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

beginner’s mind

•25 September 2022 • 2 Comments

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

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

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

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

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

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

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

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

supervillainry revisited

•4 September 2022 • Leave a Comment

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

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

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

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

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

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

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

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

Posted in bizarre and random things

reflections on aikido

•21 August 2022 • Leave a Comment

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

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

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

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

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

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

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

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

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

the individual versus the collective

•31 July 2022 • 1 Comment

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

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

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

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

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

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

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

Posted in bizarre and random things

reflecting on a story I once heard

•10 July 2022 • Leave a Comment

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

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

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

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

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

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

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

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

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

Posted in bizarre and random things, mathematics

a meditation on story

•5 June 2022 • 2 Comments

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

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

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

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

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

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

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

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

Posted in writing ephemera

the many variations of we

•29 May 2022 • Leave a Comment

This is going to be a bit of a ramble.

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

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

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

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

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

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

Posted in bizarre and random things

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