That thing that you are writing might look better as a fern. Yep. One of those green frondy things that grows in damp corners.
Before you conclude that I have totally lost my mind, let me explain. I often talk to people who are having difficulty jumping to the next stage up with their writing: maybe they have written short essays before, but now they need to write an 8000 word dissertation. Suddenly they need to hold all their thoughts together over a much longer and more complex piece, and it’s hard to see how the thing can have any shape to it. Sometimes they might be moving on from undergraduate dissertations to a masters thesis, or a PhD, or even a hefty book. How to you even begin to think about structuring a BIG THING? This is where I think that the fern analogy can help.
Here’s the basic summary if you don’t have much time:
- Tiny parts of ferns look much the same as the bigger bits that they comprise, and the bigger bits look like the whole fern of which they are a part.
- They do this by following the same basic rule at different scales.
- You can think of your writing in the same way: a section is like a mini-chapter, a chapter is like a mini-book.
- By applying the same simple rules at different scales, you get a surprisingly complex finished product.
- This breaks down at a certain scale because the basic units create limitations. This is true of ferns and of your dissertation, thesis, or book.
Ferns are amazing!
When we moved into the house where we now live, we inherited a shady, damp, north facing garden, overcanopied with several mature fruit trees. For several years I tried to grow showy flowers, but nothing really stuck. I decided to give in and work with plants that loved those conditions, and many ferns are the perfect candidates.
Gradually I became fascinated with these plants. I’m in good company: the amazing neurologist Oliver Sacks was a huge fan, and just about everyone during a certain period in the nineteenth century. Importantly for us, they have also often been objects of interest for mathematicians.
Optional historical bit:
Pteridomania was the name given to the Victorian fashion for ferns. Between the 1850s and 1890s, fern designs were everywhere: on crockery, fabric, glassware, and even gravestones (death, of course, was another Victorian preoccupation).
I’ve heard it said that fern collecting was regarded as a suitable activity for young women because ferns reproduce asexually, so unlike flowers, it wouldn’t lead them to have impure thoughts. This sounds to me like one of those myths about Victorian censoriousness, like all that stuff about covering table legs. Nonetheless, there was definitely a view that appreciating ferns, unlike appreciating flowering plants, involved a certain sophistication and a well-trained attentive eye that could enjoy the subtler beauty of the natural world. The hobby allowed many young women to spend time in wild places alone, which must have been incredibly liberating.
So why do maths fans like ferns so much? There are a couple of reasons for this. First of all, many ferns have a form that is very close to a fractal. Fractals are patterns that look the same at different scales. If you zoom in on one part, it will resemble the whole. Zoom in on part of that, and it will resemble the larger part, and so on. This picture shows a baby Japanese shield fern (Dryopteris erythrosora) that I’ve been growing in a pot, ready to transplant to a pile of slowly rotting old logs.
You can see that there are a number of branches coming out from the main stem. Each of these branches looks like a smaller fern. The leaves coming out from the branch look like miniature versions of the branch itself.
Another reason why maths geeks often love ferns is that the new emerging ferns form interesting spiral shapes, which can in some cases be described according to the Fibonacci sequence.
This connects with the fractal thing in a really cool way – the emerging main stem of the fern is wrapped in a tight spiral, and inside that are the curled up branches, each itself a smaller spiral with the same properties. Inside each of those spirals, the miniscule leaves are curled into tiny spirals of their own. As the whole thing gradually unfurls, the spirals on every scale unwrap themselves, revealing a living moving dynamic piece of mathematical loveliness.
Complexity from Simplicity
Why do ferns often look like this? One reason is that they are among the oldest plants still surviving on the planet. The first ferns emerged around 360 million years ago, well before flowering plants allowed for sexual reproduction. In evolutionary terms they are really quite simple. Although the final shape of the fern looks very complicated, it is created by following exactly the same rules on lots of different scales.
Flowering plants and animals are rather different from this: the different parts of our bodies look very different from each other, our organs don’t much resemble our bodies as a whole, and our different bits work in different ways. That means that you need loads of different rules to make an organism like us, according to which bit you are making and what job it needs to do. For ferns on the other hand, you simply follow the same rule over and over again at different scales, until you get from your one simple rule to an object that looks very complex.
Writing like a Fern
Good pieces of writing in English-language philosophy often resemble ferns, not just because they are very old and sexless (although there’s often that) but because the parts have a similar structure to the whole.
Think about the short 1500-word essays that you might write in the first year of an undergraduate degree – these typically have an introduction in which you provide context for what you will say, a main body where you make your arguments, and a conclusion where you sum up what you have argued. Usually, for each argument, you also want to give a mini-version of this structure – you explain what you are about to do, do it, and then tell the reader what you have done. So we can already see something like the fern shape here. When you scale it up, to a MA thesis, your chapters might be about 1500 words long, and they will ideally look a bit like those first year essays (although rather better, you might hope) but when you put them together, they also look much the same shape as a whole. In turn, a PhD thesis or a chonky book might look rather like a collection of MA theses, which when put together also have a thesis shape.
So how do I do it?
What does this mean in practice? Well one way to do it is to think about your BIG question, and work out which smaller questions you need to answer in order to answer it. Then each of those smaller questions will involve answering even smaller questions. This could be one way to determine how to split up your thesis into chapters, chapter sections, and maybe even subsections. Think of it as the fern unfurling. In your introduction you are showing the tight little spiral of the main stem: inside that are all the other smaller spirals at every scale, but we can’t see them yet. Then it unfurls in the main body of your thesis: each chapter begins with the tightly spiralled branch in the chapter introduction, which then unwraps itself as the chapter goes on, and so on.
Mathematical fractals can go on forever: you can keep zooming in indefinitely, and each part is a microcosm of the whole. In the everyday world of plants and animals, things don’t work like that. Eventually you get down to scales where different rules need to apply, whether we’re talking about the level of plant cells (which, even in ferns, don’t look like tiny ferns) or whether we’re talking about departing from the everyday to the quantum level where really weird stuff starts to happen and none of the normal rules for anything seem to apply. In fact, it starts to break down much sooner even than the cellular level – when you look at the lobes on a fern leaf, they look a little bit like the leaf (and the branch, and the fern…) but they are already starting to look less detailed.
This is equally true in writing, where the way that language works imposes some limitations on how far down your fern structure can go. Some analytic philosophers are fond of saying that the sentence is the basic unit of meaning. I’m not sure if that is absolutely true, but it seems to apply here. A sentence cannot be a microcosm of a thesis, because it can’t really announce what it will do at the beginning, say the thing, and then summarise what it has said. A paragraph can do this to a certain extent, but in a much shorter simpler way than a multi-paragraph section.
So if you’re stuck on structuring your thesis or dissertation, try breaking it down, then break each section down further, and so on. What are the lobes, leaves and branches of your fern? Finally, there’s no point in making something as beautiful and apparently complex as a fern without showing people what you have done, so remember always to make it clear through introductions and conclusions – look! I made a fern!
And with all that said, I think it’s time to do some gardening.