reading in hindsight: The Weapon by Fredric Brown

•4 June 2023 • Leave a Comment

On my shelves, I have many books, some read but most unread. Among these are collections of stories that I’m slowly working, or reworking, my way through. (And my but some folk wrote a lot of stories: Sturgeon collected stories run to 12 volumes, and others like Vonnegut are large enough to count as weight lifting.)

One I like picking up is the collected stories of Fredric Brown. Writing in the 1940s to 1960s, Brown had some lovely ideas, albeit wrapped in stories that are problematically of their time, and one idea that I was reminded of today is from his 1951 story The Weapon. If you haven’t yet read it, there will be spoilers.

Dr James Graham is working on an ultimate weapon, a fact evidently publicly known. He is visited by a stranger named Niemand, who asks the question, ‘Is humanity ready for an ultimate weapon?’ Graham doesn’t listen and so Niemand then provides a demonstration of the dangers of giving a weapon to someone not capable of wielding it.

I’m sure that some amount has been written about possible interpretations of the story, but I will note that Ivy Mike, the first fusion bomb, was tested on 1 November 1952, and so this story sits in that complicated time in the early days of what became the nuclear arms race.

But if we take a step back and focus not on weapons but rather ideas, are we in the same situation? Are we, the collective we of humanity, developing ideas that we may not be capable of handling well in the end?

The first possible answer goes back to what might have been Brown’s initial inspiration and the nuclear bomb. If I remember correctly things I read a long time ago, there is an upper limit to the size of a fission bomb but there is no theoretical upper bound to the size of a fusion bomb, except where limited by imagination. And so this had to count.

But there are others. There may be an argument that the idea of a corporation might be an idea that we’re not entirely capable of handling well. One aspect of this I’ve encountered on more than one occasion is the view that corporations are the first instances of an artificial intelligence, something ultimately non-human (though made up of human agents) that has agency and desires.

The version of this filling the news at the moment are the chatbots. Again, I think the argument that we’re not prepared for the consequences of this creation is a strong one, even taking into account that this isn’t an artificial intelligence as such, but rather is a reflection of who we are. After all, the chatbots are trained one what’s been written and so in some strong sense, they’re a distillation of what we collectively have expressed over the years, decades, centuries.

This is a slightly different conversation than doomsday devices, another topic I feel worthy of consideration if only to understand paths not to walk, but still a conversation that we need to have lest we sleepwalk into a world that is significantly less comfortable than our current world with all its faults and complications.

So one very short story with a moral, are we ready for the things we make with our hands, but regardless of the answer, the big question remains. What next. What happens when we have built a weapon, in however general a sense. This ties into other thoughts about the toolmaker koan, that loosely it’s easier to build a tool than to use it well, and perhaps developing our understanding here is the next great quest.

a time for some reflection

•28 May 2023 • Leave a Comment

The current academic year is coming to its end; I taught my last class a week and a bit ago, and my next proper class (besides the occasional seminar) will be in the autumn. There is a vast amount to be done over the summer, not directly related to teaching but directly related to the job as a whole. One research paper is largely done, needed a bit of tidying and some attention at one point of the argument. Another paper dances before my eyes, a mirage on the horizon, as yet unformed and nascent.

There are other projects as well, problems I would like to spend some time thinking about and working through. This is a part of the job, voyaging beyond the frontiers of extant human knowledge (how grand it sounds).

And both of these aspects of the role are aspects of it that I enjoy. Working with students and expanding their mathematical horizons, and then expanding the horizons of mathematics itself, are engaging and awesome experiences.

But this time, at the end of the teaching year, is a time for reflection. The teaching year went well, I think. I picked up a new class in semester 2, and I learned a lot and I hope the students did as well. This intertwines in some way to topics I’ve covered in previous chapters in this extended scree, such as the distance between teacher and student.

So in this case, though I hadn’t taught the class before, I have a few decades of both the experience of doing math and making sense of math, but also of teaching, of making sense of new things and relating them to other aspects of math. And what’s interesting is that in the process of preparing and teaching, I came across one or two things that I might be able to use in some of my mathematical project work.

There are other sides to this reflection, beyond the day job. There is the old parable of rock and gravel and sand. And it’s again time to undertake the audit, to empty the jar as it were and to examine my current rocks, my current gravel and my current sand. It’s a tricky examination, because all come with their sunk costs. And the fallacy notwithstanding, it’s hard to grind rocks into sand or to press sand to form gravel. It’ll be an interesting summer.

watching in hindsight (again): Colossus the Forbin Project

•14 May 2023 • Leave a Comment

A few years ago, I wrote about a 1970 movie I find myself coming back to from time to time, Colossus the Forbin Project. What struck me today was not the naïveté of the creators of Colossus and Guardin, but rather the prescience of the movie, and the books it’s taken from, in setting forth the emergence of new properties.

In the movie, this emergence comes at the beginning; the extent to which Colossus begins almost immediately to exceed the expectations of its human creators, amazingly without causing panic. This is the theme that drives the movie, that Colossus is more that was was created, and the humans never catch up to how Colossus is growing.

One key moment of this emergence of capabilities is the moment that Colossus makes use of the tools available to it, to enforce its demands. And when Colossus decides not to answer.

The reason this struck home with me today is the almost constant speculation in the news and commentary about the unexpected emergent properties of our current artificial intelligence systems, as well as the speculation about the danger of continued development.

I will admit that I don’t see the development stopping or even slowing down. As has become obvious, we humans can be short sighted in our thinking, chasing the shiny at the expense of running into the road, into oncoming traffic.

But I suspect we’ll continue to experience unexpected emergent properties of the systems we develop, and this should also not surprise us. We are creating systems where we understand the basic shape of the system, but the details of the system are beyond the ability of our human minds to contain. I suspect the systems we build will continue to surprise us, and we should not be surprised by those surprises.

Another interesting aspect of this is that we saw this possibility, decades ago. Runaway robots, Colossus, Hal and all the others, they were Cassandras of sorts, ghosts from the dark corners of our imaginations, perhaps now brought to life by our hands. Interesting, isn’t it, the extent to which we don’t pay attentions to our own stories.

A random collection of moments

•30 April 2023 • Leave a Comment

Some long time ago, measured by where it sits on the list of collected things, I wrote down the sentence, ‘a user guide is an admission of failure.’ I can see what I meant by this. Devices have become much easier to use, going back to the original iPod with its scroll wheel.

I had an interesting conversation with a colleague not so recently, about how students learning to code don’t understand file structures, because they never needed to. They don’t need to organize themselves; they can just search and they will find.

What implications does this observation about user guides have for education? I’m not sure, but education is full of user guides: textbooks, lecture notes, problem sheets, all can be thought of as user guides to particular areas of knowledge. But I don’t think this is the right visualization.

Rather, I think that the textbook or the lecture notes or the problem sheets are the devices rather than the user guides to those devices. So in this interpretation, the lack of a user guide translates to having a well structured textbook.

Bob the cat has developed the habit of walking across my keyboard and sitting on the papers on my desk when he wants a bit of attention. I of course indulge him, scratches under the chin.

It takes time and effort, and a lot of thought, to write a good textbook. I’ve written one, on Hyperbolic Geometry, and like potato chips, it’s hard to write just one 😉 And so part of what is on the list of things to think about is, what might be the next one.

the parable of the oak and the willow

•23 April 2023 • Leave a Comment

There is an old story, which I might be misremembering. An oak tree and a willow tree, who had grown up next to each other, were having a conversation. The oak was glorying in the strength of its trunk and its branches, claiming that it could withstand the strongest of storms. The willow extolled the virtues of flexibility, of rolling with the strength of the storm rather than fighting it directly.

When the storm came, as storms always do, the oak found itself broken, where as the willow, aside from losing some leaves and smaller of its branches, remained standing.

I have a lot of sympathy for this parable. I’m not sure of the strength of its horticultural veracity, but I’ve always found it to make a certain kind of sense. It’s come to mind recently, I suppose, because of the storms, physical and cultural, that are currently swirling around. (I think perhaps I watch too much news.)

Beyond that, my aikido practice is much more willow-like than oak-like. Falling like a tree is not a good way to fall, for instance. And as I get older, the idea of using strength rather than technique and movement and flexibility becomes less attractive over time.

But it applies elsewhere as well. It can be applied for instance to teaching. The oak stands and says, this is my way and this is the way, and requires students to do as they do. The willow is more flexible, more adaptable to the individual student. Or so goes one interpretation.

I contemplate this parable particularly at times when I feel more oak-like than willow-like. Because there is an easiness to being oak-like; I will stand here and I will be, and I will let the winds whistle through my branches and leaves.

I find there to be a theoretical, hypothetical attraction to the way of the willow, but it does require more effort to move and be flexible than it does to stand in glorious ignorance of the world. And some days, it’s just hard to move, and it’s hard to move in response to the world. But still, the parable I think holds a clue to something more. The quest continues.

Eastercon 2023 diary – day three

•9 April 2023 • Leave a Comment

The formal duties for the day are done; the Milford panel has been panelled and we sold more copies of the Eclectic Dreams anthology today, though I will be taking a few home tomorrow.

I will keep coming back to this point, but it’s good to see people. That said, there is one topic that keeps coming up in conversation, which is that engaging and interacting with large groups of people takes a remarkable amount of energy.

This is something I’m used from teaching, and the occasional feeling of dragging the class through the journey from blissful ignorance to understanding, but just interacting takes a lot of energy. Meeting new people, remembering names and context, fitting them into the growing context of the community, takes more energy than I’d remembered.

This is perhaps because in the Before Times, it was just a cost that we didn’t think about; I dealt with people every day, new and old, and I never thought to put a cost on it, because it was just part of what the days involved.

But the calculation is different now, if only because it is more explicit. And the question I’ve been asking myself today is, how to build that cost into future considerations. I like people, at least as much as any extroverted introvert likes people (namely, until we don’t).

In my work life, and my aikido life both, the group of people I deal with is constrained, mainly people I already know and work with (or throw around, respectively), and I don’t do much in the way of Eastercon people. So something to think through.

Eastercon 2023 diary – day 2

•8 April 2023 • Leave a Comment

I’d intended on writing from Eastercon on each of its days, but alas got distracted by seeing old friends and making new friends, and fell down on day one. We’ll see how the rest of the weekend goes.

But here we are in day two, and it’s going well. The sun is shining, the panels are humming and I’m currently sitting in the Room of Buying and Selling with a small pile of copies of Eclectic Dreams.

This is an anthology of stories (which I was pleased to co-edit, with Pete Sutton and Liz Williams) that have passed through the Milford Science Fiction Writers Conference. We had the formal book event yesterday afternoon, and should you not be at Eastercon, you can order your copy via the links contained HERE (so get your copy today!).

Beyond that, being here reminds me of this sprawling community of science fiction and fantasy that I’m a part of. I’ll admit that sitting here in the Room of Buying and Selling, the temptation to buy yet more books for the already over-burdened shelves at home is exceptionally tempting.

More than that are the people. Going to panels and listening to others talking about things they know and things that excite them, evening conversations in the bar, and catching up with people is good for the soul.

The hosts of the Deadline City podcast often talk about the necessity of filling the well, and that’s part of Eastercon does for me. I experience the same refilling in other parts of my life, with aikido summer school and the occasional math conference, and I do love the energy of being in the midst of so many like minded folk.

reading in hindsight: Jokester by Isaac Asimov

•2 April 2023 • Leave a Comment

I like dipping back into the (personally) distant past and seeing what stories from those days have to say to us today. I picked up Jokester by Isaac Asimov earlier today; the core idea of it had stuck with me since I read it the first time, because I enjoyed the twist, but it was a smaller aspect of the story that caught my attention.

To add a bit of context, the news over the past few weeks and months have been filled with stories about ChatGPT3 and its cousins, and the impact that they might have on education (where I spend a chunk of my days), among other fields.

The aspect of Jokester that caught my attention was the core fact of the existence of the Grand Masters, such as Grand Master Meyerhof who drives the action in this story. This core fact is that there is a subtlety and a skill required to appropriately frame a question for a computer such as Multivac.

Or for ChatGPT3. I’ve not done a lot of playing around with it directly, but I know folk who have spent more time than perhaps is entirely wise. One thing that’s come out of my conversations with them, and the reading I’ve been able to do, is that, the output can depend a lot on how the question for such Large Language Models is framed.

And this brought me back to Grand Master Meyerhof; not actually the questions he asked, as interesting as they are, but that the skill of the dozen or so Grand Masters was to be able to frame the question.

Thinking of Large Language Models and their impact on education, just to focus attention, it seems that this provides a bit of direction for us to work to work with. These tools are not going away; the main question for us is, how to use them and more even than that, how to use them well.

I’m reminded here of the toolmaker koan, a novel by John McLoughlin, that I haven’t read for a long long time. But it does contain the basic question, is it always the case that a civilization will develop tools before it develops the ability to use them, and this strikes me as where we are at the moment.

We have developed some awesome and mighty tools. Perhaps these tools won’t allow us to answer Grand Master Meyerhof’s question as Multivac was able to, but they do pose this question for us. Will we have or develop the wisdom to use them well? Or won’t we? We will soon find out.

Moby Dick as a metaphor

•12 March 2023 • Leave a Comment

Every couple of years, I go back and read Moby Dick. I first read as a university student, and I’ll admit that the first time through was something of a slog. But as I’ve gone through and through again, it’s begun to grow on me.

Moby Dick contains many things that we can view as metaphor; we’ve become familiar of the great white whale as the elusive object of obsession. For me, the great white whale is often a research question, one of the questions on the LIST, which recedes every time I make an attempt.

I haven’t thought too deeply about the metaphor, beyond trying to prevent myself from becoming a mathematical Ahab. I don’t know for instance where Queequeg makes an appearance in this metaphor, or Ismael. But I do often have Starbucks whispering in my ear, advising me, persuading me to spend time on the questions on which I can make some progress, despite the howls of protest from Ahab and his old questions.

The metaphor of Moby Dick also works for aikido and writing. The things to do, the voice of obsession, the dissenting voice and Ismael at the end holding on to the coffin so carefully made and carved by Queequeg.

But this leads me down another line of inquiry (enquiry?) entirely. (In the balance, probably a bit more enquiry than inquiry.) Would Melville be surprised at the metaphors we pull out from his story? Would he be surprised at how Moby Dick and Ahab have become part of the imagery we use and the descriptions we give?

I don’t actually know. I hope he would be appreciative. But I do know, as do we all, that we each read things into stories and novels that the author may not have intended. And that’s just part of the way of things.


•26 February 2023 • 3 Comments

On the one hand, fiction is an integral part of our lives, and impossible to imagine without. For all of recorded human history and beyond, we have told stories around the fire to keep our worries occupied and our minds warm.

The bookshelves around the house are full of fiction, and I enjoy exploring its pages. Some contain stories I want to explore again and again, Gilgamesh comes to mind and Dune, and some are stories through which once was sufficient. At least so far.

But on the other hand, fiction is a strange thing. I’m wandering far afield here, but is it really the case that human experience is so thin that we require stories beyond that experience?

I wonder some times what might happen when we do encounter an alien race, extraterrestrials, that don’t understand the concept of fiction. I’m sure that people have written variants of this story, and if you have recommendations for what I should read, please let me know.

But from this, we can spiral into speculation, about what that first encounter might be like. Their lack of comprehension, our lack of comprehension at their lack of comprehension. And so, what’s the story.

Can there exist a race that doesn’t tell stories, that doesn’t so exercise their imagination? And more importantly, would we want to be friends with such a race? Trading partners perhaps, but we would have to answer the question, how much do our stories mean to us?

And I think our answer would have to be, quite a lot really. Everything perhaps.

reading in hindsight: The Man Who Had No Idea and chatbots

•19 February 2023 • Leave a Comment

Barry Riordan is The Man Who Had No Idea, the protagonist of this 1978 short story by Thomas M. Disch. I’d first read the story a long time ago, in a collection of short stories acquired possibly in a second hand book shop of the sort I spent a lot of time and money in when I was significantly younger.

The idea of the story (no pun intended) stuck with me, even if the details and characters (such as Mad Madeline Swain the poet and Cinderella Johnson and her love of single shoes) had slipped through the cracks of memory. The basic idea is of a world in which people need a license to engage in conversation, and the story follows Barry in his almost unsuccessful quest for his.

The story came out mind amidst all of the recent news stories and commentary about the various chatbots and the difficulties they’re having with engaging in conversation. Admittedly, they don’t have Barry’s difficulty, of not knowing how to start a conversation, but rather difficulties of a very different sort.

As much as it’s something that we as humans engage in to a quite significant extent, I think that part of what we’re seeing through these news stories is that conversation is difficult. It requires pulling together, bringing together material from many places and doing real time reflective engagement through the process.

As we go through the short story, we watch Barry get better, to the point of generating a list of ideas for poor mad Madeline, a few of which become some of her better poems. In the same way, I’m sure we’ll witness the various chatbots getting better at chatting, through I do suspect it might take somewhat longer than it took Barry.

Those who know me moderately well will know that I sometimes express some degree of surprise and dismay that we are working ever so hard to equip the machine world with the tools it needs to pull a proper Skynet, or something much deeper and even more effective.

Robot dogs that can run and climb stairs. Facial recognition. Autonomous drones and other weapon systems. Voice recognition. Applying machine learning to develop toxins unlike any seen before. Gait recognition. And how, the conversational, so that even the Turing test won’t save us.

This is an old story and one told many times. This is the story of our capacity for developing tools before or without developing the wisdom needed to use the tools effectively. And so, might the future savior of humanity be the person who can’t be emulated by a smooth talking chatbots, as our last defense against our own creations?

reflections on reflections

•12 February 2023 • Leave a Comment

Scrolling to the bottom of its homepage, I note that the first blog post I wrote is dated 10 February 2013, ten years ago this weekend. I suspect in fact that this is a bit of a artifact, in that I suspect I started drafting it then but didn’t publish it until later, and somehow the date assigned was the date the drafting started until the date the drafting finished. One piece of evidence for this is that the second post didn’t show up until nine months later, in November, and another is the first line of the piece itself.

That first piece was entitled the power of number, and it sets out the basic observation that once we start assigning numbers to things, perhaps for the purpose of ranking, then the meaning drifts into the number, at the expense of that to which the number was assigned. And over the past ten years, I have become more convinced that it’s true.

Another of those early posts was on another aspect of numbers, namely that the words we use to describe number hide the magnitude of the numbers themselves, and this also ties into the difficulty that we humans have in appreciating the scale of the very large and the very small.

There are things that I have the vague memory of putting on the various lists of things to do as part of those early posts, but which have slipped down the list, or off the list entirely, with the continuing accumulation of the ephemera of daily life, the weeds which grow quickly and sometimes hide the paths on which we walk. And so time perhaps to pull some weeds and find these hidden things, and finally work them through.

Beyond that, though, there are larger pieces of work as well. For instance, I’ve written some significant number of words on aspects of teaching, both in math and in aikido, and it’s not clear to me that the current me will agree with all of the words that past mes have written. In part, this is an inevitable consequence of gaining experience through the years, reflecting on my practice through the years, and also the reflection on the experience of the past few years and how that will have changed everything. What to keep, for instance, and what of the old to allow to be gracefully retired or abandoned.

And so I think the time has perhaps come to go back, read old pieces, and have that conversation between current me and the many past mes, though interspersed with the emergent thoughts of the days to come.

the relentless march continues

•5 February 2023 • 1 Comment

Last week, I wrote about ChatGPT and the impact that it (and its siblings and cousins and distant descendants) will have on education. I would like to sketch out an optimistic potential future, because I’ve been marking today and so I’m leaning much more towards the optimistic than the pessimistic at the moment

This is a utopian vision, fueled by Federation and Culture and all of the optimistic futures that science fiction authors have projected for us over time.

At some point after we’re born, we are each assigned or gifted an artificial intelligence companion who teaches us, shepherds us, guides us on our path through the world.

Our Companion will suggest reading or watching to fuel our interests but also to stretch the outer bounds of our imagination. Our Companion will test us, working assessment into every one of our days, all of our activities. Our Companion will have as its primary objective to make us, each of us as an individual the best of us we can possibly be.

It’s a seductive future, and a future that I would love to live long enough to see, but there are issues that I can see, that we all can see, and I’m not sure how to get over those hurdles. One is, how do we bridge the gap between rich and poor. It’s easy to imagine such an optimistic and enabling future, but how do we make such a future available to everyone.

And now, a left turn. I have an idea kicking around in my head. Perhaps some day it will become a story (and before you ask, the line of ideas waiting to become stories is long and winding, and so if you have a story from this idea, have at it. I’ll do what I can to catch up). The aliens arrive and in order to join the Federation, the civilized races of our galaxy, we have only to answer a single question.

Tell us the story of humanity. Tell us the story of humanity through its individuals. So tell us the story of everyone who lived today, everyone who died today. Tell us the story of each of you, and you can join us.

I don’t know what to do with this idea, but there is a part of me that wants the aliens to land tomorrow and ask us this question. And there is a part of me that’s afraid that they might. Because we can’t answer this basic question, how do we take care of everyone. All of everyone.

I suspect this idea will lead me down some interesting alleys of consideration. But back to the original question, I would like to see a future in which each of us and all of us are granted this opportunity, to be enabled in such a bespoke way.

I don’t know though how to get from here to there. It’s easy to imagine an optimistic and utopian future, and why not dream a utopian dream. Why not. But plotting the course, ah therein lies the rub.

the relentless march of technology

•30 January 2023 • 2 Comments

When I was taking high school physics, back in the very early 1980s, sigh, my year was the first year to use a calculator rather than a slide rule. I don’t remember the model number, beyond it being Texas Instruments, but I do remember the excitement of CALCULATOR and the relief of many about not having to learn the slide rule. I’ll admit that I was always a bit bummed, though not bummed enough to go back and learn the slide rule on my own.

This memory came to mind during a recent conversation about ChatGPT and the impact it may have on education. Technology always advances, sometimes more quickly than our ability to handle the implications and aftershocks. If memory serves, Socrates all those many years ago was against writing, as it would erode memory and confuse students into thinking they had knowledge when they had only data. And so these thoughts about different technologies are not recent.

What’s interesting about this conversation is that ChatGPT is just the tip of an iceberg. The technology is advancing, and perhaps we will soon find ourselves in a science fictional universe where we are each followed from our early days by a bespoke Artificial Intelligence, teaching us and testing us and either shaping us to serve a malevolent social order or developing us into the best humans we can be, within their own limits.

But that’s the future. What happens tomorrow, and next week, and next month. How do I design an assignment that the students would be doing in their own time. The easy and simultaneously difficult answer is to impose conditions on the time and space in which students take their assessments, but I would like to contemplate a different direction, if only briefly.

For me, the question is, to what extent should we try to reduce the artificiality of assessment. One aspect of this is, why not design and deliver assessments that allow students to use all available tools. After all, out in the world, people will make use of all available tools to do the jobs they’ve agreed to do and are paid to do.

This is a long conversation, as befits a question that speaks to the foundations of what we do and how we do it. One of our basic purposes, after all, in education is to assist students in developing their knowledge and tools for engaging with the world, understanding the world, changing the world (hopefully for the better), and indeed developing a definition of better in this context.

Having put down some words, I have come to the realization that as vast a question I thought this was, it is actually a larger and broader and deeper and more complicated question. I think I need to step away, stare into the dancing fire and contemplate for more time. More to come, and I hope soon.

and lo, the new year calls

•8 January 2023 • 2 Comments

Let me start with an apology. I don’t keep close and careful track of the topics I work my way through here, and so it may be that I cover ground that’s already been covered. And more interestingly, it may be that I cover old ground along a different path, and I’m certain that I will.

One thing (among admittedly many) that I’ve let slip over the past few years is the annual reading project. The first in 2017 was the Book of a Thousand Nights and a Night, the tales of the Arabian nights, the Sir Richard Burton translation. The second, through 2018 and the first half of 2019, was the collected works of Kurt Vonnegut.

I then, in a fit of what can only be described as ambition, set myself the task of reading the literature of humanity in chronological order, from the beginning. That was a task made in ignorance of the volume of what we’ve written and what we’ve translated. I am still reading around ancient Sumer, because I find it an interesting place to visit and spend some time.

For 2021, I picked a list of 100 fantasy books to read, and I’m still working my way through that list; I’ve read a few on that list and I’ll continue to read. But for the purpose of a reading project, I don’t feel that for me, such a list makes a good project.

What I enjoy about a reading project is to immerse myself in the works of a single author, and this is something that the lists don’t offer. And so, I find myself asking, what should be the reading project for 2023. Or rather, who should be the reading project for 2023.

But how to decide? What is my process for making such a decision, since I’m deciding with whom I’ll spend a lot of 2023. (And I’m thinking about the process, because I find myself teaching a module of algorithms in semester 2 and so I’m thinking a lot about decision making processes in general).

One idea was to walk through the house and examine the various book cases and ask, whose books have I bought over the years. From whom do I have a complete or near complete collection. One idea is to ask, who do I want to read.

One idea is to do something a bit different and play two authors off one another. The benefit of this, as I learned while reading Vonnegut, is that sometimes the conversation with a single author can invoke a bit too much familiarity with their voice, depending and depending, and that sort of alternation might then prove helpful.

I’ve not read all of Samuel Delany, and so perhaps this is the year. I’ve not read all of Octavia Butler, and so perhaps this is the year. Roll on 2023.

Being interestingly wrong

•11 December 2022 • 1 Comment

We are coming to the end of our teaching term; we have one week of teaching left, before the University closes for its Christmas break. And for me, this is always a time of reflection; looking back over the past weeks of working with students and thinking about things to work into the teaching for next year.

One thing that I always reflect on is that the students are seeing the material we’re covering for the first time. I’ve taught this particular class for ten years now, and one thing I need always to bear in mind is that while I have an opportunity to continue to develop my understanding of the material, I must always remember that the students won’t have had that opportunity.

And so I need to allow them to be wrong, to miss connections between different things or to not understand why we’re taking a particular approach. And I would like them to have the opportunity to be wrong, because we learn a lot when things don’t work as we expect.

This ties into an old thing from aikido, that we don’t learn as much when things are going well. When the arguments make sense, when the techniques are working, we don’t learn. But when the arguments remain in shadows and we struggle, when the techniques aren’t moving uke and we struggle, we then need to think through the details of what we’re doing and that’s where we learn.

Another aspect of this, when we’re struggling, is to take advantage and to be wrong in interesting ways. And this is a reasonable goal, I think. We will always be learning things, and part of the process of learning is to explore and make mistakes during that exploration, but why not be wrong in new and unusual and interesting ways.

After all, why spend my time and effort, only to be wrong in a way I’ve done before.

the koan as a lens

•20 November 2022 • Leave a Comment

Last week, I wrote about the Art of the Question. As is often the case, the act of writing served to agitate the settled bits in my brain and the ideas have continued to ring in my head.

There is one particular form of question that I’ve always been partial to, and that is the koan: so, what is the sound of one hand clapping, and all of its kin. But what are the koans that run through my days?

Or viewed slightly differently, what of the questions I’m searching for, so that the answer becomes clear from the form and wording of the question, and can I form that question as a koan? I don’t yet have an answer to that, but it’s an interesting lens through which to view this whole process.

I’m not sure of the extent to which this is formally true, but I’ve always viewed a koan as an almost unanswerable question, whose purpose is to generate contemplation. This is how I’ve always viewed the one hand hand clapping question.

What I’m finding very interesting at the moment is that despite the readings I’ve done over time, this idea of using the koan as lens is not something I’d thought of doing before.

What might be the koan of the finitely generated intersection property, for instance. We (the collective we) have a reasonable understanding of this property though there is much we do not yet know. But I don’t know what the underlying koan might be, or if I wander into the forest of recursion, whether this question of what the koan might be, is itself a koan?

And what might be the aikido koan? This one is especially fascinating, since I’m not sure what the question to be koaned might even be. And so all I can say at this point is, the contemplation continues.

the art of the question

•13 November 2022 • 5 Comments

When I was young, I came across the statement, the belief, that if one were to phrase a question just right, then the answer would be obvious. I’ll admit that I’m not sure I ever actually believed this, but it’s something that I’ve always carried with me.

Looking back, I can see that this belief has always lurked in the background of my mathematical life. If we can find the right way of asking the question, then we will be able to see the path to the answer. But it has always been in the background, and this is not a danger free path. It is possible to spend a lot of time looking for that correct formulation of the question but never then get to the question itself.

This is a more interesting line of enquiry (inquiry? I need to remind myself again of the distinction) when I think of aikido. I’ve been studying aikido for a few weeks more than a quarter of a century at this point, and what’s interesting there is that I’m not sure of the question I’m trying to answer.

I didn’t begin aikido with a question. I began aikido because I’d always wanted to do a martial art, and I found myself with time I need to fill and a friend who was in the local aikido club, and once I started it just took. I’ve enjoyed it since and I enjoy it still, and I’ve moved through the ranks at a reasonable pace, but I’ve now (probably long since) reached the point where I am asking the question, why.

Why this among all other things, and going back to the beginning of this rumination, that isn’t the right question. Why in general is a strange question, because it’s so very non-specific a question. How can I move in a way to move someone else, is a better question. It’s still not the right question, but it’s closer. The quest continues.

Writing is more like mathematics, in that there isn’t a single question. In both, I have a number of different directions of wanting to understand. With mathematics, I want to understand structure, how this particular thing came to be, though there are many individual questions to formulate here.

But with writing, my questions are much less coherent. The human condition is complicated and multifaceted, and writing is an exploration of that condition. There are so many questions, from how we get through individual days to larger meaning.

Looking back, I can see that I’m still dancing around the formulated specific questions; I can see the things I want to understand, on distant hilltops, and I’m still working to formulate the questions that set out the paths to be able to find their answers.

the size of the multiverse

•23 October 2022 • Leave a Comment

I’ve been thinking recently about the size of the multiverse, and how we experience the multiverse in movies. It’s showing up a lot at present, particularly in the Marvel Cinematic Universe, as well as older shows such as Sliders.

The reason, or a reason, why I’ve been having these thoughts is that I think the multiverse has to be much more complicated than what we’re seeing in its representations. And this comes from some nineteenth century mathematics due to Georg Cantor.

My understanding of the standard interpretation of the multiverse is that at each moment, reality branches to take into account all possibilities. One issue with this description is that at each moment, there are infinitely many possibilities, and so the structure is remarkably difficult to imagine.

There is a way of approaching this structure, but there is a piece of information we need first. Namely, if we have an infinite branching of possibilities at each moment, then one question we have to ask is, which infinity.

And this is the piece of nineteenth century mathematics. Infinity is not a unitary concept: there are multiple sizes of infinity. Strange, yes? But more than this, we mathematicians have a machine for comparing infinities, and a machine for generating a larger infinity from any given infinity, and other questions such as whether there are infinities between the ones we can construct using our machine.

But in movies and in television, the multiverse is often portrayed as a discrete object, the different universes separated from one another and labelled. And I’m happy to agree that this might be easier.

But one of the thoughts I can’t shake, one of many, is how it might be possible to describe the multiverse in a way that takes all of this on board, for an audience that may not have had exposure to this reality of multiple different infinities.

Challenges, oh all the challenges. Perhaps this story has already been written and I just haven’t come across it, and if this is the case, please do let me know.

the inverse TARDIS effect

•16 October 2022 • Leave a Comment

Over the course of my days on this Earth, I’ve seen a few episode of Dr Who but it wasn’t part of my science fiction heritage growing up. That said, I’m familiar with some of the basics and I’ve always been taken with the idea of the TARDIS.

While the TARDIS is a masterpiece of engineering and design, my focus here in on a particular aspect of the TARDIS, namely that it’s much larger on the inside than it appears from the outside. There are structurally similar ideas elsewhere. For instance, there is the bag of holding in Dungeons and Dragons, and the different manifestations of the portable hole.

But the idea of the inverse TARDIS effect first came to my attention some years ago, when I was moving from a smaller office in the Maths Tower to a larger room, and I found it difficult to fit into the larger office, everything that had fit reasonable well in the smaller office.

On a rational level, I have a clear idea of what might have happened. Perhaps I had more shelves in the old office and perhaps I had more cabinets. But regardless, in conversation with colleagues, they also expressed some experience with this effect as well.

But I think the inverse TARDIS effect is much broader than just its application to physical space, whether offices or moving house. It also applies to time.

Again, there is I think a rational explanation. When I was in a major administrative role, the small moments in the day, 15 minutes here or half an hour there, were exceptionally valuable, and I had to make good use of them. But now, out of that role, there isn’t the same external pressure to make best use of those small pieces of time through the day. For me, the external pressure made it easier to focus, and it’s been a relearning process to get myself back to the point of using those small pieces of time well.

Anecdotally, colleagues have mentioned that retirement can be similar. I suspect, fueled by a lack of personal experience, that this might be similar to the previous example; fewer constraints on time allow for the other activities to expand to fill the available time, no matter how much time there is available.

And this then raises the question, which only occurred to me as I was writing this, of the extent to which the inverse TARDIS effect is related to Parkinson’s law, that work expands to fill the available time. But that I think is a question for another day.

strange questions I don’t have the time to work through

•9 October 2022 • Leave a Comment

The new academic year has started and teaching is going well. But between the teaching, working through the mathematical questions on the list, aikido and the various writing projects, and life, there isn’t the time to ponder and speculate on the random questions that meander through the alleys of mind.

And so I thought I’d put a few of them down here. It may be that these questions have been explored to some greater or lesser extent by others, in which I would appreciate the knowledgeable reader dropping a comment and pointing me to some appropriate references. But even if not, I’d be interested in any thoughts you might have.

1. Chess has an interesting ranking system, in which a player earns (acquires perhaps) a ranking based on the rankings of the players they defeat and the players to whom they lose in combat on the 8×8 arena. From what little I know (I know the rules of chess but I don’t play enough to have a ranking), this ranking is dynamic, and so here’s a question.

There is a significant body of evidence that one of the impacts of covid-19 is shorter or longer term cognitive impairment. Has anyone conducted a study, correlating changes to chess rankings with (perhaps self reported) covid-19 infection. It might be difficult to do something retrospectively, but it seems to me that there might be an interesting project here, even if it were only to get underway now.

2. I have an old question that is set out here

3. In English, ‘we’ is a remarkably nuanced word. There is the ‘we’ of me and you but not them; there is the ‘we’ of the collective of all of us now alive on Earth; there is the ‘we’ of everyone who is or has been; there is even the ‘we’ of me and none of you but unnamed others; and others as well.

So here’s the question: to what extent does the story of human civilization run parallel to the broadening the definition of ‘we’. Naively, I think there’s an argument to be made that ‘we’ would have been an extraordinarily interesting word in early human cities, when we were used to living in much smaller, much closer groups.

What for me is particularly interesting at the present time is how acceptable definitions of ‘we’ seem to be narrowing. Or at least, that’s one way of interpreting some aspects of the news.

4. And then there are doomsday devices, for instance money and agriculture, which I haven’t thought about in far too long.

the beginning of a new academic year

•2 October 2022 • Leave a Comment

Teaching begins tomorrow, the first day of the new academic year. That isn’t entirely accurate; students have been arriving on campus for a week or more, and this week just past was fresher’s week, induction, orientation and lots of students trying to pair square images on a map with the brick and concrete and wood buildings around them.

I’ve been teaching this particular module for several years now, and I’m always amazed at the strange dance between its continuity, in terms of the material covered and its basic structure, and the difference between years in terms of the personality of the students, as a group beyond as individuals. I meet them tomorrow and I’m looking forward to getting to know them.

Beyond this, there are other changes. Administrative responsibilities, committees and working groups and the other connective tissue of university life, pick up again. Seminars restart in earnest, each of them bringing new ideas, new faces, new math, and what could be better than learning new math.

This all ties a bit into my previous reflections. We of necessity bring with us the shadows and echoes of everything we’ve experienced, and it’s hard not to let all of that that’s past color the present and near future too much.

I find this particularly important when teaching, whether teaching math or teaching aikido. This is a point that I’ve worked through a lot and I’ll continue to work through, but beginners are encountering all of these things for the first time, and I can’t let the fact that I’ve been doing them for years, teaching these things for years, get too much in the way of me trying to bring the beginners along.

And so, the work continues.

beginner’s mind

•25 September 2022 • 2 Comments

We are a week here from the beginning of teaching in a new academic year. I’ll have new students but I’ll be teaching a class I’ve taught for many years at this point, and as always I feel that it’s a good idea to reflect.

I’ve reflected on these points before, over the years, because I feel they are important points for reflection. One is the notion of distance: as my understanding of the subject increases, as it necessarily will each time I teach, I need to work to remind myself that the mathematical distance between me as teacher and my students as beginners increases, and the responsibility of bridging that gap lies with me as the teacher.

Part of how I deal with this is to try and put myself in the position of being a student seeing the material for the first time, and this can be a tricky thing to do. But it’s a challenge I enjoy, because that approach can expand and enhance my own understanding of the material.

But for me, and this isn’t anything original to me, beginner’s mind goes much deeper than this. A different arena will be the aikido classes; again we’ll have beginners, and again I’ll need to put myself in the mindset of a beginner.

What’s interesting to me is that aikido is something I took up as an adult. I’ve always approached aikido with a degree of awareness that I didn’t have as a high school student (or before), taking math classes. One result of this is that I’ve approached the two subjects differently, in that I am much more consciously and deliberately aware of the aikido basics than I am some of the mathematical basics.

And perhaps this is part of things, that being aware of basics but not being enchanted by the basics is part of the path to achieving a beginner’s mind. After all, part of what we need to do is to achieve a bit of (a different sort of) distance from what we know, because what we know can be a barrier to the mind of a beginner.

My work on this will continue. There is great value for me in this work, because it makes me a better teacher, and it also makes me a better student.

supervillainry revisited

•4 September 2022 • Leave a Comment

I’ve been thinking a lot recently about supervillains. Too much perhaps, but I do find them intriguing. As a side note, it’s clear to me that there are no actual supervillains, as one would surely have made their presence known by this point in time, though perhaps that’s just wishful thinking on my part.

Most supervillains, in the Bond universe or one of the comic book universes, Marvel or DC, want to take control, of the planet or something larger. (Interestingly, Thanos from the MCU is an outlier from this point of view, because he had an objective other than total control, achieved that objective, and then retired to a cabin in the woods, for all the good it did him in the end.)

Why. This is the question that’s always intrigued me. Why take control. Why be the boss, for instance, of Earth. I’m reminded of the character from the Hitchhiker’s Guide to the Galaxy, living alone, not even clearly understanding the decisions he’s making (if memory serves; it’s time for a reread of the extended trilogy). But one of the aspects of their characters that we don’t often see is why they want to be in charge of all things.

Perhaps it’s just that I’m relying on my own memory at this point and there is investigation that I need to do; a Bond marathon might hit the spot, once I’ve managed to make my way to the top of Task Mountain, as might the chronological rewatch of the MCU, movies and series combined.

But my memory is that absolute power had become its own end, and I have to say that strikes me as remarkably unsatisfying. Being in charge of a country, much less the whole planet, takes a lot of work. It’s not for the faint of heart.

Our superheroes exist in counterpoint to their super foes; they spend their time fighting to prevent their corresponding supervillains from achieving their nefarious (love that word) goals, but we don’t often see superheroes tackling the problems that some people, many people face: thirst, hunger, shelter, making the most of their time on this round rock of ours.

And so I’m pondering, as the clouds gather outside (literally in this case, as we have rain coming in our direction) and as the light of day fades, the liminal space between superheroes and supervillains, where we have combined the desire of supervillains and the morality of superheroes, and things magically become better.

And then I stop myself. Supervillains, like superheroes, are fantasies, creatures of our imaginations that have little to nothing to do with what we’ve done today or what we’ll do tomorrow. (At least for most of us. 😉 ) There is work to be done, and it won’t be done for us by the Son of Krypton. So let’s shift the wording a bit. There’s work for us to do.

reflections on aikido

•21 August 2022 • Leave a Comment

Almost exactly 25 years ago, I began my aikido journey. Just over a week ago, I reached one of the major milestones towards which I’ve been working for all of that time; I successfully made it through my last grading. This isn’t to say that further advancement up the ranks isn’t possible; it just won’t involve me standing in the middle of the tatami, being watched by all as I take bokken and jo away from attackers, for instance. But hitting this milestone got me thinking.

One immediate direction of thinking is that I find it helpful to have goals in mind, milestones to work towards, shining cities on distant hills towards which I’m making my way. And so, I need to develop some new milestones, and I have some ideas for what those might be but that’s not what I’d intended to explore today.

Rather, I wanted to explore some of the connections I’ve found between aikido and other areas of activity in my days. This is something that I’ve touched on from time to time. (I won’t give a complete list here, but if you’re interested, you can find them by clicking on the aikido category in the right hand menu of the home page.) Many of these have some connection to teaching, as I do spend some significant time in these pages thinking about issues related to teaching and education, but there are others.

One of the basic principles of successful aikido, I think, is maintaining contact with the attacker (or receiver of the action). And what I mean is not physical contact, but a wider, more enveloping sense of contact. I’ll admit that I’m not entirely convinced that contact is the best term, but it’s one that’s commonly used within the wider aikido community.

This is one of these aspects, though, where the language can be a bit tricky, in the sense that the notion of contact I am thinking of here is something that’s partially non-verbal, having been developed over those 25 years of regular practice. This is something I wrote about so long time ago (see here and here), and I’m aware that I need to go back and look through those old posts again. (Indeed, one project on the LIST OF MANY PROJECTS, and one I may have mentioned before, is to go back and read all of those old posts and pick up the threads I’ve left half woven.)

There are different levels of contact at play here, but the basic idea is that I as one part of this particular dance have an understanding of the attacker’s (or attackers’) intentions, but not in such a way that they have that same understanding of my intentions. This notion of contact has relevance elsewhere, such as in teaching (between a teacher and their students, gauging for instance how well the students are grasping the material being covered or even whether they’re paying attention in a session) and in writing (between an author and their audience).

This reuse of standard words to mean something different and something specific to the given activity is something that I’m well familiar with, because we do this all the time in mathematics; we take words (regular, normal, map) and given them a technical mathematical meaning that sometimes has little to do with their standard meaning, though there is often a connection however diffuse it might have become.

Back in the day, as part of preparing for my shodan (first degree black belt) grading, I had to write an essay on Aikido in Daily Life. I remember what I wrote (and no, it’s not a piece of writing I’ll share) but it’s also a question I’ve been thinking about ever since, and for me it ties directly to where I started off this ramble. Some of the lessons from aikido that are applicable to daily life are somewhat straightforward (not least, first get out of the line of attack) but there are others that have become more apparent over time. And that’s what I’ll spend some time exploring over the coming weeks.

the individual versus the collective

•31 July 2022 • 1 Comment

One of my favorite non-human races in Star Trek is the Borg, a collective intelligence that assimilates any member of any race that it encounters. Resistance is futile. I still carry the time-tempered memory of the first time I watched an episode containing the Borg, and I was fascinated by this idea of the true collective intelligence (and yes, I will admit that the introduction of the Borg queen did make me sad, but that’s another conversation).

I can recognize that many people view the Borg as a villainous race, breaking down the individual as they do, giving the collective a higher value over the individual. But I’m starting to wonder.

If we consider climate change, it is becoming more and more clear that agreed collective action is needed in order for humanity to survive in anything like its current state, and at present that collective action is still halting. This haltingness is part of the news every evening, and yes I do have the news on in the background as I’m typing this.

A basic theme of Star Trek is that we have learned to act for the good of all, even when the good of all doesn’t agree with the good for the individual, though many of the episodes still involve working through the issues inherent in such a way of being. Star Trek is far more utopian than dystopian, as opposed to some others, but even then the utopia hasn’t yet been firmly established.

So there is a balance point to be found, a shifting dynamic balance point at which there is no rest but only a constant surfing on difficult waves and the constant work of maintaining balance on unstable ground.

What’s interesting is that this then ties into aikido, in the sense of maintaining balance while under stress. But that’s only a side thought, the mechanisms of maintaining balance.

This conversation between the individual and the collective has been going on since the beginning of conversation, and I don’t know what at present I have to offer that conversation. But I can see that I have a lot of homework to do, as do we all I think, And that work continues.

reflecting on a story I once heard

•10 July 2022 • Leave a Comment

There is a story I once heard, for the first time many years ago. Time and again I’ve encountered this story, like commuters with a nodding familiarity with one another but never speaking, but I’ve been thinking about it a lot recently, in the light of current events.

Kurt Goedel was one of the great mathematicians of the twentieth century, a logician, an explorer of rules and the consequences of rules. For me, his incompleteness theorem is one of the great mathematical theorems of all time, an unexpected result and one that continues to ring in me, even though logic is not an area I’ve spent any time exploring.

The story I heard is known as Goedel’s loophole. The short version is that one his way to become sworn in as a US citizen in 1947, with Einstein as one of his witnesses, Goedel expressed the view that he had found a legal constitutional way for the US to become a dictatorship. Goedel seems to never have written down his loophole and so we don’t know precisely his proposed loophole was; I suspect, and this is a very personal view based on what little reading I’ve done, is that he may have found a formal route but not one that was necessarily a political feasible route.

But reading the news and watching the events of the day, I’ve been wondering about the security of constitutions written and unwritten. The US has a written constitution, both the original document and an ever expanding body of interpretation around that original document, going back to the Federalist papers. The UK has an unwritten constitution, and for both constitutions (and other constitutions underpinning national governments around the world), there is an inescapable question, just how secure are these constitutions.

For me, and again this is a very personal view, we as humans like to set formal rules for our behavior, back to the Ten Commandments and the Code of Hammurabi, and we then like to spend enormous amounts of effort thinking about the fractal hinterlands of these formal rules, and where precisely the boundaries are between acceptable and unacceptable behavior within that set of formal rules.

I’m not surprised that I find myself pondering these fractal hinterlands, if only because I’ve spent some time thinking about the nature of fractal sets in my day job as a mathematician.

The rules underpinning fractals often appear to be simple rules, but one common property these sets of rules have is that very small changes of inputs can result in widely and wildly differing outputs. So for instance two mathematical cases with similar but not identical sets of inputs might result in very different outcomes; this is why the Mandelbrot set is so delightfully complicated on smaller and smaller scales. Two legal cases might have similar but not identical sets of facts but end up with very different outcomes.

Seemingly simple sets of rules, so for instance John Conway’s game of life, can result, perhaps often result, in complicated behavior. And this same basic observation seems to apply not only to mathematical sets of rules but also to legal sets of rules, and that this includes sets of rules such as national constitutions.

Looking back, I’ll admit that I’m not entirely sure of the point I was trying to make here. Perhaps it’s that we need to acknowledge and respect and understand that any set of rules will result in difficult cases of similar inputs resulting in widely different outputs. Perhaps it’s that a naive faith in seemingly simple sets of rules to provide clear answers will never be satisfied. Perhaps it’s a plea, for sources of reading where legal scholars have taken Goedel’s loophole as a serious subject of inquiry, because I’m curious.

a meditation on story

•5 June 2022 • 2 Comments

I’ve been reading a lot of short stories over the past few years, and I’m a fan. I like a novel (or a series) and I’m always up for some non-fiction, but I think my heart will always be with the short story. I can remember going to used book stores when I was in high school and focusing on old beat up science fiction short story collections. And I will always have some minor regrets that I didn’t keep them all, even moving across oceans.

I remember literature class in high school when we talked through the structure of story, with rising action and then the climax of the action, followed by the denouement. And I love a story that nicely subverts this classic structure.

There are some stories that continue to ring with me, like The Lady and the Tiger, with its beguiling ambiguity at the end. I won’t list all the stories in this category, but beyond the stories whose title I remember, there are other stories, their title long forgotten, whose core idea is still one that rings.

One that still rings particularly strongly, perhaps after having been an associate dean for some years, is a story in which the humble bureaucrat saves the day and gives new life to an alien species whose planet we’ve taken, all the while leaving no fingerprints of his own on the critical decisions.

I like how some basic ideas echo through stories over the years and the decades, but this leads me to think what it says about us that these are ideas that continue to echo. One of these, loosely put, is that we as humans aren’t able to organize ourselves to do well by ourselves, and so we require an external threat to bring us all together. And while I’m not meaning to be pessimistic, but recent world events lead me to think that this basic storyline is one that we might need to rework.

But I’ve been thinking through my own stories that I’m working on, and one thing I find interesting there is the extent to which some of these old ideas echo through what I’m trying to write. Can I do justice to some of these ideas that I can only think of as classic ideas? I would like to think I can, but that’s still a road I’m walking.

But interesting things sometimes happen. There is the occasional idea that seems as though it might lead to an uncomfortable ending. And the question becomes, do I want to work through this idea, among all possible ideas, because there are lots of ideas. And to this, I think the only answer can be, does that idea lead to somewhere sufficiently intriguing to make the journey worthwhile.

And so, stories. We have always been story tellers. We entertained each other by telling stories born from the stars overhead, to each other as we sat around fires we’d wrested from nature. Long let the stories continue.

the many variations of we

•29 May 2022 • Leave a Comment

This is going to be a bit of a ramble.

Some long time ago, I read something about the word WE, namely that there are human languages that contain different variations of we, and once we start to think about it we can see there are many different variations of we. What follows will be a bit self-referential, but often I’ll be using the variant of we that includes everybody, which admittedly is somewhat presumptuous of me.

Let’s suppose that you and I are talking in a room (and isn’t it strange that writing ‘I and you are talking in a room’ sounds so strange to our ear). There is the we consisting of me and you but not the people outside the room; if there are many people in the room, one we is me and some of the people in the room but not the others, and if we wish to count this consists of many possibilities. And there is the case of me and some of the others in the room and some of the people outside the room. If I am talking to you, then there is the we of me and someone else but not you. And we bring all of these different possibilities into a single word.

This requires of us some skilful navigation in conversation, the work in understanding which variant of we is being intended every time the word is used. This is an unavoidable piece of work, because it’s not possible for a language to include all possible variants of we, since if we were doing to be complete, we would require a different variant for each subset of humanity, at least each subset of humanity containing me, and that is just a vast number of possibilities. It’s a number we can calculate, and it’s a number that’s so large as to be virtually infinite.

But what does this mean? One possible meaning, one possible lens, is that each of us lives in the center of an expanding and overlapping circle of variants of we. And so what if the meaning of civilization is that we need to view the world with the larger circles of we, rather than the smaller circles. Biology persuades us that we need to take small circles of we, because in the rough and tumble of natural selection, smaller circles of we allow us to better ensure our survival. And so we need to fight our biology, train ourselves to see past the darker voices of our biology.

And now I want to make a strange connection, to the fictional Vulcan Surak. I’ve mentioned Surak in a couple of other recent posts, in reading with hindsight: Superiority and beware the shiny and in how distant others might see us – the tragedy of the commons. In our stories, Surak sees a path for Vulcan to survive its biology, and so should we be seeking a surakian path of our own. Is this perhaps why we, here the non-specific global we, have the story of Surak as part of our collection.

I don’t know quite what to do with this connection. It’s a connection I’ll keep pondering. I’ll continue my reading what I can find, to work towards the understanding of how our brains work and all the tricks our brains play on us. Long is the road, and hard, that leads from darkness into light.

reading with hindsight: Superiority and beware the shiny

•8 May 2022 • 1 Comment

I recently reread the Arthur C Clarke story Superiority, which is a story I’ve always enjoyed. An outline of the story is that there is a war, in which one side (represented by the narrator) embraces technological innovation, fancier and fancier weapons, whereas the other side (represented by the victorious side in the war) makes good use of existing technology.

The first lesson I took from the story, which is I think a common lesson to take, is that sometimes we have to beware the shiny. That is, making use of untested new technology in a time of stress might not be the best of all ideas.

But there is a bit more there than this; the use of this new technology can become a trap. Once we start down that path, as the losing side did in Superiority, it may not be possible to revert to the old, well tested, tried and true technology that we eschewed in our pursuit of the shiny. In this way, the shiny can almost become something of a doomsday device, in that once we start, we cannot then stop.

Just over a year ago, Dyke, Watson and Knorr wrote in the Conversation about climate change, the rise of the gospel of net zero (my words, not theirs) and the growing move towards narratives of technological salvation. They are climate scientists and they have been thinking about this for a lot of time, and their articles resonated with me, particularly in this rereading of Superiority.

I will admit that I’m still working through the consequences of this juxtaposition, but this resonance seems to be strong, and the distant memories of physics experiments past and the Tacoma Narrows bridge all combine to make me nervous of strong resonance.

We live in an interesting time. We are able to build great machines that do great things and advance the cause of human civilization, but I am struck by the old thought that perhaps we are not yet capable of wielding these machines and this technology sufficiently well to keep ourselves out of trouble.

This is also an old idea, that our ability to make tools outstrips our ability to use those tools, and one that I have a distant memory of reading about in John C McLoughlin’s Toolmaker Koan, which I read many decades ago now (and which I hope I’m not conflating with another book).

The basic idea of Superiority, as I read it, is slightly different. It’s less that we can’t wisely use the tools we build, it’s that the tools we make don’t actually do what we need them to do and it might be too late once we figure that out. But the two ideas are close, and I think they are very important to us in our current world, this current civilization we’ve constructed.

This also ties, at least in my head, to the Surak moment of the Vulcans in Star Trek, which I suppose can be viewed as one way of working through this particular koan. I’m not persuaded that we in our current state would be able to take the Surak path, but given everything we now know, we do pick our own path to get through our current crises.

stories of Zen: every minute Zen

•2 May 2022 • 1 Comment

I’d like to pick up a thread that I’ve let sit fallow for too long, longer than I’d intended. This is a thread I’d previously written about here and here.

Number 35 of the 101 stories that make up the first part of Zen Flesh, Zen Bones compiled by Paul Rips is called Every Minute Zen.

The summary: Tenno had passed his apprenticeship and was visiting the Zen master Nan-in. It was raining and so Tenno had an umbrella. Nan-in asked whether Tenno had set his umbrella to the left or to the right of his wooden clogs, and Tenno couldn’t remember. This raised doubt in Tenno’s mind, as he wasn’t able to keep his Zen with him every minute, and so he became Nan-in’s student.

So why do I like this one? We’ve each experienced those moments when we’ve done something, and we know we’ve done it because we have the evidence of having done it, but we don’t have a clear memory of the process of doing. I’ve had aikido moments like this, particularly in tradings, and in retrospect it’s a strange experience.

But the world is a busy and complicated world, and it is difficult sometimes to maintain awareness, to maintain mindfulness, amidst the chaos of the world.

At this particular moment, I’m aware of how I’m sitting. I’m aware of Buttercup using her scratching post, and the fading light outside as the day winds down to evening. I’m aware of the unceasing weight of the persisting pandemic and the other events that fill the news.

I find local mindfulness to be somewhat easier than global mindfulness. It’s hard to keep the whole of the world in mind. It’s hard to properly consider the world. But I can do more work on my local mindfulness.

For instance, I had a stretch earlier this evening. During my stretch, I try to pay attention to what’s going on inside my skin, because I have always felt that a stretch is a conversation that I have with my muscles, my tendons and ligaments, my bones, and it’s a conversation that I always want to remain calm and measured, with no yelling.

This evening I’ll pay attention to my dinner, bite by bite, and in the morning I’ll pay attention to my coffee, sip by sip. And I’ll pay attention to the individual moments as they step by, and some days that’s all we can do.

And this is what this particular story has stirred up in my brain. There’s always something more to work on. Something more to do. And this provides some direction to our days.

the 2022 reading project: Jade City by Fonda Lee

•24 April 2022 • Leave a Comment

Let me start by noting that unlike many of the other reading project posts, there is a genuine spoiler alert here. Beware. If you haven’t yet read Jade City (and Jade War and Jade Legacy), they are awesome and I recommend them very highly. So go forth and read.

And I am behind on my 2022 reading project. I’d set reading through this particular list of the best 100 fantasy novels back at the beginning of 2021, but needless to say, the world got strange, through 2021 and so far through 2022. And taking heed of a piece of advice I’ve taken to heart when working with others, I’m giving myself a bit of a break and seeing what I can do on this through the rest of 2022.

Admittedly it is only Jade City that is on this particular list, but the entire trilogy, often called the Green Bone Saga, is on the 2022 Hugo award shortlist for best series and so I decided to read the whole trilogy (and I’m glad I did).

This isn’t a book review blog, but there was one thing that caught my attention in this Saga that also caught my attention in the Star Wars universe. The Green Bones were trained from childhood in the use of bioenergetic jade, focusing on six basic disciplines (channeling, deflection, lightness, strength, perception and steel). While there were some shortcuts that non-Green Bones could take, mastery required training and dedication from childhood.

The same type of training and dedication were required in the Star Wars universe for mastery of the Force. And this brought to my mind a question: if the focus were not on the use of jade for fighting, what other sorts of aspects of jade might be possible to develop. This is hinted at in the use of jade and channeling for medical purposes. I can’t help but be curious about what other things there might be, for instance through the penitents.

With the Force, my question is slightly different. Again, we get a hint of this through Yoda, and this might well be something explored somewhere in the extended Star Wars universe, but what might a very long lived being (with a life span measured in millenia, rather than decades or centuries) be able to discover about the Force.

There is for me a lesson here. though perhaps lesson is too strong a word. There is an observation here. Each story spawns a collection of other stories. Each idea calls forth other ideas, and it’s not possible for an author to explore the whole of this landscape. And each reader will have a few things that will catch their attention and that will pique their imagination.

thinking about issues of scale

•22 March 2022 • Leave a Comment

I recently went deep back into the archives and read an old post on the number liberation front. The attempt at humor aside, there was a serious idea tucked away therein. Namely, that how we view a concept (in this case, a number) depends on how that concept is presented to us. In this case, the difference in presentation of a number as a word or as in digits, and the view that presenting large numbers as words (million, billion, trillion) acts as a shield to their true size and scale, given the similarity of the words used.

I can’t claim this is an idea that’s original to me and I suspect (though my reading here is still wildly incomplete) that this is something commonly known in psychology circles. Perhaps it’s related to issues of cognitive load and what our brains can properly handle, and I’m sure there’s a good idea for a story about first contact with an alien species, where we as humans don’t have the cognitive capacity to understand the aliens and what we then have to do to mitigate this.

But this is one facet of the larger issue of how we handle discussions and contemplation of scale, particularly when the scale gets very large. We develop tools to help us handle these, and one example of this that I find very interesting is how mathematicians handle the infinite. To some extent, the infinite is the ultimate scale problem, particularly when we touch on issues like the different sizes of infinity, the infinitude of infinities.

For this, we have developed a structure of notation and conceptual tools that allow us to manipulate and explore infinity, but there is a small part of me that wonders what we’re missing. Are there aspects of the infinite that we haven’t yet encountered, perhaps that are shielded from us by the very conceptual framework we’re using to explore the infinite. And this contemplation I find exciting and interesting, because there is always something more to do.

But this is only one small example. When we consider the world in all its glorious expanse, I find it hard to wrap my head around the whole of it, and to understand what direction to take moving forward, out of all the many possible directions. The scale issue here is that the space of all possible futures is a wildly massively high dimensional space, and we are navigating a path through this space.

There are lots of difficulties with this process of navigation, only a few of which I’m sure I have sight of at present. Do we for instance want our path to be a geodesic path, one that best reflects the changing geometry of this space of possible futures. But this requires that we’re able to get a handle on this changing geometry, and that then runs back into this issue of scale and being able to capture and reasonably manipulate the amount of quantity of information needed to understand this space.

And this is one of the things I most love about being a mathematician. We have the opportunity to explore such spaces and to develop the tools to understand such spaces, and there’s always another horizon over which to journey.

how distant others might see us – the tragedy of the commons

•20 February 2022 • 2 Comments

I consume a fair bit of the news of the day, as I expect is true for others. Some of this news I read, some I watch, some I listen to; after all, the world is a complicated place, and when I sit and ponder the state of the world, I feel that I should be as reasonably informed as possible.

Looking out at the world, there seem to me to be some loose commonalities. One of these, and one that has been explored by humanity as long as we’re explored anything, I suspect, is the tension between the individual and the collective.

That is, what’s good for an individual might not be good if applied to everyone, and this we see played out in discussions of resource consumption, our impact on our planet, the phenomenon of climate change and much else that drives the news. Admittedly, there are situations in which we have developed and applied resolutions of the tragedy of the commons, but clearly we have not resolved all such situations.

One aspect of this tension comes out in the tragedy of the commons, but this is only one aspect. As tempting as it might be to put down my own thoughts on this particular tragedy, I want actually to go down a different path.

And this other path is as much as anything a question, and this question comes from a weird collision of the tragedy of the commons and Star Trek. In the Star Trek universe, we can caricature the different interstellar humanoid species with single word descriptions: the Klingons are war-like, the Vulcans logical. Perhaps the Andorians are duplicitous.

But if we consider how they might view us, what would be their brief defining characterization of humanity? Might it be that we are defined by the tragedy of the commons and our lack of clear and universal resolution of the tragedy of the commons, of this tension between the individual and the collective?

Or to phrase it another way, do we need to have a Surak-type revolution in how we think? I hold the view that we do not yet understand ourselves well enough. I’m sure for instance that should we encounter an alien species with which we can communicate, part of what we’ll need to do is to make sure that that species has no access to research on human psychology, marketing and advertising, et cetera, because of how they might be able to exploit all of this in their dealings with us.

So perhaps at a deep level, part of the solutions to some of these issues we’re collectively facing, the corners into which we’ve collectively painted ourselves, is to develop this better understanding of ourselves, because this is how we resolve the tragedy of the commons.

Or perhaps I’ve just watched too much Star Trek over the course of my days.

the administrative bends

•12 February 2022 • 1 Comment

For the past eight years, I’ve held a significant academic administrative role in the university, that of Associate Dean Education for my Faculty. I very much enjoyed the role; hard work but enjoyable work, and I took advantage of the opportunity to get more engaged with the wider work around the university.

The end of last month was the end of my time in the role, and it’s been an interesting couple of weeks. The associate dean role came with some amount of pressure. There was always something to do; always another meeting in the diary; always an email that needed a response; always a question that required consideration. And over the past eight years, I got used to that constant external pressure.

And now, that pressure is gone. There are still some things that require time and attention in the short term, things that remain uncompleted that remain for me to work through. There are some things that I got involved in that I’m remaining involved in, which are not directly related to the associate dean role but where I suspect being an associate dean caused my head to poke above the parapet.

But the email traffic has significantly slowed down and there are far fewer meetings in the diary, and this is where the title comes from. This very quick release of the external pressure of the role has given me, for lack of a better term, a case of the administrative bends.

There is still a lot to do: I’m transitioning back into being a working academic mathematician. I don’t have any significant teaching in the second semester but I have a long long list of research projects with which I need to renew my acquaintance, and with which I want to renew my acquaintance, and that’s a road I’m starting to walk down.

But it is interesting. Looking back, the external pressure of my former role provided a structure, doing work between the meetings and other requirements of the role. And now that structure, that skeleton is gone, and it now falls to me to remember how things were before.

I will miss the role. I will miss the way that it helped me, required me in fact, to interact with people across the university in a way that I can only hope to replicate (to a lesser extent) through other work.

But I also look forward to the change of role. I look forward to doing more teaching and getting back to my list of questions of interest. But I can tell that the battle against these administrative bends will take some time and some effort.

I can see, looking around, that this phenomenon isn’t uncommon in universities, where particularly the academic staff move between roles, taking on larger academic-related administrative responsibilities and then giving them up. Slow decompression isn’t always an option, and it would be interesting to hear from others who have experienced something similar and whether they’ve found a good way to ease the bends.

legacies in old lists

•23 January 2022 • 1 Comment

I am looking for a word, and I’m not sure whether that word even exists. As I’ve written about on several occasions, I’ve been spending some time recently going through old lists, doing occasional pruning, and bringing my collection of many small lists into one single list containing all listable things.

One thing I’ve learned through this exercise of list consolidation is that I do like my lists. Lists upon lists upon lists and I keep finding lists, tucked away in places I didn’t expect to find old lists. And it is also interesting the extent to which I am circling around a few ideas that keep rearing their heads in these lists.

But the word I’m looking for is a word describing an item that keeps getting moved from one list to the next, never acted upon. And yes, the reason why such a thing exists is in part my old fried procrastination, the not grasping of that particular nettle. But here, I want to highlight the difference between the why such a thing exists, and what that thing is and how we denote that thing.

It’s not quite a fixed point, not in the way I understand fixed points from my limited engagement with dynamical systems. That it, it’s not that I’m transforming my life one day to the next (acknowledging a subtle and unintended pun here), or one week to the next or one month to the next, with this one thing persisting through all of these transformations.

Rather, it’s more the rock in the river of my life; my days flow by but leave this thing essentially untouched.

One of the interesting thing about such things, is that they acquire a peculiar weight over time. The task itself doesn’t change; the thing to be done remains the thing to be done, perhaps with an accumulated understanding of what would be required to undertake or complete the task, if I’ve done some investigation.

But it is as though the non-completion of the task, the non-engagement with the task, comes with an accumulated weight that increases with the number of days or weeks or months (or years) for which the thing, the task has been on the list.

There is a strange relief when the task gets done, as they do on occasion, and the completion leaves a hole in the shape of future lists. But I do think there should be a word for such a thing, as well as some words to describe the various stages of its lifecycle: its moment of conception; the early days when the hope of quick completion exists; its spread into middle age; and either its immortality or its completion.

I have a few of these, enough that I now have a LEGACY section in my list, as though to remind myself that these tasks have been on the list for far too long and perhaps soon, their time will come. Perhaps. We’ll see.

looking ahead into 2022

•22 December 2021 • Leave a Comment

The introspection continues, and this is very much an introspective moment. There is a large part of me that finds this passage from one (Gregorian) year to another an arbitrary marker in time, with no external marker separating days from days, weeks from weeks, months from months.

But given our calendars and our jobs, this also marks a pause for some of us. Email falls quiet. Offices close. I recognize that this doesn’t hold for everyone, but I’ll also admit that it’s a pause I’ve been looking forward to for a while now.

And in this pause from the day job, my mind turns to the near infinite collection of projects and the current plans for 2022.

An old project, one that’s been on the list for a long time now, is to go through all of these posts from the beginning, remind myself of what I’ve written and the themes that run through these posts. I’ve been doing this piecemeal in places, but not consistently, and I have to admit, I’m curious about the threads in this labyrinth I laid down but never followed.

I’ve been reminding myself of old math questions, scribbled in long ago filled notebooks and filed on shelves. Some of them I suspect have been solved by others, given how long ago I wrote them down, but there are still some with life in them. All they need is the slow steady rain of attention, and I hope to be able to give them that attention, that rain come the spring.

For a while now, I’ve kept a file, bits and scraps, single lines, scenes that were not yet stories. I made the mistake of printing that file out, and it runs to a lot of pages. And so one part of the plan is to carve out some time to go through and just what I have stashed away in there, and how much of it might be salvageable.

And this I think is the only real plan I can have for the next few months, moving into 2022. We don’t know what the world holds for us, but the world abides. I have my list, and some of it I’ll get done, some I won’t, but that’s just the same as it’s always been.

And this is part of the lesson. We’ve all been through something exceptional in its difficulty, extraordinary in its breadth, almost unimaginable from our world of a couple of years ago. And yet, our plans persist. Our hopes and plans for the future persist. And we nurture these hopes and plans as we go through our days.

an early reflection on 2021

•12 December 2021 • Leave a Comment

I know I’m a bit early on this, with a few weeks left in 2021, but I find myself in an introspective mood this evening. Flames dancing in the fireplace are the ghosts of the plans from the beginning of the year, but they’re not haunting ghosts.

At the beginning of 2021, we began to see the path that would allow us to escape our current circumstance. The path remains rocky, as the news reminds us every day, but watching the news every day sometimes hides the longer term progress. When we focus on our feet for every step, we don’t always realize just how much distance we’ve covered.

Aikido restarted. After months of station keeping via Zoom, which provided an opportunity to explore aspects of the arts we didn’t cover to this depth or intensity, we made our way back into the dojo. Strange as it sounds, it’s good to be thrown properly and with some vigor, and to get up and do it again, and again, and again. I’m looking forward to my first national course, meeting up with old friends too long unseen.

The Milford Science Fiction Writers Conference met in September, old friendships renews and new friends made. I was reminded that I can string words together, and once we get into the spring, I’m looking forward to having more time to do that stringing.

One of my points of focus for the autumn has been my teaching. It felt good to be back in the classroom with students, I keep finding gems in the material I’m teaching that I hadn’t noticed before, and I’m always heartened by the students who do the same.

I’m coming to the end of my term as the Associate Dean Education for my Faculty. The past couple of years have been difficult, as they have been for everyone, and our current circumstance highjacked some of the plans we’d made a couple of years ago, but we’ve made it this far. I’ve described it at times as rebuilding a ship mid-voyage, at night, in the middle of a storm, but we had a stout ship and an exceptional crew.

There are things I haven’t done. I haven’t put down as many words as I’d like to have, but I’ll fix that next year. I haven’t done as much math, and yes, again, next year. And the same for the reading project, which has languished for almost all of 2021.

But all of that’s OK. We’re in the midst of something the likes of which none of have ever seen. We need to take care of each other and recognize that Hofstadter’s principle applies: it’s all harder than we’d planned, even taking into account Hofstadter’s principle, and it’s all taking longer than we’d planned as well.

We continue to take care of each other, recognizing the state of the world. And we need to take care of ourselves as we take care of others. In spite of the world, or perhaps because of the world, I can only remain optimistic. But I do look forward to the parting of the clouds and the end of this storm.

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 • 1 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.

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.