an echo of moments

•14 November 2021 • Leave a Comment

I write down a lot of fragments and phrases but I’m very bad about making note of their context. I often don’t remember what I was doing when the fragment came to mind, when the phrase rang in my head, and so that connection of the fragment to its source is then lost in the mists of time and memory.

In one sense, I’m sad that I don’t have that context; that the phrase has lost its connection to its moment of generation. But on the other hand, the lack of connection creates a window of freedom; the fragment isn’t bound by that context, that connection, and it is then free to develop in a completely different direction.

And that holds for the title of this blog. I found it on the page of blog notes in the soon-to-be-completed volume of my daily journal, waiting patiently for me to stumble across it and give its time.

And there is a recursiveness here. These fragment and phrases that I note down, they echo. There was something in them, which caused me to note them down in the first place, and regardless of their origin story, they then continue to echo.

Six syllables is precisely the wrong number of syllables, between five and seven, to be used in a haiku. Perhaps I’ll see whether I can tinker with the phrase, modify it, bend it to fit cleanly in a haiku, or perhaps I’ll leave it as it is. Perhaps its destiny is not haiku.

But moments do echo. As I go through my days, I can still hear echoes from years ago in some cases, individual moments that should be inconsequential but nonetheless still ring, the peal of distant bells across the years.

spending time with an old friend

•7 November 2021 • Leave a Comment

I find myself spending time with an old friend today, a friend named procrastination. Over the years, I’ve written about time spend with this old friend, here and here if you’re interested. What I find interesting about today’s visit is that they mentioned something I hadn’t realized before.

I often feel bad about procrastinating; I think of it as spending time not doing something needs to be done. But as they mentioned, dropping a line into a conversation about something else, sometimes what we think of as procrastination is actually just the making of a judgement of the order of importance of things.

We all have many things we want to do, and at any particular moment in time, we can do only one of them. This is one of the lessons I’ve worked my way through, which is that there is no such thing as proper multitasking. There is serial focus on individual tasks, with quick switching between the tasks, but I’ve come to realize that at least for me, I can do one thing at a time.

At this moment, writing these words, I feel as through I’m sitting at a table full of projects old and new; each of them is making their case for my time and attention of the moment, and all I can do is to listen to their points made, some more persuasive than others, and act accordingly.

We could push this analogy a bit further. We have all had the experience of that conversation being interrupted by someone coming into the room, letting me know that there is a call. Sometimes, I can say that I’ll call back but sometimes, I have to take the call, however interesting the conversation.

And so we settle into the evening, the conversation continuing and the various projects continuing to make their cases. I enjoy their company, even knowing that as I bring each to its natural end it will leave our table. But so is the way of the world.

the richness of old lists

•31 October 2021 • Leave a Comment

I am a maker and keeper of lists. I have lists of mathematical projects, writing ideas, blog ideas, tasks that need to be done soon, tasks to be completed at some indeterminate point in the near to medium term future. Lists, lists, lists.

Some lists I write on random scraps of paper, items to be crossed off when completed or transcribed into more permanent lists. Some lists I keep in my daily journal, pages in which are full of items crossed out and occasionally circled, for particular attention. My list of writing ideas I keep on my computer, scraps and fragments, to be printed out and explored from time to time.

I have a drawer in my desk of blank journal volumes, each waiting patiently for its turn to come. I went through that drawer recently, finding one journal that I’d inexplicably put back in the drawer only half completed, and other volumes with nascent lists on their first few pages.

One reason I like finding an old list is that it provides a window in a moment of a before time. A reminder of things that had been occupying my attention, of things catching my eye. Very occasionally, of something that remains to be completed.

The writing list is a collection of beads, some bright and shiny, some dull because I don’t remember the thought that gave rise to the idea, to be strung onto the string of a plot or a character, to give rise to a story.

The mathematical list is as much as anything the list of things to understand, distant acquaintances that intrigued me when we first met, with whom I’d like to spend significantly more time. And I’ll get to spend some time with them soon, come the new year.

One reason that lists are on my mind, despite the several different themes that are inhabiting my recent posts here, is that I’m coming to the end of my current journal volume and I’m looking forward to the new volume, and the items that will be part of its initial list.

a reflection on teaching 3

•24 October 2021 • Leave a Comment

A couple of weeks ago, I wrote about the idea of contact and connection with students in teaching, and I know with this idea that I am standing on the edge of a deep lake, wet up to the ankles, and I will keep coming back here to drink. This is particularly true now that we are again practicing full contact aikido, that other laboratory of contact.

But this contemplation of contact leads naturally to contemplation of other aspects of teaching. Two of these are design and delivery: how I structure my interactions with students, face to face and on-line, scheduled and spontaneous, and how I take this developing map of (in this case) graph theory and get it out of my mind and into my students’ minds.

Because to a great extent, this is what I’m working to do. One aspect of this, which I’m sure I’ve mentioned before at some point, is the basic fact of distance. As I teach a subject year after year (graph theory, calculus, aikido), my understanding continues to develop. I see deeper into the subject, and my distance from those just beginning their journey increases.

And so part of what I have to work through, in terms of design and delivery, is how to manage and mitigate this increasing distance in understanding. The issue I find with design is that I want to show my students the nifty things I’ve found, but I have to be careful in doing this.

What I like about graph theory is that there are some (relatively) easy to state questions relevant to the material we’re covering, where I can give my students their statements and then point to (sometimes very) recent papers and preprints where mathematicians are still working through those questions.

But there is a deeper question kicking around here. The past year and a half has changed how we think about delivery. The lessons we’ve learned will change what we’re doing, how we design and how we deliver, and the landscape here is constantly shifting as we digest these lessons.

What will this landscape look like in 10 years? 15 years? I can make guesses, but they can be only guesses, as my Magic 8-Ball doesn’t provide sufficiently nuanced answers to my questions. And I’m very curious to journey through this landscape.

lenses and the shape of the world

•17 October 2021 • Leave a Comment

Earlier this year, I wrote about lenses and how they affect our observational windows. This relates as well to the Rashamon moment, that I touched on briefly some long time ago. I’m thinking about lenses again, and there is one train of thought I’d like to chase for a bit, that starts in a weird place.

I thought about this a long time ago; you can find them here and here, and I’ve come back to that old speculation, but from a different viewpoint. Through, perhaps, a different lens.

Supervillains are rife in the literature. They populate Bond movies, Dr No and Blofeld from the Bond movies, and others, independents and those who’ve worked for SPECTRE. More recently, there is Thanos from the Marvel Cinematic Universe and perhaps even Lex Luther and the Joker from the DC Universe. And there are many many more beyond these few.

There is something to work through here, namely what is the fractal nature of the boundary between mere villain and supervillain. but that’s a practical application of a mathematical idea to be explored another day.

Often, though not always, supervillains wish to take control, to be in charge of the world or the universe, and I find myself wondering, why? Being in charge is complicated. There are difficult decisions to be made, often in situations where there is no clear right decision. There is paperwork. There are unhappy but ambitious minions.

I will say, Thanos had a clear goal. He had a plan. While I very much disagree with both his basic goal (there were so many other things he could have done once he had the Infinity Stones and even before), I have to take him out of this discussion because there is a clear argument for why it doesn’t apply to him.

This question for supervillains then leaks into my thinking about, well, everything else. What is the shape of the world we are working towards, and I know that if I were to ask a dozen people, I would get at least a dozen answers.

And so, over the next few weeks, I would like to explore a particular lens through which to view this question of the shape of the world of the future, and how we might view purpose as the guiding spirit on our journey to this world of the future.

This choice of lens is inspired in part by the world of Star Trek and the dream of the Federation. The lens I choose is Maslow’s hierarchy of needs, and I’ll come back to this next week.

a reflection on teaching 2

•10 October 2021 • 1 Comment

And the week went very well. The students were keen and engaged, they were (essentially all) undertaking our institutionally expected precautions, and we are all working our way back into a Before Times rhythm of classroom interaction. I’m sure that the nervousness will persist for some weeks, until we can all see how things will settle down.

Aikido has also been going well; my reactions are less rusty than I’d feared they would be under the pressure of an actual grab, but yes there is still some rust and it will take time and practice, but positivity reigns at the moment.

I’m starting now to work through old things, ideas that have been circulating around in my brain for some long time now. One of these, which I may have touched on in some post in the past, is the notion of contact.

In aikido, contact is critical to the success of anything. This may be physical contact, uke with a firm grasp of my wrist, or mental contact, where I as tori, the person doing the technique, manifest my attention in both my movement and my uke’s movement. This ability to be able to invade my uke’s intention and influence my uke’s intention is what I have been working towards and continue to work towards.

The same notion of contact applies to teaching. I can walk into a room and start talking, but if I don’t have the attention of the audience, if I’m not influencing the intention of my audience, then all I’m doing is contributing to noise to the room.

This gets back to some of the points I touched on last week. I was nervous about my ability to make this contact with my students, but that nervousness seems to be misplaced, as we have made contact. People coming up with questions after a lecture, a session, is a key indicator for me, because if someone has been paying enough attention to be curious about something or confused by something, then at least they’re been paying some attention.

So I will continue to think through ways of making contact with my students, my mathematics students and my aikido students. Part of this will be thinking through my presentation of the material, both in the classroom and through the virtual channels such as the module Blackboard site. And part of it will be moments of structured spontaneity.

a reflection on teaching 1

•3 October 2021 • 1 Comment

Tomorrow, I am back in the classroom for the first time in almost two years, and as much as I’m looking forward to it, I’ll admit that I’m a bit nervous. Yes, I did teach last year, with some live on-line sessions as well as some significant recorded material. But it wasn’t the same.

I miss the performative aspect of teaching; I miss working with my students, my audience. I miss gauging how well they’re following the current argument. I miss backtracking and tangents and doing what I can to provide an entertaining and informative overview of the subject. I miss working with the students as they engage with the material and work through the details of the assessment.

I wrote about one aspect of this getting back to teaching recently, when I wrote about the physical space. I walked through the rooms I’ve been assigned last week, stood at the front of the room looking out over the seats. I’ve taught in both of my rooms before, and so they’re comfortable spaces for me, as comfortable as any room can be in our current circumstances.

But it’s much more than this. I am an inveterate list maker, and I’ve spent some time (as I do from time to time) going through old lists, finding ideas that I’d written and forgotten and thinking, how might this work in the classroom.

Beyond some now-standard things, perhaps having a single question on-line quiz at the beginning or middle of each teaching session, picking up on some point I think an important point to stress, making use of the reflection on the changes we’ve all thought through after the past year.

But there are other things, that I’d written down and then forgotten. Watching old documentaries about stand up comedy, there’s a lesson for teaching from improvisational comedy: never say no. No matter how strange or ridiculous the thing being thrown at you, by the audience or by one’s partner, respond instead with a ‘Yes, and…’ Build on it, perhaps turn it around.

And this turning becomes then a form of instructional jiu-jitsu. Taking the energy of the comment or the question, and changing its path into a path that allows for illumination and learning. And this I think is the core of my nervousness.

In person aikido has only recently started, and I can feel the rust in my bones and my reactions. And I worry that this same rust might affect my ability to handle the stadium, the arena of the lecture theatre. I’ve been teaching the same module for a number of years now, and I’ll admit that my scripting of each session has become more skeletal over time.

But for this year, I will go back to a full scripting, reminding myself of what might be some pressure points, some particular topics that have in the past generated interesting and tricky mathematical questions. We’ll have fun and in the end it will all be fine.

the power of place

•26 September 2021 • 3 Comments

After a long time, we have restarted in-person aikido classes, with all appropriate mitigation measures in place due to current circumstance, and it’s great after so long to be able to practice more-or-less properly. But walking back into the dojo for the first time in more than a year and a half (we had been using other rooms), I was reminded of the power of that a place can have.

We bow when we enter the room, we take off our shoes before getting on the tatami, and this short ritual carries an enormous amount of internal weight. I feel the liminal shift, leaving my day job behind for some little while, and the ritual is part of how I focus my attention on aikido and to let other things slip away.

This same liminal shift happens elsewhere as well. The annual Milford Science Fiction Writers Convention ended a week ago. We gather, we critique each others’ pieces, and walking into the critique room (always the same room), taking off my outdoor shoes and putting on my slippers, I get the same feeling as I get entering the dojo.

And the critique room is a dojo of sorts; we have a task of focus, we all throw ourselves into that task. As in the dojo, we are there to be the whetstones to allow each other to sharpen our craft.

Universities are reopening and I start teaching in a week’s time, and the classroom has the same feel as the dojo and the critique room. The students and I are all there for the same purpose – to explore (in this case) graph theory – and we have that same focus.

It may be that I have a slightly different view of the classroom than my students, and if so, then that different view comes from these other spaces, each dedicated to the study of a particular craft.

There are many spaces that don’t have that same feeling associated to them; the lounge and the kitchen are rooms that serve many different though functions. My office at the university also serves different functions: it is not a space purely for research, and it is not a space purely for teaching and education, and it is not space for administrivia and email, but rather is a space for all of these.

I find this sensitivity to space and the functions of space interesting; as is often the case, I’m sure there’s more to dig out of this idea, and that’s something that I’ve now added to the (near infinite) list of things deserving some time for contemplation.

education and training

•5 September 2021 • 5 Comments

There’s an idea that’s been kicking around in my brain for a little while now, and so I thought I should start exploring it. As with many things, I’m sure that exploration will come in stages. So, consider this the first step in a thousand mile journey.

The genesis moment for this was the question, what is the purpose of education. We live in a complicated and fast changing world, and knowledge and the application of knowledge are what are going to get us through. This is a common trope in science fiction, the scientist as savior. It should be noted that this is also the starting point for many a classic disaster movie, but that’s a topic for another day.

But there’s a recurring discussion regarding the difference between education and training. Underlying this discussion is a common view that one of the core functions of our educational system, particularly pre-university but also impacting on undergraduate level at university, is to prepare students for the world of work, developing transferable and key skills.

And so I thought it might be interesting to try to slide a thin sheet of paper between training on the one hand and education on the other. When I think of training, I think – perhaps a bit unfairly – of preparation for a known task. This might run from something straightforward like touch typing through to leadership training.

But the basic structure is that there is a body of knowledge or information, and the task is to transfer that knowledge from the trainer to the student. We could at a small stretch include such things as some first year university modules, like calculus, because much of an introductory calculus class is to make sure that students have a basic understanding of how to address relatively standard questions.

Education on the other hand we can take to be preparation to answer questions for which we don’t yet have the answers, and this is where the key distinction lies. In training, there is no surprise at the end point; with education, there should be some surprises at the end.

Following on from the comment above, an undergraduate degree can then be viewed as a transition from training to education; from modules that cover standard material, necessary vocabulary and the foundation on which the education will be built, through for instance project work and dissertations that allow students to take a question and properly explore it, not necessarily knowing where that exploration will lead.

Perhaps this is an artificial distinction, and it needs to be set against the wide body of research in education, but it’s an idea I’ve found useful in my own thinking. There is much reading for me to do, I’m sure, and much more thinking. The second step and the third, and the rest of the journey.

aspects of balance

•19 August 2021 • 1 Comment

I’ve been thinking recently about different aspects of balance. One aspect is the basic physical aspect, so not falling over while standing or walking, and being able to maintain our sense of physical perspective while being thrown or throwing someone else, which is critical for proper aikido.

It’s been a year and a half since we’ve been able to engage in standard aikido practice; we’ve been practicing, via Zoom or doing solo weapons practice together in a large, well ventilated room. While that practice has been helpful and interesting, and has given me the opportunity to focus on the weapons work in a way I hadn’t done before, I do miss what had been our standard practice.

Our aikido club is currently on its usual August break and we don’t have a summer school this year. But come September and October, we’ll begin the process of working back to standard practice, and it will be fascinating to throw someone else, and to be thrown by someone else.

One thing that I do remember is that physical balance is a fragile thing. I feel this going down the stairs first thing every morning, on my way to the first coffee of the day. But I also remember is that it is much easier for us to take our own balance (or give it away) than to take someone else’s.

This is a lesson that I’ve tried to export out to other parts of my daily activities, namely that maintaining balance can be tricky, and this is certainly true in our current circumstance.

Some days are like having a head full of bees, and balance can be tricky on these days; it’s easy to focus on one bee at a time, try to follow and catch one bee at a time, and the bees act of their own accord and don’t make themselves easy to follow or easy to catch.

I don’t know how to tame the bees; I don’t whether the bees can even be tamed, and so our maintenance of balance amidst the bees can’t rely on taming them. This can at times be tricky, but it is something that improves with practice.

The core lesson from all of this, I think, is that maintenance of balance is a relentlessly dynamic process. There are occasional moments when our balance persists without constant attention, without the small tweaks that corrects for the constant bumping by the bees, but these moments are few and far between, and always far shorter than we hope they might be.

bits and pieces of time – with highlighted minor spoilers

•31 July 2021 • Leave a Comment

I’ve been thinking recently about time and it’s passing, and I know some of the reasons. We’ve come to the end of our academic year, and like with the calendar year, the end of the academic year is a time for reflection of what’s in the past and what lies in the future.

Recent birthdays, mine and others, provoke a similar speculation, and one interesting aspect of this is the number of different annual cycles that we have in our lives: one birthday to the next, a calendar year and an academic year, one anniversary to the next; so perhaps there some thinking to be done on the intersectionality of cycles.

I’ve also recently watched Loki, and here lie some minor spoilers. Loki is a time travel story, with its branching timelines, and I realized something while watching. A lot of our representations of timelines, in Loki and in Avengers: Infinity War as well, we have a very discrete view of how timelines branch.

What I mean here by a discrete view of branching is that the points at which the branching happens don’t pile on top of one another and there are only finitely many different timelines at each branch. While I can understand, from a narrative point of view, that this discrete branching of timelines makes for a more straightforward story, but the universe doesn’t have any need to adhere to what we find narratively convenient.

I’ve done a small bit of reading about the many worlds interpretation of the multiverse, where (loosely) each action at each moment creates a branching across all possibilities, and there are many many possibilities. Here, the different timelines are different forward evolutions of the universe, sitting alongside one another, somehow.

But I’ve become fascinated by this branching, because it brings together two mathematical ideas that I’ve spent some time thinking about. One is that there are many – infinitely many in fact – sizes of infinity, with the necessary recursive issues that come into this contemplation. The other is the notion of a real tree; this is nothing to do with forests, but is a mathematical concept that extrapolates and abstracts a normal backyard tree.

But digging into those two ideas is for another time. The more interesting question is, how to bring those two ideas into the narrative structure of a story, in a way that carries some mathematical fidelity but doesn’t put off the reader and doesn’t wash out the plot and characters from the story itself.

And this is part of a larger challenge. There are some great stories that have a mathematical idea at their core, and creating such a story is something that I’ve always been interesting in working through.

And this cycles back to the start of this post, the cycles of time. I was hit recently by the image of our remaining days as a jar of coins; different coins might have different values, as different days carry their own impact and their own value, and we don’t know how many coins are remaining. And so let’s spend today well.

experiences of note and further reflection

•17 July 2021 • Leave a Comment

I’ve had an interesting experience recently, one that continues to ring like a bell that’s been struck. I’m confident that over the coming weeks and months, I’ll continue to listen to and interrogate that ring. But part of what this experience caused me to do is to investigate the foundation of my beliefs.

It’s easy to get caught up in the busyness of daily life, of the demands of work and and the personal projects (about which I’ve written enough over the course of days and previous posts), and not to take the time to think about the source of things. And I like to think about the source of things; perhaps this goes back to how I approach my mathematical life, returning to first principles where I can.

So one of those foundation stones comes from a reflection on Buddhism by Stephen Batchelor, where he takes a secular approach to Buddha’s teaching and frames the Buddhist principles as calls to action. The first is a call to understand, namely to understand that a cause, perhaps the cause, of anguish is the disjuncture between the world as it is and the world as we might want it to be.

So consider the world. I watch news on television and I read news, from multiple sources, and themes arise from that consideration. One aspect of this consideration carries echoes of Star Trek.

The Vulcans were at one point in their history were like us, subject to their emotions. Perhaps ruled by their emotions. That brought them to the precipice of disaster, and it was a turn to logic that saved them. So considering the world, I wonder whether we are approaching a similar point in our history. If we take a step back and examine ourselves calmly, perhaps the time has come for us to honestly explore how we think, how our brains work, and then start down the path of working through how we can best train ourselves.

And this leads to an idea. Assume, as I’m willing to do, that we make contact with one or more extraterrestrial species and they are similar enough to us that we can establish meaningful communication. Would we allow them to study human psychology? Would we allow them to understand humans as well as marketing executives and advertisers understand humans? Because I think the answer would have to be no; we wouldn’t be able to take that chance.

Or perhaps, we might think, what could possibly go wrong.

beware, there be spoilers: Le Mort d’Arthur volume 2 by Thomas Malory

•30 June 2021 • Leave a Comment

So, let’s get this out of the way here at the beginning: King Arthur does indeed die at the end. But I’m not sure that actually counts as a potential spoiler.

What I hadn’t expected, though, is that Sir Gawaine would be the bad guy, the unforgiving wedge between Arthur and Lancelot, the final nail in the coffin for the whole saga.

Another thing I hadn’t expected was how relatively small a part the quest for the Sangreal, the Holy Grail, plays. It happens in volume 2, but it is an inconclusive quest, though it does contain the end of Galahad. And though I didn’t take notes, I seem to remember it was Galahad who pulled the sword from the stone, but this wasn’t the act that created the King.

There are small things that happen in passing, that saddened me with their lack of future appearance. Glatisant, the questing beast tracked by Sir Palomides, and we never get to know Glatisant. Perhaps this is just the version of Le Mort that I chose.

But one of the deepest lasting impressions that this left on me, weirdly, is the economics of knighthood. Being a knight is expensive: there is the retinue, the weaponry (and all of the very many jousting lances), the armour, the horse, the castle back home.

We come across battles involving thousands, tens of thousands of knights, and one hundred thousand die in the climactic battle between Arthur and Mordred that ends the saga. The sheer cost of knights and knighthood (and yes, I am taking into account the possibility of hyperbolic inflation on the part of the author) must have seemed a doomsday device of sorts, this giant machine that consumes everything it encounters so that it can perpetuate itself.

It’s tempting to speculate on the current incarnations of this doomsday device of knighthood, but that’s something perhaps for another time. I’m beginning to wonder, though, whether part of the reason we, the collective we, sometimes find ourselves caught in these cycles of consumption for no clear purpose, is that the collective we has no clear purpose. But that’s not a rabbit hole for today.

But I will need to speed up my reading; I did make my through the Tales of 1001 Arabian nights a couple of years ago, and it’s now taken me half a year for Malory. And this is only the first 2 on this list of 100. To work!

labyrinths and minotaurs

•27 June 2021 • Leave a Comment

Looking back, a recurring theme in these pages (and other places) is labyrinths and the minotaurs that inhabit them. I’m not sure exactly why, but I have always found it a captivating image. A piece of homework not yet done is to go back and reread (in translation) the original tale of Theseus and the Minotaur, since it’s been a while and I’m sure there are details that I’ve missed.

A labyrinth (according to the Merriam-Webster on-line dictionary) is a place constructed or full of intricate passageways and blind alleys. In the original, Theseus laid out a thread as he searched the original labyrinth for the Minotaur, so that he would be able to find his way back.

But intricate passageways and blind alleys are a reasonable characterization of many of the aspects of the lives we lead. A research question is a labyrinth, and one we don’t know how to navigate. What seem to be exits turn out to be the blind alleys of an argument we can’t successfully articulate or perhaps even the beautiful idea slain by the facts of the world.

I’m currently exploring a question that arose only recently, while I was thinking about something significantly different, and while I’m enjoying my time in this particular labyrinth, I can’t help but wonder what the minotaur in this labyrinth will be. Will it be that, as might happen, the question is much easier than I expect it to be, more of a hallway than a labyrinth proper, or will it be that the question is much harder than I expect it to be, from what I’ve done so far, requiring everything I know and perhaps a bit more. I don’t know yet, as I haven’t yet faced that labyrinth’s minotaur.

And it is the minotaur that I find more interesting than the labyrinth itself. The minotaur is the beast trapped in the labyrinth, not able to leave, attacking those who dare enter. This is why I need to go back and read the original. What agency was granted to the Minotaur, for instance, and to what extent did they inhabit the labyrinth by choice.

Though this may well drift very far from the original myth, to what extent is the minotaur the soul of the labyrinth? If we view the labyrinth as the question we’re trying to answer, or the situation we’re trying to work our way through, be it large (climate change) or small (my math question from above), then perhaps the minotaur is that which keeps us focused on the question or situation, and provides some incentive for us to keep moving, to keep developing our understanding, to keep working towards a solution.

I suspect I have drifted too far from the original, but then again, perhaps the time has come to revisit the labyrinth and the minotaur, and how in particular I use that image. Perhaps some labyrinths will have the one minotaur, angry and wielding its ax to terrible effect. Perhaps some labyrinths will be inhabited by groups of smaller minotaurs, each of which we can handle on its own but potentially overwhelming when they swarm.

And there are the other aspects of the myth that I haven’t considered here. What of Theseus and his role, and what of the golden thread. And what of Daedalus, he who constructed the labyrinth as well as the wings for young Icarus. There is perhaps even some historical context and with so much to explore, I’m sure this is a topic I’ll come back to, and more than once.

on lenses

•13 June 2021 • 1 Comment

Since the age of eight, I’ve worn glasses. At the beginning, I was only required to wear them to see the teacher from my preferred seat at the back of the room, but my memory is that I wore them all of my waking hours, except when I was reading, and that habit has persisted all the years since. And so, I have always been used to the fact that the lenses I wear have a significant impact on how I see the world.

Recently, I started reflecting on the other lenses through which I examine the world. Mathematics is one of those lenses; I have an appreciation for the power of clarity in definitions and description, as well as the structure of argument and abstraction. One aspect of this lens is the unexpected joy of discovering sometimes unexpected commonalities in seemingly unrelated situations.

I have always found this mathematical lens to be a useful lens through which to view some aspects of administration and governance. In discussions around policy development, to take one example, having clarity in definitions can be invaluable, to minimize the potential ambiguities that can arise in interpretation, particularly once the history and context around the policy have been lost in the mists of time.

Aikido is another lens, and one that’s come up a number of times through these (virtual) pages. One critical aspect of aikido is contact, and applying the mathematical lens to this, establishing what we actually mean by contact is important here.

Taken somewhat broadly, contact can be interpreted to mean engagement or focus. When applying an aikido technique on uke (the person on whom the technique is applied), there is nothing gained from the movement unless as tori (the person applying the technique), we are moving uke in some essential way.

And this notion of contact is useful elsewhere. In teaching, establishing and maintaining contact with the students is core to teaching. In administrative work, it is important to maintain contact with the core of arguments and not be distracted by the sound and fury of the surrounding discussions.

Somewhat recursively, this notion of lenses is itself a helpful lens through which to reflect on the world. And that’s something for further ponderation.

a lesson from the kitchen arena

•6 June 2021 • Leave a Comment

For reasons I’ll admit I can’t completely track, I have a soft spot in my heart for gladiatorial cooking shows. Hell’s Kitchen, in all its subtle polite glory. Top Chef, with the spectacular weird extravagance of some of its competitions. Cutthroat Kitchen and Iron Chef Gauntlet and the sometime surreal febrile imagination of Alton Brown. And there are many others. I have never had the desire to be a chef, and each of these shows reinforces that non-desire.

I have enormous respect for chefs, in the same way that I have enormous respect for all people who dedicate themselves entirely to their craft. And I also have respect for the chefs who put themselves forward to participate in such shows, particularly when the shows get into their latter series and none of the participants can claim to be unaware of the gauntlets that each of the shows offers.

Food is a necessity and so it’s a bit strange that food has become such a big part of our entertainment landscape. Alton Brown, during his Hot Ones interview, made the point that food is comfort. When times are complicated and difficult, as they have been for some time, people turn to food.

Interestingly, I can see that the applicability of this argument to the calmer, gentler cooking shows, with their recipes and conversation. But these more gladiatorial shows, they are more entertainment than comfort. And entertaining they are.

But they also offer their lessons. For instance, the structure of Hell’s Kitchen is such that it prioritises communication within a team, and it is only towards the end of each season that the participants engage in properly individual challenges. Far beyond the horizons of the kitchen, communication is clearly critical, and my mind turns in strange directions. How possible might it be to take some of the Hell’s Kitchen challenges and adapt them as training exercises in academia.

Top Chef on the other hand, with its quick fire challenges, encourages creativity in pressured situations. One way of viewing this is that we need to be comfortable in understanding what we know, so that we can take that understanding and adapt it in somewhat unusual situations.

Cutthroat Kitchen for me is the most difficult to adapt to a collegial working environment.

Looking back, one of the themes that runs through a lot of these blogs is a continual investigation of the ways in which we can take lessons from one part of our lives and apply it to others. And even the gladiatorial cooking shows offer us something, if we approach them with a beginner’s mind and an open heart.

the glorious interconnectedness of all things 4

•31 May 2021 • Leave a Comment

For a little while now, I’ve been gathering together threads from past contemplations, some explored through these posts, to see what cloth I can weave. This is the fourth in a series; I include here links to the first, the second and the third, for any who might be interested, pulling together observations from one area of my experience and exploring how it advances my understanding of another.

This particular thread involves a connection between aikido and administration. As the English lockdown eases, we have restarted in-person aikido classes; we are still distanced from one another, but we are able to meet in the same room. One big difference that we’ve noticed is that now, as opposed to a class via Zoom, is that we can each other from head to toe.

This sparked a thought. One of the aspects of aikido that I have always enjoyed is that feedback is immediate. Our ability to successfully perform a technique is evidenced by how our uke, the person receiving the technique, moves. Likewise, our inability to unsuccessfully perform a technique is evidence by how our uke doesn’t move. There is the third pillar of the overly compliant uke, where the uke moves because they know they’re supposed to move, but not because they’re compelled to move by tori, the person performing the technique.

There are other aspects of this feedback process as well. If for instance I allow myself, through my movement as tori, to become unbalanced, then I provide my uke with an opportunity to take control of the movement. Thus, I move from being tori to being uke, and I find myself laughing up from the tatami.

The thought that caught me is, to what extent is this same dynamic in play in other parts of my experience. As a teacher, this can happen if I do not prepare myself sufficiently well, for a lecture or a problem class, and I find myself facing a student who has. They ask a question, I fumble the answer, and they continue to press.

In aikido, we have an exercise. Uke will press their hand against tori’s shoulder. Tori needs to move with that pressure, not losing their own balance and in the process, taking over uke’s balance. It’s been more than a year, and I am very much looking forward to being able to do this again.

But this also has a distinct administrative parallel. Sometimes, when circumstances change quickly, decisions need to be made quickly. Events exert their pressure upon us, and we need to react calmly, without losing our balance, in order to have some productive impact on the situation.

An applicable lesson from aikido is that practice helps. Another applicable lesson from aikido is that the test needs to be genuine. In aikido, this is the uke giving tori some of their weight, so that tori has something to work with.

But in an administrative context, it can be difficult to provide genuine practice. Case studies can help, but they often come with incomplete information and they come to us out of context. Here, we come to a lacuna. I’ve never interrogated the training or management literature, to explore how deep this particular pool actually is. And so, another project is born.

And interestingly, we seem to be drifting into the realm of challenge based learning and how the framework around challenge based learning can be adapted to some of these aspects of training. But this is a topic for another day.

a reflection during eurovision 2021

•22 May 2021 • 1 Comment

Here on a Saturday evening in May, when the weather in southern England is more reminiscent of winter than late spring, I’m watching the finals of the 2021 Eurovision song contest. And as often happens, my thoughts get lost in the labyrinth of my imagination.

How long have we been singing? Not tonight, because that an easy question to answer, but overall, how long have we and our hominid cousins been singing? It may well be an impossible question to answer, since singing is ephemeral. A note, a song is sung; it goes out into the world and fades into the distance. Unless we have an artefact of the song, we don’t know the song has been sung.

I suspect that sheet music with lyrics would have to be considered evidence of singing – otherwise, why write it all down – but writing is a very recent invention. We have musical notation going back a few thousand years, but from the (admittedly limited) reading I’ve done, the few thousand years of musical notation is roughly the same as the few thousand years of writing.

Musical instruments, so perhaps bone flutes, indicate music but I’m not sure that the existence of musical instruments is sufficient to conclude the existence of singing.

Graham Norton is good, but I miss Terry Wogan. And Wilma the cat isn’t particularly interested.

Singing is clearly embedded deep as part of being human. Music permeates our lives and singing permeates our lives. And for me, there is a stark difference between a song and a spoken poem. Both are powerful, but for me, there is something about a song that can catch me in a way that a spoken poem doesn’t, though this might be that I’ve just heard more songs than poems over time.

I think I read something, not too long ago though I don’t remember the specifics, that work has been done that demonstrates that our Neanderthal cousins were capable of speech and perhaps also capable of song, though we will almost certainly never know if they did sing around their fires.

This touches on one of those points that periodically recurs, namely that for most of our history, we haven’t been able to capture stories or songs. We could tell them and sing them, remember them, pass them to the next generation, but there was always the possibility of their loss, in a way that I think we have difficult comprehending.

And if we were able to travel back in the past, this might be the question I would want to answer. I wouldn’t want to see dinosaurs. I would want to hear the first stories and songs being shared around fires.

productive procrastination

•14 May 2021 • 1 Comment

Procrastination is a topic I’ve written about before and think about a fair bit, though often when I should perhaps be doing something else. I think the title is an oxymoron, but I hope by the end of the next few hundred words, I’ll have persuaded you that it’s not as much of an oxymoron as it might seem now. And if you’re interested, some earlier reflections on aspects of procrastination can be found here and here, and here and here, and here and here.

I am a list maker. I make lists of the things that need to be done, and rarely a list of lists, and from time to time I review and refine my lists, and then have a clean new list containing the contents of previous lists. But I’ve come to realize that while having lists is fine, lists are a remarkably fertile environment in which procrastination can grow. A long list, with many things to do, allows for the possibility of necessary reprioritizing.

But reprioritizing allows for the possibility that some things will keep slipping down the list. I’ve recently gone through one of those exercises of reviewing and refining my lists, and I was struck by how many things are still on my list. They have, in a strange sense, become familiar friends. Part of the issue, entertainingly explored in a TED talk by Tim Urban, is that some of these tasks don’t have explicit deadlines. To paraphrase Mr Urban, the Panic Monster never has its excuse to get out of bed.

In the spirit of perspicacity, I have to admit that I am inconsistent in how rigorously I’m able to apply internal deadlines. And the more times I push something into the welcoming arms of tomorrow, the more ethereal weight that task acquires. Push forward enough times, and the weight of the task can start to become problematic; the task becomes harder to pick up, because of the weight and also sometimes perhaps because the task is itself unwieldy.

What’s interesting is that these ideas all have a familiar feel to them. Many are old friends, but this realization of grappling with this issue of prioritization is the newly made friend at the table. In retrospect, this is an obvious realization, perhaps one that I should have had some long time ago, but I cannot change my past. I can acknowledge it, I can learn from it, and that learning will now be at the top of the list.

But where does productive come from. Part of this issue of reprioritizing is that I can move things to the top of the list, and get them done, with the concomitant feeling of accomplishment, even with the heavy and awkward tasks remaining on the list, wanting attention. The challenge is to keep in mind the medium to long term, and to complete those tasks without explicit deadlines in good time, and not allowing the shiny of the easily doable tasks to overly distract.

yet another phrase about management

•8 May 2021 • Leave a Comment

Looking back over the past years of this (public) notebook, I’ve written a fair bit about issues around management, which reflects my current role in the university. If you’re interested, some of these past posts can be found here and here, here and here, here and here, here and here. Another thing I’ve discussed along these lines is transparent head syndrome, and at the risk of piling things a bit too high, I’d like to add one more.

In the Hitchhikers Guide to the Galaxy series, Zaphod Beeblebrox at one point finds himself in the Total Perspective Vortex, which provides him with an accurate representation of his place in the universe as a whole. Fortunately for Zaphod, he happens at that time to be in a small pocket universe that was created for him, and so he has a very different experience than anyone else who’s been through the Vortex.

Interesting and not surprisingly, there has been some formal research into aspects of the Total Perspective Vortex, but what I’d like to include here are some personal reflections.

Like transparent head syndrome, I’ve always found the Total Perspective Vortex to be a helpful image to keep in mind, and for similar reasons. Going through days filled with meetings, it is sometimes easy to forget the larger picture, or to have the wider picture obscured by the small and large details filling the days.

And actually, it’s both parts of the story of the Vortex. It’s both the need to understand the perspective of where we stand in the scheme of things, which is the Vortex, but also that there are times when the Vortex can be misleading. Sometimes, after all, we are involved in something important. Rarely is it so stark as it is for Zaphod, but I do think that the breadth of the view in the Vortex can be misleading.

Perspective requires work, to acquire initially and also to maintain. Each of us has the issues that are important to us, and those issues will differ across the piece. So what’s critically and immediately important to one person may be less important to someone else. Remembering the importance that an issue has for others is part of the overall context that we always need to keep in mind.

Someone once told me that not every job deserves our best. I’d resisted this for a long time, not wanting to seen to be giving something less than my best, but I’ve learned that part of perspective is knowing what effort different tasks require. And it is true. For instance, producing an initial draft, the first part of a longer process of consultation and drafting, consulting again and re-drafting, requires care but doesn’t need to produce as polished a version as results at the end.

And I’ve come to realize just how important maintaining perspective is, particularly when the world is complicated. And right now, the world is complicated.

stories of Zen: a cup of tea

•3 May 2021 • Leave a Comment

Number 1 of the 101 Zen stories that form the first part of Zen Flesh, Zen Bones, compiled by Paul Reps, can only be described as a classic among classics. Among other appearances, for instance, I remember this story as being part of the opening scenes of the movie 2012.

Nan-in, a Zen master, was (in this version) visited by a university professor, who wanted to talk about Zen. Nan-in served tea, continuing to pour tea into the cup even after the cup is full. The professor could no longer restrain himself, commenting that the cup was full and no more tea would fit. Nan-in said, ‘Like this cup, you are full of your own opinions and speculations. How can I show you Zen unless you first empty your cup?’

I had forgotten until recently rereading that Nan-in’s visitor was a university professor, and being a university professor myself, I recognize that this full-mindedness is something of an occupational hazard.

But this isn’t the core of this particular story. Rather, the core is the question, how do we learn new things? We spend our lives learning, formally and informally, through structured schooling and independent work, and as we learn (naively) we construct a model of the world. That model then can become the lens through which we see the world.

Beginner’s mind is a phrase that that captures this idea, at least for me. What does it take to retain at least some of the perspective of a beginner, a novice, as we increase our own understanding. How can we bridge the inevitable distance that grows between us as beginner and us as experienced practitioner or as expert.

I’m finding this particularly difficult at present, on one of the projects I’m working on. It’s the paper I wrote about recently, which I’ve been working on for too long, and it’s becoming difficult to maintain the perspective that I feel would be most helpful to work through some of the remaining areas for attention.

Unfortunately, or inevitably, I think that the lesson buried in the story is that the only way to get around this issue of full mindedness is to practice, to actively remain aware of the issue and actively keep space in our minds so that we can take a different perspective.

beware, there be spoilers: Le Mort d’Arthur volume 1 by Thomas Malory

•22 April 2021 • 1 Comment

We are getting rather deep into 2021 and I am still working through the first book of the 2021 reading project. I’ll admit that Malory is (a bit) longer than I’d thought, but it’s an interesting journey so far (and there is still volume 2 ahead of me).

We have encountered some of the main characters of the Arthurian mythos. This includes the many knights of the Round Table, though I’ll admit that I hadn’t realized (or remembered) that Sir Tristram was such a major character; but then, one of the reasons for this reading is to back, read and fill in those gaps in my knowledge. We have encountered, though only very briefly, the Questing Beast, and Merlin has been imprisoned in his cave.

There is a lot of jousting. Every time two knights meet, it seems that there is an obligatory joust, followed by a sword fight on foot, since of course the knight who remains on their horse after the joust must then meet his dehorsed opponent on foot, in the spirit of knightly fairness.

There is so far remarkably little magic. Arthur has Excalibur, but another aspect of Excalibur that I think is less known, is that whoever holds the scabbard of Excalibur does not bleed. Given the jousting and sword fighting, this is a remarkably handy property for a scabbard to have.

One of the things that struck me early, and continued to strike me (like a jousting spear into my carried shield) throughout volume 1 is the economic madness of a society which seems to exist only to support knight who seem only to wish to joust and fight, fight and joust, and occasionally rescue the fair damsel imprisoned by the evil knight.

I know that this isn’t the point of Le Mort. We see here the exploration of knights and perhaps the creation of the culture of chivalry. But for me, this reflects a sensibility that is so embedded in modern fiction, including much science fiction, that has become part of what I enjoy in my reading.

I like the worlds of stories to make sense in themselves, and I like the stories to make sense in their worlds. With Le Mort, it makes sense in its world, but its world doesn’t make sense, however much we might like a joust.

So I’ll keep reading. I’m curious to see whether this relatively early (I haven’t done the research to know if this for instance is whether the Arthurian mythos begins) telling of Arthur contains in volume 2 the quest for the Holy Grail, which has become the canonical Arthurian story.

And in the back of my mind, I’m wondering; am I misremembering or did Monty Python neglect poor Sir Tristram?

the glorious interconnectedness of all things 2

•18 April 2021 • 4 Comments

I am currently working on both a mathematical paper (and to be fair, I’ve been working on it for longer than I want to admit) and a story (built around the same basic idea of my second published story). Both are still in progress, and I thought it would be interesting to (very occasionally) compare and contrast my thoughts as I go through the process of finishing both.

The math paper keeps growing. The original paper was relatively short and focused on one theorem, which is a question that had been kicking around my head for twenty years. It’s a question that I gave to a PhD student, who decided to focus their attention in a different direction and never focused their attention on this question. And so I have an idea, and I went back to it, and I was able to push the idea through.

There is still some work to be done in the details of the proof of that theorem, but I’m confident that I’ll be able to make them work. One of the interesting things about a math theorem, a math paper, at least for me, is that until I actually work through all of the details, in their full detail, there is always the ghost of a nagging doubt that I’ve missed something that will come back and haunt me.

There is an aspect of this ghost in crafting a story, in that there are the continuity errors. If I want something to happen later in the story, the early part of the story can’t then set up something that precludes that which needs to come later. In the math paper, though, the ghost can be something we can’t get around. If only I can do this thing that unfortunately isn’t true, is something that I suspect most mathematicians have said to themselves, and the art and craft then comes in finding the true steps to the true end result.

For me, and for these two projects, the interesting thing is that I can see the ending to the math paper much more clearly than I can see the ending to the story. For the math paper, I know all of the results that I want to be part of the final work, whether I can push them through and make them part of this paper or whether they will require more thought and be part of a future paper. I have a very clear picture in my head of what I believe should be true.

For the story, I have no idea how it ends. Reflecting on the stories I’ve half-written but haven’t yet brought to a final version, I have a problem with the endings. And I can see what I’m doing. I have an idea, I craft a story around that idea, and I lose my energy and end up with something that I don’t find satisfying at the end.

I read a lot of short stories, science fiction and fantasy and neither, and there are some spectacular stories out there. I don’t like to think about how some of those authors would handle my ideas, because they’re (for the time being at least) my ideas, and I want to see what I can do with them. (And it can also be remarkably intimidating.) The same thought also lurks in the back of my mind with the math paper, but both have the common feature that once we send those ideas out into the world, others will be able to read them and start doing their jazz with the ideas.

With both, there is the temptation to keep going. I’ve accepted that fiction needs editing, and editing, and a bit more editing, constantly refining, and removing everything that doesn’t advance the story. With the math paper, there is more of a temptation to include all of the associated and related results, not being as concerned about removing everything that doesn’t advance the story of the paper, and perhaps this is something to reconsider.

I can see that I’ve always adopted the Columbo protocol with math papers – just one more thing, and so an exercise I’ll add to my list of exercises is to read math papers with the same eye I use when reading and critiquing the stories I read. I’m curious to see what happens.

the glorious interconnectedness of all things 1

•10 April 2021 • 3 Comments

Poker players, to be successful, must not only study the structure of the game itself, but also must become aware of the leaks in their game. A leak for a poker player is a a hole in their game though which they leak chips or money; it’s an area of their game in which they are making suboptimal decisions.

The key here is perspicacity. Poker players need to be aware of their own leaks, as well as the leaks in the games of the folks with whom they’re playing. I’ve given some thought to the leaks I have in my own poker game, and I hope you’ll forgive me if I don’t set them out here. If I were to decide to move from recreational player to a more serious player, I would find a coach, someone who I would ask to watch my game and give me their perspective on my play.

Leaks are a much broader phenomenon than just poker. What are the leaks in my writing practice? What are the leaks in my mathematical work? What are the leaks in my aikido practice? What are the leaks in my administrative work? And it is this wider applicability of these ideas from one area to other areas that reflects this glorious interconnectedness, or at least one aspect of this glorious interconnectedness.

Though not in these terms, I’ve written before about the leaks in my writing practice, particularly the leak of not finishing. I don’t like rewriting and I don’t like editing, and it’s always a more attractive prospect to start a new story than to fix an old story, one that’s almost but not quite completed. And so this is the leak I’m currently working to fix. And I’m aware of other leaks as well, but that’s for another day.

I’m pondering the leaks in my aikido practice, and this is difficult. We haven’t been able to hold a typical aikido session for more than a year, and so it’s been a long time since someone has grabbed me with intent. We’ve been keeping ourselves going with regular zoom classes, of necessity focusing on aspects of solo practice.

And so, not only will any extant leaks that had been in place a year ago still be present, they will be larger, due to the lack of practice, and I’m sure there will be a host of new leaks as well. We will all for instance need to be a bit cautious as we work our way back into regular practice, given our time away and our lack of practice in falling down.

The leaks in my administrative work is a fascinating area of ponderation, and one that I’ll come back to at another time.

But I find pondering this interconnectedness, applying the terminology of one area to another, to be illuminating, and inordinately so at times. As much as anything, I find it useful to have as many ways of interrogating my own practice as possible.

in and out of the line of sight

•21 March 2021 • 3 Comments

I had an interesting experience last week. I’ve been doing a lot of management training courses recently, in part because it’s available but mostly because I’m putting in some work to cement the skills I’ve been acquiring through experience.

During the discussions, I bring up some of the things I’d read about at some point in the past, those that stuck with me. One of the first popular management books I remember reading was the Peter Principle, which is basically that people in an organization are promoted to their level of incompetence. That is, being good opens doors to promotion and then no longer being good closes those doors.

The interesting experience last week was bringing up the Peter Principle and having to explain it, because the others hadn’t heard of it. This led me to start thinking and my thoughts went down several different roads.

The first is wondering whether these references I’m pulling out of my past are outdated or have been superseded. My reading wasn’t from the academic literature but rather was from books written more for the popular audience. I haven’t gone back and checked what research has been done for instance on the validity of the Peter Principle. I’m hesitant to add this to the near-infinite list of projects, but perhaps a conversation with one of my colleagues in the Business School might be in order.

Another road, and one that is common to many academic endeavours, is that the literature continues to grow. Humans are curious, about ourselves and the world around us. We keep exploring and we keep publishing what we have found.

As glorious as this is, the issue for each of us is that it becomes harder and harder to keep up; it becomes harder and harder to keep track of what remains true and what becomes superseded by new research. And with an idea like the Peter Principle, it is easy to see how more research, more data and a closer examination of that data, could lead to that verification. It may be that this has been done, and that’s what I want to find out.

Yet another road is that my examination of the literature is somewhat haphazard. I would like to believe that I’m good at keeping track of what’s going on in my area of mathematics, what questions remain open and what is the direction of work being done.

But my casual reading remains casual; reading what catches my eye and my attention. And I want to keep it that way. And so a piece of work to do, is to think through how I can reasonably keep track of some of these other areas, outside of my own mathematical patch. And there are always things to do.

the glorious interconnectedness of all things 3

•16 March 2021 • 2 Comments

Somehow, I think I managed to delete this and so have reloaded it. Not quite sure what I’ve done, but I’ll try not to do it again.

In the first of this loosely connected series of posts, I wrote about leaks, exploring how a poker concept can be illuminating elsewhere in other aspects of my life. In the second, I explored some similarities between writing a math paper and writing a story. Here, I would like to start digging into connection in a bit more generality.

In my Book of Many Lists, I have written down the phrase administrative connection. This phrase came into my head uninvited during a recent meeting (one of many), when I was hit by the nagging feeling that however interesting was our conversation (and it was interesting), I couldn’t see the path between our conversation and the implementation of the change we were talking about.

This struck me as a different aspect of this general idea of connection that I’d written about some long time ago, namely about how the idea of connection we use in aikido, and specifically working within the grasp, is so much more widely applicable. In aikido, we have an advantage, as often being grasped is a tangible, physical thing, whereas in other contexts, the grasp is much more of an ephemeral concept. But nonetheless, there are still the constraints that we have to recognize and within which we must work, in the administrative setting as well as in the dojo.

In my aikido thinking and practice, there is a clear path (or rather, many clear paths) between the initiation of the movement, even before the grasp itself, and the end of the movement, with uke thrown or pinned. But in the administrative sphere, I find it easy sometimes to be captivated by the end goal, and not to spend enough time thinking through, working through the details of getting from beginning to end.

There is a different aspect of administrative connection as well, and one that goes back to yet a different thing I’ve written about before. This is the notion of distance. When teaching, be it math or aikido, I have worked hard to build into my teaching practice this observation that as I teach and practice, my understanding deepens, whereas my students always start as beginners, and so the distance between me as teacher and the beginner can only increase over time, and requires work to bridge.

The relationship of this to connection is that the greater the distance, the greater the difficulty in creating and cultivating and maintaining the connection. To overcome this inevitable and unavoidable difficulty requires care and attention, and practice.

In ways I’ve (unaccountably) only started thinking about, the same applies to the administrative sphere. Practice and exposure increase distance, and increasing distance makes connection more difficult, and so creates the expectation and the need for those with the practice and experience to actively work to bridge this distance and to constantly cultivate this connection.

At the risk of making a bit of a right turn into the weeds, this brings to mind an analogy of the administrative and governance of any organization. Governance is like unto an iceberg, where only a small piece of the processes of governance are generally visible. This is both inevitable and necessary, I think, because proper governance is complicated and multifaceted; it’s both formal and informal, and it takes time and energy to keep track of everything going on.

I haven’t yet through just how appropriate this analogy actually is, but I think it has some life to it. Of course, part of having an analogy is an aid to understanding, and this one clearly needs some refinement, but perhaps that’s for another day.

There are other aspects to connection and interconnectedness that I’ll keep working my way through; for me, each time I write, I feel I’m climbing a bit higher up the mountain, and the view I get, clouds notwithstanding, is that little broader. If you’ve made it this far, thanks for taking this journey with me.

when it’s easy, I’m not learning

•14 March 2021 • Leave a Comment

As I work through the backblog, I come across phrases or suggestions to future Jim that I wrote sometimes a long time ago. For most of them, I can remember the underlying thought that sparked the backblog entry.

One of those underlying thoughts arises from conversations I’ve had around aikido and my development as an aikidoka. It has admittedly been a year since I’ve been in the dojo, though we have been keeping ourselves going via zoom and (distancing requirements allowing) meetings in the Common. One thing the absence from the dojo has done for me (to me?) is that I’ve been reflecting on my progression as an aikido practitioner.

The first few days back in the dojo, when they come, will be strange but I’m looking forward to them. But one thing I’ll be gauging in those first days back is, where is my aikido. I expect that the first weeks, perhaps months, will be difficult. But I don’t mind the difficulty.

One thing those conversations about aikido showed me, revealed to me, is that learning involves struggle. I don’t mean this in a negative or pessimistic way. Rather, if I’m working through things I do not yet understand, which is a key part of learning, then I can’t expect what I’m doing to be smooth.

So learning involves bumps in the road. I don’t know the path I want to tread; I can take heart from the fact that in aikido, others have walked that path, and so I have the comfort of knowing that the path can be successfully walked.

With mathematics, there are some similarities and some differences. The road can be bumpy; I was going through an old notebook this evening, noting questions I still haven’t yet worked my way through; questions that I’ve solved since; and questions that others have solved since.

But one significant difference is that it isn’t always clear that the question can be resolved, or at least resolved by me. With aikido, I have some confidence that I can learn, to some extent, how to do each of the techniques. But with mathematics, I have to admit that there are questions that may well remain unresolved.

Remembering this basic point, that learning is a bumpy road, is an important point of reflection in my own teaching. The road will be bumpy for my students; they are encountering the material, the techniques, for the first time, and I may have been working through the material for years, or longer. This ties very directly back to a point I’ve made in earlier writings, about the increasing distance between teachers and the beginners they’re teaching.

There are depths to this thought that I’m confident remain to be explored, and I’ll keep digging.

and this will be a bit random

•6 March 2021 • Leave a Comment

We each have the things from which we take comfort, and for each of us, they are different. Some may be structural – how we structure our days, the things we wish to have done, or expect ourselves to have done, between waking and going to sleeping. Some may be specific things to which we turn.

I like gladiatorial cooking shows. Hell’s Kitchen is a favourite, as is Top Chef. There are many others, all of the different variants of Masterchef for instance. I don’t know why these particular shows have such a hold on me, and alas, neither do those who are close to me.

There are other food shows as well. Hot Ones on YouTube, the show with hot questions and even hotter wings, is a neighbourhood whose streets through which I like to perambulate. I have to admit that I have some favourite episodes of Hot Ones – Gordon Ramsey (playing even as I type these words) is one that I like revisiting from time to time.

Most of us I suspect have movies or TV or books that we have to come back to. The Adventures of the Stainless Steel Rat by Harry Harrison, the Usual Suspects, and Airplane and its siblings are amongst mine, though there are others. (I’m about to embark on rereading both Dune and Moby Dick, as it’s been too long.)

My structural pieces include the daily journal, where I dust the cobwebs from the darker corners of my imagination some days and just babble other days, and the daily haiku, which I’ve written about before but which I’ll also admit that I didn’t expect to keep going for as long as it has, though I will admit to enjoying my exploration of the form.

So why this. We are living in extraordinary times, bizarre times, times that none of us expected to live through. And these extraordinary times, I suspect, are causing each of us to consider the things that we support us. The things that we turn to to support us. There may be the people in our lives, and for me this is critical. But we each also need our private space, the things we do just for us, and I also thing this is critical.

And in these times, we need to take care of each other and we need to take care of ourselves, and so I think we each need to embrace, and embrace unapologetically, those things that we each have as part of our personal care package. Because, after all, why not. So I’ll rewatch Police Squad soon, and I’ll reread Dune, yet again, amidst the new things. As should we all.

staring into the abyss of deep time

•28 February 2021 • Leave a Comment

I’ve been thinking about time. Minutes and hours, days and weeks and months, years and decades, these are the time scales that we as humans tend to encounter in the course of our days, and they are the scales on which we’re comfortable measuring time.

On the longer end, even centuries can become problematic for human memory. Currently, we have writing, paper on which to write, stone into which to carve, but we’ve had these for only a few thousand years. Before that, we had the stories we told ourselves around the fires that kept away the dark, and oral histories can drift.

Were I to have a wish that I could spend on myself, rather than one to use to heal the world, I would want to know the first stories we told ourselves around those fires. After all, the human history with fire goes back an exceptionally long time, perhaps hundreds of thousands of years, and perhaps our history with stories does as well. And when I say we, I mean us and our hominid cousins, Neanderthals and Denisovans and whichever told the first stories.

I’ll admit that one reason I’m curious is something that I’ve speculated on before. Namely, can we, and to what extent can we, still detect the echoes of those original stories in our current stories. How persistent have themes of our stories been over the longer time scales.

But we can go back further still. Back the tens of millions of years to the dinosaurs and their extinction, or the billions of years to the beginnings of our solar system. And I will admit that these timescales baffle my imagination. Here, we don’t have stories of the sort we’re used to telling each other, but we are getting better at deciphering the stories that the Earth tells us.

One of the writing projects I’m working on takes place, in its current version, over tens of thousands of years, and I’ll admit that working through the details of the story is part of where this pondering about time comes from. There are great stories that I’ve read that deal with these long time scales, and so let’s see if we can do this idea justice.

the current me and the younger me

•15 February 2021 • Leave a Comment

Perhaps because of the circumstances and difficulties of the past year, I find myself from time to time thinking about the younger me. There are some very immediate reasons. Working with students, I can’t help but be reminded of my own student days, and in particular working through for the first time bits of math then encountered for the first time. There are other reasons as well; as part of the poetic science project, we’ve been asked to explore our own professional foundation myth, and create a poem from it.

I don’t remember starting aikido. Or rather, I remember that I started aikido (more than twenty years) and I have memories, flashes from those early days like snapshots, but I don’t remember the struggle of learning the mechanics of ikkyo for the first time, or kote gaeshi. My struggles these days are very different, working on refinements rather than basic mechanics.

It’s interesting trying to put myself, albeit figuratively, back into the skin of the younger me. Part of this I think is the old phenomenon is distance, the distance between teacher and student that I’ve written about elsewhere in these pages. The teacher continues to develop and deepen their understanding, whereas the new student always arrives fresh, ignorant for lack of a better term, perhaps knowing only the basics, if that. Thus, distance.

Here, though, that distance is between the current me and the younger me. The current me has continued to develop, to deepen my understanding, and this clouds the memory of the younger me. There are some things I’ve just been thinking about for a long time now. One thing that requires work is to find and appreciate the joy we feel at the new, at encountering for the first time. But it’s work that I’m willing to put in, that I like to put in.

The world has also changed. My much younger self didn’t have the Internet, for instance, and the Internet has wreaked some fundamental changes on how we live, how we communicate, how we access the information and knowledge gathered over the centuries by humanity. Different skills are required to navigate this current world.

And so, the old question. There is a trope in science fiction, going back in time and inhabiting our younger skin, reliving our lives, correcting our mistakes and taking different paths. This comes I suppose from our belief, our fear, that our younger selves would be somehow disappointed in our current self. Disappointed perhaps that we haven’t achieved all that we dreamed. Disappointed perhaps that we haven’t lived all of the adventures we planned. And as tempted as I am to hope that my younger self would look at me and be content, I’m also struck by how there’s no way of knowing. The distance is too great, the river of time too fast and too deep, And all we can do is to move forward from where we stand at the moment.

stories of Zen: a parable

•6 February 2021 • Leave a Comment

Number 18 of the 101 Zen stories that form the first part of Zen Flesh, Zen Bones, compiled by Paul Reps, is a parable reputably due to the Buddha himself.

A monk running from a tiger climbs part way down a cliff. Below him, at the base of the cliff, is another tiger, looking up at him with hunger. Two mice start chewing the vine. The monk sees a wild strawberry growing nearby; he plucks it and eats it, savouring its sweetness.

People talk of mindfulness, of living in the moment, and this parable for me is very much a parable about the moment. The monk cannot climb up the cliff, because one tiger; cannot climb down, because of the other tiger; and cannot remain where he is, because of the mice. I’m ignoring for the moment whether tigers and mice would or wouldn’t behave this way, though this does fall into my wheelhouse of overthinking.

So. Watching the news, it’s easy to put names and faces to the tigers that are stalking me and the mice that are chewing my vine. But it’s harder, some days, to clearly identify my wild strawberry (or perhaps strawberries).

Reading is a strawberry; I love immersing myself in a book or a collection of stories, a biography or some popular science, exploring worlds existing and only imagined. But – and here comes the overthinking again – is exploring other worlds a sufficiently mindful activity? I think yes – replacing the tang of the strawberry with the sight of a sunset composed of streaks of red and orange.

Aikido is a strawberry. At present, we are only able to hold classes via Zoom, working on movement but not throwing each other or being thrown. But this regular focus on movement is an important part of my week.

But I also wonder. What are other readings of this parable, beyond this obvious one. I ask this, because I like to look for the non-obvious meanings, though looking for them is far far easier than finding them. Perhaps I need a map. Perhaps I need to learn how to take a left turn into an additional dimension. Or perhaps I’m looking for something that might not be there.

But as things stand, I have some strawberries. I see the green shoots and nascent beads of strawberries just sprouting. And as much as I can, I will try to give the tigers and mice no more attention than they deserve.

craft and the daily haiku

•24 January 2021 • 1 Comment

Roughly a thousand days ago, and I say roughly because I don’t remember the day I first started, I have been tweeting out a haiku every day (albeit with a very few missed days here and there). If you check out the hash tags #dailyhaiku and #haiku you can find these and haiku by other authors as well; there is a remarkably robust and active haiku community on Twitter.

Haiku is a structured short Japanese poetic form; in its English incarnation, it consists of seventeen syllables, in lines of five, seven, five in that order. I don’t remember why I started ; I suspect it was a bit of whimsy. Why I’ve continued is probably due to some combination of momentum and an appreciation of craft.

What do I mean here by craft? Some many years ago, I read The Unknown Craftsman by Yanagi Soetsu. (Unfortunately, I don’t remember the translator of the edition I read.) I have a copy of Yanagi’s book on my shelves of books to read again (shelves which are locked in eternal combat with the shelves of books as yet unread and the shelves of books unwilling to resign themselves to never being read) and I know that I need to re-read it, but one point that I took from my reading is that craft arises from reflective repetition.

By reflective repetition, I mean doing a task over and over again, whether it be pulling together seventeen syllables with some developing understanding or whether it be shaping clay to be fired into mugs or whether it be, drifting somewhat far afield, executing a proper aikido technique among many repetitions.

When I look over the things where I spend my time, I can see aspects of this reflective repetition in many places. Whether it be herding words into a haiku each morning, or the swing of a bokken or jo, I see that this reflective repetition occasionally creates magic. A haiku perhaps that sings as opposed to being a mere collection of syllables, or one particular shiho nage where uke’s eyebrows rise in surprise.

But there is something beyond this, because there are other areas where if I am honest, I can see the dark side of this quest for the few perfect moments among reflective repetition. This I think is something that bedevils my writing. I don’t want to find the one great paragraph, the one great story among all the words I write, and I stand at the edge of the abyss of recognizing that there is no other path.

I am not yet at the point of being able to bring forth perfection from the void in which ideas perambulate like ghosts. And perhaps I will never get there, but I can get to the point of putting down the words, revising the words, and creating something good that spark interest and a (deliberate) laugh from the reader. And that is the lesson to take to heart.

working through the backblog

•27 December 2020 • Leave a Comment

As is tradition at the end of one (Gregorian) year and looking forward into the next, I’ve been considering my accumulated lists, the projects underway but as yet uncompleted and projects waiting to be considered. I’ve written about the various projects, like the annual reading project and indeed projects in general.

Aikido is an ongoing project, and one that’s been difficult over the course of 2020, given the restrictions on physical contact and distance, and the challenge there has been maintaining contact with aikido without being able to maintain much in the way of contact with other aikidoka. We’ve done as well as we could, I think, with massive thanks for the others in the club, and I think it’s reasonable to say that my jo and bokken work is a bit better.

One of the habits I’ve acquired over time, perhaps related to daily journaling, is keeping track of the small ideas that pass through the brain over the course of a day, set off perhaps by something I’ve read or a conversation, or something whispered into my ear by a passing imp. And some of those ideas, which I track on their own page, are those ideas that make up what I sometimes refer to as the backblog.

I had lost track of just how long I’ve been posting these (hopefully) entertaining bits of randomness, or quite how many I’d composed over that time. Looking back over them, and I (almost ironically) can’t remember whether I’ve written about this before, there are themes that recur over time, themes that I started but didn’t then continue. And so one possible project, should I find myself (ha ha) lacking a project, would be to go back and work through both of the back blogs, the blogs not yet written but also the themes begun but not yet completed.

I can also see that I’ve become inconsistent in terms of the timing of the blog, and so looking ahead to the year to come, I don’t want to overpromise. Working through the whole of the back blog would be, I think, an overpromise, given that we don’t yet know for certain what shape 2021 will take, but I can try and be more consistent in my timings, with an aim towards writing on some topic once per week.

So why am I even writing this? In part, I think, to set the stage for the year to come, as part of the process of Gregorian reflection. In part, because I think that setting down my plans for the year has an almost talismanic power to convert words and intentions into actuality. And on that point, we will just need to see what the year to come will bring.

the reading project for 2021 (and perhaps 2022)

•7 December 2020 • 2 Comments

For the past few years, I have set myself a reading project. The first was The Book of a Thousand Nights and a Night, translated by Sir Richard Burton, largely, solely perhaps for the reason that it had been sitting on my shelf for years, asking me to spend some time with it. The second was the complete works, novels and short stories, of Kurt Vonnegut. Both of these I completed, though Vonnegut took a bit longer than a year.

The third, a project that in retrospect was far too vast in its scope, was to read humanity from the beginning. I have spent the past couple of years wandering through ancient Sumer, and I will spend more years there still. Sumer is a fascinating place, and one that’s captured me.

But I will never read all of Sumer, and so the project of reading humanity from the beginning is a project that made sense only because I didn’t understand how many of our early stories have been travelled through time to us, even knowing that the recorded stories are but a small part of the stories that were told, in front of hearths and in public fora.

And so I need a new reading project, one that I can actually complete, if not in one year then in two.

The (moderately) recent Time Magazine list of the best 100 Fantasy Novels recently came to my attention. Two things struck me. One was how few of its books I’d read. The other is how many of its authors I recognized. And so this becomes the project. A century of novels in a single year is a lot, two a week, and that might well be beyond what I can do, particularly given that some of them are properly long. Even giving myself two years, and removing those I’ve already read, will be a stretch, but let’s give it a shot.

One of the things that Vonnegut taught me during our year (and a half) together is that it can be difficult to focus attention on one author, one voice, however entertaining and captivating that voice might be. Two thirds of the way in, there comes the desire for a bit of variety, a voice that’s a bit different. This was less of an issue with Burton and his Nights, a collection of tales brought together by the whim of this old Victorian.

Let the journey begin.

a meditation on Hofstadter’s Law

•6 December 2020 • Leave a Comment

In Godel, Escher, Bach: An Eternal Golden Braid, a book that is on my list of books to reread, Douglas Hofstadter set forth what has since become known as Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law.

There are many reasons that I ponder Hofstadter’s Law, or as I (perhaps inappropriately) prefer to refer to it, Hofstadter’s Principle. One very tangential reason is the context in which I first encountered it, through my reading of Hofstadter’s book. I have always had a soft spot in my heart for the perspective bending art of Escher, and in fact my area of mathematical research is reflected in some of his works such as Angels and Devils. Perhaps there is scope for exploring this internal connection in some future post.

A second and much less indirect reason is the recursive, self referential nature of the Principle. As we work through the details of a situation or a task, we sometimes find ourselves enmeshed in the details contained within the details, the grit that can on occasion create the grinding friction that emerges as we work to refine our approach to the details. I spend a part of each day pondering grit and its consequences, and the truth of the Principle makes itself felt every day.

But perhaps the main reason is the extent to which modifications and variations of the Principle also makes themselves known and felt. It’s harder than you expect, even when you take into account the Principle. It always requires more attention to detail than you expect, even when you take into account the Principle.

In aikido, part of what we are working to do is to retrain the ways our bodies react when we’re attacked, when we’re held. We react by instinct blazingly quickly some times, and so yes, this retraining takes longer than we expect when we first start (or at least longer than I naively expected when I started), even when I began to appreciate the application here of the Principle.

When teaching, we spend a significant chunk of our preparation time cutting paths through the tangle of material that constitute the jungle of a discipline, grown tall and green through the work of scholars over decades or centuries. We then act as guides for the neophyte students encountering the jungle for a first time, and one of several things we need to keep in mind as teachers is that for our students, the Principle applies and we need to give them the time and support to come to their own understanding of the material we are presenting to them.

So for me, Hofstadter’s Principle and its variants form some of the bedrock of how I encounter the world. I work to minimize its impact but I recognize it is always there, watching from the shadows. Waiting, like one of our house panthers, for its moment to strike.

the balance of one thing against another

•29 November 2020 • Leave a Comment

Something occurred to me this week that I’d like to spend some time exploring. It hit me during a short segment on CNN about Encyclopaedia Britannica, of all things. But then it’s interesting to follow these chains of memory sometimes.

I can remember visits to my grandparents’ house when I was young, and leafing through the 1912 edition of the Britannica that lived in a trunk in the attic. I loved the weight of the volumes in my hands and the feel of the pages. And when we were cleaning out the attic some years later, we found the original wooden crate in which it had been shipped, and we could see the extent to which the volumes had expanded over time and would no longer fit in that original container.

But the recent thought was a thought in a different direction. The Britannica is still for me, to a lesser extent than it used to be, a symbol of the totality of human knowledge. I’m sure that even the writers of the Britannica would probably acknowledge that they provided a summary, even in that 1912 edition, but holding those volumes gave me the illusion of being able to develop an understanding.

Developing that understanding has become more difficult over time, and becomes more difficult day by day. The speed at which we as humans are producing knowledge is fearsome. I subscribe to a daily update on the submissions in some areas of mathematics, and even that very limited picture is more than I can absorb, and I’ve chosen the areas I’m interested in.

And this brings me to the core of this thought. Even in very small patches in the overall space of the exploration of things known and not yet known, it is becoming increasing difficult to keep an eye on and understanding of what is known. On the one hand, this is very exciting, because the more hands, the merrier in terms of developing our understanding.

But on the other hand, and I am extrapolating from my personal experience here, we explore these areas because we want to understand, and so there can be a joyous frustration in trying to keep up with everyone else on the same quest.

So that is the balance that sparked this whole scree. The balance I’m thinking of here is the balance of breadth versus depth. We can focus our attention on a very very small patch, thereby denying breadth, and work in increasing the depth of our understanding. Or we can focus our attention on larger patches, with the consequent necessity of mining this patch to a lesser depth, if only because we are finite creatures and we have only a finite amount of time and effort that we can put into this work.

And we can leave this first part of what will undoubtedly be a discussion of several parts, by remembering VGER from Star Trek: The Motion Picture, naively tasked with understanding everything there was to understand, and then not knowing what to do once it had accomplished this mission. Fiction perhaps can bridge this divide between breadth and depth, but it seems to me to be beyond what we can do at present.

on projects

•23 November 2020 • 2 Comments

I have many projects. Over the life of this blog, I’ve explored a number of different aspects of my engagement with my projects. What this number is, I’m not entirely sure, but it’s a reasonably large number. Even for this Project Blog, I have a page in the journal where I collect ideas for possible future blogs.

I’m not precisely sure why tonight has become the night of project contemplation. Perhaps it’s the fire in the corner of the room, orange flames dancing on logs that are slowly disappearing. Perhaps it’s a bit of wishful thinking, looking towards the end of the year which is still some weeks away. Perhaps it’s a manifestation of my old friend and colleague, procrastination.

I’ve not devoted as much time as I would like to my mathematics recently, but in part that’s because the past few weeks have been devoted to teaching, and the teaching has (I think) been going pretty well. But come the new year, there should be more time for the quiet contemplation (that word again) of the warped geometric spaces I explore when I have the time.

A few years ago, almost four I think, I set myself a reading project – to read Sir Richard Burton’s The Book of the Thousand Nights and a Night. It took a year, some Nights every day, and it sparked some interesting ruminations. The next year, I set myself another reading project and I read the complete Vonnegut.

Last year, I set a more ambitious target – read humanity from the beginning. I am still wandering through the streets and wild places of ancient Sumer, and I will be wandering there for some time yet, because there is much to see and much to read. I have learned two lessons from this. One is that ancient Sumer is a fascinating place, worth the time spent there. The other is, do the research before setting a reading project. And so while Sumer persists, I will spend the next month looking around for the 2021 reading project.

I haven’t mentioned writing projects, but there are many. Stories mostly written and (dare I say the words) the novel. This is where Procrastination has made its home.

The past months have not been helpful months for my relationship with my projects. But there is now some light, albeit the tunnel remains. I can see glimpses of space, and I can see the possibility of projects being brought to an end. And so, what can we say but, the work continues.

stories of Zen: the muddy road

•12 November 2020 • Leave a Comment

The past few years, and 2020 in particular, have been extremely hard on my personal practice of Zen. I am very much an amateur, doing some reading and some solo practice, and needless to say, recent events have proven to be very distracting.

One of my personal sourcebooks is Zen Flesh, Zen Bones, a Collection of Zen and pre-Zen Writings, brought together by Paul Reps. One of my favorite stories is 14. Muddy Road. Two monks, Tanzan and Ekido in this version, are travelling after a heavy rain. They come across a swollen stream and a washed out bridge, and a young woman unable to cross. Tanzan, the older of the two, carries the woman across the stream and sets her down, and he and Ekido continue on their way. After some time, Ekido upbraids his older companion; they are monks, and they shouldn’t go near women. Tanzan then says, I’ve already set her down; why are you still carrying her.

I think about this story a lot. My head constantly buzzes with things other than what I am attempting to focus on at the moment, but more than that, I find it difficult to set things down and walk away from them.

The world at the moment is a swirling maelstrom of complications and distractions, of events far beyond my control to influence. Amidst all of the complications, it is hard sometimes to see clearly, what are the things to set on the side of the road and what are the things worth carrying. What are the things that need to be carried.

A small, non-political aspect of this is something I’ve written about before, namely the List of Things To Do. Like most others, I have my list of projects, some with deadlines and some without. I have set some (few) projects down on the side of the road and walked away, but I have difficulty even here not pausing and looking behind me, wondering what if I were to go back and give them one more chance.

I recognize that this is drifting away from the core of the story, and there are analogies that I am tempted to stretch and push beyond their capacity to maintain their internal cohesion. But I do sometimes think of Ekido as the angel on one shoulder, telling me what I should do, and then I think of the angel on the other shoulder, whispering that those things left on the side of the road still deserve my attention, and it is a difficult voice to still.

But still it I must. Each day brings new opportunities, new projects, new ideas and new possibilities, and yes new deadlines. However long I’ve carried them, there are things to be set down and left to their own devices, so that the weight of all of them doesn’t sink me into the road.

windows into the past

•25 October 2020 • Leave a Comment

Mom has been doing some cleaning over the past few years, and from time to time she sends me pieces of my past that she’s come across. Most of these relate to high school or university days (for instance, multiple copies of my university graduate programme, in a box on a shelf), but occasional she finds something properly interesting.

Over the weekend, she sent through a report written at the end of my second grade year, in the summer of 1972. I won’t go into the details, and it has been interesting to reflect on some of the points raised therein, but rather than these specific details, I’d like to spend some time perambulating around the fact of having such a window.

These occasional reports, this recent one and others previous, as close as I will ever come to having a conversation with the young Jimmy, on the cusp of 8 years of age, a time long enough ago that my memories resemble snapshots of moments more than moving pictures. And for those incidents that are formative if only because they’re the moments and memories that persist, we have to accept the possibility that decades of reviewing those memories have corrupted the tape.

I think about this whenever I read history. I’ve recently finished The Sleepwalkers by Christopher Clark, a detailed account of the discussions and deliberations that took place across Europe in the few years leading up to the beginning of World War I in 1914. I enjoyed the book and the exquisite level of detail, but even here we have only what was written down and what survived, and we can only speculate on the conversations of which we have no record.

The farther back we go into our collective human history, the more pervasive an issue this becomes. The written record becomes thinner as we go back through the decades and centuries and millenia. And it’s not just that the record becomes thinner; it’s that what is written becomes more focused on particular areas of our past lives. This might be why we appreciate the individual voices from the past that sometimes arise, in documentaries for instance.

It’s this I think that lead to the reading project I set myself a couple of years ago, to read human writings from the beginning. I am still wandering through the streets of ancient Sumer. I listen to stories whose context I don’t yet understand. I wonder about the events and beliefs that sit behind these stories. And I ache to know what stories we told to each other and our cousins, sitting around fires tens of millenia ago, and what echoes of those stories still inhabit our stories today.

some useful images

•23 May 2020 • Leave a Comment

Over the years, I have accumulated what I feel are some useful images, that I used to help me make sense of some frequently encountered aspects of life and work.

1. One of the twelve labours of Hercules, traditionally the second, is the slaying of the hydra, a multi-headed serpent. (And I hadn’t realized that in some tellings of the story, the hydra was created purely to defeat Hercules. The things we learn.) For all but its one immortal head, two new heads for the hydra would grow in the place of each head cut off, and it required Hercules using a torch to cauterise the stumps to prevent them regrowing.

The image that came to mind is of email as our own personal hydra. For each email to which we send out a response, we then have two (or more than two) additional emails in the inbox. And what I don’t have most days, is a torch.

I do like as well the version of the telling that includes Hera sending a giant crab to distract Hercules, once she sees him prevailing with his sword and torch. It’s tempting to speculate on what the giant crabs that wander through my days, and who is my Hera.

2. Hymenoepimecis argyraphaga is a wasp whose larvae take control over its prey spider. Ophiocordyceps unilateralis is a fungus whose larvae take control of the behaviour of its prey ant. I’m sure there are others, but there are days when I feel that aspects of the roles I play are treated me like the spider or the ant.

It’s an interesting topic for ponderation, because it’s something many of us have felt; that we are acting, but without knowing fully what’s causing us to act.

The next step in this ponderation is to start identifying what I might do to prevent the wasp or the fungus from taking hold in the first place. This I think is a negotiation that I need to have with my work; I understand that in the workplace, I am subject to forces that are not entirely (or even partially) within my control. But I also feel that I can learn to moderate, though perhaps not entirely control, these forces. This will require understanding them more deeply than I do now.

3. Surströmming is a fermented tinned Swedish fish product, a newly opened can of which is believed to be one of the most putrid foods on earth. Cans of this should be opened under water.

Every once in a while, we come across complicated issues in our professional lives. Some of these are complicated only because they’ve been allowed to ferment over time, whereas others are complicated just by their nature.

The image I take here is the need to be careful in unpacking these issues, so that they do not explode once they’re punctured. Or if they are going to explode once punctured, then at least under water, they’re under some small amount of moderations.

The interesting questions then become, how can we tell whether the issue we’re dealing with is one of these cans, and if we decide that it is, what is the under water that we then need to open it safely, so as not to do wider damage. These will be different for every issue, but accumulated experience gives us tools to help make these decisions.

4. In the Hitchhiker’s Guide to the Galaxy saga, Zaphod Beeblebrox at one point finds himself inside the Total Perspective Vortex, which shows him his place in the universe. [SPOILER ALERT] Fortunately for Zaphod, he was at the time in a bubble universe created solely for him, and the Vortex just reinforced the view he had of himself.

So what is the Total Perspective Vortex of academia, or of aikido, or of writing, and how can we without creating our own bubble universe, how can we survive these Vortices?

Each of these areas has multiple Vortices and each Vortex is its own swirling maelstrom. For me, the best way to survive the Vortices is to never enter them in the first place, as escaping a Vortex requires navigating a labyrinth, and we may not have been unspooling the thread to allow us to find the exist and we don’t know what our Minotaur might be, if you’ll give my mixing of images.

a meditation on things I have read

•10 May 2020 • 2 Comments

Some long time ago, I read a story that rang a chord that’s continued to echo through the years. The story was set in a society in which everyone wore masks, in public and if I remember correctly, in private social occasions. They wore different masks for different moods and different situations, and no one showed their biological face, for lack of a better term. Unfortunately, as has happened before and will happen again, I don’t remember how long ago I read it, or where.

As a side note, before going back to the main theme, it would be lovely if there were a searchable database of stories. Stories like the one mentioned above, or others that I’ve remembered and written about, that I would like to go back and reread, but I don’t know how to find them. I don’t know if we could build such a thing,

As I remember, the story contained no memory or explanation of why this society had come to this point of wearing masks. But in light of our current circumstance, I can see a path along which a society forget its faces.

For a bit of time, we may well become such a society, wearing masks in public, and though in retrospect we could easily have imagined it, one path to such a society is less mucky than it used to be. Masks are becoming more common, required in some places. In the darker corners of our imagination, we can speculate on a path through time along which masks become acceptable, a fashion statement of sorts, and fashion can develop an inertia.

But I don’t want to spend too much time speculating on masks; we’ll see over the coming months and years how our future develops.

Rather, I’ve become curious about the prescience of science fiction. This half-remembered story of masks is one, which might or might not predict some aspect of our future.

But this led me to another moment of connection between our world and a fictional world, this time the remade Battlestar Galactica. Dirty Hands is an episode in series 3, about the refinery ship that’s part of the human refugee fleet. Those people who happened to have been put on that ship during the initial flight from the Cylons became essentially trapped, working the dangerous jobs on that ship solely because of fate and regardless of their talents or desires.

Watching the news struck a chord with this episode: stories of health care workers, those people working in stores and delivering groceries, warehouse workers. People who have to be at work, rather than working from home.

And from here, it is only a few steps to our modern variant of India’s Net, the interconnectedness of all things. One evening, I contemplated the services that support our modern world, and our dependency on all of them, much as the Galactica and its fleet were dependent on the refinery ship.

In a sense, this extreme interconnectedness and dependence is a symptom of the world we’ve built over time. I don’t grow my own food and I don’t weave my own cloth, I don’t generate electricity and I didn’t make the bricks of which my house is built. I am but one node in some vast interconnected net.

the rise of the machine world 2, with teaching

•26 April 2020 • Leave a Comment

Each year, I realize that little bit more how much I love teaching. I realize how much I enjoy taking a small piece of the mathematical universe, digesting it and showing my students all of the strange and wonderful flowers I have found growing along the sides of our path. I am reminded of how much I enjoy the engagement with students, inculcating in them in the joy of mathematical exploration.

What does this have to do with the machine world? Through one lens, it can be viewed as a manifestation of an old story of Issac Asimov, The Feeling of Power. These days, a retelling might result in a cautionary tale a la Skynet and the Terminator, or Colossus, of outsourcing aspects of how we understand the world, and gifting the machine world with dominance. When it was written, though, while it was a cautionary tale, it was a hopeful tale, with humanity slowly, painfully, discovering its gifts.

And what does all of this have to do with my teaching? One of the readings I give my students is The Feeling of Power, because I like to be reminded each year and I think it’s a story worth everyone reading. We make us of our colleagues in the machine world, to undertake calculations beyond for reasons of practicality our ability to do ourselves. But I make use of the machine world with the understanding that we might get out answers to our questions, but we still need to provide for ourselves the reasons why those answers are actual correct answers to our questions.

Mathematics has for some time been an experimental science, wherein we can use the machine world to conduct our experiments, under our direction. We take the outputs from these calculators experiments and we can then formulate conjectures about the behaviour in situations far beyond our ability to calculate, and we then try to construct the arguments that allow us to pierce the veil of the logistically practical and make statements in truth about the infinite.

And this is what I work to share. The deep intellectual joy we can find in our quest, in our exploration of the infinitude of possibility. The harnessing of the power of the machine world to assist us in our quest. The use of language to provide short cuts along the path of understanding, and the exploration of the subtleties of that use of language.

And now, I go to write the next lecture, the next episode for my students, taking them a bit further along the path.

how the little green men might defeat us humans 5

•13 October 2019 • Leave a Comment

Up to this point, we’ve been exploring this general topic by considering human internalities: what are the aspects and traits about us as humans that might provide ways for the little green men to bring us to our collective knees.  We will come back to these internalities, as there is much much more to explore, but today, I would like to consider some of the externalities that could be brought to bear.

I have not done much in the way for formal research, on this post or on the others in this particular series.  There is a lot of research to be done and it is research that should be done, but I’m taking the opportunity to speculate, pulling from my memories ideas that have stayed with me, variants of some of which I’m trying to work into my own writings.

Perhaps for instance the little green men, who might be none of the above, come to our solar system but remain out in the Oort cloud.  If they were able to calculate sufficiently well, which one would hope they would be able to, then they could be patient and drop well-aimed rocks from the Oort cloud into the inner solar system.

Here, we encounter a potential discussion of aesthetics.  Might they reshape the rocks into shapes or compositions of relevance or importance to them, or would they use the rocks in their raw shapes?  Might they accept the greater challenge of playing billiards with the moons and planets, for no reason other than that is what they feel like doing?  How much damage, for instance, might they be able to do with a single well-aimed rock? And yes, I recognize that this this is drifting into supervillain territory, but I think that might be unavoidable given the topic at hand.

There are variants of the dropping a rock theme.  One that I have never been able to get out of my head is the narratively simple but physically challenging variant of attaching an engine to a rock and accelerating it to some appreciable fraction of the speed of light.

I think the reason this sticks with me is that all of the disaster movies that I love that involve asteroids and meteors, like Deep Impact and Armageddon and Meteor, and the innumerable others, always give us the time to react, to build and equip a ship to go forth and meet the offending rock.  But with a rock moving incredibly fast by our usual standards of movement, there would be no such opportunity.

There is another idea lurking in the bushes here as well, the idea that if something is difficult given our current capabilities, then in some sense it’s legitimately and properly difficult.  I come across this from time to time among my students, more the mathematics students than the aikido students, but I am less and less willing to accept that it’s true. We practice, we evolve our understanding and as we do so, our threshold of difficulty changes.

But there’s more than dropping rocks on our heads.  One of my favorite movies from my early days is the Andromeda Strain.  An alien microbe, for lack of a better term, finds its way to Earth via one of our own space probes sent to collect (as we’re now doing with comets, but that’s another exploration entirely), and it starts misbehaving, at least for a time.

Given the technologies that we’re currently developing, it would be relatively straightforward for an alien species to hire the expertise of human genetic coders to so nefarious things, and it wouldn’t even be necessary to attack humans directly.

Some of these things might not involve an external agent.  A book that I dimly remember, and that I need to read again, is Toolmaker Koan by John McLoughlin, which as I remember it explores the basic issue of civilizations developing tools and technology more quickly than they develop the ethics and sensibilities about using those tools and technologies.

This is an issue that we read about every day, and have since we first developed the ability to sterilize the surface of our planet.  Artificial intelligence might one day find its way into this list of tools and technologies, to go along genetic engineering, nuclear power and even perhaps the internet.  I would probably put human psychology on this list as well, and I would be interested in knowing what things you would want to add to this list.

the notion of edition in the digital age

•2 March 2015 • Leave a Comment

In exploring the dark and dusty corners of the drafts folder, I found a piece that I’d started writing back in 2015. I’m not sure how I lost it or why I stopped working through the idea, but it’s something I’ve been thinking about recently.

In part, this revisitation comes from the materials I’ve been preparing for my class this semester and thinking through how they change from one year to the next, as I continue to work through the examples and navigate the ever-changing structure of the notes.

Another reason comes from the thinking I’ve been doing about a possible third edition of the Hyperbolic Geometry text book and what that might look like. There is a permanence to a book that I very much like; words on paper and once the words are printed, effort is required to shift them into other words. This is especially relevant in a field that’s moving quickly.

I’ve also been thinking about the couple of stories I’ve had published, as I’ve been persuaded to look for reprint possibilities for them, and this raises the question of the extent to which I might want to tinker.

This is a problem for readers as well as authors, and perhaps even a larger issue for readers. I’m not sure I’d want to buy a book knowing that the book might well shift and change, as the authors continues to shape and refine their work. It’s tricky, because I also want a book as well crafted as possible.

This brings to mind the old joke, that a paper or a story or a thesis are never finished, they are merely submitted. There is a variation on this theme, that a paper or a story is never finished, merely published. (And I do hate writing ‘merely’ and ‘published’ as consecutive words in any sentence.)

And so an answer to the question implicit in the title might then be, an edition is a snapshot, a moment in the life of a work, setting down a marker of sorts.

I do have great sympathy for the librarians and archivists, trying as best they can to track and keep a record of what’s being published. Trying as best they can to keep a record of these moments.

As a reader, I can see the benefits of constant updating, constant refining, but as noted above, there is also the frustration of the reader with having a constantly shifting piece of reading. I can also see the attraction to the author, wanting their work to be as good as it can possibly be.

But since we started making marks in clay tablets, we have been keepers of records. We have the notion of canon and we have a fondness of the version of record. I’m not sure what happens to all of these basic assumptions we make of the permanence of published works.

Perhaps it will depend on the purpose. I can see an educational text book shifting to reflect the class as taught; this might also reflect a change in teaching towards more of a challenge based structure on top of a basic syllabus, and so the underlying work might well need to shift to reflect this style of delivery.

l can see fiction having a more rigid structure, but it would be a curious thing to read, a story that shifted with the reader, almost like the old adventure books (‘there are two doors’). I’m not sure a human author would be able to keep up with the authorial demands, but might a rigid published story or novel find itself someday replaced by an extended conversation with an artificial intelligence? I’ll be interested to see.