Real Learning
HPMOR, Ch. 23:
“But,” Harry said. “That’s only one hypothesis. Suppose that instead there’s only a single place in the recipe that makes you a wizard. Only one place where a piece of paper can say ‘magic’ or ‘not magic’. And there are two copies of everything, always. So then there are only three possibilities. Both copies can say ‘magic’. One copy can say ‘magic’ and one copy can say ‘not magic’. Or both copies can say ‘not magic’. Wizards, Squibs, and Muggles. Two copies and you can cast spells, one copy and you can still use potions or magic devices, and zero copies means you might even have trouble looking straight at magic. Muggleborns wouldn’t really be born to Muggles, they would be born to two Squibs, two parents each with one magic copy who’d grown up in the Muggle world. Now imagine a witch marries a Squib. Each child will get one paper saying ‘magic’ from the mother, always, it doesn’t matter which piece gets picked at random, both say ‘magic’. But like flipping a coin, half the time the child will get a paper saying ‘magic’ from the father, and half the time the child will get the father’s paper saying ‘not magic’. When a witch marries a Squib, the result won’t be a lot of weak wizarding children. Half the children will be wizards and witches just as powerful as their mother, and half the children will be Squibs. Because if there’s just one place in the recipe that makes you a wizard, then magic isn’t like a glass of pebbles that can mix. It’s like a single magical pebble, a sorcerer’s stone.”
Harry arranged three pairs of papers side by side. On one pair he wrote ‘magic’ and ‘magic’. On another pair he wrote ‘magic’ on the top paper only. And the third pair he left blank.
“In which case,” Harry said, “either you have two stones or you don’t. Either you’re a wizard or not. Powerful wizards would get that way by studying harder and practicing more. And if wizards get inherently less powerful, not because of spells being lost but because people can’t cast them… then maybe they’re eating the wrong foods or something. But if it’s gotten steadily worse over eight hundred years, then that could mean magic itself is fading out of the world.”
Harry arranged another two pairs of papers side by side, and took out a quill. Soon each pair had one piece of paper saying ‘magic’ and the other paper blank.
“And that brings me to the prediction,” said Harry. “What happens when two Squibs marry. Flip a coin twice. It can come up heads and heads, heads and tails, tails and heads, or tails and tails. So one quarter of the time you’ll get two heads, one quarter of the time you’ll get two tails, and half the time you’ll get one heads and one tail. Same thing if two Squibs marry. One quarter of the children would come up magic and magic, and be wizards. One quarter would come up not-magic and not-magic, and be Muggles. The other half would be Squibs. It’s a very old and very classic pattern. It was discovered by Gregor Mendel who is not forgotten, and it was the first hint ever uncovered for how the recipe worked. Anyone who knows anything about blood science would recognize that pattern in an instant. It wouldn’t be exact, any more than if you flip a coin twice forty times you’ll always get exactly ten pairs of two heads. But if it’s seven or thirteen wizards out of forty children that’ll be a strong indicator. That’s the test I had you do. Now let’s see your data.”
And before Draco could even think, Harry Potter had taken the parchment out of Draco’s hand.
Draco’s throat was very dry.
Twenty-eight children.
He wasn’t sure of the exact number but he was pretty sure around a fourth had been wizards.
If I had to name the top six skills that you need to write real science into fiction - just name them, I don’t have time to describe them fully, but at least naming what they are seems like more help than just telling you to sink or swim:
1) Know the actual material to one technical level higher than the level that appears in the story. Mendelian genetics was the first piece of modern genetics ever discovered, and so it’s extremely simple by comparison to modern population genetics with math. I learned about Mendel when I read _The Coil of Life_ at age ten, and I assumed for story purposes that Harry had done exactly the same. You don’t need to know all the finicky details of modern population genetics, or even Price’s Equation, to write what Harry thinks. You do need to know Mendel and know it very solidly, to make sure that your character is getting it right.
To ensure this solid knowledge, try to know at least one technical level higher than the character or story is invoking. You don’t need a doctorate in population genetics, but it is wise to know enough about genes and phenotypes and chromosomes that Mendel is just a special case to you rather than the most advanced thing you know after having read it in a popular book. (The character may have just read the popular book, like I modeled Harry as having done, but I needed to know at least one level above that.)
2) Be able to see the material as it applies to story situations. The root of this skill tree is Richard Feynman’s “Look at the water!“ principle, as described in http://v.cx/2010/04/feynman-brazil-education.html which you should go read right now.
One way to train “Look at the water!” is what CFAR calls the Monday-Tuesday exercise. On Monday, cellphones work by radio waves. On Tuesday, cellphones work by magic (for whatever magical universe you care to name, say, _Buffy the Vampire Slayer_). How do Monday and Tuesday look different? How can you tell which universe you’re in? Imagine alternatives to the scientific principles you know, ask how the world would look different if that alternative were true.
3) You must be able to master the art of relevance; this is the ability to see exactly which aspects of knowledge are necessary for a particular conclusion or set of reasoning steps, and then include only the questions and ideas that are relevant to the plot. You would call on the art of relevance to realize that the fact that human beings have 23 chromosome pairs is not actually relevant to anything that Harry says to Draco—-that the reasoning goes through exactly as well in an alternate world where humans have 90 chromosome pairs—-and so there’s no need to mention it, even if it’s a fact that pops up prominently in your mind when you think of genetics.
Unfortunately I do not know how to train this ability very well, and it appears to be a very common deficit—-would-be explainers meandering through facts like “human beings have 23 chromosome pairs” even though it’s not the critical issue on which other things hinge. (I usually say the rare art of relevance in conversation.) A basic test is that for any science fact you want to explain, ask how the story would be different if that fact were itself different. If this causes your brain to throw an error rather than yielding an answer, see skill #2
Without the ability to pare down explanations by rephrasing to eliminate function calls to concepts more powerful than the bare minimum required for plot relevance, Harry would have tried to explain to Draco what a “chromosome” was. If Harry can apply the “Look at the water!” principle and just pull out two pieces of paper instead, that replaces the abstract, powerful concepts of “chromosomes” with a concrete illustration that doesn’t have the full power of the abstract concept, that is just exactly powerful enough to support the core plot, and hence is far easier to write out at as text.
4) You must be able to explain things in your own words, to a much higher level of “in your own words” than teachers ask for in essays. Harry, in the example above, says not a single word about “genes” or “chromosomes” or “traits” or “recessive” or “allele”. Nor does Harry define his own words that mean the same thing. Harry never tries to define what a “recessive trait” means in general, so he can appeal to this standard notion of “recessive traits” as authority for his conclusion that one-fourth of the children born to two Squibs should be wizards. A cache lookup would say that this is because of ‘recessive traits’, and so if you were blurting things out, you would just appeal to that and then try to say how ‘recessive traits’ work in general. This means you cannot apply the skill of relevance until you first learn how to get past the cache lookups.
Harry is shown translating Mendel out of the concepts he read in _The Coil of Life_, not just into different words, or more concrete and immediate ideas, but (an even higher level of the skill) a demonstration with pieces of paper. Because of this fluency with using simpler or more concrete concepts instead of the standard cached ones, Harry is able to pare away ideas that Draco doesn’t need to know immediately, decrease the overall size of the explanation, and make it sound less like a college lecture thrown into the text.
To improve your level of this skill, play Rationalist Taboo (this is also the name of the skill).
5) Be able to imagine what it feels like to not know the material, without being stupid. Modeling the reader you’re trying to teach, or modeling a character who must learn, calls on the same kind of empathy as creating realistic villains and passing their Ideological Turing Test. Your empathy be able to leave the safe, comfortable confines of your own mind, where certain concepts are already known and certain principles are already trusted.
This is why Draco doesn’t immediately nod and agree with Harry after Harry explains “statistical significance” (thereby invoking the great trust in statistical significance that any intelligent person must have as soon as the concept is explained to them) nor does Draco stare blankly at Harry as Harry talks about “statistical significance” (because anyone who doesn’t understand that can have no inner life). You have to comprehend Draco as a truly alien intelligence, sapient and capable of complex language use, yet so extremely different from life as you know it that he doesn’t even know what a gene is. You have to leave the comfortable confines of your own mind and enter a mind with different concepts and heuristics, a mind that is still a powerful intelligence even though it doesn’t agree with you about certain things. This is who you must explain to in the person of the reader, and who Harry must explain to in the person of Draco, the two problems mirroring each other.
6) You must be able to explain technical ideas to other people. This is a skill. It can be practiced. I did not always possess this skill, and by some people’s standards I still don’t, but I’ve become better over time. You can practice it in-person and get feedback. You can practice it in blog posts and get comments. You can practice it with respect to the particular knowledge that should appear in your story—-just find someone and try to explain the same facts the story must explain, without the story context.
These are the six skills which are called upon to put real knowledge, of a sort that the reader will actually pick up, into a story without totally disrupting the literary flow which is the additional hard part. Explaining science in a way that people will learn is difficult in itself—-you may have noticed large parts of the schooling system botching it. Slipping it into a story without disrupting the flow is an additional difficulty on top of that.
The key to this, again, is relevance. “Relevance” doesn’t mean “conceptually associated”, it means “the plot goes differently depending on how this thing goes”. Suppose that you said, “Well, I want to work some science in here… and Draco’s all worried about blood purism… so I’ll have Harry explain about DNA, these little spirals inside people, since that’s relevant to blood purism”. It really isn’t. It’s conceptually associated in your mind with heredity, but it’s not plot-relevant. Suppose that DNA were made of little square crystals instead of little spirals. Suppose it were called PROOMBAH instead of DNA. Does Ch. 24 end differently? No. So it’s not plot-relevant.
On the other hand, if human chromosomes came in triplets instead of pairs, Mendel’s laws would have been different and two alternative alleles for magic-nonmagic wouldn’t imply three different phenotypes for full-magic, half-magic, and no-magic. Harry doesn’t say “chromosomes come in pairs”—-it is superior to show the science, and if this is done correctly, it need not also be told—-but Harry does lay out two papers side by side, on his way to explaining Mendelian genetics. For a story to facilitate the explanation of science, it must be the case that if the science were different, the plot would be different. That is what makes the reader care about the science.
When you think up your magical system involving runes which have both a Color and an Element, or whatever, its laws are naturally relevant to your story. There are fantasy authors who fail even then, inventing systems which have no meaning for the plot. But still, on some level it’s basically easier to have your own invented magical system be truly plot-relevant to your fantasy novel, than it is to force Mendelian genetics to be relevant to your fantasy novel.
So, if at possible, don’t force it! Most of the relevant science in HPMOR is there as a target of opportunity, not something I strategically backward-chained into the story starting from the desire to teach it. I didn’t start from genetics and invent Ch. 24. The Mendelian explanation came to me while contemplating wizards, Squibs, and Muggles; and then this background fact, which I decided would be true, seemed like an interesting discovery that Harry could make and verify in a way that the reader could see completely laid out (no technobabble, no authoritative incomprehensible math, etc.), and would also be relevant to Harry’s goal of seducing Draco Malfoy to Science.
Ch. 6 revolves around the planning fallacy, but I didn’t start from the Moral Lesson and then construct the chapter around it. I just went on writing Harry’s visit to Diagon Alley to purchase his school supplies, letting story events happen. At some point my brain recognized a situation where I would explicitly think about the planning fallacy and use it to calibrate my own preparedness with an appropriate level of pessimism, so Harry thought the same thing, and then I decided the title of that chapter would be “The Planning Fallacy” and that other events in the chapter would fit that theme.
In HPMOR the title of the chapter almost always came to me after I started writing the chapter (except for the Stanford Prison Experiment, which was a big arc and needed an advance title for the whole arc; and you’ll note that I ended up not finding anywhere to even mention the actual experiment until Ch. 60, and then only as a passing remark).
So if you want to include science naturally into your stories, without effort, you should get into the habit of constantly being on the lookout for science facts relevant to your own life—-which may be a good idea for other reasons, I note parenthetically—-and constantly apply Monday-Tuesday tests of asking how the world would look different if the science was different (also a good general plan, and you will notice that the sciencey-sounding words are never relevant at all by this definition).
At this point you may be wondering what the point is of trying to put Real Science or Real Math or Real Learning into a story in the first place. The difficulty of this is the difficulty of explaining science intersected with the difficulty of writing good fiction. So why try to do both at the same time? Why put in the practice to gain the skills to eventually pull off that sort of thing successfully? What is there to accomplish, which can be best done in this way?
I once read—-though I don’t remember where—-a proverb which has stayed with me ever since:
Nonfiction conveys knowledge.
Fiction conveys experience.
When we enter a fictional world, we aren’t just learning facts about the characters and the world, we are living their lives and vicariously gaining their experiences.
If you do the practice and learn the skills of both science writing and fiction writing, you can do something that ordinary textbook authors cannot do, which is to put the reader directly into the shoes of a character as they use a science the way it is meant to be used. You can share the experience (not just the facts) of what it is like to understand and apply simple Mendelian genetics.
Of course Mendelian genetics wasn’t really the point of Ch. 22-24. The experience of the scientific hunt, of formulating alternative hypotheses, of understanding what they predict, of testing them—-that’s the real experience I wanted to convey to the reader. If I’d only wanted the reader to understand Mendelian genetics, I could have produced a blog post with helpful diagrams… or maybe not. How much good would a blog post really have done? If you want people to really think about recessive genes, in some life situation where it becomes relevant (is your baby at risk for a genetic disease?) then reading Ch. 23 might go beyond reading a blog post with diagrams, even if the diagrams seemed clearer than reading a text description of what Harry does with pieces of paper.
Ch. 23 tries to put you into the shoes and the experience of someone using Mendelian genetics, applying it to an understandable situation around them. Even colorful diagrams showing alternative alleles and phenotypes aren’t trying to do that.
If there’s anything I hope that Serious Writers pick up from HPMOR, it’s the idea of using fiction to convey the experience of cognitive skills.