the relentless march continues

•5 February 2023 • 1 Comment

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

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things

the relentless march of technology

•30 January 2023 • 2 Comments

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

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

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

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

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

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

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

Posted in bizarre and random things, education and university life

and lo, the new year calls

•8 January 2023 • 2 Comments

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things

Being interestingly wrong

•11 December 2022 • 1 Comment

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

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

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

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

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

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

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

the koan as a lens

•20 November 2022 • 1 Comment

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

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

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

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

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

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

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

Posted in aikido, bizarre and random things, mathematics

the art of the question

•13 November 2022 • 5 Comments

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

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

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

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

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

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

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

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

Posted in aikido, bizarre and random things, mathematics, writing ephemera

the size of the multiverse

•23 October 2022 • Leave a Comment

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

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

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

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

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

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

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

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

Posted in bizarre and random things, mathematics

the inverse TARDIS effect

•16 October 2022 • Leave a Comment

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

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

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

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

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

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

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

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

Posted in bizarre and random things, education and university life

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

•9 October 2022 • Leave a Comment

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things

the beginning of a new academic year

•2 October 2022 • Leave a Comment

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

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

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

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

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

And so, the work continues.

Posted in aikido, education and university life, mathematics

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