a connection between unrelated things

•2 December 2018 • Leave a Comment

So here’s a weird thing. I’ve always enjoyed watching professional wresting, though I don’t view that in itself as a weird thing. It’s popular for a reason, and part of that reason is that the basic storylines are the sorts of stories we like to watch.

I’ve been thinking a lot about story and our oldest stories. This is sparked by articles like the recent Atlas Obscura article, which are very much the sort of article that appeals to me and sparks my curiosity.

But the connection I made was not between professional wresting and the stories we tell from the stars. Rather, the connection was between professional wresting and the Commedia dell’Arte. Both after all are performances that are based around types, though I’ll admit it’s been some time since I’ve done any serious reading about the Commedia.

And this then starts to spark off other thoughts. To what extent are we bound by the types of characters in the stories we tell each other, and to what extent are our stories bound by these types.

Because this would shape all sorts of things. We are story telling creatures. We have always told each other stories. We have told each other stories to explain the world around us. We have told each other stories to chase away the beasts that prowl around in the night.

We have told each other stories to structure and pass along facts about the world expensively gained over time.

And what are the stories we are telling each other now. I recognize that I have drifted a bit off topic, but I’ve decided to follow the thought. We have started focusing our attention, not on the stories about the world as it is, but rather the stories we are comfortable with.

Perhaps one of the functions of story telling is to pass along the uncomfortable truths about the world. That, as we as mathematicians have learned to our benefit and interest over time, the world does not always bend to our will, however much we wish that it would.

And so this has sparked a project for the year to come. Let’s read the old stories. The oldest stories. And let’s start to explore the connections between these old stories and see where that takes us.

from an observation to some wild speculation

•25 November 2018 • Leave a Comment

Earlier this week, Tuesday I think, I noticed something that I’d noticed many times before, but this time it sparked a question it hadn’t sparked before.

Winter is working its way towards us and so the sky was clear and the moon hung almost perfectly full, with only a slight fuzziness on its left hand side.  I’d noticed this fuzziness before but I realized I didn’t know whether the moon was waxing towards full in the next night or two, or whether the moon had just been full and was now waning.

I realized then the extent to which I’d lost the night sky.  I can remember being on camping trips as a kid, either family trips or as part of the local Boy Scout troop, looking up at the sky.  But for the past couple of decades I’ve lived in or near cities, and so it’s only the light of the moon, the planets and the brightest stars that survives the trip.

And that’s when I started to speculate.  And one thing I know is that others have speculated along these lines, and so one task for the new year is to go and see what they’ve written about all of this.

Go back far enough and the night sky was the television and the internet of the age, and perhaps a bit more.  Everyone had access to the night sky, and one question is whether we’ll be able to unpick how much of our mythology is tied up in our observations of the night sky, the movement of the planets, the precession of the equinox.

Just how observant were our distant ancestors and what mechanisms did they have for preserving their observations, before we had the written word?

And this is part of the difficulty.  Oral histories disappear with the people who are no longer around to tell their stories, and I don’t know what work’s been done, or can be done, to try and catch the echoes of these old stories in the stories we currently tell each other.

What I think is an even more interesting subject of speculation is, what were the stories our cousins, the Neanderthals and the Denisovians and all the others, were telling each other around their fires.  How did they see the night sky.  What for instance did they think of the planets, moving through the stars night after night, as though engaged in some grand quest?

And the big question, to which the answer is almost certainly no.  Are there any echoes of these cousin stories in our own myths and stories?  And how would we know?

 

teaching with Rumsfeld’s taxonomy of knowledge

•18 November 2018 • Leave a Comment

I like that thing I have come to refer to as the Donald Rumsfeld taxonomy of knowledge: the decomposition of human knowledge into the four categories of the known knowns, the known unknowns, the unknown knowns, and the unknown unknowns.  (See https://en.wikipedia.org/wiki/There_are_known_knowns for Rumsfeld’s original quote and some discussion.)

Perhaps I’m overstating things by using the term taxonomy. I’m not a philosopher of knowledge, and I don’t want to focus on how Rumsfeld’s quote fits into current discussions of what knowledge is, how we know things, et cetera.  Rather, I want to talk about using Rumsfeld’s taxonomy as a tool in teaching.

In our aikido classes recently, we’ve been exploring aspects of internal movement, specifically aspects of how we use our deep musculature to move ourselves and to move others.  What I find interesting in this exploration is the amount of time I’m currently spending dwelling in the unknown unknown area of Rumsfeld’s taxonomy.

Because for me, this is an exploration of unknown unknowns. One interesting aspect of this, which I’ve started exploring elsewhere, is the nature of the language we use and the language we have to use.

I find these explorations difficult. I am having to find a way of making contact with parts of this deep musculature, the muscles around my spine for instance, that I hadn’t ever thought about before. I don’t yet have a good language for understanding what I’m trying to do and developing that language takes time and practice.

This is a point that those who know me, know that I think about a lot, because I do think this issue of distance between teacher and student is critical, as is the effect that growing mastery has on the language we use.

There is the question of how we move things from the quadrant of unknown unknowns to elsewhere in the taxonomy, and I think that a significant part of this move has to be the development of language that allows us to gain some traction on these items we don’t understand.

After all, a large part of a thing being in the quadrant of unknown unknowns is that we don’t recognize the existence of that thing, because once we have awareness, we can interrogate and ask, is this thing an unknown thing or a known thing.

This same general question is a big influence on my teaching of mathematics. I need to become the guide for my students, guiding them from the dark cave of the unknown unknowns.

Here, similarly to aikido, the unknown unknowns aren’t always, and aren’t often, issues of fact. Often, they are issues of processing of facts. How for instance can we take a question apart, explore its pieces and solve the pieces, and from these create a solution to the original question.

A journey, a quest is then to become the better guide, for myself and for those I’m teaching. And this is a journey I expect never to complete, however much I might improve along the way.

beware, there be spoilers: Deadeye Dick

•10 November 2018 • Leave a Comment

It’s an interesting experience, to read all of the books of a single author in a somewhat limited period of time (and yes, yes, I know I’m behind in my reading; I’m doing what I can to catch up).  With Vonnegut it’s doubly interesting, because of how he works characters from one book into another, or several others as he is wont to do.

Deadeye Dick is a very pleasant read, set in a place we’ve visited before.  Not my favorite, I’ll have to admit, but then it has none of the science fiction weirdness that I’ve come to enjoy.  There’s no Kilgore Trout, for instance, and no random extraterrestrial visitation.

But he does something here that resonates a bit, given the current politics of some countries in the West.  The city of Midland City, Ohio is destroyed by a neutron bomb, and while the explosion is described as an accident involving a truck-borne bomb, presumably being moved from one place to another, the whole story of the bomb is not explored in any detail at all.

I do like the unnamed mathematician who claims to have constructed a proof that the bomb detonated some sixty feet in the air, thereby proving that it couldn’t have been a truck-borne bomb, thus invoking conspiracy theories.  The unsolved assassination of President Kennedy is also mentioned (in those terms), and this attempt to foster the belief in conspiracy is one of the things I find a bit frustrating.

This whole conspiracy theory aspect is only briefly explored towards the end of the book.  Vonnegut does bring it in earlier, in the sense that the destruction of Midland City is mentioned but no one, particularly not our narrator, seems to be particularly concerned by the fact of destruction by the bomb.  Admittedly, the narrator doesn’t have a strong connected to the city, but I think I would have liked the conspiracy theory to have been more evenly infused throughout the book.

It reminds me of a small incident during Gordon Ramsey week of the current, now nearly completed tenth series of Masterchef Australia, my favorite of the Masterchefs.  He says to one of the contestants, season (that is, salt) your food through the whole of the cook, a little at a time, rather than trying to fix the seasoning at the end.

And this is then a lesson for me to bring into my own writing.  Scatter the weirdness a bit more evenly throughout, rather than concentrating it at the end, where the reader might not be willing to accept the big dollop of weirdness all at the end.

the futility and non-futility of resistance

•4 November 2018 • 1 Comment

We had a very engaging aikido class this morning and I would like to work through an observation that I had during the class. To be fair, it’s an observation I’ve had many times before and it’s something I’m sure I’ll be working through this particular observation for some time yet to come.

Beyond that, I’ve been thinking about how my developing understanding of this observation can apply more broadly, for instance to administration within universities; I’ll come to this at the end. (So please keep reading, he asks politely.)

When we are uke, the person receiving an aikido technique (which is the polite way of saying, the person being thrown or put to the ground), one of the questions we often have is, what is the extent to which we would resist. This is a question that beginners often ask.

A basic and interesting fact is that if I know what technique the tori (the person performing the technique) is doing, then I can often find a way of blocking or countering that attempt at that technique.

But this blocking almost entirely relies on my knowing and on tori performing that particular technique. If I do commit myself to so blocking what technique the tori is doing, then I open myself to being susceptible in many many other ways. An advanced student of aikido can take advantage of that susceptibility (and they have, on more than one occasion, and no doubt will again) but a beginner doesn’t have the experience or the technical skill todo take advantage.

So when a beginner is practicing a technique, I know from experience that my resistance as tori is counterproductive to their practice. And one of the things that I wish to cultivate in the beginners I work with is to remove this resistance from their practice.

This is difficult, because resistance in such a physical situation goes against our natural reactions, and so part of what we’re doing in our aikido practice is in essence retraining our instincts, so that we accept without engaging our own willingness to resist.

So my advice to beginners in the aikido classes is, don’t resist. Take the opportunity to learn the shape of the technique through accepting what your tori is giving you.

But for more experienced practitioners, this resistance can be important to understanding. If I am giving my uke the opportunity to resist, then I’m not doing the technique properly.

So there are two things I have to do. One is to reflect on how I’m undertaking the technique and to understand on what I need to change. But the other, and this is where things sometimes get very interesting, is to adapt to and work with that resistance, attempting to neutralize it.

So how does this apply to university administration? There is a growing body of writings about how to apply aikido principles to non-aikido situations. I suppose this can be viewed as my minor contribution to this literature.

A common situation in university administration is the attempt to change hearts and minds. One way of doing this is to reflect the changes to policy and process, and to work with colleagues to implement this new policy and process, about which we as individual members of staff have no significant agency.

But beyond this, I have come to believe that there are deep and fundamental assumptions that universities need to shift. I recognize that this is a controversial view to hold, as some of my colleagues have let me know.

The nature of universities is changing, particularly in the UK where I work. Some of the old embedded assumptions are slowly eroding away and are being replaced by different, more explicit and externally forced assumptions. The assumptions are important, but not for the point of this particular discussion.

Changing the assumptions that people hold is something which engenders resistance. After all, how many academics does it take to change a light bulb? And so the question I find myself facing is, how to work with this resistance. How to neutralize this resistance. How to perform the administrative kaeshiwaza that then presents itself. And that bundle of how is what I’m currently working my way through.

some management phrases that I use fairly often

•27 October 2018 • Leave a Comment

I’ve been in what might be best described as middle university management for a few years now, and reflecting on the conversations I have in passing with colleagues, there are some phrases that I use often.

I’m not sure where I picked them up or from whom I took them, but I like them because I find them remarkably helpful in describing how I find some of my days.

One of these, and a particular favorite of mine, is too many plates, not enough sticks. We sometimes find ourselves in situations in which we find ourselves dealing with many different things, the plates, and they split our conversation into too many pieces. The sticks are our ability to focus, the limit to the number of things on which we can focus.

And there are times when the number of things going on is greater than the number of pieces into which we can split our ability to focus. These are then difficult and complicated times, and all we can do is to make our way through them as best we can.

Our only hope is that the plates don’t break when they find themselves dropped.

An old phrase that I find myself using from time to time is that we cannot let the perfect be the enemy of the good. One of the things that lives within me that I am often fighting, and consciously so, is that I have a great respect for the perfect.

But I have learned to accept over the course of time that as admirable as the perfect is, perfection is hard and perfection is costly, and there are times when perfection is not what is required.

There are some tasks, and I do hate to admit this, that do not deserve our best efforts. These can be transient tasks, things that have to be done to advance a task or process to its next stage, but our best is not always what is required.

Not my circus, not my monkeys is a phrase that I haven’t yet used conversationally, but I am keeping it in the arsenal of comments that I might want some day to use, should the occasion arise.

This goes back to something that someone once told me about how they deal with requests to undertake tasks. (And my apologies, it was a long time ago and I don’t remember who described to me this particular visualization.).

They said that they envisaged each current task as a chimpanzee loose in their office. And each additional task was an additional task let loose, to climb and scream and run riot, and their ability and willingness to take on an additional task then became their ability and willingness to have yet another chimpanzee running riot in their office.

And as we move forward through time, we’ll accumulate additional phrases and we’ll share the interesting ones here.

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.