Chapter 26 — A Cusp Problem
Rufus relates cusp points to various aspects of life.
Followed by Chapter 26 —— A Cusp Problem, in which Mica describes a new problem to Saskia.
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Hello Friends,
Today’s chapter is about the cusp on a curve, that is the point on an otherwise smooth curve where it doubles back on itself creating a sharp spike. That’s the mathematical content, but the context is a little more about how we live in the now, whether we like it or not.
Writing is curiously similar: I always have the greater arc of the story in the back of my mind, but it is the moment in the narrative that I’m bringing to life that matters when I’m putting pen to paper, since that is what will be reflected on when the words are being read. (Unless, the words I’m writing are later edited out in a future pass anyway, but even in that case, their ghosts will linger).
This same architecture holds for many aspects of life. Travel has a similar quality when you look at it the right way: we bring context with us, but when there’s a mountain or castle in front of us it’s hard not to marvel at the present vista.
Of course, wherever we find ourselves in life must be informed by our path to the location that we’re standing. Cusp points are distinguished by the fact that they are a place where we also turn about. They are the point at the end of the trail to the lookout; there might be a magnificent spectacle in front of you, but your journey going forward requires you to double back right there and then. To crash into where you’ve been, even if only briefly.
Anyway, that’s what a cusp point is. Unfortunately, as Saskia will realize in today’s chapter, the fact that we’re not idealized points forces this crashing into ourselves in other, smoother, contexts too.
Until next week, be kind to someone and keep an eye out for the ripples of joy you’ve seeded.
Cheerio
Rufus
PS. If you think of someone who might enjoy joining us on this experiment, please forward them this email. And if you are one of those someone’s and you’d like to read more
And now, without further ado, here’s chapter twenty six, in which Mica describes to Saskia, a problem Wassily noted.
— 26 —
A Cusp Problem
Mica gave Saskia a big hug. “I could have come to you.”
“I know, but you’re by the beach, and I had a meeting this side of town anyway.” Saskia’s second rationale had been a stretch, but she had felt the need to compensate, to cover for the concern that her double might have shown up at home. She pulled back and gave Mica a smile. Mica, in turn, gave Saskia’s bum a gentle squeeze before slipping back around to the tight galley kitchen.
“I’m having a Negroni,” Mica announced. “You want one? Or something else?”
“You twisted my arm.”
Mica pulled two glasses from a shelf above the counter that Saskia sat on the other side of. “I did some research.”
“Oh?”
Mica retrieved a bottle of Campari from a cupboard beside the fridge. “Yes, and I’ve got some partial theories. Ice?” Saskia nodded and Mica clinked an oversized cube of ice into each glass. She then launched into a recounting of Wassily’s explanations. It felt to her like an odd game of telegraph, and it reminded her of the time her college roommate had diagnosed a problem on her laptop and she’d found herself attempting to describe the diagnosis at the Apple store. Both then and now she’d worried that at any point she might suddenly find that what she thought she understood was totally bunk. Happily, Wassily’s tendency to periodically check and make sure she’d been on the train he was charting now paid clear dividends.
“Point is”——Mica had been excited as she reached the crux of a serious conundrum that Wassily had identified——“The point is, despite that first flowing curve I showed you, things could have gone wrong. We could have crashed back into ourselves.” Mica produced another of Wassily’s scribbled sketches. “Something like this.”
It was odd how a hand drawn curve had a signature, and unless Saskia was mistaken she recognized the hand by which this one had been drawn. The context of the content bolstered her suspicion, and her thoughts shifted to Wassily. How was it Mica knew him?
“See the pointy part on this curve?” Mica directed Saskia’s attention. “That’s the point that you decided to start rolling time backwards, but this time, you weren’t moving. You just turned time around. You couldn’t help but for a moment bump back into yourself. That’s called a cusp point. And that’s a problem, even if you are just a point.”
Saskia nodded; it certainly amounted to a problem. And it wasn’t just the suggestive spike.
“At first I imagined getting impaled on that spike,” Mica laughed at herself.
“It’d be even worse though if you weren’t a point.”
“Right!” Mica agreed, recalling Wassily’s lesson: “In that case maybe the front of you collides with the back of you. Even if you were back on the smooth curve.” Mica tapped the top of the first of Wassily’s curves. “Wassily explained that in that case you’ve got to imagine lots of parallel curves, and the front-of-you-curve might bump into the back-of-you-curve.”
Saskia’s eyes glazed over. Mica’s mystery mathematician was Wassily.
Mica reassured her that she too had been exactly where Saskia was now, yesterday, when Wassily explained it all to her. Saskia nodded, but her mind was elsewhere. A dozen years in the past, to be precise. The last time she’d seen Wassily. It felt like another form of time travel. Time travel of the mind, as it were. Memories to anyone else.
While Saskia explored her past, Mica placed another sketch in front of her.
In the two curves, Saskia saw herself and Wassily. Their lives intersected, then ran in parallel. Well, not truly parallel, but apart for a while. She knew he’d gone on to do a PhD, but she had no idea where he was now. Only that their lives appeared to be about to intersect again.
Mica pointed to the thinner of the two curves. “This is the front of you. See, it’s nice and smooth. No cusps. And the thicker curve is your butt.” She winked at Saskia and with the pretext of identifying the second curve in their world, gave Saskia’s bum another pinch. “Not saying you’ve got a big butt.”
Saskia nodded and pretended to study the curves. “You said Wassily is at UCLA?” She was preoccupied with the gangly college student she had experimented with, back when she was curious if she’d missed anything not being with a man.
Mica looked at Saskia, perplexed. “Yes.”
“Sorry, I didn’t mean to derail you.” The ideas Mica was describing clearly represented a new way for Mica to see the world. “Go on,” Saskia encouraged her. But Saskia’s own mind drifted to Wassily and the leafy campus nestled in the foothills below Bel Air.
“Okay, so neither curve intersects itself,”——Mica indicated the smooth flow of both the thick and thin curves——“but they intersect each other. At certain points. And that would be a pretty big disaster. Two wheels on the same spot of the tightrope at the same time.”
“Two wheels?” Saskia asked, absently.
“The wheel for the front of you and the one for your butt. Remember, we’ve moved past the idealized point that made you one wheel. If the thin curve was your front and the thick curve your butt, then you’re old butt would be sitting on your new front. Like literally in the same spot at the same time. And that couldn’t be be good!”
Again, Mica mistook Saskia’s vacant gaze for confusion, but Saskia had been thinking about Wassily, and the one time she’d shared his bed. Then suddenly everything coalesced. Saskia glanced back at the spike on Wassily’s cuspidal curve. That spike had skewered her. In Mica’s bed, that moment she had decided to go back in time. That pain she’d felt in her chest. That was the cusp.
“So, how can you ever go back in time?” Mica asked. “If one line is the line that maps your heart, if you start going backwards in time, then that has to intersect with at least some portion of the flesh surrounding it——flesh inside your chest——right before you start moving backwards in time. There’s no way around having two pieces of you in the same place at the same time. You don’t even need the cusp points to run into problems.”
