the value of an old lesson

•24 May 2017 • Leave a Comment

When I a young in the ways of being a grad student (postgrad to the British), my advisor Bernie Maskit gave me some advice that I’ve always carried with me.  To be a successful mathematician, he said, you need to have two things.  One is a good noise generator, the (figurative) voice in the back your head that spits out possible things to do, ideas to try, directions of mathematical travel.

The other is a robust filter.  After all, most of the ideas that come out of the dark nooks and crannies of your mind will be crazy (in the best possible way, perhaps), or unworkable, or wrong, or already done (as has happened a few times), or things to save for later, or things that are beyond what you know or even what can be done.  That’s not to say, don’t write them down, and so I got into the habit of writing things down.  But rather, not for now.

This is the first piece of advice I give to grad students when they start with me, and other grad students over an afternoon beer, or to anyone who will listen, to be honest.  And people who’ve known me for a while will have heard the bones of this story more times than I can count.

But lately I’ve been thinking about this basic structure of the idea generator and the filter, and the more I think about it, the more robust it gets.  In thinking about my teaching, for instance, I have lots of ideas that to be fair are crazy or unworkable or to be done later.  And both having the ideas, things to try, and the filter, the thing to try next which might be the one that works best, have stood me in good stead.

But the area where I think this basic structure has perhaps the most value is the administrative work I do.  Higher education in the UK is entering a period of turmoil, with the Teaching Excellence Framework and Brexit and just the general uncertainty now in the world, but also because the fundamental model underlying higher education everywhere is changing.

And here, we are always looking for new ideas, new ways of doing things, new things to try to address the problems that no one has yet been able to solve, and it is here that I think that we need better filters.

It’s easy to come up with an idea and launch into a new scheme.  But the question I’ve started to ask myself is, if in my research there are ideas that need some time to develop or a quiet place to be laid to rest, then why isn’t this true in the other areas of my work.  And I think it is.  There is great pressure to change, to do things differently, and we are all a-changing.  But perhaps we also need to engage our filters, to make sure that the change we’re enacting is change that will do us good in the long run.  Just a thought.

reflections on EasterCon 4: tying up loose ends

•14 May 2017 • Leave a Comment

While at EasterCon last month, I set myself a challenge, as noted in reflections on EasterCon 2: the beginnings of things.  I started with an idea and I set myself the challenge of writing (the first draft of) an entire story during EasterCon.  Not surprisingly, I didn’t entirely succeed.

I spent time going to panels, talking to friends, the occasional drink in the bar, and I spent significantly less time writing than I’d intended.  But I have now finished the first draft of that story.  I will admit that I cheated a bit, in that I melded the current political news of the day with an idea I’d been playing around with for some years.

And it’s this last part I found interesting.  I have an idea.  It’s a crazy idea, an idea that anyone who read my first drafts will recognize as a genuinely bonkers idea, and it’s an idea that I’m still trying to find the right home for.  Is this current draft the right home for this idea?   Perhaps, but I’m not entirely sure.

But this now leads me down another read.  We write for particular audiences.  We each as authors have the ideas we like to explore.  And we all have a list of ideas for future projects, stories or longer, not all of which will be written.  Not all of which can be written.

But perhaps ideas are like pegs.  Some ideas are round ideas, and some stories are square holes, and round ideas can’t always be made to fit into square story holes.  I’ve tried a lot of different story possibilities for this one particular idea, and I’m not sure what the right shape of story is for this idea.

But even if the current story doesn’t work, I’ll keep trying, and I will find a good story shape for this idea.  One day perhaps it will be out there for all to read.  I’m coming to the point where I feel I’ve made a promise, not as much to myself as to this idea.  I will find it a good home.  I will do it justice.

What I find fascinating is that I don’t have the same reaction to some mathematical ideas.  There are some mathematical projects I’ve been working on for a lone time, and will never abandon.  But there are some ideas, some directions of mathematical travel, that haven’t worked, or that I haven’t been able to make work, and what I find strange, and what I have a hard time admitting, is that abandoning a mathematical idea is harder than abandoning a fiction idea.

Perhaps it’s just that it’s easier to see the flaws in a mathematical idea, the reasons it can’t be made to work, than it is for an idea for a story.  There’s a malleability to fiction, a freedom to make ideas work, that doesn’t hold for some mathematical ideas, where there is a notion of truth by which we have to abide.

Lulu Hurst and the physics of aikido

•23 April 2017 • Leave a Comment

I recently read an interesting article in Atlas Obscura, a site which contains many interesting and unusual articles.  This specific article, The Victorian Teenage Girl who Entertained Crowds by Overpowering Men, introduces us to the story of Lulu Hurst.  For a couple of years in the 1880s, she had an act where she used the principle of the lever and the fulcrum to defeat much stronger people.

The reason I find this whole episode as fascinating as I do is not that it is an example of a simple physical principle being dressed in the guise of a seemingly impossible feat of mysterious power, though I do have a great appreciation for that, and for the inability of so much of her audience to recognize or understand the physics of what she was doing.

Rather, it’s because of the applicability of the principle of the lever and the fulcrum to aikido.  I have seen demonstrations which are equally as mysterious as those ascribed to Ms Hurst, and even though I have some experience of aikido at this point, I am not able to reproduce or even to provide a sufficiently good explanation of what is actually going on.  This last point is relevant when I find myself teaching.

There is a tendency among some to ascribe a greater or lesser degree of mysticism to aikido, which is not the direction I want to take.  Rather, we are physical beings operating in a physical universe, and I wish to find the physical explanation of what I’m doing and the effect I’m having on others on the tatami, and the effect they’re having on me.  That’s one reason I find the story of Ms Hurst so fascinating.

It does raise some questions, though.  I wonder for instance how she came to her power.  From what little I’ve read, it seems she taught herself, and I would have loved to hear from her the story of how she started that journey of discovery and her experience of travelling so far along her path.

I’m not claiming that a knowledge of physics is necessary for the understanding of or fluency in aikido.  But I do think that if we pay attention to what we’re doing on the tatami, and in particular the things we’re doing that we don’t need to do and the parts of things that are actually the effective parts of what we’re doing, then we learn a lot about physics.

But the body is a massively complicated mechanical system, the workings of which are often hidden by clothing and the skin, and it’s hard to figure out what’s going on just from experiencing the effect of it.  This is I suspect part of what Ms Hurst used in her act, the difficulty of sufficiently clear observation on the part of the audience to figure her out, along with our not being nearly as attentive as we think we are.

But this week and in future weeks, as I’m either student or teacher on the tatami, I’ll bear Ms Hurst and her act in mind.

reflections on EasterCon 3: how we write for our audiences

•17 April 2017 • Leave a Comment

One of the general themes that underlay a lot of the discussions of which I was a part at EasterCon was the difference between academic writing and non-academic writing, of either fiction or non-fiction.  Some academic writing has the reputation of being impenetratable, seemingly sometimes for the purpose of being impenetrable.  This is mocked beautifully in an old Calvin and Hobbes cartoon.

I don’t think that this reputation acquired by academic writing is entirely deserved.  One thing of which I am aware in my own writing is that academic writing sometimes requires of us a degree of precision, in definition and in the use of terms, that not all writing requires.  Splitting hairs is difficult and splitting hairs requires that we have a clear idea of the difference between one part of the hair and another part.   There is of course the question of whether splitting hairs as we do is something we need to do, and I believe that it is.  To understand something, we need to understand it in its fine detail, and that’s part of what we do.  But it does lead to another way in which the fundamental notion of fractalness enters into our discussions, and so I can see that talking about fractals is not something that I can ignore any longer.

But back to the topic at hand.  As a pure mathematician, precision of definition is a fundamental part of what I do when I’m doing mathematics and when I’m writing mathematics, but I have noticed something interesting in my ponderations.  When I am writing mathematics, my primary goal is to be precise in my statements and to be precise in my arguments.  I take for granted that my target audience, in this case other mathematicians, is also interested in this precision, and so I don’t worry about people beyond that intended audience.

This isn’t to say that the mathematics I write is deliberately obtuse, because I don’t think this is the case.  I spend a lot of effort in my mathematical writing, because I want my audience to be able to read what I’m writing.  This is by and large true of my colleagues as well.  I don’t write for me, but I write for the people who might read.

But the way I approach writing a story is very different from how I write mathematics.  And I think part of the reason is that I think I have a much clearer idea of the nature and composition of my mathematical audience, as opposed to my fiction audience.  My mathematical audience and I share a clear vision of the structure of a good mathematics paper, and it isn’t a form that allows for a great deal of variation.

Fiction, on the other hand, is much more wide open in terms of allowable and reasonable forms, and this is one of the things that I took away from the panels and discussions at EasterCon.  This freedom of form is one of the things that I enjoy about trying to create stories, and it is also one of the things I find most daunting.  I am sure that there is a lot of work that’s been done on forms of stories, and this structure of stories is one of the things that I want to dig into at some indeterminate point in the future.

reflections on EasterCon 2: the beginnings of things

•16 April 2017 • 3 Comments

So, in what can only be described as a fit of recklessness, I have decided to try and draft a story during EasterCon.  I did this a couple of years ago at LonCon 3, starting from an idea that came to me from the events of the news, bringing it together with an idea that I’d put on my List of Ideas for Stories to Write and managed to create a draft.  A flawed draft, admittedly, one I submitted for a quick rejection, and one that I need to get back to, revise and polish.  

And now I’m trying to do it again, again starting from an idea in the news, combining it with another from my List of Ideas, and to be honest, it’s going all right.  But thinking through the structure of the story has blended in my brain with some of the discussions over the past couple of days, listening to panels and in casual conversation with the people I’ve been meeting, and now I’m thinking about the origin stories of stories.

Some aspects of this I’ve pondered before, in Giants, Neanderthals and old stories.  But the origin story that came to mind this morning concerns the fables and myths we have.  I’m reading the Tales of 1001 Arabian Nights, which is a fascinating experience and I’m currently in the part, about 140 nights in for those who have read it, where we are getting lots of short fables, like the Thief and his Monkey, the Sparrow and the Peacock, and the Mouse and the Flea, each of which is explicitly being used by Shahrazad to try and persuade the King to behave more sensibly.

But the one that’s most relevant to the story I’m trying to pull together is Pandora’s Box.  We have an idea of who first wrote down the story and we have the characterisation of Pandora’s Box as an origin myth, trying to explain the origin of the evils of the world.  But I’m interested in a different variation of origin, in that I want to know why Pandora and a jar were used to tell the story, as opposed to anything else.  I’m completely convinced that there is a body of scholarly literature on the subject of why for instance it’s a woman who unleashed evil on the world.

But what I actually want is something that I know is impossible, namely I want to be sitting around the fire when the first version of what would eventually be the myth of Pandora’s Box was told.  What was the event that caused that first teller to start telling the story, and I am fascinated by this history of stories.

I think there is an inevitability to thinking about writing while being here at EasterCon, given the number of writers who are here and the amount of discussion of writing in all its glory and possibility.  It’s also interesting to watch how the story I’m trying to compose here is changing each time I sit down to put down words.  I think the story has reached a sufficiently stable form and all I need to do now is to finish it, but as part of that process of stabilisation, I have found several variants of the story that might be as interesting as the story I’ve decided to tell.   But this leads into a different topic for another day.

reflections on EasterCon 1: mosaic novels and the Rashamon moment

•15 April 2017 • Leave a Comment

I need to see Rashamon again.  It’s been too long, and I need to watch it without any of the usual distractions I heap upon myself when I watch a movie I’ve seen before.

I just attended a panel session on the mosaic novel here at EasterCon 2017, and it’s gotten me thinking about the construction of story.   As a very loose definition, a mosaic novel is one composed of a collection of stand alone stories, held together by the glue of a unifying narrative.  A lot of the discussion between the panel and the audience turned on aspects of the definition of what precisely is a mosaic novel, and John Clute, one of the panelists, made the comment that the notion of mosaic novel is fractal.

Having spent some time pondering the issues and examples brought up in the discussion, I can only agree on the fractalness of the definition of mosaic novel, but then I have taken the view that most of these it is/it isn’t definitions of the things we do are of necessity fractal, and this necessary fractalness of things is something I’ll explore elsewhere.

And this is where my desire to see Rashamon again comes from.   Different descriptions of the same event from different points of view, held together by the narrative of trying to understand the event from the tales told by the different witnesses, and I don’t remember enough of the detail to know whether Rashamon can be reasonably considered to be an example of a mosaic story, film though and not novel, even though it isn’t science fiction or fantasy.

Beyond this consideration of whether Rashamon is a reasonable mosaic story is the place that the Rashamon moment has on the list of things I’ve learned as a manager, tying together here things that don’t necessarily need to be tied together.

Up to this point in the writing I’ve done, I’ve tried to tell stories but I haven’t thought much about the structure of the story that I want to tell, or even whether the way I’ve decided to tell the story is a reasonable choice of structure for the story I want to tell.  And this is one of those interesting moments when I feel the floor open up beneath me a bit, as there is a vast amount I know that I don’t know about the structure of story.

We humans have been telling each other stories for as long as we’ve been able to speak to one another, and I suspect that the stories we tell each other structure the way we approach the world in which we live and vice versa, so that the approach we take to coming to understand the world we live in then fundamentally shapes the stories we tell.  And this isn’t the standard if and only if equivalence of statements we get in mathematics.  Rather, this is the snake eating its own tail of a positive feedback loop, where each thing drives change in the other.

And I know there is a temptation for me to resist, and resisting is going to be hard.  I need to resist the temptation to stop telling stories until I’ve spent some time reading about story, learning about story, studying story, because I know what will happen.  I’ll read and learn and study, but write even more slowly than I’m writing now.  And that slowly, I don’t want to write.

And so now, in this gap I have in the things I’m doing, let’s write a bit and see what sort of a story we can start to tell.

those who can, teach.  those who can’t teach, just do.

•2 April 2017 • 2 Comments

I would like to do something strikingly unoriginal and take issue with George Bernhard Shaw.  Specifically, I would like to take issue with Shaw’s quote that ‘He who can, does.  He who cannot, teaches.’  To be fair, I have not gone back and researched the context of Shaw’s quote.  Perhaps he was being sarcastic and didn’t mean what we have all taken the quote to mean.  And it is a quote that many of us have extended, so for instance ‘Those who can, do.  Those who can’t, teach.  Those who can’t teach, administrate.’ and so on and so forth.

As faithful readers will know, I think a lot about my teaching, both my teaching of mathematics and my teaching of aikido.  This includes not only teaching in the class room, but also such things as public lectures at the Cafe Scientifique and my attempts to explain bits and pieces of mathematics to friends and colleagues over coffee, not always successfully.

Great teaching is hard.   Inspiring and engaging people, particularly with difficult things, is hard, and many things are difficult the first time we encounter them.  And sometimes the second.  And sometimes the third.   Almost everyone has their story of the great teacher that inspired them, opened a window onto another world that they then assisted in the exploration thereof.  And almost everyone has their story of the bad teacher that shut that window and destroyed their interest in the topic.  As a teacher of mathematics, I have heard more stories of bad mathematics teachers than I can count.

But I don’t think teaching as such has to be hard.   Structuring the material, developing exercises to engage the students, creating the path for the students to take in engaging with the material and then working with the students as they walk that path, these are all things that anyone can learn.  Anyone can be a competent teacher.

But I do strongly feel that there is one thing that any competent teacher needs, whether or not they are a great teacher, and this is a sense of reflection.  This gets back to the main point of discussion in the language of mastery versus the understanding of the student.  As we as teachers explore topics and subjects in greater and greater depth, we increase the distance between ourselves and our students, who are new each year.  

There is also a major difference between being good at something and being good at teaching that something.   And in fact, the better we are at something, the harder it becomes to teach that thing.  This is something that I encounter when talking to people about mathematics.  There are things in mathematics that I don’t remember struggling with, and these are the ones that become difficult to explain.  That I sometimes find difficult to explain.  This is a reflection, I think, of the fact that I never had to pull them apart when I was learning them, and so I don’t know off hand how to pull them apart for someone else.

Or perhaps it’s just been long enough ago that I don’t remember that first pulling of things apart, and so I have to do that over again.  Either way, it doesn’t matter.  It is the things we know best that are the most difficult to teach. 

And so this is why I would like to recast Shaw’s quote.  I think it is easier to be good at something than it is to be good at teaching that something to others.  And so I think it’s those who can, who can do the teaching, whereas those who can’t teach, just do the things to do.  But beyond that, I think that it’s not entirely appropriate to refer to those who can’t teach, because I don’t feel there is anyone who can’t teach.  Yes, there are some who don’t teach well, but perhaps somewhat controversially, I think that someone saying they can’t teach is a choice they’re making.