Sørina Higgins gave a talk recently at the Brazilian Mythopoeic Society about how time flows in fantasy. This is something that has interested me ever since I read Umberto Eco’s essay “The Woods of Loisy”1. One of the techniques Eco used there to describe the temporal flow in a story was to make a graph of the “in-world time”, what the calendar on the wall says, versus the reader’s progression through the narrative. I’ll use “page number” to stand in for that. Eco uses it for The Odyssey, and Sylvie by Gerard de Nerval, and a limerick about a man from Peru.2 I want to use it for stories about literal time-travel, instead of a narrative that shifts about in time while the characters all go forward.
Figure 1.
For experimental purposes, let’s construct a trivial time-travel story: A mad scientist in Texas invents a time machine. He uses it to go back to last February in Brazil. While he’s sight-seeing there, a butterfly lands on his shoulder and he brushes it off. Then he climbs back into his time machine and returns to the time he left. Well, we all know about the awesome power of butterflies in Brazil. When he returns, his lab has been blown apart by a tornado, the infrastructure for time-travel is wrecked, and so he sets about the job of rebuilding, one day at a time like the rest of us have to. The End.
Figure 1 is what that story looks like when it’s drawn as one of Eco’s diagrams. An upward-sloping line is what we all do all the time. A big jump straight up or down is when the time machine causes a change of the in-world time on a single page for the reader. These parts are the pure science fiction.
Among Sørina’s citations are Ted Chiang’s “The Story of Your Life”3 and Richard Feynman’s Nobel lecture. Though she didn’t mention it, these two texts share a deep structural element. Chiang’s protagonist learns an alien linguistic form from creatures who perceive language as a kind of variational principle, and ends up seeing her daughter’s life in that way, instead of via pedestrian linear time. Chiang, according to the end-notes in my copy of the book, is fascinated by Lagrangian dynamics, so he wrote them into a story.
Feynman earned his Nobel Prize for applying Lagrangian variational principles to Quantum Electrodynamics, and in the process inventing a way to compute preposterously-complex integrals4 without making your head explode. That method is now called a “Feynman diagram”. A Feynman diagram has solid lines with arrows for electrons, quarks, etc. There are wavy lines for photons and curlicue lines for gluons. Other bosons are represented by dashed lines. (E.g. the famous Higgs boson, but there are lots of smaller ones.) There are rules about how different lines connect at vertices, and if you follow all the rules, you can read the function you need to integrate off the diagram, and you’re sure to be doing a calculation that makes sense.
One of the key insights that made diagrams possible was that we can think of a particle of anti-matter as a particle of regular matter traveling backward in time. That’s because the critical parameter describing motion is the product of energy and time, so, mathematically, there’s no difference between something with positive energy going forwards and something with negative energy going backwards. -iEt = i(-E)t = iE(-t), right? But the corners of the red zigzag in Figure 1 all have one arrow coming in and one going out, which means they obey the most important rule of Feynman diagrams.
Figure 2.
In Figure 2, let’s fix the diagram in Figure 1 so that it obeys the rest of the rules, too. Those blue dashed lines are some kind of boson. They represent a force coming into the story from outside, which causes the time machine to turn on or off.
The upper left corner, when the time machine is first turned on if we read from left to right, has a forward-in-time arrow and an backward-in-time arrow if we read from bottom to top. That’s particle anti-particle annihilation. The bottom left corner is the reverse, called pair production. The third and fourth corners are good old scattering, as a particle gets kicked so it moves differently but doesn’t change into antimatter or anything. Another fun thing is that the internal lines don’t have to obey one law of physics (E=mc2); breaking one law of physics is very useful for someone in a science fiction story.
Now, if I were a French philosopher, I’d say something like we’ve drawn the role of the author into the story. And the next step is to add up the contributions from all the possible locations of the vertices and all possible trajectories of the internal lines, which means that all stories involving turning a time-machine on and off twice will be added together. Most of them will cancel each other out, but the ones that reinforce each other will be the enduring Ur-myth of the Time Machine. Good thing I’m not a French philosopher!
But that means that I don’ t know what is represented by those blue dashed lines. I know they aren’t eternal; the number of them isn’t conserved. They can be created or destroyed by interaction with a plot. What do you think they are?
Appendix
Here are Feynman diagrams for two simple scattering events.
time flows left to right
Søri Higgins
Goodness! You’ve done it! May I repost on The Oddest Inkling?
Joe
Certainly, now that we’ve figured out how. But the C.S. Lewis part won’t be along until tomorrow.