Sunday, March 02, 2014

Watching fractals emerge at the edge of chaos

We may have an innate ability to recognise mathematical results as beautiful, but that can prove difficult if they're buried under an unhelpful press release. I was intrigued by the headline 'Probing the edge of chaos', in a recent release from the European Physical Journal B, but I wasn't surprised that it wasn't one of the ones picked up by the mainstream press. There didn't seem to be much that would grab the attention of a non-specialist journalist or editor, or be of obvious interest to the general reader. Someone clearly thought differently, though, otherwise why the press release? But as so often happens with mathematical papers, the point got a bit lost in translation.

Chaos is particularly hard to explain, of course. It's easier to describe than define; one of those you- know-it-when-you-see-it types of things. That's an odd thing to find in mathematics, the one place where we expect everything to be perfectly logical, clear and well-defined. But then, it's called chaos for a reason.

Chaos in this context is something that happens to dynamical systems, and these were the main focus of this paper. A dynamical system is any set of possible events that can happen; together with a 'rule' that dictates how the events develop over time. That covers a vast range of possible scenarios, from a simple pendulum swinging back and forth, to the behaviour of a complex weather system. A deterministic dynamical system is one where we should —in theory — be able to predict what happens next, based on what came before. But sometimes, what should be doable in theory becomes virtually impossible in practice — and that's probably as close as we can get to a definition of chaos. The butterfly effect is a well-known example, where a small change in a complex system can have dramatic and unpredictable results.

But even a chaotic system tends to reach some kind of equilibrium eventually. This 'attractor' is the state the system reaches eventually, when it's explored all the possibilities it's going to: when the more things change, the more they stay the same. There are also 'repellors', areas of possibility that the system tends to shy away from. These change at different points in the system's lifetime. What areas are attracting and repelling our process when it's operating in its normal, non-chaotic state? How does that change when it becomes fully chaotic? And, most interestingly, what's going on at that critical transition point when it's just about to tip over into chaos? This 'edge of chaos' is a curious place, mathematically. Strange things happen there.

There's more than one route to chaos. A common one, though, is the period-doubling cascade, when changes in the behaviour of the system start happening at twice the previous rate, and then twice that new rate itself, taking it accelerating rapidly into chaos and unpredictability. Write down the equation for this process, and use it to plot a graph of the results when it reaches its attractor, and you'll end up with a startling fractal pattern. This is the famous Feigenbaum attractor, and its existence is well-known. What wasn't so clearly understood, however, was exactly how it happens, and what the steps along the way look like.

The researchers here broke down the process, watching the gradual evolution of the attractor as it changed from the simple limit of the non-chaotic system to the perfectly formed fractal of chaos. The path was not a smooth one. Studying their results, the authors remarked on the complex structure, the many 'rough, jagged features'. And it got more interesting, the closer they looked. With each step, it was accumulating a hierarchical structure, a pattern that emerged on multiple scales; the fractal building up little by little, emerging before their eyes with each successive step. We now have the equations and histograms to describe exactly how that process happens.

The press release vaguely mentions that the results might lead to better understanding of chaotic natural phenomena. That's difficult to judge as they don't explain exactly what or how.

But if we really have that ability to see beauty in pure mathematics, maybe it doesn't matter so much. Maybe what this story really needs is not a vague practical 'application' tacked onto it to justify its existence, but a visualisation of the data, so we could see the system evolving from simplicity to chaos, along that wild and rugged road into multifractal complexity. The idea of it is beautiful, I think. But seeing is believing. And sometimes it takes more than a histogram.

Saturday, February 22, 2014

Interdisciplinary research: my Guardian article

The Guardian's Higher Education Network recently published my article on interdisciplinary research from an early-career researcher's point of view, and what the trend means for our future careers. Based on discussions in real life and on social media, I suspected I wasn't the only one with concerns about this, but I was still surprised by how many positive responses I got from others in the same situation. Clearly this is something we need to talk about.

There were some interesting comments from researchers in other fields (apparently this is just as much an issue in arts and humanities as in science), and in other countries (some suggested the narrow focus of the UK university system might be part of the problem).

It was also curious to see that there was much more of a response and discussion on Twitter than in the 'below the line' comments on the article itself. Maybe that says something about the future of comments?

Sunday, May 05, 2013

New story: Over The Sea

I have a new story, Over The Sea out today in the May issue of Sorcerous Signals from Wolfsinger Publications. It's also in issue 18 of the print magazine, Mystic Signals, which is available from CreateSpace

So, what to say about this one? It's a high fantasy tale, referencing various tropes of the genre but trying to find the real human emotions and stories behind them. Thinking about it, this is also another one that tries to subvert the 'princess needs rescuing' trope. Sometimes there are no eagles. And sometimes the princess doesn't need or want (or deserve) rescue.

Thursday, April 18, 2013

On the radio, nobody knows you're an introvert

Here's an interesting experiment: get a randomly selected group of people together to make a short radio program, record it as if live, and then listen to it played back. You might have some expectations about how it'll be. The confident, chatty, extroverted types who love to talk -- surely they'll be naturals at radio, they'll come across great. And the quiet introverted ones, who find this sort of group-work/public-speaking a form of torture -- well, you can imagine...

Recently I was on a science communication course where we did exactly this. An interesting experience in many ways, but for me the most surprising thing was just how badly that 'natural' talkative extroverted style can come across on radio (which ruthlessly shows up all those hesitations, filler words, odd interjections etc that you probably wouldn't notice in face-to-face speech). And how some of the people you'd expect to be awful at this actually sounded quite polished and professional (listening to the recording, you can't tell that they're reading a prepared speech...or that they're maybe literally shaking with fear!).

Maybe the skills and personality types that make for good radio presenters are not the ones you'd think.

Turns out I'm not the first to come to this conclusion. Several people have observed how the same thing happens with public speaking and presentations -- the usual reasoning being that if you're shy and lacking confidence about such things, you tend to prepare better.

But I think it goes a little deeper. Because as an introverted type, everything you say is a performance. Almost everything you ever say is scripted and rehearsed, even if it's only in your head in the milliseconds before you speak. That's pretty much the definition of an introvert: you think before you speak -- unlike extroverts, for whom speaking is essentially the same thing as thinking.

You probably also tend to be an observer of, always aware of how you look and sound from an outside perspective. That's probably why introverts are more likely to be shy or socially anxious. But it also means you're consciously thinking about the technical details of your speech, like pacing and intonation. This is likely why social interactions are so tiring for an introvert: but it can give you a head-start in public speaking. Those who are not naturals at social interaction also spend a lot of time observing others, analysing and mimicking (or avoiding in some cases!) the way they speak and behave.

Apparently many professional actors are self-described introverts.I don't think that's surprising at all.

Wednesday, April 10, 2013

New story: And Though Worms Destroy

My latest story And Though Worms Destroy is up at Every Day Fiction.  They publish a new flash fiction piece every day: ideal for when you have a spare few minutes during the day!

This story was another idea I had around Christmas-time, inspired by snippets of Handel's Messiah which were playing over and over in my head, and all that related apocalyptic imagery.

I was also wondering about these female archetypes -- the sinful temptress and the pure virgin mother, both defined entirely by patriarchal religion and set up in opposition to each other -- and what they'd actually have to say to each other if it was up to them.

Wednesday, April 03, 2013

More on lectures

Previous post: Sliding towards a conclusion

So a lot of lectures and presentations are done badly. Overuse of slides and visual aids is part of that. The fact that often people who are good at academic work and research are often not so good at the performance aspect of public speaking is part of it too. But what if the problem is more fundamental than that? Maybe the lecture itself is an archaic and inefficient way of transferring knowledge.

It's difficult to concentrate on a monologue for a full hour. How often do you do that in your everyday life? It's difficult to concentrate on a monologue for two minutes, as you know if you've ever been stuck in conversation with the sort of person who's prone to them.

It's difficult to take in new information in real-time like that, since most people need to reflect on difficult concepts in order to understand and absorb them - but in a lecture if you stop paying attention for a moment you miss something. Sometimes you miss something that means it's impossible to catch up and you don't understand anything that's said for the rest of the hour. Unless you record it - but then why not just have the recording and skip the live performances?
In my personal experience, lectures were the least efficient way of learning I could have imagined. I often left knowing no more than I did at the start.

What was useful for me was studying the handouts and textbooks afterwards, when I had the space and time to think without having to listen to someone talking at the same time (surely that's a challenge to anyone's multi-tasking abilities?). What was also very useful occasionally was going to see the lecturer during office hours to ask for clarification on any point I couldn't fully understand on my own. Tutorials and problem classes were good too.

But the lecture itself seemed irrelevant, a waste of everyone's time. Judging by the amount of sleeping, reading,whispering, texting etc going on, I wasn't the only one to feel that way.For many students, the lecture seemed almost a form of religious observance, as though attendance was what counted, as though knowledge (or credit) would be magically absorbed just by being physically there.

An alternative model could look like this: lecturers provide or recommend materials for students to study in their own time (could be online courses, might be a chapter from a textbook for first-year undergraduates learning the basics, maybe some relevant papers or review articles for more advanced years or postgrads). This would be followed by small-group tutorials for questions, discussion, detailed explanations. All of which would mean more when everyone present was familiar with the material.

This might even help us move towards real learning, instead of the current exam-driven model where the lecturer reads stuff out, the students write it down, memorise it, and write it all over again in the exam.

It's not just undergraduate teaching though. The lecture in some form can be found in research-group meetings and journal clubs, and at academic conferences as well. It even exists in industry and business, where often the standard format for meetings is someone delivering a presentation (usually accompanied by the dreaded slides). It's such an established way of doing things that it's difficult to imagine these occasions without someone standing up and delivering a lecture. But is it the best way?

My experience of these meetings is that the most productive time is the ten or so minutes at the end for questions and discussion, especially in smaller groups. Where people actually interact with each other, where real engagement and understanding take place. Imagine if the full hour could be like that.

Wednesday, March 27, 2013

Sliding towards a conclusion

In some ways, the CDT Festival of Science at Imperial College was your usual university-based science symposium. Long day of over-running PowerPoint presentations: check. Needlessly male-dominated line-up of speakers: check. Bored students whispering, fidgeting and Facebooking: obviously, check.

But an interesting thing happened when the last speaker of the morning, Professor Lord Robert May, got up to talk about his experiences as a government science advisor. Because there was no PowerPoint, no slides, no visual aids of any kind. He just stood at the front and talked.

 This was unusual enough in itself, but the really interesting thing was the audience reaction. During the first few talks, the usual general general hubbub of chatter and disturbance had prevailed, at the back of the lecture theatre at least. But as Lord May's talk got underway, it slowly diminished and then stopped. People actually started sitting still, looking at the speaker, and apparently listening. In fact certainly listening, because they laughed when he said something funny, instead of the usual awkward silence.

So what was going on here? Was it the lack of slides that somehow changed things? This is just one anecdote, of course. More data needed. Correlation is not causation, and there could be other reasons.

Maybe presenters who don't use slides tend to be more confident (and accordingly more experienced and skilled) speakers. So their talks would be more engaging regardless of the presence of slides. Maybe though, having no slides tends to change the way people present. Their style becomes more informal, more conversational, and that is usually going to be more engaging than an over-rehearsed formal presentation.

But looking around at what was happening, I couldn't help but feel that not having the slides there was changing the dynamic between the speaker and the audience somehow.

It's interesting what happens when a lecturer stands up to present material to a class of students. Because in a way, it's as though they're not there. Judging by the student's behaviour, there's rarely any sense that the lecturer is an actual person, that normal rules of politeness apply (like at least pretending to listen when someone is speaking to you). No one is really looking at the lecturer. They're looking (if not at their laptop or phone or the person next to them) at the screen.

But without slides, it becomes more like a normal conversation. People actually look at the speaker, react to tone and body language, relate on a human level. Whether that means they absorb the information better is a different question, but being more engaged surely can't hurt.

Even when I was an undergraduate, it was rare for a lecturer to speak without slides. I believe it is very unusual now. This may not be a good thing. My view tends to be more that the lecture as a way of teaching or delivering information is inefficient and archaic —but that's a separate issue. If the lecture format is here to stay — and with the growing popularity of MOOCs it looks like it might be, we might as well try to do it right.