thinking about issues of scale

•22 March 2022 • Leave a Comment

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

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

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

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

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

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

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

Posted in bizarre and random things

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

•20 February 2022 • 2 Comments

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things, writing ephemera

the administrative bends

•12 February 2022 • 1 Comment

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things, education and university life

legacies in old lists

•23 January 2022 • 1 Comment

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things, mathematics, writing ephemera

looking ahead into 2022

•22 December 2021 • Leave a Comment

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

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

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

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

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

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

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

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

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

an early reflection on 2021

•12 December 2021 • Leave a Comment

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

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

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

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

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

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

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

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

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

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

an echo of moments

•14 November 2021 • Leave a Comment

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

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

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

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

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

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

Posted in bizarre and random things, writing ephemera

spending time with an old friend

•7 November 2021 • Leave a Comment

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

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

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

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

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

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

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

the richness of old lists

•31 October 2021 • Leave a Comment

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

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

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

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

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

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

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

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

a reflection on teaching 3

•24 October 2021 • 1 Comment

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

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

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

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

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

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

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

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

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