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vol 8: A theory of Peace
page 9: Evil

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a personal journey to natural theology

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Lecture 9: Evil


1 Last week I gathered up all the pieces of my theory of peace and showed you approximately how they fitted together. This week we have to approach the question which is the life and death of any theory: is it true?

2 Let us start again with the notion of symbol. Remember that a symbol is a definite thing with an infinite range of interpretations. A good example of a symbol is a game.

3 Every game has rules. These are the finite part of the game which define its structure. If you step outside the rules you are not playing the game. You are doing something else.

4 The rules are the definite part of the game. They can be written down in a book and enforced by umpires, referees and boards of control

5 The other part of the game is the play. Play is the interpretation of the rules. Because the rules are a symbol, their interpretation is infinite, and so play within the rules is infinite. It is a free exploration of the space defined by the rules.

6 How we explore that space is not and cannot be defined by the rules.

7 There are times when the rules seem silly and the game becomes boring and repetitious. Then there are moments when the magic sets in and the game becomes something else. These are the moments we play for, for we cannot make them happen. They are the goals, but they are not effectively attainable. They lie in the realm of the infinite and uncertain.

8 The magic moments are not effectively attainable, but we can approach them by increasing their probability. On the one hand there is natural ability, something definite that you can be born with. On the other hand there is training.

9 By combining natural ability with training, we can increase the probability of that moment when it all pays off. All the moves you have practiced so often come together, the crowd is on its feet screaming as you go over the line ... etc.

10 I hope you know what I mean. I am sure we all experience a bit of magic now and then. I do not mean, by my choice of example, to limit the discussion to sports., We can use the symbol game to cover all human activity.

11 The game I am playing here is science. Science is the game where you watch another game and try to work our what the rules are. The work of science is to learn the rules by which the universe works and plays.

12 The rules of cricket are the boundaries that define cricket. Inside those rules is cricket. Outside is not cricket, but it is something. The rules that science seeks, called laws of nature are the boundaries of nature. Inside them is nature. Outside them is not nature.

13 We know that the laws of nature contain the rules of cricket. A cricket ball moves according to the laws of nature whether it was played according to the rules or not. If you throw a ball directly at another player's head and hit her, nature will take its course. Whether you will be allowed to go on playing cricket is another matter.

14 What contains the laws of nature? In other words, where do we end up if we break a rule of nature? That is a question for science to answer, if it can.

15 I believe that it is now generally agreed that science needs only two rules. The first is our old friend, the law of consistency. Science says that anything that is demonstrably inconsistent cannot be true.

16 The second says that a scientific theory should be formulated in such a way that it can be tested by experiment to see if it consistent with experience.

17 Notice carefully that science does not tell us what is true, only what is not true. We use scientific theory to deduce what is true from what is not true. When Newton published his theory of universal gravitation, it fitted the movements of the moon and the planets within the accuracy of the observations and calculations possible in his day.

18 Newton's discovery triggered rapid growth on mathematical research. This gradually improved the accuracy of the calculations that could be made with the theory.

19 Improved theoretical predictions encouraged astronomers to improve the accuracy of their observations. In time the improved observations coupled with the improved calculations revealed a discrepancy between theory and observation. The orbit of the planet Mercury was found to move in a way Newton's theory could not explain.

20 This one inconsistency was enough to show that Newton's theory was not the whole truth. Einstein's theory of gravitation can account for the motion of the orbit of mercury, but it may one day fail to account for an observation and have to be replaced by another theory.

21 The logic of discovery says that you cannot call a theory true. All you can say is that it has not yet been shown to be false. Of course, as a theory yields more and more useful insights into nature, we gain confidence in it, but confidence is not the sort of certainty I am looking for here.

22 Falsehood can show up in either of two places. Either the theory can be shown to be inconsistent with itself, or it can turn out to be inconsistent with experience.


23 Now we can ask ourselves whether or not this theory of peace is good science.

24 First, a word about words. I have been using the phrase a theory of peace because it is convenient, but it is rather unscientific. The term theory is usually reserved for things like gravitation, quantum mechanics and evolution which have a long track record of success.

25 The proper name for an idea like mine still in the fantasy stage is hypothesis. Hypothesis means assumption. What I am saying is: let us assume that the universe is so and so and see what comes out.

26 If this assumption fits the facts, our confidence in it will grow. When it has been shown to fit all the known facts, and begins to predict new facts that have not yet been observed, it will start to make the transition from hypothesis to theory.

27 I have avoided the word hypothesis to cut down on the amount of greek in these lecture. But you will have noticed that I use the word assumption liberally.

28 At this point we have an assumption, not a theory, and we are starting on the process of confronting it with the facts. Before we do that, however, we need a clear statement of the hypothesis.

29 In its briefest form, the hypothesis is that the rules that nature obeys are the same as the rules of science.

30 The first of these is that nature must be consistent.

31 The second is that inconsistencies can exist in nature without nature being aware of them or acting on them. Such inconsistencies appear to us as uncertainties.

32 Let me try to explain this. The rules of football specify what players may and may not to, and they try to minimise unnecessary violence. They also provide for umpires and referees whose task is to see that the game is played within the rules. There are various penalties for breaking the rules.

33 Sometimes a player may break the rules without being seen by the referee. From the point of view of the rules of the game, anything that the referee did not see and act upon did not happen. The fans see it, though, and can argue for years about what would have happened of the referee had not been so blind.

34 My hypothesis is that nature, like science, can only pronounce on breaches of the rules that it sees. All those things that it does not see did not happen.


35 My hypothesis, in its present form, is not easy to put to any test. We have to develop its implications until we come to a testable assertion.

36 Newton's theory of universal gravitation is expressed by a very simple mathematical statement. When it was first proposed it fitted the known observations. This very success encouraged further work, so that the tests became more and more precise.

37 Finally the testing became so accurate that it showed up the discrepancy between the theoretical and actual positions of the planet Mercury. This was enough to throw the theory into doubt.

38 The testing of my hypothesis about peace may follow a similar track. If it passes cheap and simple tests, and confidence builds, it will be subjected to more and more rigorous exposition and testing.

39 At no point, however, will we ever be able to say that it is the whole truth. All we can say is that it has not yet been shown to be inconsistent. There might be things going on behind the play that the referee cannot see . As confidence in the hypothesis grows, the referees will go to greater and greater lengths to catch it in inconsistency.


40 The first matter I would like to take up with the hypothesis is the existence of evil. A good theory of peace should have a coherent explanation of war and evil in general.

41 Last week I emphasised the personal nature of my quest for peace, and explained how I see the force that has driven me on an obsessive search for a new way to look at the world. That force is the discrepancy between my life as I experience it and life as I learn about it from my religious and cultural milieu. I was confronted with inconsistency.

42 In the last lecture you heard my cry of pain. For me an essential part of these lectures is a clear expression of the evil they are intended to ward off. The first task of any new theory is to account for the perceived weaknesses in the theory before it.

43 My explanation of evil is very simple.

44 I think that evil is the penalty we pay if we try to step outside the laws of nature. This statement is not meant to have any specific human or moral implications. It is intended to apply to everything.

45 The bomb kills sleeping people as well as those who are awake. It kills friends as well as enemies. It is simply inconsistent to have living human beings in the space occupied by an exploding nuclear weapon.

46 Evil marks the boundaries of our universe. Trying to break the boundaries brings an automatic penalty: evil.

47 The law of gravity is the prototype of this. It is a very gentle law, most of the time. In many physical systems, the forces due to gravity are tiny compared to the other physical forces operating.

48 It is gravity that makes us fall and possibly hurt ourselves. A short fall is not too bad, but if we fall far enough it can be fatal. The biggest fall of all is into a black hole, which destroys all structure.

49 A black hole is not nothing but it is very close. The only point that physics knows that is closer to the edge of the universe is the initial singularity, that point which lay at the origin of the big bang.

50 The creative force that brought the universe to be out of nothing also works on a black hole. Some believe that the energy trapped in a black hole will eventually become part of the structure of the universe again.

51 Before I develop this notion of evil any further, I must tell you another reason why I have chosen evil as the first test of the hypothesis.

52 I have complained about my past and the pain it caused me. I have attributed this pain to the discrepancy between myself and my religion. I am saying, in effect, that I am right and the religion is wrong. That is why I am trying to revise the religion.

53 This fate came to me through the hands of real people. I am running a risk, giving these lectures, of offending these people by appearing to accuse them of treating me badly,

54 This is not my intention. I believe that this theory of evil, properly developed, will show that the link between pain and human action is tempered by uncertainty. Pain and evil exist at the edges of the universe, in the realm of uncertainty where nobody can seem clearly.

55 Knowing the laws of nature, we can do evil and inflict pain deliberately. A good navigator with a good chart can pick a rock and run onto it. But the ship will sink just the same if it runs onto an uncharted rock.

56 The evil that I am pursuing in these lectures comes from uncharted rocks. I have led a charmed existence in my relationships with other people. I have never been aware of being treated with malice.

57 The deliberate violence I have suffered was administered by people whose religion taught them that it was necessary for my own good. My argument is not with them, it is with the religion.

58 I am not exporting any blame, and I don't think I have to accept any either. I have often given people a hard time, at least that's what they say, but I have very rarely set out to do just that. The stresses within me have often made it very hard to communicate. From my point of view, this is precisely the difficulty I am trying to resolve through these lectures.

59 My deepest feeling is that there would be peace if we could all find a way to communicate freely. The barriers to communication are not our fault, they are part of the nature of the universe.

60 They are not an arbitrary part that can be removed by hope or prayer, they are there, like rocks in the ocean. The purpose of a theory of peace is to find these rocks so that we can keep away from them.

61 The hope that lies in this hypothesis is that the boundaries to communication are definite and separate things which can be found and avoided. Evil, in other words, is finite while good is infinite.

62 This result appears informally from the game metaphor that I have been using in this lecture. A game is a symbol. The rules are the finite aspect of the symbol, the play is the infinite aspect.

63 The penalties come not from the play but from transgression of the rules. Because the rules are finite, we know exactly what they are and so we know exactly how to avoid the penalties.

64 In the universe pain and evil are a sign that we are stepping beyond the boundaries. Since these boundaries are finite, we can discover them, and having once discovered them, avoid them if we wish to avoid pain.

64 This all sounds pretty coherent to me as I have expressed it, but its not quite science yet. We must now get this down in more testable language by developing the hypothesis further. Let me remind you of the statement I made a few minutes ago:

In its briefest form, the hypothesis is that the rules that nature obeys are the same as the rules of science.

The first of these is that nature must be consistent.

The second is that nature cannot know when it is consistent, only when it is inconsistent.

65 I am trying to define the rules of the game of life, that is the boundaries that we must respect if we are to avoid evil and pain.

Hilbert's questions

66 My hypothesis is that the boundary of the universe is the same as the boundary of science. The boundary of science is perceived inconsistency.

67 To develop this idea we turn to mathematics and Hilbert's program. Hilbert asked three questions:

1. Is mathematics consistent?

2. Is mathematics complete? and

3. Is mathematics decidable?

68 These three questions were answered by two proofs. Kurt Goedel showed that if mathematics is consistent, then it is complete. Alan Turing showed that if mathematics is consistent, then there exist undecidable propositions, that is symbols whose consistency or inconsistency cannot be decided.

69 Now we can introduce another hypothesis. Assume that the universe of experience contains exactly the same information as the universe of mathematics. I have expressed this before in the words: the universe is mathematics incarnate.

70 Although it is not proven I will assume that this statement is equivalent to the statement that the limits to nature are the same as the limits to science.

71 If we assume that the universe is mathematics incarnate, then we can apply the answers to Hilbert's questions to the universe itself. From Kurt Goedel we learn that insofar as the universe is consistent, it is incomplete. From Alan Turing we learn that insofar as the universe is consistent, it contains undecidable symbols.

72 You will notice that these are hypothetical statements. We are not saying that the universe is consistent, or that it is not complete or decidable. These statements are relative, linking these properties of the universe. If it is consistent, it is incomplete.

73 Let us look now at the implications of consistency. Consistency is the foundation of mathematical proof. Goedel's theorem and Turing's theorem are statements that arise from the assumption of consistency.

74 Consistency leads us to another theorem, Cantor's theorem, which states that in the realm of consistency every symbol gives rise to an endless hierarchy of further symbols.

75 As I see it these three theorems define the boundaries of the universe. I do not think the universe is any narrower than this, and I do not think it could be any wider.

76 I do not think that it can be any wider, because the three theorems are non-constructive. They are results that flow from the assumption of consistency alone, without any arbitrary structure.

77 Let us return to the notion of symbol, and assume that the universe itself is a symbol. It is a mark, and it is a space. Imagine the mark aspect of the universe to be a point on a line , and the line on each side of the point to be the space aspect of the symbol.

78 Now take the mark aspect to be consistency, and the space to be inconsistency. What do we know about this symbol?

79 First, Cantor's theorem, which holds in the realm of consistency, tells us that the mark will spawn an infinite hierarchy of new symbols.

80 The other two theorems, Goedel and Turing, define the boundary between the mark and the space. Goedel tells us that when we are inside the mark, that is within the domain of consistency, we are bounded by incompleteness. Outside the realm of consistency, we may have completeness.

81 Turing tells us that inside the mark, that is the zone of consistency, we are bounded by undecidability.

82 Thus we arrive at a picture of the consistent aspect of the universe defined by one infinity and two boundaries. The infinity is represented by Cantor's theorem, which says any consistent symbol will grow without limit.

83 One boundary is defined by Goedel's theorem, which says that within the realm of consistency, we must be prepared to face the reality of incompleteness. In other words, the infinite growth of symbols predicted by Cantor's theorem is accompanied by the incompleteness predicted by Goedel's theorem.

84 The other boundary is defined by Turing's theorem, which says that within the realm of consistency, the infinite growth of symbols predicted by Cantor's theorem is accompanied by undecidable symbols.

85 This is the hypothesis stated in a mathematical way. To set up realistic tests of the hypothesis, however, we need to go from here to things we can actually experience.

86 We have already done this in a general way. We have identified the uncertainty principle of quantum mechanics with the incompleteness predicted by Goedel's theorem. We have linked the undecidability predicted by Turing's theorem with the impossibility of communication in some circumstances.

87 We make this link by observing that communication requires translation, and that translation is a communication problem which may in some cases be undecidable. In any case translation takes time, as the history of science demonstrates. It has taken us a long time to learn the language of nature.

88 This hypothesis is intended to cover the whole universe, however, and these links are yet too vague to make firm connections with the existing body of science. If the hypothesis is any good, it will eventually yield numbers that correspond to actual measurements.


89 To make these connections, we need an interpretation of the hypothesis which links it to existing theory and is easy to handle. I think such an interpretation is the theory of communication. The limits to the universe defined by Cantor, Turing and Goedel are the limits to communication.

90 Evil comes when we transgress these limits. What causes a road accident? Perhaps we did not see the other vehicle coming? This is clearly a communication problem. Perhaps we did see it coming, but could not do anything in time.

91 This too is a communication problem. Steering, braking and accelerating are attempts to tell a car to do something. The are attempts to communicate the message: get out of the other vehicle's way. The laws of physics limit how fast this message can be communicated. There comes a moment in the trajectory of a motor vehicle when no amount of skill can avoid an accident.

92 So how do we avoid accidents? By driving within the limitations set by the laws of nature. That means by driving in such a manner that no matter what happens within the space that you can see, you can get out of the way in time. If you cannot see far, do not go fast. If you want to go fast, make sure that you can see a long way.

93 The practical motivation of a theory of peace, like any other theory, is to improve our vision of nature so that we can move more quickly and safely. On the one hand it tells us where danger lies, where not to go. On the other hand, by exposing clearly the rules of the game, it opens up a new realm of play.

94 In this lecture I have spoken about evil and the boundaries of the universe. In the next we will concentrate on the play which lies inside.

Originally broadcast on 2BOB Radio, Taree, NSW on 13 August 1987


Cantor, Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.'  Amazon  back
Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechaincs, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)   Amazon  back
Goedel, Kurt, Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...'  Amazon  back
Howard , Michael, War and the Liberal Conscience: the George MacAulay Trevelyan Lectures in the University of Cambridge, Temple Smith 1986 Jacket: 'For centuries liberal minded men have been horrified by the pain and waste of war. ... Throughout the whole story runs the continuing contrast between those who hoped to find a single cause for the disease, leading to a lasting cure, and those who understood that, in Professor Howard's words, 'this was a task that needs to be tackled afresh every day of our lives'.'  Amazon  back
Leiss, William, The Domination of Nature, McGill Queens University Press 1972 'One must ask: Why is there apparently a connection between the conquest of nature and the 'conquest of man'? Is it inevitable that the scientific and technological instruments utilized in the domination of nature should produce a qualitative transformation in the mechanisms of social despotism?'  Amazon  back
Misner, Charles W, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. ... this is a book on Einstein's theory of gravity (general relativity).'  Amazon  back
Rogasky, Barbara, Smoke and Ashes: The story of the Holocaust, Oxford University Press (first published by Holiday House, New York) 1991 'To say the truth straight out, this is a book about murder. In twelve years, almost six million peaople were deliberately murdered. ... They were all killed because they were jews. That was the only reason. ... How did it happen and why? What did they do? Couldn't anyone stop it? ... This book tries to answer these questions and many more besides.' [pp3-4] k  Amazon  back


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