The magic of iteration: fractals, writing, and translation

By | October 4, 2021

Today I want to post about some ideas I’ve had running around in my head for at least a year; I actually had originally planned to make a “Ted Talk” style podcast or YouTube video about it, and had gotten as far as recording a couple of attempts. But I ended up abandoning the audio format and decided to just write a regular blog article instead. One of the reasons was my allergies make it difficult to produce a high-quality recording. Also, while I do have a YouTube channel with a handful of videos, this blog has many more followers and hits. I’ve seen some interesting Ted Talk videos, but ultimately I think sometimes the dramatic way of speaking and presenting can cause form to overtake function, whereas in an article like this the content can be understood in a more unbiased way (not to mention that it is easier to get into more complex topics without worrying about the listener getting lost).

But enough of the preamble. At a young age I was fortunate to have access to computers and learn how to program, which eventually led to a career in IT. The way I learned coding is a bit different than how children do nowadays: rather than using visual tools like Scratch and easy-to-understand tutorials, I had little more than a monochrome screen and a bunch of awkward-looking characters. Of course, there was no internet to use for quick reference on nearly any topic like we have now; all I had was a few technical magazines and books, like Byte. Early on I didn’t even have the ability to save my programs, so I learned how to quickly rewrite certain programs, like simple games or simulations.

One of the most memorable things I discovered in those times was fractals, which is the first of three topics I’d like to introduce.

Fractals are a complex topic that relates to several important areas of math and science, but can be simply defined as curves or patterns produced by some well-defined mathematical process that has the characteristic of being self-similar, meaning that a part of the pattern at one scale is similar to a part of the pattern at another scale. Fractals actually connect strongly to nature, from which we can pull a simple example: a tree whose branches each branch off into more branches, which in turn branch off again (see this page for more details). Essentially, the shape created by branching occurs at different scales of the tree. By the way, this process of repeating the same steps over and over is called iteration, which happens to be the main overlying topic of this discussion.

However, my interest was not piqued by such trivial shapes; it was more complex fractals that really amazed me decades ago, and still do to this day. For example take the Mandelbrot set, perhaps the most famous fractal among the general populace (to the degree that at one time T-shirts with Mandelbrot fractals could be seen in public).

A detailed explanation of the Mandelbrot set would take up a lot of space here, and frankly isn’t necessary, but suffice to say it involves repeating (iterating) a set of steps involving performing mathematical operations on numbers (adding and multiplying) and basic comparison operations (greater than, etc.). The trick is that the process doesn’t work with regular numbers, but imaginary ones––where imaginary numbers are based on “i”, a constant defined such that “i * i = -1”. As you probably know, multiplying any two numbers together should never result in a negative number, which is why these numbers are so special. If you want to learn how to write a program to render the Mandelbrot set, you can see this as an example of it here (in the C programming language). This is an example of visualization, the act of taking something which would be otherwise abstract (the result of a series of mathematical operations) and making it visible for anyone to see at a quick glance.

Here’s an example of the Mandelbrot set, rendered with the Ultra Fractal program:

The really amazing thing about the Mandelbrot set and similar fractals made with imaginary (or more formally complex) numbers, is that despite being produced with a relatively simple process, they appear to be infinitely complex, not to mention can be seen to have a certain beauty not normally associated with mathematical operations. If you zoom into a certain part of a Mandelbrot set, you will see a new set of shapes (and colors, depending on the program) that look similar, yet have differences, and if you repeat the process of zooming again and again (another form of iteration), you can travel through an apparently endless landscape of fractals. There are many YouTube videos of this zooming process, you can see one here that is over fifteen minutes.

Many fractals are represented in a 2D space, yet others can be rendered in 3D for an even more immersive and dazzling experience. This video, which explores what is essentially a mysterious city-like construct purely made from math, is an excellent example of the possibilities and sense of wonder fractals can have.

Now we have gotten a taste of the real magic of fractals, and of iteration––the ability to produce something that is apparently infinitely complex and, more importantly, unpredictable and even arguably beautiful.

Having come this far, our next topic is “writing”, which perhaps may seem unrelated to math and pretty computer-generated pictures. However, as we’ll see there are surprising similarities between writing and producing fractals.

I still have a lot to learn about writing, but I think I have a reasonably good sense of what makes excellent prose. Sure, it takes inspiration, a good command of the language you are writing in, and a great deal of effort (among other things). But notable writing often involves an extended process of rewriting and editing, which we can see as a form of iteration.

It’s true that there are elements to this process that are hard to codify or even put into words. But I think the fact that authors exist who are able to pump out novel after novel––if not Pulitzer prize material, at least good enough to sufficiently sell and please the fans––shows that, for at least good writing, there is a somewhat well-defined process involved. (On a side point, I would argue that actually selling to the point of becoming famous also requires a strong dose of luck and in some cases personal connections).

You can view this process as a type of evolution. You start with some idea, and through a cycle of rewriting and revising the content gradually changes, such that the end product looks very different from the initial idea. I think this effect applies more to creative writing (like fictional novel or short story writing), but perhaps it applies even to technical or informative writing like you are reading now. Just like fractals, the results of our writing can end up becoming complex in an unpredictable way, despite a simple process being used.

As an example of how iteration has produced great literature, take Bradbury’s Fahrenheit 451, which started out with a personal experience that led to a short story that was eventually rewritten several times, eventually becoming a full-length novel. Dr. Seuss (Theodor Geisel) was another author who, in my opinion, produced many works of amazing quality and creativity. He was said to be a perfectionist, spending months, or even a year on a single children’s book, no doubt going through many cycles of iteration before sending the manuscript to the publisher.

Certainly we can come up with counter examples where a certain hit song or book was produced in one go without iteration, or when the author truly seemed to have divine inspiration. But nevertheless I think it’s clear that the cycle of rewriting and editing is important for most writing.

You can actually apply the process of iteration beyond the actual act of writing, to the thought process before pen touches paper (or fingers hit keys). Even for notable works of literature or other writing that was produced with little iteration, the author likely had aspects of the work––ideas, if not the words and sentences themselves––evolving as they spin around in their head. For me personally, I would say that blogging for around ten years has given me the ability to make what are essentially drafts of articles, or at least the general topics and flow, in my head as I go on a walk or lay in bed. You can even include the process of factoring in book sales and reviews to help decide what to write next, making the production of each book one iteration.

Finally we come to the topic of translation. This too may seem to be utterly unconnected to fractals and the process of writing content from scratch. After all, isn’t translation just taking what someone wrote and matching up words and phrases to express it in a different language?

I do have a bit of experience translating, and can say with certainty that the cycle involving rereading and revising is a very important part of the process (I wrote a detailed article on my translation process some years ago here, though things have evolved a bit since then). It’s a bit hard to explain to someone who hasn’t tried it themselves, but even during translation, where the source text is already defined, the target text can gradually evolve over many iterations. For example, a reread of the source text may yield a different interpretation of a certain passage, or a better non-literal way to express it in the target language. The final stages of iteration for me usually involve putting away the source text, and letting the translation freely evolve––all while keeping in mind the source text which I’ve partially memorized.

Sometimes when I reread one of my translations, especially after taking at least a few weeks away from it, I’m surprised by what I read, and to tell the truth, I often enjoy reading it more than the original source text (though this is probably, in part, because I’m able to more easily feel emotions and nuances in my native English). A translation can evolve to something quite different from the original text, all the while remaining connected to it in the most important areas. That’s perhaps why legally translations (and even translations of translations) carry their own copyright as unique creative works. Another way to get a feel for this is to compare two different translations of the same author, something fellow blogger Tony has done to good effect in this article.

Ultimately, even if the content of a story is already finalized (as in who does what, or what is described), when translating you still have a lot of freedom in terms of how it is described. Word choice and how sentences are constructed can make a huge difference on the reader’s experience, and it’s wonderful if a translator can manage to express that special something about an author’s prose in another language.

Now we can see how the process of translation shares things in common with fractals and writing, namely how we can end up with an unexpected result despite using a simple process. One can argue that writing content from scratch is more work (and more praiseworthy) than translating what someone else wrote, but if you consider that a translator has many more limitations to work around, it’s clear there is a completely different type of challenge than a forum where you can write anything.

Now that we have seen how these three topics relate, and learned a little about the magic of iteration, where does that leave us? How can you leverage iteration to help your projects?

To me the most important lesson here, especially for writers and translators, is to understand that iteration is an important tool to not only improve the quality of our work, but in some cases create something that is unexpected and different from our original intentions, what you could call the heart of creativity. You’ve probably heard the phrase “it’s all been done before”, referring to the idea that most if not all creative works have similarities to previous works. You can pick apart and analyze nearly any creative work and find the elements it is built from, finding places where those elements have been used before, sometimes decades if not centuries ago. But the important part is how these elements are put together, their interconnections, interrelations, and the subjective experience that the result gives to the reader, viewer, or listener. I feel it is this process of iteration that helps us choose elements and interconnect them into a synergistic whole that is greater than the sum of its parts.

A budding writer may read a masterpiece of literature and think to him- or herself, “I could never write something like this.” But such a thought process focuses more on the destination, not the journey involved in getting there. If we consider how the author might have gone through a grueling process of writing, rewriting, and revising, taking in some cases years, it helps us to understand how even creative activities can be more about effort than inspiration (and even if inspiration is required, sometimes the right type of effort can help you find it, like reading books or traveling). This iteration-focused approach makes the act of writing a great novel, or even a short story, a little more manageable. And it helps us understand that you don’t have to be a genius, or a superhuman, to eventually make an enjoyable, or maybe even award-winning result.

Thank you very much if you’ve managed to make it to the end of this article. If you are interested in some of my ideas about the process of learning a foreign language, please check out my latest self-authored book here, or you can see all my books (including translations of Japanese literature) here.

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