Stoopid is Stoopid Does

file

Image courtesy of idpinthat.com

I hate this illness. First I miss years of school because of it and now as I begin studying (again) at the age of 39, I find it’s taken me about five goes to get right something I would otherwise think of as basic algebra. Every time I am making really, really stupid mistakes, basic mistakes like copying the wrong number into an equation. Repeatedly. I could cry. But I guess a better thing to do would be to get a good night’s sleep and try again tomorrow. Patience is indeed a virtue.

 

Not to be confused with Lambada

Probability and statistics can get a little dry (according to some people – personally, I don’t see it, I find it fascinating). Today I have learned a new symbol, lambda:

The lower-case Greek letter ‘lambda’

In probability theory lambda, in the words of wikipedia, ‘represents the density of occurrences within a time interval, as modeled by the Poisson distribution.’

The page helpfully instructs ‘Not to be confused with lambada‘. At once I was imagining brown corduroy-clad male Maths teachers whipping their mustard-yellow ties above their heads in time to raunchy Latin rhythms, with a feisty lady teacher (because the female science and Maths teachers were always rather lively) standing at the side launching haddock at the whirling dervishes and shouting “Poisson distribution! Poisson distribution!” with each fishy missile.

This mad image had me in fits of giggles. I seem to have been alone in my mirth, however. Much like Sheldon. Frank just raised his eyebrows. He’s a very placid fellow. That’s why we complement one another so well.

********

I start EMDR in earnest next week. From what I understand, it’s like going through the trauma all over again, only this time the brain processes it all properly, so that it doesn’t keep leaping out at you like ghosts from the past that you have no control over. I have to make a ‘comfort box’ filled with things that help me feel ok. I think humour is definitely going in that box, one way or another.

Why I Love Statistics

I am loving my studies. It’s so much fun. I get to play games with numbers, call it academia(!) and learn something that will be such a useful, practical tool. Today I have been rolling virtual dice and studying the patterns in the outcome. This chap explains it all so well, although he’s not even a statistician. Watch this – just the raw enthusiasm will make you smile.

Guest Post: Does God Play Dice?

Albert Einstein’s quote ‘God does not play dice’ refers to Quantum Mechanics (see here for what he was on about). However, as a student of the Mathematics of human behaviour and of the teaching of Jesus of Nazareth, I think I can play with that idea in other contexts. What I am thinking about here is predestination vs an Arminian version of free will, but also the much more real world question of why more people don’t go to church.

Let’s start with the latter. Church-going in the West by percentage of population is a minority sport, one could say – except that by comparison it isn’t. Attendance at weekly worship is regularly in excess of attendance of Saturday football matches. The two groups are, of course, not mutually exclusive, but we’ll consider this in the light of what I shall write later. However, this comparison does put into context church attendance figures as not being too bad. If church exceeds what is viewed in the UK as being a popular activity then we have to question what we are ‘expecting’ the results to be.

There is a lot of history here. John Bunyan’s autobiographical ‘Life and Death of Mr. Badman’ and John Wesley’s ‘The Almost Christian’ remind us that in the English-speaking evangelical tradition the standards for commitment are set at a high level. Yet both of these are coming from a historical situation where not attending church would incur a monetary fine and where, in Bunyan’s day, non-conformist preaching led to imprisonment, including his own!

In a society where freedom of religion is recognised and religious belief technically protected from discrimination, perhaps we should see a decline in church attendance. If a thing is not personally costly it is easy to see it as having no value.   And as G. K. Chesterton is paraphrased as saying ‘When a man stops believing in God, he doesn’t then believe in nothing, he believes anything’. Certainly banality in belief seems to be on the increase, but determining how you would statistically test this assertion would be a challenge.

So then, do those who remain attending church constitute a committed remnant?   A Calvinist elect or Kierkegaard’s Knights of Christ?

In the study of statistics, minorities are interesting. What causes them? Are they the extremes (outliers) from the norm? If they are the anomalies that you get within any population, for example those who are unusually tall or exceptionally fast runners, you can ask: what exactly are the characteristics they posses? What causes them? For the unusually tall the thing you are measuring is objective and simple, but it does have multiple contributing causes, such as genetic inheritance and childhood nutrition. With a fast runner, current influences such as training regimes and even technology can be a factor. Statistically you can attempt to measure the degree of likelihood that something has a cause or link, but you can never be certain.

The fastest man in the world

Randomness is used to cover the inevitable inaccuracy, either of your measuring instruments or the fact that it is generally pretty much impossible to have all of the data (so you never know if you have the complete picture). Some statistical models will allow you to make a guess of the degree of influence that something has. But again, because of shortcomings in data or measurements, there will always be a gap between what is observed and what the model predicts. ‘Only the angels know everything‘ says Aquinas, and a good statistician knows this only too well. Human knowledge is limited, not only because the sheer volume of data that constructs our universe is far beyond our three-score-years-and-ten comprehension, but also because we cannot count how many angels dance on the proverbial pin head.

Statisticians use randomness to fill the gaps of what they cannot explain, knowing that something is always out there that does not fit the predictions.

Perhaps we of faith need be reminded to have the same humility before the mystery of God and Creation, rather than make so many pronouncements from an ill-founded certainty. What stirs the human heart to faith is mysterious and inexplicable. John Wesley and Billy Graham may have been very effective in particular contexts and at particular times, but their methods did not work on even the majority of the population, let alone a specific soul drawn at random. Jesus himself in the parable of the sower uses an image of wheat seeds falling at random on hospitable and inhospitable ground as a metaphor for the acceptance of the word of God. Has then God (randomly) predetermined an elect? A mischievous suggestion but, like I say, randomness (or why someone appears to be chosen while another does not) is a cover for not being able to perceive everything at once.

The statistical idea of randomness, I think, has another thing to teach us. Randomness will generally cause things to group around a central middle value. Anyone who bets on rolling two dice should know that score of seven will appear more times than two or twelve, this is because there are more ways of making seven than two or twelve. The more times you do this, and the more dice you add, the truer this statement becomes. To go back to an earlier point, this is also true of tall people and those that run fast. Most of us are grouped closely in a central band. As you move away from this central point the quantity of people who are taller or faster runners decreases more and more. The factors that determine our height or how fast we run pull us together into a central point rather than push us out to the extreme.

Church attendance is an unusual activity, but here we are using it as an indicator of something even more ephemeral: spiritual devotion. I agree with Bunyan and Wesley that the two are not synonymous and I agree with Jesus and the Prophets that what God seeks is worship in Spirit and in Truth.

I would also say that frequent acts of spiritual devotion are rare rather than common. To say this I am not pretending to be able to see into the hearts of men people, rather using my personal experience and that which has been historically reported by sources I trust. If spiritual devotion is rare, a statistical outlier, it perhaps confirms the writings of the many divines from the epistles, through the desert fathers, through medieval monks and nuns, through to puritan writers and further through to more modern writers like C.S. Lewis: spiritual devotion is difficult and the distractions are many. We are all being pulled towards a relatively inactive centre.

Based on the above, let me humbly suggest something: if we are truly to advance the kingdom of God then we should perhaps devote our time and efforts not in trying to find those highly unusual souls capable of maintaining a high degree of spiritual activity – I dare say they have found their place already, as the groaning of their souls beyond words is so deafening to their inner life they can do nothing else but tend to it – we should work to build up the ordinary souls so that they can become more extraordinary, helping them make the small steps towards a deep faith, not presenting them with an expectation of what they should be, with no clue how to get there.

What we have found when we have crunched the numbers for church attendance is that what is most effective is not finding new souls, but keeping those we have. Let us never deny the gospel to anyone, but in our enthusiasm to tell all the Good News, let us make sure we feed the sheep that are already in the fold, and make sure that they are not joining the number that have strayed.

Written by Frank

Numeracy and Mathematics

I have asked for a little space on the new blog created by my wife, as I had recently come across something I felt worth sharing with the interweb, and felt I might come across similar things as time goes on.

The specific thing was a quote on the nature of Mathematics and how it may relate to this ill-defined thing, Numeracy. 
I guess I need to give some background to this before progressing to the quote and some thoughts on it. A few years ago I completed a Level 5 qualification in teaching Adult Numeracy, to go with another qualification that I got a few years before in teaching Adult Literacy. These qualifications are undertaken by those who teach, or are interested in teaching, individuals over 19 years old ‘basic’ Maths and English. They are specified as a requirement to teach the subject full time with government funding (though this often gets overlooked as the qualification is far from universal).
As part of the course we had to write a short piece on the history of Mathematics and also another piece on the difference between Mathematics and Numeracy. Both ideas caught my attention somewhat and they are subjects that I have returned to in my thoughts from time to time. 
When I studied, I was lucky enough to have access to a reasonably well-stocked set of libraries (by no means exhaustive, but I know other colleagues have not had such opportunities). Not only that, as I continue to read and think about these things I come across things that make me say, “I wish I knew about that when I was reading for the first time.” These blog posts are my effort to share things that I have found interesting, and save those who come after me a little bit of effort in hunting these things down.
Last week I bought the the Loeb Classic’s Greek Mathematical Works – Thales to Euclid, compiled and translated by Ivor Thomas,  initially in 1939. See here. It has both the Greek and an English text and looks as thought it will keep me challenged for a while. The very first quote in the book is from Anatolius, who Ivor Thomas tells us was Bishop of Laodicea about AD 280. He said;
“[Some teachers] say that … poetry and the whole of popular music can be understood without course of instruction but no one can acquire knowledge of the subjects called mathematics unless he has first gone through a course of instruction in them;”
p3, Greek Mathematical Works, vol 1 Thales to Euclid (Loeb Classical Library No 335)  Ivor Thomas, Harvard University Press, Cambridge Mas, First printed 1939 Reprinted with Additions 1980
What I find interesting here is the idea that Mathematics is something that is defined by the fact it has to be taught. Almost by implication you may wish to define Numeracy then as something that does not need to be taught. I think that does a disservice to Numeracy, and to those who struggle to pick it up. Perhaps what we are reaching for in 21st Century education, though, is a truth that was stated all those years ago in the 3rd Century AD: that Mathematics requires formal study to be understood, whilst Numeracy can be learned through more informal learning. Mathematics then is the stuff of the academy, a world of rigour, technical language and thought. Numeracy though, consists of the everyday informal conceptions of quantity and amount. I would say defining Mathematics by its need for formal tuition is almost a back to front definition, defining first not what it is, but what it needs. It is like finding a burglar by the impression of their boot by the broken window. It is an interesting clue to the nature of Mathematics that it needs to be defined in such an unusual way.
Frank