Chapter 69 — Memories
The Curve of Time, Chapter 69 —— Memories, in which Saskia dives to the seabed.
Followed by some musings on the Koch snowflake.
Listen to full episode :
— 69 —
Memories
Encountering her future self, Saskia knew that——for certain——she couldn’t die right now. It gave her a feeling of invincibility. A sort of superhero feel. It was yet another superpower; the superpower of belief in herself.
It again begged the question of causality: whether the world was, and always would be, a certain way; if there was anything she could do to change that. For now, though, she put the question of agency aside and bathed in the upside. Heading to the wellhead and guiding the capping stack atop was evidently destined to succeed. This wasn’t the Deepwater Horizon, and Saskia wasn’t wearing roller-skates atop of the proverbial Empire State Building.
Even so, she still had to figure out how to slow time down and place the capping stack on the wellhead without alarming Jeremy and his crew.
For the logistics, her plan was simple enough: use her super strength to maneuver the giant concrete plug over the open cap at the wellhead. When that was done she could leave it to the DBG rig operators and their hydraulic systems to engage the seals and valves, ultimately securing the cap. The crew had earlier tried placing the capping stack, but the torrent of oil and the lack of ROV visibility had been an insurmountable obstacle; with the turbid conditions near the wellhead, even the powerful lights on the ROVs struggled to penetrate further than a foot or two; the churn of the oil and seabed matter simply absorbed too much light.
Further back——back where Jeremy insisted that safety demanded they observe from——visibility was as good as ten or twenty feet. And it was those extra feet of exposure on her path to the wellhead that compounded the difficulty of escaping Jeremy’s watchful gaze.
It had taken almost fifty minutes to descend to the ocean floor and her target was now tantalizingly close. There, in the dysphotic zone, where the ambient light from the ocean’s surface was barely a faint twilight, Saskia wrestled with how to evade Jeremy’s protective eye. Sure, he was absorbed with indicating the layout of the wellhead that he’d described in detail back on the rig, but his focus was on her.
Gazing into the hazy ambiguity dead ahead, a peculiar parallel sparked in Saskia’s mind: the infrastructure obscured below city streets around the world. Like pipes under the roads, the foundations at the wellhead, once visible, were now a matter of belief. Invisible. Forgotten, unless directly contemplated, and yet relied upon in perpetuity. Like our memories, they could be recalled. Saskia trusted that she’d find the wellhead, just as those fluorescent jacketed road workers——unlikely the same workers who’d laid the pipes originally——always trusted they’d find their pipes when repairs were called upon.
Was her trust based on Jeremy’s accounts? Or the assurances of her older self?
What if the woman giving her the thumbs down and OK sign wasn’t her older self. Could it have been the other Saskia? But, surely the other Saskia wouldn’t deliberately——how would she even know that now was the time to give a thumbs down.
To Saskia’s left, Jeremy indicated thick banners of kelp, the long blades furling and unfurling hypnotically as the dark tendrils prowled their way. That bigger fish sought out smaller species seeking cover——suddenly, Saskia had an idea.
She angled herself behind a giant undulating serpentine ribbon, as if merely avoiding its mass. And then, she disappeared within the sea-forest.
Out of view of Jeremy’s camera, she killed the high-intensity lamps of the integrated lighting system on her ADS suit, and dramatically slowed time down. Simultaneously she gave herself the superpower she needed to manouver the capping plug and the speed to evade Jeremy’s watch.
∞
On the flight back to LA, Mica admitted to Saskia that she had been jealous about Elena, Saskia’s college roommate who’d taught her to dive.
Saskia laughed at her gently.
Mica acknowledged that it made no sense to be jealous, but jealousy wasn’t really about being rational. “It’s kind of like being jealous of an old girlfriend——actually, it’s not like that, that’s exactly what it is.” Mica laughed at herself too, at the absurdity of it all. “It makes no sense. I didn’t even know you back then!”
Saskia’s life today shared so little with that of a college student’s, and her college crush ...that girl was not a threat. Except that she was. Maybe not a threat of whisking Saskia from Mica, but there would always be that piece of Saskia’s heart that belonged to Elena.
“I’m sure it wouldn’t have mattered as much, had I not envisioned that diving——that I was destined to stake out that territory, in your mind. And all the while I was deluded.”
Saskia pulled Mica’s forehead close and planted a kiss on it.
“Elena was already ensconced there.”
“You couldn’t have known about Elena.”
“I knew diving was important to you. That it was so important——that should have told me there was history.”
Saskia dropped her arm back down to Mica’s shoulder and pulled her in tighter. “There’s no short cut to history. You just have to put in the time. And some moments will always mean more than others——we’ll always have the lottery.”
Saskia flipped up the armrest between them and pulled Mica over to snuggle with her. The two women gazed out of the window at the clouds that passed below. The shadow of their plane rippling over the giant fluffy cotton landscape slipped Mica back to the moment, just a few days earlier, when she’d been looking up at a plane in the sky wondering when Saskia would return from her first visit to Dallas. Now, here they were, together, their mission accomplished.
Below the clouds, Saskia glimpsed a city, with roads and traffic. She tracked the cars inching forward. “Did you know traffic has a memory?”
“What?”
Saskia pointed out the window. “Your talk about memory, and the traffic below.” Saskia shook her head softly. “Traffic remembers accidents. Hours later. Long after an accident, traffic on a road will mysteriously go bumper-to-bumper for a stretch——they call it memory. Brake lights keep causing braking and the cycle continues, even after the battered vehicles have been removed.”
Mica kissed Saskia’s cheek. It made Saskia smile.
“You know what else has memory?” Saskia turned to Mica, who gave a subtle shrug of her shoulders that indicated she had no idea where Saskia was going but was eager to hear. “Neural Nets. Actually that’s kind of all that they have. That’s what the training data gives them.”
“The adjustments of the dials and knobs?”
Saskia beamed back at Mica. “I guess the lottery isn’t the only memory we’ve made.”
That was chapter 69, Friends, I hope you enjoyed it!
It’s been a while since we talked about anything mathematical, but with today’s chapter title as a thin connector, I’m going to take the opportunity to return to the memory of our earlier discussion of the different types of infinity that we had back in chapter 49. Specifically, I’d like to talk about how many points make up a particular fractal image.
The picture I want to talk about has been on my mind for a couple of months since my buddy Rob and I are including it in the calculus book we’ve been writing. Moreover it is a pretty image, and the related question is intriguing.
The picture in question relates to the so-called Koch snowflake:
A mathematically generated outline of a snowflake
And I’d like to focus in on what I’ll call “one side” of the Koch snowflake.
What do I mean by one side? Well, the picture you’ve just looked at (which is actually just an approximation of the actual Koch snowflake) is made up of three slightly doctored sides of an equilateral triangle that’s resting on the bottom vertex (recall an equilateral triangle is simply a triangle in which all sides are the same length). The doctoring of each side generated as follows: start with a line and swap out the center third out with a new equilateral triangle, then remove the side of that triangle that overlapped with the original center third. That is, in the first iteration you give the center of each side a sharp hump. The “top” side of the initial Koch triangle would change thus:
Repeat this process with each new line segment.
Can you see the top side of our Koch snowflake coming to life? Do this for all three sides of the originally inverted equilateral triangle.
Cool snowflake, right!
As an aside, notice that the distance “around the Koch snowflake” is infinite.
“Wait, what?” I hear you ask.
Well, notice that at each stage in our generation we replace every line segment from the previous step in our generation by a new one that is one third longer. Repeat this infinitely many times and you have an infinitely long path around your Koch snowflake. Of course traversing that infinite path means zigging and zagging around tighter and tighter turns.
Anyway, the question that I wanted to focus on was not how far it is around the snowflake, but rather how many points make it up.
If you think about it for a moment, you might come to the conclusion that the corners are the only points that will be involved in the final product, since excepting the “corners” every other point we see during our construction will eventually be replaced by a little hump, right? Makes sense?
The thing is, there are actually a lot more points on the final snowflake. Perhaps, for those of you who were really comfortable with the ideas around countable and uncountable infinities, it is not surprising that there are an uncountably infinite number of points on the snowflake and moreover the points I’ve described so far——the “corners”——make up just a countable set, an obvious contradiction to them accounting for everything.
Unfortunately, this commentary has already ballooned a little too much, and I don’t want to bloat it. So, let’s save the counting of the corners, and the why they don’t account for all points on the Koch snowflake for another time.
For today, I’ll leave the Koch snowflake as a happy something to muse on.
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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