multijimbo

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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The year 2016 has truly been a year of surprises, with more than a month still to go.  This includes a seemingly endless string of celebrity deaths, though perhaps my generation has just reached the age where the celebrities of our youth are of that age.  The vote for Brexit and the election of Mr Trump as President of the United States were both political surprises, and perhaps they are but the first of a string of political surprises over the coming months and years.

But the biggest surprise of all, one that I did not expect to see during my lifetime, was the victory of the Chicago Cubs in the 2016 World Series.  I grew up spending spring and summer afternoons watching the Cubs play on WGN, through the miracle of cable television and a seemingly insatiable desire to procrastinate.  For more on that, I direct you dear reader to this if you should feel the itch of curiosity and the need to do something other than the thing you should be doing now.

I am an academic and I have something in me that reacts to change as any academic reacts to change.  Living in a world of change, particularly uncomfortable change, is tiring, and perhaps this is why the Cubs winning the Series gets to me as it does.

Don’t get me wrong.  I am as happy for Cubs fans in their moment of joy as I’m sure they were for those of us who grew up in Georgia when the Atlanta Braves won the Series in 1995.  And in looking up things, I didn’t realize that the Braves and the Cubs had something in common, namely that they are the National League’s two remaining charter franchises.

I grew up in Georgia in the 1970s and 1980s, watching the Braves when they were far from World Series champions.  There was for instance the season, I forget which, when they were only a few tens of thousands of fans short of reaching 1 000 000 home attendees for the season with 3 games to go, only to have those 3 games rained out and the decision was made to just let those games go and not be replayed.

The Braves winning the Series was a bit disorienting, given their history, but they had last won the Series in 1957 and so while it was the breaking of a period of futility, it wasn’t the breaking of the historical certainty of futility that belonged to the Cubs.  But now, that futility is broken and there is a new order in the world.

And all I can say to that is that this new world order will be an interesting one.  So, all the best to all Cubs fans out there, and I can only hope that the gap between this victory and the next Series is not quite so long as the last gap.  And to the rest of us, we will do what we need to do to survive this world of change.

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When I was an undergraduate, oh more years ago than I care to think about, I was for a too short a time a member of the Demosthenian Literary Society at the University of Georgia.  At that time, we had a faculty advisor, a member of staff whose role was to provide inspiration and guidance of a sort.  And he regularly said something that’s stuck with me ever since those bygone days.

He would often speak towards the end of a debate, as I remember things, saying that we had made good points but that we hadn’t gone far enough.  And often we hadn’t.  Casting my mind back, we would focus on the details in our back and forth, but we would allow ourselves to be constrained and restrained by what we were given.

Nowadays, in my own teaching, I find myself coming up against the same thing in my students.  They, like me back in the day, focus on the specific question and don’t allow themselves the freedom to push out and explore the question from outside the box.  And so I try to inculcate this same willingness in my students, to try and look at questions from a different perspective.

And it’s hard.  It took some time for me to develop the confidence to allow myself the freedom to cast myself adrift a bit, to wander beyond the safe boundary of a question, though I always had that voice in the back of my mind, reminding me that I hadn’t gone far enough.  And I think it’s hard for my students, because of the pressures they’re under, for their time and attention and my class being just one of several.

This pushing beyond the safe boundary of a question does not come naturally to most of us.  It’s something we need to work on and something we need to practice, even if the relatively safe confines of a pure mathematics class.  But we persist.

Why is this important?  What bother writing it down at all?  I spent the weekend at Mozfest, the annual festival run by the Mozilla Foundation, and I spent the weekend beyond the safe boundaries of most of what I know.  It was invigorating and refreshing and it’s going to take me some time to make sense of what it all means.

I was particularly taken with the talk by Eliot Higgins of Bellingcat, using open source data to allow citizens to investigate the news.   All they do is to push beyond the safe boundaries of questions and the things we’re told are true, working to discover what’s actually true.   In fact, one of the themes of the weekend was data, what data we give away, what data about us others have, and what we can do with enough data.

I am beginning to believe, as many others have said, that we are creating and entering a remarkable phase of human history.  We not only have vast quantities of data about us and about the world around us, but we also now have the tools and the technology to meaningfully analyze that data and extract proper information from it.   And we need to be careful about this world we’re creating, because we have no precedent for it.  As I suspect is always the case with the future.

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