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vol 8: A theory of Peace
page 10: Freedom

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1: About
2: Synopsis
3: Development

Next: A Theory of Peace, Afterword
Previous: 9: Evil

4: Glossary
5: Questions

6: Essays
7: Notes
8: History

9: Persons

10: Supplementary
11: Policy



a personal journey to natural theology

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Lecture 10: Freedom


1 These lectures are about law. They are a search for a way to establish planetary law so that we no longer have to depend upon a balance of terror for our security.

2 I begin with the idea that at the legal level, war is due to the absence of effective law to protect human life. The abolition of war, therefore, requires the establishment of a global law which effectively protects all human lives.

3 I can imagine two ways to establish law. One is by authority. The other is by nature.

Authority and violence

4 An authority is some power whose power enables him to dictate the behaviour of other people. Breaches of the required behaviour are discouraged by some sort of punishment, that is the judicial application of pain.

5 There is a simple test to detect the presence of authority. Question it. If the response is: Don't question, obey! then you are dealing with authority. The only reason to obey is fear of punishment.

6 In the final analysis, that punishment is death. An authority administers the death penalty when it finds that an offence is inconsistent with its own continued existence.

7 Although an authoritarian approach to establishing law has been used often in the past, it cannot be the approach we are looking for. We are looking for global law that protects all human lives. A method of establishing law that is sanctioned only by the death penalty is obviously inconsistent with our purpose.

International violence

8 The international scene provides empirical support for this argument. The greatest authority is the one whose violence is greater than all the others. Over the last four thousand years or so we have seen a long struggle to determine the greatest authority.

9 The authorities of the world have fought it out, improving the technology of violence on the way, until we have just two authorities left on the planet. Each of them asserts that it has the right to destroy the other in order to survive. Each of them is ready to back its claim with violence great enough to destroy us all.

10 You might consider this analysis simplistic. I disagree. The arms race is genuinely on and the only end to it I can see is war or the economic exhaustion of the competitors. Neither of these finishes can be guaranteed to be stable.

11 Disarmament has made no progress at all. To the best of my knowledge, neither side has ever removed a useful weapon from its arsenal. On inspection, all apparent successes in disarmament turn out to have dealt with obsolete, useless of impossible military technologies.

12 The importance of disarmament talks is that they are another line of communication among the belligerents, and build mutual trust and confidence.

Natural law

13 Since there is no authority on earth than can guarantee the safety of the human individual, we must turn to the other track, law not by authority, but by nature.

14 There is a problem with words here. For the moment the term natural law, as I am using is, does not necessarily mean the law of nature as science understands it.

15 What is a natural law? From one point of view, a natural law is something that stays constant over time. A natural law is something which is conserved.

16 This does not, however, distinguish a natural law from an authoritarian law, since authoritarian law also establishes structures that last over time. The conservation of authority itself is generally the primary concern of authoritarian law.

17 The specific difference lies, I think, in the method of enforcement. If I break an authoritarian law and get caught, the punishment comes not from the law itself, but from the authority that enforces the law.

18 Natural laws, on the other hand, are self enforcing. They are tempered, of course, by uncertainty and incomputability.

19 The ultimate sanction of authoritarian law is death at the hands of the authority. The ultimate sanction of natural law is also death, but death as a consequence of our own action. On this definition, global nuclear was is a breach of natural law for our species, just like driving into a tree or jumping off a fatal height is a breach of natural law for an individual.

20 Natural law does not impute guilt, and its sanction is not punishment. It is simply a fact of life. Because natural law embraces all that can be, to be outside natural law is not to be.

21 This is my definition of natural law. It is consistent with the hypothesis that the universe is god, that is that the universe fills the whole space of possible being.

22 A natural law, as I have defined it, could not be otherwise. This is its naturalness. Any alternative to natural law is inconsistent with existence.

23 This definition of natural embraces what the old scholars called eternal law. Eternal law is the law of god. Because I have identified god and nature, I have also identified eternal law and natural law.

24 Now we can ask ourselves a question: are the laws of nature, discovered by physics and the other sciences, natural laws? The answer to this question is yes if these laws could not be otherwise.

Conservation law

25 In physics, each law of nature has two expressions. On the one hand it is a conservation law. The most basic and well known of these laws is the principle of conservation of energy. We believe that every natural process conserves energy to the precision allowed by the uncertainty principle.

26 Energy is like money. It is something which can be counted. The principle of conservation of money is based on the laws of arithmetic. You can check a bank statement using the arithmetic laws of addition and subtraction and the law of conservation of money.

27 The law of conservation of money says that the change in your current balance must be equal to the difference between the credits to you account and the debits to it.

28 Every single financial transaction on your account must obey this law, which is the fundamental law of accountancy and bookkeeping. The law of conservation of money is based on the fact that money is countable. It comes in discrete units.

29 There is an uncertainty principle in the law of conservation of of money. Our smallest monetary unit is a cent. Any amount of money smaller than a cent is uncountable and has to be ignored. We do this by rounding up or down to the nearest cent.

30 Every physical transaction obeys the law of conservation of energy. The conservation of energy is for us at present the fundamental law of bookkeeping in nature.


31 The second expression of a law of nature is symmetry. Symmetry means sameness. I am more or less symmetrical, meaning that my left side is approximately the same as my right side. A cube is symmetrical because all its faces, sides and corners are the same.

32 Conservation and symmetry are connected by a mathematical theorem proved by Emmy N[oe]ther. You can see this connection if you consider that things can only be can only be conserved if they can be counted and they can only be counted if they are in some way the same.

33 You cannot deposit gold in your bank account because gold and money are not symmetrical. The can be made symmetrical, however, by attaching a monetary value to the gold and depositing that amount of money in your account.

34 At present our understanding of physics resolves the whole world into a small number of conservation laws and symmetries. These conservation laws and their associated symmetries have a natural order. Some are more general than others.

35 In modern physics the laws of conservation of energy and momentum apply to everything. The law of conservation of electric charge, on the other hand, applies only to electrically charged particles. Each particle has to obey all the conservation laws that are relevant to it.

36 Particles and conservation laws are duals of one another, and Emmy N[oe]ther's theorem appears to me to guarantee that the same information is to be found in both the particles and the conservation laws.

37 Symmetries correspond to conservation laws and so are, by definition, static. The universe has static structure, but it also moves. So we need a law to describe how it moves. Physics has such a law. It is known now as Hamilton's principle, after William Hamilton.

38 Hamilton's principle is that any system will move in a way that either maximises or minimises the action involved in the motion. One way or another, the action in nature is extremal.

39 In its general form, this is a very old idea. From the beginning, natural philosophers have always considered that the universe moves toward some natural goal or extreme.

40 When it reaches an extreme, the action ceases to change. We assume that events whose action is extreme and therefore static are guided by a symmetry of law in nature. We have found that Hamilton's principle is consistent with all the laws of physics.

41 In physics the tendency to extremise action is studies with a mathematical symbol called the Lagrangian, which is named for Joseph-Louis Lagrange. The Lagrangian describes the relationship between structure and motion.

42 Once again we have a duality. At the level of the action defined by the Lagrangian, we can say that the static and dynamic aspects of the universe contain the same information.

43 Physics has, at present, a small set of conservation laws and symmetries which appear to explain all the known particles and their interactions. This is called a unified field theory. The only principal open question is: are these the only possible laws of nature? Has physics found some of the natural laws of the universe?

44 It is at this point that my hypothesis comes into contact with physics. My claim is that this is the only possible universe, since it fills the whole space of possibility.

45 If this is true, and physics has truly found the basic laws of the structure of the universe, then it should be possible to prove that the laws discovered by physics are the only laws possible in a consistent universe.

46 Such a proof would add considerable weight to my hypothesis, but I do not know how to do it and I have very little time left in these lectures to speculate on the subject.

47 The lecture I promised on the relativity of transfinity deals exactly with this question, but I am afraid it will have to wait. Next year I might be able to get the Peace Group to give me time for another series of lectures.

48 My hypothesis in its bare mathematical form is very general. It says that the nature of the universe is bounded by three non-constructive mathematical theorems, Cantor, G[oe]del and Turing.

49 We have here a rather peculiar use of the word bounded. To say that the boundaries of the universe are non-constructive is to say that there are no boundaries to the universe. The universe is what makes sense. There is nothing that we can make sense of outside of what makes sense.

50 This is the logical hypothesis, that our universe is everything that is logically possible. In theological terms, everything that is logically possible is part of the notion of god.

51 What are these non-boundaries of the universe? They all come to the same thing. The unboundedness of our universe is contained in the fact that insofar as it makes sense, it must remain forever incomplete.

52 Cantor's theorem tells us that it remains incomplete because it must grow without limit. G[oe]del's theorem tells us that it is incomplete because there are symbols that have no proof or disproof. Turing's theorem says that it is incomplete because there are symbols whose proof or disproof can never be decided.

53 My most general approach to the problem of proving that the universe embraces all possibilities is this. As we have them, the transfinite numbers are an infinite hierarchy of symbols defined by Cantor's proof. Each transfinite symbol comprises all possible subsets of the transfinite symbol before it.

54 Cantor's proof assumes that we can realise infinite sets of symbols, since this apparently involves no contradiction.

55 In physics, however, we are talking about the actual realisation of symbols, bounded not just by Cantor's theorem, but by Turing and Godel as well. This introduces a time element into the process.

56 From a physical point of view, the infinite hierarchy of symbols predicted by Cantor's theorem takes time to create. Right now we are in the middle of the creation of the universe which we know will never be complete.

57 What I suggest is that when we apply the abstract theory of transfinite symbols to a universe with just one symbol, we can interpret two as a transfinite symbol, since it is distinct from and greater than all the numbers that can be represented by one discrete symbol.

58 There is an arithmetic relationship connecting the transfinite symbols. The cardinal number of each is two raised to the power of the one before it. If we make one the first transfinite cardinal number, then the second is 2, the third 4, the fourth 16 and the fifth 65536

59 The surprise comes with the sixth, which shows how fast even this reduced sequence of transfinite cardinals can grow. The sixth of the 'physical' transfinite numbers is two raised the 65536th power. This number is huge, comparable to some estimates of the number of subatomic particles in the universe. There may be some links between these numbers and the symmetries of modern physics.


60 We must leave this speculation and focus on the question of global law. My contention is that the answer to the problem of peace is natural law. Natural laws, like the laws of physics, are not made by human beings, they are inherent in reality, and must be found.

61 Even authoritarian lawmakers are aware of this. A sovereign needs authority and wisdom. As Canute demonstrated, royal authority is not respected by tides or any other natural law.

62 Natural laws are the boundaries of the universe and to transgress them is to step outside the universe into nothing. The boundaries are themselves nothing. A conservation law tells us that nothing happens. When you balance the books, you final act is to arrive at two numbers which are exactly the same.

63 Natural laws are the widest possible boundaries. Any authoritarian law, insofar as it is not natural, is an artificial restriction on the nature of the universe. The creative power of the universe is such that no matter how strong the authority, such an artificial restriction will eventually be broken.

64 The natural law approach to peace says this: there are certain laws that guarantee peace, where by peace we mean the structure of the universe. We know some of them, but not all. We know, for instance, that if you do not eat you will die.

65 Even though we do not know all the natural laws, they are there, like rocks in the ocean. They are self-enforcing, and act whether we are aware of them or not. As we get to know them, one by one, we can exploit them to establish new technologies to make life on earth easier.

66 It would not be far from the truth to say that the whole technology of the industrial age is based on two physical laws. One we have already met, the conservation of energy and momentum. The other is the second law of thermodynamics, which says, like Cantor's theorem, that situations have a natural tendency to become more complex.

67 We are looking for the natural law of peace, the law that guarantees all structure in the universe. I will tell you my contender. It does not say much, but it I believe it says enough.

68 For want of a name, I will call it the law of complete symmetry.

69 We have already noticed that in physics each conservation law gives rise to a symmetry. Symmetry is expressed by a mathematical object known as a group.

70 A group has a certain structure related to the number of elements it contains and the way they interact. It is possible, given some of the elements, to work out what the other elements are.

71 Physics, and science generally, is a dialogue between mathematics and observation. The history of particle physics has demonstrated this beautifully. First we find a few particles. From them we can guess at a conservation law, and from that law we can guess at a symmetry group.

72 Some of the places in this symmetry will be filled by the particles which led us to the symmetry in the first place, but there are usually gaps where particles are missing. The symmetry itself will tell us something about the nature of these particles, and armed with this information we can go looking for them.

73 The physics of this century is punctuated with the discovery of symmetries which predict weird particles, followed by the discovery of the particles themselves. It is this predictive quality of the symmetries we discover in nature which gives us such confidence in them

74 Paul Dirac wrote down an equation which expressed the symmetry of the interaction of electrons and light. This symmetry has a place for an antiparticle, like the electron, now called the positron.

75 At that time nobody had dreamed of antimatter. It was weirder than the weirdest physical concept then imaginable. Experimenters, motivated by the law of complete symmetry, started to look for it. A couple of years later, Carl Anderson discovered positrons in cosmic rays, and was able to make them in his laboratory soon afterwards. Antimatter had become a reality.

76 We can express this same idea informally as a mathematical foundation of global law. I believe that when the mathematical theory is developed to its full generality this theory will be found consistent with everything we take to be human nature, and predict a few things we have yet to think of.

77 I make this statement because the mathematical theory of symmetry, like all mathematical theory, has only one foundation and that is consistency. If we assume that human nature is consistent with itself and the universe in which it evolved, we are forced to the conclusion that we will never discover an inconsistency between humanity and mathematics.

78 We will of course encounter incompleteness and incomputability, but we will never, if we get things right, encounter inconsistency. Any inconsistency will tell us, as it tells any scientist , that we have lost the track somewhere.

79 So let us assume an aggregate whose elements are human beings. The elements of that aggregate are all the members of the human species. This species is defined by human reproduction, human DNA and many other criteria. No matter how deformed a living human being may be, it is possible to determine that he or she is human and not some other species.

80 Human beings are countable, and so the aggregate of human beings has a natural cardinal number which we call the population of the earth.

81 Human beings all have a unique genotype, and can be uniquely defined by this and other attributes. We therefore have the foundation for a global application of habeas corpus.

82 We can also apply the ideas of a symmetry group to ourselves.

83 This symmetry group will correspond to a law of conservation of humanity. We have already noticed that conservation laws are nested. The law of conservation of humanity therefore contains all the conservation laws that go to make up humanity.

84 This fact immediately writes all the symmetries of nature into our understanding of ourselves. It also tells is that if we want to conserve ourselves, we have to conserve all those things which are part of us, like plants and animals.

85 The law of complete symmetry suggests that we will only understand humanity if all human beings are elements of the human symmetry group, and all places in the group are filled by human beings.

86 Without going any further, we can draw some strong political conclusions.

87 First, human beings are equal. We all partake identically in the symmetry defined by the conservation of humanity. The elements of a group all participate in the full life of the group. If any element is missing, the integrity of the group is destroyed and the law of complete symmetry demands that it be replaced.

88 Second, we are all free. The only restraint that a group structure puts on its elements is that when they interact with one another, the result is also in the group. This means that the law of complete symmetry says that we may all communicate with one another in any way that is human, and the result will be human.

89 The law of complete symmetry also says that any form of action that takes us outside human symmetry by destroying elements of the group damages the whole group. Killing and violence fall into this category.

90 The law of complete symmetry is just another expression of my contention that the universe embraces all possibilities. The symmetry defined by the law of conservation of humanity expresses the whole of human possibility. Any restriction on this possibility is unnatural, and will eventually lead to violence.

91 If I am right, this is a natural law. It has precedence over all the laws established by authority.


92 I believe I have found what I have been looking for, a hypothesis about peace that fits the experience of my life. It is a testable hypothesis, because it should fit the findings of all science. It is useful, because it suggests myriad new ways of looking at human beings and human laws.

93 In particular, it shows promise of being able to criticise human laws from a firm mathematical standpoint. Because its standpoint is mathematical, no reasonable person can dispute it as long as the mathematics is sound.

94 What good is such a theory, since will people disobey it anyway?

95 The advantage, I claim, is that the theory expresses the language of nature. People will disobey it, they can disobey it. The uncertainty principle allows this. But the conservation laws of the universe say that eventually the books must be balanced.

96 If they cannot be balanced peacefully, they will be balanced violently. The purpose of the theory of peace is to avoid violence. It can and must do this by studying all the different conservation laws in the universe and their associated balances and educating human behaviour toward conformity with these balances.

97 Natural law is not enforced by human violence. It enforces itself. All that is needed is education. The sort of education necessary is simply an understanding of the use of symbols, that is reading, writing and arithmetic. With this basis, the next step is simply a generalisation of the notion of symbol from letter and number to everything.

98 This, I contend, is sufficient. People will remain free to break natural laws, because uncertainty and incomputability allow it. Sometimes they may do themselves harm. Sometimes they may do others harm. Sometimes they may beak through into a new realm of consistency.

99 I have prepared a list of books that helped me develop the ideas in this lecture. This list is in the file following this one.

100 I am pleased with the distance I have covered in these lectures. I apologise for the obscurities and loose ends. I think they are the best bit of work I have done in my life. I thank you for listening. For the moment, I rest my case.


Originally broadcast on 2BOB Radio, Taree, NSW on 20 August 1987


Auguste, Dick, Emmy Noether 1882-1935, Birkhauser 1981   Amazon  back
Buchan, James, Frozen Desire: the meaning of money, Farar, Strauss and Giroux 1998 Jacket: 'In Buchan's view, money is civilization's greatest invention. ... As Buchan explains, money is "frozen desire" - and because money can fulfill any mortal purpose, for many people the pursuit of money becomes the point of life. In a learned and elegant survey, Buchan illuminates the many differnt views of money across the centuries. ... Whether or not money is humanity's greatest invention, its meanings reveal a great deal about human nature; in showing us what we think of money JB shows is who we are.'  Amazon  back
Dodd, J E, The Ideas of Particle Physics: An Introduction for Scientists, Cambridge UP 1991 Jacket: 'This book is intended to bridge the gap between traditional textbooks on particle physics and the popular accounts of the subject ... Although entirely self contained, it assumes a greater familiarity with the basic physics concepts than is usually the case in popular texts. This then allows a fuller discussion of more modern developments.'  Amazon  back
Elkana, Yehuda, The Discovery of the Conservation of Energy, Hutchinson Educational 1974 Jacket: 'This book chronicles historically and in a philosophical context the discovery and gradual develoment of the concept of energy ... Metaphysical beliefs in the principle of 'conservation of something' in nature resulted finally in the statement of the physical laws of the conservaiton of energy in the work of Hermann von Helmholtz.'  Amazon  back
Holy See, Canon Law Society of America, Code of Canon Law: Latin-English Edition, Canon Law Society of America 1984 Pope John Paul XXXIII announced his decision to reform the existing corpus of canonical legislation on 25 January 1959. Pope John Paul II ordered the promulgation of the revised Code of Canon law on the same day in 1983. The latin text is definitive. This English translation has been approved by the Canonical Affairs Committee of the [US] National Conference of Catholic Bishops in October 1983.  Amazon  back
Noone, Val, Disturbing the War: Melbourne Catholics and Vietnam, Spectrum 1993 Chapter 1, Prologue: 'In this book I will make the following five main points: Powerful individuals and forces in the Catholic Church in Melbourne ... gave religious justification for that war. ... a growing number of Melbourne Catholics came to believe ... that the war was based on lies ... Leadership in peace work was given ... usually by individuals and groups outside the Catholic Church. ... Melbourne Catholic peace workers contributed to gaining the withdrawal of Australian troops from Vietnam ... this story can be interpreted as one of social sin and a call to change of heart, and as a sign of hope.'  Amazon  back
Pais, Abraham, Inward Bound: Of Matter and Forces in the Physical World, Clarendon Press, Oxford University Press 1986 Preface: 'I will attempt to describe what has been discovered and understood about the constituents of matter, the laws to which they are subject and the forces that act on them [in the period 1895-1983]. ... I will attempt to convey that these have been times of progress and stagnation, of order and chaos, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big moneys.' AP  Amazon  back
Walker, Geoffrey de Q, The Rule of Law: Foundations of Constitutional Democracy, Melbourne University Press 1988 Jacket: 'The author argues that the survival of any useful rule of law model is currently threatened by distortions in the adjudication process, by perversion of law enforcement (by fabrication of evidence and other means), by the excessive production of new legislation with its degrading effect on long-term legal certainty and on long-standing safeguards, and by legal theories that are hostile to the very concept of rule of law. In practice these trends have produced a great number of legal failures from which we must learn.'  Amazon  back


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