multijimbo

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.

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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.

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Since I first wrote about the parable of rock and gravel and sand in a previous post, I’ve continued to ponder on aspects of the parable and I’ve also had a few comments from others.  

My writing friend Sue Thomason in an email made some excellent points, more than I bring out here.  She makes the observation that, like the rocks we find while walking, with fossils and without, so are the parabolic rocks in our lives.  She notes, and this is something that hasn’t left me since I first read it, that sand isn’t just the stuff the fills the space between all the other things.  Sand is also the firmament which supports everything else. 

And so I continue to ponder.  Just looking at my own days, I see that this parable has to be dynamic.  From one day to the next, one week to the next, one month or year to the next, the shape of the mouth of our jars changes, and the volume of our jars changes as well.  Some days, I have the space to do some writing and think some mathematics, do a bit of reading and watch a movie.  But those are rare days.  Other days, the time I have to do things is more limited.

I’ve been keeping track of the things I want to view as my rocks, the things I want to view as important, and I am not doing all of them.  My patient, tolerant colleagues in my writing group have nonetheless given up on ever seeing the novel I started more than ten years ago.  I’m still working on it, and I’ve made one of my daily goals to put down at least 500 new words per day, and I’ve been achieved that goal more days than not.  And Fiona has challenged me to finish it by her birthday, and that’s the current deadline.

I also like Sue’s introduction of a bit of geological reality, that rocks get broken down into gravel and gravel gets broken down into sand, and so things can move of their own volition or because of the action of external forces from one category to another.   Sitting and thinking, I see that even though we can sometimes stretch an analogy more than the analogy can reasonably handle, this bit of geological reality is one for fertile ponderation. 

There are some things in my life that have shifted from rock to gravel or from gravel to sand, and a big part of this is that new things are hard to embed into our lives as business as usual.  New things require some focus and effort, on a day by day basis, to become part of the regular everyday.  For me, aikido is that way.  After almost 20 years, it is just a part of what I do, and it is one of the things I make time for, weekend courses or going to class during the week.  Keeping a daily journal has become a part of what I do.  But for both of these, it took effort to create the habits of doing them as regularly as they require.

As all analogies, this one has flaws.  It’s easy to poke holes and to find areas where the analogy is weaker than others, and that’s to be expected.  An analogy is an approximation, missing out details minor and major.  Overall, I think that pondering this particular analogy brings me value and so I’ll keep pondering.

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One idea does not a story make.  Having attempted to write many a one idea story, and not yet succeeded, I have learned, truly and deeply, the truth of this statement.   But there are times when an idea comes along that seems to have some legs to run, but which doesn’t have the legs to finish the race.

At the end of last week, Fiona visited the office in the library she’ll soon be moving in to.  In the corner stands an old filing cabinet, and I wrote, It would be cool if there were a locked drawer in that filing cabinet, containing a map to the lost treasure of Captain Hartley.  And yes, I do think it would be cool, because I still not so secretly wish to find the map to a treasure whose value comes in the finding. I loved this sort of story when I was younger, and it’s a storyline that’s never let go its hold of me.

I should say that part of this is trying to create a local legend that doesn’t exist.  Our university library is the Hartley Library.  I have no idea of whether the Hartley for whom the library is named was ever a captain, and in fact I suspect he was an educator and never part of any military organization whatsoever.  But as contrary to fact as it is, I like the idea of the legend of a Captain Hartley.  I like this idea that this Captain Hartley has a secret significant enough to warrant a map.

I spent part of the time driving back from Oxford earlier today thinking about Captain Hartley, and what sort of map he might draw, and what sort of treasure he might hide, and how that map would find its way into a locked filing cabinet drawer in an office in the library. 

I have a file that I keep, of all of the ideas that I’d like to build into stories, and it’s getting long at this point.  Captain Hartley has a place on that list, along with Leavenworth for magic users (a story that I think I’ll never write, given the scale of the genre); pirate Santa (yo ho ho); anything involving Wilma the cat; the person whose job it is to distribute the last few possessions of people about to be executed; rewriting books I read as rewritten from a science fiction point of view, like Incarnations: 50 Indian Lives (which I’m very much enjoying); and ideas that are good enough that I want to save them for myself. 

But I also know that Captain Hartley has now stolen a piece of my attention that he’s not willing to give up.  And so at some point, there will be a story about Captain Hartley, and all I can hope is that, when it’s finally written and when you finally read it, it’s not the story you expected but it’s still a story that you will have enjoyed reading.

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I like the parable of rock and gravel and sand.   Briefly, imagine that one’s life is a jar.  The rocks represent the things that are most important.  The gravel, intermediate sized, represent the things of intermediate importance.  And the sand represents all the unimportant grit that fills ones time.  If we start by filling our jar with the unimportant sand, then there is little room for the intermediate gravel and no room for the important rocks.

If on the other hand we start with the important rocks, then we can fit intermediate gravel around the important rocks, and there is still a lot of room for the unimportant sand. 

We can then spend a pleasant evening reflecting on the things in our life that are rocks, the things that are gravel and the things that make up the sand.  This is not a parable original to me.  I don’t remember when or where I first heard it but it’s been with me for a long time.   But I’ve never been entirely satisfied with the parable as it stands, because I think it’s missing something.  As I’ve told it above, this parable is static.

One facet of this missing something is our process of deciding what is rock and what is gravel and what is sand.  One approach is to decide what is most important and make that the rocks, what is least important and make that the sand, and then the gravel is the intermediate stuff that remains.  But I think there is a more honest approach.  This more honest approach is to first conduct a time audit and see how we spend our time.  The things on which we spend the most time, these are the rocks.  The things on which we spend an intermediate amount of time, this is the gravel.  And the sand is the remainder, the small things that fill up the time between all the other things.

Conducting such an audit is an interesting experience, because what we think are the rocks, are not always where we’re spending the bulk of our time.  And this led me to the next point.  Suppose I examine my life and I decide that I’m not happy with my current balance of rock and gravel and sand.  How do I change?  How do I convert gravel to rock and rock to sand, et cetera.

For me, this is the most difficult aspect of this whole parable, this process of change.   Making this parable dynamic rather than static.   And I’m not sure about the whole of the road to making this change.  I know that a first step is to be mindful.  I have been paying more attention to how I spend my time, though the process of converting gravel to rock is as hard as I thought it would be.  And the difficulty is habit.

Habit has an inertia that makes changing its direction difficult.  And habit has a memory of its former life, and it likes to return to its old ways.  So when we try and reshape the jar that is our life, empty out the current mix of rock and gravel and sand, some of that gravel and sand will somehow find its way back in the jar before we have the opportunity to fit in the rocks that we wish to be rocks.   And so there is some learning still to do.

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As we begin the year 2017, I like many others have spent some time looking back on the year just come to a close, and perhaps years farther back, and I find pieces of unfinished business.  One big piece involves something that I’ve tried my hand at a bit, not as much as I want to, and this piece is explaining hard bits of mathematics, interesting bits of mathematics, to people who are not mathematicians.  If you wish to read the current state of my efforts here, you can find them in the numerology of unrelated constants 1 and the numerology of unrelated constants 2.

A couple of years ago, one of my non-mathematician colleagues challenged me to do exactly this, to take my 10 favourite mathematical facts and find a way of describing them in a way that he would understand.  I’ve not yet risen to the challenge, but I do think about it most days.  What are my 10 favourite mathematical facts?  How can I winnow down my list of favourite facts down to 10?  And more interestingly, how to describe them, explain them, in a way that a non-mathematician would be find intelligible and interesting.

Looking back at those two earlier posts on the numerology of unrelated constants, I can see that I am still trying to explain mathematics as I would for my students, rather than aiming at the broader audience of people who might find the concepts interesting.  And to be frank, I’m not entirely sure how to explain some of my favourite things, such as the many different sizes of infinity, to non-mathematicians.  It’s a challenge, and not one that I’ve entirely yet come to terms with.  But I do like a good challenge.

I think that I fallen afoul of one of the things I’ve written about in the language of mastery versus the understanding of the student, which is the difficulty inherent in explaining something that I’ve spent a lot of time thinking about, to someone who has never encountered it before.  And the more I think about it, the more interesting and difficult a challenge I think this is going to be.

For instance, consider the idea I mentioned above, which will be one of my 10, the many different sizes of infinity.  One of the great achievements of 19th century mathematics, which arose from Cantor’s development of set theory, is the idea that sizes of non-finite sets can be made precise, and in the realisation of this precision, we get an infinitude of different infinities.

Where the challenge arises is that when I mention this idea to non-mathematicians I know, they give me the strangest look.  Infinity is infinity, isn’t it.  How can one infinity be different from another infinity.  They sometimes use choicer language, but what comes across is the perfectly reasonable lack of knowledge and understanding of a part of 19th century mathematics, that we don’t teach to pre-university students and increasingly don’t teach to university students.  And so, the question is, where to start unpacking this strange and beautiful idea and how to pull out the essential non-technical bits.

I will admit that there’s something I’m not doing as part of this whole process.  Perhaps I’m being a bit too reductionist, in wanting to figure out how to construct such explanations on my own, without reading about how others have done it, but for me that’s part of the challenge. There are some excellent expository of mathematics for the general audience in the world, but I am taken back to a story I read as a much younger man.

In a future society, those with exceptional talents are noticed and cultivated from a young age.  As part of this cultivation, they are prevented from knowing what others have done, so that their talents are not contaminated.  The story revolved around a musician who had heard none of the classic and classical composers but rather took his inspiration directly from rain and streams and the wind through the trees.  But someone sneaks in and plays some Bach, and this changes the young man’s music.  Elements of fugue disappear from his works, and it becomes obvious that his music has been fundamentally changed by this external influence.  And so I’m going to give myself to see what I can do on my own, knowing that I can always learn should I desire to do so.

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I am not one for new year resolutions, for two reasons.  First, I’m really really bad about keeping them.  Looking back over my time on this planet, I think there is one actual resolution I’ve kept to any significant extent, which is to take stairs rather than elevators.  But even on so simple a resolution, I find myself faltering at times, often for no good reason, and I find myself constructing tales to tell myself about why this time, taking the elevator is a reasonable thing.

Second, and yes this second reason is a bit tongue in cheek, but which year?  I am primarily bound culturally to follow the Gregorian calendar whose new year 2017 begins in a few days.  But there are many many other years and calendrical systems, and if I were go to a-digging in my family tree, I suspect that I would find direct ancestral attachment to several of them, and I know I have weak cultural attachments to others.  For instance, I like having been born in the year of the dragon, because dragons are cool, but I tend not to make resolutions attached to the Chinese New Year.

But this year, I’m going to make and then make every effort to keep a resolution.  This resolution involves the separation of work and non-work.  I don’t want to call it work versus life, because my life is heavily influenced by my work.  I like what I do, a lot, and so the different aspects of my work, the teaching and the doing of mathematics and even yes the administrative side of things, are all part of the big rock of Work that sits in my jar.  (And if you don’t get the reference, I’ll be writing about rocks and gravel and sand at some point soon, so stay tuned.)

I know though that I am not good at keeping Work in all its various incarnations from seeping into the rest of life, and this is my resolution for the new year, and it’s a complicated resolution.  Part of it will be ensuring that the different aspects of Work each get their due attention, which I will admit I haven’t been good at in recent years.  But more than that, I will keep Work from seeping into all parts and times of life.  That is the main focus of this resolution.

Time is the important word here.  We are not our jobs, however much we might like our jobs.  But I haven’t been good at maintaining the time and the space for me to do much beyond Work.  So I will write more and read more in the coming year, and spend more time with family and friends, just being and just doing the things we do.

But I will also be more respectful of my colleagues divisions between work and non-work.  I have developed a bad habit over time, of emailing my colleagues in the evenings, sometimes in response to their queries and sometimes with queries and requests of my own, and this is not an entirely healthy thing to do.  What started me thinking seriously about this was when a colleague commented that when he gets ‘one of those’ emails from me, he starts to panic, and panic is the last thing that I want communications from me to engender in anyone. 

There is a game that I am not particularly good at, the game of ‘out of my inbox and into yours end of the day office email ping pong’, and one reason I’m not good at it is that I don’t like to lose.  I like to return those late afternoon serves into my inbox as soon as I can, and this is the thing I’m going to change.  Another of my colleagues doesn’t do email in the evenings or on weekends, because he needs to have time away, and I can see the attraction in this, and I’m happy to work towards this even if it is a Zeno-like working towards. 

It will take me some time before I get to that point, but I do hereby resolve to refrain from causing the hearts of my colleagues to sink when they arrive to work in the morning, because there is a pile of stuff from me that I sent out late in the evening when I should have been doing something else.  I will moderate myself.  I’m aware that this cannot be an absolute thing, as there will from time to time be something that needs a response before the next day, but I will try and keep those as few and as far between as I possibly can.

I know this is going to be difficult for me.  No one will be in the office until the middle of next week, and many people won’t be in the office even then, but the temptation to respond to the things sitting in my inbox is proving very difficult to resist indeed.  And so, it’s time for a bit more coffee and perhaps a bit of reading, and I’ll deal with the inbox later.   And a happy Gregorian new year to all.

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