From the Logs of Captain Dave:

I had rescued the men from their dangerous video game addictions when Doc’s console froze. He realized we had to return to the ship, so he sedated Decker and me and dragged us back to the ship on a cart. I was very proud to have again proved my excellency to the crew.

The next planet on our survey mission was right next door, and by that I mean it was only 5.7 light years away.

“Decker,” I said commandingly, “plot a course for the next star system on our exploration chart.”

“Um, Dave, I’m the engineer. You actually plot the course.”

“First, it’s Captain Dave, and I’ll ask you not to question my orders in front of the men.”

“Your authority is unquestionable, sir,” said Doc. “Crews of three must be kept under tight discipline.”

“Thank you Doc. Now, I will plot a course to the next system. Decker, what is the next star system called, and what are its coordinates?”

“Are You Kidding? We Ran Out of Names A Long Time Ago.”

“Damn it, Decker. I don’t need your smart remarks. What is the name of the system?”

“No, Captain Dave. Are You Kidding? We Ran Out of Names A Long Time Ago is the name of the system. It has 17 planets. I’m sending you the coordinates now.”

The coordinates failed to come thru on the computer, so Decker wrote them down on a sheet of paper. He spent about ten minutes making the sheet into a paper starship. He launched the paper starship carrying the system coordinates, but one of the wings was uneven, so the paper craft tilted crazily to the left. It tilted to the paper ship’s left, not my left or the ship’s left. The big ship. The Delineator. The one we’re flying in. Not its left. Of course, since I’m the captain and I’m facing forward, my left and the ship’s left are the same. I think there’s a name for the ship’s left, but I can’t remember. I think it’s just called the pilot’s side.

It’s a good thing Decker’s not the engineer. He can’t even make a paper starship fly straight. Wait. Maybe Decker is the engineer. I got out some paper of my own and set out to make a paper starship that was better than his.

Decker’s paper ship continued its meandering flight across the cabin before splashing ignominiously and wetly into Doc’s beer. Doc cursed and pulled the paper from his drink. He wadded it up and threw it back at Decker. Decker yelped as the paper struck him fiercely on the arm.
Finally my paper starship was ready. With a triumphant yell, I rose from my seat and launched my folded flying wonder. It sailed gloriously for almost several feet before a freak wind current sent it tumbling to the ground.

“That was an excellent flight, sir. I despair of ever defeating you,” said Doc, who was furiously at work on his own paper starship.

Decker was also constructing a new model. We spent the next several hours locked in furious competition. Paper starships of different models danced and flew and, in Decker’s case, crashed throughout the cabin.

“Decker,” I said, “lend me some paper. I’m out.”

“I only have two sheets left, Captain.”

“Doc, how about you?”

“I’ve been stealing paper from Decker for the last half hour.”

All of the ship’s printer paper was piled up in the mounds of paper starships strewn throughout the cabin. We had to get it unfolded so we could print out the coordinates for the mission.

“We have to get this paper unfolded so we can print out the coordinates for the mission,” I said.

We each dug in, unfolding our magnificent planes and putting them back in the printer trays at our consoles. There were several mysterious paper jams over the next few weeks. I blamed Decker, because I made sure to really straighten all of my sheets. My printer jammed too, but those were probably the ones Decker put in.

So we were back where we started. I needed the coordinates for the AYKWROONALTA system. Decker printed them out after only two paper jams. He wadded the paper up and threw it at me.

The throw hit me right in the eye. My vision was a little blurry, but I had to show toughness for my crew, so I bit my lip and entered in the coordinates.

The ship displayed a brief countdown, then started going really fast. Maybe it jumped into hyperspace or something. The workings of the drive are really a complete mystery to me. My job as Captain is about leadership and people skills. I leave knowledge to the members of the crew.

“Decker, how does the interstellar drive work?”

“I have absolutely no idea.”

“Right. So no one on board knows how the ship’s engines work?”

“I do,” said Doc.

“You’re a Doctor, Doc. Leave this to the Captain and the Engineer.”

It looked like it was going to take a lot longer than it should to reach our destination. I’m not one to stand idly by, so I went to take a nap.

I was rudely awakened by Decker a few hours later.

“Captain, we’re off course.”

“Impossible,” I said, returning to the bridge in my pajamas. “I entered the coordinates myself.”

“Yes, but the coordinates are not taking us to the AYKWROONALTA system.”

“Those were the coordinates you sent me. Decker, you’ve earned a demerit for sending us off course.”

“Good work Captain. You must enforce discipline and protect the crew,” said Doc supportingly.

“Captain, the coordinates you entered were not the ones I sent you. Look,” said Decker, pointing at an incomprehensible star chart he had somehow called up on my console, “our initial position was here. The AYKWROONALTA system is here, only a few light years away. Our current course is carrying us here, a really long way away.”

“I don’t understand. Why did you send me coordinates that were so far away? And which blinking dot are we again? Are we the red one?”

Decker screamed. He must have stubbed his toe.

“Let me give you an example. Suppose we were here, on your console.”

“Ok.”

“Now, the coordinates should have taken us here, to the other end of your console. Instead, we’re on course to end up way over there, in my chair.”

“A chair, huh? Well that seems like a pretty good spot. You’re saying the system we’re heading for is comfortable?”

Decker looked like he was going to choke. He started to go back to his seat, but he tripped and fell.

I was going to help him up, but that was Doc’s job.

I was glad to see Doc had switched to drinking water. He was drinking it out of an awfully small glass though. Maybe the big glasses were dirty.

After several weeks of travel, we arrived in the new system. Our supplies were dwindling, but I figured there would probably be a resupply station in the system somewhere.

The star had seven orbiting planets. There were a couple of other planets, but they were just kind of floating off to the side, so we ignored them.

“Dave, I’ve never seen planets just floating outside the orbital plane. Shouldn’t we investigate?” asked Decker annoyingly.

“It’s Captain Dave, and if those planets can’t have the basic decency to fall into orbit around a massive body like everyone else, then they are not worthy of our time or our attention.”

Each of the seven planets was orbited by seven moons. This made for a nice even 50 planetary bodies.

“50 planetary bodies. What a nice round number.”

“49,” Doc said.

“Huh?”

“There are 49 planetary bodies. I know you were thinking 7×7 is 50, but it’s not. It’s 49.”

“Are you sure?”

“You give the system too much credit, sir.”

“Yes, that is a fault of mine. Always thinking the best of people. I’m disappointed in this system. They need one more planet.”

We moved closer. Something unusual appeared. At least, Decker said it was unusual. As far as I know it happens all the time.

Each of the 7 moons was orbited by 7 smaller moons.

“343,” said Doc.

“Huh?”

“There are now 343 planetary bodies. Don’t try and hurt yourself.”

“That’s good medical advice. Thank you Doc. You’ve always got your eye out for my well being.”

We moved in closer to the first planet. Sure enough, around each of the 7 smaller moons were 7 really small moons, and then 7 more around that. As far as we could move our sensors in, there were seven moons orbiting around each of the seven moons orbiting around each of the seven moons orbiting around each of the seven planets.

“This is amazing!” exclaimed Decker in amazement. “This is an amazing pattern!”

“Isn’t there a name for this kind of pattern, Captain Dave?” Doc asked.

“Yes. Isn’t this a fractional pattern? No, wait. That’s the thing where you divide up the pies. Fractured pattern? I think that’s it.”

“Fractal pattern. What you’re referring to is a fractal pattern. It’s an element of chaos theory,” said Doc.

“No, I’m pretty sure it’s fractured. Fractal is when you fall and break something. Haven’t you ever heard that? You fall and get a fractal arm?”

Doc seemed about to say something but instead he went for a refill of his water glass. I was glad when he came back with a bigger glass this time.

“We will name this system the Fractured Orb System. That way everyone will know the planetary orbs are in a fractured pattern.”

We pulled up to the third planet in the system, Fractured Orb III. The best lifeforms are usually found on the third or fourth planets of a system. Life can evolve on the outer planets, but the life forms there are usually in a really bad mood because it is so cold and dark all the time so far away from their sun.

Sure enough, the FO III had a flourishing civilization. They had some communications technology, but hadn’t made it into space yet. Since we had made it to space, I was comfortable knowing we were superior to them in every way.

The first thing we do when confronting a new culture is to send them a nice copy of the Standard Alien Approach Document (SAAD). If they don’t immediately understand it, sometimes we shoot at them, but most of the time we must begin to establish a rudimentary level of communication based on mathematics. Once you understand a culture’s mathematics, you can communicate about science, and learn the remainder of the language from there.

I always thought this was a little fishy. Most alien cultures will understand if you just yell loudly enough. Still, I decided to let Decker do it his way this time.

We were all at our computer consoles for several hours. Doc and I were playing Galactic Wedgie of Doom VI against one another, and I assume Decker was working.

Finally Decker let out a yell. I knew he was clumsy, but this was getting ridiculous.

“Dave, we have reached a fundamental communications impasse!”

“It’s Captain Dave.”

“We cannot agree with the alien culture on basic mathematical properties.”

“Give me an example.”

“What’s 6×7?”

I thought for a moment.

“42!” I said triumphantly. I remembered it from a flash card from when I was in college.

“Right. The aliens, however, seem to think 6×7 is 41.”

“But 6×7 is 42. I know because I wrote it on a flashcard. I wouldn’t write it on a flashcard if it wasn’t true.”

“Your epistemic reasoning is unassailable as always, Captain,” said Doc. He had destroyed most of my Galactic Wedgie of Doom pieces. If I didn’t recover quickly, I would be forced to accept another draw.

“Dave, the aliens still think 6×7 is 41! What do I do?”

“Well, the best thing to do when you can’t communicate with an alien civilization is to just go down there and see what happens. If we get into trouble, we’ll just shoot a bunch of them and leave.”

I bravely manned the autopilot as it landed on the planet’s surface. I hoped it was nice outside, because I hadn’t brought a jacket.

The surface of the planet was soft and uncovered by vegetation. It had a pleasant reddish brown color to it. The aliens, who I called the Fractorbians for short, were a similar color themselves. They were also very round. Their torsos were large and spherical, topped by smaller spherical heads and shorter spherical limbs. They waddled up to us as soon as we got out of the space ship.

Decker had apparently established some rudimentary communication, and he and several of the Fractorbians sat down a few paces away and began drawing figures and symbols in the dirt, or whatever the surface was here.

Doc and I set off towards town to get some supplies. We needed fuel for the drive and food supplies for the ARF. I was surprised when they didn’t have a store selling exactly what we needed, but Doc said we could buy raw materials and convert them on the ship.

“Really? We can do that?” I asked.

Doc didn’t say anything. He must not have heard me, so I asked him louder.

“Yes. Captain. We can do that.”

“Oh. Great.”

We passed several stands with enticing wares, but we did not have anything to exchange. Then we saw the logo for Universal Credit and ducked inside.

The bank was located in a hemispherical building. In fact, everything was located in a hemispherical building because all the buildings were hemispherical. Unless, of course, something was outside of a building.

“It’s a good thing we found the bank,” I said. “I figured they would have one.”

“How does a culture that has never made alien contact before have a bank with intergalactic exchange rates?” Doc asked.

“The forces of intergalactic capitalism are very powerful.”

We stepped up to the teller’s desk and smiled. The Fractorbian said something with a lot of clicks and whistles.

“We would like to exchange our credit for your local currency,” I said enterprisingly.

The spherical man behind the desk clicked and whistled again.

“We would like to exchange our credit for your local currency,” I said. I was much louder this time so he would understand.

He just stared at me with his perfectly spherical eyes set in his perfectly spherical head.

Doc stepped in front of me and pulled out the ship’s credit card. The teller took it and disappeared. He returned several minutes later. He and Doc did some rapid scrawling in the soft surface of the counter. The teller left again, then returned carrying several perfectly circular disks of varying size and color.

Doc explained the transaction that had just taken place.

“Sounds like they really boned us on the exchange rate,” I said.

“Yes, they did. I wanted 42 credits but I got 41 instead.”

“That’s terrible.”

“The exchange rates on worlds without previous contact are usually pretty bad.”

“You wouldn’t think the local currency would trade so strongly.”

“Yes, but they’re at considerable economic advantage since they have no need of our currency and we are in desperate need of theirs,” said Doc.

We took our newly acquired disks to one of the merchants lining the streets. We watched as the man in front of us purchased several containers, all either spherical or cylindrical. He pushed all of the objects as closely together as possible. The two haggled for a few moments. Then the customer rearranged his items and they haggled again. Finally the man paid two small yellow disks and one medium blue one and left.

We were thirsty, so we selected three beverages in tall cylinders.

“We should check to see if those are poisonous,” said Doc.

I leaned over. “No, they smell okay.”

I set all three containers in a line on the counter. The vendor wrote a number in the soft surface of the counter. Doc punched the number in on his Personal Computer Widget.

“Captain, I think this man wants 1300 credits for these drinks.”

“How much do we have?”

“41, remember.”

“Right. I’ll negotiate.”

I turned to the vendor.

“That is too much. You can’t charge 1300 credits for three drinks, unless maybe they’re Salvarian Liquid Nitrogen Martinis, but you guys don’t have spaceships, so you haven’t ever had one of those.”

The vendor clicked and whistled at me for several seconds. I took a deep breath and prepared to repeat myself at a higher volume when Doc stepped forward. He rearranged the cylinders in a circle.

The vendor clicked, whistled, and wrote down another number.

Doc did the calculation and shook his head. He rearranged the cylinders again into a smaller circle.

The price went down.

Doc packed the cylinders together as tightly as he could. The vendor quoted a lower price. Doc did some scribbling on the counter. Then the vendor scribbled, then Doc. Finally Doc took out two small yellow disks and paid the man. We took our drinks and left.

“How much was it?” I asked.

“Around 4.71 credits,” he said. “1.5π credits to be exact.”

“What do pies have to do with buying drinks?” I asked sagely, knowing I had Doc trapped.

“π is the ratio of the circumference to the diameter of a circle. I’m sure you were just making a joke, Captain.”

“Of course. But I’m glad you explained it in case the Fractorbians didn’t know.”

Doc waited until I had tried the drink before he took a sip of his. I thought that it was very polite of him to show respect by letting the Captain, me, go first. The drinks were dark blue, somewhat gooey, and very refreshing.

“I have some ideas to talk over with Decker,” Doc said. “Let’s take him his drink.”

“I thought the extra drink was for me, but you have a good point. We could give it to Decker.”

“You’re always thinking of others, sir.”

We arrived to find Decker and several round aliens drawing back and forth furiously in the dirt.

“Decker, I brought you something to drink,” I said. “What have we learned?”

“Well, there are several interesting things going on here. First, we agree on the area and diameter of a circle, and we agree on some simple arithmetic. There is still a disagreement on 6×7 though.”

“Have you tried multiplying any larger numbers?” asked Doc.

“No. Every time we get to 6×7 the dialogue breaks down.”

“I have a theory,” said Doc. “What do you notice about the shapes in this world?”

“They are all circular or spherical.”

“And what do you think of when you think of circles and spheres?”

“Breasts?” asked Decker.

“Naked buttcheeks pressed against the window of a space port. Those are circular. We used to do that back when I was in the Academy,” I told them proudly.

“How about π?” said Doc.

“That’s true!” I said supportively. “Pies are round.”

I leaned over to Decker.

“Maybe Doc isn’t ready for the birds and the bees yet. Don’t harass him about it; everyone develops at their own pace.”

Decker seemed to ignore my comment, but I hoped he would be sensitive to Doc’s preference of pies over breasts and prank exposed buttocks.

“We live in a very discrete angular world, and our math is based on discrete numbers and our geometry upon angles,” continued Doc.

“I see,” said Decker. “So you think that since their world is full of circles, their number system is based on the circle?”

“Not only based on the circle, but I believe their number system uses π as a base!” exclaimed Doc.

This discussion was boring. It was too technical for me. I went back to the ship for a slice of pie. I remembered what Doc said about converting mass to supplies, so I went to the store and bought some rocket fuel and some snack cakes. Whatever we didn’t use of one, we could convert to the other.

Doc and Decker began working through some of the problems using π for the aliens’ base instead of 10 like any normal civilization would do. Sure enough, the discrepancies began to disappear.

“But this still doesn’t explain why they think 6×7 is 41,” said Decker.

“Sure it does,” said Doc, who wasn’t responsible for knowing any mathematics whatsoever. “Have you noticed how offended they get when we try to round a number up?”

“Ah. That’s what they mean when they say ‘A number is not a number until it fully reaches that number! All else is heresy!’ I was wondering about that,” said Decker.

“So if they take 6=1.909π and 7=2.228π, then 6×7=41.978, but rounding up is against their religion, so 6×7 has to be 41!”

Doc and Decker set about establishing a basis for scientific communication with the Fractorbians. It turns out the aliens had their own name for themselves, but I forgot what it was. Decker told me all of this later, but I wasn’t really listening then either.

I was jolted rudely out of my nap by Doc and Decker storming aboard the ship.

“We’ve got to take off! A mob of Fractorbians are after us!” Decker exclaimed with emphasis.

We began powering up the ship for take off.

“What happened?” I asked.

“Doc showed them a square!”

“You should have seen the guy we were talking to. I drew a square, and his eyes rolled back in his head, and he went into convulsions. Apparently they have never contemplated such a thing.”

“Good thing you didn’t show him a trapezoid. He might very well have died!” said Decker as he worked furiously at his console.

“I think the square is in violation of their sacred order of proportion and balance. I should have known that any culture that was that uptight about rounding should never be exposed to the parallelogram family,” said Doc.

“Captain, we can’t take off. They’re hanging onto the hull!” said Decker.

“I’ll take care of it. These spheroids don’t like squares, eh? I’ll give them something to freak out about! Doc, help me grab these boxes!”

We had a variety of cardboard boxes in the hold. Unfortunately, only a few were empty. We grabbed the empty ones and opened the hatch.

The Fractorbians recoiled in horror as we held our cubes aloft. They backed away from the hatch. We threw the boxes into the soft ground, where they landed and stuck at strange, offensive angles. Fractorbians all around the boxes threw up their hands to shield their eyes and ran away in fear and terror.

We had made a dent, but there were still many more spheroids coming. We needed more parallelograms!

“The paper!” I exclaimed.

All of us grabbed printer paper and began folding it into the most angular, irregular shapes possible. We opened the hatch, and all three of us let loose with a barrage of irregularity and angular folding.
The spheroids fell back, overwhelmed. The ship pulled free of their grasp and lifted safely into the welcoming sky.

The area around the great paper dump was declared forbidden and unholy by the Fractorbians. The people of the town were evacuated, and no one returned to the area for many years. It turns out that the compound used to whiten the paper was toxic and leached into the soil after it rained, so it’s probably a good thing they left.

I looked out into space. I was feeling contemplative.

“And what about the geometry of space? Is it angular, like ours, or spherical, like theirs?” I asked.

“I think it’s square,” said Decker.

“Actually, Captain, it’s neither. Space is best represented as a four dimensional continuum of space-time, in which space forms three dimensions and time a fourth . . .” rambled Doc.

“Doc,” I said, interrupting him captainingly, “leave the math to the Engineer and the Captain.”