On brundecidedness

So this post will probably annoy some people. And its not even funny. Let’s call this my Michael Macntyre post.

As Joe Strummer once said. “Should we stay or should we go?” I’m surprised that has not become the theme tune of the brundecideds. I admire the brundecides. I myself, however, am just leaving the brundecided zone, and would like to suggest why. And in which direction. Tantalising I know. You’ll have to read on.

Let’s admit upfront that noone really knows whether or not we will be better or worse off in or out. This is not a decision about finances.

Let’s also admit that this is not a decision about personalities. This is good news for me, since in my view Farage, Cameron, Osborne and Johnson are all equally hopeless, untrustworthy and cynical. But voting bremain to spite Farage, or brexit because you think Boris is a charming man would not be wise.

It should also be said that this is an extremely important vote. Get your general election vote wrong and at least you get to change your mind in five years. Get this wrong, and it’ll be many years before the chance comes round to change things. (Which is perhaps a small mercy).

Anyway, here is my view and you can like it or lump it. First, it seems undeniable that we are faced with all sorts of not insignificant problems and challenges. I won’t list them. It is too depressing. It is also undeniable that none of these problems are fixed by brexiting or bremaining. Whichever we do, we wake up the next day and global warming is still a problem. Syrians and Libyans will still want to avoid living in a war zone. There will not be enough fish in the sea. Antibiotic resistance will still threaten our health. And so on. (See, it is depressing). (I did say).

So the question is – do we solve these problems best in the EU or out the EU?

It seems to me that, couched in these terms, the decision is quite straightforward. The EU is a pretty hopeless organisation, which spends far too much time and money and effort trying to fix problems the wrong way. It has screwed up on many many occasions, and should be ashamed of itself. It is unaccountable, heavy-handed and insufficiently democratic.

But none of the really important issues can be fixed on our own. We can bury our heads gloriously in the sand for a while, singing Rule Britannia and feeling chuffed about regaining sovereignty (whatever that means, if anything), but these problems will still come and bite us just as hard. (This is an important point. The world has moved on since Churchill, whether you like it or not).

Or we can try to work with a bunch of other people to sort problems out. Cooperation and all that. If you don’t believe me, this is a very convincing song.

Perhaps that all sounds very flippant. It’s hard to make bremain sound inspiring. Brexit can go all Dunkirk and Johnny Foreigner and Churchill and Her Maj and This Sceptred Isle and all that stuff.  Wave the flags. Bremain is just a rather tedious and uninspiring decision to suggest that our best hope is to get together with a bunch of other democracies and try to sort stuff out. But that is what we have to do, if we care about the future.

Antiblogging

It appears no one at all read my last blog post.

This is not surprising, because I made no effort to publicize it.

So here, perhaps, is a new form of blogging. Private blogging. No one reads it.

If you stumble on this blog by chance, do enjoy yourself.

But, please. Keep mum.

On education

This is not the second part of the two part series on creativity I promised earlier. You will have to wait for that. Do try to control your excitement.

As a maths teacher, the two questions I probably get asked most often by pupils are ‘Can we have a fun lesson Sir?’ and ‘When will we use this in our lives Sir?’.

The first is easily dealt with. ‘All maths lessons are fun. Now get on with Exercise 56’, normally does the trick.

Here is someone who thinks maths is fun. They have no nose. I say no more.

The second is more subtle, and more ingrained not only within pupils but within society as a whole. One can hear the Daily Mail at the door shouting – “yea, go on, when, when are they going to use this“. It seems to miss the point so entirely it does not even deserve to be called a proper question.

Let’s leave aside the basics. Clearly we all need to be able to read, write, have some basic numeracy, etc. These are critically important, and I would not want to devalue them at all. But this is not what pupils means when they ask this question in a Trigonometry lesson, or while trying to draw an equilateral triangle with only a pencil, ruler and compass.

And surely such an excellent question. When, oh when, are they going to find themselves on a desert island, armed with a compass, pencil and ruler and needing – quickly, oh so quickly – to construct an accurate equilateral triangle to avoid a grisly fate. You, Sir, must help them be ready for the world of work. Be off with you and teach something useful. At once.

Well, this is depressing.

Well, the most obvious point is that how is anyone supposed to know what to teach them? Out there in the class are (say, in future) one chef, an airline pilot, a failed wrestler turned hotelier, two marketeers, a manager of McDonalds, a market gardener, three (three I tell you) school teachers, a candlestick maker, four shop assistants, a bicycle repair man, and a chick-sexer. Do they really think I can devise a maths lesson which will help them be successful in these roles that they don’t know they will have and neither do I. And of course many of them will have several roles; sales assistant, teacher, mother, author, carer, candlestick maker. Are they expecting to learn here and now the skills that will equip them through a lifetime?

Well, yes. That is my job. To equip them with the key skill which will get them through a lifetime. The skill of learning itself. Pupils are here, predominantly, to learn how to learn. Then, why they start that great role as Supplementary Products Marketing Manager (Europe, Middle East and Asia) they have some idea how to start, what questions to ask, what to do and what not to do, how to get their head round the complicated new set of issues they are facing for the first time. And learning how to D an ET with only a P, C and R is helping them learn how to get their heads round new, apparently pointless but challenging skills. This is a subtle point. I am not going to try to explain it further. Plus I, personally, think Maths is fun. Including Trigonometry.

This is all a bit rambly. But I don’t really care.

On maths and creativity

This is the first of two posts on the topic of creativity. Do not get too excited. I may not get around to the other.

Most people, I suspect, do not think of mathematics as a creative endeavor. This is understandable. If all you have seen is quadratic equations, ratios and trigonometry, you can be forgiven for finding the creative aspect hard to identify. Indeed creativity is the enemy of success. Pupils who try to find their own way to solve quadratic equations always gain null points in the exam. Just follow the process, and all will be well.

On the other hand, really good mathematics is, necessarily, profoundly creative. If you are going to solve a difficult problem – one which has been around a while – there is no point trying the obvious stuff, because that will all have been tried before. Difficult problems only get solved when a mathematician tries something really left-field, and it still somehow works.

Reading this sort of work takes your breath away. When I read (for example) Dennis Sullivan’s no wandering domains theorem, I am left gasping. Wow. How did that happen? I felt the same way I felt when I saw this picture:

This is one remarkable picture

Or when I watched Memento. Or read Northern Lights. It just seems incredible. Someone somewhere thought of that and it came together and then blam something amazing happened. People are astonishing.

So now I am going to really push the boat out.

Taking myself too literally again

Actually in Maths something even more remarkable is happening. Not on has someone done something amazing, breathtaking, awe-inspiring. But it worked – in other words the whole universe has this amazing, breathtaking, awe-inspiring but totally objective thing going on. And that is what really astonishes me, and keeps me doing this whole maths malarkey.

On winning and losing

Three things lead me to today’s blog. The first is the suggestion (attributed to Rick Gekoski) that

Life is about winning and losing.

The second is the announcement that Martha Fox will be Chancellor of my university. Someone who is such an eminent ‘winner’ that she bears an extra name and – just to remind us of her achievements – a jolly title. How we love these things.

The third was an alumni gathering at my old college. A chance to meet up with old friends after 30 years, chew the fat, and think about what has happened to us in the interim. Did we win, or lose? And to what extent? And is there an SI unit for this? If so, I reckon I am at about a pico-Lane-Fox.

Is that it then? Life? It is about winning and losing? About being like Ms Fox on one side, or cleaning the toilets at Heathrow Airport on the other? Note my question is not asking if winning and losing are a part of life. It is the about I am interested in.

Possibly my most dreaded place to work

After at, it often seems that our society does agree with this notorious about. There are no gold medals awarded for exceeding-your-personal-best-by-a-good-margin. No Nobel prizes distributed for getting quite-a-nice-result-considering. No Oscars handed out for trying-really-hard-to-make-a-good-movie. No Booker prizes cheerily conferred for really-a-pretty-decent-novel-in-the-circumstances.

Well, if this is what life is about, I advocate a return to the Stone Age. If that is the best we, as a species, can come up with, then let’s give the mice a go. No, really. They probably already run the world anyway. Douglas Adams had inside knowledge.

They also do quantum field theory

Why so? Well I was going to give you a nice, tidy list of neatly bullet-pointed reasons. Discussions about the marginal extent to which the world is meritocratic anyway, about the need for us to – well – look after each other, however talented or not, about the measure with which we utterly depend on those people who clean the toilets at Heathrow airport (but never award them a title), about the caustic psychological effects of winning on the winners.

But I won’t. You will only get bored. No, really. You will. So let’s just say it is deeply unimaginative. Let’s try, just now and then, maybe for five minutes before breakfast, to imagine a world in which we celebrate how things are done, rather than what is done. Prizes and awards to be dished out for character and personality and doggedness and compassion and persistence and thoughtfulness and genuineness and sheer, unalloyed humanity.

At the very least, it would be interesting. A refreshing change. And perhaps a little more just. Perhaps.

PS. My mathematical readers – if they got this far – may be wondering if this has anything to do with Maths. Well, the intersection is non-empty. But probably of zero Lebesgue measure. Here is Lebesgue, just in case you needed convincing.

What a jolly fellow

On not being the best at something

I am reasonably good at Maths. This is not a boast – everyone is good at some things and less good at others. I am pretty hopeless at drawing and at swimming. If you don’t believe me, the sketch below is proof. On average I am pretty average; what I gain in the algebra department I lose in sketching and natation. We are all like that.

I rest my case.

When I went to university I discovered that there were many people much, much better at maths than me. They made my maths look like my swimming.Perhaps I could do a PhD, but I would do in three years what someone else could do in a month. And probably they would do it better and then realise it wasn’t particularly valuable anyway. It seemed to me the best thing to do was to give up on the whole maths project. So I became a computer programmer instead.

You may be thinking that that was pretty dumb. Well, I would challenge that. Being a computer programmer had its moments. On the other hand, you may be thinking that that was a pretty dumb reason to give up maths. Well, I agree with you, and I am going to try to explain why. But if you already see why, do feel free to move on. There is nothing interesting to see here.

Computer programmers are pretty cool.

I think this kind of thinking is not unusual. I have never met someone who was the best at something. We are all in this boat and have to deal with it. So, let me suggest a couple of reasons why this was a terrible way to deal with this particular boat.

Firstly, and to repeat myself, hardly anyone is the best. I suspect that most mathematicians look at the Field’s medalists and sigh. And probably most Field’s medalists look at someone like Edward Witten and just groan. This is a mathematician so good, he managed to complete a PhD in applied mathematics following a BA in History. And Witten in turn, perhaps, has nightmares about John von Neumann. And they probably all wish they were Carl Friedrich Gauss. If everyone took my approach, all we would have would be the works of Gauss. And that would leave the world somewhat incomplete. I guess this is just the boat business all over again.

This is quite an attractive boat. In contrast with the sort of boat we are discussing.

More importantly, though, is the following. It is just rubbish. It is nonsense. Really. It just doesn’t matter if someone else could do something better. It is good to do things. Make up some theorems. Sketch a tree. Swim a loch. So what if someone else’s theorem was better, their tree more realistic, and they swam the loch ten times, in the winter, having broken the ice with their teeth, swimming along with one hand behind their back while whistling the theme tune from Ski Sunday.

Its probably an age thing, but I really don’t care any more. I love doing maths; we will talk about why another time, perhaps. My theorems are my theorems, and they are quite cute. About five people in the world will ever read them. I will never do anything groundbreaking. But I just don’t care. Because we all have to do what we can do, and that – for each of us – is somehow an amazing thing.

You really don’t have to be bitten by something radioactive to be amazing.

And if that sounds a bit inarticulate, it is because there are plenty of people who can express themselves better than me. But this is my blog …..

On trusting people, and Ofsted

This post has nothing to do with maths. Which will disappoint about one of you, and my other two readers will be delighted.

I used to work for Hewlett Packard, back in the days. It always seemed to me that Dave Hewlett and Bill Packard were really rather remarkable people, because they had built their company based on a somewhat unintuitive management philosophy. Their approach was based on the idea that most people want to do a good job, and will do a good job provided you let them get on with it. Given that Bill and Dave started in a garage and ended with a company employing tens of thousands, either they were lucky or something positive is to be said for their management style.

Here they are, back in the days.

One often hears an argument somewhat at odds with the Bill and Dave approach. I am going to focus on this in the field of education, which is just what I know well. I am sure this applies elsewhere. The argument is this. Something must be done. Something must be done about poorly performing schools. Something must be done about underachieving teachers. Something must be done about coasting establishments. You know what I mean. Something must be done. (Parenthetically, did you ever hear a politician say “something must be done about underachieving politicians”?)

And, after all, why not? Surely we should do something to fix schools which are not helping their pupils, teachers who sit idly by enjoying their long vacations and watching students fail? Bill and Dave were just naive. There are bad guys out there. And something must be done. And up steps Ofsted, with a cheer and a hurrah, to make sure something gets done.

Ofsted. They will do something.

Yet, when you hear these words “something must be done”, you must ask two questions. Two rather subtle questions which Bill and Dave understood, and are easily forgotten. First will the doing something actually do anything? It is quite hard to tell if someone is doing a good job, so all one can really do is check a few key indicators – what percentage of GCSEs are A*-C? did the teacher write the lesson objective on the board; stuff like that – and see if these are met. Trouble is, the small number who don’t care about doing a good job are not, on the whole, stupid. They see these things coming and make sure they tick the boxes. Meanwhile, the majority who do are often see these things, realise that doing a good job is somewhat bigger than these smaller indicators, and often get picked of by the cavalry. So, how is that helping something be done?

Secondly, is the harm you are doing in one place less than the good you are doing in another? OK, so maybe you identify a poorly performing school here and a bad teacher there. Meantime, a whole bunch of otherwise excellent teachers are suffering from stress, another group are putting hours into trying to placate Ofsted in a way which will help no actual pupil, and school managers are running in circles not to help improve the school, but to make sure the next inspection runs smoothly. Is that supposed to be helping? Of course, if you think teachers are an idle bunch who need to be sorted out, then you’re probably cheering. If you care about the standard if education of young people, you should be scratching your head.

This is not particularly relevant.

Bill and Dave’s point was this. Yes, of course, in the real world there are some bad guys out there who are not doing a good job. But, they really are in a minority, and trying to oust them will probably cause more harm than good. So how about you spend your efforts trying to help the people who do care about doing a good job do an even better job. Make sure that people feel supported, encouraged and motivated. And then see what happens.

But that doesn’t make much of a Daily Mail headline, does it.

On doing maths

So, I do maths. People say to me, what do you actually do when you are doing maths. That is not easy to answer. I study the dynamics of transcendental entire functions. Given that there is nothing actually dynamic, certainly nothing mystical, and no relation to the sort of things which are held in large rooms hired from pubs, you can already see there is a problem.

I can try to use a metaphor. It is from cooking. It is not a very good metaphor, but I am not a writer am I. So, perhaps you can deal with it.

Think of a chef.

A chef. Looking thoughtful. Which is appropriate.

Let suppose our chef reads that cheddar cheese on toast is a delicious meal. Well, of course, he could make cheddar cheese on toast. But that would be boring. (And spoil the metaphor). So he tries something else. Perhaps a different cheese. Or maybe beans. Perhaps a little parsley. Pushing the metaphor, perhaps he realises that cheese on toast is not only an excellent meal, but also helps cure indigestion. Or maybe provides good sustenance to dogs. There are all sorts of things our chef can conjure up. And good luck to him. Or her.

What has that got to do with what I do doing maths? Well, I start by reading what other mathematicians have done. Perhaps I read:

Theorem: If X = Cheddar Cheese + Toast, then X is a delicious meal.

So I get out a pen and paper and I try some variations on this. (I use a lot of paper). Perhaps

Theorem: If X = Cheshire Cheese + Toast, then X is a delicious meal.

Or maybe

Theorem: If X = Custard + Toast, then X is a delicious meal.

Not all theorems work out. Or I can try to generalise things. Perhaps

Theorem: If Y is a dairy product and X = Y + Toast, then X is a delicious meal.

It is better than cooking, because there are all sorts of things I can try. For example I can define a food as ‘good-with-toast’ if, when Toast is added, I get a delicious meal. Perhaps foods which are ‘good-with-toast’ have some interesting properties.

Theorem: If Y is good-with-toast, then Y is good-with-bread.

Well, you get the idea. So then I write it all up, and make it available to other mathematicians. Who knows, perhaps they will read it and then make their own new theorems.

I think it is pretty exciting.