Chapter 81 — Fermi Paradox
The Curve of Time, Chapter 81 —— Fermi Paradox, in which Mica connects time travel to the Fermi Paradox.
Followed by a return to the question of how many points are on the Koch Snowflake.
Listen to full episode :
— 81 —
Fermi Paradox
Saskia ended up staying the night, and during her fitful slumber another thought occurred to her; she voiced it over breakfast the next morning: “It’s all very well to realize that I can change the past, and thus the future, but Sienna has obviously figured out how to teach others.”
“Did she figure it out?” Mica pushed back. “Or was it an accident? Why would she want to teach all those people to slip in time?” She put Saskia’s chai tea in front of her. “You didn’t want to.”
Mica was right. Sienna was essentially the same person, and it wasn’t something Saskia had wanted; Saskia had been reluctant to try teaching Wassily, someone she knew well. It didn’t make sense that Sienna would teach a cohort of people she barely knew. “What if it has something to do with meditation?”
Mica cocked her head at Saskia. “And she somehow taught them all inadvertently?” She popped the toast down again. “Then go back and stop her.”
Saskia liked Mica’s idea. But another thorny conundrum was chaffing at her: what if while heading back something changed her own mind. “What if you were right? Earlier, when you thought it was me.” Saskia’s gaze pierced past Mica. “How can I be sure that, if I go back, something doesn’t change my mind——make me decide to use my middle name.”
“You mean something might convince you it’s a good idea to teach other people to slip in time? And that Sienna is really you?”
“If something did convince me——it’d give me the confidence that using the meditation retreat would work.” Saskia felt a clammy sweat on her neck. It was an uncomfortable thought that she might not know herself as well as she thought she did. “For all we know, my going back is the first step in a chain of events that triggers a worldwide disaster.”
“But, you know it’s not a good idea. Two people are dead.”
On the other hand, if she decided not to go back——committed to that promise——then maybe it was Sienna ...was this Schrödinger’s cat come to life again? That was a big problem, because now the cat was out of the bag!
The thought of Schrödinger’s feline reminded her of her own boy. “Hey, I really should get back to Tomato. Come to Pasadena with me?”
∞
It was early enough that the snarl of LA peak hour was yet to subside. Then again, there was never a good time that made the trip East quick. They inched forward in a staccato rhythm that pulsed inside the spasmodic flow that surrounded them, both women, lost in thought.
“It answers the Fermi paradox.” Mica stole a glance over at Saskia as she changed lanes.
“The reason we’ve never found Aliens?”
“Sure. And it’s probably also why we haven’t seen more of you time travelers before.”
Saskia squinted out the window of Mica’s car, as if the answer to Mica’s riddle might be found in the traffic around them. “How do you connect slipping in time to the Fermi paradox?”
“I didn’t; Jeff did. Though he found it in a book.”
“Really?” Saskia was impressed by how effectively Mica used her AI assistant. It highlighted that there was a difference between developing a technology and using it.
The book Jeff referenced was a sci-fi novel titled Lost In Time, and it posited that rupturing the timeline was what destroyed universes. “The mess we’re ‘slipping’ into”——Mica put ‘slipping’ inside air quotes——“doesn’t seem so different. Perhaps time travel is an inevitable development in the growth of a civilization, and the unfortunate, equally inevitable outcome: its misuse brings civilizations down.”
“Unless the time to learn is suddenly right? Right now. Maybe others are learning too.” Saskia was reluctant to head back in time. “Maybe things are destined to go haywire now?”
“You want to believe there’s nothing we can do about it?”
“You said it. Maybe time travel was always going to happen.”
“Alternatively,” Mica objected, still clinging to her sense of agency, “you could go back and stop Sienna from attending the meditation retreat.” She hit the brakes as her lane merging onto the 110 came to an abrupt halt. “You have a chance to save the world.”
Saskia laughed. Mica’s framing was so wildly over the top, she couldn’t help herself.
The corner of Mica’s mouth tipped up in recognition of the wildness of her claim. But she held firm. “You might be the most advanced time traveler, at least for the time being. Maybe you can go back the furtherest. The fastest.”
“But it’s all already happened,” Saskia objected. “We know our past.”
“I’m not disputing the past, but don’t you care about the future?”
The traffic that had engulfed them began to dissolve, one car drop at a time. And as they lurched forward, the thoughts clogging Saskia’s mind loosened and tumbled out. “The problem is: what if someone else goes back earlier. Someone who Sienna has taught. What if they go back before Sienna taught them, and everyone else at the meditation retreat. Maybe they teach themselves earlier. It could leapfrog its way back. Before we know it time travel has always been a part of the human experience.”
“Or you could just go back and tell me we can’t change things——reverse oil spills; save the world——by going back and fiddling with the past.”
Saskia shook her head. The world was already written. “We’d already see it, I tried to change things and the universe conspired to the improbable to stop the impossible from happening. We already know what today looks like.”
“But we also know: you can change things. Sienna proves that. And if you change the world before anyone else learns to slip in time then that’s it: nobody else gets to learn to slip in time.”
Maybe Mica was right. Maybe she couldn’t pick an arbitrary strand of the multiverse——no more than she could pick a specific rational number from the bag of all numbers——but, maybe she could at least guarantee that she picked a rational timeline. Even if such timelines were vanishingly few among all the possibilities. Was there even the possibility of going back to a world without doppelgangers?
“You think if I can make people appear——Sienna for one——I can maybe also go back and disappear people too?”
That was chapter 81, Friends, I hope you enjoyed it!
Having returned to a glancing reference to infinity in this chapter, I thought it would be fun to return to our Koch Snowflake musings from chapter 69, and our discussions of the different types of infinity in chapter 49.
As a quick refresher, a set, or collection of things, is countably infinite if it is possible to count off every element, thereby setting up a correspondence with the counting numbers: 1, 2, 3, 4, …
On the other hand there are infinities that are much bigger in size, namely uncountable infinities, which simply means that, try as you may, you can’t just line the elements up and tick them off one by one.
The question we left chapter 69 on was: How many points are on the Koch Snowflake? Recall, the Koch Snowflake was generated by adding a bump to each side of a triangle, and then doing the same to all sides of the new figure again and again ad infinitum; recall, I put a visual construction up on Instagram.
To set the stage, there are two possible intuitions for the number of points on the Koch Snowflake: 1) there must be uncountably many points on the Koch Snowflake, since any line segment, no matter how small has uncountably many points on it, and 2) there are only countably many points on the Koch Snowflake, since there are only finitely many points on the final snowflake that crop up at any point during the construction phase (namely the new corner points we identify at each point in the construction), and we can just count off those points as we construct it.
So which is it?
Rather than just tell you the answer, let me remind you that the set of real numbers——that is all possible decimal expansions——between zero and one form an uncountable set (if this feels hazy, you could always revisit the construction we walked through in chapter 49). My point here is that this is really the only uncountably infinite set that I’ve told you about.
On the other hand, the rational numbers (or fractions) form a countable set, since we can, in fact, line them up (again, chapter 49 is worth another listen if this has receded from memory). Now, here’s a snazzy thing: if we consider the decimal expansion of any rational number, it will always start repeating from some point on. For example 1/3 = 0.333333… and 1/4 = 0.250000… (or, equivalently, 0.2499999…) while 1/11 = 0.0909090….
Irrational numbers——real numbers that are not rational——on the other hand are all the other numbers. And as we just noted: there are a lot more of them!
Why bring up different types of numbers? Well, maybe you can see that, somehow, although we will pick up many points on the Koch Snowflake by collecting the new corners at each stage in the construction, there are even more points that are sort of the “corners” at infinity: that is, points on the Koch Snowflake that are described by which segment approximates them best at each iteration (left of a new bump, right of a new bump, or on the left or right side of a new bump). Can you see how this “feels” like a decimal expansion of an irrational number? That feeling is precisely the sort of thing mathematicians call intuition. And for today, I’ll leave it at that, because the feeling is kind of more important than whether or not I can convince you of a solid proof.
In any event, while the “finite corner points” are countable, there are a lot more points on the Koch Snowflake.
One last thought: Today’s chapter had a shout out to a book I read a while back, A.G. Riddle’s Lost in Time. Definitely a different flavor of time travel, but one with a big loyal audience.
Anyway, just as the LLMs are often accused of “plagiarism”, it’s always hard to know how much I am stealing when writing——even thoughts that I feel are original, are often later realized to have been seeded years before. At least, though, when I’m completely conscious of an idea I’m appropriating, it feels only right to acknowledge it. So, the in-text reference to Lost in Time is a genuine one, and it is A.G. Riddle’s resolution of the Fermi Paradox that I couldn’t resist including. If you like Michael Crichton, I think there’s a good chance you’ll enjoy A.G. Riddle’s works. He often includes some sort of philosophical musings wrapped up in technological elements.
Until next week, be kind to someone and keep an eye out for the ripples of joy you’ve seeded.
Cheerio
Rufus
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