TT2.37: Geography & Geometry

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Hank Waterson stared down at the prone form of his daughter, lying on the hospital bed. For once, Carrie seemed conscious, but her eyes were blank. She didn’t seem to be aware of her surroundings.

“Carrie?” Hank whispered to her, again taking her by the hand. “Carrie, it will be all right, do you hear me? I’ve got the doctors doing everything that they can. So stay strong, honey, we’ll get through this. And then… then maybe we’ll go to a hockey game? Or anywhere you like. Okay? Please, you’ve got to stay with me.”

Hank squeezed his eyes shut to try and hold back the tears. ‘I can’t lose her now, not like this,’ he pleaded silently. ‘Please, someone… find a way to help my daughter…’

The teenagers in Frank’s basement couldn’t hear Mr. Waterson’s plea. But they were working on a plan.


“Right then,” Frank said, placing his palms upon the lab table. He looked out at the faces of Luci, Tim, Chartreuse and Clarke. “Let’s get this meeting underway.”

He turned to Chartreuse. “Do you have any further news concerning Carrie’s condition?”

Chartreuse shook her head. “I did another vision quest last night but got, you know, the same results,” she reported. “Namely that Carrie won’t get any worse until after this weekend. It could be as early as Monday that she, well…” The pink haired girl bit her lip.

“So, if this doesn’t come together, I’m revealing the truth about Julie being her shooter tomorrow. Sunday night,” Frank decided. He glanced at Clarke. “You realize we’ll have no choice.”

Clarke nodded. “I… I understand,” he said. “It is nice that you’re still giving Julie every chance.”

Frank rubbed the back of his neck. “Honestly? I nearly told the police the morning after Shady called. Luci talked me into waiting through the weekend, as I’d originally intended.”

“I simply don’t trust this Shady guy who called Frank,” Luci piped up. “He seems to have his own agenda, and doesn’t care about the rest of us at all. Besides, we have our own future divining rod.” She smiled over at Chartreuse.

“W-what is it that you’re proposing then?” Tim wondered.

“We’re coming to that,” Frank replied. “First of all, Clarke, were you able to verify at least part of Shady’s story?”

Clarke nodded. “Yeah. It wasn’t hard to track down the article, once I knew what to look for.” He produced a sheet of paper. “I made this copy for the rest of you.” The others crowded around to have a look.

“Mysterious girl hit by ambulance?” Chartreuse read in horror. “That’s, like, terrible! Though… you’d think she’d have been close enough to receive medical help?”

“I guess Julie’s wounds were too severe,” Clarke said, swallowing. “Besides, no identity, no insurance, and not the biggest hospital in her hometown.”

Frank eyed the article. “The state of Illinois? Hold on, Julie’s American?”

Clarke nodded. “That’s where she was born, anyway. When Jeeves told me, I was as surprised as the rest of you. Not sure how long she stayed there, as her parents moved around quite a bit.”

“I-Is there any chance that this article isn’t about Julie?” Tim asked. “Maybe this ’Shady’ lied.”

“There’s always a chance,” Clarke admitted. “It doesn’t give her name. But… it seems unlikely.”

“Long curly brown hair, wearing a dark green sweater… sounds like Julie on the day she left our time,” Luci agreed.

The five of them stood staring at the article for a moment. “Okay then,” Frank said at last, pushing the paper aside. “Here’s the plan. A bunch of us travel back in time, save Julie, and return to the present with her. If Carrie’s condition is a result of some ability to sense Julie’s untimely death in the past or present or whatever – problem solved.”

“Uh, wait,” Chartreuse objected, raising her hand. “Julie, you know, took the time machine. So how can we travel back?”

“Consider Clarke’s logic about our present being her future,” Frank countered. “And recognize that Julie can’t still be using the time machine if she’s no longer alive.” Chartreuse still stared at him in confusion. “Basically think of it this way,” he decided. “Have you ever seen Back to the Future, part three? If so, picture us as being in 1955, having to go back to 1885 to prevent the Doc’s death.”

“Oooooooh,” Chartreuse said, comprehension dawning. “You mean we just have to figure out where Julie left the time machine in the past. Knowing that, we can track it down in the present.”

“Exactly,” Luci confirmed. “That time machine must now exist somewhere in our world. The idea occurred to me and Frank, after we realized how Shady seemed to think it was possible – if inadvisable – for us to go back and mess with the day Carrie got shot.”

“B-But Julie didn’t leave us a note telling us where to look,” Tim objected.

“True,” Frank admitted. “Which is why we requested that you do that additional research yesterday, Tim…”

Tim face-palmed. “OH. Of course.” His gaze fell to the floor. “I… I wasn’t able to turn up anything though. No w-weird occurrences in early November of that year, no indications of unknown scientific devices in public records, no discussions out on the Internet about the device… I’m s-sorry, I don’t think I even have the beginnings of a lead to follow up on.”

Frank exchanged a glance with Luci. “I suppose it was too much to hope that it would be that easy.”

“I’ll keep searching though, if it w-will help save lives,” Tim assured. “All w-weekend if need be.”

“I’m sure you’ve been doing your best,” Clarke said, resting a hand on Tim’s shoulder. “And having exhausted the Julie angle, I can help you now. If you like.” Tim nodded eagerly back at his friend.


Luci walked around the lab bench to stand by Frank. “Setting that aside for the moment then,” she remarked, “we have one additional problem. Temporal-spatial relocation. Which is particularly bad if we want to end up in Illinois.”

Frank winced. “Oh, DARN. I knew this plan was coming together too well… how are we supposed to end up in the United States?”

Chartreuse waved her hand frantically in the air again. “Wait, what’s that about temporary specials?”

“Time-space relocation,” Luci reiterated. “See, whenever we use the time machine, we don’t stay in the same place. Sometimes we travel a few blocks away, sometimes we wind up at the school – Frank and Carrie have even been on trips taking them out of town.”

“So, if you’re not careful, you could end up in the m-middle of the P-Pacific Ocean?” Tim said, eyes widening.

“Quite true,” Luci confirmed. “However, Frank has a working theory relating to the machine’s destination. We’ve checked it out in retrospect, and it’s held up for every single trip.”

“I should have realized it after Luci was abducted,” Frank admitted. “Once we discovered that the readings Linquist had on her were somehow related to the electronics in the time machine’s activation handle. But it took Shady’s mention of Algonquin Park for things to really click. Now, granted, we don’t have the machine to test this theory out…”

“Still, the answer is so obvious, I’m sure it’s correct,” Luci interjected. “I mean, I feel pretty stupid for having missed it in the first place.”

“Care to, you know, clue us in then?” Chartreuse pressed.

Frank nodded. “Okay. Consider, the time machine needs to pinpoint its destination location in four dimensions, three in space and one in time.” He went over to the nearby chalkboard. “That last is taken care of with the year of the coin used to power the device. The other three… those are actually the trickier ones.”

“The earth spins,” Luci elaborated. “And moves around the sun. The point we’re at right now, spatially, is different from the one we were at even five seconds ago.”

“Right,” Frank confirmed. He drew a line across the chalkboard, giving it a very sharp crest on the left and a long runoff to the right. “Now, this represents the ravine running through our town. Here’s Carrie’s house.” He marked an ‘x’ on the left of the board, near the top of the sharp crest.

“A lot of her trips remained near her house, or took her into Willowdale Park, on the other side of the ravine.” Frank shaded in the small area just under the crest and marked in ‘park’. “When I traveled with her, there were a number of times that we also ended up in the park. The explanation for that lies in the position of my house, about two blocks away from the ravine, but on the opposite side.” He marked in a second ‘x’.


“Okay, so… the park’s kinda halfway between your houses,” Chartreuse observed.

“Then it’s locating based on where you live?” Clarke mused.

Luci shook her head. “Not where we live. Where we ARE. Tim, Chartreuse, you remember the trip that me, Frank and Carrie took to the future? We ended up on the street outside, near our meeting place. The time before that, when the three of us traveled to the school dance, we ended up less than a block away from the school building.”

“And then there was my second trip with Carrie,” Frank added, tossing aside his chalk. “On a day when past me was visiting relatives in Sudbury. I asked Carrie’s father, and he says it’s possible he and Carrie had spent that day in Ottawa.” He raised his two index fingers, and slowly brought them together. “With Sudbury and Ottawa, the midpoint is…”

“Algonquin Park,” Clarke finished.

Frank nodded, pointing at the blonde boy. “Bingo. Everything fits. Even a trip we took to an airport. It also explains why recent trips are occurring in town. No one’s left here in the last couple of months.”

“B-But how is this possible?” Tim protested. “Like, what if you travel to a time where you aren’t, um, there? Can you only travel back and forth within your own lifetime?”

“Valid question,” Frank yielded. “Given one could time travel forward with no plan to return. Except, I did travel with Carrie back to the 1950s. We stayed in town. Meaning either there’s some sort of geographic failsafe, or, I don’t know, it’s doing geometry based on similar DNA. Found in our ancestors or other relatives.” He shrugged. “We’d have to test that empirically.”

“More to the point, what if you take the same trip twice?” Luci put in. “The machine seems to account for the structures around us, but what about the danger of overlapping its own arrival?” She smiled. “THAT is where the random variance comes in. By randomizing the time by a few minutes, along with the space within a certain radius, you shouldn’t have to worry about rematerializing on top of yourself.”

“Wait, Julie’s death,” Tim realized with a start. “That fits your pattern. She died back in the town where her parents were.”

Chartreuse let out a low whistle. “This is SO COOL,” she said. “The inventor must have, you know, put a lot of thought into this thing.”

Frank came back to the table. “As you say. It also means that we’d better not play with the electronics in the handle, as I have no idea how the heck this device is scanning all of space for its users, then accounting for the curvature of the Earth and whatnot.”

“Right,” Clarke mused, nodding slowly. “It would suck if your past selves were on opposite sides of the planet, leading to the machine placing you under the Earth’s crust or something.”

Frank nodded. “Unfortunately,” he added, “this makes our trip to retrieve Julie that much more difficult. I mean, short of recruiting her parents…”

“Bad idea,” Clarke asserted, with some bitterness. “Hell, they didn’t even stick around town past Day 3 of the search for their missing daughter.”

“Okay.” Frank looked to Luci, then back at Clarke. “Then we’re either going to have travel down to Illinois the long way – which is problematic in our present and a pain in the past – or we get fancy with geometry.”

“And for that,” Luci summarized, “we’re going to need all of your birth places.” She sighed. “Of course, since I’m younger than Julie, and I don’t even know who my parents were, I can’t join the rescue mission. It adds too much additional randomness to the calculations.”

“You can co-ordinate our efforts here, Luci,” Frank noted, reaching out to touch her shoulder before looking at the others. “Now, I had a map of Canada, but if Julie was born in the States, that’s not going to be big enough. I’ll run and get an atlas.”

He hurried off upstairs.


“Tim, what’s up?” Clarke inquired, after scanning everyone’s expressions. “You’re looking unusually pensive.”

Tim flushed slightly. “Oh, w-well… I g-guess I’ve gone back to wondering where the time machine might be.” He paused. “I mean, since it’s so important that we find it, can’t you do it, ah, temporally? L-Like, declare that whoever goes back to save Julie, they’ll place the device somewhere that it can be easily found now or something?”

“Set ourselves up you mean?” Luci piped up. She shook her head. “We haven’t been able to do that yet. Frank’s tried, and to a lesser extent, so have I. And while Carrie is a different story – she’s somehow adept at paradox without even trying – at present, she’s obviously unable to help.”

“Hey, you think maybe Carrie’s connection to paradox is, like, part of the reason she’s having trouble now?” Chartreuse proposed.

“It wouldn’t surprise me,” Luci agreed.

“Okay, I’ve got an atlas,” Frank called out as he hurried back downstairs. “The map of North America is a bit crude but will hopefully serve for our purposes.”

He laid it out on the table. “Now, I was born in Ottawa, Ontario,” he began, drawing a circle around the nation’s capital. “And with Luci staying here, I’d better go as a specialist on the time machine. Clarke, it’s probably best if you come too, since Julie’s unlikely to respond well to anyone else. Where were you born?”


Frank let out a breath. “British Columbia. Of course.” He circled the west coast city, pulled out a ruler, and connected the two points. “Which means that according to the midpoint theory, we end up somewhere southwest of Winnipeg, Manitoba.”

“I was, like, born here in town,” Chartreuse added.

“Okay, so if we do a triangulation and take the midpoint of that… hm, practical use for this math stuff.” Frank located the centroid. “Okay, I think it pulls us closer to Thunder Bay,” Frank concluded. “Tim…?”


Frank drew a few more pencil lines on the map. “Er, second triangle then… uh, with me, Clarke and Tim, the arrival point borders Lake Superior? Then if we add Chartreuse back… hm, quadrilateral. How does this work… we should automate these calculations…” More lines were drawn. “Okay, er, I think we’d be IN Lake Superior.” He frowned, staring down at the map for a few seconds. “This isn’t going to work at all, is it.”

“There’s also the fact that, since the Earth’s surface is curved, the shortest distance between two points isn’t such straight lines,” Luci realized. “Or maybe we’re supposed to use the circumcenter, not the centroid?”

“Is there NO way to work around that part of this locating procedure?” Clarke asked.

Frank shook his head. “Figuring that out would take time and effort, both things we don’t have, given how we still have to track the machine down in our present in the first place!”

“If I might, you know, offer a suggestion?” Chartreuse piped up.

Frank gestured back in her direction. “Go ahead.”

“It seems that what we really need for the time trip is a point somewhere south of Julie. To pull us into the States. So, like, how about Miami? It looks like you might get good results if you, you know, calculate a position including that city.”

“But we don’t know anyone from Miami,” Frank protested.

“We might. Calculate it,” Chartreuse insisted.

Shrugging, Frank drew in more pencil marks and triangle medians. “All right, well, if we calculate right back to me, Clarke and ‘Miami’…” He blinked. “Illinois. West of Chicago. A little too far west, but it’s the closest yet.” He frowned. “Still, as I said, we’d need someone in Miami.”

Chartreuse pursed her lips. “Well, actually… Laurie Veniti was born there.”

“Oh boy.” Frank flipped the pencil forward onto the table and pressed his hand to his forehead.

“See, the Venitis had an uncle living here in town who, like, died when the twins were five,” Chartreuse continued earnestly. “He left his house to their family, so they all, you know, decided to move into the area at that time. But originally, they were born in America too.”

“Y-You think Laurie will be okay with this insanity?” Tim asked.

“Or CORRY?” Luci added.

“Yeah, why would Corry allow anything that might help Julie out?” Clarke agreed.

“Stop going on about Corry – Laurie will help if I tell her it’s going to help Carrie,” Chartreuse countered. “And if I go along as well, I can make sure my friend isn’t any trouble.”


“Except – you can’t go with her,” Luci interjected. She had retrieved Frank’s pencil and drawn in a couple new lines herself. “If you do, everyone ends up in the middle of Lake Michigan.”

“Those Great Lakes keep getting in our way,” Tim observed.

“Okay, so… what if Tim, like, joins all of us too?”

“Stop, this is out of control,” Frank protested. “First things first, do we really want Laurie, and potentially Corry, to find out about the machine?”

“Well, the situation HAS changed,” Luci yielded. “Not only are we pressed for time, we’re under surveillance by some guy from the future. Extra help from a truly unexpected place could come in handy. Assuming we can trust the Venitis to keep quiet.”

“I guess,” Frank said dubiously. “But you know how Laurie tends to babble. This isn’t something we want the whole school to find out about.”

“Hey! Laurie can, you know, keep secrets,” Chartreuse protested. “And she’ll see the importance in not telling anybody.”

“But don’t you think her brother would take advantage of the situation?” Clarke insisted.

“S-Seems to me that Corry is the bigger question here,” Tim agreed. “I mean, even if we only tell Laurie, won’t he figure it out eventually?”

Frank drummed his fingers on the table. “Probably.” He frowned. “Okay Chartreuse, you probably know Corry best. If he were to find out about the time machine, what would he do?”

Chartreuse pondered. “Well, he does know how to listen to reason. Though it might be touch and go, given Laurie’s potential involvement. Still, yeah, if we can’t keep him out of this indefinitely, I guess it’d be better to, like, be up front with him about it.”

“We certainly want to avoid him discovering things in a manner similar to Julie,” Luci concurred.

“So should we put off deciding anything until we find the time machine?” Tim offered. “I mean, if we can’t find it, this is all moot.”

Frank shook his head. “Annoyingly, time is against us. Remember, come tomorrow night, I talk to the police and the situation changes again. So once the time machine turns up, we’ll want to take the trip, not waste hours on explanations.”

“Okay, I propose the following plan,” Luci declared. “Chartreuse, you tell Laurie – discretely – about the trip to rescue Julie. If she’s agreeable, we ALL go to present a united front to Corry. That way we’ll know straight out if he’s going to cause us trouble. In the meantime, the rest of us can try to figure out what happened to the time machine between Julie’s arrival in the past, and our present.”

Glances were exchanged. “It sounds like our best shot,” Frank agreed.

“Then let’s do this, for Julie!” Clarke chimed in.

“A-And Carrie too,” Tim added.

“I’ll totally make that unanimous,” Chartreuse concluded, beaming. She thrust her palm out into the middle of the group. “So let’s, you know, make it official!”

Luci and Tim instinctively reached out to place their palms on top of Chartreuse’s. Frank and Clarke blinked in surprise, but then added their own hands to the group. “To the future!” Chartreuse declared.

“You mean the past,” Luci observed, amused.

“Like, whatever,” Chartreuse countered with a wink. She left for the Veniti house minutes later.

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    1. Well done! As a rule I’m pretty meticulous about typos, but I missed that, thanks. Chartreuse is indeed more divining rod than diving rod. Though now I’m picturing her in a swimsuit. Also, thanks again – this is, like, the only post that might appeal to math teachers out there. ^_^


      1. I agree that you don’t have many typos, but, sorry to say, there is one error you often make – you frequently use “it’s” when you should use “its”.


      2. Aha, yes, you’ve hit on my one weakness. Possessives. It makes sense to me that “apostrophe-s” denotes ownership, because that’s what it does with every noun (“Carrie’s hair”), and even when used as “one’s” (“one’s particular weakness”). But not its. So I feel like that’s less a typo, and more, as you say, an error… because it’s not accidental. It’s a total blind spot.

        If it’s that frequent though, I should take better care. In particular, I’ve been meaning to tidy up the earlier parts again for another online site, so I’ll keep an eye out. Thanks.


  1. Carrie being teleported to the airport in the past makes sense as explained, but I wonder why the location of 3 year old Frank didn’t send them elsewhere.


    1. You are observant, Mez! The short answer is the author is handwaving the details a bit. Possibly even lampshading it, given how Frank says “Everything fits. Even a trip we took to an airport.” without actually explaining that one. We do know Carrie’s location was away from the airport when the both of them arrived, as she was at the dinner with her parents. So one could assume that Young Frank was somehow an equal distance away on the other side. (Why did Mr. Waterson drive past the airport to get to the dinner place? Dunno – recommendation? Discount? Was Frank’s family returning from a trip, maybe?)

      Since it’s come up, the more extended answer boils down to… I wasn’t sure which airport to use. Knowing what we know about their town (it’s in Southern/Eastern Ontario, on a railway line) and the airport (it’s likely International, having a flight to Miami) there’s a limited number of possible locations. The “Ottawa Macdonald-Cartier Airport” (YOW), the “Smiths Falls-Montague Airport” (YSH), or maybe the “Kingston Norman Rogers Airport” (YGK). Since I didn’t want to pin myself down narratively, I went generic. And in the end, the specific location never really mattered – aside from, I suppose, this scene.

      So I specified how “Algonquin Park” was possible, and then hoped that readers would mentally accept something similar for the other trip without my giving details. It occurred to me that I could fit things in to the YOW airport, but I also felt like added explanation might have slowed down the scene, not to mention presenting me with the additional trouble of needing to figure out the restaurant for Carrie. Does it work as presented? Well, I suppose only the readers can tell me. Which you have!

      I’m kinda glad it feels more like a wondering, and less a nitpick. 🙂 Thanks for your attention to detail! (No, really, it lets me babble like this about my research that never made it into the story.) Let me know if you see a better way, or a way to bridge any gap that still exists.


      1. I don’t think it’s a problem if you don’t explain it or it doesn’t fit perfectly. You can always say it comes down to peculiarities connected with Carrie’s presence (I’m being vague so as not to give spoilers for upcoming chapters).


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