NZ First MP Richard Prosser has rightly come in for international condemnation for his Investigate Magazine column in which he suggested young Muslims shouldn't be allowed to travel on Western airlines because "most terrorists are Muslims". It doesn't matter how he hedged this statement and his subsequent mealy-mouthed apology has not repaired the damage to New Zealand's reputation as a tolerant and inclusive society.
I became a NZ citizen three months ago. During my application for this privilege I was often asked why I wanted to be a citizen rather than just a permanent resident. My answer was always the same: I love the tolerant spirit of New Zealand, its relative absence of a class system, and its secular system of government. That Richard Prosser should make such dishonest remarks, and still more that he serves as an MP, makes me extremely distressed for our international image.
Dishonest remarks? Absolutely. What's a terrorist? Surely someone who terrorises innocent people whether the terrorist is a member of a guerilla group, an outright criminal, or a member of some country's official armed forces. How about the terror inflicted by US drones in Pakistan and Afghanistan, or the brutality of the Israeli government to the Palestinians, or the genocide of the pygmies in the Congo Civil War; these are just a few examples. Terror acts committed by Muslims are in a minority.
Even if Richard Prosser made a full and contrite apology which showed a genuine acceptance that he got things badly wrong he has nevertheless shown such poor judgement that he should be sacked immediately. But to compound the aftermath his party leader Winston Peters has said there was an "element of truth" to Mr Prosser's comments and says he does not believe Prosser should apologise.
What a disgusting pair they are.
Tuesday, 12 February 2013
Sunday, 10 February 2013
On mathematical Platonism and faith
Mathematical Platonism is, roughly described, the belief that the entities considered in mathematics (numbers, functions, algebraic systems, etc) have a reality beyond their existence as neuronal configurations in our brains. Non-mathematicians are often disposed to reject the belief ("Where do these entities exist?" seems to be a rather compelling objection) but many practising mathematicians are Platonists, and many more (maybe a majority, but I don't have any statistics to support this) behave as though they are Platonists.
Another way of expressing the belief is to say that mathematics is "discovered" rather than "invented". In his short essay Barry Mazur calls this "The Question" that all mathematicians come to at some point in their metaphysical speculations.
Why does Platonism have such a strong foothold among mathematicians? I am fascinated by this question because when I was a young pure mathematical researcher I would often maintain that the entities I thought about had an independent existence (and this was when I was only dimly aware of Platonism at all). I had, for example, an absolute conviction that when humankind came across star-faring species they would have a mathematics in which simple groups (a particular interest of mine at the time) would play the same fundamental role that they play in terrestrial mathematics. Why did I hold this view so strongly? In this post I want to speculate about this psychological predisposition rather than whether it is defensible.
I suggest that Platonism has such a powerful grip on the mathematical mind because mathematical discourse is packed with the language of discovery rather than the language of invention. This language biases us to subconsciously accept that we are finding out about things that already exist. This tradition is very deeply rooted in our mathematical discourse and certainly appears in Euclid ("The sum of the three interior angles of a triangle equals two right angles": no doubt here that a triangle exists somewhere outside our minds). In our modern mathematics how often do we say "There exists..."? - we even have a mathematical symbol for this phrase. Mathematics is written in a certain style and this style abounds with phrases that suggest discovery of already existing objects. For example here is paper published today that I selected at random: here is its abstract.
What this tells us is that a Platonist ought to consider his/her position in the light of these strong linguistic pressures that produce cognitive bias. Maybe they can mount a metaphysical defence (and I confess to a wistful hope that they can). But if they cannot it is only honest to admit that they are holding similar opinions to a committed theist. And that brings me to the final point I wish to make.
A few studies have shown that, among scientists, mathematicians tend to hold a theistic stance more so than others. A few years ago the US National Academy of Sciences conducted a survey about god beliefs among their members. Apparently 14.6% of mathematicians believe in god whereas the figure for biologists is 5.5%. I am sure we should be cautious about such figures but other surveys have also shown that mathematicians tend to belief in god in higher proportions than other scientists.
Is it not plausible that someone who has committed unthinkingly to a position of faith in the real existence of mathematical entities will be more prone to commit to a faith in the real existence of supernatural beings?
Another way of expressing the belief is to say that mathematics is "discovered" rather than "invented". In his short essay Barry Mazur calls this "The Question" that all mathematicians come to at some point in their metaphysical speculations.
Why does Platonism have such a strong foothold among mathematicians? I am fascinated by this question because when I was a young pure mathematical researcher I would often maintain that the entities I thought about had an independent existence (and this was when I was only dimly aware of Platonism at all). I had, for example, an absolute conviction that when humankind came across star-faring species they would have a mathematics in which simple groups (a particular interest of mine at the time) would play the same fundamental role that they play in terrestrial mathematics. Why did I hold this view so strongly? In this post I want to speculate about this psychological predisposition rather than whether it is defensible.
I suggest that Platonism has such a powerful grip on the mathematical mind because mathematical discourse is packed with the language of discovery rather than the language of invention. This language biases us to subconsciously accept that we are finding out about things that already exist. This tradition is very deeply rooted in our mathematical discourse and certainly appears in Euclid ("The sum of the three interior angles of a triangle equals two right angles": no doubt here that a triangle exists somewhere outside our minds). In our modern mathematics how often do we say "There exists..."? - we even have a mathematical symbol for this phrase. Mathematics is written in a certain style and this style abounds with phrases that suggest discovery of already existing objects. For example here is paper published today that I selected at random: here is its abstract.
For every infinite sequence of simple groups of Lie type of growing rank we exhibit connected Cayley graphs of degree at most 10 such that the isoperimetric number of these graphs converges to 0. This proves that these graphs do not form a family of expanders.I suggest that mathematicians cannot read that abstract without having their Platonic tendencies confirmed. This and the entire manner in which mathematics is written explains why Platonism is the default subconscious belief of so many working mathematicians.
What this tells us is that a Platonist ought to consider his/her position in the light of these strong linguistic pressures that produce cognitive bias. Maybe they can mount a metaphysical defence (and I confess to a wistful hope that they can). But if they cannot it is only honest to admit that they are holding similar opinions to a committed theist. And that brings me to the final point I wish to make.
A few studies have shown that, among scientists, mathematicians tend to hold a theistic stance more so than others. A few years ago the US National Academy of Sciences conducted a survey about god beliefs among their members. Apparently 14.6% of mathematicians believe in god whereas the figure for biologists is 5.5%. I am sure we should be cautious about such figures but other surveys have also shown that mathematicians tend to belief in god in higher proportions than other scientists.
Is it not plausible that someone who has committed unthinkingly to a position of faith in the real existence of mathematical entities will be more prone to commit to a faith in the real existence of supernatural beings?
Friday, 1 February 2013
The poverty of faith
I live in Otago in the South Island of New Zealand. We have a reasonably good local newspaper, The Otago Daily Times, that informs us of local, national and world issues in decreasing levels of detail. On 1 February it published an opinion piece from a local resident called Ivan Grindlay entitled
No room for fantasy if you understand dynamics of God's plan. Mr Grindlay is an elder at the Caversham Community Church. His article was a summary of a bizarre theology that told of God's intention for humanity, its perversion by the "defection" of Adam, and an ultimate resolution as the Second Coming brings the nation of Israel back into the Christian fold. It wasn't clear whether this was Mr Grindlay's personal theology or that of the Caversham Community Church. At any rate this world-view cuts off its adherents from the understanding that we now have about the natural world. The explanation of our world and the huge cosmos in which it is situated is grander by far than the explanations in Mr Grindlay's theology. Many readers must have smiled rather sadly that such arbitrary fantasies still hold the minds of some people in thrall.
Perhaps among the smilers will be found some members of mainstream religious beliefs. Good Christian folk who regularly attend their church, recite the Lord's Prayer and the Apostle's Creed, engaged in good works to support their own community and possibly communities overseas. Ladies and Gentlemen of these benign religious persuasions you are complicit in Mr Grindlay's ignorance. Your own supernatural beliefs are the ambient culture that nurtures Mr Grindlay's less mainstream opinons. While you, through a mental contortion in which you cherry-pick those pieces of scripture that are convenient to believe, have access to the understanding of our wonderful universe (biology and the unity of all life because of the DNA molecule, physics and the mathematical explanation of nature's laws, astronomy and the workings of a cosmos now unimaginably larger than ever envisioned in religious tracts) you are doing more credulous folk a grave disservice. Shame on you.
Mr Grindlay has chosen a certain portion of scripture on which to found his world-view. Anglican Christians choose another portion while Roman-Catholics choose yet another (and even this ignores the schisms within these broad churches). Still another portion is seized on by Sunni Moslems, and again another by Shi'a Moslems. And then there are Jews, Hindus and many other groups each elevating certain historical writings to the status of divine revelation.
I called Mr Grindlay's fantasy an arbitrary one in my first paragraph. Indeed it is arbitrary. But so are the fantasies of every other religion. What distinguishes them from the Mr Grindlay fantasy is that they have more adherents and with numbers come respectability. But all of them to one degree or another prevent their followers from truly appreciating the world we live in - the only one we will ever have.
No room for fantasy if you understand dynamics of God's plan. Mr Grindlay is an elder at the Caversham Community Church. His article was a summary of a bizarre theology that told of God's intention for humanity, its perversion by the "defection" of Adam, and an ultimate resolution as the Second Coming brings the nation of Israel back into the Christian fold. It wasn't clear whether this was Mr Grindlay's personal theology or that of the Caversham Community Church. At any rate this world-view cuts off its adherents from the understanding that we now have about the natural world. The explanation of our world and the huge cosmos in which it is situated is grander by far than the explanations in Mr Grindlay's theology. Many readers must have smiled rather sadly that such arbitrary fantasies still hold the minds of some people in thrall.
Perhaps among the smilers will be found some members of mainstream religious beliefs. Good Christian folk who regularly attend their church, recite the Lord's Prayer and the Apostle's Creed, engaged in good works to support their own community and possibly communities overseas. Ladies and Gentlemen of these benign religious persuasions you are complicit in Mr Grindlay's ignorance. Your own supernatural beliefs are the ambient culture that nurtures Mr Grindlay's less mainstream opinons. While you, through a mental contortion in which you cherry-pick those pieces of scripture that are convenient to believe, have access to the understanding of our wonderful universe (biology and the unity of all life because of the DNA molecule, physics and the mathematical explanation of nature's laws, astronomy and the workings of a cosmos now unimaginably larger than ever envisioned in religious tracts) you are doing more credulous folk a grave disservice. Shame on you.
Mr Grindlay has chosen a certain portion of scripture on which to found his world-view. Anglican Christians choose another portion while Roman-Catholics choose yet another (and even this ignores the schisms within these broad churches). Still another portion is seized on by Sunni Moslems, and again another by Shi'a Moslems. And then there are Jews, Hindus and many other groups each elevating certain historical writings to the status of divine revelation.
I called Mr Grindlay's fantasy an arbitrary one in my first paragraph. Indeed it is arbitrary. But so are the fantasies of every other religion. What distinguishes them from the Mr Grindlay fantasy is that they have more adherents and with numbers come respectability. But all of them to one degree or another prevent their followers from truly appreciating the world we live in - the only one we will ever have.
Thursday, 31 January 2013
It's hard to kill your neighbour
There is a series of psychological thought experiments (the Trolley problem) in which participants are asked moral questions which produce increasing levels of discomfort. These experiments - investigations of philosophical consequentialism - are a litmus test to the commitment of a utilitarian's position but this post is not really about that issue so much as about how it is connected to our feelings about personal and impersonal violence.
Two of the trolley problem scenarios concern what you should do if you see a trolley on some rail tracks hurtling towards a group of 5 people who will die on impact. In one scenario you have a lever that will divert the trolley onto another track but, on the other track, there is a single person who will then be killed by the trolley. Should you pull the lever? In another scenario you are standing on a bridge alongside a fat man and you know that, by toppling him over the bridge, he will halt the trolley but die in the process. Should you push the man?
Even if we cannot come to a conclusion about what actions are right for these scenarios most of us will feel that the second scenario presents a more challenging moral conundrum, and its resolution has been debated at least since the time of Thomas Aquinas. But philosophy and morality aside the scenarios point to an aspect of our innate makeups that we need to acknowledge if we are to make sense of why individuals and societies act as they do under stress. We might call this aspect of us our human empathy.
I offer the speculation that whatever it is in our psychology which makes us more leery of positive action in the second scenario is also what has contributed to the greater slaughter of people (military and civilians) in modern warfare.
Of course the huge mortality rates in modern warfare are definitely connected to another factor: the much greater killing power of weapons of mass destruction (WMD). (By the way, the definition that WMD just means nuclear weapons is, I think, completely arbitrary. The London Blitz: 40000 dead , the Dresden firebombing: 25000 dead, the Hiroshima bomb: 100000 dead but estimates wildly vary).
However I think that if WMD were not activated at a distance, if the immediate connection between opening a bomb hatch and the resulting killing could be witnessed, then WMD would not be deployed as they have been. Imagine having to achieve the same mortality figures if each life had to be taken by slitting the throat of the victims. It is not simply that it would take more time: it would be viscerally opposed by our human empathy.
Of course, war warps our human empathy. To be successful in war, military commanders have to force their troops to carry out actions that in peace-time they would not consider. That is one of the reasons why very strict disciplines are practised. And it must be one the reasons why, when the conflict is over, so many returning war heros are deeply traumatised (for example, in 2012, more US serving troops committed suicide than died in war action).
So there is the thesis: we are more leery about pushing a fat man off the bridge because it is more "hands-on" than pulling a lever, and this is for same empathetic reason that we would be more leery of knifing a civilian rather than bombing them.
In my opinion this human empathy is embedded in our brains. Examples of its functioning exist in all areas of our society. For example, it is a common phenomenon that when two individuals of different nationalities, skin colour, or political persuasion get to know each other they often overcome antipathies they might have felt towards one another before their empathetic sense was triggered. This all suggests that our human society should become more harmonious the more we trigger our empathetic response - and this means that, as far as possible, we should engage with those we find the most at odds with our own predispositions.
Two of the trolley problem scenarios concern what you should do if you see a trolley on some rail tracks hurtling towards a group of 5 people who will die on impact. In one scenario you have a lever that will divert the trolley onto another track but, on the other track, there is a single person who will then be killed by the trolley. Should you pull the lever? In another scenario you are standing on a bridge alongside a fat man and you know that, by toppling him over the bridge, he will halt the trolley but die in the process. Should you push the man?
Even if we cannot come to a conclusion about what actions are right for these scenarios most of us will feel that the second scenario presents a more challenging moral conundrum, and its resolution has been debated at least since the time of Thomas Aquinas. But philosophy and morality aside the scenarios point to an aspect of our innate makeups that we need to acknowledge if we are to make sense of why individuals and societies act as they do under stress. We might call this aspect of us our human empathy.
I offer the speculation that whatever it is in our psychology which makes us more leery of positive action in the second scenario is also what has contributed to the greater slaughter of people (military and civilians) in modern warfare.
Of course the huge mortality rates in modern warfare are definitely connected to another factor: the much greater killing power of weapons of mass destruction (WMD). (By the way, the definition that WMD just means nuclear weapons is, I think, completely arbitrary. The London Blitz: 40000 dead , the Dresden firebombing: 25000 dead, the Hiroshima bomb: 100000 dead but estimates wildly vary).
However I think that if WMD were not activated at a distance, if the immediate connection between opening a bomb hatch and the resulting killing could be witnessed, then WMD would not be deployed as they have been. Imagine having to achieve the same mortality figures if each life had to be taken by slitting the throat of the victims. It is not simply that it would take more time: it would be viscerally opposed by our human empathy.
Of course, war warps our human empathy. To be successful in war, military commanders have to force their troops to carry out actions that in peace-time they would not consider. That is one of the reasons why very strict disciplines are practised. And it must be one the reasons why, when the conflict is over, so many returning war heros are deeply traumatised (for example, in 2012, more US serving troops committed suicide than died in war action).
So there is the thesis: we are more leery about pushing a fat man off the bridge because it is more "hands-on" than pulling a lever, and this is for same empathetic reason that we would be more leery of knifing a civilian rather than bombing them.
In my opinion this human empathy is embedded in our brains. Examples of its functioning exist in all areas of our society. For example, it is a common phenomenon that when two individuals of different nationalities, skin colour, or political persuasion get to know each other they often overcome antipathies they might have felt towards one another before their empathetic sense was triggered. This all suggests that our human society should become more harmonious the more we trigger our empathetic response - and this means that, as far as possible, we should engage with those we find the most at odds with our own predispositions.
Tuesday, 22 January 2013
On historical causes
One of the most boring episodes of my high school career was the few weeks in fifth form history when we were taught the causes of the French Revolution. To this day I really can't remember much of what we were taught but, looking up Wikipedia today, I read that one cause was the high level of taxation of the peasant class while the nobility led lives of conspicuous consumption.
But what exactly does "X causes Y" mean in the context of history? Can we deduce that if the French peasantry had not been taxed highly then the revolution would not have occurred? Of course not. In fact we cannot know the answer to that question because we cannot rerun history. Does it mean that there is a tendency for Y to occur when X is present in any historical situation? Perhaps so, and this is indeed a hypothesis that could be tested by an examination of historical situations where X was present. But the dataset might still be unconvincingly small.
I was led to these thoughts by two massive books that I've read over the last two years. One was "Guns, germs and steel" by Jared Diamond, the other was "Ideas, a history from fire to Freud" by Peter Watson. Both of them are staggering accomplishments that offer a comprehensive account of how hunter-gatherer societies developed into modern-day societies. Inevitably the authors colour their accounts with opinions that can only be hypotheses, despite their persuasive arguments to support their opinions.
Diamond's main intent is to give an explanation of the factors that contributed to the greater success of European civilisation compared to its historical counterparts. He completely rejects explanations based on racial differences and argues convincingly for geographical differences. Among his explanations are, for example, the greater number of domesticable animals in the Old World compared to the new; and the larger number of plants that could be farmed for food production. I strongly recommend the book for it is thoughtfully presented and hugely informative.
Watson's book offers a number of reasons why some ideas surfaced at a particular moment in history, and why they originated in a particular country. Again it is all plausible coherent stuff and I greatly appreciated how he related the historical contexts to the development of key ideas.
But, just like the causes of the French revolution, what does it mean to say that a particular constellation of geographical factors made the Old World develop more quickly than the New World? What does it mean to say that a particular constellation of social and historical conditions caused a certain set of ideas to be developed? To make these claims is not to say that if X was not present then Y would not have occurred. History is not a repeatable experiment.
Neither in the case of the Diamond and Watson claims can we even test the hypothesis "Y tends to happen in the presence of X". We can't do this because they have already used up all the experimental data. In other words they did too complete a job!
If we were to encounter a plentiful number of alien races not too unlike us we would have more scope to make historical claims of the form "X causes Y". Since this is not likely to happen we appear to be stuck. However there is a possible avenue that might enable us to test this type of causality. We could simulate various worlds and societies in a computer, seed them with various initial conditions, and study how they evolved. Such simulations already exist, some on a very large scale: some online computer games depend for their very fascination on watching how a virtual society develops under the constraints of the game.
So here's the ideal academic project: conduct history and sociology (and other inexact disciplines) through the medium of computer gaming. Wouldn't that be great fun for the young folk of today?
But what exactly does "X causes Y" mean in the context of history? Can we deduce that if the French peasantry had not been taxed highly then the revolution would not have occurred? Of course not. In fact we cannot know the answer to that question because we cannot rerun history. Does it mean that there is a tendency for Y to occur when X is present in any historical situation? Perhaps so, and this is indeed a hypothesis that could be tested by an examination of historical situations where X was present. But the dataset might still be unconvincingly small.
I was led to these thoughts by two massive books that I've read over the last two years. One was "Guns, germs and steel" by Jared Diamond, the other was "Ideas, a history from fire to Freud" by Peter Watson. Both of them are staggering accomplishments that offer a comprehensive account of how hunter-gatherer societies developed into modern-day societies. Inevitably the authors colour their accounts with opinions that can only be hypotheses, despite their persuasive arguments to support their opinions.
Diamond's main intent is to give an explanation of the factors that contributed to the greater success of European civilisation compared to its historical counterparts. He completely rejects explanations based on racial differences and argues convincingly for geographical differences. Among his explanations are, for example, the greater number of domesticable animals in the Old World compared to the new; and the larger number of plants that could be farmed for food production. I strongly recommend the book for it is thoughtfully presented and hugely informative.
Watson's book offers a number of reasons why some ideas surfaced at a particular moment in history, and why they originated in a particular country. Again it is all plausible coherent stuff and I greatly appreciated how he related the historical contexts to the development of key ideas.
But, just like the causes of the French revolution, what does it mean to say that a particular constellation of geographical factors made the Old World develop more quickly than the New World? What does it mean to say that a particular constellation of social and historical conditions caused a certain set of ideas to be developed? To make these claims is not to say that if X was not present then Y would not have occurred. History is not a repeatable experiment.
Neither in the case of the Diamond and Watson claims can we even test the hypothesis "Y tends to happen in the presence of X". We can't do this because they have already used up all the experimental data. In other words they did too complete a job!
If we were to encounter a plentiful number of alien races not too unlike us we would have more scope to make historical claims of the form "X causes Y". Since this is not likely to happen we appear to be stuck. However there is a possible avenue that might enable us to test this type of causality. We could simulate various worlds and societies in a computer, seed them with various initial conditions, and study how they evolved. Such simulations already exist, some on a very large scale: some online computer games depend for their very fascination on watching how a virtual society develops under the constraints of the game.
So here's the ideal academic project: conduct history and sociology (and other inexact disciplines) through the medium of computer gaming. Wouldn't that be great fun for the young folk of today?
Thursday, 17 January 2013
Weapons of personal destruction
In the aftermath of the shootings at Sandy Hook in Connecticut a vigorous debate is taking place about gun control and President Obama has just announced measures to put before Congress. Outside America there is overwhelming support for much stricter gun control but inside the country opinion is more divided.
As an outsider it seemed to be a no-brainer to me until very recently; surely the case for gun control was overwhelming. But two arguments in the debate have given me pause for thought. Both of them derive from the obvious thought that what we should be trying to do is not restricting Second Amendment rights just for the sake of it, but preventing innocent victims being killed by guns.
The first argument is that there are already over 300 million guns in the hands of private citizens. How can restricting the purchase of further guns have much effect?
The second is that nearly all the shooters in the depressing list of US gun tragedies are people with mental health problems. Since the 1970s it has been US health policy to allow such people to be managed and cared for in their communities rather than under supervision. Sadly, very little funding has been given to such communities. The result is that a large proportion of homeless people are victims of mental illness. Would it not be better to address the root cause of shooting incidents?
I don't maintain that these two arguments should necessarily carry the day in the debate but I would like to see it focussing on the actual problem: of preventing shooting incidents rather than bashing the odious NRA and perfectly responsible gun-owners. That new debate would have to come to grips with the gun culture in the US and the glorification of ever more powerful weapons.
So how should one address a culture where so many people own killing machines, have easy access to them, where accidents happen (fatal or otherwise) together with deliberate abuses; all of them regarded as the necessary price for the freedom to own those machines? Every developed country has faced such a problem in trying to make its roads safe from the automobile killing machine. Can we learn anything from that parallel?
A generation ago there was a much laxer approach to the misuse of automobiles but there has been a sea-change in attitude. It is no longer a lark to get behind the wheel of a car when impaired, and designating a safe driver has become routine. In the last 20 years the number of road fatalities in my own country (New Zealand) has dropped by more than 50%; much of that decline is because of the attitudinal change to drunk-driving. We know why this change has occurred: it is because of the far more severe penalties for driving while impaired.
There are other lessons also from the automobile parallel. Many countries have regular safety checks on vehicles. A road license fee is levied and is hopefully used to improve road safety. Drivers themselves can be checked periodically when their own license is renewed. Motoring organisations are strongly behind automobile safety concerns rather than (as the NRA) act as lobbying groups for the rights of their members.
I cannot pretend that to solve the gun death problem we merely have to imitate the solutions we have found to the automobile death problem. The analogy is not perfect (not least because the automobile death problem is far more severe). The gun death problem will have some peculiarities of its own to reckon with but we have to stay focussed on solving the "gun death problem" not the "gun control problem".
As an outsider it seemed to be a no-brainer to me until very recently; surely the case for gun control was overwhelming. But two arguments in the debate have given me pause for thought. Both of them derive from the obvious thought that what we should be trying to do is not restricting Second Amendment rights just for the sake of it, but preventing innocent victims being killed by guns.
The first argument is that there are already over 300 million guns in the hands of private citizens. How can restricting the purchase of further guns have much effect?
The second is that nearly all the shooters in the depressing list of US gun tragedies are people with mental health problems. Since the 1970s it has been US health policy to allow such people to be managed and cared for in their communities rather than under supervision. Sadly, very little funding has been given to such communities. The result is that a large proportion of homeless people are victims of mental illness. Would it not be better to address the root cause of shooting incidents?
I don't maintain that these two arguments should necessarily carry the day in the debate but I would like to see it focussing on the actual problem: of preventing shooting incidents rather than bashing the odious NRA and perfectly responsible gun-owners. That new debate would have to come to grips with the gun culture in the US and the glorification of ever more powerful weapons.
So how should one address a culture where so many people own killing machines, have easy access to them, where accidents happen (fatal or otherwise) together with deliberate abuses; all of them regarded as the necessary price for the freedom to own those machines? Every developed country has faced such a problem in trying to make its roads safe from the automobile killing machine. Can we learn anything from that parallel?
A generation ago there was a much laxer approach to the misuse of automobiles but there has been a sea-change in attitude. It is no longer a lark to get behind the wheel of a car when impaired, and designating a safe driver has become routine. In the last 20 years the number of road fatalities in my own country (New Zealand) has dropped by more than 50%; much of that decline is because of the attitudinal change to drunk-driving. We know why this change has occurred: it is because of the far more severe penalties for driving while impaired.
There are other lessons also from the automobile parallel. Many countries have regular safety checks on vehicles. A road license fee is levied and is hopefully used to improve road safety. Drivers themselves can be checked periodically when their own license is renewed. Motoring organisations are strongly behind automobile safety concerns rather than (as the NRA) act as lobbying groups for the rights of their members.
I cannot pretend that to solve the gun death problem we merely have to imitate the solutions we have found to the automobile death problem. The analogy is not perfect (not least because the automobile death problem is far more severe). The gun death problem will have some peculiarities of its own to reckon with but we have to stay focussed on solving the "gun death problem" not the "gun control problem".
Monday, 14 January 2013
Word game for those sleepless nights
I'm an enthusiastic solver of cryptic crossword puzzles and also have a keen interest in words (their spelling, meaning and origin). I don't know which interest came first but they seem to reinforce one another. In particular I love anagrams. I was tickled pink recently listening to an episode of the BBC's News Quiz which touched on the story last year of the Duchess of Cambridge being photographed topless: I learnt that 'Kate Middleton' is an anagram of 'Naked Tit Model'.
Anyway that is a bit off-track for this post, which is about a solitaire word game based on anagrams. You take any word you like and remove its letters one by one (in any order you like) and, at each stage, you have to make an anagram of the current set of letters. For example, if you start with 'wonderer' you could proceed as drowner, wonder, drown, down, own, no, o. Such a word is deemed to be a success, otherwise it is a fail.
With practice the game can be played in your head and the more experienced you get the longer the word you can start with. I find words of 9 or more letters a bit of a problem but I've discovered many 8 letter successes.
Here are some more examples of successful words to give you the idea:
many, man, an, a
words, word, row, or, o
demand, named, name, man, an, a
diligent, tingled, tingle, glint, lint, tin, in, i
efforts, forest, store, rote, toe, to, o
Obviously, to be a success the word has to contain at least one of the letters a, i, o (the only one-letter words). A stronger necessary condition for success (but not so easily checked) is that the set of letters you start with must have letter subsets of all sizes which have anagrams. For example 'ice' is a failure because it has no two-letter anagrams. On the other hand
It is astonishing how many successful words there are (especially if you restrict yourself to words satisfying these necessary conditions). When trying to "solve a word" I find it easiest to begin with the word itself and reduce it to one letter as in the examples above. This would be 'top-down' approach. But I suspect that a bottom-up approach - building up longer and longer words in several ways - would be a more efficient approach for a computer program; a natural use for the approach called 'dynamic programming'.
There are several ways in which one can 'mathematize' the basic idea. For example one could define a graph whose vertices are English words and where there was a directed edge from one word to another if the second word was an anagram of the first word without one of its letters. Then one might ask about the connected components of this graph.
But you don't have to be a mathematician to enjoy the game. Have a go yourself (ourself, flours, flour, four, for, of, o).
Anyway that is a bit off-track for this post, which is about a solitaire word game based on anagrams. You take any word you like and remove its letters one by one (in any order you like) and, at each stage, you have to make an anagram of the current set of letters. For example, if you start with 'wonderer' you could proceed as drowner, wonder, drown, down, own, no, o. Such a word is deemed to be a success, otherwise it is a fail.
With practice the game can be played in your head and the more experienced you get the longer the word you can start with. I find words of 9 or more letters a bit of a problem but I've discovered many 8 letter successes.
Here are some more examples of successful words to give you the idea:
many, man, an, a
words, word, row, or, o
demand, named, name, man, an, a
diligent, tingled, tingle, glint, lint, tin, in, i
efforts, forest, store, rote, toe, to, o
Obviously, to be a success the word has to contain at least one of the letters a, i, o (the only one-letter words). A stronger necessary condition for success (but not so easily checked) is that the set of letters you start with must have letter subsets of all sizes which have anagrams. For example 'ice' is a failure because it has no two-letter anagrams. On the other hand
It is astonishing how many successful words there are (especially if you restrict yourself to words satisfying these necessary conditions). When trying to "solve a word" I find it easiest to begin with the word itself and reduce it to one letter as in the examples above. This would be 'top-down' approach. But I suspect that a bottom-up approach - building up longer and longer words in several ways - would be a more efficient approach for a computer program; a natural use for the approach called 'dynamic programming'.
There are several ways in which one can 'mathematize' the basic idea. For example one could define a graph whose vertices are English words and where there was a directed edge from one word to another if the second word was an anagram of the first word without one of its letters. Then one might ask about the connected components of this graph.
But you don't have to be a mathematician to enjoy the game. Have a go yourself (ourself, flours, flour, four, for, of, o).
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