maths · philosophy · storytelling

The narrative of scientific discovery

I wrote this bit just before my doctorate defence, which was December 2017, but somehow I never got around to publishing it. With some delay, then, here it is.

Cyclic or linear?

The defence of my doctoral thesis is coming up. Ironically, perhaps, this gives me some time to think and reflect. One standard component of the defence is to give a 10 minute summary of my work. Now, many of my friends and family will be there and most of them aren’t scientists. Me being a mathematician, I am arguably a scientist and in my thesis I describe what one arguably could call a scientific discovery. I say arguably, because I can imagine there are people who wouldn’t call mathematics, or even applied mathematics, science. Yet, I believe it is and I want to elucidate, if I can, what it’s like to make a scientific discovery.
The classical way of thinking about this is by formulation of hypothesis, prediction and experiment. The hypothesis is cyclically updated until prediction and experiment agree. I don’t wish to dispute this cyclic way of thinking as I think it’s more or less correct. However, as an alternative perspective, I propose to think about it as a linear narrative.

The importance of narrative

Humans are peculiar creatures. We eat, sleep, talk, go to work, travel, dance, sing and so forth and so on. What makes us unique compared to other, “lower”, animals? A common answer is our  tool usage. However, this is not entirely uncommon in the animal kingdom, just think of otters using stones to smash open clams. Surely then, you might say, we can talk whereas other creatures don’t. Yes, but there are plenty of animals that can communicate with one another, maybe not with the same accuracy and lucidity, but that’s just a matter of degree. What is truly unique about humans? Well, we tell each other stories. Complete fabrications of things and characters that may not even be possible in the real world. We use them for example for entertainment or learning important lessons. Storytelling may even have been central to our evolution.
Even more extreme, according to Dan Dennett, we are ourselves narratives in some sense. In his excellent book “Consciousness Explained”, he proposes that a self is what he calls the Centre of Narrative Gravity. According to him, our brains generate Multiple Drafts of reality and we experience our selves as the thing all those drafts revolve around. Narrative is not just important theoretically. Practically, in my experience, people learn things better if there’s a clear narrative. Giving historical context and examples really helps when people are trying to learn something.

Wherefore art thou Isaac?

The narrative of scientific discovery is closely related to the classical three-act dramatic structure. In a classical drama, the first act establishes the setting, characters, plot and perhaps most importantly the protagonist. In the second act, the protagonist faces various obstacles and problems. The third act describes the overcoming of those obstacles. The bad guy is defeated, peace is achieved and usually the hero gets the girl in the end.
Scientific discovery works, as a narrative, quite similarly. In Act 1, the scientist is first to get familiar with a new field or topic. They study the setting and the characters: the existing theory or data. Then the spark of creativity, the plot, which is the one Big Idea. An important new concept, which can usually be stated in a few short sentences. Act 2 involves the immediate practical problems and obstacles that arise when trying to apply the Big Idea. Act 3 finally sees the scientist victorious, the obstacles are overcome and a scientific discovery is born. However, here’s where science departs from drama: there’s usually a fourth act in scientific discoveries. This fourth act I call pushing the frontier of knowledge. The scientist uses the discovery to explain something that was previously a mystery. In fact, it’s quite common that the motivation comes from getting to the fourth act, to explain previously unexplained phenomena.
As an example, I’ll use Isaac Newton and his discovery of the laws of motion. Now, when Newton came to the scene there was already some theory on mechanics. Galileo Galilei had already proposed his principle of relativity, for instance. Newton, according to modern legend, had his Big Idea when an apple fell on his head. Act two, however, saw the immediate practical problems of Newton: he didn’t have any mathematics to express his Big Idea. He couldn’t write down his Big Idea accurately in any way that made sense, let alone use it to make predictions. In act three, Newton invented calculus to overcome this problem. He invented an entirely new branch of mathematics out of necessity. With this new tool, he could finally express his laws of motion and the scientific discovery was complete. However, I think Newton’s work would not have gotten the attention and acclaim if he hadn’t carried on to act four. Now don’t get me wrong, Newton’s laws are without a doubt one of the greatest scientific achievements ever. But what really blew people away at the time was his ability to produce from his theory the motion of the heavenly bodies. With Newton too, the motivation for the whole thing was getting to act four: Edmund Halley asked him to figure out what makes the planets go round the way they do.

Focus your mind

My idea is to explain the key ideas and results of my thesis in the context of the narrative of scientific discovery. This is because the audience consists mostly of lay people. However, I think the idea can also be useful if the audience does consists of fellow scientists. It can help to structure a presentation or paper and focus your thoughts in terms of the four acts. I don’t think there’s a need to be explicit about it and say “Act 1: the setting” etc., but it presents a logical and natural flow of a story.

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