taming the hydra

•17 September 2017 • Leave a Comment

I suspect that what I’m about to write is a thing well known to others, and a thing that other writers have experienced.  Perhaps it’s a thing that’s an inescapable and necessary product of the act of writing.  But it is one of the things on my mind today and so I thought I’d scree a bit.

I’m at the moment taking a short break, or engaging in a bit of a procrastinatory frenzy, from the current story project depending on your point of view, as I’m having difficulty keeping to the straight and narrow of the path I’ve planned for this story.  Because I have a clear plan.  I know how I want this story to be unfold, beginning and middle and end.

In fact, I have many many many ideas for how I can see this story unfolding, beginning and middle and end.  There are two main characters, and either one can be the main character.  There is the main moment of action, which can take place here or there, where here and there are very different places.  There is the degree of bat shit craziness in which I’m willing to engage, from the very mild to the garden sheds in the rather extreme outlying suburbs of my imagination.  And each of these leads to a different story.

Like the hydra in full flow, each time I sit to write, I find that one of these other heads seems to be the more attractive story than the story, the head, I’ve sat myself down to write.  And so I find myself to be the victim of temptation.

Each writer has their demons to defeat.  For some, it’s the fear of writing something unworthy or stupid, and some have described this relationship with their fear, and the bargaining they regularly have to undertake with their fear, in heartfelt and compelling detail.

And I’m beginning to realize that perhaps my demon is this hydra of distraction.   This hydra affects not only my writing, as once I see it for what it is, I can see this hydra of distraction at work in my mathematical life.  And I can see that for my mathematical hydra of distraction, I have found some strategies for fighting my hydra with some success.

And so now, I need to develop strategies for battling my writing hydra.  I need to kindle the torches that I will use to cauterize the stumps when I cut off its heads.  It will take some time, and I am sure that I will never defeat my hydra, but I am confident that I will find a way of keeping it in some sort of check.  And so now, back into battle.

the atemi of committees and policies

•10 September 2017 • 1 Comment

This one is going to be a bit of a strange one. One of the early lessons I learned around the I moved to England and started working at Southampton came from the then Secretary and Registrar of the University. He came to the Department to give a session on the University committee structures, and during that session, he said something that’s stuck with me ever since.

Paraphrasing, his point was that by the time a proposal or a policy, anything needing a decision, reached one of the main University committees, it should essentially be decided. It was an interesting lesson he presented, and it’s entirely possible that my memory of that session is not perfect. But it was an interesting lesson that shaped how I started my path of learning to be a member of committees and learning how to be the chair of a committee.

To be honest, I’ve come to disagree with that sentiment, as I think there can be real value in deep discussion at the committee stage. Yes, there are times when extensive consultation takes place and it falls to the committee to distill that consultation and produce a proposal for consideration further up the chain. But there are also times when the final decision falls to the committee. There is a matryoshka effect here, with committees within committees within committees, each playing their own part. Each feeding into the others.

But I want to talk about a different aspect of committee life, one that is inspired by the aikido that I do. There is a particular aspect of aikido that I’ve been paying attention to for a while, namely atemi. In a very direct way, atemi is a strike, possibly a punch, that the person doing the technique executes on the person of the person on whom the technique will shortly be done, not with the intention of wounding but rather with the intention of distracting, for lack of a better term.

It’s a bit difficult to picture, but very very loosely indeed, if for instance someone swings a sword at me in an overhead strike, attempting to do to my head what a knife might do to an apple, then I will step to the side and give them an atemi to their ribs. This has the effect of disrupting their follow up strike and provides me with the time and space to remove the sword from their possession and gently but firmly persuading them of the error in their ways for swinging their sword in the first place.

And so atemi is distraction. But more than this. My favourite description of atemi, a wider translation of the term but one whose origin I’ve forgotten over time, is the taking of another’s mind. So the purpose of my atemi is essentially to so disrupt my opponent’s mind that I have taken their attention away from them.

And this is a useful thing to be able to do in a committee setting, whether it be a deliberative committee or a deciding committee, to give them names. Sometimes it is a very useful thing to do, to distract, to steal away from them the attention of the members of a committee. The most straightforward way of doing this is to put something on the agenda that the chair knows will attract the attention of the members, something controversial, but to have the properly contentious item elsewhere on the agenda. The members may then exhaust themselves on the planted agenda item and not have the energy to discuss the properly contentious item.

I do find it a bit strange that I’m writing about this, potentially giving away one of the secrets to how I approach things, but then I realised that I’m actually not giving away anything. No one knows what I view as the properly contentious items and as the other items. For those on the same committees as me, particularly on those I chair, they might well need to pay attention to all of the agenda items, given that they won’t know which is which.

But now, we take a left turn into the wilderness that is zen. One of the basic lessons of zen, as I understand it at present, is that it is the experience of the moment that demands and deserves our full attention. This is a common interpretation of zen in the martial arts, where each encounter with an opponent has to be experienced fully and has to be taken for what it is, which is a moment that will never come again. And a moment around which we will not get a second chance. This is the zen of the tea ceremony, in which each cup of tea is poured only the once.

One of the things I like about zen is its universality. The same zen that underlies how we experience martial arts and how we experience the tea ceremony, this zen underlies everything. And in particular, it underlies how we experience moments in committees. Zen underlies how we experience those occasionally interesting and awkward moments in committees.

Perhaps I’m overstating the case, but I do think that this is all connected. I do think that all of these different parts of my life impact on and inform one another, and reflecting on my experience of each makes me better at the others. I’ll admit that how sitting in committees improves my aikido is still one I’m working one, but I’m sure I’ll find something there if only I dig deep enough.

exterminants and the lost arts of mathematics

•3 September 2017 • 1 Comment

There are several -ants in mathematics.  Determinants are the classical -ant of mathematics, easiest to define and understand for small matrices but with a wide degree of usefulness and a remarkably wide range of definition.  Resultants are another, again very useful and again with a wider range of definition than initially apparent.  And perhaps, there are other more obscure -ants.

How mathematicians name concepts and objects is an interesting discussion in its own right and a topic we leave for another day.  But one thing I don’t know, because it’s not something we tend to talk about at conferences or over coffee, is whether other mathematicians find a term they like, write it down and save it, and then look for an appropriate concept or object for that particular term.

The term I’ve been saving for a long time is the exterminant.   The terminology of mathematics can sometimes seem to be violent, with its annihilators and Killing vector fields, though admittedly the later is named for Wilhelm Killing rather than for any violence that the vector field itself might perpetrate.

I was tempted, I’ll admit, when I first had the idea of exterminants, to write about the discovery of a lost manuscript, or the rediscovery of a lost mathematical method, due to an obscure mathematician, perhaps Georg Eigen.  And perhaps some day, I will because it’s an idea that I’ll admit haunts me.

And this haunting is part of something much larger that I’m still working my way through, which is my personal vision of how to blend mathematics and fiction.  What are the stories that I want to tell and how do I want to tell them.  There are others who have done this very successfully, including but not limited to Rudy Rucker, Greg Egan, and Larry Niven, and others such as Robert Heinlein with their occasional mathematical stories, all authors I’ve enjoyed reading for as long as I’ve enjoyed reading.

And perhaps one day I’ll define something for which the term exterminant is an appropriate term.


mathematical ideas in every day life: squaring the circle

•14 August 2017 • Leave a Comment

I suspect, given where my thoughts currently are, that the following is going to be a bit rambling and somewhat labyrinthine. And even this, for a reason I’ll get to at the end, is not entirely correct, but I like the word, labyrinthine, and I’m feeling a bit indulgent today.

I was in a meeting a couple of weeks ago, and one of the other people in the meeting used the phrase, it’s like squaring a circle, to describe something difficult. I think the look on my face gave away my internal view, since everyone turned to look at me and started laughing in a friendly way at my evident discomfort. I decided that this was a situation in which discretion was truly the better part of valour, and I just let it slide.

I think that ‘squaring the circle’ and ‘we need to square the circle on this one’ have become commonly used phrases for something difficult, but this is not what these phrases should mean. And my apologies, gentle readers, but now I need to go into a bit of mathematics.

One of the classical geometry problems from antiquity, so from the ancient Greeks of roughly 2500 years ago, was the problem of squaring the circle. A reasonably constructed sentence, that of course tells you the reader no more than you knew about a question you didn’t know was in fact a question, except that it’s a old question. The Wikedia article is good, but I’ll summarise the essential bits. And this touches on what I started to do, and never finished, in the numerology of unrelated constants 1 and the numerology of unrelated constants 2, the completion of which has now gone back on the LIST OF THINGS TO DO.

So.  Take a circle in the plane, which has a radius R and which encloses an area of size A. The size of this area is given by the formula A = π R² and this is a formula that we have known since early days in school.

A question that you may wish to ponder is, why is this formula for area true?  It may be that you’ve never pondered this.  Of course, your teachers and the textbooks used state that this is the correct formula, but it isn’t until much later in our mathematical education that we develop the techniques that allow us to construct an argument to explain where such formulas come from.

Back to the question at hand.  The question of squaring the circle is this.  Given a circle C, of any radius R, construct a square S which encloses an area of the same size as the area enclosed by C, using only a compass (which allows for the construction of a circle of any center and any radius) and a straight edge (which allows for the drawing of lines of any length).  We can reframe this a bit.  We know that if S is a square whose sides of length s, then the area is enclosed by S is s².

And so, given the circle C of radius R enclosing an area of size A = π R², find a square S which also encloses an area of size s² = π R², again using only compass and straight edge.  And so things boil down to is, how to construct the square root of πusing only compass and straight edge.

And this is impossible to do, as we learned in the late 1800s.  The reasons are complicated, but the point that I would like to make is that this is actually impossible.  It’s not that it’s difficult.  It’s not that it might be possible but we don’t yet have an argument.  Rather, it cannot be done, and this impossibility is not something that sits well with most people.

Mathematicians I think are used to this notion of impossibility, and in fact I suspect that each of us, when we’re working on a question we’re finding difficult, always have the faint worry in the back of our minds that perhaps we’ve hit upon one of these impossible questions.  Almost always, it’s just that the question is hard or we haven’t yet seen the path to a solution.

As it turns out, there is a way of squaring the circle, if we allow remove the restriction of compass and straight edge.  But this other way involves doing violence to the circle in a way that is exceptionally hard to imagine.  Perhaps another day.

on the zombie apocalypse

•5 August 2017 • 4 Comments

I’ve been thinking about the zombie apocalypse. Not the middle or late stages of the apocalypse, since that always seems to follow a straightforward and predictable course, as we see in World War Z and 48 Days Later and many many other books and movies.  Wherever they have come from, zombies bite people and create new zombies, and so it continues until it reaches an end.

Rather, I was thinking about the early stages of the apocalypse, of how the apocalypse begins. Whether for instance, a la Night of the Living Dead and Thriller, the dead rise from the earth.

Driving through Georgia over the past couple of weeks, I made an observation. We passed many cemeteries and memorial gardens on the road: some were old and some more recent; some were small family plots and some large scale community enterprises. But only one of them was enclosed by a fence or a wall. Particularly given that The Walking Dead is set in Georgia, I would have thought the locals would be more concerned with the dangers of the rising dead.

In England, on the other hand, almost all of the cemeteries are surrounded by a wall high enough to impede zombies from freely wandering the landscape. Perhaps there is a simple cultural explanation about how we should remember the dead.

Or perhaps there’s a deeper explanation, that this difference relates back to a now forgotten but recent zombie apocalypse, which struck Europe, hence the walls, but missed the US, hence the lack of walls and fences. I know that it’s a bonkers idea and that it’s a horrible thing to wish upon people, but I want this zombie apocalypse theory to be true. I want there to have been a zombie apocalypse and some deep, persistent cultural amnesia, the only memory of which is the existence or lack of walls around cemeteries.

And once one idea gets started, other ideas start creeping in. What would happen to nuclear power stations during a zombie apocalypse. I’ll admit that I am not an avid or extensive reader of the zombie canon and so perhaps this idea has already been done, and done well, but I suspect there is a good story about a group of workers holed up in a nuclear power station, desperately trying to keep the core from going critical while being besieged by zombies.

This ties into a different thread of ideas, namely that of the doomsday scenario, in which we have created something which we cannot undo. We then have to spend more and more effort in keeping this thing we cannot undo from going bad, until at some point this takes all of society’s effort, and then something breaks. Admittedly, the zombies are not the doomsday scenario but this might be a strange way of exploring some of the issues around nuclear power, an idea that’s been explored to some reasonable extent.

I think that money might be considered as a doomsday device, and that there are others. But this is taking us away from the zombies. Though this has admittedly been a bit for a facetious zombie rant, I think it highlights something different. Namely, how do we as humans build systems to remember things that we do not want to forget.  This preservation of knowledge against the ravages of time and disaster is something that I’m starting to explore, and a fascinating topic it is.

when ideas disappear

•5 August 2017 • 1 Comment

A few nights ago, when I was more than halfway asleep, I found myself besieged by some ideas that I thought might be worth saving.  Like everyone else who’s ever admitted to trying their hand at stories or a novel, I get asked where my ideas come from.  Sometimes, the answers are more interesting than the question, though I’m not sure about the case at hand.  For me, some of the time, they come from the random confluence of two tangentially or unconnected things that happen to mesh in my brain.  Amusingly, these will sometimes reveal themselves, unbidden by any wish of mine, in the flow of conversation.   But some of the time, they are just the bumps in the road as I’m walking to the Land of Nod.

Working by the light of my phone, I dutifully wrote them down, trying to include enough information to allow me to reconstruct them come the morning. Of the four that I wrote down, three made sense in the light of the new day. One is a different take on a idea I’ve been kicking around for some long time now.  Keep watching, in hope 😉  One was inspired by the book I’d finished before turning out the light. One is an idea that came while driving. But the fourth consisted of a single word. Lucy.

And I have no idea what this fourth note was supposed to be. Lucy is the name of my parents’ dog. A lovely dog, and we were visiting mom and dad a few days ago, at the time I wrote this note to myself, but for the life of me (and how English have I become) but I can’t reconstruct the idea I had. All I have is the knowledge that half asleep, I thought that I had a good idea for a story that somehow related to Lucy, but no information and no idea of what that idea might actually be.

And it has to be Lucy the dog, since there are no other Lucys that I’ve been thinking about. There is an aikidoka named Lucy I used to practice with occasionally, years ago now, but I hadn’t thought about her for many years until I started conducting this most recent internal Lucy audit. There is the Scarlett Johannson movie, which I haven’t seen and which is on the list but not at present high on the list. There is I Love Lucy, but again, not something that’s had been in my mind recently. And I still have no idea why I wrote Lucy in my list of ideas, though I am half convinced that it was a good idea. Clearly, at the time I thought it was once worth saving, and that the single word Lucy would provide a sufficiency.

In retrospect, the irony of all this is that had I not woken up and written down Lucy on my list, I probably wouldn’t have remembered that I’d had an idea in the middle of the night, and I wouldn’t have found myself in this position of being haunted by the ghost of an idea but without the body of the idea to bury.

This has happened before. For more than 20 years, I’ve been haunted by the ghost of a mathematical idea, one that I didn’t write down before falling asleep. One that left the same hole in my imagination. It was after this mathematical ghost visitation that I started keeping paper and a pen by the bed, writing down the ideas that hit as I’m falling asleep. I’m still waiting for that mathematical idea to reveal itself, though I’m beginning to suspect that it just might not. Hopefully I won’t have to wait as long for Lucy to reveal herself.  But she hasn’t yet.

the commencement address I should have given

•24 July 2017 • Leave a Comment

Earlier today, I delivered a speech at one of our graduation ceremonies.  The British tend not to refer to them as commencement speeches, but it’s the same sort of thing, namely a mildly rousing, now-you’re-going-forth-into-the-world-and-don’t-forget-us inspirational address to the new graduates.

I didn’t write the speech, and I’m glad of that for reasons I’ll get to in a few paragraphs.  It was a good speech, referencing the university and its mission, highlighting achievements from some of the students, and by all accounts I delivered it fairly well.

But had I been given the opportunity, and more importantly had I been willing to seize the opportunity, offered or not, there is a different speech I should have given.  I’ve always been captivated by the non-Vonnegut non-commencement address, because it sings to me.  I was tempted, I’ll admit, to forget the speech I gave earlier today (with all apologies to its author) and give the non-Vonnegut non-commencement address, but I didn’t, perhaps to my eternal regret.

But it did start me thinking.  What things would I try and blend into a commencement address?  What sorts of messages and lessons would I want to pass on, even if to a group of students and parents who at this point in the ceremony are looking forward to celebrating, rather than sitting and listening.  And there are a lot of things I would want to bring in.

I’ve always been taken by The Invitation by Oriah Mountain Dreamer.  I chose to give it as a reading when my sister got married and it’s something I find myself coming back to regularly.

Somewhat weirdly, I’ve always been fascinated by the four enemies of the [person] of knowledge  by Carlos Castenada.  I read the Teachings of Don Juan at a young and impressionable age, and this one part in particular has never left me.  Though I’ve not explored this in any depth, I’m sure there are connections between this and the Bene Gesserit Litany Against Fear, and with many Buddhist teachings.  Something to add to the list of things to do in retirement.

There are other things as well.  I’ve been collecting sayings and aphorisms and bits and pieces for years, which I go back and read through from time to time, and there is a lot in that list that is valuable and interesting and perhaps sufficiently worthwhile to subject others to.

I’m not sure what the perfect commencement address would be.  I suspect that it could only occur at some strange temporal and spatial intersection between me and my state at that moment, my audience, the phases of the moon and the sun, and many other things besides.   And I can only hope that some day in the not too distant future, I find myself at that intersection point, written and ready.