a mildly revelatory teaching experience

•21 October 2018 • Leave a Comment

Recently I gave a talk to some prospective students and others at a university open day. It’s the talk I’ve given before, many times in fact, and it’s a talk I enjoy giving. In this talk, I take the audience on a journey from the Pythagorean Theorem, possibly the oldest mathematical fact that we as humans have, to Beal’s conjecture, an unsolved problem to which I don’t expect to see a solution in my lifetime.

The talk went well, I think. People came up to me and asked questions afterwards, always a good sign, and they laughed at the few jokes I scattered through the talk (and not at non-joke times), also good signs.

Reflecting after the talk, though, and thinking about ways of improving the talk for the next time I deliver it (since we are always in a cycle of continuous improvement), I found myself wondering whether the time had come to develop a different talk.

And I started thinking about why I was thinking this.  The audiences for this talk are essentially disjoint from one another, except perhaps by some coincidental happenstance, and so for the audiences the talk is new each time.

The reason I was thinking this is that I am beginning to get a bit bored of this talk.  Looking back, I can see that this is not an uncommon pattern: give a talk some number of times, and it can become difficult for the speaker to generate the same enthusiasm the n-th time they give the talk as they had the first or second time.  And a large part of carrying an audience is precisely that enthusiasm.

And this is a much broader issue.  This issue has the potential of leaking into teaching, particularly if someone teaches the same class for several (or many) years in succession.  Unless they take active steps in refreshing their material, perhaps finding new illustrative examples, then they might find their enthusiasm waning and their energy falling, and ultimately their students drifting off.

Part of this I think comes back to this issue of the distance between experienced practitioner and beginner, an old theme.  But it’s more than that.  This issue of distance is one that requires work but can be overcome.

But the issue of enthusiasm is a different sort of issue, and one that might well be harder to directly tackle.  I think there’s great value, as a teacher, in engaging with a certain collection of material on an extended basis over the course of several years, because that does provide me with the opportunity to shape how newcomers will first encounter that particular part of mathematics, or aikido, or whatever it is I find myself teaching.

But I’m beginning to see that this issue of my enthusiasm is a bit more insidious of an issue, because the students I’m sure are very perceptive to my levels of enthusiasm and engagement.  If I wane, they wane.  If I engage, they engage.  And so this is something for me to bear in mind when I go into the classroom or the dojo, and teach.

In some arenas, there is a seemingly straightforward solution to this, which is to rotate teachers among the classes taught, so that no one teaches the same class for more than a few years in a row.

But I have issues with this.  Sometimes, as with me and aikido, this sort of rotation is not possible and so the issue is one I have to confront directly.  It also can prevent this deeper engagement with the material that needs some years to develop, particularly when what I’m teaching is not directly related to my area of greatest familiarity.  And ultimately, I think it’s better to address these issues rather than put into place strategies that might or might not mitigate its effects.


reflections on the beginning of a new academic year

•10 October 2018 • Leave a Comment

Campus is alive again. Students have returned, teaching has started, and I love this time of year. Among my other duties, I get to speak to groups of new students, and having just come out of one, I’m reflecting on things I tend to include in those induction talks.

I’m honest with the new students that I feel a non-insignificant amount of envy. They are starting a grand and glorious, and there is a part of me that would dearly love to go back to school, pick a new subject and in some sense start over again.

This wanting to go back and relive parts of our lives we’ve already lived is a not uncommon theme in science fiction and more generally, with both positive and negative outcomes. I’m not sure I would consider Groundhog Day to be science fiction in the traditional sense but it is an interesting exploration of a possible reaction to the lack of consequences of living the same day over and over and over and over again. And Bill Murray rocks.

And while I’m typically not a fan of the Q episodes of Star Trek: The Next Generation, I do enjoy the episode where Q gives Picard this particular gift, and Picard’s ultimate lack of acceptance of the gift.

I suspect that one of the reasons this going back and starting over is an attractive topic for speculation is that it is not in any way, shape or form a thing which is possible for us to do. With that impossibility, it’s largely consequence-free speculation. I suspect that someone has written the story or the novel about how a society might react or be shaped by such a thing actually being possible. If you have a suggested reading along these lines, I’d be interested in a reference.

But one thing about the picking up a new topic and starting the learning process with this new subject is something that we can always do. The constraints on time that come from the day job might make this difficult, but I do like to remind myself that this is always something I can decide to do.

It might require a shaping of my current life to make enough time available for such a new thing, amidst all the current things, and it might well also require a slight renegotiation with the current day job. And I’ve started thinking about what this new thing might be. I have a few ideas. Let’s see where they lead.

thrashing and attention theft

•1 September 2018 • Leave a Comment

I recently learned the term thrashing as used by computer scientists, as a thing experienced rather than a thing to be given.  Loosely, thrashing describes when a computer becomes debilitated by spending all of its time moving things in and out of memory, rather than doing any processing.

It would be interesting to understand the etymology of this particular use of thrashing and how those that chose, chose thrashing as opposed to other seemingly apposite words such as flailing.  But that investigation is for another day.

For me, this sense of thrashing is a useful term to describe situations far beyond what’s going on inside computers.  It’s also good for describing what sometimes happens inside our heads.  I find myself thrashing from time to time, moving from one project to another without making any real progress, responding to external demands on my time and attention.

And this is where I think thrashing and attention theft are connected.  Attention theft is I think sufficiently self explanatory a term that I won’t try and formulate a precise definition, but the modern world is as rife with attention theft as it is with thrashing scenarios.

One connection between these two notions is the time we lose to attention theft, keeping track of the world via Twitter for instance and constantly pinging to check whether new email has arrived, and how this time lost contributes to the creation of thrashing situations.

I am coming more and more to appreciate having some time to sit and think, to start working through the details of some of the pending projects, and make some progress.

The complicated question is, how.  How to carve out that time that no one else has access to.  How to carve out those spaces where no one else can find us.  This can be particular tricky for those in roles that require them to be available to others, to answer their questions and on occasion make the decision that needs to be made.

And somewhat self referentially, this leads to yet another project, which is the project of being more active in carving out this time for thought and reflection, and battling the forces of thrashing and attention theft.

beware, there be spoilers: Jailbird

•25 August 2018 • Leave a Comment

One of the interesting ideas that Vonnegut introduces in Jailbird, as a passing comment by our narrator Walter Starbuck is the notion of government as a Ponzi scheme.

There is something to this idea, but I’d like to unpick it a bit and see where we find ourselves. We find ourselves at an interesting point in our history, having as we have unbound our monetary systems from extrinsic sources of value. Fiat currencies, underpinned by our faith in government rather than something we can hold, such as gold.

Some long time ago, I speculated about money as a doomsday device, and I think there’s a lot more there to unpick. But looking around, we see governments racking up large debts for future generations to pay.

The solution of course, as we have been told many a time, is to grow the economy, so the debt burden becomes a smaller percentage of the nation’s ability to create wealth, but we are then faced with the issue of our elected officials not adequately curating the nation’s ability to grow.

But this isn’t a Ponzi scheme. We are borrowing from the future to fund our present, and I think this is an issue that’s fundamental to governments of the people, by the people, for the people. Perhaps it’s that we’ve become used to our governments not providing a clear picture of the consequences of our actions and requests, and of us not looking for a clear picture.

I’m writing this as the sun comes up on a beautiful day, and so I don’t want to get too pessimistic, but I’m beginning to wonder. What is the path we should be taking? We cannot get everything we want, because wanting more and more is an asymptotic process, and we seem to have found ourselves in a situation where more and more is never enough.

Perhaps the basic problem is one of time. Perhaps we are setting our time horizons too near to the present, and not considering the consequences of our actions in 100 years time, or 200. Predicting the future is a difficult thing, but I wonder if we can start to take the view that we shouldn’t make our future lives any more difficult than we need to.

So perhaps government is a Ponzi scheme, borrowing more and more from the future to satisfy the demands of the present, with everyone being complicit in the scheme.

beware, there be spoilers: Slapstick, or Lonesome No More

•19 August 2018 • Leave a Comment

When I first started my 2018 project of reading all of Kurt Vonnegut, I will admit I had no idea what to expect. I’d read a bit: Cat’s Cradle, the Sirens of Titan, and Welcome to the Monkey House, all of which have a science fiction flavor to them.

But I hadn’t realized the extent to which Vonnegut framed everything in a science fiction context. But up until this point, that’s what he’s been doing. Like Player Piano, Slapstick is a near future story, with telepathic communication, habitable asteroids, and plagues and the consequences of plagues.

All good stuff. But there was one thing that made an appearance in Slapstick, one idea, that I thought was an idea worthy of far greater exploration than occurred therein, and so I would, as unseemly a thing to do as it is, pick a bone with Mr Vonnegut.

Don’t get me wrong. I love his writing and I’m enjoying my Year of Vonnegut. He has a sense of humor that I will be chasing for the rest of my days. He has a collection of characters that I can only marvel at.

But he does have a habit, and it is something of a habit, of introducing a spectacular idea and not exploring it. In Cat’s Cradle, we have the different crystalline structures of water, one of which is Ice-9, which leads to the cataclysm at the end of the world, but that cataclysm isn’t explored in any real depth. What are the logistical issues, for instance, around getting drinking water? Is skin permeable to Ice-9? And so forth.

And here, in Slapstick, comes the idea that gravity has a time dependence to it. That gravity on Earth is sometimes stronger and sometimes weaker, and that we happened to have been living at a time when gravity had decided (for lack of a better term) to be constant.

The pyramids were built when gravity was weak and workers could just lift the stones, for instance.

But what would human society look like, how would we have developed, what beliefs might we hold, if gravity were sometimes weaker and sometimes stronger. Because I think this would have had a massive impact. We are story telling beings, after all, and we have over the course of our history been good at capturing some significant historical events with our stories, such as flood myths and the flooding of the Black Sea.

We believe that gravity acts independent of time. That it is mass that determines gravity, and essentially nothing more, and this leads me to ponder a clear and difficult to embrace human trait. We have been truly aware of our surroundings for a remarkably short part of the time that the Earth has been around, much less the universe.

Many of our beliefs contains these hypotheses and assumptions, such as gravity being time independent, because that’s all we’ve ever known. Well, that and the fact that the math of the situation works out well.

But what if. What if. And I do expect at least one physicist to write in and tell me why the what if isn’t really, but I would like to believe in the possibility with the same fervor as any academic being unwilling to admit that they’ve been fooled by a good magician.

the things we know and how we know them

•19 August 2018 • Leave a Comment

Years ago now, I went to an internal university course of being a better lecturer and the person presenting, whose name I don’t remember, started with an exercise. List, he said, as fast as you can, the months of the year.

This is something we can all do incredibly quickly, as long as they’re the months we grew up with. (Not like the calendar in an episode of the Simpson’s that contained a thirteenth month.).

Now, he said, with a twinkle in his eye, list the months of the year in alphabetical order. And needless to say, we crashed and burned. Some of us did what we thought was the reasonable, logical thing, namely going through the months time and again, looking for the alphabetical first, then the alphabetical second; getting lost on which one we were looking for since we were trying to hold too much in our heads all at once, thereby running into a different notion from psychology that I love, namely cognitive strain.

But it took us a lot lot longer to generate the alphabetical list. And ever since, I’ve loved this little exercise, because it is an invaluable lesson that we as teachers need to remember. Namely, just because people might know something (for instance the months of the year), they know it in a particular context.

And that context is important. It’s like the months of the year are olives in an olive loaf, and the loaf is the chronological context. (Perhaps a bad analogy, but it’s close to dinner time and I’m getting hungry.). We can’t ignore the context and use the information as freely as we want to. And neither can our students, who won’t even have practiced manipulating the information in the same ways that we have.

It’s an infinitely flexible exercise too, since we can change the list of things and the manipulation of context. A good one is to say the numbers from 1 to 20, alphabetized by their spelling, because here the context is particularly strong.

Why is this exercise fresh in my mind today? Because I start teaching my graph theory class in a month (yikes) and I’m starting my preparations, and I’ve been teaching the class for a few years now.

I can sense how my own understanding of some of the topics has changed from when I first taught the class, and I need to be mindful that I don’t make assumptions about how my students will be able to use the facts we will be working through, since they’ll be seeing for the first time things that I’ve have seen multiple times and will have worked through multiple times.

We’ll also have new students in the University of Southampton Aikido Club, and I’ll need to maintain the same awareness with them as with my graph theory students. And there, the issue will be a stronger issue for me. I’ve been doing aikido for 21 years just about, and so my internal context and internal language for my aikido is deep at this point.

And what makes this an especially interesting challenge and imposes a duty on me as an instructor, is that the language of aikido is a language of movement, as opposed to the logical definitional language of mathematics. Translating the lessons from one type of teaching to the other is an interesting challenge, and one that I enjoy.

beware, there be spoilers: Breakfast of Champions

•5 August 2018 • Leave a Comment

And the year of Vonnegut continues, and entertainingly so.  As he did with his other books, Vonnegut continues to weave familiar characters from earlier books into the book under consideration, with Eliot Rosewater having a minor role.  But herein one of the main characters is our old favourite, Kilgore Trout.

But what I found most interesting was the role of the narrator, the point of view character.  Partway through my reading, I wrote myself a note on the inside cover (and yes, I am one of those who makes notes, relevant to the reading or just random thoughts and ideas, in what I’m reading, as long as the copy is mine).

I asked myself, who is the narrator, because Vonnegut had begun to hint that the narrator stood a bit apart from the other characters.  This came through in part because of how the narrator was reflecting on the events affecting the characters.

And indeed he did.  In Breakfast of Champions, the narrator is the author of the book, and who particularly towards the end takes an active role in the lives of the characters, sometimes while he’s face to face with them.  He shapes their actions.  He introduces things to distract the characters.  But he’s not messing with them for the sake just of messing with them.  Though I’ll admit it’s not entirely clear to me the message the author/character was working to get through to me the reader at the end.

And so, I start to think, and my thoughts go in many different directions.  Might I ever use this particular narrative device, of having the narrator  be the author of the book, who then finds himself or introduces himself into the action of the story.  While I enjoyed reading the book, I think I would find it a hard device to use myself, and I can also see that after a time, reading several different books with the same device might become a bit tiresome, depending on how it’s handled.

And when was such a device first used?  I’m sure there’s a scholarly tome out there somewhere, which traces the history of the author being a character in their own work, and it would be interesting to know.  (And so yes, if you happen to know of such a tome, please let me know.)

There are many ways to tell a story, and this is something that in my own writing I know I can get hung up on.  I set up a scenario, I set the characters in motion, and then I think, ooo but what if I did this, what if I did that, what if they knew this extra thing, what if they didn’t know this important thing, et cetera.  And I find my stories bifurcating again and again, creating a tree of possible stories and I don’t have the capacity to explore all of them.

And so the discipline has to be, explore the ones you can explore and get the words on paper.  And that is my plan for the rest of the afternoon.