his acts are good acts.

SOCRATES: Ah, so am I to understand that beauty must express good in order to be beautiful?

ATREUS: Yes Socrates, that is right. What has beauty must express good.

SOCRATES: Good Atreus, you are doing better. I feel we are getting closer to understanding what beauty is. Now, is beauty a part of good, or is good a part of beauty? Or do both terms have identical meaning?

ATREUS: I am afraid I don’t understand the question Socrates.

SOCRATES: Is all that is beautiful good, or is all that is good beautiful?

ATREUS: All that is beautiful is good.

SOCRATES: Yes, but what about the second part of the question, Atreus? Is all that is good beautiful?

ATREUS: No, Socrates. All that is good is not beautiful. For example, we might say that Pythagoras is good at math, but it would be inaccurate to say that Pythagoras is beautiful at math. So good and beauty are not interchangeable terms.

SOCRATES: Very good Atreus. So we shall say that beauty must be good in order to be rightfully considered beauty. But let me ask you this Atreus. Do you consider plays to be beautiful?

ATREUS: Of course Socrates, there is great beauty in plays. A play is a work of art. A play is a beautiful thing, it expresses raw human emotion, it teaches, it entertains, etc.

SOCRATES: And what about the play Orecleia, Atreus? Have you seen it? (This is a fictional play created for this dialogue)

ATREUS: Yes Socrates, I have seen it. It is a beautiful play, with all of its elegant costumes, poetic dialogue, and so on. Orecleia is a true work of art.

SOCRATES: But Atreus, the central message in Orecleia is terribly immoral; it is about cheating, stealing, and lying. Its main characters are completely immoral too. Are we to still say that it is beautiful even though it contains much that is not good?

ATREUS: Of course Orecleia is still a beautiful play, Socrates, even with all the immoral elements.

SOCRATES: But why, Atreus? We have already said that that which is beautiful must be good, yet Orecleia has much that is bad. Are we to now say that beauty can express something bad and still be beautiful?

ATREUS: Yes, it looks that way Socrates. I am not prepared to say that Orecleia is not beautiful just because it contains bad; I maintain that it is a beautiful play. Therefore, I am left to conclude that beauty can contain bad and still be beautiful.

SOCRATES: Lets not be too hasty now in our conclusions Atreus. Maybe people find the play beautiful in spite of the fact that it contains some bad? In other words, maybe the play is beautiful because it contains more good than bad?

ATREUS: By Zeus, Socrates, that’s it. Beauty can still be found in that which contains some bad, as long as there is more good overall than bad.

SOCRATES: So do the people only like the morally good parts of the play? That is, do they only find beauty in the parts of the play that have a good moral message?

ATREUS: No, people enjoy the immoral aspects of the play too. People enjoy the conniving characters who cheat, lie, steal, etc. These characters do not detract from the beauty of the play; in fact, I think they add to its beauty. These unsavoury characters serve to make the play more interesting and more realistic; true to life.

SOCRATES: Do you not see what you have done just now, Atreus? You have admitted that people find beauty in badness too. Therefore, how can we hold that beauty must express good in order to be beautiful?

ATREUS: I don’t know Socrates. I just know beauty when I see it. I sometimes find that which is bad beautiful, sometimes that which is good beautiful. Beauty is up to the person judging it.

SOCRATES: I see Atreus. Perhaps this new revelation will lead us to the answer of what beauty is. If beauty is up to the person judging it, then can everything be beautiful? Can even the most disgusting of creatures, the most mournful music, and the most conniving character be beautiful?

ATREUS: No Socrates, of course not. There are limits as to what can be beautiful.

SOCRATES: Great Atreus. We are now on the brink of discovering what beauty is. Tell me what the limits are to beauty. For surely where the limits of beauty are to be found, we will find the true essence of beauty.

ATREUS: Please Socrates, I have grown weary upon this endless questioning. I am not able to describe the limits of beauty. I will give one last attempt at defining beauty. See this flower that grows here? This flower is beautiful.

SOCRATES: In virtue of what is this flower beautiful?

ATREUS: This flower is beautiful in virtue of the way it makes me feel. This flower instils in me a feeling of beauty.

SOCRATES: So beauty is a feeling?

ATREUS: Beauty is that which one feels when one is looking at something appealing, or pleasing to the senses, such as this flower.

SOCRATES: So beauty is that which one feels when sensing something appealing. But appealing is the word you used to describe beauty. Therefore, your claim would be that beauty is that which one feels when one is looking at something beautiful. My dear Atreus, you have not given me any clearer picture of what beauty is than what I already had before I came here. I feel that if we spend just a few hours longer, we will be able to determine just what beauty is, Atreus. Won’t you stay and enlighten an old fool?

ATREUS: Please Socrates, I must go. I have just remembered some final preparations for the gallery that I need to do right away. Goodbye Socrates.

What I have intended to show here is an example of a Socratic dialogue. Like most other dialogues, Socrates, or one of his friends is confronted with a dilemma of a philosophical nature. At the heart of this dilemma is the true meaning of the term “beauty.” In this dialogue, Socrates claims to have no clear notion about what beauty is, yet his interlocutor, Atreus is considered somewhat of an expert in this area. Atreus, feeling confident he knows what beauty is, gives in to Socrates’ plea to define the term. In Atreus’ attempt to define beauty, Socrates finds problems with each definition.

The philosophical aim of this dialogue was to demonstrate that Atreus’ understanding of beauty was inadequate. Continually Atreus has to expand his definition of beauty in order to please Socrates. The end goal was to get Atreus to contradict himself. Just when Atreus feels as though he has given a thorough, all-encompassing definition of beauty, he ends up contradicting himself. He says that all that is beautiful must be good, but then he is forced to admit that there is beauty in what is bad too. Finally Atreus gives one last attempt at defining the term, but this too, is not good enough for Socrates.

Thursday, March 4, 2010

SYSTEMS SENSITIVE DIALOGUE INTERVENTION - by Sebastian Slotte

Systems Analysis Laboratory, Helsinki University of Technology, Espoo, Finland
P.O.Box 1100, FIN-02015 HUT, Finland
Email: sebastian.slotte@hut.fi
Tel. +358 50 376 1967
Fax +358 9 451 3096

Abstract

The paper presents a general methodology for dialogue interventions, Systems
Sensitive Dialogue Intervention Dialogue interventions are viewed in the light of Gerald
Midgleys general presentation of systemic intervention. By focusing on the dialogue
philosophy of Martin Buber and the key elements in two popular dialogue methods it is
proposed that a) enhancing individual participants sensitivity to the unique human system
they form is the primary task of a dialogue intervention, b) when designing dialogical
interventions it is useful to creatively use elements from different available dialogical
methods and c) dialogue interventions should be designed in experiential and existential
rather than in metaphysical terms.

Keywords: dialogue, systemic intervention, methodology

INTRODUCTION

Dialogue methods consist of specific rules and guidelines that aim to improve group
interaction, collective learning and investigation. The central task of a dialogue is to provide
a setting for communication and thinking in a group. Normally, the guidelines and rules for
everyday debates, discussions and meetings are tacit. Of course, tacit rules vary from
organization to organization and from culture to culture, and it is contingent which rules are
applied. In dialogue interventions these rules and guidelines are made explicit.

Over the past ten years, dialogue has made a breakthrough in a number of fields.
Dialogue has been recommended by organizational theoreticians and introduced in
organizations for various purposes. The systems thinking variant of the learning organization
(Senge, 1990; Senge et al., 1994), the knowledge creating company (Nonaka and Takeuchi,
1995) and the notion of corporate culture (Schein, 1999) are examples of general
organizational theories which regard dialogue as a central organizational practice. Dialogue
and dialogical methods are presented as a core practice of specific organizational areas such
as team learning (Senge, 1990; Senge et al., 1994), leadership programs (Frydman et al.,
2000), corporate responsibility and human rights (Frankental et al., 2000) and Business
Ethics (Maclagan, 2000; van Hooft 2000).

Moreover, dialogue has been implemented in participatory planning(Väntänen et. al,
2003) community building (Freire, 1972), and in national and international conflict
resolution (Deutsch and Coleman, 2000; Susskind et al., 1999). Educational dialogue has
been presented as an alternative to traditional teacher and fact centered education (Norris,
2003). Moreover, general recipes for dialogical interventions and consultancy have been put
forth by theoreticians and practitioners alike (Ellinor and Gerard 1998; Flick, 1998; Isaacs,
1999; Simmons, 1999; Yankelovich, 1999).

The effort of this paper is to contribute to the development of a methodology for
Dialogue Interventions called Systems Sensitive Dialogue Intervention. In accordance
with Midgleys (2000) theory of systemic intervention, it is proposed that a methodology
is an important aid for practitioners and researchers in designing proper and effective
dialogue interventions.

A proper dialogue intervention is defined as aiming at enhancing participants’
sensitivity to the human system they form together. This sensitivity to the relational,
inquiring, and synergetic is constitutive to dialogue. An effective dialogue intervention
produces through appropriate dialogue produces a desirable outcome e.g. improvement,
from the whole systems viewpoint.

The notion of Systems Sensitive Dialogue Intervention is a result of empirical
experimentation with various dialogue methods and combinations. The interventions
where carried out in various fields such as education (Hjelm and Slotte, 2001; Slotte and
Hjelm, 2002; Slotte 2003), decision making (Slotte and Hämäläinen, 2003), and natural
resources conflict management (Väntänen et al., 2003).

The research is related to a multidisciplinary research project on Systems
Intelligence (Hämäläinen and Saarinen, 2004) of which dialogue is an integral part.
The presentation of Systems Sensitive Dialogue Intervention is organized in the
following way. Firstly, dialogue interventions are discussed in the light of Midgely’s
(2000) theory of Systemic Intervention. Secondly, reservations against the benefits of
dialogue are discussed with references to Stacey (2001). Systems Sensitive Dialogue
Interventions are presented as enhancing systems sensitivity in participants, resting on a
creative use of methods and avoiding normative metaphysical demands.

METHODOLOGY

Recently, there have been some disputes about which methods create proper and
efficient dialogue an are the most accurate (Kessels, 2001; Platts, 2002). The claim
made here is that such discussions become obsolate if one takes the human system and
its particular needs as a starting point for dialogue interventions. Rather than asking
which method is the correct one, the practitioner should consider what he can do and
which actions and methods in any particular situation create proper dialogue e.g. an
atmosphere of joint investigation, thinking together, inquiry, reflection and respect
(Boele, 1997; Bohm, 1996; Buber, 1947) in a human system, such as a team, a class, a
family, a group of stakeholders, a management team etc. The laws of social behavior are
not as rigid as the laws of mechanism and nature. The same method is likely to produce
different outcomes in different settings. Accordingly, we cannot expect that one method
will produce proper dialogue in every situation. Rather, proper dialogue is reached
through a creative use of different methods.

According to Midgley (2000), a methodology for systemic intervention should
take action for improvement as an explicit starting point. Improvement is defined
temporarily and locally as different human systems and agents may use different
boundary judgments (Midgley, 2000). In Systems Sensitive Dialogue Intervention,
improvement is viewed through the realization of the desired consequences of the
human system engaged in dialogue. The goals of the different dialogue methods
include, for example, the clarification of a concept, conflict resolution and improved
joint investigation. When a particular aim is realized it represents improvement, if the
system engaged in dialogue judges so.

Thus, the methods to facilitate dialogue interventions should not be regarded as
static but flexible and should be chosen in compliance with the expectations, needs,
fears, values and maturity of the individuals participating, and with the human system
they together create.

Finally, it is proposed that not only the facilitator of a dialogue intervention
should be open about his normative vision (Midgley, 2001; Midgley and Ochoa-Arias,
1999) but not impose it.The that participants engaged in a dialogue intervention should
be encouraged to reflect on ideological, metaphysical and pragmatic boundaries
(Midgley, 2001).

CHALLENGES

In recent criticism the impact of dialogue has been questioned. A powerful
argument against dialogue as presented by Senge and Bohm is made by Stacey (2001).
Stacey makes a strong case about learning and knowledge creation in organizations and
argues that dialogue is an attempt to return to the ancient wisdom and conversational
patterns of old cultures, such as those of North American Indians. Stacey rebukes this
attempt as a nonsensical romantic idea of a lost Eden.

However, the references to Native Americans should be regarded as a
pedagogical way of illustrating alternatives to aggressive debate, advocacy and
dialectics. The rise of the principles and the practice of dialogue is, in fact, a highly
modern phenomenon with purely European roots (Taylor, 1989; Walker,1999). Of
course, dialogue was a central way to engage in theoretical matters with practical
implications in the days of Socrates (Zanakis et al., 2003) and during the Hellenistic era
of philosophy, the practice of dialogical skills, such as listening and presence became a
central skill in the philosophical quest for a good life (Hadot, 1995). But not before the
first half of the 20th century did philosophers, such as Leonard Nelson, Martin Buber,
and Mikhail Bakhtin formulate the basic ideas of dialogue as a practice that all men and
women can and should engage in (Bradbury and Lichtenstein 2000). It is these
philosophies of dialogue that organizational practitioners, theoreticians, educationalists
and consultants today, indirectly or directly, are building on in real world interventions.
In opposition to Bohm’s and Senge’s dialogue conception, Stacey (2001) wants to
draw attention to the multitude of everyday conversations that can be very creative but also
very destructive. Moreover, Stacey claims that organizational theoreticians and consultants,
instead of presenting dialogue and other conversational tools of an idealized kind, should
focus on understanding the communicative interaction we currently engage in within
hierarchical organizations. The answer to Stacey on this point is that there is extensive
evidence suggesting that ordinary communication and the thinking that accompanies it often
goes wrong in ways that may have negative, sometimes fatal, impact on a wide variety of
organizational aspects: failure of organizational change programs, failure of strategic
programs, and collapse of internal and external ethics (Dalla Costa, 1999; De Geuss, 1999;
Senge et al., 1999). It is widely accepted that ordinary communication and thinking can, and
at times should, be the object of change (Huczynski and Buchanan, 2001; Janis, 1982). Far
from being an idealization, dialogue takes into account ordinary ways of communication and
can, in the form of dialogue sessions, be a complement to these. The lessons and skills
learned in dialogue session can also be transformed and incorporated into other more
ordinary forms of communication and interaction (Slotte, 2004).

According to Stacey (2001), dialogue assumes a distinction between the
individual and the collective mind. Stacey argues that the individual and the group are
the same phenomenon and that there is no transcendent whole, or group mind, or
common pool of meaning outside of it. Rather, common meaning emerges in the
communicative interaction between people in their local situation in the present (Stacey,
2001). However, dialogue is fundamentally not resting on such an ontological split, but
rather in line with the view Stacey holds on this particular issue. Bohm whose ideas
about dialogue the argument is directed against, clearly states (Bohm 1992; Bohm 1996)
that individual thinking is dependent on cultural structures of thought and that
individual thinking has an impact on the common structure and content of thought in a
given culture. In fact, dialogue rest on the idea that individual thoughts and collective
thought are not separate but necessarily affecting each other. Dialogue is rather in line
with constructivism (Gergen et al., 2002). However, Stacey must be credited for his
indirect criticism of attempts to present dialogue as resting more or less on mysticism
and as a strive for predetermined metaphysical insights. I will return to this point in the
next to last section of the paper.

SYSTEMS FOCUS

Common for the different conceptions and methods of dialogue is the attempt to
overcome individual and social barriers for sharing meaning, values and understanding.
Dialogue has proven to be a powerful way of intervening, for example, in situations
were threats to joint investigation, mutual respect and meaningful communication such
as groupthink ,(Janis, 1982) defensive and limiting interpersonal reasoning are strong
(Kahneman et al., 1982).

Martin Buber’s (1947) philosophy of dialogue paves the way towards seeing a
group of dialoguers as a special kind of human system. Buber’s views on dialogue have
been applied in counseling and to some extent in conflict situations (Schuster, 1999) but
when it comes to dialogue interventions in larger human systems, such as as
organizations, his views on dialogue and especially his view of relationality have
remained somewhat in the shadow (Bradbury H and Lichtenstein B, 2000). For
example, Dixon (1998), Flick (1998) Isaacs (1999), Senge (1990) and Yankelovich
(1999) all mention Buber as an important figure. However, they do not explicitly apply
dialogue with reference to his discussion on applied dialogue (Buber, 1947). Though
Buber did not envision a dialogue method, he claimed that the necessary conditions for
dialogue to emerge as a practice are the recognition of relationality, trust, the idea of
communication with and responsibility (Buber 1947).

According to Buber (1947) engagement in dialogue must be promoted by
pointing to the relational character of human systems. The importance of the relational
aspects of dialogue cannot be emphasized enough. First and foremost dialogue becomes
a way to relate with the other participants partaking in the dialogue. The challenge of
the participants in dialogue is to recognize the uniqueness of the particular human
systems they comprise. It is through the notion of this engagement that the dialogical
skills such as listening, suspension, respecting and voicing (Isaacs, 1999) gain their
meaning.

The entrance to dialogue is the realization that man is a relational creature that
has the possibility to meet, communicate and create in a “space between”. The
relationality and the “space between” is not just something one might choose or wish to
engage in. According to Buber (1947) it exists independently of any particular action
between human beings. The “space between” is not observable in space and time in the
same sense that a single individual and a collective are. For example, changes in a
person, such as aging, can be seen when observing that person for some time. Likewise,
a collective and its changes can be observed in space and time. However, the “space
between” is not observable in similar fashion. It is something re-constituted in every
accidental encounter between two persons (Buber 1947).

Engagement in dialogue is to fully engage oneself with the other. Dialogue is not
primarly a detached presentation of ones ideas and a detached inquiry into the ideas of
others. Dialogue is not communication about but communication with (Buber, 1947). It
is not plainly aimed at exchanging views between contributors from to different
perspectives or human systems. The focus of a dialogue intervention should primary be
on the values, knowledge and ideas within the system currently engaged in dialogue, not
on the values, knowledge and ideas of the individuals or the system they represent. To
engage in dialogue does not necessarily mean giving up ones own point of view or fully
accepting that of the other. Buber statets that the individual sphere is untouched, but
when people enter into dialogue the law of individual points no longer holds (Buber
1947). Thus, for Buber the ontology of the dialogical, e.g. the reality and nature of
dialogue is systemic in the systems thinking sense of the word: human systems in
dialogue develop and create something new out of what the participating individual
values, ideas and knowledge bring with them. In dialogue, participants set aside the
belief that thoughts or ideas can only be communicated from an individual to another, or
that rules and forces external to these two individuals determine what is spoken. The
space between can be characterized as a form of common reason where multiple voices
create and work on single ideas.

The idea of the relational character of communication differs strongly from the
so called conduit metaphor which is the dominant view of communication, for example,
in the lion part of managerial textbooks (Bokeno, 2002; Axley, 1984). According to the
conduit metaphor, successful communication is like a pipeline. Messages are
understood as information that are transmitted from a sender to a receiver, decoded by
the receiver, and successful if the meaning of the message is the same at both ends
(Bokeno 2002). According to Bokeno the conduit metaphor which describes how the
understanding and practice of communication is perceived in organizations, is
theoretically inappropriate, often dysfunctional and ineffective and a hindrance for
implementing programs for creative, playfull and innovative communication such as
dialogue. If the conduit concept is dominating and not questioned, dialogic modes of
interaction are in danger of being covered as yet another management concept, rather
than modeled or developed as the rich, constructive and productive mode of interaction
that it is (Bokeno 2002).

An example of why a dialogue intervention might fail due to the mistake of
viewing dialogue as conduit communication is found in the practice what is called
cross-cultural dialogue (Du Bois and Hutson, 1997). Cross-cultural dialogue has
recently been criticized for encouraging such knowledge of other participants that is
considered inappropriate (Jones 1999). In a cross-cultural dialogue where white and
black students were participating in order to exchange information about their own
culture the demands by white students to know marginalized black students enforced
colonizing attitudes and strengthened prejudices. According to Jones (1999), emphatic
knowing in cross-cultural dialogue can thus prevent us from recognizing our own
systematic complicity.

From the viewpoint presented here, cross-cultural dialogue is not dialogical
because its reliance upon the conduit metaphor prevents participants in dialogue to
perceive each other as forming a unique human system. In a dialogue situation
participants practice and focus on the virtues of dialogue, pay attention to their own
habits of thought, mental models and possible prejudices. Especially dialogue that aims
at mediating in conflicts between participants should aid understanding and respect for
their counterparts by encouraging to meet the person behind the system or position they
represent. Engagement in group dialogue leaves personal integrity intact but allows for
surprise and unpredictable innovations in the interplay between dialoguers. According
to Buber, a criteria for dialogue is that participants have the intention of establishing
mutual relations (Buber 1947).

Naturally, participants in a dialogue also have obligations and commitments to
other systems and goals. The point emphasized here is that dialogue is especially well
suited for understanding and working with the human system one is temporarily
engaged with. When a dialogical relationship is established, it can well serve as a basis
for discussing and reflecting on commitments to other human systems.

MIXING METHODS

The systems emphasis in Systems Sensitive Dialogue Intervention bears
consequences on method. The proposal here is that the starting point of a dialogue
intervention should not be one given method and its utilizations for a given purpose but
rather the needs and challenges of the human system that is to be engaged in dialogue.
The human system comes first, then method. This is not to say that methods are
superfluous. However, the design and facilitation of dialogue is situational. Methods
chosen should correspond to the motivation and maturity of the participants of dialogue.
In the following I shall briefly present two popular dialogue methods, Bohmian
and Nelsonian dialogue in order to show that both, despite their differences, have
strengths and can be used in dialogue interventions.

The Bohmian Method

According to the Bohmian School of dialogue, the focus in dialogue should be
on process rather than on content. A dialogue should not have a predetermined agenda
or a given content (Isaacs 1999; Senge, 1994; Simmons, 1999). By paying attention to
the guidelines or virtues of dialogue, the agenda or issues are said to emerge during the
dialogue process itself (Bohm, 1992; Bohm, 1996). Isaacs (1999) discusses four
principal virtues of dialogue: listening, suspension of judgment, expressing and
respecting. The virtues are not simply presented as virtues that one can automatically
turn to but rather as skills that one should develop and learn to practice. Other important
virtues or skills presented by Isaac and other theoreticians and practitioners include
thinking together, encouraging others to speak, focusing on the issue and not on the
personal character of other participants, winning together rather than winning for
yourself, speaking from experience, and changing the viewpoint.

The reason to engage in dialogue is, for Bohm and others who share his views
on dialogue, a practical matter. Dialogue creates shared meaning, values and a sense of
community that supports joint action and the creation of culture (Bohm 1992). By
making dialogue one of the core principles of an organization or a community a new
communication and thinking culture can emerge. Isaacs (1999) and Senge (1994)
provide a lot of examples of this. For Senge et al. (1994) dialogue becomes a way to
align action. According to Senge (1990), Bohmian type of dialogue gives access to such
information and meaning that cannot be accessed individually, enhances new action,
provides individuals with collective meaning and offers a place for innovation and
inquiry. Furthermore, all these capabilities are thought to improve efficiency in groups
and in organizations.

The Socratic Method

Leonard Nelson (1956) developed the Socratic Method. Today it is chiefly
known as Socratic Dialogue or Neo-Socratic Dialogue. Socratic Dialogue is a way to
engage people in an advanced philosophical dialogue. The method should naturally not
be confused with the Socratic dialogues of Plato even if it is inspired by Socrates
(Boele, 1997). Participation in a Socratic dialogue does not require prior experience in
philosophy but an interest to discuss philosophical and ethical questions and a
willingness to distance oneself from one’s own commitments (Boele, 1998; Van Hooft,
2000). In organizational contexts, Socratic dialogue has become especially popular in
developing and investigating values and business ethics (Bolten 2001, Kessels 2001,
Van Hooft 2000). In contrast to the idea that dialogue is rather process than content
Socratic dialogue stands out by always focusing on a predetermined topic or question.
The core of Socratic Dialogue is called “regressive abstraction”. Regressive
abstraction is an inquiry into the everyday experiences of participants and their
understanding of these experiences by comparing, analyzing and seeing them in the
light of the general concepts they are founded on. For example, a concrete experience
conceptualized and described as an instance of freedom is contrasted with a general
definition of freedom. Both the concrete experience and the abstraction are developed in
the course of the dialogue by the dialoguers themselves.

A Socratic Dialogue starts with a question of investigation, for instance: “What
is meaningful work?”, “What is freedom?”, or “What is love?”. The dialogue starts with
all participants giving a personal example of a situation were they feel that an instance
of the matter of investigation was realized. The participants, when presenting their
examples, do not have to prove that their examples are an instance of the matter of
investigation. Intuition or feeling is enough. The example should be one in which the
participant herself is a main character. Also, the example should be concrete in space
and time. For example; “Two weeks ago on Sunday, when visiting a friend of mine the
following happened”. The dialogue proceeds by discussing which one of the examples
should be chosen as a core example of the investigation. After choosing one example
the dialogue gradually reaches an increasingly abstract level culminating in a core
definition: E.g. “freedom is X” were X stands for a sentence of attributes suggested and
dialogued about amongst the participants. Thereafter the dialogue proceeds back to the
concrete by analyzing the abstract judgments principles and rules and ending at the
question about its applicability in concrete life.

Content and Process

For a general methodology of dialogue in Systemic interventions, both the
Bohmian and Nelsonian methods are important. Systems Sensitive Dialogue
Intervention takes into consideration both content and process. Dialogue intervention
can focus solely on content but often such dialogues does not have an impact on the way
people interact. It does not provide dialoguers with a new ability for interaction e.g.
systems sensitivity. The merits of Socratic Dialogue in a Systemic Intervention is that it
provides a structured way to engage in dialogue about a given issue and that dialoguers
find perspectives on the issue from personal experience, thus avoiding speculation and
possible power differences due to, for example, educational level or position.

When the choice of method is based on the needs of the human system engaging
in dialogue, a combination of methods can be useful. For instance, a conflict situation
might require that participants improve their listening skills, are encouraged to show
respect for other stakeholders, and learn to thinking together. However, to engage in a
dialogue with no agenda can easily grow into a feeling that it is a waste time especially
if it is a conflict situation and in times of pressing problems (Frydman et al., 2000;
Slotte and Hämäläinen 2004 ).

Systems Sensitive Dialogue Intervention emphasizes creative design of dialogue
interventions. This has, for example been done in a natural resources decision making
context (Slotte and Hämäläinen 2003) where the reflection on boundaries as an
improvement itself became important. The creative mix of dialogue methods can also be
strengthened by other dialogue-related methods such as Appreciative Inquiry
(Copperrider and Whitney 1999; Norum 2003) and Communication Other/Wise
(Bokeno 2002).

FROM METAPHYSICS TO EXPERIENCE

Commitment to any particular metaphysics of dialogue is not a necessary
precondition for engaging in dialogue. In a Systems Sensitive Dialogue Intervention, the
facilitator refraims from advancing any metaphysical agenda of her own. Midgley (2000)
points out and questions the fact that some people in the Community OR research
community have included political agendas in their interventions. What applies to political
agendas in Midgleys analysis applies to metaphysics in dialogue interventions . Bohmian
dialogue, Socratic dialogue and Bubers presentation of dialogue include metaphysical claims
such as ”the unfolding of thought”, ”the implicate order” ”the self-confidence of reason” and
”unity with God”. Ethically, practitioners and theoreticians are in their full right to ascribe
metaphysical characteristic to dialogue but these meta-level descriptions should not inform a
dialogue intervention. When the applicative literature presents the metaphysical hypotheses
and metaphors of the philosophies of dialogue as hard facts of dialogue, dialogue runs the
risk of becoming a quest for these metaphysical and metaphorical states and thus perceived
by participants as a mystic procedure were the ultimate goal is to experience a metaphysical
state such as the implicate order, collective intelligence, the one, God or the Platonic world
of ideas.

For example, if dialogue is defined as a quest for the platonic ideas or unity with
God, it would be difficult and ethically questionable to engage a relativist respectively
an atheist in the dialogue. Participants in a dialogue should be given the sole right to
draw their own metaphysical conclusion about the dialogue. Systems sensitivity does
not involve, preclude or exclude any predetermined metaphysics but concerns
observable relational aspects. In other words, it is proposed that the classification of the
metaphysical nature of these experiences should be left to the dialoguers themselves.
A Systems Sensitive Dialogue Intervention assumes that imposing any
metaphysical ideas on dialoguers is at odds with the core ideas of dialogue. Participation
in a dialogue which assumes some alien metaphysical principle can be awkward and
restrain people from engaging in dialogue. When such metaphysical entities are
presented as the goal of dialogue, the core philosophical principle of dialogue as a free
encounter between dialoguers, becomes endangered. Ethically, there is a risk that the
metaphysical entities are at odds with the personal worldviews of the dialoguers.
Pragmatically, the methods to facilitate dialogue become guided by the metaphysical
entities in favor of the needs, creativity and engagement of the dialoguers. Instead of
creating a strong personal experience and a new attitude towards discussed issues it runs
the risk of becoming a ritual predetermined by a metaphysical agenda.
It should be noted that dialoguers often express their personal experiences in
subjective terms, sometimes reflecting personal, sometimes cultural values. When a
group uses terms such as “magic” or “energy” to express their experiences, it should not
automatically be viewed in metaphysical terms. Actors, as well as dialoguers, often use
the world “energy” metaphorically or poetically to describe the level of co-operation. If
understood literally the experience of “energy” and talk of energy levels could easily be
dismissed as unscientific, but interpreted metaphorically, it can make perfect sense
(Collins 2004).

However, practitioners should not hide their personal views on metaphysical
questions if they are strongly committed to some. They should, however, make it clear
that the participants are free to draw their own metaphysical conclusions.

SUMMARY AND CONCLUSION

This paper has sought to contribute to a methodology for dialogue interventions.
Systems Sensitive Dialogue Intervention presents dialogue as one of many possible ways
humans engage in communication. Systems Sensitive Dialogue Intervention recognizes the
value of other language games in human systems and is not an effort to challenge these but is
an aid in designing dialogical intervention in situations where such are perceived to be
appropriate.

When participants learn to engage in dialogue, they learn a new way of relating that,
in itself, is more of an act than mere speech or contemplation of ideas. This ability is can be
used in any human encounter.

In a Systems Sensitive Dialogue Intervention the main focus of the participants
is the human system that is comprised out of the participants. Of course, participants in
dialogue bring with them their values, ideas and knowledge. However, a Systems
Sensitive Dialogue Intervention strives not to compare, transmit or evaluate these.
Instead, it focuses on what values, ideas and knowledge emerge from the dialogical
relation.

Systems Sensitive Dialogue Intervention encourages scientists, philosophers,
consultants and managers facilitating a dialogue to creatively combine content and
process focused methods with the human system that is engaging in dialogue as the
starting point.

The paper identifies the value of different dialogue-methods for dialogue
interventions. The notion of Systems Sensitive Dialogue Interventions was developed as
a result of empirical work with dialogue. It can be developed further by case studies of
dialogical interventions that are designed in accordance with the recommendations
presented here.

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