The Chaotic Pendulum

Double pendulums are pretty awesome. Funnily enough, they’re pretty much what they sound like – a pendulum, with another one attached to the bottom. But the cool part is come from their twin nature, but the type of motion they exhibit – chaotic motion.

People often confuse chaotic behaviour with random behaviour; random behaviour has no deterministic qualities (so you can’t tell from previous physical conditions what is going to happen), whereas chaotic behaviour is actually deterministic, meaning it is possible to predict. The difference between chaotic deterministic behaviour and regular deterministic behaviour, however, is that tiny, tiny changes in initial conditions in a chaotic systems can bring about massive changes, unlike a normal deterministic system, where tiny changes in initial conditions will bring about tiny changes overall. You may have heard of something called “the butterfly effect” – where a butterfly flapping its wings on one side of the world can cause a hurricane on the other. This is a chaotic system, as even something as small as the miniscule breeze from a butterfly flapping its wings can cause massive changes in weather, which may at first appear random but actually do have a deterministic cause.

The fact that double pendulums are chaotic is that go can set two different pendulums up to be almost exactly the same, but not quite, and after a period of time they’ll be totally different from each other. It also makes the path a double pendulum traces out amazingly beautiful and crazy, almost like those geometric roses, or the drawings you made using spirographs as a kid.

There are chaotic systems everywhere in nature, from geology to robotics, and biology to economics. Chaotic systems can be very difficult to detect, because they can appear so similar to random systems unless you measure them closely. Because of this, there are certain traits of dynamical systems that scientists will look for to see if a system is chaotic. These are things like the fact that there isn’t any periodic (repetitive) behaviour in time, but there  is in something called phase space, which is a bit like the variation of the speed of the pendulum with its displacement. Also, the fact that tiny initial differences between two pendulums will grow exponentially with time. There are other chaotic properties, like the fact it’s nonlinear, and that it must have at least three independent, first-order autonomous differential equations which describe it, but those are harder to explain within bringing up the ridiculously long and complicated equations of motion, which are what you use to describe how the pendulum moves (funny that, what with their name).

Chaos is such a wonderful thing, because at first it appears completely crazy, and random, and completely unordered. However, if you have the ability to actually look close enough, it’s perfectly deterministic, and not at all unpredictable. A bit like so many messy things in life, if you have the patience and the time to look for the source, and untangle the enigma, you’ll be able to to decode the whole thing, and know what’s actually going to happen.

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Okay, so this week, I’ve been very busy with my summer project – building a simulation of a double pendulum. Double pendulums are pretty damn cool, exhibiting chaotic behaviour and being hypnotising to watch. So, I thought it’d be more interesting to write a quick thing about them (and a lot easier for me, given that I’ve got my final report deadline on Monday, so am spending most of my time thinking about them), and also show you guys some of the simulations I’ve built. It might be a little bit more mathsy that usual, but I’ve tried to keep it so that the majority of it is all understandable.

 This does mean that I don’t actually have a shoot to go with this piece, and given that I’ll be working on the project till the end of Monday, I probably won’t have time to do one. Don’t despair, though, I’ll still be giving you pretty pictures! You like that one gif up there? Well, on Wednesday you’ll get to see gifs of double pendulums on all the different planets and more – it’s pretty cool. My favourite one is the moon – it’s much slower than the pendulum on Earth, and really relaxing to watch. 

Also, I must give credit to my amazing project partner, Kiyam Lin, who pretty much did all the confusing code whilst i just sat there learning all about chaos. Everything would have been far more confusing without him. 

 

Exams and the Universe

So I was hoping that this week I’d be able to get a blog post written even with all the revision I have currently going on (I even did some stuff in advance). However, it looks like that’s not going to be the case – I have some notes and images, but I don’t have anything that I would feel comfortable or happy actually publishing on here. Sorry! Tis the hard life of a uni student.

However, I’m not going to leave you completely in the lurch! You’ll still get something to cool to read (or look at!), it just won’t be mine, and it won’t be on this blog. Since my mind is currently crumbling into pieces, I thought maybe I could give you some help getting yours into the same state, and blow your mind with the Universe and it’s scale!

This is The Scale of the Universe, and even as a physicist, it completely blew my mind when I first saw it. It’s one thing knowing the numbers, another completely trying to comprehend them.

Hope that gives you a bit of fun, and sorry for the temporary exam hiatus! Back to schedule next week, I promise.

P.S. Also, once exams are over I’ll be uploading some essays, and other written work of mine for you guys to read if you want – quite a bit longer, but I’m far better at essay writing than I am at blog writing, so probably far more interesting!

Imperial Geek Chic

Geek chic is a look that has been done many times, and all too often seems to revolve around a pair of glasses and a button-up shirt. Although I wanted to keep elements of this, I also wanted to portray the modern ‘geek’, someone who is more than just books and libraries, someone who I would identify with, and whose outfit I would want to wear. I also didn’t want the look to be too androgynous or masculine as too often intelligent women are seen as intelligent despite their femininity, whereas in fact many are both  intelligent AND feminine – one does not negate the other.

Even though the official colour of Imperial College London is purple, we’ve got navy blue everywhere, and my deep imperial blue Uniqlo shirt was one of the first pieces I knew I wanted to include, accessorising with my brass feather necklace (a charity shop find). Initially I was going to pair this up with a pair of dark trousers – but I own mainly jeans, and as soon as I tried that ensemble on I knew it wasn’t going to work. After being stuck for a while, I opened up my cupboard to browse, and as soon as I saw the black pleated school-style Topshop skirt I knew it was meant to be.

As always, it was then the eternal question of what shoes to wear – heels to make it classy, DMs to punk it up, Converse to make it fun. In the end, I wanted to go with a strong feminine edge, so it was my (surprisingly comfy) lace up heels.

The whole look ended up being quite a slick/glam geek chic look, which I liked – it most definitely wasn’t the stereotype of the physics student stuck in the library, but the type of girl who can is intelligent and attractive, fashionable and bookish – like geek girls most definitely are.

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Once again, most of the stuff I’m wearing is no longer available in stores; the Uniqlo shirt and Topshop skirt are both from previous seasons, although I’m sure you can find similar garments in store now. The brass feather necklace was a charity store find, so I have no idea where that’s from, and the heels are from Office, but from at least five years ago (if you find any like them, please tell me as they’re falling apart and I want new ones!). Finally, the backed seamed tights were from trusty old M&S who are really great when it comes to that sort of thing. 

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We (meaning me and the fabulous Freya, who you should definitely follow on twitter and instagram) shot this look out and around Imperial, in an area colloquially known as ‘Albertopolis’, which encompasses the Albert Hall and the surrounding areas such as the museums. We were very lucky with the weather – about half an hour before we shot this in the dazzling sun it was raining! It’s such a great area to shoot in – there’s so much great architecture, and even the brickwork is fabulous. There’ll definitely be future shoots done around there, both because of the beauty, and because it’s right around the corner from my halls! 

 

The Da Vinci Code

The general understanding of science in society heavily influences where and how science turns up in art. However, often that understanding is flawed, with many misconceptions. Whether it be the fact that here in Britain we start academic specialisation very early (first GCSEs, then A-levels, before down to usually a single subject at university), or simply the way that art and science are taught as mutually exclusive subjects, most people in the artistic community have little core knowledge of science through no fault of their own (although many do hold pet interests in the topic).

One of the major problems faced with people trying to get their heads around science isn’t even a problem of academic knowledge; it’s one of definition. Too often scientific terms lack clarity; the Big Bang wasn’t actually a big bang, the ‘God Particle’ doesn’t have many religious properties (apart from the fact it holds mass, hah!). If you don’t know the details of the theory (as most don’t), terms such as this can really throw the whole concept into confusion – I’ve had a number of people ask me questions about the Higgs boson, having heard of it as ‘the God Particle’, who are severely disappointed when I inform them that it isn’t actually the be-all and end-all of particles. Yeah, it’s pretty damn important, but it’s more part of a pantheon than the One True God.

Even if you do happen to understand all the terminology, you could still be doomed if you wanted to try to understand the science in more detail. Ever tried reading a scientific paper? I wouldn’t recommend it – they’re usually dry and boring, filled with equations and without any human touch. The reasons behind this writing style are valid – it can reduce bias to remove the human elements – but it creates a form which makes the media very hard to access, and difficult to get used to. The whole thing makes papers read like all experiments were performed by some kind of magic science fairy, who makes things happen with a puff of their wand, instead of actual human involvement having happened.

All this opacity within science added to the general misinformation and ignorance surrounding scientific topics means that effective scientific communication is absolutely crucial. This has been getting better in recent years – we’ve got all of Brian Cox’s programs, and then we’ve got David Attenborough as always – but there’s still a long way to go. For one thing, whilst we love our mainstream science celebrities, they don’t truly show the great variety of people who love science – that science isn’t just for scientists, it’s for artists, and musicians, and dancers, and writers: it’s for everyone. We need to demystify the language of science – to clear up the hazy metaphors, and inject some life into the whole thing. We’re in luck though, because there are people out there who do that, people who show just how varied science can be. When I went to Imperial Festival this weekend – a festival held by Imperial College London (my uni!) to showcase and celebrate so many really cool scientific things –I had the privilege of encountering so many people who went outside the stereotype of scientists being maths geeks who never leave the library. I met a doctor of material sciences who does ballet on the side (and she’s pretty damn good – she’s en pointe) with whom I made cocktails with in the name of science, a science songstress with the voice of an angle (get it???) who did the same course as I’m currently doing at Imperial, and shares my interest in the bizarre sexual habits of animals (definitely look up angler fish – you may be scarred for life, but it’s worth it!) and so many others. When people try to portray science as some dull, textbook filled subject, it might be a good idea to remind them that one of the greatest artists to walk this Earth was also one of the greatest scientists – Da Vinci! Maybe we should try and take a leaf out of his book, and add some science to the art, or perhaps some art to the science.

 

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Being a student of Imperial College, I felt that this week I definitely had to write something up on the Imperial Festival, so I have! I saw so many wonderful and interesting things there, and unfortunately I haven’t been able to mention them all, as that would have become extremely cluttered. The en pointe materials scientist I mentioned is the lovely Dr Suze Kundu, whilst the science songstress is the amazing Helen Arney, who was joined by Simon Watt (Life President of the Ugly Animal Preservation Society) and Gemma Arrowsmith as part of The Science Comedy Collider. The other group of people who really helped with this piece are the wonderful Science Communications MSc students, whose talk ‘Playing with Perception’  informed the topics discussed above. 

Although Imperial Festival only happens once a year, there are events going on at Imperial College throughout the year, and at the Science Museum and Natural History Museum right next door. If you want to keep on top of all the events going on, I recommend following them on twitter at the links I’ve just given. I particularly recommend the Lates at both museums, and also the Imperial Fringe events (mini themed versions of the festival) which’ll be starting back up again in September. In the meantime, you can keep on top of imperial events by following Imperial Spark.