the reading project for 2021 (and perhaps 2022)

•7 December 2020 • 4 Comments

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

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

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

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

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

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

Let the journey begin.

Posted in bizarre and random things

a meditation on Hofstadter’s Law

•6 December 2020 • Leave a Comment

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

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

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

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

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

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

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

Posted in aikido, bizarre and random things, education and university life, mathematics

the balance of one thing against another

•29 November 2020 • Leave a Comment

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

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

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

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

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

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

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

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

Posted in bizarre and random things

on projects

•23 November 2020 • 2 Comments

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

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

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

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

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

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

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

Posted in bizarre and random things, education and university life, mathematics, writing ephemera

stories of Zen: the muddy road

•12 November 2020 • Leave a Comment

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

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

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

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

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

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

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

Posted in bizarre and random things

windows into the past

•25 October 2020 • Leave a Comment

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

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

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

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

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

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

Posted in bizarre and random things

a reflection on the shapes in the universe

•5 July 2020 • 2 Comments

There is a shape. There are of course infinitely many shapes, the universe being the wildly complicated place that it is, but this is a particular shape.

This shape has shadows of circle, triangle and square in three perpendicular directions, when illuminated by a bright light. It’s a simple shape, akin to a wedge or a door stop.

The circle, triangle and square are important shapes in some theories of aikido as basic shapes that we use as a scaffold for our movements, but that exploration is for another day. I mention this here because this is where I first encountered this shape, and this shape is the starting point for the thought I’ve set myself to start exploring.

Let’s start with an obvious statement. Most shapes, when illuminated in three different directions, have three different shadows, and so having a shape with three different shadows is not a surprise.

However, even here, there are mathematical questions lurking in the shadows, as it were. For instance, suppose X is a shape whose shadow in every direction is the same; what can we then say about X? A lot of work has been done on this question, and perhaps one day I’ll gather myself sufficiently to produce a summary. But as a teaser, while circles and spheres have this property, other shapes do as well.

We can also shift our perspective and view this question from a different direction, and this is what I would like to explore here. Our starting point is the observation that the question we’ve set out above has a direction to it. We start with a shape, we shine a light on it from different directions, and we see what shapes emerge as shadows.

But we could also ask, take three shadows. Does there exist a shape whose shadows in three (perpendicular) directions are these three shapes? Just asking this question, we are taking our original question and we’re inverting its direction.

My intention here is not to answer this inverse question, as I haven’t yet done the work I would like to do to understand the answer well enough to explain it here. That is for another day.

But looking back, I can see echoes of this question ringing though earlier days. This is in some sense the basic question of Rashamon: the testimonies of the different witnesses are the shadows, and we wish to understand the original shape, the event witnessed.

This is also a basic question that underpins the foundation of my mathematical life. Looking back, there are several questions that I have explored through a number of different papers. For one, the limit set intersection question is one that I started exploring in my doctoral thesis and is a question I’ve kept coming back to. Over time, the question has continued to grow into broader contexts, but I still have the feeling that all of the work done provides different shadows, and it isn’t clear to me that we yet have a clear view of the shape at the center.

And in the writing I’m doing, which is mostly half finished versions of stories at this point, I can see the same phenomenon at work. There are a few basic shapes that are lurking, and all of those half finished stories are the shadows.

If I am honest, I can say that part of what stands between me and finishing are the desire to see the shapes rather than merely the shadows they are casting. But I realized something during a long drive today.

I have been dancing with my unfinished stories for too long. The only way I’ll come to see these shapes is to first come to see clearly their shadows. And that is my task for the rest of the day.

Posted in aikido, education and university life, mathematics

some useful images

•23 May 2020 • Leave a Comment

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Posted in aikido, bizarre and random things, education and university life, writing ephemera

a meditation on things I have read

•10 May 2020 • 2 Comments

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

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things, writing ephemera

the rise of the machine world 2, with teaching

•26 April 2020 • 1 Comment

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

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

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

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

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

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

Posted in bizarre and random things, education and university life, mathematics

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