Love, the Answer to the Problem of Human Existence

[ A paean to, and exposition of, love, extracted as an extended set of quotations from Erich Fromm’s The Art of Loving. This book, in my view, is possibly the best answer in existence to the question of “What is this earth thing you call love?”  The answer makes clear that it is not an earth thing at all. Gender-specific pronouns are annoying but I leave them untouched; the work is from 1956. ]


Any theory of love must begin with a theory of man, of human existence. While we find love, or rather, the equivalent of love, in animals, their attachments are mainly a part of their instinctual equipment; only remnants of this instinctual equipment can be seen operating in man. What is essential in the existence of man is the fact that he has emerged from the animal kingdom, from instinctive adaptation, that he has transcended nature — although he never leaves it; he is a part of it — and yet once torn away from nature, he cannot return to it; once thrown out of paradise — a state of original oneness with nature — cherubim with flaming swords block his way, if he should try to return. Man can only go forward by developing his reason, by finding a new harmony, a human one, instead of the prehuman harmony which is irretrievably lost.

When man is born, the human race as well as the individual, he is thrown out of a situation which was definite, as definite as the instincts, into a situation which is indefinite, uncertain and open. There is certainty only about the past — and about the future only as far as that it is death.

Man is gifted with reason; he is *life being aware of itself*; he has awareness of himself, of his fellow man, of his past, and of the possibilities of his future. This awareness of himself as a separate entity, the awareness of his own short life span, of the fact that without his will he is born and against his will he dies, that he will die before those whom he loves, or they before him, the awareness of his aloneness and separateness, of his helplessness before the forces of nature and of society, all this makes his separate, disunited existence an unbearable prison. He would become insane could he not liberate himself from this prison and reach out, unite himself in some form or other with men, with the world outside…

The deepest need of man, then, is the need to overcome his separateness, to leave the prison of his aloneness… Man — of all ages and cultures — is confronted with the solution of one and the same question: the question of how to overcome separateness, how to achieve union, how to transcend one’s own individual life and find at-onement…

The question is the same, for it springs from the same ground: the human situation, the conditions of human existence…

The unity achieved in productive work is not interpersonal; the unity achieved in orgiastic fusion is transitory; the unity achieved by conformity is only pseudo-unity. Hence, they are only partial answers to the problem of existence. The full answer lies in the achievement of interpersonal union, of fusion with another person, in love.

The desire for interpersonal fusion is the most powerful striving in man. It is the most fundamental passion, it is the force which keeps the human race together, the clan, the family, society. The failure to achieve it means insanity or destruction — self-destruction or destruction of others. Without love, humanity could not exist for a day.

Love is union under the condition of preserving one’s integrity, one’s individuality. Love is an active power in man; a power which breaks through the walls which separate man from his fellow men, which unites him with others; love makes him overcome the sense of isolation and separateness, yet it permits him to be himself, to retain his integrity. In love the paradox occurs that two beings become one and yet remain two.

Envy, jealousy, ambition, any kind of greed are passions; love is an action, the practice of a human power, which can be practiced only in freedom and never as the result of a compulsion… Love is an activity, not a passive affect; it is a “standing in,” not a “falling for.” In the most general way, the active character of love can be described as stating that love is primarily giving, not receiving…

For the productive character… giving is the highest expression of potency. In the very act of giving, I experience my strength, my wealth, my power. This experience of heightened vitality and potency fills me with joy. I experience myself as overflowing, spending, alive, hence as joyous. Giving is more joyous than receiving, not because it is a deprivation, but because in the act of giving lies the expression of my aliveness…

Beyond the element of giving, the active character of love becomes evident in the fact that it always implies certain basic elements, common to all forms of love. these are care, responsibility, respect and knowledge.

Love is the active concern for the life and the growth of that which we love. Where this active concern is lacking, there is no love… Care and concern imply another aspect of love; that of responsibility. … Responsibility, in its true sense, is an entirely voluntary act; it is my response to the needs, expressed or unexpressed, of another human being. To be “responsible” means to be able and ready to “respond.” …

Cain could ask: “Am I my brother’s keeper?” The loving person responds. the life of his brother is not his brother’s business alone, but his own….

Responsibility could easily deteriorate into domination and possessiveness, were it not for a third component of love, respect. Respect is not fear and awe… Respect means the concern that the other person should grow and unfold as he is. Respect, thus, implies the absence of exploitation. I want the loved person to grow and unfold for his own sake, and in his own ways, and not for the purpose of serving me. If I love the other person, I feel one with him or her, but with him as he is, not as I need him to be as an object for my use. … Respect exists on the basis of freedom: “l’amour est l’enfant de la liberté” as an old French song says; love is the child of freedom, never that of domination.

To respect a person is not possible without knowing him; care and responsibility would be blind if they were not guided by knowledge. … There are many layers of knowledge; the knowledge which is an aspect of love is one which does not stay at the periphery, but penetrates to the core. It is possible only when I can transcend the concern for myself and see the other person in his own terms…

Knowledge has one more, and a more fundamental, relation to the problem of love. The basic need to fuse with another person so as to transcend the prison of one’s separateness is closely related to another specifically human desire, that to know the “secret of man.” While life in its merely biological aspects is a miracle and a secret, man in his human aspects is an unfathomable secret to himself — and to his fellow man. We know ourselves, and yet even with all the efforts we may make, we do not know ourselves. We know our fellow man, and yet we do not know him, because we are not a thing, and our fellow man is not a thing. The further we reach into the depth of our being, or someone else’s being, the more the goal of knowledge eludes us. Yet we cannot help desiring to penetrate into the secret of man’s soul, into the innermost nucleus which is “he.”…

[The] path to knowing “the secret” is love. Love is active penetration of the other person, in which my desire to know is stilled by union. In the act of fusion I know you, I know myself, I know everybody — and I “know” nothing. I know in the only way knowledge of that which is alive is possible for man — by experience of union — not by any knowledge our thought can give.

Love is the only way of knowledge, which in the act of union answers my quest. In the act of loving, of giving myself, in the act of penetrating the other person, I find myself, I discover myself, I discover us both, I discover man.


Written by dan

January 28th, 2016 at 1:29 pm

More excrement

(A technical term – see Le Guin.)



The economy pumps more excrement.

So the exhaust fumes suffocate,

So the carbon accumulates,

And the mercury rises,

And the science advises

Panic! in cold blood,

Beware the great flood,

That raises the ocean

In decades slow motion

And swamps the islands

Unleashes the violence

Of cyclonic depressions

Imperial aggressions

Extinctions of species

And dreams smashed to pieces.

Problems unseen

in media smokescreen,

the rulers deny,

the consumers buy,

And the economy pumps more excrement.



Written by dan

January 27th, 2016 at 2:24 pm

Force and restraint

Simone Weil wrote about the Iliad, how it dealt so beautifully with the notions of force, how force crushes the soul, turns the body to stone, renders life into death.

But our morality has moved on from the time of the Iliad, though foreign policy largely has not. Warriors in war no longer carry automatic heroism. Their weapons are too lethal, their causes too unjust.

Today, the great cause is not in fighting the good fight in war; there are no good sides in wars. Perhaps not every armed conflict in the world today is entirely a clash of the equally bad; the world is plagued with enough violence that among them a few less-evil causes can be found — perhaps even one or two good ones. Among every thicket of bleeding thorns there is a rose whose struggle one may cheer on, depending on one’s inclinations. But the general fact remains.

The great cause in war today, in almost every case, is not in winning the war, but stopping the war, preventing the war, civilizing the vengeful and callous impulses of the great leaders of the world. The great cause is ending the senselessness of death and destruction among groups having no good reason to kill each other, and in crushing the nonsense that justifies it, whether claims of ethnic or religious superiority, national exceptionalism, or murderous foreign-policy cynicism.

The drama and the poignancy of the Iliad — which, like all ancient texts, comes at once from a cultural origin now buried in the collective subconscious, speaking in the language of a darker and simpler age — reverberated to Weil writing in the midst of Nazi occupation in 1940. One can only imagine, now, how force and violence then hung in the air, turning the world to stone and rubble — the stone no longer then the body of the vanquished, or the suppliant to Achilles with their life in his hands, but the citizen before the air raid siren signalling random sky-drawn death-blows, the village lined up before the machine gun, the Jew facing industrial extermination, the family in the wooden firebombed house, the Japanese schoolchild splattered into atoms.

For those in the global north, the west, Europe, North America, Australia, even there in the supposedly richest, cleanest, privileged nations, force remains today. Just causes still often retain the character of a struggle involving violence. Nothing, of course, compared to those actually facing war. But it is a different type of force; or rather, it is a type of restraint that turns us to stone.

Struggle leads, in one direction, straight into the streets where it is met with, if it is at all effective, force. And it leads, in another direction, straight into a pit of snakes. A media, a trolling ground, a culture that functions as one head with a thousand snakes lunging, biting and spitting venom.

It is not Achilles, but it is enough to turn the contemporary citizen — weakened, compromised, ashamed, guilty, knowing too much, doing too little — to stone. We have seen the medusa.

Written by dan

December 28th, 2015 at 10:26 pm

Forty years on

It is forty years on from the Dismissal, or coup, that ended the Whitlam government.

Forty years ago, to the day, Australia learned it would not be permitted to have an effective progressive government. The fires of change were extinguished, stamped out, and the old dead certainties returned.

A government that caught Australian society up – to some extent – from its benighted past, that brought it into the present, and even threatened to push it forward into the future, was cut down in its prime, aged not yet three years. For a short while, at least in one part of the world, despite obstructions and turbulence every step of the way, and despite numerous imperfections, another world seemed possible. This world was possible, she was breathing, but she was attacked, mercilessly, until she was killed.

I was not yet born. Hope was killed before I was born, and I grew up with innate desires for justice, equality, dignity and sanity in a society that acknowledged nothing of them. It professed amnesia on the topic; instead there were shiny toys, consumer goods, grades, jobs and mortgages. I did not know for a long time that such beliefs were what is called “politics”: I grew up in a society where “politics” was the bickering of boring men in suits on TV about issues so far from the central, real ones that I could not even recognise what the subject was. Only much later did I realise they were debating the ramifications, the elaborations, and the fine parameters of the solutions imposed in previous generations to foreclose on the real questions. It was precisely the hope of optimistic answers to these questions that had long ago been killed.

So one thing is not in doubt as to what the Dismissal represents, forty years on: its crushing of the human spirit. Forty years on we are afar and asunder.

It is important to understand such a crucial historical event. And so I would like to present a summary of my understanding and its significance, so that others might learn about it and what it means, and I might learn from others what it means to them, in terms of history, law, culture, and politics, from the small-P politics of the technicalities of the coup through to the capital-P politics of covert intervention and geopolitical significance. For the episode is simple in many ways, complicated in others; clear and well-documented in some ways, murky in others; subject to much controversy, but some parts are less controversial than others.

For three brief years, 1972 to 1975, a society tucked at the corner of the world, a backwater country in the bottom right corner of the world map, a long-time colonial outpost of various empires, with an appalling history of genocide and racism but an admirable supply of salt of the earth, caught up with history.

As elsewhere in the world, a cold conservative establishment had ruled for generations. With important exceptions, and occasional interruptions, Australian society had maintained its backwards, consumer capitalist, depoliticised, conservative culture. To a large extent it sleepwalked through the cultural change experienced elsewhere in the 1960s. It entered the 1970s largely left in the 1950s.

Those years have become in some ways a myth; in some ways romanticised; no doubt I am, to some extent, propagating myths and romantic notions of a time that was, in many ways, not particularly different from all the other years of Australian history. But those years have had such a definite and lasting impact on Australian institutions and politics, at least, that some of the awe expressed at the rapidity and extent of the change is justified.

* * *

The Australian Labor Party was the first labour party ever to take charge of any nation in the world (in 1904), but after the second world war steadily lost both its ability to win elections and its ability to hold itself together. Whether because of internal strife, ideological schisms, factionalism, too many moderates and too much compromise, too many hardliners and too much radicalism, poor leadership, poor institutional structures, an implacably hostile media, structural opposition to entrenched economic and political power, strategic ineptitude, proximity to communism, hostility to communism, significant economic growth, comfort and complacency, or a federal Constitution that stymied every plank in their programme, they spent decades in the wilderness. To some extent all of these causes played a role; there are certainly others too. It is an interesting and important task to untangle them.

But that does not change the fact: for the entire postwar era, from 1949 to 1972, the Australian Labor Party fought nine elections and lost them all. Nor was it a quixotic era of romantic, valiant efforts and tragic losses; it was continual bitterness, division, and infighting.

Whitlam emerged as a leader from the centre and the right of the party. Politically he was far removed from the idealists that sought the nationalisation of the means of production, distribution and exchange. Socially he was born into a privileged family; his father was the Commonwealth Crown Solicitor and he grew up in Canberra surrounded by erudition, bureaucracy, politics and law. He studied law and became a barrister practising in Sydney; far from a classic Labor background and far from working class.

With a mixture of eloquence and arrogance, punctilious legalism and reckless brinkmanship, strategic politicking and passionate crashing through, movement-building and legal creativity, he became leader of the party and united it around a programme that was both a pale shadow of the party’s official socialist programme and a blueprint for a revolution in Australian society.

Whitlam was relatively conservative, as far as Labor party ideology went, but the official party ideology was staunchly socialist – though of course the practice by elected politicians was very different. He was legalistic to a fault, but specialised in finding creative legal means to establish Labor party policy within the constitution, which like in many other places essentially outlaws many progressive reforms (especially socialist ones) – or at least places great constraints on them. It took a Queen’s Counsel like Whitlam to come to centre the party’s policies around loopholes in the constitution. Whereas previous Labor governments had tiptoed for a few years, then tried something bold like nationalising the banks, only to have it struck down by the High Court, Whitlam was much more politically and legally effective.

In practical effectiveness and impact, if not in ideology, Whitlam remains perhaps the most revolutionary democratically-elected reformer in the Western world. The country really did change more in 3 years than in the 20 years previous. When he passed away last year, Australians were inundated with enormous lists of the reforms achieved: universal health care, consumer protection, Papua New Guinea decolonisation, no-fault divorce, redistributive school reforms, commitment to international law, recognising China, abolishing conscription, getting out of Vietnam, free university education, massive arts programs, legal aid, urban development, a national sewerage program, territory representation in Parliament, removal of British remnants in governmental structures, anti-discrimination laws, abolition of the racist White Australia immigration policy, the beginnings of indigenous land rights, welfare for the homeless, legislating equal pay for women, abolition of the death penalty, the list goes on. I know of no equivalently broad and rapid set of reforms anywhere in the world achieved by constitutional legal means. This was not the whole of the programme on which the government was elected, but it was most of it. Some of it has been rolled back, but much of it remains. Australian society is enormously better as a result.

One can imagine, with such a torrent of change all occurring in an historical instant, after long sleepy decades of conservative rule, the reaction of elites. It was absolute screaming paranoia and anti-communist hysteria. The conservatives – the Liberal and National parties – in Parliament tried fervently to block all the legislative change; they were implacably obstructionist and irredeemably hostile to all this change as they saw their relaxed comfortable country fading away before their eyes. The country was simply having a catching-up with history, but for them it was like the end of the world.

They blocked everything. Labor did not control the senate and instead of just blocking standard legislation, in 1974 the Liberals threatened to block the supply bills – the ones that provide the supply of money so that government can function. This tactic is subversive of the parliamentary order: it puts a figurative gun to the government’s head, and says that as long as the government does not command unusually large majorities it will not be permitted to function. It is a method approaching the level of a constitutional coup; within the system, it could only be legitimate, if at all, when a government had committed a vast crime or abuse for which no other means of accountability were available. Whitlam, of course, had merely passed progressive legislation. Moreover, he held his government accountable to high standards, and sacked ministers when they failed to meet such standards.

In any case, as a result of such obstructionism incompatible with representative democracy, well short of having run a full first term, in 1974 Whitlam performed a constitutional manoeuvre. In the Australian constitution there is a special provision to dissolve both houses of parliament, and then both houses sit together in a joint session and their vote overrides any previous blockage. Despite all the hysteria and fanatic hostility from the media, Whitlam won the double-dissolution election convincingly with a 5-seat majority (marginally reduced from 6) and got his program through in the joint sitting. Triumph.

Into 1975 the conservative paranoia turned maniacal. Despite the Whitlam’s government’s clear and renewed electoral mandate, the Liberal s again found an excuse to block supply. Their excuse was the so-called “Loans Affair” – see below. It was a scandal which engulfed the government, but what is clear is that it was far from any sort of crime of impropriety which would justify the extreme action of blocking supply. The media, hostile as always, became especially vicious, and the matter escalated and escalated. The crisis continued and deadlines for supply loomed, with the possibility of the government shutting down for lack of money. Finally Whitlam decided, against the entrenched obdurate opposition, to call an election of half the senate, which would resolve the impasse and decide the issue. As Australia is a monarchy, he had to formally advise the Queen’s representative, the Governor-General, John Kerr, who by constitutional convention would then issue writs for the election.

One very poor design fault in the Australian constitutional system is that these two people – the Prime Minister, and the Governor-General – each have the authority to sack the other with immediate effect. In 1975 there was an even greater design fault: not being designed at all. Because the Australian constitution is largely unwritten, deriving from convention and ultimately from British tradition, it was not clear exactly what the Governor-General’s powers were or how they should be used.

Whitlam went to Kerr’s “palace” (Government House) on November 11, 1975 – forty years ago to the day – and met Kerr to call the election. But before Whitlam could pass Kerr the document advising the election, Kerr passed Whitlam a document which was his letter of dismissal. Whitlam was sacked as Prime Minister with immediate effect.

It was a carefully premeditated plan: Kerr had known exactly what Whitlam’s plans were, but had kept his own plans secret and indeed had been conspiring in secret with the leader of the opposition and two High Court judges.

Immediately after Whitlam was sacked and, shell-shocked, left Government House, Kerr called on the leader of the opposition, Malcolm Fraser. Fraser had in fact hidden himself in another room, at the opposite end of Government House, while Whitlam had come and gone. In a pure moment of palace intrigue, Fraser literally emerged from the shadows, was ushered up the hallway, whereupon Kerr appointed him Prime Minister with immediate effect.

Tragedy. And it continues to burn in the heart of every progressive Australian ever since.

* * *

It is a sore point – and an expressly partisan political one – in Australian electoral politics ever since, to respectively denounce or justify Kerr’s actions. At the time little was known about the exact thoughts, meetings and communications of Kerr and Whitlam, but more has come to light over the years. Amazingly, more continually comes to light, right through to the last few days. But as the historical evidence has accumulated, all arguments in defence of Kerr have been comprehensively demolished by the facts.

In the Australian government, the Prime Minister is the head of the government and, as in Westminster-style parliamentary systems, by convention is the politician who is the leader of the political party with a majority in the lower house. The Governor-General is a largely figurehead position: their signature is required for laws to come into effect, and to appoint governments and call elections, but they essentially act as a rubber stamp. Unlike the Prime Minister, the Governor-General is not elected – they are appointed by the Prime Minister – and has no democratic legitimacy to set any policies of the government, nor (essentially) any discretion in following the government’s wishes to sign legislation or call elections. As a vestige of the British constitutional monarchy, the Governor-General does however act as Head of State (representing the Queen) and does have some so-called “reserve powers”, including the formal ability to sack the government in a constitutional crisis. The extent of these powers is debated, but it is clear that such powers, so far as they exist, are only to be exercised in the most extreme of circumstances; and in any other case they remain a mere figurehead.

Kerr had met with Garfield Barwick, the Chief Justice of the High Court – which is supposed to be an absolutely independent body from both the executive government (which included Kerr and Whitlam) and the Parliament – the day before the sacking. Twice. This was done in explicit defiance of unqualified advice given to Kerr by Whitlam not to do so. Kerr and Barwick had in fact met several times over the preceding months to discuss the issue. Separate from these meetings, Kerr had also established a “seminar” group at the Australian National University several months earlier to advise him on his powers. This again was done in secret, without Whitlam’s knowledge, and even worse, the meetings were attended by another sitting High Court justice, Anthony Mason, who was an old friend of Kerr’s. The “seminar” was hardly an academic exercise in archaic constitutional law and its conventions: it happened through the period that Liberal senators threatened, then outright refused, to vote on supply bills. By October the attendees had become acutely uncomfortable, as the issues – and possibly illegitimate readings of them – were being practically considered by Kerr.

Nonetheless, Kerr continued to confide in the High Court judge Mason every step of the way. Mason even wrote a draft letter sacking Whitlam (Kerr eventually used his own version). Kerr also sought out the Queen’s private secretary to discuss his own position, again in secret, without Whitlam’s knowledge. None of this was known at the time, and has only come to light as Kerr’s papers have been released and read by historians, and discussed in the most recent and leading historical work on the topic, Jenny Hocking’s two-volume biography Gough Whitlam: His Time. (Much of my account here is based on that book.) Mason put out one statement on the issue but still refuses to talk about it. To call this a “conspiracy” is not hyperbole or rhetorical – it is simply to state what happened. Kerr took some pains not to explicitly tell his co-conspirators, particularly Barwick, to his precise plans, but compartmentalisation of knowledge and deniability are standard features of conspiracies.

It gets worse for Kerr. On 6 November, Whitlam told Kerr of his intention to call an election, with the formal written documents to be presented on 11 November. So Kerr knew the crisis would be resolved by an election, and knew exactly what Whitlam would do. Incredibly, on the same day Kerr decided, and wrote in his diary, that “no compromise could be found” – even though Whitlam had just found one, and explained it to him – and that he would have to act on the advice of the Liberal opposition leader Fraser. The “independent” Governor-General Kerr – supposedly in a position above electoral and party politics – was thus in active allegiance with the Liberal opposition to the elected government, despite having direct and first-hand knowledge that any political crisis would be averted, right down to the exact details of the election and its date of announcement. While Whitlam was making arrangements to resolve the crisis, keeping Kerr fully apprised of developments, Kerr instead drafted a letter of dismissal. This 14-page draft, never used but found later in Kerr’s papers, gave the official reason for dismissal as Whitlam being “unable to obtain Supply from the Parliament” – just as Whitlam had just told Kerr of his plan to hold an election so as to resolve the impasse and pass supply. Not even these basic facts could stop Kerr writing down falsehoods as an excuse to sack Whitlam. In fact, much of Kerr’s draft focused on himself, his own sense of personal affront, and the “public criticism” he had “endured”. Kerr did this all in secret. Kerr’s reasoning was factually wrong and completely indefensible as a matter of both constitutional law and political legitimacy. Whether he was deluding himself or simply unable to comprehend Whitlam is an interesting question of forensic psychology, but in any case his written self-justifications fail for the most elementary of reasons.

Whitlam, sadly, never got wind of Kerr’s subterfuge, missing several hints along the way. The first Whitlam knew of it was being peremptorily sacked in Kerr’s office. But Kerr did tell others of his plans – including the High Court justice Anthony Mason, to whom he mailed directly various documents of advice. And Kerr met the High Court Chief Justice Barwick on the 10th – the day before the dismissal – twice.

A combination of naiveté, attendance to protocol, and legal formality meant that the very idea of a “palace conspiracy” was unthinkable to Whitlam. Whitlam simply took the view that the Governor-General could only act on the Prime Minister’s advice. Whitlam had told Kerr as much, advised Kerr not to do otherwise, and assumed that was that. And Kerr knew this; he used Whitlam’s innocence against him. Incredibly, Kerr wrote in his diary that Whitlam “was not entitled to know… my thinking… because he was not open to reason”. Kerr’s attitude to Fraser, the Liberal leader, was of course entirely different, and demonstrates his true allegiance.

On the very day of the dismissal, Whitlam, in blissful ignorance and on the(poor) assumption that his opponents were minimally reasonable, quite rightly sensed complete victory in the Labor Party’s continuing parliamentary impasse with the opposition. When he explained his plans to the party room his colleagues erupted in cheers. He telephoned Kerr to tell him what time he was coming – 10 am – and Kerr pushed back the meeting time to 1 pm. Whitlam even triumphantly started debating Fraser in Parliament, as it was a Parliamentary sitting day. When Fraser, without notice, walked out of the chamber to hide in the shadows of the “palace”, Whitlam had no inkling of what was going on. When Whitlam later of course also went to Government House, and was sacked, he left without any knowledge that Fraser was hiding in the shadows down the hallway. Even many Liberals who were happy that Whitlam had been sacked were shocked to find that Kerr had gone further and actually appointed Fraser Prime Minister – a clear usurpation of parliamentary democracy, forming a government clearly against the electoral will, and rewarding years of Liberal obstructionism with government.

There has been considerable speculation that Whitlam could have manoeuvred to reinstate himself. Perhaps he could have refused to accept Kerr’s letter of dismissal. Perhaps he could have torn it up in front of Kerr. Perhaps he could have, as his wife suggested shortly afterwards, slapped Kerr in the face and told him to pull himself together. But a stickler for protocol, and unwilling to take any steps that might escalate into a potentially violent confrontation and rupture the decorum of parliamentary procedure, Whitlam immediately returned to the Parliament to pass a motion of no-confidence in Fraser’s supposed new government. The lower house passed a resolution advising the Governor-General to form another government under Whitlam.

Perhaps the most effective way Whitlam could have fought back would have been for Labor now to defer or block a vote on supply themselves; Labor did not have an effective majority but with some independent or opposition votes they could. Labor senators had been instructed previously to try to pass a supply bill again. Incredibly, due to a tragic lack of communication, Labor senators voted without knowing Whitlam’s government had been dismissed hours earlier. (Incomprehensibly, at least one senator did know but said nothing.) Liberal senators could not believe their luck as supply was passed, and with supply secured, Fraser returned to the Governor-General.

A final unprecedented scenario then occurred – another rush to the palace. Fraser raced there with supply secure, while the Speaker of the House took the house’s no-confidence motion advising (arguably, legally forcing) the Governor-General to sack Fraser and re-appoint Whitlam. Fraser arrived first; Kerr promptly dissolved the Parliament and his plan was complete. The Speaker’s no-confidence motion then stood for nothing. This final, shocking usurpation, was far beyond any constitutional conventions regarding the Governor-General’s powers – not just dismissing the government in a crisis, not just appointing a Prime Minister who had no mandate, but also dissolving the entire Parliament once the vice-regal representative’s policy wishes had been achieved. That is why we it deserves the title of a coup rather than simply a dismissal.

Thus hope was killed in Australia.

* * *

Putting aside the minutiae of Parliamentary chicanery, and the intricacies of palace intrigue, one sees in hindsight a clear common set of values and interests among the elite sectors of Australian society. At one level this clear set of allegiances was expressed in the meetings and understandings between high-ranking officials such as Kerr, Barwick, Mason and Fraser. At another level such allegiances were expressed between Liberal politicians, with all their old-boys-clubs and connections, the business establishment, and other privileged and reactionary sectors of society which united against the government. And at yet another level it was expressed through cultural conservatism, in the media screaming for Whitlam’s head, the hysterical fears of socialism and communism, and the horror at the old world giving way to the new. These elite and conservative sectors were united in their preference to overthrow a legitimately elected government rather than endure progressive reform.

This was an elite that could not believe it no longer ruled, that still believed it was born to rule, and acted to reinstate the correct order of nature. And in so acting accordingly they managed to obstruct, to destabilise, to plunge into crisis, and finally to remove an elected government. It was, in the final analysis, a coup of the elites.

One interesting question that arises – one that is particularly important to the Left – is to what extent this elite opposition included, or was assisted by, military and intelligence services, domestic and international. Many, particularly on the Left, described it as a CIA coup and many still do.

So let us examine this question – to some extent, at least, and to the level of my own understanding.

* * *

Anti-communism and US subversion. At that period of time throughout the world, US foreign policy, and especially intelligence activities, were primarily, at least by their own account, motivated by anti-communism and containment of Soviet influence. This anti-communism regularly bordered on paranoia. Where that paranoia existed, and where it was in US interests to do so, governments were subverted or even overthrown. Reformist, social-democratic or independent nationalist governments were regularly painted as “communist” as justification for US intervention – from Iran, to Indochina, to Brazil, to Nicaragua, to Greece, to Indonesia and many other lands. It is not at all surprising that they would take an interest in a government committed to such rapid social change as Whitlam’s – no matter how meticulous its adherence to constitutional parliamentary practice and democratic processes. It did not stop them destabilising the democratically elected governments of Italy, British Guiana, Chile, or Guatemala. Neither being a Western democracy nor an American ally provided immunity against such actions. So there is no reason the US would not take a similar approach in Australia – indeed, it would be surprising if it were otherwise.

In 1974, true to form, the US appointed Marshall Green as ambassador to Australia. Green had played an important part in overthrowing Sukarno’s government in Indonesia, and the massacre of hundreds of thousands of left-wingers. No doubt he was trying to influence matters; he is reported to have made incendiary speeches against the government.

Whitlam, the privileged Queen’s Counsel, committed as he was to the Westminster Parliamentary system, to representative democracy and social-democratic reforms without altering the basic economic framework of capitalism, was about as far from a communist as it was possible to be, among reforming politicians. Whitlam explicitly eschewed the old-school Labor party programme of socialism by nationalisation of the means of production, distribution and exchange; never did anything of the sort; and never so much as suggested it. But Arbenz in Guatemala was equally non-communist; as was Mossadegh; as was Lumumba. A rational evaluation of the policies of any of these politicians would have revealed their distance from communism and the Soviet Union, but that did not stop intervention, and nor did it with Whitlam.

To some extent, no doubt, CIA officers were deluded by their own propaganda that Whitlam represented another menacing domino in the communist march through south-east Asia. But there are also more rational reasons for US intervention in each case. There were threats to US interests. Arbenz was a threat to the United Fruit company; Mossadegh to BP (then AIOC) of which the US wanted a cut; Allende to Anaconda. And all of these examples, further, constituted the potential threat of a good example, an alternative model of development, an alternative economic system, beyond the domination of the US and capitalism more generally.

Whitlam equally represented the threat of a good example; indeed, an exemplary one, of progressive change within the existing system. He also, certainly, attempted to pursue a more independent foreign policy, by recognising China, forging closer ties with Japan, opposing nuclear testing in the Pacific, and in general reorienting foreign policy with Asia. But beyond extricating Australian forces from Vietnam, however, he did little to oppose US policies in the region. Indeed he defended the brutal US-backed Indonesian dictator Suharto, and his attitude towards the genocidal Indonesian invasion of East Timor was based on staying out of the problem. As he put it to the Indonesian government, his aim was to “minimise the public impact in Australia” – and this attitude, according to Australian diplomatic cables, helped to “crystallise” the thinking of the Indonesian government, “now firmly convinced of the wisdom of this course”. Of course a green light from Ford and Kissinger meant far more to Suharto than Whitlam closing his eyes, but Whitlam’s effort, or lack thereof, was not inconsequential.

So, while independent by some measures, Whitlam’s foreign policy hardly presented a threat to US interests, and even descended to an acquiescence in US-supported Indonesian genocide. But there were also more specific threats.

Refusal to cooperate in subversion. Whitlam also had a troublesome propensity to disapprove of his government’s intelligence services being used to subvert democracy abroad – a disturbing level of independence. In 1973 he was informed that two officers of ASIS, the Australian Secret Intelligence Service, were stationed in Santiago working with the CIA in their program of subversion of the democratically-elected left-wing Chilean government of Salvador Allende. It has been argued that the ASIS officers were “only” collecting intelligence from CIA agents in the field, rather than actively engaging in subversion. But the distinction is minimal; Australia was actively participating as a proxy in the CIA’s covert program of destabilising democracy. Whitlam ordered the ASIS station to be closed in April 1973.

Incredibly, ASIS defied the orders of the government they were supposed to serve. ASIS took months to remove the ASIS officers from Chile, continuing to collaborate in overthrowing Allende. Later, ASIS also misled the government about its operations in what was then Portuguese Timor.

The domestic intelligence agency, ASIO, was no better. ASIO had long served as a political police, amassing vast files on left-wing activists and politicians, including a significant proportion of the Labor party. Many literary, cultural and political figures in Australian life have been subjects of ASIO surveillance; a recent documentary series details the relentlessness and depths of their invasions of privacy. This included an especially large file on Jim Cairns, who became Whitlam’s Deputy Prime Minister and Treasurer. As soon as Cairns assumed the role ASIO promptly leaked his file to a favoured journalist, scaremongering about Cairns’ alleged communism. This was nothing new. The previous Liberal government had a longstanding arrangement with ASIO to feed damaging information on left-wing figures to favoured media contacts. (As it turns out, this arrangement was approved by Garfield Barwick, who was then Attorney-General, before he went on to become Chief Justice and conspire with Kerr to sack Whitlam.) As a Royal Commission later found, ASIO had also been providing such information to the CIA.

While ASIO had been carefully surveilling social democrats, Labor politicians and non-violent activists, it had ignored actual terrorist threats like Croatian fascists, who had been conducting bombings and arson attacks on Australian soil for a decade – leading Attorney-General Lionel Murphy to raid ASIO offices in early 1973.

Perhaps not surprisingly, Whitlam felt that ASIO’s relationship with the US was too close, and eventually in September 1974 ordered ASIO to sever ties to the US. Again, incredibly, the order was defied. According to ASIO’s own official history, the head of ASIO, Peter Barbour, “felt this would be harmful to the nation”, and so decided to maintain relations, albeit less formal ones. Whitlam finally sacked Barbour in September 1975 on the recommendation of a royal commission into the Australian intelligence community.

The only conclusion is that the allegiances of the intelligence community to their US counterparts were stronger than their allegiances to their own government.

Pine Gap. Primary among US interests in Australia was intelligence infrastructure crucial to American signals intelligence collection. The US base at Pine Gap, near Alice Springs, was essential to US communications with its satellites, whether for spying, nuclear weapons verification, or otherwise. The US lease over Pine Gap was due for renegotiation in late 1975, and US officials were deeply concerned about losing this base.

On 3 November 1975, barely a week before the Dismissal, Whitlam accused the CIA of channeling funds to the National Country Party – the Liberals’ Coalition partner – via an agent in Australia. Though Whitlam did not name the agent, it soon came to light the Whitlam was alleging a CIA operative named Richard Stallings had provided funds to Doug Anthony, the leader of the National Country Party. The revelation was made by Anthony himself in Parliament on November 4. Unfortunately for the CIA’s efforts to protect Pine Gap, Stallings had been the first head of the Pine Gap base. It was not previously known at that point that Pine Gap was a CIA base, and US officials were alarmed at their cover being blown.

Ted Shackley, who was head of the CIA’s East Asia Division, berated ASIO representatives in Washington in a meeting a few days later, on 8 November, declaring that the “the whole Australian intelligence relationship with the US” was “under threat”. It was later reported that Kerr “sought and received a high-level briefing from senior defence officials” about this threat the same week, apparently at the Defence Signals Directorate in Melbourne, while he was there for the Melbourne Cup. (In subsequent years Kerr was to make a very public drunken fool of himself at this horse race.) But Kerr and others denied it, and Hocking in her book, having examined Kerr’s copious diaries and papers, reports nothing further of it.

On 10 November – the day before the dismissal – Shackley sent a secret cable on a dedicated CIA-ASIO link. It was not intended to be seen by Whitlam. This cable warned that Whitlam’s statements on CIA agents threatened to “blow the lid” on CIA operations in Australia, and ended ominously: the “CIA feels that everything possible has been done on a diplomatic basis… if this problem cannot be solved they do not see how our mutually beneficial relationships are going to continue”. The CIA essentially viewed Whitlam as a security risk. However, by this time the previous head of ASIO, Peter Barbour, who had defied Whitlam’s orders, had been replaced by Frank Mahony, whose loyalties lay with the Australian government. He immediately took the cable to Whitlam, but Whitlam intended to reveal the connection between Stallings, hence the CIA, and Pine Gap on the next day, November 11. Events, of course, intervened.

The incredible timing – Whitlam sacked on the very day he was due to report the Pine Gap-CIA connection – of course, looks deeply suspicious.

Funding opposition parties. Funding the opposition would certainly reflect a common CIA tactic. It had been used in Chile, for instance, in the 1964 and 1970 elections – indeed, in 1964, the CIA spent more per voter on the campaign of Eduardo Frei in the Chilean election, than was spent by the Johnson and Goldwater campaigns per voter in the US Presidential election of that year. The allegations made by Whitlam of CIA funding of opposition parties are certainly not unique to him; Victor Marchetti, an ex-CIA officer, has claimed that the CIA funded both Liberal and National parties; and it has been alleged the CIA offered the opposition “unlimited funds”.

Union influence. Attempts to gain influence within the union movement around the world, in order to promote anti-communist, ideologically moderate forms of trade unionism, were run by the CIA and its fronts throughout the Cold War period. A long-running scheme of “Leadership Grants” brought talented, more conservative trade unionists from around the world to the US where they were given “leadership training”, inculcating into a “labour elite” and inoculated against communist ideas. Clyde Cameron, Whitlam’s Minister for Labour and Immigration, testifies of first-hand experience of the CIA funding opposition tickets against him in internal elections of the Australian Workers Union.

In this Australia appears to have been treated similarly to other Western nations; however, more serious and specific allegations of US influence over Australian unions were made by Christopher Boyce. Boyce worked in the “vault” at a CIA subsidiary in California, a communications relay room which received messages from Pine Gap, and read telex messages which implied the CIA had infiltrated leadership of Australian unions and were able to exert influence to achieve their own aims. Specifically, Boyce read a telex from Langley at a time when shipments from the US bound for Pine Gap could have been disrupted by imminent strikes by Australian pilots and air controllers. The telex stated that the CIA had suppressed the strikes and the shipments would continue. Boyce was outraged and lashed out, attempting to sell secrets to the USSR; he was eventually convicted of espionage; later he escaped from prison and committed several bank robberies. Today, having served his time, his story remains consistent.

Boyce also relates first hand the culture of the CIA contempt for Whitlam – and how his CIA employee workmates referred to the Governor-General as “our man Kerr”.

Kerr’s CIA connections. Kerr was quite deeply involved with several organisations connected to the CIA. Despite being a Trotskyist in the 1940s, Kerr worked as a barrister specialising in representing anti-communist unionists in their internal union battles. He then moved from the Labor to the Liberal party and became heavily involved with the Australian Association for Cultural Freedom, the local branch of the Congress for Cultural Freedom, a CIA-financed anti-communist cultural organisation. Kerr also became president of the Law Association for Asia and the Western Pacific, another CIA front. As such, the CIA was paying for Kerr’s travel.

These associations prove only that Kerr mixed in some social, political and cultural circles which were sympathetic to the CIA’s anti-communist stance. They could have also provided a social milieu in which he would have developed personal connections to those close to the CIA. Quite likely they would have tried to court him as best they could.

It has been alleged that a deputy CIA director said that Kerr “did what he was told“.

Tirath Khemlani and the Loans affair. There are significant allegations about CIA involvement in one of the scandals that enveloped the Whitlam government, the so-called loans affair. This affair concerned efforts by the Whitlam government to obtain loans for an ambitious development project for the Australian resources sector, the “magnificent obsession” of Whitlam’s Minister for Minerals and Energy, Rex Connor. The government approved an authority for Connor to seek a $4 billion loan; it was an unusual procedure, to vest authority in the Minister for Minerals and Energy rather than the Treasurer, but Treasury was resolutely opposed to the loan and the government circumvented it. It was a creative financial strategy for a government, and in its legal creativity followed other political strategies of the government, but was not improper or illegal. Connor soon came into contact with a London-based Pakistani commodities dealer named Tirath Khemlani. Khemlani was a rather dubious character: he made various demands of the government but was rebuffed; he sought loan funds from various governments and eventually announced that funds were available; and interminable delays followed, with the money never materialising. Connor could have refused to deal with him, but having spent his whole life dreaming of his development projects, he was desperate to get the loan. Eventually Whitlam had to call off the search for loan funds, causing great damage and embarrassment to the government. It has been alleged that Khemlani relied on a company with CIA links, Commerce International to supply the funds, and indeed that the whole affair was a setup by the CIA.

The loans affair however did not end there, because a similar situation then occurred with the Treasurer, Jim Cairns, who sought funds via a Melbourne businessman named George Harris. Cairns insisted on various conditions in their agreement, including the condition that no brokerage fee be included. Some weeks later newspapers published copies of a letter purporting to be signed by Cairns and promising just such a fee. It is possible the letter was a fabrication; or that Cairns signed a letter containing a paragraph in error; or that the letter was drafted maliciously; there are other possibilities also. The published letters were dubious in origin; the CIA’s Daily briefing report on the matter noted that “some of the evidence had been fabricated”.

Meida attention on the loans affair intensified, leading to escalating, wild allegations and assertions circulating in the media. It has been alleged this media circus involved “a welter of supposedly incriminating documents forged by the CIA”. A CIA employee Joseph Flynn later claimed he had forged some of these documents, having been paid by Michael Hand of the infamous Nugan Hand bank. (Michael Hand, having been living under protection under an assumed identity in the US for many years, has been found as of only a few days ago.)

The loans affair was seized upon by Fraser as an excuse again to attempt to block supply. In this way, the loans affair directly destabilised the government. But Fraser had been constantly scouring the government’s activities for a “reprehensible circumstance” it could use for this purpose, and no doubt if Khamlani had not come on the scene they would have found an alternative. The Whitlam government committed no great impropriety, but handled the matter with great ineptitude.

* * *

Covert intelligence operations, by their nature, are difficult to assess in detail. They breed rumour and innuendo – indeed, misinformation is often a crucial component – and usually involve unreliable or otherwise dubious characters.

The above is not meant to be comprehensive, or complete, but a summary of some evidence in relation to CIA activities against the Whitlam government.

But it does make clear that the CIA threatened action against Whitlam to potential co-conspirators, did in fact view Whitlam as a security risk, and sent a secret cable to ASIO which was meant to be kept secret from Whitlam with sinister implications. The CIA expressed every intention to move beyond “diplomatic means” in Shackley’s cable, one day before the dismissal.

Moreover, there is evidence that the CIA engaged in disinformation – producing false, forged, and incriminating documents for the media – in the loans affair, and possibly even deliberate fraud against the government, if Khemlani had a direct CIA connection. This affair successfully destabilised the Labor government, since Fraser used it as an excuse to withhold supply – but Fraser would likely have found some excuse in any case.

There is also evidence of funding opposition parties and conservative tickets in union elections. And there are less specific allegations of a closer CIA connection: that Kerr was “our man” and “did what he was told”.

Thus, we say for sure that the CIA wanted Whitlam out. We can say for sure that the US government was alarmed at the highest levels about the possibility of losing Pine Gap, crucial as it was (and remains) to signals intelligence and spying capabilities. We can say that Australia was not immune to worldwide CIA tactics of anti-communist influence, for instance through its trade union leadership program, and that its anti-communist cultural institutions included within their orbit the key figure of John Kerr. We can say for sure that Australian intelligence agencies were more aligned with their US counterparts than with the Whitlam government whose orders they were required to follow, but which they instead defied; although Mahoney appears to have been a loyal replacement.

There is also evidence of CIA activities to destabilise the Labor government, whether by funding opposition parties, spreading misinformation or forged loans affair documents. They no doubt did what they could to advance their own interests.

It is clearly fair, then, to say that it was the coup was actively supported by the CIA.

* * *

Less importantly, it is not so clear that Kerr was in direct contact with the CIA or other intelligence agencies or their agents, or followed their orders in any way. The strongest argument here is Kerr’s character and the extensive self-documentation he provided throughout the period.

Kerr’s personality was well known. He was a haughty, arrogant caricature of an elite who wore a top hat and essentially lived as if he were in Victorian England; the associated politics go without saying. He was thin-skinned, insecure and an inveterate drunk. After 1975 he was wracked with guilt and loathing for the rest of his life, continually trying to justify his actions for decades afterwards. Given his propensity to self-justify, his stream-of-consciousness diaries, and his lack of discretion, it seems unlikely he could have failed to mention or kept a secret of any direct CIA contact.

Moreover, Kerr’s own papers show that he had made up his mind to act, even writing a draft letter, several days before the dismissal and several days before the Shackley cable – which appears to have been taken directly by the loyal ASIO replacement director Mahony straight to Whitlam. If he had shared a briefing from the DSD, it may have been of some influence, but not enough to mention in any of his notes. As far as the former barrister and judge Kerr was concerned, the issue allowing him to sack Whitlam was inability to obtain supply – however false that argument was – not any national security or intelligence considerations.

The coincidence between the Shackley cable and the dismissal the next day may be less incredible than it seems. There were many dates in that period that had special significance to the intelligence community. Had the dismissal occurred on a day where an intelligence official was sacked, or a particular CIA activity took place, or an announcement made by Whitlam on foreign policy, the dismissal may have seemed equally suspicious. Given the government’s turbulent relationship with the intelligence agencies, there were many such days during its term of government.

For CIA operatives to describe Kerr as “our man” is quite possibly simply an expression that Kerr shared their anti-communist and conservative values. He even mixed in some of their cultural circles, and they were cheering on their man in Australian politics, as they would cheer on their football team. Kerr proved his anti-communist credentials while sitting as a judge on the Commonwealth Industrial Court, where he sentenced a communist union member, Clarrie O’Shea, to an indefinite prison term for contempt of court, for refusing to turn over the accounts of his union.

It appears that Kerr acted to achieve the CIA’s desired result, for his own independent reasons.

The allegation that Kerr “did what he was told” is emphatic, but it is an isolated assertion, and intelligence officials are renowned for braggadocio. There remain, however, many things we do not know.

* * *

There are still many things we do not know, but amazingly, more evidence comes to light each year. Christopher Boyce, released from prison, gave a rare interview only last year. ASIO’s official history of the period has only been released this year. A declaration by Malcolm Fraser as the events on the morning of the dismissal was released only last week. Michael Hand’s whereabouts were discovered just a few days ago. And the correspondence between Kerr and Buckingham Palace –with the Queen and her advisors – has not been released, and is not due for release until 2027.

Much evidence remains in the shadows. Some will remain there, and some will see the light.

For many purposes, however, it is enough to know that the CIA wanted to remove an elected Australian government, and acted accordingly.

There was domestic opposition to Whitlam, and it was fanatical, hysterical, powerful, and ruthless. The Liberal party, business, and other elites had governed the country for the previous 23 years, and for a majority of the time since federation. An entire class had developed with the arrogant belief it had a right to rule; a tradition inherited from British colonialism. And when an upstart government started to be effective in implementing progressive reforms and social change, it broke all of its own established rules and conventions in a ruthless attempt to overthrow them. Their rage snowballed into crisis after crisis. The intelligence agencies, including the CIA, were enthusiastically all in favour, and enthusiastic participants, but domestic opposition was likely sufficient on its own account.

In the end, who precisely bears the responsibility for killing hope in Australia is not the most important question. It is enough to know what was done and who was involved.

It is important to understand that a rich, western, parliamentary democracy like Australia is not immune from the subversion of foreign intelligence. No doubt the CIA (and, for that matter, MI6) were doing so as they pleased. They have done that everywhere they can, especially when there’s a government left of Genghis Khan. The dismissal of the Australian government in 1975 earns its place in the long lists of US military and CIA interventions. Indeed it appears as one of the 56 chapters in William Blum’s chronicle of the subject.

I avoid calling the Dismissal a “CIA coup”, however. A more accurate phrase might be “CIA-supported coup”, but the more important reason is that when Australians say that the dismissal was a CIA coup, it lets Australian elites off the hook.

Australian elites – from the Liberal party, to various organs of government, to the media, to business owners – were united in their hatred of the Whitlam government. They, as much as any subversive foreign intelligence organisation, should not be let off the hook. They have crushed our dreams once, and we should not let them do it again.

* * *

Hope was killed by elites who could not bear to see progressive change, even in its most legitimate, democratic form.

This all happened before I was born. There has never been such hope in Australian society as there was in that period. It is not romanticising the period to say so. We are all tired of this hope-starved world.

Whitlam moved the Labor party rightward, away from nationalisations and on a more moderate, more creative, social-democratic course. After the dismissal, subsequent leaders moved the party further rightward, in parallel with other social-democratic parties around the world. It has long been a pale shadow of its former self.

As the party moved right, those of its dreams which had been implemented became routine and part of the basic minimum of a civilized society: who could now imagine a society without no-fault divorce, consumer protections, anti-discrimination laws or a public health system?

But those of its dreams which never came to fruition were forgotten, consigned to oblivion along with all those dreams which were more distant utopias, those which had never even been dreamed. The light on the hill became indistinct, faded away and in the end became nothing more than a bigger, better, shinier, electronically-glowing version of the ever-consuming present.

With the collapse of communism around the world, an authoritarian yoke was lifted off a vast portion of the world’s people. But with its collapse and social democracy’s retreat, the promise of a world not based on rapacious individualism, the very idea of a better world disappeared too.

Social movements still maintain that a better world is possible. It is an admirable and necessary position, but it is minimal. To insist something is possible is merely to remind ourselves of the idea, to guard against amnesia. The struggle of people against power is often the struggle of memory against forgetting, but it is also more than that.

These forty-year-old memories must be replaced by another flourish of progress, to renew the hopes of the next generation.

Hope was killed by elites before I was born, but I was not born then to have my hope killed.

They did not kill my hope.

Written by dan

November 11th, 2015 at 12:32 pm

Paranoid defence controls could criminalise teaching encryption

(This article was also published at The Conversation.)

You wouldn’t think that academic computer science courses could be classified as an export of military technology.

But unfortunately, under recently passed laws, there is a real possibility that innocuous educational and research activities could fall foul of Australian defence export control laws.

Under these laws, despite recent amendments, such “supplies of technology” — and possibly a wide range of other benign activities — come under a censorship regime involving criminal penalties of up to 10 years imprisonment.

The Defence and Strategic Goods List

How could this be?

The story begins with the Australian government’s list of things it considers important to national defence and security. It’s called the Defence and Strategic Goods List (DSGL). Goods on this list are tightly controlled.

Regulation of military weapons is not a particularly controversial idea. But the DSGL covers much more than munitions. It includes many “dual use” goods – goods with both military and civilian uses – including for instance substantial sections on chemicals, electronics, and telecommunications.

Disturbingly, the DSGL veers wildly in the direction of over-classification, covering activities that are completely unrelated to military or intelligence applications. To illustrate, I will focus on the university sector, and one area of interest to mathematicians like myself — encryption — which raises these issues particularly acutely. But similar considerations apply to a wide range of subject material, and to commerce, industry and government.

Encryption: An essential tool for privacy

Encryption is the process of encoding a message, so that it can be sent privately; decryption is the process of decoding it, so that it can be read. Encryption and decryption are two aspects of cryptography, the study of secure communication.

As with many technologies subject to “dual use” regulation, the first question is whether encryption should be covered at all.

Once the preserve of spies and governments, encryption algorithms have now become an essential part of modern life. We use them almost every time we go online. Encryption is used routinely by consumers to guard against identity theft; by businesses to ensure the security of transactions; by hospitals to ensure the privacy of medical records; and much more. Given that email has about as much security as a postcard, encryption is the electronic equivalent of an envelope.

Encryption is perhaps “dual use” in the narrow sense that it is useful to both military/intelligence agencies as well as civilians; but so are other “dual use” technologies like cars.

Moreover, while States certainly spy on each other, essentially everyone with an internet connection is known to be spied on. Since the Snowden revelations — and much earlier for those who were paying attention — we know about mass surveillance by the NSA, along with its Five Eyes partners, which include Australia.

While States have no right to privacy — this is the whole point of Freedom of Information laws — an individual’s right to privacy is a fundamental human right. And in today’s world, encryption is essential for citizens to safeguard this human right. Strict control of encryption as dual-use technology, then, would not only be a misuse of State power, but the curtailment of a fundamental freedom.

How the DSGL covers encryption

Nonetheless, let’s assume for the purposes of argument that there is a justification for regarding at least some aspects of cryptography as “dual use”. (Let’s also put aside the efforts of government, stretching back over decades now, to weaken cryptographic standards and harass researchers.)

The DSGL contains detailed technical specifications covering encryption. Very roughly, it covers encryption above a certain “strength” level, as measured by technical parameters such as “key length” or “field size”.

The practical question is how high the bar is set: how powerful must encryption be, in order to be classified as “dual use”?

The bar is set low. For instance, software engineers debate whether they should use 2048 or 4096 bits for the RSA algorithm, but the DSGL classifies anything over 512 as “dual-use”. It’s probably more accurate to say that the only cryptography not covered by the DSGL is cryptography so weak that it would be foolish to use.

Moreover, the DSGL doesn’t just cover encryption software: it also covers systems, electronics and equipment used to implement, develop, produce or test it.

In short, the DSGL casts an extremely wide net, potentially catching open source privacy software, information security research and education, and the entire computer security industry, in its snare. This is typical of its approach.

Most ridiculous, however, are some badly flawed technicalities. As I have argued elsewhere, the specifications are so poorly written that they potentially include a little algorithm you learned at primary school called division. If so, then division has become a weapon, and your calculator (or smartphone, or computer, or any electronic device) is a delivery system for it.

These issues are not unique to Australia: the DSGL encryption provisions are copied almost verbatim from the Wassenaar Arrangement, an international arms control agreement. What is unique to Australia is the harshness of the law relating to the list.

Criminal offences for research and teaching?

The Australian Defence Trade Controls Act (DTCA) regulates the list, and enacts a censorship regime with severe criminal penalties.

The DTCA prohibits the “supply” of DSGL technology to anyone outside Australia without a permit. The “supply” need not involve money, and can consist of merely providing access to technology. It also prohibits the “publication” of DSGL technology, but after recent amendments, it only applies to half the DSGL: munitions only, not dual-use technologies.

What is a “supply”? The law does not define the word precisely, but the Department of Defence seems to think that merely explaining an algorithm would be an “intangible supply”. If so, then surely teaching DSGL material, or collaborating on research about it, would be covered.

University education is a thoroughly international and online affair — not to mention research — so any such supply, on any DSGL topic, is likely to end up overseas on a regular basis.

Outside of academia, what about programmers working on international projects like Tor, providing free software so citizens can enjoy their privacy rights online? Network security professionals working with overseas counterparts? Indeed, the entire computer security industry?

Examples of innocuous, or even admirable, activities potentially criminalised by this law are easily multiplied. Such activities must seek government approval or face criminal charges — an outrageous attack on academic freedom, chilling legitimate enquiry, to say the least.

To be sure, there are exceptions in the law, which have been expanded under recent amendments. But they are patchy, uncertain and dangerously limited.

For instance, public domain material and “basic scientific research” are not regarded as DSGL technology. However, researchers by definition create new material not in the public domain; and “basic scientific research” is a narrow term which excludes research with practical objectives. Lecturers, admirably, often include new research in teaching material. In such circumstances none of these provisions will be of assistance.

Another exemption covers supplies of dual-use technology made “preparatory to publication”, apparently to protect researchers. But this exemption will provide little comfort to researchers aiming for applications or commercialisation; and none at all to educators or industry. A further exemption is made for oral supplies of DSGL technology, so if computer science lecturers can teach without writing (giving a whole new meaning to “off the books”!) they might be safe.

Unlike the US, there is no exception for education; none for public interest material; and indeed, the Explanatory Memorandum makes clear that the government envisions universities seeking permits to teach students DSGL material – and, by implication, criminal charges if they do not.

On a rather different note, the DTCA specifically enables the Australian and US militaries to freely share technology.

Thus, an Australian professor emailing an international collaborator or international postgraduate student about a new applied cryptography idea, or explaining a new variant on a cryptographic algorithm on a blackboard in a recorded lecture viewed overseas — despite having nothing to do with military or intelligence applications — may expose herself to criminal liability. At the same time, munitions flow freely across the Pacific. Such is Australia’s military export control regime.

Now, there is nothing wrong in principle with government regulation of military technology. But when the net is cast as broadly as the DSGL — especially as with encryption — and the regulatory approach is censorship with criminal penalties — as with the DTCA’s permit regime — then the result is a vast overreach. Even if the Department of Defence did not exercise its censorship powers, the mere possibility is enough for a chilling effect stifling the free flow of ideas and progress.

The DTCA was passed in 2012, with the criminal offences schedule to come into effect in May 2015. Thankfully, emergency amendments in April 2015 have provided some reprieve.

Despite those amendments, the laws remain paranoid. The DSGL vastly over-classifies technologies as dual-use, including essentially all sensible uses of encryption. The DTCA potentially criminalises an enormous range of legitimate research and development activity as a supply of dual-use technology, dangerously attacking academic freedom — and freedom in general — in the process.

This story illustrates just one of many ways in which basic freedoms are being eroded in the name of national security.

Unless further changes are made, criminal penalties of up to 10 years prison will come into effect on 2 April 2016.

The day after April fool’s day. Jokes should be over by then.

Written by dan

May 9th, 2015 at 5:12 pm

The CIA 119

Years and years on, abuses continue.

The Bureau of investigative Journalism, together with the Rendition Project, is still trying to piece together the CIA’s kidnapping (“rendition”) and torture programme.

Only in December 2014 did the US Senate Intelligence Committee release its <summary of its report into the programme — a programme which, at least according to this report summary, effectively ended in 2006.

It took nearly ten years after the fact for an official report to arrive.

And this report, despite arriving so late on the scene, had only its summary published — the rest of the report is still classified to this day — and even the summary was the subject of bitter controversy among politicians. (Though what counts as controversial among US mainstream politicians is not a very good guide as to what matters are deserving of controversy: take global warming, for instance.)

Only with this report, well over a decade after most of the facts, only then did we learn the most basic facts about the program, like the number of people captured under it. The answer to that question, at least according to the report, is 119. They appear to have included people from dangerous terrorists, through to innocents sold to the CIA for profit.

The Bureau’s report begins to pull together the evidence to find out what happened to them. They were disappeared from their lives, disappeared into unaccountable captivity, disappeared into a legal black hole — and, in several cases, disappeared from history. The Bureau was unable to determine the fate of 39 of the abductees.

It is a story of no accountability, brutality and incompetence. To be sure, it apprehended some terrorists — though it appears that following a proper legal process, in every case, would have led to better results in terms of security and preventing terrorism, as well as, of course, following the law and abusing human rights. But other cases are ridiculous.

There is Laid Saidi, who was tortured by submersion in a bathtub of icy water and interrogated about a conversation in which he talked about aeroplanes (as if that were a crime) — except it turns out, thanks to faulty translation, he was talking about tyres. Saidi was later released — except he was released to the wrong country, so had to be taken back into custody and released again months later.

There is Khaled el Masri, who was detained by Macedonian authorities and held in a hotel in Skopje, then handed over to the CIA and taken to Afghanistan. There he was tortured by beatings, solitary confinement, and sodomy. His crime? Having a name similar to that of an alleged terrorist. He eventually won damages from Macedonia in the European Court of Human Rights, but his case is unusual in having won some recompense.

Of course, this is only one of many programs of the CIA as part of the “War on Terror” — a “war” which, for the most part, appears to have consisted of terror. And the CIA is only one of numerous US government agencies to have engaged in abuses. And, the United States is only one of many nations to have engaged in abuses — indeed, they all do, though the US still reigns supreme in its ability to project force around the globe. Australia has assisted many of these abuses.

Almost fourteen years after September 11 2001, more than ten years after most of the kidnappings, the struggle remains ongoing to find out what happened and why. These events offer not just a window into a particular time and circumstances, but the institutional circumstances in which unaccountable force is used and unpunished (or even “legal”) crimes are committed.

In Australia we have heard a lot recently about “lest we forget”. We should above all remember the abuses perpetrated by ourselves and our allies — lest we forget them, and in so doing enable them to happen again. The struggle of people against power has always been the struggle of memory against forgetting.

There is also the constructive question, in examining abusive organisations and programmes like this one, to identify what factors caused, or at least allowed, such horrors to happen. What better set of institutions can we build to ensure that similar abuses never happen again — and maintain peace and security for all?

Written by dan

May 2nd, 2015 at 3:14 am

The lower classes of things

Everything is free to move across borders, except… some lesser things.

It’s a long-standing principle of law, in the “developed” world at least, that “freedom” means the ability to move across borders without hindrance or restriction. This is commonly called “globalization”. Borders fade away and become irrelevant; non-discrimination becomes a defining, enlightened principle; and the world becomes one cosmopolitan village. Except, of course, that this otherwise laudable, advanced, cosmopolitan version of “freedom” applies only to inanimate material objects. To be fair, it does also apply to immaterial objects such as transfers of capital that exist only as abstract ideas, entries in spreadsheets or bits of information.

But one only needs to try to catch a boat from Indonesia to Australia to find out how much this well-established “freedom” and crowning glory of inanimate objects applies to living, breathing, feeling, thinking human beings.

Nonetheless, though it may be a great hypocrisy, this “freedom” of inanimate objects to move across borders is well-established. Such is the world we live in, where consumer goods such as cars and washing machines have advanced rights that humans do not have. This principle is enshrined in international treaties such as the General Agreement on Tariffs and Trade, and the various protocols adhered to be all member States of the World Trade Organisation.

However, this glorious liberty granted to inanimate objects, and even abstract objects, does not quite apply to all objects. Exceptions can be made, provided there is a special reason for it.

And, our world, divided into nation-states, is so organised that the highest decision-making authorities in the world pertain to geographic regions established largely by war, conquest and colonisation. So there is no more sanctified reason to limit freedoms than the military interests of States. In particular, weapons of war have much less freedom to flow across borders. The flow of weapons is tightly regulated — or at least, when it suits a State’s interest to do so.

Such is the idiosyncrasy and backwardness of human civilization in the early 21st century. Rights are given to inanimate objects — even abstract immaterial objects — but not sentient beings. Power lies with a tumultuous collection of clashing commonwealths, whose military interests are the highest good. Destructive weapons plague the world, but weapons are almost alone among inanimate objects in being subject to regulation.

Weapons are deprived of the rights accorded to other inanimate objects, and in this lie with other lower classes of things, such as hazardous waste, disease carriers, dangerous chemicals, plants, animals, and human beings.

Written by dan

April 20th, 2015 at 2:34 pm

Why your calculator (and computer, and phone…) is a weapon

The Australian government may have classified your calculator — and phone, and computer, and every electronic device you own — as military weapons.

You wouldn’t think your phone, or calculator, or laptop computer, is a weapon on par with tanks, rockets, and missiles. But the Australian government may well have classified it as one, thanks to a very interesting display of scientific and mathematical ignorance.

Now, most people, I think, wouldn’t have too much of a problem with the government sensibly regulating things like munitions, artillery, and weapons of mass destruction. But if that regulation were not sensible, then there might be a problem. And if that regulation extended to include things like your iPad, then there might be a big problem. Unfortunately, the Australian government has quite possibly done precisely that.

The Australian government maintains a list of all the things it considers important to national defence and security. It’s called the Defence and Strategic Goods List. Goods on this list are tightly controlled: there are heavy penalties for proliferating them.

Now, to be fair, compiling such a list is not easy. The list needs to remain current with science and technology, which in many fields is rapidly advancing. Moreover, defining what is and isn’t a military-grade weapon may be a bit more difficult than you think. Some objects have dangerous military uses as well as safe civilian uses.

Nonetheless, there is very little to indicate that the Defence and Strategic Goods List has been designed with the requisite degree of diligence.

Others have raised issues about the List: for instance, the National Tertiary Education Union (NTEU) is running a campaign on the issue and has set up a very informative website about it. Even the Senate Foreign Affairs Defence and Trade Committee report on the topic concluded that the law “would benefit from further scrutiny”, with half the committee describing it as “a complex and flawed piece of legislation”.

That’s not to mention the specific issues have raised about its effects on various research fields. For instance, my colleague Kevin Korb at Monash has calculated that 18 out of 61 masters level courses in the Faculty of Information Technology would fall under the strict controls of the List.

As a mathematician, I want to focus on one particular part of the list: encryption. And this particular part of the list, properly understood, overreaches enormously into everyday life.

Encryption: for people, not the State

But before going into the details of the List‘s definitions, it’s worth considering: why should encryption be regarded as a weapon in the first place?

Encryption is not a physical thing; messages and information are encrypted by algorithms running in programs on computers or other devices. An algorithm is a procedure, or recipe, that can be implemented on a computer; it’s an abstraction, an idea. Can an abstraction really be regarded as a weapon, or a “strategic good”?

Even if it can, encryption is by its nature not a uniquely military or intelligence thing. Anyone who wants to send a private communication on the internet does it by encryption. It’s a “dual use” technology, in the sense that it has both military and civilian uses. But there are dual use technologies like gas centrifuges, which have a small number of specific usages: gas centrifuges can be used for civilian nuclear reactors, and alternatively for nuclear weapons development. On the other hand, there are “dual use” technologies like cars, which are general purpose objects, used by almost everybody, for a wide variety of uses, but which nonetheless can also be useful to military and intelligence agencies. Encryption is much more like a car than a gas centrifuge.

Military and intelligence services may well use encryption so that their enemies can’t read their messages. But you and I also use encryption so that eavesdroppers can’t read our messages. Everyday users of the internet use encryption to safeguard their privacy. Consumers use encryption to guard against identity theft. Banks use encryption to assure customers of the integrity of financial transactions. Businesses use encryption to ensure the security of online transactions. Hospitals use encryption to ensure the privacy of patient medical records.

Basically, any time anything is done electronically with a need for privacy, encryption is used, and must be used. In a modern technologically advanced society, almost everybody uses it, whether they know it or not. It is far from the unique province of national security, military or intelligence agencies; it has become an essential and routine part of modern life.

When we don’t want our messages to be read by others, we can encrypt them; everybody needs to do this, should do this, and often does do this. So can the military; so can intelligence. What’s the difference?

Well, there is an important difference: ordinary people face highly technologically sophisticated adversaries.

On the one hand, recent military engagements have been fought in weak States such as Iraq, East Timor and Afghanistan. Those wars which have been fought in our name, when not killing hundreds of thousands of civilians, have been fought primarily against weak militaries and relatively unsophisticated armed groups (though, to be sure, these armed groups have sometimes possessed dangerous and lethal weapons, and effective organisation).

On the other hand, since the Snowden revelations — and much earlier for those who were paying attention — essentially all internet users have at least one known adversary snooping on their communications, which is extremely well financed, resourced, and technologically sophisticated: the NSA, along with its Five Eyes partners, which include Australia. Governments might rightly suspect that other governments are spying on them, but we know the NSA engages in mass surveillance of essentially the whole world; as such, citizens are arguably entitled to at least as much self-defence over their information, in the form of encryption, as States. Indeed, States have no inherent right to privacy — the whole point of Freedom of Information laws is that they should be transparent in their operations unless they have good reason — while an individual’s right to privacy is a fundamental human right.

As the comedian John Oliver pointed out in his recent interview with Edward Snowden, many people might not purport to care about surveillance, if they think they’re doing “nothing wrong”. But if it is made clear that mass surveillance means that the NSA has copies of your most private and embarrassing communications — because the nature of mass surveillance is to collect everything — then they might have a different view. Very few people would agree that the government should have copies of dick pics. And more people have sent dick pics than you might think.

Nonetheless, let’s assume for the purposes of argument that there is a justification for regarding at least some aspects of cryptography as “defence” or “strategic goods”. After all, there’s more to cryptography than encoding and decoding messages; encrypted messages can also be analysed, attacked, hacked; and some cryptographic algorithms are more secure than others. (Let’s also put aside the efforts of government, stretching back over decades now, to weaken cryptographic standards and harass researchers in the field.) If the Defence and Strategic Goods List only purported to regulate a truly ultra-secure encryption system, which was out of the reach of individual citizens, and hence was irrelevant to the everyday lives of ordinary people, it might not be quite as bad as if it covered encryption algorithms widely used and available to all.

Which it does. And much, much more — like calculators. But we might need to look at some mathematics in order to understand why.

Encryption in the Defence and Strategic Goods List

Section 5A002.a.1.b.3 of the List (yes, it really has sub-sub-sub-sub-sections) declares certain things to be subject to its control:

5A002 “Information security” systems, equipment and components therefor, as follows:
a. Systems [and] equipment… for “information security”, as follows…
1. Designed or modified to use “cryptography” employing digital techniques performing any cryptographic function other than authentication or digital signature and having any of the following:
b. An “asymmetric algorithm” where the security of the algorithm is based on any of the following:
3. Discrete logarithms in a group… in excess of 112 bits

This definition appears extremely technical and advanced. But when those words are understood, your calculator — indeed any technology that can do multiplication and division — has just been described as a weapon.

Let’s see why.

A little pure mathematics — groups

In pure mathematics — specifically, in abstract algebra — there are things called groups. Many of the things that scientists, engineers and students do every day involve groups. Like many concepts in pure mathematics, they are abstract objects: they are defined in terms of axioms, and anything that satisfies the axioms is a group. Many objects that engineers, scientists, and programmers work with every day are groups, and much of the arithmetic everyone knows from primary school can be understood as a special case of group theory.

Roughly speaking, a group — I’ll call it G — is a set containing certain elements, with a certain operation. The operation could be anything, provided it satisfies the axioms. The operation gives you a way to take two elements a,b of G and get a third element c . You can denote the operation by a dot, as in

\displaystyle a \cdot b = c.

However, the operation must satisfy some requirements, such as: there must be an identity element that “does nothing”; and each element must have an inverse element that “undoes” it.

Sound confusing? Well, it’s an advanced concept and I don’t have space here to give you an abstract algebra course! But here are some examples.

For instance, the group G could be the integers, or whole numbers (often written as \mathbb{Z} ), and the operation could be addition + . Well then, when you put 2 and 2 together, you get 4. (See, abstract algebra is as easy as putting 2 and 2 together! Maybe.) When you put 7 and 2 together, you get 9. When you put 7 and -2 together, you get 5. When you put 0 and 11 together, you get 11. In fact, when you put 0 and any integer n together, you get n , so 0 “does nothing”: 0 is the identity. And when you put 3 and -3 together, you get 0. When you put 7 and -7 together, you get 0. Each integer n has an inverse, which is the negative -n of that number. We can write these facts as

\displaystyle  2 \cdot 2 = 4, \; 7 \cdot 2 = 9, \; 7 \cdot (-2) = 5, \; 0 \cdot 11 = 11, \; 0 \cdot n = n, \; 3 \cdot (-3) = 0, \; 7 \cdot (-7) = 0, \; n \cdot (-n) = 0.

(Usually at school we reserve the dot symbol for multiplication! And, admittedly, mathematicians use the + symbol for some types of groups too. But it’s important for our purposes to emphasise the group operation, so, despite being possibly confusing, I will always write it with a dot.)

For another example, the group G could be the positive numbers (often written as \mathbb{R}_+  ), and the operation could be multiplication \times  . When you put 2 and 2 together, you again get 4! (Again, as easy as putting 2 and 2 together! Again, maybe.) But now when you put 7 and 2 together, you get 14. When you put 2 and \frac{1}{3} together, you get \frac{2}{3} . When you put 3 and 1.4 together, you get 4.2 . When you put 1 and 17 together, you get 17. In fact, when you put 1 and any positive number x together, you get x , so 1 “does nothing”: now 1 is the identity. When you put together 3 and \frac{1}{3}  , you get 1; when you put together 7 and \frac{1}{7}  , you get 1; and in general the inverse of each positive number x is its reciprocal \frac{1}{x}  .

\displaystyle  2 \cdot 2 = 4, \; 2 \cdot \frac{1}{3} = \frac{2}{3}, \; 3 \cdot 1.4 = 4.2, \; 1 \cdot 17 = 17, \; 1 \cdot x = x, \; 3 \cdot \frac{1}{3} = 1, \; 7 \cdot \frac{1}{7} = 1, \; x \cdot \frac{1}{x} = 1.

Is this reminding you of primary school arithmetic or high school algebra? Good, because you’ll need it to understand why your calculator has just been criminalised.

One last example is one you know intuitively when you tell the time. Let’s say we tell the time on a 12 hour clock. What time is it, 4 hours after 11 o’clock? It’s 3 o’clock. This means that, in clock arithmetic, 11 + 4 = 3 . When we add 11 and 4 in this way, we perform addition as usual but then take the remainder upon division by 12. This kind of arithmetic is known as “modular arithmetic” and it defines for us another group, often written \mathbb{Z}_{12}  . This group consists of 12 elements, namely the numbers from 1 to 12, and the operation is “clock addition”, which amounts to adding the numbers and then taking the remainder upon division by 12. You can check that 12 is the identity.

OK, enough abstract algebra for now.

Returning to the DSGL definition, you’ll see that it refers to a

group… in excess of 112 bits.

What does this mean? Nothing, it’s nonsense! Groups don’t have bits in them, they have elements in them. It goes to show that you shouldn’t get people who don’t understand what they’re talking about to write laws.

But what I think the authors of the DSGL meant, was a group that requires more than 112 bits to describe an element: that is, a group with more than 2^{112}  elements.

Now, 2^{112}  is a rather enormous number. But it’s not so enormous you can’t write it down:

\displaystyle  2^{112} = 5,192,296,858,534,827,628,530,496,329,220,096.

Know any groups bigger than that? I do, and I just told you two of them. OK, the clock group \mathbb{Z}_{12}  only has 12 elements, which is slightly less than 2^{112}  . But how many elements are there in the group \mathbb{Z}  of integers? Or, how many elements are there in the group \mathbb{R}_+  of positive numbers? Infinitely many — staggeringly more than 2^{112}  . Indeed, compared to infinity, any finite number is basically nothing. So actually, when the DSGL refers to a “group… in excess of 112 bits”, it could be referring to… well, you know, just your usual number systems, and addition or multiplication.

Discrete logarithms

Now, the next phrase to understand in the DSGL is “discrete logarithm” — something that sounds truly scary. Who even remembers what logarithms are, and what on earth are “discrete” ones?

Well, I’ll try to remind you of some high school algebra. Think back to when you learned about powers: for instance, 2^5 usually means to multiply 2 together with itself 5 times. So, if you were asked to find 2^5 , you would do some repeated multiplication and get 32.

But suppose you were asked the reverse question: how many times do you need to multiply 2 by itself in order to get 32? What power of 2 gives you 32? From above, we know the answer is 5. And that is just another way of saying that the logarithm of 32 to base 2 is 5.

\displaystyle  32 = 2^5  \; \text{means the same as} \; \log_2 32 = 5.

That is, the logarithm of 32 to base 2 is the power to which you need to raise 2 in order to get 32. And more generally, the logarithm of a to base b is the power to which you need to raise b in order to get a . Written in terms of equations,

\displaystyle  a = b^x \; \Leftrightarrow \; \log_b a = x.

What does this have to do with groups? Well, just as we usually write an exponential like 2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 to mean the you multiply 5 twos together, we can do the same in any group. Instead of repeated multiplication, we now do the group operation repeatedly. So we write, for instance,

\displaystyle  g^5 = g \cdot g \cdot g \cdot g \cdot g

to indicate that you do the group operation on 5 g ‘s together.

This leads to some rather strange-looking results. For instance, let’s consider what exponentials mean in the group \mathbb{Z} of integers with addition. Remember that in this group, the operation \cdot means addition. So, for instance,

\displaystyle  3^6 = 18,

because you do the group operation — addition — on 3, 6 times, and 3+3+3+3+3+3 = 18 .

On the other hand, in the group \mathbb{R}_+ of positive numbers with multiplication, the group operation is multiplication. So in this group

\displaystyle  3^6 = 729,

which is a more standard notation! This is what you would normally mean by 3^6 ; you multiply it together 6 times.

Finally, in the “clock arithmetic” group \mathbb{Z}_{12} ,

\displaystyle  3^6 = 6.

Why? Because you add 3 to itself 6 times to get “18 o’clock”, which is 6 o’clock on a 12-hour clock.

Now, just as we can write exponentials, we can also write logarithms. Above, we wrote that, in the groups \mathbb{Z}  , \mathbb{R}_+  and \mathbb{Z}_{12}  respectively,

\displaystyle  3^6 = 18, \; 3^6 = 729, \; 3^6 = 6.

Using the logarithm just how we did above, this means that, in the groups \mathbb{Z}  , \mathbb{R}_+  and \mathbb{Z}_{12}  respectively,

\displaystyle  \log_3 18 = 6, \; \log_3 729 = 6 \; \text{and} \; \log_3 6 = 6.

When you do a logarithm like this in a group, the exponent is always a whole number, and for this reason it’s called a discrete logarithm. (Well, there are some technicalities, but this is the gist of it.) And that is what the List is referring to.

Actually, the discrete logarithm in the group \mathbb{Z}  with addition is just a ridiculously fancy way of describing something you learned in primary school. What does

\displaystyle   \log_3 18

mean in the group \mathbb{Z} ? It’s asking: how many times do you have to add 3 to itself to get 18? The answer, as we wrote above, is 6. And this is all a very roundabout way of saying that 18 divided by 3 is 6.

So, when you’re talking about the group \mathbb{Z} with addition, the “discrete logarithm” is just a ridiculously fancy way of talking about division: dividing one number by another.

And when the DSGL mentions “discrete logarithms in a group… in excess of 112 bits [sic]”, it covers the division of whole numbers. Therein lies the beginning of a serious problem.

Recall, the List (now annotated) refers to:

b. An “asymmetric algorithm” where the security of the algorithm is based on any of the following:
3. Discrete logarithms in a group… in excess of 112 bits division

You’d better hope there aren’t any asymmetric algorithms, where the security of the algorithm is based on division!

In the next section, I will show you an asymmetric algorithm where the security of the algorithm is based on division.

Cryptographic algorithms

Now finally, we get to cryptography. The DSGL refers to an “asymmetric algorithm”. Helpfully, the DSGL has a definition section, which defines this phrase as meaning

a cryptographic algorithm using different, mathematically related keys for encryption and decryption.

Well, let’s start with what an algorithm is: an algorithm is just a clear, well-defined procedure that tells you how to do something. It’s like a recipe, except it’s a recipe so precise that it can be implemented on a computer.

A cryptographic algorithm is an algorithm that, as you might surmise, involves cryptography. When you want to send a message, and don’t want it to be read by eavesdroppers, you encrypt it: you apply some procedure to it, called an encryption algorithm. The data is then written in code, or encrypted, and can’t be read by anyone unless they have a secret key to decrypt it. When they do, they use the key on the encrypted message, applying a decryption algorithm, to recover the original message. Taken together, this encryption-and-decryption protocol forms a cryptographic algorithm.

Now, the encryption of a message usually uses a key, and the decryption of a message also uses a key. This key can be a message, a password, a number, or a chunk of data, or something else, but whatever it is, it involves some extra information that goes into the encryption or decryption, in addition to the message itself.

If the key is the same for both encryption and decryption, then the algorithm is called symmetric. If the encryption and decryption keys are different, then the algorithm is called asymmetric.

Now, there are some extraordinarily clever and elegant cryptographic algorithms out there. In one common type of asymmetric algorithm, called public key cryptography, the encryption key is made fully public and open to everyone to see, while the decryption key is kept secret. For instance, on my website you can get my public key, so if you want to send me a secret message you can encrypt it with that public key; but only I have the decryption key, (unless the NSA or ASIO has been snooping into my stuff), so only I can decrypt it.

But there are also some very basic cryptographic algorithms.

For instance, suppose I want to send you a message:

The arc of the moral universe is long, but it bends towards justice.

One of the simplest cryptographic algorithms is known as the Caesar cypher, so-called because Suetonius wrote that it was used by Julius Caesar. This algorithm just shifts every letter along the alphabet a fixed number of places. So, for instance, we might shift every letter three places, as Caesar did: so A becomes D, B becomes E, and so on, up to W becomes Z. Then the alphabet “cycles” so that X becomes A, Y becomes B and Z becomes C. The encrypted message is then

Wkh duf ri wkh prudo xqlyhuvh lv orqj, exw lw ehqgv wrzdugv mxvwlfh.

To decrypt the message, you just shift each letter back by 3!

In a certain sense, the Caesar cypher is based on addition and subtraction: in the above example, we “added 3” to each letter to encrypt, and “subtracted 3” to each letter to decrypt. We could say that the encryption key was 3, and the decryption key was -3.

What I’d like to do now is describe to you a similar idea based on multiplication and division.

The first step in this encryption algorithm — like most encryption algorithms used today — is to convert the message into a number using a standard encoding scheme. Hexadecimal numbers are usually used, because they work well with computers. When I convert my message above to numbers, using a standard scheme, and putting some spaces in, I obtain

54 68 65 20 61 72 63 20 6f 66 20 74 68 65 20 6d 6f 72 61 6c 20 75 6e 69 76 65 72 73 65 20 69 73 20 6c 6f 6e 67 2c 20 62 75 74 20 69 74 20 62 65 6e 64 73 20 74 6f 77 61 72 64 73 20 6a 75 73 74 69 63 65 2e

Importantly, although this number is s written in hexadecimal, this is just a number. In decimal it is (with spaces inserted)

18 987 169 229 968 478 188 669 534 957 610 737 354 921 264 295 841 525 766 864 288 444 422 566 874 896 162 027 606 162 208 969 778 556 762 033 277 602 447 021 524 083 143 238 081 863 623 539 907 326 688 954 151 036 206.

Now, I’m going to perform an encryption algorithm by choosing a secret key. My secret key will be the number 6. (Well, the key’s not so secret now…) There are many reasons to like the number 6.

My encryption algorithm will multiply the message by the key, because, why not. Multiplication is, after all, the name of the game. So I multiply my message by the key (6), and it becomes, in hexadecimal,

1f a7 25 ec 24 8a e5 2c 29 c6 4c 2b a7 25 ec 29 09 ca e4 88 8c 2c 09 67 8c 66 0a eb 45 ec 27 8b 2c 28 a9 c9 66 b0 8c 24 ec 0b 8c 27 8b 8c 24 e6 09 65 ab 2c 2b a9 cc c4 8a e5 ab 2c 27 ec 0b 4b a7 85 45 f1 4

If you try to convert that to text, you’ll get something completely unintelligible: it renders on my computer as

?%?$??,)?L+?%?) ??, g?f
?E?’?,(??f??$? ?’??$? e?,+????,’? K??E?

This is the encrypted message. Although the encryption is just based on a simple multiplication, this message is certainly encrypted, and most people would be unable to decrypt it.

Now when you receive the message, you have your own secret key, which you are going to multiply by. Your secret key is \frac{1}{6} . This number is chosen because when you multiply a number by 6 — as I have, to encrypt the message — and then you multiply by \frac{1}{6}  — as you will, to decrypt it — you get the number you started with.

So, you take the unintelligible message, convert to hexadecimal, multiply by \frac{1}{6}  , back to text, and obtain the original message.

Now, I definitely do not recommend you use this algorithm! It is far too simple and easily broken! But it is not so different in flavour from algorithms that are actually used.

In the famous RSA scheme, for instance, rather than multiplying by the encryption key to encrypt the message, you raise the message to the power of the encryption key, and reduce like clock arithmetic. (However, rather than dealing with a 12-hour clock, the “clock” in RSA has an enormous number of “hours”. The number of hours is the product of two large prime numbers.) And rather than multiplying the encrypted message by the decryption key to decrypt, you raise the encrypted message to the power of the decryption key, and reduce. The encryption and decryption keys in RSA, however, are reciprocals: they are chosen to multiply together to 1 — once reduced like clock arithmetic (again, using a “clock” with an enormous number of “hours”).

So the idea I’ve described above is a bona fide cryptographic algorithm, similar in several essential ways to the widely used RSA algorithm, just much much weaker: it will not be decipherable by most people, but will be mincemeat in the hands of the NSA. It is an asymmetric algorithm, because it involves different keys for encryption and decryption (like 6 and \frac{1}{6} respectively), in a similar way to RSA.

And, disturbingly, my cryptographic algorithm is based on using whole numbers, i.e. the group \mathbb{Z} with addition. The encryption algorithm involves multiplication, which is just repeated addition. Indeed, in the (rather strange) notation we used above, just as 3^6 = 18 ,

\displaystyle  (\text{original message})^{(\text{encryption key})} = (\text{encrypted message}).

If you followed the discussion of logarithms above, you might remember that any time we consider powers in a group, we can alternatively consider logarithms. Indeed, the above equation is equivalent to

\displaystyle  (\text{encryption key}) = \log_{(\text{original message})} (\text{encrypted message}).

Now I’ve told you how to break my cryptographic algorithm. If you know an original message and an encrypted message, you can work out the encryption key by doing a discrete logarithm — also known as division.

In other words, the security of this algorithm is based on discrete logarithms in the group \mathbb{Z}  . And, as we’ve discussed, the group \mathbb{Z} of integers is a group “in excess of 112 bits” [sic].

We have now come under the terms of the List.

The weaponisation of division

Having described a weak-but-bona-fide asymmetric encryption algorithm, let’s recall the definition in the DSGL:

5A002 “Information security” systems, equipment and components therefor, as follows:
a. Systems [and] equipment… for “information security”, as follows…
1. Designed or modified to use “cryptography” employing digital techniques performing any cryptographic function other than authentication or digital signature and having any of the following:
b. An “asymmetric algorithm” where the security of the algorithm is based on any of the following:
3. Discrete logarithms in a group… in excess of 112 bits

Well, I’m afraid everything I’ve just told you is certainly “cryptography, employing digital techniques to perform cryptographic functions”. (It’s not authentication or digital signature; those are different things.) It uses an asymmetric algorithm. And the security is based on discrete logarithms in the discrete group \mathbb{Z}  of whole numbers, which is infinite, with far more than “112 bits [sic]”.

And the “cryptography” I’ve just told you involves only two mathematical operations: multiplication and division. The “digital techniques” used to perform cryptographic functions are the good old \times  and \div  you learned in primary school. We described it in fancy language like “discrete logarithms”, but that’s only because the List uses this obfuscatory language.

So, the cryptographic algorithm I just described above is certainly covered by the List. But unfortunately the List covers more than just the algorithm itself. It also covers “systems” or “equipment.

Now a calculator is certainly a “system” or “equipment”. It is “designed” to do things like multiplication and division, and hence to do the “cryptography” described above. It employs “digital techniques” performing the “cryptographic functions” of multiplication and division. You “modify” the calculator to use this “cryptography” by typing the numbers and multiplying them. It has the “asymmetric algorithm” of multiplication and division built right into its hardware.

Your computer has a calculator on it. So do your smartphone and tablet, if you’ve ever looked. Indeed, any “equipment” you have that can do multiplication and division, is likely covered by this definition.

In the most generous reading, the List only covers your computer when you use it to actually perform the cryptographic algorithm. But it seems to me that the most natural reading of the List covers any computer which “has” the asymmetric algorithm of multiplication and division built into its hardware or software. That is, every computer.

The DSGL turns division into a weapon, and your computer into a delivery system for that weapon.

Now, I think that education can be a “weapon” used in self-defence against propaganda, and that mathematical fluency can be a very powerful “weapon” in understanding, and perhaps even changing, the world. But this is ridiculous!

The criminalisation of division

If you were accused of violating the List‘s controls on cryptographic technology by using your calculator, you could argue that section 5A002.a.1.b.3 should be read only to apply to you when you actually implement multiplication and division in an encryption algorithm. (Some also argue that “discrete logarithms” only exist in finite groups, effectively exempting the group of whole numbers \mathbb{Z}.)

But that sort of legalistic reasoning, searching for loopholes, is not exactly an argument on which you would want to hang your freedom, when faced with criminal charges.

And criminal charges there are.

Section 10 of the Defence Trade Controls Act (DTCA) makes it a criminal offence to “supply DSGL technology” — that is, things on the List — to anyone outside Australia, unless you get a special permit from the Minister.

Now, to be fair, the DSGL and DTCA make many exceptions. It’s just that none of them apply to multiplication and division.

For instance:

  • There is an exception (Note 2) which states that the DSGL “does not control products when accompanying their user for the user’s personal use”. So if you are carrying your calculator and laptop and smartphone with you, you might have an excuse; but if you leave one of them at home, perhaps not. And if you are using it to send, say, messages about human rights activism which displeases the government, do you expect the government to regard that as your “personal use”?
  • There is another exception (Note 3) stating that the DSGL does not control goods that meet 4 conditions. Unfortunately, one of these conditions is that “The cryptographic functionality cannot easily be changed by the user”. I’m afraid that your calculator has a highly adaptable interface that allows you to enter any numbers you please as encryption and decryption keys, and multiply and divide as you need. The functionality is easily changed to fit new keys.
  • Under recent (April 2015) amendments to the DSGL, “basic scientific research” is not regarded as DSGL technology. Are you really going to claim that my woefully insecure “encryption algorithm” rises to the level of “basic scientific research”? I’m not.
  • Under the same amendments, technology in the public domain is not regarded as DSGL technology. Is my multiplication-and-division encryption algorithm in the public domain? While multiplication and division are certainly publicly known, for the algorithm described here it is not so clear. By publishing it here, where you’re reading it, I suppose I am putting it in the public domain; though you’ll see a Creative Commons “some rights reserved” sign below. And moreover, isn’t the act of publishing this actually my “supply” of it to you? Again, I wouldn’t be relying on this defence.
  • Also in April 2015, the DTCA was amended so that supplies of dual-use technology made “preparatory to publication” are exempt. Sadly, I fear my bona fide woeful encryption algorithm is not exactly publishable in a reputable scientific journal.
  • At the same time, an exemption was introduced for supplies of technology made orally. Alas, I’ve now written all this down…
  • I could rely upon the exemption for educational activity or public interest material. Oh, except there isn’t one.
  • Finally, I could rely on the blanket exemption granted to munitions supplies between the Australian and US militaries. Apart from the slight problem that I’m a civilian and my algorithm is only a dual use technology, not technically a munition. It works well to exempt actual weapons from control though!

So, if you are not in Australia, then by explaining to you a very bad but nonetheless bona fide asymmetric encryption algorithm now, I have arguably breached this section of the law.

Well, perhaps because you didn’t pay me for the information, it wasn’t a “supply”? No, the Act makes clear that a “supply” need not be for payment.

The penalty? Ten years’ imprisonment, or a fine of $425,000.

And, just in case our lawmarkers were afraid they didn’t cover every possibility, they also included in the same Act a section 14A which makes it a criminal offence to “publish” or “otherwise disseminate DSGL technology to the public, or to a section of the public, by electronic or other means”. Again, a penalty of 10 years in jail or $425,000 fine applies. However, there is an exception to this one, if the technology has already been lawfully made available to the public.

Luckily, multiplication and division have already been made available to the public. Times tables are not yet illegal… I hope. (And in recent amendments in April 2015, this offence was limited to munitions; it no longer applies to dual use technologies. Phew!)

Other concerns about cryptography

Now, the idea of turning multiplication and division into weapons and criminalising their use is so ridiculous that it’s almost impossible to imagine the List being interpreted that way — despite the fact that, taken at face value, this is exactly what it says.

But there are other, even greater concerns with the definition of cryptography in the List. Again, we put aside the question of whether it is legitimate to control cryptography at all.

I only quoted one sub-sub-sub-sub-section of the List. The section on cryptography covers much more. It essentially covers any sufficiently “strong” cryptography, including symmetric algorithms with key lengths over 56 bits, and RSA with integers over “512 bits”. Now what is a strong key and what isn’t changes rapidly as technology advances. And I don’t think many in the field would say that these prescribed key lengths are so overwhelmingly ultra-secure that they should only be left to military or intelligence agencies. In fact, keys of this length are widely regarded as very weak. For instance, software engineers debate whether they should use 2048 or 4096 bits, well over the prescribed 512.

It’s probably more accurate to say that the only cryptography not covered by the List is cryptography so weak that it would be foolish for anyone to use. Supplying it to someone outside Australia is again made into a crime with punishment of 10 years prison or a $425,000 fine.

Broader concerns

Concerns over the contents of the list are not limited to cryptography: problems have been raised regarding its impact on various fields, including pharmaceuticals, and science generally.

The law which introduced the crimes of supplying and publishing DSGL technology is the Defence Trade Controls Act, passed in 2012. However, the criminal offences were not due to come into effect until 16 May 2015. With a deadline looming that could criminalise vast amounts of scientific research — including research which is entirely non-military-related — the law was amended and the changes came into effect on 2 April 2015.

These new changes do little to alleviate any of the concerns raised here. They do however provide a year of breathing room: the crimes of supplying and publishing DSGL technology now will not come into effect until 2 April 2016.

Now, while the criminal offences in the Defence Trade Controls Act are unique to Australia, the listing of “weapons” in the Defence and Strategic Goods List is not. Much of the List is based on the Wassenaar Arrangement, an international arms control agreement between 41 countries.

The section of the Australian List on cryptography is copied verbatim from the Wassenaar control list on “Information Security”.

So the criticisms of cryptography in the Australian List are not unique to Australia — they are common to any of the 41 States in the Wassenaar Arrangement.

Yes, that’s right — calculators, computers and phones are covered by international arms control treaties. The madness is worldwide; your calculator is part of the global arms trade.

Written by dan

April 19th, 2015 at 5:17 pm

The Lost Art of Integration Impossibility

Integration is hard.

When we learn calculus, we learn to differentiate before we can integrate. This is despite the fact that, arguably, integration is an “easier” concept. To my mind at least, when I am given a curve in the plane, the notion of an area bounded by this curve is a very straightforward, intuitive thing; while the notion of its “gradient” or “slope” at a point is a much more subtle, or at least less intuitive idea.

But whether these ideas are natural or not, one is certainly mathematically and technically more difficult than the other. Integration is much more subtle and difficult.

These difficulties highlight the extent to which integration is less a science and more an art form. And in my experience, those difficulties are seen very rarely in high school or undergraduate mathematics, even as students take course after course about calculus and integration. So it high time we shed some light on this lost art.

Really existing differentiation

In order to see just how hard integration is, let’s first consider how we learn, and apply, the ideas of differentiation.

When we learn differentiation, we first learn a definition that involves limits and difference quotients — the old chestnut \lim_{h \rightarrow 0} \frac{ f(x+h) - f(x) }{ h } . We pass through a discussion of chords and tangents — perhaps even supplemented with some physical intuition about average and instantaneous velocity. From this we have a “first principles” approach to calculus, using the formula f'(x) = \lim_{h \rightarrow 0} \frac{ f(x+h) - f(x) }{ h } .

This formula, and the whole “first principles” approach, is then promptly forgotten. After we learn the “first principles” of calculus, we then learn a series of rules, techniques and tricks, such as the product rule, quotient rule and chain rule. Using these, combined with a few other “basic” derivatives, most students will never need the “first principles” again.

More specifically, once we know how to differentiate basic functions like polynomials, trig functions and exponentials,

\displaystyle   \text{e.g.} \quad \frac{d}{dx} (x^n) = nx^{n-1}, \quad \frac{d}{dx} e^x = e^x, \quad \frac{d}{dx} \sin x = \cos x

and we know the rules for how to differentiate their products, quotients, and compositions

\displaystyle   \text{e.g.} \quad   \frac{d}{dx} f(x)g(x) = f'(x) g(x) + f(x) g'(x), \quad  \frac{d}{dx} \frac{f(x)}{g(x)} = \frac{ f'(x) g(x) - f(x) g'(x) }{ g(x)^2 }, \quad  \frac{d}{dx} f(g(x)) = f'(g(x)) \; g'(x)

we can forget all about “first principles” and mechanically apply these formulae. With some basics down, and armed with the trident of product, quotient, and chain rules, then, we can differentiate most functions we’re likely to come up against.

It turns out, then, that in a certain sense, differentiation is “easy”. You don’t need to know the theory so much as a few basic rules and techniques. And although these rules can be a bit technically demanding, you can use them in a fairly straightforward way. In fact, their use is algorithmic. If you’ve got the technique sufficiently down, then you can mechanically differentiate most functions we’re likely to come across.

Let’s make this a little more precise. What do we mean by “most functions we’re likely to come across”? What are these functions? We mean the elementary functions. We can define these as follows. We start from some “basic” functions: polynomials, rational functions, trigonometric functions and their inverses, exponential functions and logarithms.

\displaystyle   \text{E.g.} \quad 31 x^4 - 159 x^2 + 65, \quad \frac{ 2x^5 - 3x + 1 }{ x^3 + 8x^2 - 1 }, \quad \sin x, \quad \cos x, \quad \tan x, \quad \arcsin x, \quad \arccos x, \quad \arctan x, \quad a^x, \quad \log_a x.

We then think of all the functions that you can get by repeatedly adding, subtracting, multiplying, dividing, taking n‘th roots (i.e. square roots, cube roots, etc) and composing these functions. These functions are the elementary ones. They include functions like the following:

\displaystyle   \log_2 \left( \frac{ \sqrt[4]{3x^4 - 1} + 2\sin e^x }{ \arcsin (x^{\tan \log_3 x} + \sqrt[7]{ \pi^x - \cos (x^2) } ) - x^x } \right).

(Aside: There’s actually a technicality here. Instead of saying that we can take n‘th roots of a function, we should actually say that we can take any function which is a solution of a polynomial expression of existing functions. The n‘th root of a function f(x) , i.e. \sqrt[n]{f(x)} , is the solution of the polynomial equation in f(x) given by f(x)^n - 1 = 0 . That is, you can take an algebraic extension of the function field. Having done this, you can find the derivative of the new function using implicit differentiation. But we will not worry too much about these technicalities.)

Actually, the above definition is not really a very efficient one. If you start from just the constant real functions and the function x, then you can build a lot just from them! By repeatedly adding and multiplying xs and constants, you can build any polynomial; and then by dividing polynomials you can build any rational function. If you throw in e^x and \ln x = \log_e x , then you also have all the other exponential and logarithmic functions, because for any (positive real) constant a,

\displaystyle   a^x = e^{x \log_e a}   \quad \text{and} \quad  \log_a x = \frac{ \log_e x }{ \log_e a},

and \log_e a is a constant! If you allow yourself to also use complex number constant functions, then you can build the trig functions out of exponentials,

\displaystyle   \sin x = \frac{ e^{ix} - e^{-ix} }{ 2i }, \quad  \cos x = \frac{ e^{ix} + e^{-ix} }{ 2 },

and then you have \tan x = \frac{\sin x }{ \cos x } . You can also build hyperbolic trigonometric functions if you wish, since \sinh x = \frac{ e^x - e^{-x} }{2} , \cosh x = \frac{ e^x + e^{-x} }{2} , and \tanh x = \frac{ \sinh x }{ \cosh x } .

The formulas above for \sin x and cos x are relatively well known if you’ve studied complex numbers; a little less well-known are the formulas that allow us to express inverse trigonometric functions in terms of complex numbers, together with logarithms and square roots:

\displaystyle   \arcsin x = - i \; \ln \left( ix + \sqrt{1-x^2} \right), \quad  \arccos x = i \; \ln \left( x - i \sqrt{1-x^2} \right), \quad  \arctan x = \frac{i}{2} \; \left( \ln (1-ix) - \ln (1+ix) \right).

(If you haven’t seen these before, try to prove them! There are also logarithmic functions for inverse hyperbolic trigonometric functions, which are probably slightly more well known as they don’t have complex numbers in them.)

Thus, we can define an elementary function as a function which can be built from the functions \{ \text{complex constants}, x, e^x, \ln x \} using a finite number of additions, subtractions, multiplications, divisions, compositions, and n‘th roots (or really, solving polynomial equations in existing functions but don’t worry about this bit in parentheses).

The point is, that if you are good enough at the product, chain, and quotient rules, you can differentiate any elementary function. You don’t need any more tricks, though you might need to apply the rules very carefully and many times over! A further point is that when you find the answer, you find that the derivative of an elementary function is another elementary function.

Not so elementary, my dear Watson

When we come to integration, though, everything becomes much more difficult. I’m only going to discuss indefinite integration, i.e. antidifferentiation. Definite integration with terminals just ends up giving you a number, but indefinite integration is essentially the inverse problem to differentiation. If we’re asked to find the indefinite integral \int f(x) \; dx , we’re asked to find a function g(x) whose derivative is f(x), i.e. such that g'(x) = f(x). There are many such functions: if you have one such function g(x), then you can add any constant c to it, and the resulting function g(x)+c also has derivative f(x); that is why we tend to write +c at the end of the answer to any indefinite integration question. But it will suffice for us, here, to be able to find one — for the sake of simplicity, I will not write +c in the answers to indefinite integrals. In doing so I lose 1 mark for every integral I solve, but I don’t care!

We start with some basic functions like polynomials and trigonometric functions, exponentials and logarithms, some integrals are standard.

\displaystyle   \int x^n \; dx = \frac{1}{n+1} x^{n+1}, \quad  \int \sin x \; dx = - \cos x, \quad  \int \cos x \; dx = \sin x, \quad  \int e^x \; dx = e^x.

Some are slightly less standard:

\displaystyle   \int \tan x \; dx = - \ln \cos x, \quad  \int \ln x \; dx = x \ln x - x, \quad.

(You might complain that the integral of \tan x should actually be \ln | \cos x | . You’d be right, and I am totally sweeping that technicality under the carpet!)

Some inverse trigonometric integrals, perhaps, are less standard again:

\displaystyle   \int \arcsin x \; dx = x \arcsin x + \sqrt{1-x^2}, \quad  \int \arccos x \; dx = x \arccos x - \sqrt{1-x^2}, \quad  \int \arctan x \; dx = x \arctan x - \frac{1}{2} \ln (1+x^2).

So far, so good — although perhaps not always obvious! But now, in general, what if we start to combine these functions? The problem is that if you know how to integrate f(x) and you know how to integrate g(x), it does not follow that you know how to integrate their product f(x) g(x) . This is in contrast to differentiation: if you know how to differentiate f(x) and g(x), then you can use the product rule to differentiate f(x)g(x). There is no product rule for integration!

The product rule for differentiation, rather, translates into the integration by parts formula for integration:

\displaystyle   \int f(x) g'(x) \; dx = f(x) g(x) - \int f'(x) g(x) \; dx.

This is not a formula for \int f(x) g(x) \; dx ! A product rule for integration would say to you “if you can integrate both of my factors, you can integrate me!” But this integration by parts formula says something more along the lines of “if you can integrate one of my factors and differentiate the other, then you can express me in terms of the integral obtained by integrating and differentiating those two factors”. That is a much more subtle statement. A product rule would be a hammer you could use to crack integrals; but the integration formula is a much more subtle card up your sleeve.

Essentially, integration by parts supplies you with a trick which, if you are clever enough, and the integral is conducive to it, you can use to rewrite the integral in terms of a different integral which is hopefully easier. Hopefully. While the product rule for differentiation is an all-purpose tool of the trade — a machine used to calculate derivatives — integration by parts is a subtle trick which, when wielded with enough sophistication and skill, can simplify (rather than calculate) integrals.

Similarly, there is no chain rule for integration. The chain rule for differentiation translates into the integration by substitution formula for integration:

\displaystyle   \int f'(g(x)) \; g'(x) \; dx = f(g(x)).

A chain rule for integration would say to you “if I am a composition of two functions, and you can integrate both of them, then you can integrate me”. But integration by substitution says, instead, “if I am a composition of two functions, multiplied by the derivative of the inner function, then you can integrate me”. In a certain sense it’s easier than integration by parts, because it calculates the integral and gives you an answer, rather than merely reducing to a different (hopefully simpler) integral. But still, it remains an art form: it requires the skill to see how to regard the integrand as an expression of the form f'(g(x)) \; g'(x) . Finally, there is no quotient rule for integration either.

So, while differentiation is a skill which can be learned and applied, integration is an art form for which we learn tricks and strategies, and develop our skills and intuition in applying them. Now, actually there are tables of standard integrals, far far beyond the small examples above. There are theorems about how functions of certain types can be integrated. There are algorithms which can be used to integrate certain, often very complicated, families of functions.

But the question remains: how far can we go? If we see an integral which we can’t immediately solve, do we just need to think a little harder, and apply something from our bag of tricks in a clever new way? Do we just need more skill, or is the integral impossible? How would we tell the difference between a “hard” and an “impossible” integral — and what does that even mean?

In a certain sense, no integrals are “impossible”. An integral of a continuous function always exists, in a certain sense. If you’ve got a continuous function f  : \mathbb{R} \rightarrow \mathbb{R}, then its integral is certainly defined as a function, using the definition with Riemann sums — this is a theorem. Even if f is not continuous, it’s possible that the Riemann sum approach can give a well-defined function as the integral. For more exotic functions f, there is the more advanced method of Lebesgue integration.

But this is not what we have in mind when we say an “integral is impossible”. What we really mean is that we can’t write a nice formula for the integral. This would happen if the result were not an elementary function.

As we discussed above, if you take an elementary function and differentiate it, you can always calculate the derivative with a sufficiently careful application of product/chain/quotient rules, and the result is another elementary function.

So, we might ask: given an elementary function, even though there might not be any straightforward way to calculate its integral, is the result always another elementary function?

Indomitable impossible integrals

It turns out, the answer is no. There are elementary functions such that, when you take their integral, it is not an elementary function. When you try to integrate such a function, although the integral exists, you can’t write a nice formula for it. And it’s not because you’re not skillful enough. It’s not because you’re not smart enough. The reason you can’t write a nice formula for the integral is because no such formula exists: the integral is not an elementary function.

What is an example of such a function? The simplest example is one that high school students come up against all the time: the Gaussian function

\displaystyle   e^{-x^2}.

It’s clearly an elementary function, constructed by composition of a polynomial -x^2 and the exponential function. But its integral is not elementary.

You might recall that the graph of y = e^{-x^2} is a bell curve. Suitably dilated (normalised), it is the probability density function for a normal distribution. When you calculate probabilities involving normally distributed random variables, you often integrate this function.

You may recall painful time spent in high school looking up a table to find out probabilities for the normal distribution. That table is essentially a table of (definite) integrals for the function e^{-x^2} (or a closely related function). And the reason that it’s a table you have to look up, rather than a formula, is because there is no formula for the integral \int e^{-x^2} \; dx . You need a table because the integral of the elementary function e^{-x^2} is not elementary.

There’s no formula for normal distribution probabilities because integration is an art form, rather than algorithmic. And so we are sometimes reduced to the quite non-artistic process of looking up a table to find the integral.

Now, when I say that \int e^{-x^2} \; dx is not elementary, I mean that it’s known as a theorem. That is, it has been proved mathematically that \int e^{-x^2} \; dx is not elementary, and so doesn’t have a nice formula. But what could this mean? How could you prove that an integral doesn’t have a nice formula, isn’t an elementary function, can’t be written in a nice way? The proof is a bit complicated, too complicated to recall in complete detail here. But there are some nice ideas involved, and it’s worth recounting some of them here.

Proving the impossible

The fact that \int e^{-x^2} \; dx is not elementary was proved by the French mathematician Joseph Liouville in the mid-19th century. In fact, he proved quite a deal more. Suppose you have an elementary function f(x) , and you are trying to find its integral g(x) = \int f(x) \; dx . Now as the integrand f(x) is continuous, the integral g(x) certainly exists as a continuous function; the question is whether g(x) is elementary or not, i.e. whether there is a formula for g(x) involving only complex numbers, powers of x, rational functions, \exp and \log, and n‘th roots (and their generalisations).

Liouville’s theorem, amazingly, tells you that if the function g(x) you’re looking for is elementary, then it must have a very specific form. Very roughly, Liouville says, g(x) can have more logarithms than f(x), but no more exponentials. You can see the germ of this idea in some of the integrals above:

\displaystyle   \int \tan x \; dx = - \ln \cos x, \quad  \int \arctan x \; dx = x \arctan x - \frac{1}{2} \ln (1+x^2).

In these integrals, a new logarithm appears, that did not appear in the integrand. Never does a new exponential appear. If an exponential appears in the integral, then it appeared in the integrand, as in examples like

\displaystyle   \int e^x \; dx = e^x.

To state Liouville’s theorem more precisely, we need the idea of a field of functions. For our purposes, we can think of a field of functions as a collection of functions f(x) which is closed under addition, subtraction, multiplication, and division. The polynomials in x do not form a field of functions, because when you divide two polynomials you do not always get a polynomial! However, the rational functions in x do form a field of functions. A rational function in x is the quotient of two polynomials (with complex coefficients) in x, i.e. a function like

\displaystyle   \frac{ 3x^2 - 7 }{ x^{10} - x^9 + x^3 + 1}   \quad \text{ or } \quad  \frac{ 4x+1}{2x-3}   \quad \text{or} \quad  x^2 - 3x + \pi  \quad \text{or} \quad  3.

The first example is the quotient of a quadratic by a 10’th degree polynomial; the second example is the quotient of two linear polynomials. The third example illustrates the notion that any polynomial is also a rational function, because you can think of it as itself divided by 1, and 1 is a polynomial: x^2 - 3x + \pi = \frac{ x^2 - 3x + \pi }{ 1 } . The final example illustrates the notion that any constant is also a rational function.

The field of rational functions (with complex coefficients) in x is denoted \mathbb{C}(x) . You can make bigger fields of rational functions by including new elements! For instance, you could throw in the exponential function e^x , and then you can obtain the larger field of functions \mathbb{C}(x, e^x) . The functions in this field are those made up of adding, subtracting, multiplying, and dividing powers of x and the function e^x. So this includes functions like

\displaystyle   \frac{ x^2 + x e^x - e^x }{ x + 1 }  \quad \text{ or } \quad  (e^x) \cdot (e^x) = e^{2x}  \quad \text{ or } \quad  x^7 e^{4x} - 3 x^2 e^x + \pi.

Note however that a function like e^{e^x} does not lie in \mathbb{C}  (x, e^x) . This function field is made up out of adding, subtracting, multiplying and dividing x and e^x , but not by composing these functions.

We can see, then, that this second function field is bigger than the first one: \mathbb{C}(x) \subset \mathbb{C}(x, e^x) . In technical language, we say that \mathbb{C}(x) \subset \mathbb{C}(x, e^x) is a field extension. Moreover, both these fields have the nice property that they are closed under differentiation. That is, it you take a rational function and differentiate it, you get another rational function. And if you take a function in \mathbb{C}(x, e^x) , involving x‘s and e^x‘s, and differentiate it, you get another function in \mathbb{C}(x, e^x) . In technical language, we say that \mathbb{C}(x) and \mathbb{C}(x, e^x) are differential fields of functions.

A differential field obtained in this way, by starting from rational functions and then throwing in an exponential, is an example of an field of elementary functions. In general, a field of elementary functions is obtained from the field of rational functions \mathbb{C}(x) by successively throwing in extra functions, some finite number of times. Each time you add a function is must be either

  • an exponential of a function already in the field, or
  • a logarithm of a function already in the field, or
  • an n‘th root of a function already in the field (or more generally the root of a polynomial equation with coefficients in the field but as I keep saying don’t worry too much about this!).

Note that, by definition, any function in a field of elementary functions is made up by adding, subtracting, multiplying, and dividing x‘s, and exponentials, and logarithms, and n‘th roots (or generalisations thereof). That is, a function in an field of elementary functions is an elementary function! So our definitions of “elementary function” and “field of elementary functions” agree — it would be bad if we used the word “elementary” to mean two different things!

We can now state Liouville’s theorem precisely.

Liouville’s theorem: Let K be an field of elementary functions, and let f(x) be a function in K. (Hence f(x) is an elementary function.) If the integral \int f(x) \; dx is elementary, then

\displaystyle   \int f(x) \; dx = h(x) + \sum_{j=1}^n c_j \log g_j (x),

where n is a non-negative integer, each of c_1, c_2, \ldots, c_n is a constant, and the functions h(x), g_1(x), g_2(x), \ldots, g_n(x) all lie in K.

That is, Liouville’s theorem says that the integral of an elementary function f(x) must be a sum of a function h(x) that lies in the same field as f, and a constant linear combination of some logarithms of functions g_j(x) in the same field as f. The fact that h(x) and each g_j(x) lies in the same field K as f(x) means that they cannot be much more complicated than f(x): they must be made up by adding, subtracting, multiplying and dividing the same bunch of functions that you can use to define f(x)

So Lioville’s theorem says, in a precise way, that when you integrate an elementary function f(x), if the result is elementary, then it can’t be much more complicated than f(x), and the only way in which it can be more complicated is that it can have some logarithms in it. This is what we meant when we gave the very rough description “Liouville says g(x) can have more logarithms than f(x), but no more exponentials“.

Let’s now return to our specific example of the Gaussian function f(x) = e^{-x^2}. What does Liouville’s theorem mean for this function? Well, this function lies in the field of elementary functions K where we start from rational functions and then throw in, not e^x, but e^{-x^2}. That is, we can take K = \mathbb{C}(x, e^{-x^2}).

The theorem says that if the integral

\displaystyle   \int e^{-x^2} \; dx

is elementary, then it is given by

\displaystyle   \int e^{-x^2} \; dx = h(x) + \sum_{j=1}^n c_j \log g_j (x),

where n is a non-negative integer, each of c_1, c_2, \ldots, c_n is a constant, and the functions h(x), g_1(x), g_2(x), \ldots, g_n(x) all lie in \mathbb{C}(x, e^{-x^2}). That is, h(x), g_1(x), \ldots, g_n(x) are “no more complicated” than e^{-x^2}; they are all made by adding, subtracting, multiplying and dividing x‘s and e^{-x^2}‘s.

If we differentiate the above equation, we obtain

\displaystyle   e^{-x^2} = h'(x) + \sum_{j=1}^n c_j \frac{ g'_j (x) }{ g_j (x) },

On the left hand side is the function we started with, e^{-x^2}. On the right hand side is an expression involving several functions. However, all the functions g_j(x) and h(x) lie in K; they are “no more complicated” than e^{-x^2}. Now as K is a differential field, their derivatives g'_j(x) and h'(x) also lie in K; they are also “no more complicated”. So in fact the right hand side is an expression involving functions no more complicated than e^{-x^2}. They are all just rational functions, with e^{-x^2}‘s thrown in. And if you think about it, thinking about what you will get for each g'_j(x) / g_j (x), you might find it hard to avoid having a big denominator. You likely won’t be able to cancel the fraction. So you might find, then, that none of the g_j(x) can make this equality work, and all g_j(x) have to be zero; or in other words, e^{-x^2} = h'(x). But now that h(x) is, like everything else here, made up by adding, subtracting, multiplying and dividing x‘s and e^{-x^2}‘s. You might find, when you differentiate such a function, that it’s very hard to get a lone e^{-x^2}. Every time you differentiate an e^{-x^2} you get a -2xe^{-x^2}, which has a pesky extra factor of -2x. And even if it appears together with other terms, as something like x^3 e^{-x^2}, when you differentiate it you get something like -2x^4 e^{-x^2} + 3x^2 e^{-x^2}, which still has no isolated e^{-x^2} term. And so, in conclusion, you might find it very difficult to find any functions that make the right hand side equal to e^{-x^2}.

Of course, this is not a proof at all; it’s a mere plausibility argument. To prove the integral is not elementary does take a bit more work. But it has been done, and can be found in standard references.

Hopefully, though, this should at least give you some idea why it might be true, and how you might prove, that an integral is “impossible”, and can’t be written with any nice formula.

Mathematics is an amazing place.


Brian Conrad, Impossibility theorems for elementary integration, [[]].

Keith O. Geddes, Stephen R. Czapor, George Labahn, Algorithms for Computer Algebra, Kluwer (1992).

Andy R. Magid, Lectures on Differential Galois Theory, AMS (1994).

(Update 2/3/15: Typo fixed.)

Written by dan

March 1st, 2015 at 6:18 am

Is the Victoria Police Act a step forward?

(This article also appeared on the website of the Police Accountability Project.)

Law Institute Journal considers the new Victoria Police Act — a step forward?

A feature article in the most recent Law Institute Journal, In Search of Certainty, examines the issues surrounding the new Victoria Police Act and its implications for police accountability in Victoria.

The article, by Robinson Gill lawyers Jeremy King and Merys Williams, traces the history of the legislation and its likely effects in practice.

Until July of 2014, the principal legislation regarding police in Victoria was the Police Regulation Act of 1958. In July 2014, this Act was replaced with the Victoria Police Act as the new legislation came into force.

Both acts are problematic from the point of view of holding police accountable for misconduct through civil litigation, and compensating the victims of assaults by police and other wrongdoing.

It is not yet clear how much of an improvement the new Act will be. King and Williams argue that state policy will determine precisely how much. This post summarises their arguments; see their original article for full details.

Making the cops pay: The law governing civil liability for police misconduct

The specific problem is: if you suffer an assault or other wrongdoing at the hands of police, who can you sue? Who is liable? Is it the individual officers? Or is it the State, on whose behalf they act?

This sounds like a technicality — but it can mean the difference between being fully compensated for injuries suffered for wrongdoing, or receiving nothing.

If it is only the individual officers who are liable, those officers may not have the means to pay compensation. They may be bankrupted by the costs, or rendered impecunious.

It is in the interest of victims who have suffered police injustices, then, that the State be liable for police torts.

The position at common law, however, was very different. Known as the Independent Discretion rule, from the 1906 High Court case of Enever v R, it held that when an officer exercises their independent discretion, they are acting on behalf of themselves alone, not the State. If they committed a tort while exercising their discretion — which is what they do most of the time — they were liable and the State was not.

This position was altered by s123 of the old Police Regulation Act, which held that the State would be liable for “anything necessarily or reasonably done or omitted to be done in good faith and in the course of his or her duty as a member”.

This convoluted wording came to mean that when an officer was not acting “necessarily”, “reasonably” or “in good faith”, the State would again not be liable. Most police torts — assault, false imprisonment, malicious prosecution — are intentional. The State avoided liability again.

Indeed, under the old Police Regulation Act, the State avoided liability in precisely the worst cases of police misconduct. The worse the injustice suffered, the less likely the State was to be liable, the less likely the victim would be compensated.

Horvath’s case

The problems with the old Police Regulation Act reached breaking point with the case of Corinna Horvath.

In 1996, Horvath, along with her partner and several friends, were viciously assaulted by police during an unlawful raid on her home. Police violence left her unconscious, with a broken nose — then she was arrested. She suffered grave injuries. She successfully sued for damages.

But the State sought immunity under s123. Because the police were not acting “reasonably” or “in good faith” — indeed, far from it — the State was held not liable. Only the officers were liable. And the officers could not pay. Horvath won her day in court — or rather, won years of hearings and appeals in exhaustive court processes — yet received no compensation.

Horvath took her case to the UN. The Human Rights Committee found that s123 of the old Police Regulation Act was incompatible with the International Covenant on Civil and Political Rights. Her human rights had been breached, but the State had no mechanism to compensate her — only a mechanism to provide her with a Pyrrhic victory, an empty judgment in her favour.

It was only in September 2014, almost 20 years after the event, that Horvath finally received an apology and compensation from Victoria police.

The new Victoria Police Act

In something of an attempt to redress the longrunning injustice of Horvath’s case, s74(1) of the new Police Act specifies that the State is liable for “police torts”.

But the definition of a “police tort” again leads to difficulties. Section s74(2) provides an exception: the State is not liable when “the conduct giving rise to the police tort was serious or wilful misconduct by the police officer“. Again, it seems, victims will not receive compensation from the State for the worst police torts. Many police assaults are serious or wilful misconduct.

However, there is then s79(2), which requires that, in such circumstances of “serious or wilful misconduct”, the State must pay the victim “an amount” — but only when the victim “is unlikely to recover the amount from the officer” who committed the tort, and “the claimant has exhausted all other avenues to recover the amount”.

Together, this new legal regime leaves a great deal of uncertainty. What does it mean that you are “unlikely” to be able to recover from a police officer, and how do you prove it in court? What, precisely, are the “other avenues” that a victim must exhaust first? Must they first put themselves through the largely symbolic process through the Victims of Crime Compensation Assistance Tribunal (VOCAT)? And while the State is required to pay “an amount”, how much is this “amount”?

King and Williams argue that the legislation is unhelpful in answering these questions. But they see the new Police Act as a positive step forward, and conclude that

whether the [new] Police Act will overcome the shortfalls of the [old] Police Regulation Act will largely depend on the policy position adopted by the state of Victoria. The Police Act gives extremely broad discretion to the state regarding the use of the serious and wilful misconduct defence. If the state elects to use this defence in most civil litigation torts cases then the intention of the Police Act may well be undermined. Additionally, the state’s policy on how it will interpret s79(2) regarding ex-gratia payments may be key to the success or failure of the new legislation. If a technical and legalistic approach is adopted by the state then plaintiffs may find themselves no better off than Ms Horvath.

If the State insists on asserting its full legal rights in court, then, the new legislation may not be much of an improvement.

Several concerned groups, including the Flemington & Kensington Community Legal Centre, the Human Rights Law Centre, Remedy Australia, Liberty Victoria, Australian Lawyers for Human Rights, the Law Institute of Victoria, the Uniting Church, Australian Lawyers Alliance, Federation of Community Legal Centres, Aboriginal Legal Service, Victorian Council of Social Service, Springvale Monash Legal Service, and Youthlaw, sent an joint letter to the Victorian Parliament in July 2014 urging a review of Victorian police legislation to ensure conformity with our human rights obligations outlined in the Horvath decsion.

The reply from then Minister for Police and Emergency Services, Kim Wells, asserts that the new sections 72-81 of the Victoria Police Act will guard against a repeat of the circumstances faced my Ms Horvath. He states that the changes “provide an effective remedy for all torts committed by police, including assault, battery, false imprisonment and maliscious prosecution.

We await the formal response to the Horvath decision from the Australian Government.

Written by dan

December 12th, 2014 at 12:44 pm