exploring Confucius: hearing and forgetting 2

•8 October 2017 • Leave a Comment

I’d like to spend time following up something I wrote some little time ago now.  Teaching has started here and is occupying a lot of my attention.  And a significant part of my attention is on the basic question:  given that I am lecturing, how can I as lecturer best act to ensure my students are getting value for the time they’re spending in lecture.

It’s an interesting question, in part because it’s a strange question to ask.  There is a common view that the question of value is essentially the same as the question of time.  If I as a lecturer am giving you the student my time, then I am providing you the student with something of value.  And yes, I do have to say that I believe this is true of me.  Though of course, it isn’t really my question to answer.

I don’t see that time is the same question as value.  We can extract value from time spent, but it is also possible to spend time but not create anything of value.  What I need to do in the lecture is to capture your attention.  In aikido, this is atemi, which I’ve spent a bit of time exploring in a completely different context.  But it’s not a concept that I’ve explored to any depth from the point of view of teaching.

But it is critical.  We each have busy minds.  When students come into the classroom, I as the lecturer need to do something to bring their attention into the room.  In the aikido dojo, we have a way of doing this, which is the ritual with which we begin every class.  This ritual helps me to leave behind the busyness and business of the day behind, and to focus my attention on the task at hand.  I don’t have such a ritual for my mathematics teaching, and perhaps I should.

And I can see that I’ve drifted a bit off topic, but not too far off.  I hear and I forget, so what I can I do to those who hear me, to help them remember.  This is akin to the stickiness of lectures.

So, what makes a lecture sticky?  And what do we even mean by sticky in this context?  I have an idea of what I mean.  What I want is that you, having heard me talk about something, remember what I’ve talked about.  Not that you can recall the lecture verbatim, but rather that as you go through the notes, you will on occasion read a sentence and hear it in my voice, speaking the words to you as you’re reading.  I want the enthusiasm with which I approach the topic of the day, to become a hum in the background.  And the reason I say this, is that I still have that background hum from some of the lectures I attended, as a graduate student, as an undergraduate, and even a few rare hums from high school.

But how to do this?    I’m sure there are ways.  One I think is to think of a lecture as a story to be told.  And so, I need to become more of a story teller.  This actually runs deep.  Because if I need to become a story teller, then first, I decide what is the story I want to tell.  And this is the rabbit hole into which I find that I have fallen.


exploring a house of unlit rooms

•1 October 2017 • Leave a Comment
One of the things I find most fascinating about the fiction writing I do is how different it is from my day job.  In my day job, I’m a mathematician.  In my day job, I take a question, a strange little idea, and I spend time, months or years, exploring that idea, wandering through the maze of its subtleties.  Exploring its dark alleys and blind canyons that lead nowhere.  Revelling in its occasional moments of clarity and advancement.
The art of doing mathematics has been described as exploring a house.  We start in one darkened room and we grope our way around, thinking that we are finding where the furniture is located and developing an internal picture of the layout of the room.  And then the light goes on and we realize that our view of the room was largely wrong.  We missed some pieces of furniture, misjudged others, and missed a door entirely just because we never made it to that part of the room.  We then have to spend tome time reconciling the mental picture of the room we created, with the room as we can then see it.
We then go through one of the doors and start all over again in another darkened room.
But for me, writing is different.  I tend not to follow or explore a writing idea to the same depth as I do a mathematical idea.  I am much more butterfly than miner, moving from one thing to another.  And I have started to ask myself, why.
I don’t know whether other writers follow ideas as deep as they go, largely because I think I don’t read entire oeuvres.  I’ll read a novel from X, a collection of stories from Y.  But I don’t start with the first thing X wrote, and then read everything they wrote chronologically from that first thing.  I’m not sure it would help, and I’m not sure it wouldn’t.    Perhaps I’ll make it a project for the Christmas break. And I’m sure that some writers do this deep extensive exploration of the branches and twists of some single idea, and I’m sure that some writers don’t, and now I’m wondering in which group I might want to place myself.
I think that I would much more like to be the sort of writer who needs to dive into an idea, wallow in that idea, explore it like I explore the house of mathematics and find everything I can find.  And that’s what I’m doing.  But there is something more of which I need to be aware.  That is, exploring an idea to its deepest depths takes time, and my mathematician side is used to producing one paper a year, perhaps a bit more, once the exploration reaches a natural end.
But if I’m going to do this exploration as a writer, I’m going to need to change how I view things.  I’m going to need to become willing to let people see the midway points.  I’m going to need to become willing to let people see me camped in the blind alleys.  I’m going to need to become willing to expose my explorations while they are still only half formed.  And for me, this shift is the hardest thing.
And so, I put aside this rumination and turn my attention back to the writing I haven’t yet done today, stories clamouring for attention and a novel that everyone I know is firmly convinced will never be completed.

the university as a house of questions

•24 September 2017 • 1 Comment

The nature of education in general, and of higher education in particular, is changing and changing fast. I am aware that there is a vast literature on this point, and that it is a subject in which reasonable people can disagree about the details. Nonetheless I thought I’d venture into this particular fire swamp and expose some of my ruminations to the light of wider scrutiny.

Clearly, technology is driving some of this change. For most of their existence, universities have been places where facts have been stored and through which facts have been transmitted and disseminated. It is easy to forget that for most of human history, facts about the world in which we live have been expensive and hard fought to discover, in part because facts have a tendency to be hidden by assumptions about the world that persist even when the predictions arising from these assumptions prove to be false.

And beyond this, the discovery of facts requires time and equipment, bodies and laboratories and the time and the space to think, and universities provide all of these. The keen eyed among you will have noticed that I haven’t defined what I mean by fact, and I won’t. What I will say is that there are some objective things that we now know to be true beyond the shadow of any reasonable doubt; there are the seemingly incontrovertible observations distilled from vast numbers of experiments that seem to be true; and there are speculations for which the evidence hasn’t yet been gathered and perhaps cannot be gathered using current technology and technique.

But access to facts is no longer difficult. While the discovery of facts remains difficult, the dissemination and transmission of facts is now so easy that it is becoming difficult to remember what it was like before Google and the capacity to search. One of the core functions of universities as they currently exist, and one of the main reasons that universities exist, is being eroded by the internet.

And this is only one way in which technology is driving change. Looking into the near future, I can see a day when adaptive testing replaces the current system of all students taking the same assessment, sitting the same examination. This will require a change to how we think, being more clear at what we wish students to learn over the course of a module or a programme, being more clear about what outcomes we expect students to be able to demonstrate. And it will require us breaking the shackles of doing the same to everyone at the same time, and for the same amount of time.

When I started lecturing, some years ago now, I lectured as I had been lectured to. I would stand in the front of the room, talking to the students sitting in the room, giving them my take on the material of the day. And I’m now doubting the effectiveness of this method and I’m trying to break free of this very traditional way of lecturing. After all, if we truly believe that we learn by doing, then we need to build more learning into the doing and I can see this happening.

My role is not to talk to students but rather it’s to work with them. And this is where the title of this rumination comes from. For most of their history, universities have been houses of facts. But universities are changing to become houses of questions, both in terms of the research conducted by their academic staff, but more importantly in terms of reminding students that we don’t have all the answers. Rather, we know how to ask some interesting questions, and it is this skill, of asking the good question, that I want my students to take away with them. We start Monday.

taming the hydra

•17 September 2017 • Leave a Comment

I suspect that what I’m about to write is a thing well known to others, and a thing that other writers have experienced.  Perhaps it’s a thing that’s an inescapable and necessary product of the act of writing.  But it is one of the things on my mind today and so I thought I’d scree a bit.

I’m at the moment taking a short break, or engaging in a bit of a procrastinatory frenzy, from the current story project depending on your point of view, as I’m having difficulty keeping to the straight and narrow of the path I’ve planned for this story.  Because I have a clear plan.  I know how I want this story to be unfold, beginning and middle and end.

In fact, I have many many many ideas for how I can see this story unfolding, beginning and middle and end.  There are two main characters, and either one can be the main character.  There is the main moment of action, which can take place here or there, where here and there are very different places.  There is the degree of bat shit craziness in which I’m willing to engage, from the very mild to the garden sheds in the rather extreme outlying suburbs of my imagination.  And each of these leads to a different story.

Like the hydra in full flow, each time I sit to write, I find that one of these other heads seems to be the more attractive story than the story, the head, I’ve sat myself down to write.  And so I find myself to be the victim of temptation.

Each writer has their demons to defeat.  For some, it’s the fear of writing something unworthy or stupid, and some have described this relationship with their fear, and the bargaining they regularly have to undertake with their fear, in heartfelt and compelling detail.

And I’m beginning to realize that perhaps my demon is this hydra of distraction.   This hydra affects not only my writing, as once I see it for what it is, I can see this hydra of distraction at work in my mathematical life.  And I can see that for my mathematical hydra of distraction, I have found some strategies for fighting my hydra with some success.

And so now, I need to develop strategies for battling my writing hydra.  I need to kindle the torches that I will use to cauterize the stumps when I cut off its heads.  It will take some time, and I am sure that I will never defeat my hydra, but I am confident that I will find a way of keeping it in some sort of check.  And so now, back into battle.

the atemi of committees and policies

•10 September 2017 • 1 Comment

This one is going to be a bit of a strange one. One of the early lessons I learned around the I moved to England and started working at Southampton came from the then Secretary and Registrar of the University. He came to the Department to give a session on the University committee structures, and during that session, he said something that’s stuck with me ever since.

Paraphrasing, his point was that by the time a proposal or a policy, anything needing a decision, reached one of the main University committees, it should essentially be decided. It was an interesting lesson he presented, and it’s entirely possible that my memory of that session is not perfect. But it was an interesting lesson that shaped how I started my path of learning to be a member of committees and learning how to be the chair of a committee.

To be honest, I’ve come to disagree with that sentiment, as I think there can be real value in deep discussion at the committee stage. Yes, there are times when extensive consultation takes place and it falls to the committee to distill that consultation and produce a proposal for consideration further up the chain. But there are also times when the final decision falls to the committee. There is a matryoshka effect here, with committees within committees within committees, each playing their own part. Each feeding into the others.

But I want to talk about a different aspect of committee life, one that is inspired by the aikido that I do. There is a particular aspect of aikido that I’ve been paying attention to for a while, namely atemi. In a very direct way, atemi is a strike, possibly a punch, that the person doing the technique executes on the person of the person on whom the technique will shortly be done, not with the intention of wounding but rather with the intention of distracting, for lack of a better term.

It’s a bit difficult to picture, but very very loosely indeed, if for instance someone swings a sword at me in an overhead strike, attempting to do to my head what a knife might do to an apple, then I will step to the side and give them an atemi to their ribs. This has the effect of disrupting their follow up strike and provides me with the time and space to remove the sword from their possession and gently but firmly persuading them of the error in their ways for swinging their sword in the first place.

And so atemi is distraction. But more than this. My favourite description of atemi, a wider translation of the term but one whose origin I’ve forgotten over time, is the taking of another’s mind. So the purpose of my atemi is essentially to so disrupt my opponent’s mind that I have taken their attention away from them.

And this is a useful thing to be able to do in a committee setting, whether it be a deliberative committee or a deciding committee, to give them names. Sometimes it is a very useful thing to do, to distract, to steal away from them the attention of the members of a committee. The most straightforward way of doing this is to put something on the agenda that the chair knows will attract the attention of the members, something controversial, but to have the properly contentious item elsewhere on the agenda. The members may then exhaust themselves on the planted agenda item and not have the energy to discuss the properly contentious item.

I do find it a bit strange that I’m writing about this, potentially giving away one of the secrets to how I approach things, but then I realised that I’m actually not giving away anything. No one knows what I view as the properly contentious items and as the other items. For those on the same committees as me, particularly on those I chair, they might well need to pay attention to all of the agenda items, given that they won’t know which is which.

But now, we take a left turn into the wilderness that is zen. One of the basic lessons of zen, as I understand it at present, is that it is the experience of the moment that demands and deserves our full attention. This is a common interpretation of zen in the martial arts, where each encounter with an opponent has to be experienced fully and has to be taken for what it is, which is a moment that will never come again. And a moment around which we will not get a second chance. This is the zen of the tea ceremony, in which each cup of tea is poured only the once.

One of the things I like about zen is its universality. The same zen that underlies how we experience martial arts and how we experience the tea ceremony, this zen underlies everything. And in particular, it underlies how we experience moments in committees. Zen underlies how we experience those occasionally interesting and awkward moments in committees.

Perhaps I’m overstating the case, but I do think that this is all connected. I do think that all of these different parts of my life impact on and inform one another, and reflecting on my experience of each makes me better at the others. I’ll admit that how sitting in committees improves my aikido is still one I’m working one, but I’m sure I’ll find something there if only I dig deep enough.

exterminants and the lost arts of mathematics

•3 September 2017 • 1 Comment

There are several -ants in mathematics.  Determinants are the classical -ant of mathematics, easiest to define and understand for small matrices but with a wide degree of usefulness and a remarkably wide range of definition.  Resultants are another, again very useful and again with a wider range of definition than initially apparent.  And perhaps, there are other more obscure -ants.

How mathematicians name concepts and objects is an interesting discussion in its own right and a topic we leave for another day.  But one thing I don’t know, because it’s not something we tend to talk about at conferences or over coffee, is whether other mathematicians find a term they like, write it down and save it, and then look for an appropriate concept or object for that particular term.

The term I’ve been saving for a long time is the exterminant.   The terminology of mathematics can sometimes seem to be violent, with its annihilators and Killing vector fields, though admittedly the later is named for Wilhelm Killing rather than for any violence that the vector field itself might perpetrate.

I was tempted, I’ll admit, when I first had the idea of exterminants, to write about the discovery of a lost manuscript, or the rediscovery of a lost mathematical method, due to an obscure mathematician, perhaps Georg Eigen.  And perhaps some day, I will because it’s an idea that I’ll admit haunts me.

And this haunting is part of something much larger that I’m still working my way through, which is my personal vision of how to blend mathematics and fiction.  What are the stories that I want to tell and how do I want to tell them.  There are others who have done this very successfully, including but not limited to Rudy Rucker, Greg Egan, and Larry Niven, and others such as Robert Heinlein with their occasional mathematical stories, all authors I’ve enjoyed reading for as long as I’ve enjoyed reading.

And perhaps one day I’ll define something for which the term exterminant is an appropriate term.


mathematical ideas in every day life: squaring the circle

•14 August 2017 • Leave a Comment

I suspect, given where my thoughts currently are, that the following is going to be a bit rambling and somewhat labyrinthine. And even this, for a reason I’ll get to at the end, is not entirely correct, but I like the word, labyrinthine, and I’m feeling a bit indulgent today.

I was in a meeting a couple of weeks ago, and one of the other people in the meeting used the phrase, it’s like squaring a circle, to describe something difficult. I think the look on my face gave away my internal view, since everyone turned to look at me and started laughing in a friendly way at my evident discomfort. I decided that this was a situation in which discretion was truly the better part of valour, and I just let it slide.

I think that ‘squaring the circle’ and ‘we need to square the circle on this one’ have become commonly used phrases for something difficult, but this is not what these phrases should mean. And my apologies, gentle readers, but now I need to go into a bit of mathematics.

One of the classical geometry problems from antiquity, so from the ancient Greeks of roughly 2500 years ago, was the problem of squaring the circle. A reasonably constructed sentence, that of course tells you the reader no more than you knew about a question you didn’t know was in fact a question, except that it’s a old question. The Wikedia article is good, but I’ll summarise the essential bits. And this touches on what I started to do, and never finished, in the numerology of unrelated constants 1 and the numerology of unrelated constants 2, the completion of which has now gone back on the LIST OF THINGS TO DO.

So.  Take a circle in the plane, which has a radius R and which encloses an area of size A. The size of this area is given by the formula A = π R² and this is a formula that we have known since early days in school.

A question that you may wish to ponder is, why is this formula for area true?  It may be that you’ve never pondered this.  Of course, your teachers and the textbooks used state that this is the correct formula, but it isn’t until much later in our mathematical education that we develop the techniques that allow us to construct an argument to explain where such formulas come from.

Back to the question at hand.  The question of squaring the circle is this.  Given a circle C, of any radius R, construct a square S which encloses an area of the same size as the area enclosed by C, using only a compass (which allows for the construction of a circle of any center and any radius) and a straight edge (which allows for the drawing of lines of any length).  We can reframe this a bit.  We know that if S is a square whose sides of length s, then the area is enclosed by S is s².

And so, given the circle C of radius R enclosing an area of size A = π R², find a square S which also encloses an area of size s² = π R², again using only compass and straight edge.  And so things boil down to is, how to construct the square root of πusing only compass and straight edge.

And this is impossible to do, as we learned in the late 1800s.  The reasons are complicated, but the point that I would like to make is that this is actually impossible.  It’s not that it’s difficult.  It’s not that it might be possible but we don’t yet have an argument.  Rather, it cannot be done, and this impossibility is not something that sits well with most people.

Mathematicians I think are used to this notion of impossibility, and in fact I suspect that each of us, when we’re working on a question we’re finding difficult, always have the faint worry in the back of our minds that perhaps we’ve hit upon one of these impossible questions.  Almost always, it’s just that the question is hard or we haven’t yet seen the path to a solution.

As it turns out, there is a way of squaring the circle, if we allow remove the restriction of compass and straight edge.  But this other way involves doing violence to the circle in a way that is exceptionally hard to imagine.  Perhaps another day.