Translating mathematics

Recently I wrote an article for Skymania about some fascinating cosmology. Briefly, black holes might have formed in the first second after the Big Bang (https://arxiv.org/pdf/1612.02529.pdf and https://arxiv.org/pdf/1706.09003.pdf), be responsible for dark matter (the idea that primordial black holes might account for all or part of the dark matter in the universe has been toyed with for many years) and even for heavy metals (https://arxiv.org/pdf/1704.01129.pdf). You can read it here.

The original papers are theory-heavy, relying on background knowledge from several different disciplines and weaving in concepts from the physics of heat and gases to supersymmetry (the idea that every fundamental particle has one or more superpartners; this sounds strange, but it would solve some mysteries of particle physics). They start off in plain English for the first, oh…half a page, and then the maths begins in earnest.

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Getting hit by maths. (Like the scientific papers, when you understand the maths this image is a lot less weird.) Credit: Gerd Altmann

I find that there’s something cruel in how more theoretical disciplines, which usually require more mathematics (and there’s already a lot of mathematics in the experimental or computational stuff – the mathematics can be very different, though), are treated as mysterious or weird. It puts a great deal of distance between people who don’t understand the maths and thus rely on other people’s interpretations in words and between people who understand at least some of the maths, but might not be willing or able to describe that maths to someone with very little knowledge.

While I can understand how this comes about – a lot of concepts are genuinely weird even if you find the mathematics straightforward and explaining mathematics with a limited word count is hard – I’m not sure its effects on the public perception of science have been positive. Yes, it’s good to emphasise wonder – we live in a wonderfully strange universe. I worry that the mystery angle is played up sometimes. I worry that people see science as just another dogmatic belief system rather than a uniquely self-correcting way to understand our world.

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I don’t think this would have happened in a mathematically literate society. Credit: Nick Havok
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I don’t actually have any words for how wacky I find this, but it illustrates how people give more power to specific numbers and less to mathematics. It’s also interesting to see how they’re really clutching at straws here to “prove” that the idea of a round, tilted, rotating Earth is somehow Masonic. Credit: A Terra é plana

(I’m giving credit to the sources out of some sense of politeness, but I’m not linking to Flat Earth nonsense.)

Okay, these people are flat earthers. They are on the far end of the weird scale. I don’t think that glossing over mathematics is going to make us all into flat earthers within 20 years. I think that mathematics and mathematical methods underpin science, and that without at least attempting to explain the underlying mathematics non-scientists get an extremely incomplete picture of what science is about. Whether that incomplete picture can drive non-scientists into the arms of conspiracy theorists is another question entirely.

What I do think, however, is that this incomplete picture can really distort someone’s view of science. Let me give you another example.

I first realised I liked science when my dad tried to explain atoms to me. He said that they were things so small you couldn’t see them. Six-year-old me was having none of that: why should I trust my dad’s authority when I couldn’t see these so-called atoms for myself?

Instead of telling me to shut up, my parents got a book out of the library for me, which I sat and read when I should have been doing my schoolwork. Rather than having to spend all day learning to spell words, I could read all about how the ink making up the words was made of these special things called atoms. I even learned what the atoms were made of!

I got into trouble for not doing my work, but six-year-old me totally thought it was worth it. And I never looked back – I filled the house with science books until I turned eighteen. (I’m twenty-one and now I fill my own flat with science books, rather than my parents’ house. Some things never change.)

I remember one of my favourite books was about big ideas in physics. The final big idea was about cosmology and the Big Bang, which I was obsessed with at the time. It mentioned scalar fields possibly causing the expansion of the universe.

Of course, single-digits-old me was captivated. When I became a scientist, I was going to truly probe the nature of these mysterious scalar fields!

Double-digits-old me was quite disappointed to learn that scalar fields aren’t that mysterious or special; they’re a bunch of numbers tacked onto different points in space and time. Their importance comes in what they describe, not in what they are. I wish someone had explained that to me, so that I’d have a better understanding of why scalar fields are important. The true power and beauty in science comes from working out what the mathematics means, not from having it glossed over.

These ideals are all very well and good, but that maths can take years to learn. An article someone might finish in half an hour is not going to suddenly make them a master of quantum field theory. What are you supposed to do other than quietly gloss over the maths, especially when a lot of people are put off by mathematics?

I think I have an answer. Time (and studies) will tell whether I’m barking up the wrong tree with this, but I think it’s at least worth trying.

I don’t think maths is discovered – I think it’s invented. I think it’s an unreasonably effective way of describing our ideas about the universe; in other words, it’s a language. Just like a language, it describes and links lots of different concepts and unifies them into a coherent whole. Just like a language, it’s a powerful tool to describe what’s out there and what could be. Just like a language, it can be used to lie and manipulate as well as to make things clear.

Unlike every other language on earth, it’s purely written (never spoken), few if any people have it as a first language, and it describes certain things in far more precise ways. No wonder people find it tough – they’re being thrown into learning an incredibly strange foreign language.

As such, I see science communication as translation. It’s a matter of taking the concepts in the mathematics (and the jargon) and preserving them in prose. Just as some words and concepts can’t be completely translated, and just as some of the nuance of the original text might be lost or changed, not everything can be explained in prose. Despite this, people translate things every day. Why not maths? Why not translate an intensely compact, precise language into the messier and more ambiguous languages we work with every day?

If it were that simple (and it’s not), everyone would be doing it already. As it stands, trying to explain the maths involves explaining a lot of the simpler maths underpinning it. That maths is taken for granted by the people who work with the more complex stuff every day, but it makes little to no sense if you haven’t heard of or don’t understand that simpler mathematical foundation. So explaining the complex maths – that juicy stuff behind the latest hot paper – requires explaining at least some of the less complex maths behind that. Cue mathematical explanation adding on time, or words, or both.

My Skymania article is something like 700 words, where maybe about 150 words are dedicated to explaining scalar fields and Q-balls. I’m proud of that, because I have a different version of the article sitting on my computer. It’s more than twice as long; most of that is due to a more in-depth explanation of some of the maths and what it actually means. It’s hard. I ended up talking through a lot of it with my partner, because I like maths and tend to assume people know about as much maths as I do (most people stop studying maths at 16; I have a couple of years extra under my belt). Trying to come up with the best ways to explain the maths was frustrating.

It’s a process I want to keep going through, because I feel like it’s worth something. I feel like expressing the maths clearly and plainly goes a long way towards helping non-scientists experience the joy and wonder of science. I feel like it goes a long way towards making mathematics less scary and more comprehensible, and towards demystifying it all.

One thought on “Translating mathematics

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