Sunday 29 April 2018

The trauma of the United States

Recently I read "Loaded" by Roxanne Dunbar-Ortiz. It is a history about the US Constitution's Second Amendment and the mythology surrounding it. The Second Amendment is once again in the news for a reason that occurs with depressing frequency. This time it is the shooting that occurred at the Douglas High School in Florida in February and which has resulted in a mass movement Never Again led by some of the survivors at the school.

I must confess that I began Dunbar-Ortiz's book with pessimism. I expected to read the usual arguments for gun control and the usual counter-arguments and I thought cynically that believing anything would really change was just pie in the sky. That is not exactly how it worked out.

The first thing to say is that the book has a deep and well-researched thesis that the history of the USA from even before its foundation contains a number of deeply disturbing causes for the national gun culture that go way beyond the usual excuses. This is not about personal freedoms endowed to the citizenry by the Founding Fathers. It is not about the national hunting culture. Nor is it about the distrust fostered by the NRA that the government wants to disarm the people to enable their suppression ("from my cold dead hands").

No, it is about slavery and genocide. The US Constitution is not about all men being created equal; it is about the privileges of white male landowners and the second amendment is why white male landowners needed guns. They needed guns to contain their slaves through patrols looking for escapees. And they needed guns to carry out the systemic slaughter of Native Americans so that their lands could be seized. It is interesting to reflect that a key reason for the Declaration of Independence is that King George III tried to restrict the colonists' "right" to seize territory west of the Appalachian mountains whose inhabitants were described as "merciless Indian Savages".

This is not an interpretation of their history that most Americans will like. They are more used to a narrative in which heroic settlers fought for their freedom from an oppressive colonial tyrant and then, through the nineteenth century, expanded ever westwards claiming land for themselves. A history in which brave cowboys and fearless rangers protected farmers from violent attacks by Indians and they came into their manifest destiny much like the Old Testament Jews settling Canaan (just after God gave them their marching orders to kill every one of the original inhabitants). These myths protect them from their murderous pasts and are part of the defence of their wide gun ownership. They revere the part that guns played in taming their land, they laud the bravery of the family man whose gun is to protect his nearest and dearest as part of a long tradition, and they hold their constitution in almost superstitious awe.

So, on reaching the end of the book, I had a sense of hopelessness. How on earth could one penetrate these myths so that a rational discussion about how to go forward could be held? After a few days I began to read some other historical material in the same vein and this left me feeling a little more optimistic. To begin with the USA is not the only country burdened by a very shameful history. The Doctrine of Discovery promulgated by Pope Alexander VI in 1493 initially gave the Spanish permission to take possession of colonise any lands they  discovered which were not under the control of a Christian ruler and it became the justification for later European powers to colonise at will (and the American colonists inherited this idea from the British). The world is still suffering from the aftermath of colonisation by force but other colonial powers have at least begun to recognise their catastrophic agency with apologies, reparations, and deliberate reconciliation. The American haven't really started down this road but they did come late to the game - maybe their eyes will be opened in due time.

But also we should not overlook that there are movements in the USA that are trying to confront their racist misogynistic culture: the Woman's Movement, Metoo, the LGBT movement, Black Lives Matter and more. Some of these movements have extraordinary charismatic leaders who recognise the extreme difficulty rank and file Americans have in facing up to their past. I encourage you to view the lecture by Mark Charles; he is a native American who, for all his criticism of the oppression of his people, ends his lecture with some prescriptions that might change the discourse. We have a long way to go (and other colonial powers are still travelling that road) but it is important to try to keep reason, tolerance and understanding alive - and maybe in a couple of hundred years we can emerge in an enlightened sunshine.


Friday 20 April 2018

A Higher Loyalty

Former FBI Director James Comey published his keenly anticipated book "A Higher Loyalty" this week. I listened to the Audible edition read by Comey himself. This turned out to be a good method of digesting the book because Comey's earnestness comes through very clearly in his own voice.

The book is autobiographical but not a full autobiography. Those who read it just for the events surrounding Donald Trump should not ignore the larger part of the book which deals with episodes from Comey's childhood and career in the law. They are dramatic, thoughtful, and interesting. Comey uses them to develop his views on ethical leadership, self-knowledge and humility describing several  people he has known whose lives and personalities have been exemplars for him through the years.

He has much to say about what makes an inspiring leader and it is clear that he wishes he will have been seen as such. Readers will naturally be on their guard for self-serving stories when he talks about the organisations he himself has led but Comey's frequent admissions of his own mistakes and weaknesses lead one to think that we are reading a broadly honest account.

To many people his investigation into Hilary Clinton's unclassified email server will be the black mark forever held against him. These investigations are described in greater detail than anything else in the book. Comey admits that another FBI Director might have handled things somewhat differently but, reading his account, it is difficult not to sympathise with the way he made some incredibly difficult decisions. If (like I had been) you are slightly unclear on what this investigation was about this part of the book is a very complete account. The bottom line is that Clinton was very careless in using an unclassified email server. That conclusion was easily reached but it took the FBI much longer to trawl through the emails before being able to declare that there was nothing further to the whole issue. Comey reported the closure of the investigation to Congress in July 2016.  But two weeks before the 2016 election, the investigation had to be re-opened because further emails were found on another laptop and Comey had to decide whether to inform Congress the investigation was being re-opened. He chose to do so and it is this that Clinton and others believe cost the Democrats the election. Should he have waited until the reopened investigation was complete? That might have resulted in Clinton being elected and then the public finding out she was about to be indicted.

I feel there is an unanswered question lurking over this reopening of the investigation: Comey says he had to make this public because the ongoing examination was projected to take weeks yet, in the event, it was completed before the election; had that been known why could the announcement not have been delayed until the investigation was complete?

Donald Trump enters only in the final stages of the book but it is this part of the book that has attracted the most attention. In some ways though, one can read the previous part of the book as setting the scene for Comey's withering criticism of the US President. Comey has constructed a number of ethical principles based on leaders who have influenced his own life and we know, as the moment approaches, that Trump is going to fall very far short of those standards. And, for once, Trump does not disappoint us.

I write this as one who thinks that Donald Trump is a peculiarly awful individual and president. But, of course, some Republicans will not agree. The attacks on Comey have already begun and are being spearheaded by the web site lyincomey.com. I've just spent some time perusing this site and found that its rebuttals are weak and ludicrous. So I think A Higher Loyalty is a very credible attack on the Trump presidency and will only add to the maelstrom of difficulties now swirling around it.

Friday 6 April 2018

Prime conjunctions, and ruling families

This is positively my last post on prime conjunctions and I expect it to be read by nerds only. My purpose is to give two concrete examples of the more technical discussions in my two previous posts on prime conjunctions.
Let's begin with the children of Elizabeth II. They are (listed not by age but by the order in the year that their birthdays occur):

  • Andrew b. 19/2/1960
  • Edward b. 10/3/1964
  • Anne b. 15/8/1950
  • Charles b. 14/11/1948
Their ages at the beginning of 2018 were 57, 53, 67, 69. There's a stroke of luck - they are all odd. Indeed they are odd during the time interval 14/11/1999 to 18/2/2000. Such an odd conjunction period occurs every two years so maybe we shall find many prime conjunctions. Sadly, that set of ages has remainders 0, 2, 1, 0 on division by 3. In other words the 3-condition of my previous post fails - whenever the ages are odd, therefore, at least one age will be divisible by 3. So the only chance of a prime conjunction is when one of the is 3 itself and that would have to Edward's age. When he was 3 during the odd conjunction period the set of ages was 7, 3, 17, 19 and they are all prime. So the Royal siblings have had a prime conjunction (which they no doubt celebrated uproariously) but there will never be another.

What about 5 individuals who I shall call (in the order of their birthdays throughout the year)
  • Barron b. 20/3/2006
  • Melania b. 26/4/1970
  • Donald b. 14/6/1946
  • Tiffany b. 13/10/93
  • Ivanka b. 30/10/1981
At the beginning of 2018 their ages are 11, 47, 71, 36, 24. Oh dear - not all prime and neither are they all odd. However they do have the property that they are bunch of odds followed by a bunch of evens and so we know that eventually they will have an odd conjunction. The nearest odd conjunctive period is 14/6/2017 to 29/10/2017 when their ages are 11, 47, 71, 35, 23. Nearly all prime but not quite - maybe this will also prove impossible.

Since there are 5 people in this case we have to check both the 3-condition and the 5-condition. The 3-residues are 2, 2, 2, 2, 2 while the 5-residues are 1, 2, 1, 0, 3. Both conditions hold! So Dickson's conjecture would predict that, not only will these 5 individuals have a prime conjunction, they will have infinitely many. How do we find them?

Their earliest prime conjunction occurred when the ages were 7, 43, 67, 31, 19. To find later prime conjunctions we must add a number d to all of them that has the properties
  • d is even
  • d has remainder 0 or 1 when divided by 3
  • d is exactly divisible by 5
By a procedure called the Chinese Remainder Theorem these 3 conditions are equivalent to the condition d has remainder 0 or 10 when divided by 30. So the choices for d are 0, 10, 30, 40, 60, 70 etc. In fact d = 30 works (37, 73, 97, 61, 79). The next successful value of d is 40 and I'll leave you to find others.