a something my brain did

•24 August 2025 • Leave a Comment

Earlier this month, I was listening to the future robot avatars of Emma Newman and Adrian Tchaikovsky aboard their podcast, the Starship Alexandria (which I highly recommend). They were discussing The Golden Apples of the Sun, a collection of short stories from Ray Bradbury.

One of the stories was A Sound of Thunder, one of the most famous of stories, originally published in 1952. Interestingly, it wasn’t until 1963 that Edward Lorenz undertook the work that produced a first noted demonstration of deterministic chaos, which is in some sense the formal mathematical underpinning of this idea of small differences at the beginning result in large differences later on.

I suppose there there is also the many worlds interpretation of quantum theory, or Everett interpretation, which dates to 1957, which could be seen as a different interpretation of the story.

But this isn’t the thing my brain did. When I was an undergraduate, oh so many years ago now, we were given the poem Ozymandias by Shelley to read and interpret. I had not read the poem before, had not encountered it, and so didn’t know the standard interpretation. I don’t remember what it was I said, but it wasn’t the standard.

It’s times like this that make me wish I had kept some of my old school and university notes, so that I could look back and see what it was I said, but moving across an ocean persuades someone not to keep too many things.

But during the podcast, I remembered a line from Night Moves, a 1976 Bob Seger song. ‘I woke last night to the sound of thunder.’ It’s a song I know well; it was a standard part of radio play when I was growing up, and it was a song I was always happy to hear, the story of two young people who were restless and bored.

Could we, my brain said, reinterpret the entire song along the lines of A Sound of Thunder? For most of the story, I think the answer is no, at least among reasonable interpretations. But there is the one verse where it might be possible.

I woke last night to the sound of thunder
how far off I sat and wondered
started humming a song from nineteen sixty two
aint it funny how the night moves
when just don’t seem to have as much to lose
strange how the night moves
with autumn closing in

This verse almost works. It would have been a bit more intriguing if the song he’d been humming was from 1952, the year A Sound of Thunder was published, but alas the world is imperfect.

How wide should we sometimes cast our interpretations? On the one hand it’s clear that there is no reasonable way to interpret this song as a vision of an alternate world. But on the other, it’s fun to see how far we can go. I keep singing that line, ever hopeful that something more will come to me. Oh how strange the night moves.

cognitive decline and the feeling of power

•21 July 2025 • Leave a Comment

I would like the speculate. There is an old story from Isaac Asimov, The Feeling of Power, which I’ve referenced in these pages before. In a (perhaps not so) far future, people have outsourced their ability to do basic calculations to the machines, and the story is about the rediscovery of how to do arithmetic by hand.

Why does this story come to mind now? I’ve seen stories coming up on my various feeds and in various magazines, about how the use of what we misleading call Artificial Intelligence (AI) for such things as essay writing might be associated with some level of cognitive decline. The basic idea is that if we don’t have to do the thinking to pull together an essay, then that part of our brain will atrophy a bit.

From what reading I’ve done, these investigations are in their early days, but the brain is an efficient organism. Evolution has shaped it to be so, and so if there are things that the brain doesn’t need to do, then the brain may not hold onto the ability to do them. Perhaps, just perhaps, the brain behaves like the rest of our bodies, where muscles might lose their strength and definition if not used.

So what, one might say. One reason is that we might not always have the machines on our side. And yes, while the Skynet apocalypse is something that is never far from my imagination, there are also more mundane problems. What if we don’t have the tool handy when we need it? But my concern is larger.

I work in education. I have done so for enough decades that I’m not entirely comfortable admitting just how many. The human brain is a remarkable thing, The imaginative power of the human brain can be spectacular, as we can see with the novel we can’t put down, the twist in the movie we hadn’t and couldn’t imagine. But the strength of that human brain requires training and regular exercise.

There are things that I suspect the human brain will not be able to cope on its own. It’s doing remarkably well at present, and I take heart from browsing mathematical journals and seeing the work people are doing. Reading the New Scientist or Scientific American and seeing what work people are doing. Listing to podcasts such as the Quanta Magazine podcasts or Night Science, and hearing about the work people are doing.

I have no issue with humans making use of the tools they can build. Yes, this does lead us into the labyrinth of the Toolmaker Koan, one of those touchstones I keep coming back to, again and again. But as the Koan teaches us, the rate of increase of the power of the tools is far faster than the rate of increase in our ability to use our tools wisely, and so we have work to do.

irregularities

•29 June 2025 • 1 Comment

As I’ve done before, I’m contemplating habits. A habit is an interesting thing. We each have habits that we acquire over time, often without consciously attempting to. One day, we wake up and we realize that we have been carrying the weight of the habits we’re accumulated.

On the other hand, it can be remarkably difficult to embed a new habit. Even when we think we have the time, something else seems to fill the space.

And so it becomes something of a game of tug and war. One day we clear out some time, the next day something fills that space we thought we’d created. Or at least, this is what I’ve found over the years.

And so what to do? There is only one thing to do, and I’m reminded of an old quote from Yoda: There is only do and not do; there is no try. It’s a particularly Zen-like quote, at least for me. Seemingly simple on the face of it, both intuitive and counter-intuitive, and yet it always has something more to offer as we contemplate.

And so I think my path is simple. I stop trying. I stop trying to implement new habits. I stop trying to change. Instead, I do, or I don’t do. I change, or I accept how I am. I implement a new habit, or I don’t. It’s going to be a hard road, but what else can I do/

why we watch the things we watch

•30 May 2025 • Leave a Comment

I like cooking shows. But not the ‘here’s a recipe and here’s how to make it’ shows. I like gladiatorial cooking shows – Top Chef is coming to the end of season 22, and I’ve just finished season 2 of 24 in 24 Last Chef Standing (which I find to be a delightfully bonkers show in its basic concept). There’s Iron Chef, Next Level Chef, Chopped, Hell’s Kitchen, Barbecue Showdown, Culinary Class Wars and many many (many) others.

Those close to me have gotten used to me bringing them up in conversation from time to time, as they do form one of my touch points, along with the first 10 or so seasons of the Simpsons and classic Looney Tunes.

But I’ve been pondering this love I have for these gladiatorial cooking shows. Why, and just how bad is it? One thing to note is that clearly, I’m not alone. Each week seems to bring a new one, and there is the Food Network, and perhaps others as well. And I do like cooking and I enjoy a good meal. Not that I’ve yet tried to cook one of the dishes created in the throes of these competitions, but hope springs eternal.

But I do have this worry in the back of my mind. I think the fertile ground from which this worry sprung is a quote that I only vaguely remember, that civilizations are doomed when they make celebrities of their chefs, and we are well down that road.

But food is an important aspect of our lives. We need to eat. And I also appreciate the skill of the chefs. They train, they spend time, years and decades with their craft, and then they enter an arena, to test their skills and to find out, as sometimes happens, that they know more than they thought they did. And those are great moments.

I’ll admit that I wasn’t sure where this was going to go when I sat down to put some words down. I have an appreciation of the skills of those involved, but I do worry a bit that I am distracting myself from the cares and woes of the world.

Perhaps that’s necessary. Perhaps I’m taking advantage of my place in the world to escape the crush of the news for a bit of time, watching as a chef pulls a great dish out of an ingredient they’d never worked with before.

But I suspect as well that anyone reading this has their own escape, their own thing they keep to avoid the world for a few minutes. To which I can only say, enjoy. Enjoy those moments, and I will go back to the finale of Top Chef next week when I get the notification that it’s waiting for me.

time horizons and a definition of the classical

•6 April 2025 • 2 Comments

Some many (many) years ago now, when I was but a young and eager PhD student, in the bar at a conference, I asked a senior colleague for his definition of a classical mathematical result. I was curious because we often refer, when speaking and in writing, to classical results of X and Y. His answer was that a result was classical if it were part of the mathematical literature before one got to graduate school and started seriously studying the field.

[This senior colleague took some offense the next morning, when I referred to a classical result of his. He said, it was because it made him feel old. I didn’t say it at the time, but he was one of the Old Men of the field, from my point of view. In retrospect, I can understand his mild annoyance, but I still stand by what I said.]

This definition has always made sense to me, and for reasons that I’m sure someone has studied for the whole or part of their career (and so themselves establishing results that might well be classical). When we come into a field, we survey the landscape of what’s known at the time we make our entrance, and we (or at least I) don’t necessarily spend much time exploring the time sequence of when different results were established, unless of course that time sequence is itself important to our work.

I had a similar experience with music. I didn’t listen to music much when I was growing up; I was more of a reader, devouring lots of science fiction, particularly short stories, but that’s a detour for another day.

I was young, single digits young, when the Beatles broke up in 1970, and I remember when John Lennon’s Double Fantasy came out in 1980, and since my engagement with music blossomed at some point between those two, the Beatles were a classical band but one whose break up happened at some indeterminate point in the infinite expanse of the past.

I try to bear this in mind when I’m teaching, to be sure to provide some temporal context to the results I present to the class. When teaching Graph Theory, this leads to a broad expanse of time, from Euler and the bridges of Koenigsberg in 1736, to results that might have appeared only in the few months before we see it in class, still preprint and not yet formally published.

One reason that this came up recently was something I read, or listened to; I’ve been reading a lot of articles and listening to a lot of podcasts about current politics, and with apologies but I didn’t make note of where I first or most recently heard this.

I can remember when the Berlin wall fell, where I was and who I was with. I remember, a bit less clearly, the fall of the Soviet Union and the independence of the former Soviet republics. So my political understanding stretches from the nuclear bomb drills in elementary, middle and high school, through these significant events of the late 1980s and early 1990s, and all that has happened since.

But people significantly younger than me, those whose political awareness has blossomed during the past decade, have a very different understanding of politics than I do. They are working from a very different baseline.

And we’ll see over the coming years how difficult it is to modify or reestablish such baselines. It will be interesting. Despite a much more well developed sense of the music in my lifetime and before, born of lots of listening (with so much more to do, it must be said), but I still have this instinctive reaction to the Beatles and their breakup, and where it sits in my personal time line.

building on old foundations

•9 February 2025 • Leave a Comment

When I sat down to write on this topic, I realized a number of things. First of all, I’d mentioned this topic, the toolmaker koan, on multiple occasions (I include some of these mentions at the end of this post). This makes sense, because it is one of those ideas that has nested deeply in the attic of my brain. But there are some basic aspects and questions I’ve never addressed.

First of all, is the toolmaker koan in fact a koan? The toolmaker koan is the statement that we humans develop tools much more quickly than we develop the ability to use those tools well. This seems to me to be closer to a statement of naive fact than the standard definition of a koan, which arises from Zen, of being a paradoxical anecdote or riddle without a solution, which has the purpose in Zen of demonstrating the inadequacy of logical argument.

And so I suspect that I’ve misnamed this observation, which is not an observation in any way original to me, though probably one made under many different names. But it’s the name that’s stuck in my mind and so it’s the name that we’ll keep.

Another thing that I’ve never followed up is the connection between this toolmaker koan and doomsday devices, something else that my science fiction brain has pondered from time to time, and this is a direction of enquiry I would like to explore. There are in fact many different directions I want to take, the rise of artificial intelligence which I’ve touched on in previous posts; different inventions as doomsday devices; and what it is we need to do to prevent these observations from in fact becoming paradoxical anecdotes and riddles.

In my mathematical life, I have enjoyed the occasional paradox, and even logical weirdnesses that don’t quite rise to the level of paradox. A good paradox is tightly binding, preventing us from escaping its grasp, and I think that we need to resolve and rise beyond the toolmaker koan, and so what I plan to do over the coming weeks is to explore the toolmaker koan and doomsday devices, and see whether it’s possible to navigate a way through this stormy sea.

So going forward, I’m going to dig into this. This will require some reading around and so might not be quick, but I want to persuade myself that there is a solution, and one less extreme that the Surak moment mentioned earlier.

2022.05.08 reading with hindsight: Superiority and beware the shiny
2023.07.30 further consideration of the Toolmaker Koan
2024.03.03 speculating on Colossus
2024.09.22 the toolmaker koan, revisited yet again

the journey of a thousand miles

•5 January 2025 • Leave a Comment

‘The journey of a thousand miles begins with a single step’ is a line from the Tao Te Ching of Lao Tsu. (The translation I’m familiar with, and that I’m using here, is the 1972 version from Gia-Fu Feng and Jane English. Why this translation? It’s the one that was in the house when I was growing up, and that’s the physical version I still have.)

Interestingly, this translation has a slightly translation of the line: A journey of a thousand miles starts under one’s feet.

It’s a standard line in discussions about the need to start. We can only get to the destination if we start the journey. This is something I reflect on to some significant extent when thinking about writing – we can only finish a story or a novel or piece of editing or anything else if we make a start.

It applies to aikido; we can only develop smooth technique if we make those first steps. And here, there is some subtlety. We can practice techniques for a long time, not progressing or improving, if we don’t practice with reflection and focus. And yes, this holds for writing too.

But what we don’t always remember is that we are taking that line out of context. It is part of one of the longer verses of the Tao Te Ching. I won’t give the whole chapter here; I do though encourage you to find it and read it.

Even in context, this line has largely the same meaning, but the whole verse taking together contains other aspects of the lesson, and for me, the meaning of this line expands a bit in the context of these other lines. For instance, ‘.. give as much care to the to the end as to the beginning,’ which I find particularly meaningful since the line in question is very much about beginnings.

What always strikes me about this line is that it doesn’t address what much of the time is the most difficult part of a journey. It is easy ofttimes to motivate ourselves and begin, but what then happens a hundred miles in, when we have still so much of the journey to go. What happens on the ten thousandth step, or the hundred thousandth.

Beginnings can be hard, to get over that hurdle to action, but persisting, continuing, persisting with the journey can be where our vigor fades, where our enthusiasm fades, when the journey becomes difficult.

And so, journeys. Like many other people, I’ve taken advantage and made some resolutions for this new Gregorian year. I won’t share them here, but they are each their own journey, now begun. We have the enthusiasm and excitement of this new journey. But we are still facing the awkward middle parts of these journeys. We’ll see how it goes.

the arbitrariness of calendars

•29 December 2024 • Leave a Comment

We are approaching the end of the Gregorian year, the standard calendar we follow here in the UK. As in previous years, I find myself pondering the arbitrariness of calendars.

It makes sense that we mark the passage of the years, because there is a natural cycle to the years. The weather warms, the weather cools, with a large amount of local variation; the day todays started cold but when the clouds retreated and the sun came out, it was almost warm enough to ditch the coat, though keeping on the sweater underneath.

But it’s an interesting question, why have we chosen precisely this moment to mark the transition from one year to the next. I’m sure there are books on the topics, and I’d meant to look them up, apologies for that, but it does bring to mind an old question.

In each of the calendars we have, solar calendars and lunar, for all of the cultures across our world that have years, what are the actual or mythological events that mark the transition between years. There might be an interesting book there, but that’s a project that would require a lot of research and digging, and there are other things that are higher on the list.

And there are things we tend to do when we move from one year to the next. It’s a tempting time to reevaluate lists of projects as yet uncompleted, and to change the habits that we carry with us. This is something that we need to so with some kindness and understanding for ourselves; changing habits can be hard, and it’s not something we’ll be able to do turning on a dime.

So the new Gregorian year begins in just a few days. I have my list of habits to change, old habits to break and new habits to build into my days. I have the projects I want to finish and the ones I want to start and move along. And let’s see what I can get done tomorrow.

rhythms and rhymes

•1 December 2024 • Leave a Comment

An academic year has a rhythm to it, different business in different weeks and months. At present, we have finished week 9 of 11 in our first term of three, and tomorrow is the first day of week 10.

One thing I’ve learned over the years is that there are in fact many rhythms, many songs sung in any given year, and the songs we sing and the songs we hear depend on how deeply we are embedded in different aspects of the university’s business.

At the present time, my main focus is the student facing education focused part of the business. Students are turning in work and scheduling the work that remains, and everyone is flagging a bit. In my own class, we have covered essentially all of the material the students will need, and so soon we’ll be moving to last few Topics of Additional Interest.

But there are so many chords and voices in this rhythmic paean. Parking spaces closed to allow for leaves to be gathered and bundled. Christmas lights being turned on amidst feed stalls and festive games. Late darkness to start days and early darkness to end them.

I love wandering around campus, listening to this paean as the university and all of us who work there sing, each with our own part and each of us adding our voice to the overall song.

Tomorrow, I’ll get in early, as I am wont to do, and I’ll enjoy the song of the slowly emptying campus, as we get close to the break at the end of the calendar year, and I’ll give some time to those things that need to be done before we get to that point.

old projects and new

•24 November 2024 • Leave a Comment

Some time ago, I looked at the long list of accumulated projects, and I decided that the only reasonable decision to make would be to declare project bankruptcy and start over, wiping the slate clean.

And it’s proven more difficult than I thought, for many reasons. One is the sunk cost fallacy. A few of these projects I started a long time ago, years (or even decades in a few cases), and it’s hard to ignore all of that expended effort.

And if I stare in the mirror, there is then the question of why I’ve held onto these projects for so long, without bringing them to a state of completion, and that’s a great question to which I don’t have a good answer. In part, it might be that procrastination becomes a habit in itself and that’s a habit I’ve been practicing, too assiduously.

Another reason perhaps is that some of them are just interesting. With lots of interesting projects, there is the difficulty of focusing on just one of them, leaving all of the others watching from the sidelines. But that then is the discipline to practice this year.

Yet another reason might be that the projects are just interesting, which is why they ended up on the list in the first place.

As we approach the end of the year, it’s the time of year that many people start thinking about resolutions for the year to come. But I don’t like waiting until the new year, and so the time has come to get out the pruning shears and start removing some of these old, dead projects, so that there is room for new projects to bloom.

reading in hindsight: Maladjustment by Philip K Dick

•27 October 2024 • Leave a Comment

When I was younger, I read a lot of science fiction short stories. I would go to used book stores and buy collected stories of individual authors and anthologies, themed and unthemed. I don’t have the ones I collected in high school, but I have I think made up for that in the years since.

One of the stories I remembered reading rang a bell, and I’d been trying to find it. Google helped a bit, once I had a bit more information, but a story involving people who warp reality through their perceptions doesn’t provide enough specification.

Once I’d remembered that it might be a Philip K Dick story, I had two choices. I could go back to Google and ask again, with this additional information, or I could back and reread (rereread? though it has been enough years that the pages have yellowed) his collected stories. In the end, life being busy, I opted for the former option and alighted on Maladjustment.

In summary, parakineticists have emerged among human beings. These are people who have a particular delusion but also have the power to impose their delusion upon the world. In the story, we encounter a few of these P-K individuals. One can fly. One can grow transport craft on a vine in his backyard. One can walk through walls but not fall through floors.

There is an Agency who attempts to keep the P-Ks in check, an all female Agency because all of the P-Ks are men, but when they rightfully target an important industrialist, he decides that the Agency needs to cease.

But they need then a way of keeping the P-Ks in check, and this is where for me the story got interesting. The idea isn’t well developed, but the idea is that we will rely on our collective understanding of reality to spot those individuals who are diverging.

Not meaning to take a sharp left turn here, but there is a reason this story rang a bell. I’ve been listening to a lot of news recently, the world being a complicated place these days, and I’ve come to realize the truth of something I’ve heard from multiple different sources.

One of the impact of the Internet is that our news ecosystem has atomized. I can remember the old days, in the before times, when we had only a few common sources of news. Now we can each find, if we wish, sources for the news and opinion we want to hear, without the news and opinion we don’t.

This atomization of news reflects the fracturing of reality that we see in Maladjustment. The idea that we can use the collective to ride herd on the individual doesn’t work in the story; this is the twist contained in the last line two lines. “A man who grew jet transports from a plant in his backyard was clearly a lunatic. It was so much simpler just to flap one’s arms.”

One of the things I like about reading PKD’s is precisely this. Sometimes the settings feel very dated. Sometimes, the characters can be a bit formulaic or staid. But there is always an idea at the core of the story that will reverberate, an idea that is a mirror in which we can some aspect of our world that requires some focus and attention.

reading in hindsight: Albatross by Stanislaw Lem

•13 October 2024 • Leave a Comment

I’ve always enjoyed reading Stanislaw Lem, and one of my favorite characters of his is the pilot Pirx. As far as I’m aware, Lem wasn’t in any of the novels, but rather he can be found in two collections of stories, Tales of Pirx the Pilot and More Tales of Pirx the pilot. The tales follow Pirx through his career, from rookie pilot to grizzled veteran.

I picked up Tales earlier today and picked a story at random, Albatross. And yes, there will be spoilers. Herein, Pirx is a passenger on a space going luxury cruise liner, on his way to his next job. He notices that the liner and accelerating, and so he makes his way to the main control room. There he finds out that his ship, the Titan Aresterra, along with a handful of other ships, are on a rescue mission to the Albatross, which has suffered a cataclysmic failure.

There is a lot we don’t find out in the story, for instance what happened to the Albatross. What happened to the Dasher, one of the first ships to arrive on the scene, having broken its own engines doing so.

I like the story for the writing, even though Lem does things that I don’t always like in the stories I read. (And yes, I feel a bit as though I’m committing a sin by even writing those words.) Pirx is not directly involved; the Titan gets called off rescue duties as other ships have arrived and she is full of passengers. And even the crew of the Titan are bystanders, and so we’re just watching as they listen to the story of the Albatross unfold over the radio.

But I think part of the reason it rang a chord in me is that I read an article in the Atlantic yesterday, on Point Nemo, the point in the southern Pacific that’s the point on Earth farthest from land. When ships do pass near there, it’s sometimes the case that the nearest other humans are those in the International Space Station passing overhead.

There is mention of Michael Collins, alone on the lunar orbiter when Armstrong and Aldrin have descended to the Moon’s surface, more alone than anyone had ever been.

I was having a conversation with a friend this week just past, about how we each need, every once in a while, a bit of time alone. But this is a very different sort of time alone, because we knew that there are always people near by. There is connection near by.

We are not like the sailors passing through Point Nemo, or the crew of the Albatross, or the astronauts who went to the moon. We can take our hour, or our day, and then walk down the street, alone in our thoughts but not alone in our presence.

I suppose this echoed in me because I’m also thinking about the characters in my half written stories. Some of them are engaged in long voyages and journeys, through barren lands, and I need to think about their sense of loneliness and how that shapes them and their stories. And I will keep coming back to Point Nemo and the Albatross.

the toolmaker koan, revisited yet again

•22 September 2024 • 1 Comment

I think a lot about the toolmaker koan; if you’re so minded, some of these earlier speculations can be found HERE.

Loosely, a koan is a Zen device, a short story that’s intended to illustrate a point of Zen. A koan often involves what seems to be an internal contradiction, intended to stimulate consideration. The classic koan is, what is the sound of one hand clapping.

Strictly speaking, the toolmaker koan may not be a koan. Rather, it is a question: why is that the development and use of tools so outpaces the wisdom in the use of tools. This touches on one of those fundamental points that we find in the news a lot these days, in various guises: the difference between whether we can do a thing, versus whether we should.

The thought I had recently during a long drive is the connection between the toolmaker koan and one of the other topics of occasional contemplation, doomsday devices, see THIS and THAT.

I haven’t written about doomsday devices for a long time, though I do have some ideas, but the thought I had was, what do we get when we bring together doomsday devices and the toolmaker koan.

It is an obvious thought, in some ways. Doomsday devices are somehow archetypal tools, vis a vis the toolmaker koan, but strangely the connection between the two hadn’t occurred to me before. And so this is what I’ll be trying to working through over the coming weeks and months. We’ll see where we go with it.

a sequence of decreasingly stupid conjectures

•25 August 2024 • Leave a Comment

As we close on the start of our academic year (we start typically at the end of September or beginning of October), I’m working through the materials for my teaching. I’m teaching a class I’ve taught a number of times already, and there is the familiar deja vu.

One thing I’m always reminded of is the iceberg-ness of this preparation, and of teaching in general. Each topic in the classroom, each exercise, each paragraph and section of the Notes, all of these are just the tips of much larger icebergs.

The class I teach is graph theory, a subject that’s approaching its formal 300th birthday, though an interesting topic that I haven’t explored enough is what pre-echoes exist, in terms of graph theoretic topics before 1736 when Euler showed we cannot walk the bridges of Koenigsberg.

And so, the icebergs are large. Each small topic we take, one of my favorites being graph coloring questions, leads to an expanding cloud of related questions, variations on the basic theme. I subscribe to the daily arxiv update for graph theory preprints and each day, there are many.

I’m also in the final stages of writing a paper, one that’s been partially written for far too long. In thinking about this paper, and other papers written and not yet written, and here the iceberg is different but still large.

Here, I have a much better idea of the size of the iceberg, because I’m aware of all of the false starts, all the paragraphs that were written only to be rewritten, or deleted, and so I have a clear idea of all of the work that’s gone into my working through of the ideas, even when that work didn’t make it onto the page.

Sometimes this other work might be the starting point for a different strand of work, hopefully leading to another paper (or papers). Sometimes, it might be that what’s left out is better left out, since it wouldn’t lead to something more, or at least it wouldn’t lead to something interesting.

And where the title comes from is that sometimes, the path to a paper is working through this sequence of decreasing stupid conjectures, from the first idea, often incomplete, through to the final version.

Fiction writing is much more like writing a paper. There are the false starts, the paragraphs (or plot lines or characters or other scenes) that are taken out, perhaps put back in, rewritten over and again, until we get to a complete version.

But there is one significant difference between math paper and story. Perhaps this is just me, but I find it much easier to bring a math paper to an end than a story. There is a theorem and the path to that theorem, perhaps a few related conjectures.

On the other hand, I find it very difficult to bring a story to a clean end. It’s as though the characters don’t want to be constrained, imprisoned almost in a story declared DONE, and they fight. And I need to get better at winning that fight.

prophetics

•28 July 2024 • Leave a Comment

If poetics is the study of the different aspects of poetry, then does that mean that prophetics is the study of the different aspects of prophecy? Since prophetics doesn’t seem to yet exist in the standard corpus of English, I would like to put forward a slightly different definition for it. Thinking about my daily journal and the things I’ve been writing about there, one thing that I keep coming back to is the extent to which science fiction can and cannot be seen as prophecy.

This is not a clean discussion, since there is the obvious and inescapable element of self contamination. That is, people see something in a television show or movie, or read about it, and then have a desire to make it real in the world. Take for instance the sick bay bed in the original Star Trek. We don’t yet have these in hospitals, but I wouldn’t be surprised to see them at some point.

But I’m also thinking bigger. Not just the singular inventions, but the grand sweep of ideas. (I like thinking about the grand sweep of ideas.)

I have a vague memory of reading Norman Spinrad’s Agent of Chaos, and the necessity expressed therein of preventing the closure of society, because in that closure, freedom dies and the authoritarian observational state wins. I need to reread it, because it’s been a very long time, and I wonder how much I’ve forgotten and how much I didn’t notice the first time through.

But we are nearing such an authoritarian observational state, or at least such an observational state. The old defense of anonymity in the face of too much information to process has been broken by the capacity of the machines we’re building and the machines we’ll build in the near future. It’s no longer the case that we can just hide in the eddies of the data flow, hoping not to be noticed.

But this now seems to inspire a quest. What would be required to found prophetics as a proper discipline. What is the strangest prediction from fiction that’s come to pass, and what would be the most worrying? This latter question has me worried, given some of the predictions that have been made.

Roilations

•21 July 2024 • Leave a Comment

I know it’s not an actual word, but it nonetheless seems appropriate at this particular moment in time. I’d intended to write about the toolmaker koan, as it’s something I’ve been thinking about a lot recently. But the news of the day has taken the wind out of that particular sail.

I still follow US politics, more than I should perhaps, but I think there’s a case that can be made that the politics of the US have a significant impact on the politics of the world, especially the UK and Europe a bit more widely.

I’m curious to watch the news over the next few days and weeks, email newsletters and podcasts and all the other forms the news takes these days, as we all digest this news.

And so, roilations. The roiling, churning seas through which we’re all sailing. There is a lot going on. We’ve spent the afternoon watching news, switching from one channel to another, savoring the new as yet unheard bits of information as they come through.

And so, back to the news, and more later. I suppose every generation thinks they’re living through interesting times. But these times, they do feel especially interesting.

wandering the fractal hinterlands

•14 July 2024 • Leave a Comment

July is an interesting time in the academic year. The undergraduates have largely left for the year, having received their results from the year, the masters students are deep into their dissertation writing, and the doctoral students are lost in the labyrinths of their projects. Committees have their last meetings for a few months, and we are spending part of our time winding things up.

The university is not quiet; various groups and conferences are visiting campus. There are important moments in the cycle of the academic year that take place over summer, such as the core days of the undergraduate admissions process in mid-August and the supplementary examination period in late August and early September. But it is quieter than during the year.

As such, it’s a good time for reflection, on the year (and years) past, and on the year to come. Amidst this reflection, an idea that has been marinating over the year bubbles to the surface.

There are many aspects of life that involve taking a varied and multidimensional space, and sorting all its points into a handful of buckets. For some of these points, the bucket will be an obvious bucket, whereas for others, the determination of which bucket becomes complicated.

This complication arises from the observation that there will be points in this multidimensional space that are very close together, that nonetheless end up in different buckets. And so each bucket will contain points where a reasonable argument, and a different sorting algorithm, would result in that point being in a different bucket.

Why does this matter? It matters because it’s the answer to a fundamental question, which is, is there a fair way of doing this sorting into buckets? We take a rule we think of as fair, and we will always note that there are points where we aren’t comfortable with the algorithm’s decision. But the issue is that every rule will come up with such points, unless we do something reckless like just using a single bucket (and so making any distinction between the points).

This is something of a slippery idea, because it means that there won’t ever be a way of sorting that everyone agrees is fair for all points. Mathematicians have become accustomed to things that cannot be done, impossibilities, and this is something that most people don’t like to admit. It’s one that I want to explore and so I’ll come back to it from time to time, but I think this is perhaps enough for the moment.

the nagging power of uncertainties

•16 June 2024 • Leave a Comment

I wrote the title of this offering to the blogosphere without knowing quite what I meant by this particular sequence of words. Both of my countries, the country of my birth and the country where I live, are undergoing elections this year, one sooner than the other. While the outcome of one of these (the UK election) seems at the moment to be relatively clear, he said not wanting to tempt fate, the outcome of the other (the US election) seems anything but certain.

This uncertainty is hard to bear sometimes. It’s the weight on the shoulders, the tight twitching muscle in the lower back, the running shadow glimpsed out of the corner of the eye.

So where is the power of uncertainty? Sometimes, uncertainty can be the inspiration to action; this very much in evidence in the US at the moment. Money is being raised. Articles are being written. Talking heads on various television networks prognosticate and punditize. There are dangers to this nagging by uncertainty; it is hard to remain calm; to carefully, forensically pull apart policies and positions on issues. Loud voices, clamoring for action in the face of various disasters, rise above the quiet chaos of churning uncertainty, and it is hard to find a true path through.

So what are the enemies, the opposites of uncertainty. Certainty can lead to complacency, and complacency is so often the shackles around the ankles of action. I’m reminded of the writings of Carlos Castaneda and the quest to become a person of knowledge. If memory serves, the second enemy (after fear) is clarity. One can become blinded with seeing the world as it is, and not continue along the path.

The world as it is. This is a bit of a sudden left turn into an elsewhere, but it is difficult these days to stare the world in the face, to see the world as it is. The world is (and has always been) a complicated place, but the seeming clarity that the world wore in the early 1990s has now well and truly shown its true self.

Uncertainty reigns, and it is hard to navigate this particular uncertainty. This is not an uncertainty that nags one to action, but rather an uncertainty that erodes and corrodes, and it’s hard to see how to steer our ship. But steer we must. So I’ll watch the news and I’ll continue to read, and I’ll choose my direction of travel. Perhaps we’ll meet along the way.

On fences

•2 June 2024 • Leave a Comment

On occasion, we come across an idea that had been kicking around in a vague, spectral, undefined way inside our own head, but which someone else had crystallized decades, perhaps centuries or millenia before. In my case, this is the idea of Chesterton’s fence: “the principle that reforms should not be made until the reasoning behind the existing state of affairs is understood.

We come across a fence in the woods. Perhaps the fence is old, dilapidated, rails missing. This for me is the more interesting case, a story to be told. Who built the fence, who failed to maintain the fence. What lies on the other side of the fence?

The new fence in the old woods raises some of the same questions: who built the fence, what lies on the other side? What is the fence protecting us from, separating us from? And I like this lens that my mind sometimes takes on the wider world: each idea, like a log in a fire, brings forth a bundle, a cloud of sparks.

This idea of the fence in the woods plays a role in much of fantasy: we do the thing that then creates what then comes to pass, which then requires vast amounts of treasure, blood and steel to unwind.

But then the imagination starts to spiral. What if the fence had never been tested? Who was it that knew, a fence is needed and then went through the effort, spent the time, to build a fence. And then I dive into the small details: what sort of fence, wood or stone? How robust a fence. Does the fence enclose some specific area, on one side or the other, or does it just extend to the ends of the world in both directions.

Back in Georgia, in the neighborhood where I grew up, there were local woods that had at one point, decades ago, were farmland, fenced off into individual fields. During our family walks, we would sometimes come across the remnants of these fences, the occasional post, a bit of barbed wire.

I never explored, sought the records, of what the land had been all that time ago. Perhaps I should have. Regrets that arise from choices made when we were young are tricky, because they have a power to them that comes from their origin during those days before we knew how to protect ourselves from them.

Perhaps one day, I’ll try and find what records that might exist. Or perhaps, I’ll try and work these ideas into stories to be written, stories taking their place in an increasingly long queue of potential stories. A fence, a ruined farmhouse, lost among trees that have grown up around them. A lovely setting for a story to be written.

on words

•19 May 2024 • Leave a Comment

I’ve been thinking a lot about words recently. In part, this is because I spent the past week at the Milford Science Fiction Writers retreat at Gladstone’s Library in Hawarden, North Wales, truly a glorious place and one that I highly recommend. I spent most of the week working my way through new words. Part of my project reconsideration process involves working my way through old words, half written stories and incomplete ideas, but I didn’t spend as much time on these as I’d originally planned. The seduction of the new and shiny, I suppose.

More generally, this past week has gotten me thinking about writing. I suppose at one end of a continuum, we could describe writing as stringing words together. This is technically true in some sense, but it doesn’t capture the art of creation inherent in writing, of creating a story that captures the attention and imagination of the reader. It also brings to mind Morecombe and Wise and Andre Previn.

For the first time in a long time, I sat down with a plan for a story, from beginning through its middle and to its end. Admittedly, it was a particularly short story, just about 1000 words, but those words flowed smoothly. And even with the plan, the ending was different than from my original outline, but the current ending seemed to work better. We’ll see what the readers say.

But the story I spent most of the week on is a different beast. Each day I sat down with my outline and current draft, looking out at the other writers and the shelves of books in the wonderous space of the Library, the story slipped through my fingers.

I think I know what’s going on. I think that the idea of the story is unhappy with the outlines I’ve come up with, and it keeps trying to direct me towards a path to a better story. We’ll see; I’m about to sit down with it again, having let it sit for a day, and the idea I came up with this morning seems to work well with both my intention and what I understand of the story’s preferred path. Again, we’ll see how things go.

But this was the first time in a long time that I’ve spent a whole week with a single story, largely unperturbed by the day job, and it reminded me, as does the British Aikido Federation annual summer school, that this extended, focus attention on a single task does create an environment which can lead to interesting insights and some significant progress.

Long live the words.

a message to a younger me

•5 May 2024 • Leave a Comment

I found myself standing today at a confluence of reflective moments. One of these was my continuing exploration of old lists, and the idea I found there, an old one that might well have found its way onto my list via an episode of Start Trek: The Next Generation.

Another is just the passage of time and the reflection on what might have been versus what was. I recognize that the was cannot be changed, but there is still, still the glimmer of the if only that I can’t entirely put to rest.

And so now, the what. If I had the opportunity to write a letter to the younger me, that they could read at 15 or 18 or 21, what would I say? And yes, I’ve read enough science fiction to recognize that the pollution of the time line becomes a problem at this point, and I’m going to ignore that entirely.

I’ve never sat down to write such a letter, but it is an interesting exercise to sit in a quiet room, perhaps in front of a fire if the night is cold, perhaps with a glass of wine, and speculate on what such a letter might contain.

One realization that might hit first is that I don’t remember those days of my life all that well in their detail. I have an inventory of particular moments that I’ve carried with me, but I don’t know whether that inventory contains those events that affected the course of my days, to where I am now. There are some that looking back, I would take a different path, and others where I might not. And it may be that my change might be less events than application and approach.

Beyond this, though, is the deeper lesson. Each day, we are different than we were the day before and we are different than we will be the day after. Each day, we can change our direction of travel.

This can become difficult as we get older, as we become set in our ways, as the accumulated detritus of our days hinders change. And this for me is the lesson from this quiet contemplation. This is the mountain we climb.

foundational bricks

•28 April 2024 • Leave a Comment

When I was young, I don’t remember exactly when, I encountered an idea, that if we ask a question carefully, properly, correctly, then the answer will be obvious. The answer will emerge, on wings, from the ashes of the question being asked.

I’ve never been able to entirely shake this idea. It snuck in under the radar, an idea that took root before I was old enough to know better. I’m sure there are other dandelions, kudzu vines, that are part of my internal firmament.

But something that’s interesting about this idea, is that it still to a small extent shapes how I got about my professional life as a mathematician. I work on questions whose answers are not yet known, looking for those answers. Some of the questions are ones that I’ve developed, others are questions that I’ve learned of from others. But still, questions.

Mathematicians are aesthetes to some extent; this is illustrated in a strong way in Proofs from the Book by Aigner and Ziegler, the collection of the most elegant, the sharpest proofs of classic results. It begins, because of course it does, with Euclid’s proof that there are infinitely many prime numbers, and explores from there.

As beautiful as they are, the aesthetics of the Book are different than what I’m thinking about there, though they are related. And so, for the mathematical problems I’m thinking about, the question remains: what is the statement of the question that makes the answer the obvious statement.

I’m not sure such statements exist. Questions can be complicated, mazes with twists and turns and minotaurs, wielding their axes of reason and argument. There may well not be a statement that makes the answer to these complicated questions the next obvious thing.

And yet. And yet, for me the echo of that old belief still persists. And this perhaps is actually the thing I’m thinking about today. That there are these foundational bricks that we each have, ideas and beliefs and rumors, perhaps, that we each acquired when we were too young to know better. That we heard before we had the weapons, swords and shields, to defend ourselves.

and now, for something completely different

•7 April 2024 • Leave a Comment

The world is a complicated place at the moment. Wars, calamities, all sorts of bad going, really everywhere. Some of this arises from decisions made years ago and some of this arises from the actions of individuals. And that’s always been the case.

There are small comforts. Bob the cat comes in from a trip outside, spends some time kneading his blanket (and it is his blanket, for kneading), and then decides that it’s time for attention and HOW DARE I spend time typing when he’s sitting in front of the keyboard. And so yes, he gets his desired amount of attention. Because of course he does.

One lens through which to view this is the local global problem; the global issues are large, as everyone who follows the news knows, but there are the local comforts.

This local versus global problem comes up a lot of places. It comes up for instance in mathematics. The class I’ve been teaching for the past few (ten?) years is Graph Theory. The local structure of graphs is the same for all graphs, if we take a very local view. But the global structure of graphs, well that can be wildly complicated. And so the whole of graph theory can be viewed bridging this gap between the local information that’s easy to see and the global information that can be difficult to determine.

This is not the only place in which this local global issue arises. There is a class of mathematical objects called manifolds; very roughly speaking, manifolds locally look like Euclidean spaces. For a class of manifolds called symplectic manifolds, the localness is even stronger. But the whole field of differential geometry can be thought of as understanding how the Euclidean pieces fit together. (And yes, I’m lying to you in the sense that I’ve hidden a lot of the mathematical detail.)

But the mathematical local versus global issue is different than this Bob versus the world issue that I started with. And this is an interesting gap to bridge. And difficult. Because the local differs so much as we go around the world.

Part of this is that one of my areas of contemplation is, how do some of the mathematical ideas that have infused my day job interact with the real world. The local global idea in the real world seems to be very different than the mathematical local global idea. So, back to the chalkboard.

haiku and the ephemeral

•31 March 2024 • Leave a Comment

Six years ago today, I started writing a haiku a day and sending it forth into the world. I wrote about this a few years ago, and if you’re interested, you can find that here. My original intention had been not to keep a record of them but rather to view them as a project of transience and ephemerality.

In the end, when the ownership of Twitter changed hands, I went in and pulled copies from the memory of that platform, and so I have an incomplete record going back to 31 March 2018. I have since broadened out the range of platforms on which I send them out, and once thing that I know I need to do is to bring the information about all of those platforms together in a single place.

One direction of travel from this moment of reminiscence is the observation that this was a strange thing to do, in that I hadn’t planned on keeping a record. But I go back to Yanagi and the Unknown Craftsman, as I mentioned in that earlier post. I still like the idea.

There are other crazy ideas I’ve had but never implemented. One is to draft a story, very slowly, and release it one paragraph at a time, as part of the out of office messages I’ve gotten into the habit of setting when I’m out of the office. Perhaps that’s the next windmill of ephemerality to tilt into.

I suppose that one attraction of this ephemerality is that so much of what I do is written for someone else, recorded by someone else, occasionally published by someone else.

The mind then turns to historians. Many of the words written these days appear in our many social media platforms, or email, and how many of these will just disappear. We won’t have the occasionally voluminous correspondence, but how much of our regular correspondence consists of things we might not have wanted to save.

And so, epheremality, a watchword for our current age. Bane perhaps of the future and the record of our present day, but I’ll continue on my merry haiku path, until at some point I decide to move on to something else.

working an idea

•17 March 2024 • Leave a Comment

Last week, I pulled out a (mathematical) question I wrote down perhaps a couple of years ago. I keep notebooks for various ideas, mathematical ideas and writing ideas primarily, but I don’t date the entries. Rather, they bump up against one and another, waiting to be brought out of the cold and made use of.

Interestingly, reading through, there are some ideas that periodically recur; these are ideas that I think are worthy of some attention, if only because they’re ideas that my brain can’t quite rid itself of.

This idea mentioned at the beginning is not though one of these recurring ideas. Rather, it’s a much more recent idea, one that resulted from the deliberate smacking together of the body of material in the class I’ve been teaching for the past ten years or so, against the body of material that is the halo around my mathematical research.

I’m not going to be explicit about the idea, if only because I’m not yet sure whether it’s an interesting idea, or whether it’s true, but it is interesting to me at present because of its origin, this cross fertilization of teaching and research.

Sitting with a piece of paper and a pen, staring out the window, over the course of the week I made some notes about possible directions of exploration. But what caused the ice to crack and the log jam to break, was talking it through with someone who’d come to my office to talk about something else entirely.,

This reminded me of a (very recent) post in the sense that there is a difference between sitting in isolation and thinking, and talking through an idea with an audience. And I do find this a fascinating difference.

I’ll let you know if this idea goes anywhere. I remain optimistic at the moment,.

speculating on Colossus

•3 March 2024 • 1 Comment

I would like to spend some time today weaving together some old treads. I’ve written a couple of times before about Colossus, here (in 2018) and here (just last year). I’m not entirely sure why I keep coming back to this old story, written long before we had any strong evidence of just how computers will change our lives.

Perhaps it’s because I find it such a powerful cautionary tale. We build this machine, capable of gathering all available information and being able then to make binding decisions in the world based on its understanding of that information. And then it goes awry. This is an old story, the creation running amok. It is a reflection of that old conundrum, that being able to do something is not in itself a reason for then doing it. Can does not equal should.

So the question came to me recently: who is building Colossus. We are building more and more powerful tools; we see this in the news every day. We encounter them in our daily lives. And we don’t know how they work. This observation is fleshed out in an essay by Stephen Wolfram, and this observation is part of this ecosystem of ideas, these tools we build that we may not understand how to use.

But I’m sure that someone out there, some government perhaps, is building a Colossus. A computer, a programme, through which all information flows. A computer, a programme, that we can then ask, what are others doing. The quality of the answers will depend on the quality of the information, which is why I think it will be a government. Governments are the keepers of secrets; the image that comes to mind is the warehouse at the end of the Raiders of the Lost Ark.

If there were a machine that knew everything that was known, that possessed in its internal structures every fact known, what question would I ask of it? In Jokester, the question is the origin of humor. Others have their questions, but what would mine be, and I’m not sure.

What’s interesting to speculate about gets back to my day job. If this machine knows everything, then it knows all of the math we know, all of the math we’ve discovered (and yes, discovered and not created, and that is a different conversation entirely), and I suspect my first question would be a math question. Do we know enough to answer the questions that I’ve carried for years? Decades? For some, almost certainly not, but there are others, questions that lurk at the outer edges of the math I know well, and perhaps these.

And so, speculation. I’ll continue to ponder this question of which question, and speculate as well on what sort of answer we might expect to get.

reading and listening

•25 February 2024 • 1 Comment

I’ve been listening to a lot of podcasts recently. In part, this is just because I’ve gotten behind in listening to those to which I’ve subscribed. In part, this is because of the old ‘kid in the candy store’ phenomenon, wherein the sweets in every jar on the counter are in and of themselves, fascinating.

Some of my current list are fiction, some are non-fiction; some are very regular, others are to different degrees irregular; are though are still welcome, since if they weren’t, they wouldn’t remain on the list.

All of this listening, sometimes though not always while doing something else that doesn’t require my entire brain, has led me to speculate. And as with many of my speculations, I’m sure, willing to bet money sure, that there are PhD theses on this topic out in the world, answering any question I might craft in these idle speculations.

Listening is easy and reading is hard. This is an anecdotal claim at best, but looking around, I think that we spend a lot of time listening while we’re doing something else. We might have a conversation while talking to someone; we might be taking part in an on-line meeting, taking care of old emails and updating Amazon orders while keeping one ear in the meeting.

This isn’t to say that we’re listening well. We are in such situations just keeping that ear out for the mention of things that we’re most concerned about.

Yes, listening well is hard. Being the attentive partner to someone else’s speculations takes work, as rewarding as it is. But we can pay some attention via listening while doing other things.

For me, reading is different. Reading requires focus which is disturbed by background music, television, but strangely not the white noise chatter of a coffee shop.

Beyond this, I wonder whether we process the information we acquire from reading and from listening differently. I’m sure that we must. I have no formal evidence for this, no proof, but I do have my own experience, for what that’s worth. I can listen to a podcast while walking down the street, while I can’t read a book while walking down the street.

Perhaps this is just one part of a much larger phenomenon, with this at one end and the awkward conversations we sometimes have about the difference between the books we’ve read and the movies made from them. Something to ponder.

a strange non-linearity

•18 February 2024 • Leave a Comment

Let us go back in time. One of the first blog posts I wrote, going back to January 2014, concerned the possibility of the Number Liberation Front. It was a tongue and cheek introduction of an idea that’s persisted in my random contemplations, namely that writing numbers as words can hide their intrinsic magnitude; after all, the words million, billion, trillion are all close to each other as words, but they are very, very far from one another as numbers, at least within the realm of human experience.

How much does this inappropriate similarity impact on our understanding of such things as the budgets of nations. I think, a lot, and I’d be curious whether anyone has done the experiment of asking people, answer as quick as you can, whether 1 billion or 100 million is the larger amount.

But there are other aspects of this general phenomenon as well. One, which I can’t remember whether I’ve written about, is that we do have a strong tendency to want to rank things. And since we want to rank things, one better than the other, we do this by associating numbers to things, so that greater and lesser make sense. And over time, we’ve developed many different ways of associating numbers to things. Statistics is one of our tools for this, in all of its glory and sophistication, but this is also the argument that sports fans have, who has the better team.

What is the psychology of number? The non-linearity of the title is that most of the phenomena that we deal with, do not easily allow for such a linear ordering. The world is a complicated place, and things tend to depend on many other things. Chaos theory, as made famous to many via Jurassic Park, and its cousin complexity theory, tell us that our intuition often misleads us. We do not intuitively see the complexity inherent in worldly situations, and this is a phenomenon has been deeply explored, in Thinking Fast and Slow among other places.

And so, a challenge stands before me, astride the road I wish to walk. What is known about the psychology of mathematics and more specifically, the psychology of how we interpret number, and this is a challenge I’m looking forward to.

As the blog says, vote now, time is short

•18 February 2024 • Leave a Comment

Calling as BSFA members – we would appreciate your vote!

project miscellany

•21 January 2024 • Leave a Comment

After my recent declaration of project bankruptcy, I’ve been working through the old lists and thinking about which projects live and which are encased in carbonite and stacked in the basement. A friend and colleague has offered to be my external conscience, regularly reminding me of what projects are current and asking, so how are they going.

One project that remains on the list is a math project, a paper I should have finished some time ago. I won’t mention how much time, but yes enough time that I’m somewhat embarrassed to even acknowledge that this project remains among current projects. I’ve spent some time recently going back and reminding myself of where I am with it, what remains to be done and where the tricky patches of quicksand are located.

Quicksand. I read something recently, though unfortunately I don’t remember where or by whom (and a quick internet search gets sucked into descriptions of movies by that title, somewhat fittingly). When I was growing up, quicksand was a constant threat on television and in the movies, to the point where I suspect my generation would unflinchingly accept ‘trying to float without struggling’ as a reasonable action to take if one were to find oneself sinking in quicksand. I suspect, though, that this danger from my childhood might have been somewhat over sold as a danger we might come up against.

There is also the project that cannot be named. Those who know of the project about which I write will, I know, roll their eyes and turn away their gaze, so that they can chuckle in disbelief without doing so to my face. And those who don’t know, we’ll see if that particular project survives the Chapter 11 hearing.

Over the past couple of years, I’ve had an aikido project over the past couple of years. Last year’s project was both ambitious and ill defined, which is not the best of combinations. So for this year, I’ve decided to be a bit more specific and definite. I wish to improve my ukemi, specifically how I roll and fall out of the techniques as executed by others. At present, I think my ukemi is decent, but particularly as I’ve reached the age when I’m worrying about my age, I think this is a project that will have definite benefits both on and off the tatami.

Enough for the moment. I may spend some time this evening exploring whether I can discover from where this generational fear of quicksand arose, because the more I think about it, the more curious it becomes.

on teaching

•14 January 2024 • Leave a Comment

Looking back, I’ve written a lot about teaching over the years. Some of what I wrote has involved projects, some of which I’ve worked through, some of which I’ve started, and some of which remain nascent. Yet one more project would be to go back through all of the old posts and construct an index of those past posts involving teaching.

Some of what I wrote involves my own relationship to my teaching, and that’s what I would like focus some attention on here. The teaching for the semester ended a few days ago; I gave my last lectures of the semester three days ago, last Thursday, though the marking remains.

I’m always sad when teaching ends. I greatly enjoy teaching, the structuring of the material, working through details, seeing the light of engagement and understanding on the students’ faces.

And now, through the marking, I’ll get a hint about what I need to work on for next year, topics and techniques and theorems that I’ll need to focus more attention on.

And there are the larger questions as well. The ways of education are changing. As a caricature, there was a time, long ago, when facts were rare and precious things, recorded in books difficult to replicate. The reader, the lecturer, had access to these facts and made them available to students.

But now, facts are cheap, available via any web browser. At one point, just a few years ago, we then thought it would be the interpretation of facts that would become the important thing, rather than the memorization of facts. (And yes, this is all still a caricature of a much wider, a much deeper, a much more complicated conversation.)

But now, there are tools that seem – seem – to be able to interpret as well as we expect an undergraduate to interpret, namely the various large language models and their kin. And our current conversation is, what do these mean for us? Like most of my colleagues, this is a question I’m working on locally, in my own head, and as part of broader conversations.

Things are changing. Something that I thought would be a science fiction story might actually be an approaching reality, of personalized AI assistants that take the role of tutor, but that this would be technology that would be available to some rather than to all, exacerbating the divisions already growing in our world.

But that’s a story for another day, as it barrels down towards us like a runaway train. For now, I’ll get to marking and thinking about how to make my class better for next year.

on resolutions

•7 January 2024 • Leave a Comment

Let me start by wishing everyone a belated happy new Gregorian year. The history of years is itself a fascinating thing; perhaps that’s something to add to the ever growing list of things to consider and look into and read about.

There is a beguiling arbitrariness to where we set the beginnings and ends of years. If the orbit of the Earth around the sun were a perfect circle (which it isn’t), then there would be no one point on its orbit that would be distinguishable from any other point and the arbitrariness would be complete. But even with the orbit of the Earth being (essentially) an ellipse, there are distinguishable points on its orbit (from the lore of conic sections), but these aren’t the points we’ve chosen. And so there is something to look into here.

But that’s something for another day. There is a cultural tradition of sorts to set resolutions for the new year, changes of behavior that we wish to implement for ourselves.

We begin the year with the resolutions fresh and bright in our minds, but like a beleaguered prime minister in a race of endurance against a head of lettuce, they fade quickly as the days pass.

As we stand here on the verge of the second week of the new year, it makes some sense to ponder this cultural tradition. I have a few resolutions that are already fading, and I suspect that others might as well.

One thing I’m querying is this habit of making resolutions at a point in the year when we tend to be busy with things, family visits for instance and other calls on our time. Changing habits is difficult. Introducing new habits bring with it one set of challenges, while breaking old habits brings a different set of challenges, and those two sets of challenges are somewhat orthogonal.

And all we can do is to work through them. For me, going back to a recent piece, I’m trying to start over. I’m taking the projects I’ve given myself over recent years and I’m conducting an inventory of what should remain on the list and what should be left off. And so I’m giving myself some time and some space to decide, what are my resolutions for the year and what are then my projects that will arise from these resolutions.

And one of the difficulties with this is that I keep finding things that are interesting, and I keeping being reminded that finding and asking an interesting question (going back to the above) is far easier and far quicker than answering those questions, and so do we begin the new year.

project bankruptcy

•17 December 2023 • 1 Comment

The turn of one (Gregorian) year to another is traditionally a time from resolutions, for taking stock of the previous year and thinking forward to the year to come. I’m typically not much minded towards resolutions, but I have been known to indulge from time to time.

But I’m also aware that I have a tendency, which I’ve had since I was a much younger person, of having eyes bigger than my stomach. That is, I make plans more extensive than the available time allows.

This has a clear result, that my lists of things to do get longer, longer beyond my ability to do them given all of the everything else that life and work require.

Some long time ago, I heard the story of someone whose email inbox had gotten out of control. Too many unread emails. Too many notifications of things requiring their attention. And so they declared email bankruptcy. They deleted the whole of their inbox and sent out a message to everyone, basically saying, if you were waiting on a response then you need to resend, because it’s all gone. Just, gone.

Perhaps it’s a true story, perhaps it’s apocryphal. It doesn’t matter, for the lesson it gives. The thought that occurred is, perhaps I need to do the same with the ever growing list of projects.

What’s interesting is that my list of projects is an internal thing. They are my projects, and so it’s not the same as deleting the expectations of others. Rather, I have to think, which of these things, some of which I’ve carried with me for years, some of which I’ve carried for decades, which do I say, no more. No more attention. No more time.

Like a proper bankruptcy, it’s going to require some time, to sort through them and make the necessary decisions. But I think the time has come. More to follow.

reading in hindsight: Or All the Seas With Oysters by Avram Davidson

•26 November 2023 • Leave a Comment

Memory is a fickle thing. I’ve been doing some house cleaning recently, of the house in which I grew up, and while doing so I found lots of clothes hangers and paperclips, alligator clips and other office supply ephemera. And all of this brought to mind a story I remembered, by Avram Davidson.

So I dug around and found a copy, and it’s not nearly as strange a story as I remember it being. I have this vague memory of reading collected short stories of Davidson and them being very strange, and perhaps some of the ones I haven’t yet reread are very strange, but perhaps it’s just that my personal threshold is a lot higher than it used to be, from lots of reading.

The basic idea of the story is that there is an animal, whose life cycle goes from safety pins to coat hangers to bicycles, and the ebbs and flow of generations is why we sometimes cannot find a safety pin when we were sure we had many, or why there are so many abandoned bicycles on the side of the road.

The bit I’d misremembered were the safety pins. For some reason I thought it was paperclips, which is why my recent house cleaning experience brought the story to mind.

It’s always a strange experience reading a story from long ago; this particular story was written before I was born, around 1962, The story felt a bit old, in terms of the language, but it also felt a bit archaic, in terms of how the social interactions among the characters are described.

I can see though why the story struck in my memory, albeit imperfectly. Like many others, as gauged by the success of shows such as the X-files and Fringe, contemplate the possibility that there is something beyond the things we standardly see, and for me I can understand why.

We as humans have only been diligent in our exploration of the world around us, far and near, for few thousand years. Our ancient ancestors knew a great many things, and I keep being amazed at the articles in science magazines about what the ancients were capable of, but the world, the universe, is a vast and mysterious place, and we are to some extent bound by what we have witnessed and experienced in our local patch of the universe.

One example of this is the science coming out of the JWST and the observations we’re now able to make about the early history of the universe, and how we keep finding things that seem to test or challenge our current understanding of those early days of the everything that is.

And so why shouldn’t there be things that we have just overlooked, much closer to our own daily experiences. And this gets back to one of the reasons I like reading, particularly short stories, because they are such wonderful exercises of imagination and possibility.

the persistence of old myths

•29 October 2023 • Leave a Comment

I spent a bit of time this weekend just ending undertaking a bit of tidying of my desk at home. It is a Sisyphean task; it’s always a matter of tidy; find something more; tidy some more; find yet more, never ending.

I think I’m just in one of those Sisyphean phases at the moment, feeling that I’m never quite getting the stone to the top of the mountain. But I’m confident as well that it’s just a phase, something that will pass.

But one of the things I found, tucked away in a folder that itself was tucked away in a desk, was an old slightly faded list of possible topics for future blog posts. Some have been crossed out, but more remain.

The one that caught my eye was, ‘training closed, education open.’ It took a few moments but then I remembered what I’d intended by that. I was talking to someone, I can’t remember who, about the difference between training and education. This ties into that larger topic of the purpose of education.

One can take the view that training is a closed process: we are trained for particular tasks; we undertake training to learn or hone or refine a particular skill. But training has an end point that depends on the task under consideration. So I can go on a training course to learn Excel; I can undertake training for a marathon or a triathlon; I can (and have) undertake training to become a better line manager.

On the other hand, one can take the view that education is an open process. There is not a specific goal, in the way there is for training. Yes, it might be that as part of the education process, I become a better mathematician, but this is a much more open, a much broader end goal to the process.

Perhaps it’s just that I want there to be a significant difference between training and education. I do see a difference, but looking back, I’m not sure my thoughts are sufficient clear for me to persuade you of the difference.

I can look at the other big things in my days as well, where I spend my time. Aikido involves a lot of training. Particular techniques. Particularly break falls. But there is education there as well, which technique for instance in which particular circumstance, and how to understand how bodies move.

For writing, there is training in grammar and structure, but the education I think of a writer is a broader, more general process, that comes from reading and putting down words, putting down words, putting down words.

We are almost in November, and so it’s time now to put down some words and continue the education of this writer. I’ll keep working through this list over time, and thinking more about this distinction that I see between training and education.

more on teaching

•22 October 2023 • Leave a Comment

We are three weeks into our semester and I’m very much enjoying the teaching this year. My class, Graph Theory, seems to be going well and I’ve given a talk in the undergraduate seminar which seemed to attract some interest.

And the aikido teaching is also going well. We have some new members of the club and so I’m starting the process of learning to fall. I always find this process interesting, because falling well is something that can always be improved.

I don’t think there’s a specific reason why. Perhaps it’s that we’re a few years out from the hard years of the pandemic and students (and staff) are more comfortable. Perhaps I’ve just started seeing new things in the material and am enjoying sharing them.

Interestingly, I don’t view myself as a natural teacher; my memory of my days when I started teaching are not especially happy, but I do feel that I’ve made myself into a good teacher over the years.

And this is something I believe, that anyone can make themselves into a good teacher. It takes some practice and reflection, but it is a belief I hold, in part arising from my own personal journey.

The same holds for me as a teacher of aikido. As with math, gather and develop some experience and expertise; reflect on the good lessons and the bad, and I don’t think we pay enough attention to the lessons from the bad sessions; and steal from all the good teachers and all the bad, because there is so much that can be learned from all.

And so we move forward. We learn how to be better at the things we do, whether they are the things we do for ourselves or the things we do for others, walking the halls of the house of kaizen.

Ponderations

•15 October 2023 • Leave a Comment

The weather’s turned cold; just for the weekend, as going to warm of during the week, but winter has sent through its early calling card. The leaves on the trees are turning, some admittedly more resistant than others.

The cats like the colder weather, as they enjoy the fires in the evening, warming their bellies.

For lots of reasons, I’ve been thinking about the passage of time, the eddies and rapids in the river as it flows. Part of this, I’m aware, is my current fascination with my lists and how I’m working through them.

Part of it comes from sitting in the lounge or walking down the hallway upstairs, looking at all the books I’ve not yet read, and oh how do we make the time to do all that reading, particularly since glossy enticing books keep coming into the world.

At the beginning of the year, I set myself a reading project, but I’ve not yet started it and where has the year gone.

Thinking about it, reflecting as the sun sinks low in the sky, a significant piece arises in the accumulation of things. Work begets more work, as I develop expertise at dealing with complicated things, I remain on the list of people who get asked to deal with complicated things., and complicated things take time and attention.

I can remember an appraisal meeting with a senior colleague, many years ago now, where he told me the thing I needed to learn is how to say no. It’s something I’m still working on and is not something I do well.

But it’s all OK. I’ll reset my reading project, perhaps the same and perhaps something different. November is looming and I’ve never successfully NaNoWriMo-ed. The books are patient on their shelves, at least at the moment. And I’ll work on making my lists more reasonable for the days, because some days are by their nature busier than others.

on teaching

•8 October 2023 • Leave a Comment

We are one week into the new academic year, and I am reminded again of just how much I love teaching. There are several coal faces in academic life: one is this interaction with students; another is facing a research question that remains intimidating and mysterious; a third is taking on a new administrative responsibility and navigating a different aspect of university life.

I find joy in starting a new year and teaching a new group of students. Each group of students has its own personality, and I’ve always enjoyed the conversation involved in getting to know someone new.

Something similar happens in aikido, though not quite so starkly. We welcome beginners all through the year, but with the new students arriving at the beginning of the year, and older students wanting a change to their standard routine, we get a bulge of new people at this time of year.

This means we need to remind ourselves of the basics, falling and stances, basic movements and the foundational techniques, so that the joining beginners develop an understanding of how to move and how to fall.

But with both groups, I get once again to share the insights I’ve developed over the years. This gets back to things I’ve talked about to some extent, for instance the distance between experienced teacher and beginning student. I have to be especially sensitive to this distance in working with the new students, but I always enjoy the reminder.

on structures of words

•1 October 2023 • Leave a Comment

I’ve always been a reader, a devourer of words. Recently, I’ve felt a bit out of sorts, and I’ve come to realize that this is because I haven’t been keeping up with my reading. So this weekend, I spent some time with the words and I feel more settled for it.

But I’ve also recently been spending time stringing words together. The Milford Science Fiction Writers Conference 2023 ended last weekend, and that was an awesome week of hanging out with other writers of words.

For roughly five and a half years, I’ve been writing a haiku each day. I can’t remember why I started this particular exercise, but it’s been an interesting journey. Writing within such a tight structure – three lines, of five and seven and five syllables – is a fascinating challenge. Some days, the words come easily and some days, it requires effort to find suitable words to make up the count.

Some days, the haiku makes no sense but other days, I feel like the unknown craftsman of Yanagi Soetsu, fashioning and fashioning and on rare occasion, producing something of great beauty.

Even writing a mathematical paper puts my words (and formulae) into a particular structure, since there is a standardness to many papers. Or at least, to many of my papers.

A blank page, an idea before the words have gone down on paper, can be an intimidating sight, and so having a structure within which to work can be a useful thing, at least for me. But then, as with all of these, I’m just writing out of my own experience.

Even a blog post such as this, to get a bit recursive, is an engaging experience at the best of times. Blog posts tend to be relatively short, focusing on a single topic, raising many possible roads for exploration but alas, not having the time to walk them.

the efficiency of shelves

•10 September 2023 • 1 Comment

I’ve spent some time recently helping my sisters pack up the house we grew up in. It was an emotional experience, but I’m still unpacking that (no pun intended) (probably) and want to take this particular perambulation in a different direction.

One of our early tasks was to pack up the books, and there were a lot of books, to go off to their new homes. In doing so, I was struck by just how efficient shelves are.

This is not a particularly notable observation, but it did ring with me. Part of that efficiency is that books are heavy and one shelf can handle enough books to make a box heavy to lift. And there was much lifting. But beyond that, shelves are efficient in their tidiness; a few reasonably sized shelves give rise to a small pyramid of boxes.

At this middle stage of my life, I have some reasonably nice shelves around the house, and more books than can fit comfortably upon them. But what to do about this is a different question, and again one I won’t address here.

Earlier in my life, I had crude shelves, boards and cinderblocks, and shelves are something that we are all familiar with and may not give a second thought to. But what’s the history of shelving? What is the archaeological evidence for the persistence of shelving through human permanent settlements?

I’m sure there is a niche of scholarly activity wherein people spend their time packing and unpacking the human history of shelving, and I may have to do some exploration of that scholarly activity, because I’m curious.

After all, we are coming to understand our earlier human selves more and more deeply as time goes on, how they lived and how they furnished their permanent settlements, and I wonder now whether we have some estimate of when shelving first appeared.

But beyond that, I now need to go back and look at how I use my shelves. Books, yes many books, and other things, nicknacks and things collected over many years, some of which have been tucked away behind other things.

And so, shelves. Good things, shelves. Useful. Overpacked. Carrying the weight of memories that we’ve accumulated over the years. Viva the shelf.

the habitual

•20 August 2023 • Leave a Comment

I’ve been thinking a lot recently about habits. I’ve done some amount of reading over the years, and I’ve been considering how I work my way though the days and weeks.

I recognize that some people feel that habits are counterproductive, in the sense for instance of being a straightjacket on their passage through their days, but I’m coming to see that a set of regular habits is helpful for me.

Part of this is me reflecting on my aikido practice. Our annual summer school was last week, a good solid week of aikido, and I came away with a few souvenirs, a tweaks shoulder and a sore foot, but I also came away, as I do every year, with an appreciation of what the regular application of effort can accomplish.

In a sense, this is the opposite of a stream slowly eroding away a rock sitting in the water, as I’m building up my level of skill over time. It is the case that my speed of increase has essentially leveled off at this point, and given how long I’ve been practicing that’s only to be expected.

But there are other areas where I haven’t been as diligent about applying effort as regularly as I apply effort to aikido. And I think those areas of activity would benefit from that regular application of effort.

This is not a new realization; I’ve been through this cycle before, I’ve had this realization before, but what might be different this time is that, for all sorts of reasons around all parts of my life, I may finally be ready to listen.

And so I’m writing in praise of the habitual. Of having a structure and a schedule, and even (as in the case of my stretching regime) doing the same activities regularly, and just listening while doing them. Interrogating them through the activities, and listening to what they say.

further consideration of the Toolmaker Koan

•30 July 2023 • 2 Comments

I keep coming back to the Toolmaker Koan. I’ve written about this before HERE (and perhaps elsewhere). But the koan is basically the observation that the ability to make tools seems to outpace the capacity, the understanding to use those tools well.

We are developing, and have developed, some incredibly powerful tools, whether we use a limited definition of tool or a broad definition. I’ve been reading a lot about the machine learning tools we’ve been developing, such as the large language models that machinize a strange global average of language.

There is a lot of speculation about what impact these large language models and their successors will have on current human civilization. I work in one of the professions, education, that is sometimes mentioned as one of the professions at risk, with speculation such as individual artificial intelligences for each person, developing and monitoring their own individual educational journey.

We will spend the next few years working through the implications of this particular tool, hoping that we don’t find ourselves in a Skynet or Colossus scenario. But there are other tools.

There is the classic tool that provokes thoughts of survival or destruction: the fission bomb and its bigger, angrier cousin, the fusion bomb. I won’t spend much time here, because we’ve been living with this for decades now.

There are many directions we can go from here. One is to broaden the definition of tool. We are experiencing at the moment interesting consequences of the limited liability corporation, and I think the corporation is a fascinating tool.

One idea here is that the corporation is a form of artificial (perhaps collective) intelligence. We act as individuals, but we also act as part of this larger organization, which as its own goals, which might be goals with longer time lines than individual human lives.

So many tools to consider. And right now, I’m watching Unknown: Cave of Bones on Netflix, thinking about stone tools and the the earliest amongst us who had captured fire. And perhaps even ritual as one of our earliest tools. There is so much we don’t know and we will never know.

But I do think this is one of the fundamental questions for us to consider. How do we use well the tools we develop.

mathematical machinery

•16 July 2023 • Leave a Comment

For reasons I don’t want to go into yet, though I will at some point, I’ve been thinking through aspects of the machinery that mathematicians use to explore the mathematical landscape.

OK, fine, I’m speculating, as others have done, about how mathematics can be used as the underpinning framework for magic in a story I’m pondering, and in particular whether there’s something nifty and interesting I can bring to that conversation.

There are lots of places to start this speculation; one of them is the humble If Then logical implication. As tempting as I might it to be, I won’t dive into the glorious pool that is mathematical logic, but I will say that the basic structure of this statement is If X Then Y, where X and Y are themselves statements.

We then explore the truth or not of the whole statement ‘If X Then Y’ in terms of the truth of X and Y individually, and this is normally expressed as a table of values. (If you want to know more, you can look at the Logical Implication section of Truth Tables.)

But I want to go in a different direction here. There is an enormous power in being able to decide the scale and scope of consideration in the If statement, the X above, and then to create something in the Then statement, the Y above, so that the world created Y falls within the scale and scope of X. That is, we get something along the lines of If World Then Story.

This is one lens through which to consider fictional worlds and the stories set within those stories, whether the statement If World Then Story works as an internally consistent story.

I don’t want to get into the details of the story I’m working my way through; hopefully, in the not too distant future, I’ll be able to point you to where you might read it.

I’ll admit that I’m not yet persuaded that there is anything nifty or weirdly interesting about what I’m thinking through here, but I view it as a first step in a much longer journey. Who knows, maybe I can smuggle enough things in to make mathematicians of people without then even knowing it. One can dream, after all.

cycles and rhythms

•25 June 2023 • Leave a Comment

We are at the end of our academic year. Teaching has finished, exams have been sat and marked, and we’re at the end of our boards of examiners process, getting ready for marks release to students on Thursday. And here, I find myself thinking about the rhythm of the year.

Highs and lows, busy times and somewhat less busy times, the year does have its own particular rhythm, and so that rhythm will restart, getting ready for the next year. And so one task for the summer is to go through the notes I’ve written for the class, read some papers and make some additions to the notes, polishing and refining what’s there.

The aikido year also has its rhythm. I didn’t make as many of the courses through the year as I’d hoped, but we are getting close to our annual summer school, which I’ve very much looking forward to. I know that at the end of the week I’ll ache, and it will take a few days for that ache to ease, but it’s a bookend of sorts.

There are the quiet rhythms that inhabit individual days, from waking and journaling, reading, working and aikido and writing.

Interlocking rhythms, short and long, and what song to they combine to sing, and that’s the song of the shape of a life. Each of us with our song, the harmony and dissonance of families and friends. Together, all of us on this Earth combine in a grand and glorious opera, but our collective song is not yet finished.

I’ve been thinking about Surak, the (fictional) character who led the Vulcans away from this song of violence to their (in our watching) current path of logic. I’ve commented on Surak before, but what I find interesting today is that there were always a few Vulcans in the various series of Star Trek who didn’t follow the way of logic, or who disagreed about what the path of logic meant.

Surak comes to mind because I wonder whether we’ll find ourselves, collectively and voluntarily, looking for a Surak, a way for us to follow, and one that we can agree on. What makes this complicated is that there are already a number of different ways that various folk have promulgated as ways for humanity going forward, but we haven’t yet collectively agreed on one to follow.

What will be the song of humanity. Science fiction has been writing about possibilities, optimistic and not, of this song for decades. But what will be our song.

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 • 1 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 • 2 Comments

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 • 1 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.