Episode 23: Dumb Luck

episode-23-dumb-luck“I’ll tell you all about it when we get back — if you want me to, at least.”

“Thanks, Melinda.” Bryony smiled. “I wouldn’t mind a summary. I wish I could come with, you know? But I guess I deserved this, so really I’m getting off easy.” She shrugged.

“Yeah, I never really understood what happened with all that, but as long as you’re not miserable.”

“I’m not miserable,” Bryony assured her friend. “Go have fun and don’t worry about me.” She gave Melinda a gentle shove down the corridor, after the rest of the class. Swinging her arms, she wandered back into the common room and collapsed into one of the big maroon stuffed armchairs.

She’d been a fool to think that the Academy was all about her personal adventure and she was paying for it now. She’d been honest with Melinda: she wasn’t miserable, but she wasn’t entirely sure what to do with herself either. The common room was almost eerily quiet without the usual chatter. The only sound was the scratching of Ken’s pen.

“So you really didn’t want to go to the big match, huh?” she asked.

“I’ve got plenty of work to do and the whole robo-duelling thing makes me sick.” He looked so unhappy that Bryony believed he might feel physically sick. “I thought we came here to learn science.” He jabbed his pen into his notebook.

“We’re still allowed to have fun, though.”

“I don’t object to having fun. This is fun when it makes sense.” Ken jabbed his pen into his notebook again. “But that is just a mess.” He shook his hand in the direction the rest of the class had departed.

“You seem pretty worked up about it.” Bryony had nothing better to do and Ken sounded like he needed to talk this through with someone, so she walked over and took a seat at his table.

“It’s all just so — so stupid.” He gestured helplessly. “It’s not like they’re learning anything from all this. They’re just idolising the people who had the dumb luck to get it right.”

“Dumb luck?” Bryony raised an eyebrow. That certainly wasn’t the way Melinda talked about robo-duelling.

“There’s no direction to anything. It’s not like there’s a set of instructions you can read to figure out how to do things or process to follow so that you know you’re doing it right.”

“Well, I guess that’s how you come up with new stuff.”

“If you’re lucky!” Ken lifted his hand as if he was going to thump the table, but then laid his pen neatly next to his notebook. “Otherwise it’s just how you fail.” His shoulders slumped.

Bryony wound a braid around her finger. “I guess you can look at it either way.” She didn’t think Ken was right, but she wasn’t sure what she could say to refute him either.

“I’m not interested in dumb luck. At least with something like this –” He waved at his notebook. “With something like this, hard work will get you somewhere.”

“Are you saying Jaxon and the others don’t work hard at their robotic stuff?” Bryony took a deep breath and hoped Ken wouldn’t explode at her.

“No! Well, I mean, uh.” He trailed off. “Obviously they work hard. I’m not trying to call them lazy. But it just seems to sort of work for them. Their bots don’t crash before the audition even begins.” He picked up his pen and rammed it into his notebook. “It’s not fair!”

Bryony bit her lip trying not to giggle. She wasn’t surprised that Ken didn’t like being outside of the robo-duelling clique, but he was being a little silly about it. From what she’d heard, he wasn’t the only one who hadn’t made much progress at the robo-duelling auditions either.

“What?” Ken glared at her.

“I’m sorry, Ken. I think I know what you mean. They have all this glamour; and senior students looking out for them; and people wanting to talk to their mechs; and who knows what. And we’re just sitting here.” She hadn’t meant to mention Melinda’s mech specifically and she hoped Ken didn’t pick up on it; but that wasn’t really the point. “They have spent half their lives fussing around with these things already, though, you know. And we were doing other things. That’s okay.” It was a little annoying, if she was honest with herself, but a little annoying didn’t mean it wasn’t okay.

“Yeah, well it’s still unfair as an old Earth contract.” Ken stared down at his pen and turned it over in his fingers.

“As a what?” Bryony hadn’t heard that one one before.

Ken shrugged. “It’s something my dad says.” He dropped the pen and pushed his hoverchair back from the table. “I still don’t see what’s so special about their robots.”

“I guess they’re fun to watch. I mean, I don’t mind doing titrations, but I don’t expect anyone to watch me, you know?” She put on a commentator’s voice. “And now Adams is releasing the forty-seventh drop of acetic acid. If it’s more than just a drop she could ruin the measurement. She’s turning the tap slowly — look at her go — and there’s a single drop. The crowd goes wild!”

Ken laughed in spite of himself. “But that doesn’t make it less important.”

“Of course it doesn’t. Hey, if it helps you can show me what you’re doing and I’ll try to be an excited audience. I’m not in the mood to get my own work done anyway.”

Ken peered at her for a few moments. “If it’s a serious offer, I wouldn’t mind some help with this. There’s some chemistry stuff I don’t understand that might make more sense to you.”

“Sure, why not?” It wasn’t quite what Bryony had been thinking of, but doing chemistry was usually fun.

“See, I’m trying to model a benzene atom. Well, actually just one electron in a benzene atom, the rest is way too complicated. But the point is, there are these different kinds of bond that form in the molecule, and I really don’t understand the detailed physics explanation of what goes on there. Do you have more of a big picture view? The electron I’m modelling is supposed to be sort of free to move all the way around the molecule ring.” He flipped through his notebook and pushed it towards her. It was open to a diagram of a benzene ring: six carbon atoms connected in a hexagon. There were technically hydrogen atoms too, but people tended to ignore those in books.

“Yeah, I think I remember something about this. It’s pi bonds and sigma bonds, right?” Bryony closed her eyes, trying to reconstruct her mental picture of the benzene molecule.

“Uh-huh. The one I want is a pi electron.”

“Okay, so I don’t remember this exactly, but basically, it only takes one electron to form a strong bond between the carbon atoms. So there’s a strong bond between each pair of atoms, with an electron. Those give the molecule its basic shape and they’re called sigma bonds. But then there are other electrons left over from the atoms. You have to keep them around or the molecule would be electrically charged, but they’re not involved in such strong bonds as the sigma electrons are. In fact, they can move about and change which carbon atom they’re bonded to, as long as they stay in the molecule somewhere. That bond is a pi bond, so the electrons are called pi electrons. Does that make sense?”

“Yeah, I think so. I’m not worrying about the sigma electrons or the carbon atoms. Well, I am worrying about the carbon atoms, but not the nucleus and stuff, which is what’s all bound up there. I’m just thinking about a pi electron which can skip about from one carbon atom to another. So I guess it has a sort of track that it can move along between them.”

“It’d be sort of in the hexagon shape, although there’d be a lot of wiggling depending on how far out from the carbon nuclei it goes.”

Ken sighed. “I think we have to just simplify that out. The equation I have is for just moving in a circle, and it’s still a mess.”

Bryony pulled a face. “I guess it’s kind of a circle. How complicated can the equation for a circle be?”

Ken flipped through a few more pages of his notebook. “This complicated. Dustborn says it’s a simplified version of Schrodinger’s equation for a particle trapped on a circle.”

Bryony peered at the line of derivative signs and the tangled set of trigonometric functions that followed in the solution. “Okay, that’s pretty messy. Do you have to solve that?”

“I wish. I’m just showing that if you plug in the solution here it checks out. But that’s tricky enough, plus I have to explain why it’s reasonable to use this equation in the first place. I think I’m starting to get it now, though. I’ll have to think about why it’s easier to use a circle than a hexagon. Something about symmetry, probably.”

“Rather you than me.” It struck Bryony as sort of ironic that Ken thought that mess was more fun than robo-duelling, when she couldn’t think of anything worse.

“Nah, it’s fun.” Ken was already flipping through pages in his notebook.

 

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2 thoughts on “Episode 23: Dumb Luck”

  1. This is a touch past where I got in physics calc and molecular Chem, but… wouldn’t it be easier to model motion through a chord from one angle to the next, wash rinse repeat?

    1. If you’re modelling a particle travelling exactly along a hexagon, that would work better, but that’s not exactly what’s happening here: Ken’s using Schrodinger’s equation to model the electron in quantum mechanics, which means the electron has a probability of being (almost) anywhere in the allowed region at any given time and doesn’t have a well defined trajectory. (We’ve mostly just glossed over this quantum weirdness.) Since you have to describe the whole region, it’s much easier to describe a circle (in polar coordinates you just fix the distance from the origin and allow any rotation) than almost anything else. Ideally we’d want to model the width/volume of the allowed area and somehow account for the nodes where the nuclei are (or do a full quantum treatment of those too), but it quickly gets HARD and impossible to solve without significant computer work.
      This model is simple enough to be used in an intro to quantum mechanics, but it’s halfway decent too. If you predict what will happen in spectroscopy experiments with this model, you expect light with wavelength about 213 nanometres. When you actually do the measurements, you get about 255 nanometres.

      tl;dr It’s quantum, so the idea of motion gets really weird. Circles are relatively easy to work with. Thanks for your interest! :)

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