These posts are recaps, with very little colour commentary on my part. Some are near word-for-word recaps, others are a summary. This is the former, as I figured some people in my feeds might only be interested in the panel “Can Mathematics be the Basis of Hard Science Fiction?” that occurred Sunday at 1pm.
I want to mention that my own time travel story does try to use some underlying mathematics in the design of how the device works, even though actual time travel isn’t possible and I hand wave on components more than Steins;Gate, so I was particularly interested. The panelists were Eric Choi (Science Guest of Honour), James Alan Gardner, Derek Kunsken, Suzanne Church, and was moderated by Sheila Williams (Editor Guest of Honour).
|Panel: Eric, Sheila, James, Derek, Suzanne|
Sheila: Thank you all, This is ‘Can math be the basis of Hard SciFi’. I’m the moderator, the editor of Asimov’s. Hard SciFi can come from all branches of science - math, combined with others like philosophy. Talked to a person whose daughter, one of her first words was fractal.
Eric: Has short fiction stories, “Most Valuable Player” (in Analog SF) with baseball statistics, and “Decrypting” in an upcoming. Otherwise not given it much thought.
James: Written many short stories, novels. Eric had reminded him of another story he did on baseball statistics. And “Axial Axioms”, where the great ancient philosopher advanced math rather than philosophy, so Buddha invented the zero. Also wrote “Gravity Wells”, the model of black holes crossed with Kent State killings back in 70s. “I think math is perfectly useful, have a masters in math.” Easily exploitable.
Derek: Written Hard SciFi based mostly on physics and biology. Though he’s more biology, he still thinks math is cool. Where do you see energy budgets and that sort of thing, could do something like that.
Suzanne: SciFi fantasy and horror. Same University as James/Jim, got a teaching certificate, has been teaching high school math for 8 years. “Calculus is my friend.” In a Jr. Kindergarten conversation of math, everyone think of a big number, and her son said those others are small, how about infinity. Math can be really well done in SciFi.
Sheila: How much of a distinction is there between science and math when writing or reading?
James: Leaps in, because as Suzanne mentioned they went to same university, and at University of Waterloo, science is it’s own faculty, and engineering it is own faculty and they all hate each other. So yes, of course math is entirely different, because it’s better.
Suzanne: Even though we don’t have a Nobel Prize.
James: Math makes sense, science doesn’t have to. He went back to do some courses in geology, and the difference is night and day. The way he would set a story up - Derek talked about making stories from a biological point of view, ecosystems - that’s not at all how he would approach one based on math. He’d take something cool in math, which is almost always an abstraction, and come up with someone to whom that meant a lot, had an emotional resonance. “Division by Zero” story, about a mathematician who has come up with what she thinks certainly is an inconsistency. Internally inconsistent, and tries to commit suicide, knows that the rest of her life is going to be a lie, how does she live with that. “Again, it’s a matter of how I’d go about making any SciFi story”, whether I come from math or not, get a cool science thing that has an emotional resonance with a character and then how does that proceed. How does it get the character in trouble and what do they do about it.
Suzanne: And a whole branch of mathematics, pure mathematics, is theoretical. Does P=NP has no corner foundation, proofs not yet completed. In science, it’s a hypothesis then proving it in a lab, whereas in math it’s all about proof, about proving your theory is true. Like the four-colour math problem.
Sheila: How to put math into a story?
Suzanne: Was working on one about proof of love, an autistic kid couldn’t communicate with mom, and when they could communicate, she said “I love you” and he answered “I don’t believe you, I want proof”. He wants math to prove his mother loves him, and if he loves her does she love him, and ‘if and only if’ proves in both directions. And that kind of math is very different form a science math. Could have spent a day hand-waving and talking about it, but because it’s not proven, lots of space for SciFi. What if I change this just a little bit, what if you came up with there was a proof. Take the story from there.
James: Four colour map theorem, could be some place where the map doesn’t colour, and into Lovecraftian geometries.
Suzanne: Or quantum dimensions, slicing through the fourth colour.
Eric: And math affects all of our day to day lives. Ordering a book or online banking, lots of cryptic proofs that is built on an unprovable assumption. The idea that it’s hard to factor numbers back down. Basis of his “Decrypted”, in a post quantum world, that’s made very easy to crack.
Suzanne: Easy to find the large prime numbers.
Eric: We don’t have the computer to execute “Shor’s algorithm”.
(Suzanne and Eric say something I don’t catch.)
James: “My first research job” was looking at cracking prime number encryption beyond brute strength. And of course we still use it.
Derek: Kind of agrees with Jim, in that we see them [math/science] as separate, and also with Suzanne, in that it’s so abstract. There’s nothing to hang on except metaphors, so far from something like biochemistry.
Sheila: Involving higher dimensions is a staple of literature since “Flatland” and “-He Built A Crooked House”. (How many read?) Science has advanced, including string theory. What might we exploit with higher dimensions?
Eric: Maybe we can ask one of our mathematicians what we mean by higher dimensions. It’s very poorly portrayed in mass media, like Star Trek, where it means walking through walls.
James: What does it actually mean, yeah. From a physics point of view, 10 dimensional space is n-theory, a version - not string theory - that ties things together. That 10 or maybe 11 dimensions is the proper way to describe our universe, and some of those dimensions are so small that you can’t travel in that dimension, but gravity can leak in that direction. What does this mean? The first 4 dimensions are simple, we describe this. Longitude, latitude, altitude, and last is time. Four numbers to describe that point. What’s a fifth number? Is there a fifth thing going on? Perhaps that’s time travel, so let’s say I’m a time traveller, there’s the time I saw “that” when I was 40 but also when I saw it at 50. And the second time back, I was looking at this guy pointing to a table saying 4 numbers, but there’s a 5th number, how old I was when I saw him do that. The time travellers in the back, they need that to remember. A different way of describing things. A 5th dimension based on a time traveller, but why only one?
Derek: “I’ll say something dumb and you can fix it, Suzanne?” From Flatland and Sphereland, I get a dimension is something you can rotate around that axis. So I find it fascinating that if you take a timeline and move it this way you make a surface, then a solid, then turn through another dimension and you’ve created a 4th dimension.
Eric: A physical fourth dimension.
Suzanne: Everyone understands difference between 2D and 3D. So try then to think of the 4th dimension by reversing your steps. See this table is in three dimensions, even though it’s 2D. Then grab a box, a cube, a thick book, imagine taking it and sticking it through this 2D table surface. Makes several points where this book intersects with the flat top. This is 4th and 3rd dimension. People could be at different points in this cube book, so different points when they interact with the 2D object. That notion is how 3rd and 4th dimensions mix, all the ways they interact with a flat surface. And that’s why we have the notion of time travel. If I’m on the cube, I can move to another point, but still be in this notion of three dimensions, that’s how I could essentially time travel. Not move on the table but through the cube.
Sheila: “I have a story coming out and now I understand the table.”
James: And Suzanne’s talking about spatial dimensions, “I was talking about time dimensions”. Math, this is simple, does it have a positive or negative sign, done.
Derek: One thing in "Flatland", no matter what you do to a right handed mitten, it will always be, but if you can twist in another dimension, you can get left handed. Charge time parody, if you change all three dimensions you have the same object but it’s backwards in time, antimatter AND mirror reversed. That would be an interesting way to make antimatter, if you can move it through a fourth dimension. “Something I’ve been exploiting in stories I’m writing.”
James: Does this make lots of sense, no. But is it good handwavium, absolutely.
Suzanne: And that’s how math works.
James: How do you rotate through a 4th dimension? Derek has used double-talk to make antimatter.
Suzanne: That’s the fiction piece.
Sheila: And as an editor that’s great for me, I don’t need it all explained. For some kid out there, that’s exhilarating.
James: Poul Anderson had a story, the hero is a werewolf, it’s modern day, he has a flash link and camera that’s the wavelength of a full moon. So he can flash and be a werewolf. Secret agent for some.
(Audience Member: “Operation Chaos.”)
James: Yes! Eventually they get into a non euclidean geometry world, in a different dimension, they can take shortcuts like how Suzanne talked about. The shortest distance isn’t a straight line, and they play games with that.
Sheila: Anything else to add?
Derek: What we’ve talked is whole number dimensions, to partial dimensions now.
James: Here’s a simple story. Everybody knows... (pauses) (laughter). All right, if you take a large scale map of Britain - because this is what they did - and you trace around the boundary of the island of great Britain, whatever the technical thing is, the distance around it is about 3,000 miles. Then if you take a smaller scale map, patched together, that distance is 4,000. Because now you can see inlets and irregularities you don’t see on the large scale. If you take an even smaller scale, the boundary gets even larger, even smaller inlets and points. Accumulates into a larger distance, right down to a fractal scale where you’re looking in a magnifying glass, let’s say, tracing the coast of England. Lots of handwavium here, depends on the tide, but that can actually get up to 7,000 ish miles.
Suzanne: From a podcast.
James: Some measurement from Royal Navy. The little irregularities all add up. [Back to simple story.] What if someone gives this exercise to measure a boundary, and it keeps getting larger and larger, but as it gets larger and larger it’s not 10,000 it now looks like 100,000, and you’re looking at Lovecrafian geometries and infinities popping up everywhere. Every time we measure the boundary, this house gets larger.
Suzanne: Infinity hotel. (She explains the Hilbert Hotel premise, new guest arrives.) Room 1 moves to 2, and 2 to 3, everyone moves to Room n+1, no difference between infinity and infinity plus one, and there’s a room for you now. Even though it’s always booked solid, there’s always room for one more.
Derek: So, one of the things that I find interesting, you spoke of a line, and that’s a 1D object, but as your line gets granular it never becomes 2D but more.
James: What we call a space filling curve.
Derek: Moving 1 metre per second, there will be an infinite distance along a fractal dimension. An impassable barrier or something, a forcefield.
Suzanne: Because as a human, how do I travel along infinitesimal distance. The math versus science argument. In science, everything has a physical requirement. In math, the physical requirement doesn’t matter.
Sheila: Comes out like Zeno’s paradox.
James: That’s the first thing you resolve when you take Calculus.
Suzanne: Our [math] calculus, “I don’t know if it’s covered in the engineer’s calculus”. (reaction of ooh!) Just a joke, didn’t mean it.
James: Suzanne’s point is that physical limitations do bog you down, you can’t make a space filling curve where you won’t trip over your own feet. But Derek’s point is useful in that it can be used as a baffling route, to mess up computers if nothing else, but also gives a forcefield that has an infinite number of turns, so say that’s the way your forcefield works. You’ve got perfect forcefield tech, make a story about it.
Suzanne: Or you have the notion that it’s impossible to make a forcefield, because if you go far enough down, you’ll always find a vulnerability.
Derek: Question? Fractals can only be done on a continuous line. When can you not do that, we’re quantized.
James: “My old roommate eventually became chairman of the math department, and this is precisely his field.” Trying to throw out calculus’ continuous anything, make a granular version.
Derek: How’s it going?
James: Claims it’s more accurate with better results than versions of physics based on the traditional.
Eric: Should our panel explain briefly the difference between quantized and continuous?
James: (Explains the idea, quantized as whole pieces) If you try to draw an infinitely smooth line, there’s atomic particles, so you can’t be infinitely smooth. Jumping from atom to atom, or electron to electron. There may not even be spaces, space may be quantized, think of bubble wrap. Can’t exist between bubbles, between spaces. Or space as an egg carton, there’s places you can be and places you can’t, and you’re either in one carton hole or the next carton hole. You can’t smoothly make a transition from one to another.
Suzanne: Draw a straight line with a ruler, magnify it, you’ll get to where it’s not a straight line any more. But I like the egg carton analogy too.
James: Gap on “Math abstraction” and “How the real world works”.
Sheila: Chaos sounds really complicated, but it’s doing a calculation over and over. The math analogy of biological evolution, in play in orbital dynamics, with more than two people in a system. Butterfly effect, yielding weird order. Can Chaos be a jumping off point?
Suzanne: Absolutely. “Jurassic Park”, and he used fractals in that novel too, beginning each chapter as a fractal. You haven’t been talking in a while Eric, want to talk?
Eric: “There’s an exercise I did, the Chaos Game”, a simple thing you can probably script, He used MatLab. A piece of paper, a random dot somewhere, another, a third dot between those two. Then other dot between, a 4th dot, and midpoint between that and the prior midpoint. What do you get? Logically, random dots, but on a screen it came out to a fractal pattern of triangles. “Blew my mind.” Order really can come out of simple rules of the universe, and that’s something quite profound. There’s got to be a story in there.
Suzanne: The whole ratio of 13:11, the Fibonacci sequence in nature like seeds in a sunflower, it’s fascinating how nature keeps linking back to Math. You wonder how much is ingrained in us, and how much thinking is based on our brains and if we’re predisposed to see these patterns.
Eric: Read the novel by Carl Sagan “Contact”, there’s a huge deal in the book about pi, not in the film... is this a spoiler here?
Sheila: It’s been out long enough.
Eric: They got a supercomputer and computed pi to some outrageous digit and found a string of 0’s and 1’s toward the “end”. In a grid of numerical base [base 11], it draws a circle, called “signature of Creator”. Felt it was Sagan’s way - he’s known as a rationalist - that extraordinary claims require extraordinary proof. Felt like this would be the proof, something ingrained in a fundamental constant of the universe. Wish they’d addressed it [in the film].
Sheila: Asimov was so annoyed by that. “I can say it now that he’s long gone.”
Derek: What didn’t he like?
Sheila: It’s interesting from a philosophical point of view; Asimov didn’t like religion having a place in the novel. Give ‘em a break for proof of god. If it had been Shirley MacLaine, he wouldn’t have minded, but it’s because it was Carl Sagan...
(Audience member brings up Conway’s “Game of Life”.)
Eric: Oh, model, simulation, know of it.
James: It really is just a game of cellular automata. Assume a grid like a checkerboard but as big as you want to make it, tokens and rules. (He sets it up.) All kind of things that you can use that system for. Can make a computer out of that system, can model a gun that shoots blobs like bullets. Contentions that some cellular automata model is the basis for the universe. Thing about cellular automata, each generation affects the next, and math can prove that - aside for extremely simple cases - you can’t predict anything by shortcut. Milionsth generation can only be found by playing it out.
Derek: A limitation on math, or on technology?
James: Basic math limitation. Same way the halting problem says we can’t calculate it in advance.
Derek: So that’s the universe saying there’s no way.
James: Right, no general way except to go through the rules. So that’s the point of the universe, take an infinitely intelligent being, no way for God to predict how the universe will come out except to make one and play it and see what happens. What if the basics of physics were like this? Mathematics says (ha ha stronger than you are) there’s no way to see the final state of the universe.
Suzanne: Because math is based on foundation of proof. Can’t prove it in the general case. Specific cases we might see after 1,000 generations, but that’s a case, not proof.
James: And Godel’s [incompleteness] theorems come into this. In any formulation of math that is sophisticated enough to generate math, then there will be an infinite number of things that are true, but not provable. So you can have a perfectly wonderful basis of math that lets you do all kinds of wondrous things, and there will always be things you cannot complete.
Suzanne: Or things that are undefined, like division by zero.
Sheila: How to use this?
James: Something like that, “is it provable or not” does drive you crazy. Also by Turing’s halting problem, a perfectly rigorous thing, you can never figure out definitively whether a process for stopping will end or not. Can’t say THIS thing is unprovable though, because tomorrow someone may prove it.
Derek: “This is where my mind usually gets blown.” This is the universe’s rule, universe gives physics, gives chemistry, gives biochemistry, gives evolution. But you’re saying math puts things in contention. Looking at far, far future, if you were using neutron stars as sub-processors of a vast intellect, this will still trump those. And that says something big about us too. I love the philosophical.
James: Godel says there are things that are true that you can’t prove, these are true and don’t we already know that? Mathematics looks, said that’s discouraging, well, back to the job. That’s the nature of life.
Suzanne: Almost every story has a conflict between characters and environment, what have you, and a notion of provable in a general case versus specific. That’s where the conflict can happen. A certain theory is true, two species can never breed and make a baby that can survive, can’t live past x breath. Then what if you get that ONE case, where something genetically happens, and your mind is blown. There’s no way the general case WILL apply, because here is a species that can’t exist and how do we deal with that. Take what you’re pretty sure is true or not true and find a single instance of something you can’t prove, and get the conflict.
(Audience: Mentions “Game of Life”. Novel by Piers Anthony as an analogy for non-energy based, multidimensional life forms.)
James: Something Suzanne said reminds me of “Black Swans”. Everyone probably knows the phrase now, Nassim Taleb abused it. Europeans made it a folk saying, “All swans are white”. Wasn’t that, even in Europe, people figured it wasn’t possible, they must have realized that birds can be different colours. But they had it in their heads. So when they got to Australia and saw black, it blew their minds, not because they couldn’t believe birds were different colours, but because they had psyched themselves up, nature in this case won’t deal us a black swan. And they were wrong. And that’s an important SciFi thing to bring in, people can believe in things that are mathematically improbable, and so will SciFi come to bite them in the ass.
Eric: Like buying lottery tickets.
Sheila: So we have about 4 minutes
(Audience: Mention of “On Science” by Wolfram(?), and another by Taleb, “AntiFragile”.)
(Mention of Roger Zelazny’s “Doorways in the Sand”, gets parody flipped, and Ken McLeod.)
Eric: (Mentions how British physicist, George Gammell, played with constants of the universe. What if light was a few metres per second?)
James: FTL, done by bobbing into different frames of reference, where light moves slower.
Suzanne: Approachable books by Greg Egan. Lots of yummy charts to suggest barrier between. Permutation series. Things that prove that math has a place in fiction.
James: And here’s a terrible thing you can do to learn about math, Princeton companion of math. Costs $80, but if you go to Kindle and ask for a free sample, you’ll get the first 100 or so pages, a beautiful summery of the current state of math. You may want to buy the rest of the book eventually. A way to get a bunch of good math, free.
Sheila: I think we’re done now.
I spoke briefly with Suzanne Church after the panel, regarding “Two different models of predicting statistics”, likelihood versus expectation. Also about what books might be good for teachers, enthusing kids, and “A Wrinkle In Time” came up. (Which will be a movie in the not too far future.)
That’s everything for that panel, thanks for reading. Hopefully you found some of this to be interesting, informative and/or helpful. As always, feel free to drop a comment if you have an opinion or a question! Yay for mathematics in stories!