The Knot

George and I were afraid we might be late for our meeting with the wizard, and not wishing to keep them waiting for us, we rushed there. Just before we arrived, I checked my phone and saw that we were two minutes early. I apprehensively prepared myself to knock on the door, but it swung open before I did so, revealing an impressively cluttered office. There was no one inside. George and I looked at each other.

“Do you suppose we should go in?” George asked.

“I don't think the door would have opened if we weren't supposed to,” I said. After some hesitation, I stepped inside, and George followed. The door closed behind us, causing us both to reflexively turn back towards the door. I tried the door handle, and found that the door offered no resistance to being opened again. Reassured that we weren't trapped, I closed the door again, to return it to the condition that I presumed the wizard preferred it in.

I noticed a loop of thin red rope hanging over the doorknob. There were no ends tied together in a knot. I picked it up to look for where the ends had been fused together, but could not find any joint; the rope appeared to have been constructed in a perfectly homogeneous circle.

I placed the loop of rope back around the doorknob, and turned my attention to the other objects filling the room. There was a perfectly spherical orb sitting on the wizard's desk. The orb had a cloudy appearance, and the clouds drifted aimlessly on the surface of the orb, despite the orb otherwise appearing to be solid. There was a shelf on a wall, holding an old oscilloscope, a set of the five platonic solids, each made out of smooth black material, and a beaker that held a liquid which was dancing around violently, but never spilling out of the beaker despite appearing to come close very frequently. There was a fireplace in the corner with a fire, but the only material in the fireplace was a bird sitting in the middle of the fire, but the bird wasn't burning, and it looked like it was sleeping. The bird raised its head to look at us quizzically, and then went back to sleep. I heard a faint popping sound, which I soon figured out had come from the liquid in the beaker. There was a bookshelf, completely packed with books, covering an entire wall, and there were also a few open books and many loose sheets of paper covering the wizard's desk, as well as a few sheets of paper that had fallen to the floor. Very few of the papers I saw were in English, and most weren't in any script I recognized. Some didn't appear to have any writing at all on them, consisting only of cryptic diagrams.

I noticed a strand of rope sticking out from under some papers on the wizard's desk. It appeared to be made out of very similar material to the loop of rope on the doorknob, except that it was green instead of red. I carefully moved the papers that were on top of it out of the way so I could see the rest of the rope. Like the rope hanging on the doorknob, it formed a closed loop. There were three points where the rope crossed over another part of the rope. The crossings alternated, in the sense that if you started at any crossing, and followed the strand on top around the loop, it would lead to the bottom strand of the next crossing it encounters, and then the top strand of the third crossing, and then the strand going under the point where you started, and so on. Only part of the rope was the green I had initially seen, another stretch of rope was red, matching the loop of rope on the doorknob, and part of it was blue. The rope was arranged so that the three points where the colors changed were hidden under the crossings.
I moved the portion of red rope that crossed over the boundary between green and blue, so that I'd be able to see the point where the color of the rope changed from green to blue. To my surprise, the piece of rope that I had just uncovered was solid blue all the way up to the new point that the red strand crossed over it. George asked me how it had done that, but I didn't know, and I ignored the question. I wiggled the red strand some more, but the portion of the rope it was moving over kept changing between blue and green so that the color switch always occurred exactly under the red strand. I tried holding the red strand in place and pulling the green strand under it, but again blue rope turned green just as it emerged out from under the crossing. I lifted the red strand into the air, and moved my head around to look under it from both directions. The color of the lower strand shifted in unison with my head, so that I never caught a glimpse of the boundary between the colors. I wiggled the strands going over the other two crossings to see if they would exhibit the same phenomenon, and they did. I paused for a moment to stare at the rope in confusion, and then picked up a piece of green rope and moved it over the blue portion of the rope, forming two additional crossings. Blue rope turned red as the green strand passed over it, forming an additional stretch of red rope in the middle of the blue part of the rope, again with the color change happening precisely under the crossings. Next I tried moving the green strand over the point where the blue strand crossed over the boundary between red and green. As I had anticipated, the stretch of rope going over the crossing turned from blue to red as the green strand passed over it, and an additional short stretch of blue rope had formed out of the red rope coming out from under the crossing, with all color boundaries being hidden behind other stretches of rope. I returned the loop of rope to its original configuration, and then tried twisting part of the blue portion of the rope, so that it crossed over itself. This did not cause any color changes, and I undid the twist.

“Hey George, I want to try something. Can you go around to the other side of the desk for a minute?” I said.

“Are you sure the wizard will be okay with us messing with his stuff like this?” George asked.

“I'm sure it'll be fine. Come on,” I said, pushing George in the intended direction. I actually had no idea whether or not the wizard would mind, but my curiosity had won out over my fear of offending the wizard. George walked around to the other side of the desk as I had requested.

“Okay, now look closely at this crossing,” I instructed, pointing to where the green stretch of rope passed over the boundary between the red and blue strands, which we were looking at from opposite sides. I crouched so that I was looking at the knot from a shallower angle, and George followed my example. I lifted the green strand going over the crossing up in the air. I was looking at the crossing from the side that the red strand was coming out from, and the blue stretch of rope coming out the other side appeared to turn red as the green rope passed in front of it in my field of vision.

“What's it look like?” I asked.

“The rope under the green strand is now blue up until the point where it crosses behind the strand,” he said. I put my finger on the red rope directly under the green part I had lifted.

“So this looks blue?” I asked.

“Yeah,” he said.

“So you can see my finger touching a blue stretch of rope?” I asked.

“Yeah, that's what I said,” George confirmed. I stood up and bent over to look at the rope from above, and pressed the green strand I was holding into my face running vertically between my eyes, so that I could see the piece of rope crossing under it from opposite sides of the green strand with each eye. It was a purple blur that could have been the result of red light reflecting off the rope into my right eye and blue light reflecting off the rope into my left eye. I unfocused my eyes so that the stretch of rope I was looking at would appear in different places in my field of vision in each eye, and indeed, it appeared as separate red and blue strands.

Suddenly remembering the loop of rope on the doorknob, I dropped the rope I was holding and went to go get it. George walked back around the desk to the side facing the door. I returned with the red loop of rope and held it over the rope on the table. The green and blue portions of the rope that I could see through the red loop had switched colors, while the red portion of the rope on the table was not changed in appearance by viewing it through the red loop. I lifted part of the rope on the table, and slid the loop of red rope under it. The loop was no longer red all the way around, with color changes whenever it passed under a strand of rope of a different color. I grabbed the formerly red loop of rope by a blue stretch in the center of the loop of rope on the table, and pulled it out. I was holding a solid blue loop of rope. I put the blue loop of rope aside, took out my phone from my pocket, and opened the camera. I lifted the green strand and put my phone under it to take a picture of the spot where the rope crossing under it switched from red to blue. The camera image on the screen showed the strand changing from red to blue right under the spot where the green strand crossed over the phone, so that the boundary between red and blue wasn't visible on the screen. I took a picture, and then moved the rope out of the way so that I could see the spot where the color changed. But the picture I saw on the phone screen was of a completely red strand of rope. I moved the phone back under the green strand, and saw that the still image of a strand of rope in my camera was changing from red to blue as I moved the green strand over it. I pulled the phone back out the other side of the green strand, and it bore an image of a completely blue strand of rope. I closed the picture so I could take another one. The image of the knot in the phone screen looked the same as the actual knot, except that the colors red and blue were switched. I put down the phone, and pulled a pen and small notebook out of my pocket. I tore off a page of the notebook, and wrote on it the current color of the loop of rope I had taken from the doorknob (blue). I folded up the piece of paper, slipped it under the multicolored loop of rope with the crossings, and pulled it out through the center. I unfolded it, and found the word “green” written on it, in my handwriting, instead of the “blue” that I had written. I picked up my phone and called a friend.

She picked up, and before she said anything, I said, “Hi Kelly. Pick a color. Red, green, or blue?”

“Blue. Why do you ask?” she said.

“I'll explain later. Thanks. Bye,” I said, and hung up. I wrote “blue” under the word “green” on the piece of paper, folded it back up, and slipped it under the knot and pulled it out through the center, as I had done before. I unfolded it, and saw that the word “green” that had been near the top of the paper had turned into “red”, while the word “blue” that I had written when Kelly picked it had remained unchanged. I also noticed that the pen I was using had blue ink, and the color of the ink on the page had never changed. There were a couple more things I wanted to try. I thought through what I was going to do, and then called Kelly back.

“Can you pick a color again? Same options,” I asked.

“Red,” said Kelly.

“Thanks,” I said, and hung up. I lifted part of the knot into the air and stuck my right hand under it, so that my hand was sticking out through the center part of the knot. The plan was to hand the phone from my left hand to my right hand, and then pull it with my right hand back from under the knot, except that if Kelly had named the current color of the loop of rope that had been on the doorknob, I would only go through the motions of this without actually holding the phone. The loop of rope from the doorknob was blue, and Kelly had said red, so I kept the phone in my left hand as I moved my left hand towards my right, and I attempted to grasp the phone with my right hand. But while I saw my right hand grab the phone, I felt my fingers pass through thin air where I saw the phone. I withdrew my right hand out from under the knot, and while the phone was definitely pulled out of my left hand, and I saw my right hand holding the phone as it receded, I felt my right hand in a fist closed around nothing. As my hand passed out from under the knot, the fist became visible and the phone seemed to disappear. George gasped, as this was the first sign visible to him that anything was amiss.

“Where's your phone go?” he asked.

“I don't know. In retrospect, I probably shouldn't have used my phone for that. At least we've still got your phone if we want to try taking more pictures,” I said. I felt rather foolish, as I had actually identified this outcome in advance as consistent with previous observations, but somehow hadn't seriously considered the possibility that it would actually happen.

“You just managed to lose your phone in the magic rope. I'm not letting you touch mine,” said George. He had a point. I thought about how I might get the phone back, but couldn't think of anything, and besides, there was another experiment I'd been going to try. I reached for the red strand of rope (chosen because it was the color that Kelly had picked), but before I touched it, it started receding under the green strand, as if the blue strand on the other side was being pulled, but the blue strand itself was motionless, and rather than turning blue as it came out from under the green strand, the red rope would simply vanish as it passed under the green strand, leaving a significantly shortened stretch of red rope by the time this stopped. The point where the red strand disappeared under the green was no longer aligned with the point that the blue strand came out from under the green on the other side. I grabbed the red rope near where it crossed under the blue strand and pulled. More red rope came out of nowhere so that the red strand still continued all the way up to where it disappeared under the blue strand, even as I pulled it away, just as if the green strand on the other side were passing under the blue strand and turning red, but the green strand itself did not move. The point where the red strand passed under the blue strand and vanished also became misaligned with the point where the green strand emerged out the other side. When I stopped pulling on the red strand, there was about the same amount of red rope visible as there had been before some of it had vanished under the green strand.

“Hello, folks. Sorry I'm late,” came a voice from behind us in a heavy accent that I didn't recognize. George and I turned around and saw someone of unidentifiable gender in robes and a pointy hat, carrying a wooden staff with a hexagonal piece of metal attached to the side and a shiny truncated octahedron fastened to the top, and wearing a ring on each of their ten fingers, each in a different style. The door was closed behind the wizard. I hadn't heard it open or close. The wizard's eye caught the knot of rope on their desk.

“Oy, the bloody thing's out of sync again,” they said, and walked over to the desk, put the staff down leaning against the desk, pulled a wand out of their robes, and jabbed their wand at the knot. They put their wand back in their robes, picked up the knot of rope, and threw it up in the air. When it landed back on the desk, the strands were perfectly aligned with each other again.

“There we go,” said the wizard. They picked up their staff and gestured with it towards a wall, out of which lept two folding chairs, which positioned themselves in front of the wizard's desk and unfolded into chairs that did not look the least bit like folding chairs.

“Have a seat,” said the wizard, indicating the chairs. I put my phone back in my pocket, and sat down.

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