“Horses? What’s this madness?”
Scratch all of that, Adam thought – they’re not domesticated by the Indigenous. They are the Indigenous! But how could equines like them build a settlement without hands? No, they must have other forms of manipulation. That’s something I’ll have to find out as well.
Adam put his hand down. The Indigenous didn’t say anything else. With their limbs ending in hooves, I better use only things they can replicate. But what? And would they understand?
It spoke again: [ɹ̩s ɑzɑɹɑɡɑˈβǔ] – with a tilt of its head, which could suggest confusion or concern. A question? The tone at the end certainly suggested that. But again, their language had no connection to human languages. None whatsoëver. Literally anything could go at this point. Right now, I need something universal, something both of us could understand. But what, exactly? What sort of number could I whip up to –
Adam’s eyes went wide. Wait. Numbers! The Indigenous should have developed some form of advanced mathematics if they’re able to build a complex civilization. I’ll start with the basics and go from there. I could even figure out which base they use!
But what to use? Adam stepped away from the window, slowly, so as not to startle the purple Indigenous, and went to the cargo hold. None of the crates’ manifests said anything about stationery, that much he found. Let me make a call. . . . He grabbed the radio on the desk. “Zulu-Alfa, this is Tango-1,” he opened. “Did Dr. Konsantinov pack anything I could use to write? Just a pen and paper would do. Over.”
Louis responded, “I’m going to assume you have contacted the Indigenous and are about to begin work, is that correct? Over.”
“Affirmative.” I don’t think I should tell them about their equine nature just yet. They’d think I’m making some kind of elaborate joke.
“Hold on, let me check.” Silence then fell over the line. For fifteen seconds, Adam had to wait by the radio for Louis’s voice to return, all the while with the Indigenous staring at him through the glass. Is it angry? Impatient? Then another voice came on, this time with a Russian accent. “There is notebook and pens inside the desk, and also this thing called ‘white board’ and ‘dry erase,’ or so the Americans call it. Out.”
. . . oh. Adam looked along the cubbies, and found a set of pens with two notebooks, and a bit over, a small box of dry-erase pens near a board the size of his chest. Well, I’m blind. Thanks, Anton. He set the radio aside and grabbed what he needed, then slowly re-approached the Indigenous. I’m going to look silly, aren’t I?
He held up the whiteboard, white side out, to the Indigenous, letting it get a good look. Then he pulled a black pen out of the box, and held it up as well. Then he popped off the cap and put the tip against the board, to demonstrate to the Indigenous how it worked. He produced a random scribble, one that meant nothing – at least, I hope so. He then rubbed his hand over the scribble, to erase it.
Apparently it got the idea – it turned away from the window and shouted away from the lander. He couldn’t make out what it was saying, but he hoped it wasn’t anything terrible. Last thing I want to be accused of is witchcraft. A moment later, he saw its. . . horn, for lack of a better word, start shimmering in a violet light. Fluorescence? To communicate? Oh dear me. . . .
Then it turned back to the window – and Adam realized he got exactly the wrong idea. It wasn’t communication – it was telekinesis. An identical field appeared around a chalkboard and stick of chalk. It made a scribble on the board as well, then with a cloth in its telekinetic grip, erased it a moment later. Showoff.
Adam ‘replied’ by drawing a circle on his board – as well as he could, though it was still lopsided. The Indigenous did the same, flawlessly. Okay, we’re on the same page. Time to get serious.
After erasing the board again, Adam put down his first mathematical equation. Something very simple, yet demonstrated a lot:
| + | = ||
The Indigenous copied him – but instead of using tallies, it used something more akin to die pips. A single pip, three pips stacked in a pyramid pointing left, another single pip, an inverted solid pyramid, and two pips arranged diagonally – in that order. Interesting. Easy to write with hooves, I suppose.
Adam started jotting down the pips and shapes, taking care not to use a regular equals sign, in case they also had it and it meant something else. Now the reverse. He erased his board and wrote:
|| - | = |
And how do you do it? As if it read its mind, the Indigenous erased the board, and put down two diagonal pips, three pips in a pyramid pointing right this time, a single pip, another solid inverted pyramid, and a single pip. Fair enough. Addition and subtraction are the same signs, arranged opposite to each other. And that inverted pyramid is an equal sign. He wrote down their signs and their definitions in his notebook.
Let’s go a little higher. Multiplication! Adam erased the board again, and scrawled down:
|| × ||| = ||| |||
Internally he debated making a bundle of five tallies, but decided against it, instead spacing out the six tallies into two groups of three. Might give it the wrong idea of a base-5 counting system. Plus, it’d demonstrate multiplication better. Okay, your turn. The Indigenous took its chalk and put down two diagonal pips, three pips arranged in an upright pyramid, three pips arranged diagonally, a solid inverted pyramid, then a single pip followed by. . . a pause sign? Yeah, that’s got to mean something else. Good thing I thought ahead.
Let’s try counting from one to ten. Once he noted their multiplication symbol, Adam erased the board, flipped it vertically, and diligently set to work. The process took longer than he anticipated, but the results were hopefully clear to the Indigenous:
| = 1
|| = 2
||| = 3
|||| = 4|||| = 5|||| | = 6|||| || = 7|||| ||| = 8|||| |||| = 9|||| |||| = 10
Grouping tallies should help it out a bit, Adam thought. Can’t deny it’s decimal, no way. The Indigenous’s eyes went wide – shock? Anger? It quickly set to work writing its equivalent as well. Ten seconds later, he had an answer. It also used tallies, grouped in fives just like his, but chose to let them equal the pips. One tally equaled one pip, two equaled two pips, and so forth. With four, four pips were arranged in a square; five, four in a square plus one in the middle – but six threw him for a loop. It was one pip and the pause sign symbol again. Its counting did not go any higher. So they use positional counting, Adam saw, just like us.
He could not take his eyes off its number six, however – how it stuck out from all the others instead of making a group of six pips. Say, what if. . . ? Adam erased the board again, and wrote down:
| - | = 0
The Indigenous noted this, and copied him: one pip, three pips pointing right, one pip, solid inverted pyramid – that pause sign. Aha! That’s a null symbol! Adam realized, writing it down automatically. So their counting system really is base-6 – but what’s that based on? Decimal I can count with my fingers, but they’ve only got four hooves per. Unless they’re counting on something else as well? All of this he quickly got down on the paper – each pip from one to ten, including the zero.
And furthermore, if they have a concept of zero, and not just as a placeholder either. . . what about negative numbers? Adam tried his tally equivalent:
| - || = -|
That’s a negative number. Can you do that? he thought, but did not ask aloud. The Indigenous, after a moment, put down one pip, three pips pointing right, two pips, solid inverted pyramid, then a pip with a black arrow pointing right. Derived from a simplified minus pip-group. Makes sense. Easy enough to get down in his notebook.
But what about exponents? Adam decided to try that. Carefully, and in larger scrawls to emphasize the exponent, he presented:
||||| = |||| |||
The Indigenous did something completely unexpected to him. After looking at his board carefully for a few moments, it seemed to have an “Aha!” moment, then after some plotting, it came away with a solid upright pyramid with numbers written by each corner. The top one had three pips, the bottom left two pips, and the bottom right one pip followed by two.
This was the most impressive thing he’d seen so far from them, and he’d only been here on the surface for maybe half an hour. A single symbol to unite exponents, roots, and logs? This would revolutionize mathematics back on Earth! Adam thought this as so important, he placed it on its own page, with further explanations on how it apparently worked. Oh, if only you were here to see this, Dr. Marshall!
Then he heard something heavy land on top of the lander again. He looked up, by reflex, but of course couldn’t see through solid steel and titanium. At least it’s not dented, not as far as I can see. There came a sound of muffled talking – he couldn’t make anything out, except perhaps there were. . . clicks? Are those phonemes? I haven’t heard those from the Indigenous.
The Indigenous shouted over its head, [xõ ɹ̩ʎiluˈɸɑ . ɑzɑɹzũdɑmɑlˈβǔ xeˈɹɤ ɑlˈɹu] – which prompted more of the same muffled talk above. Eventually, the other Indigenous (presumably) leapt off – though Adam didn’t hear it land nearby. Curious. . . . The first Indigenous rolled its eyes, and returned its gaze to the linguist, with a strikingly-humanlike look of sheepishness. Tempting to take it that way, but don’t fall for it.
Now, what did Sagan say about. . . oh right, primes. I should probably get those down. Using tallies again, he jotted down the first five prime numbers in a sequence:
||
||||||||||| |||||| |||| |
I know yours is base-6, but what do you think? This took the Indigenous a bit longer to figure out than the exponent, but when it did, it turned away and wrote down a sequence: two pips, three pips, five pips, one pip followed by another, then one followed by five. Marvelous.
What operations haven’t I covered yet? And then Adam realized he forgot about division and fractions altogether. Better get those squared away, while I still have its attention. He erased his board, and wrote down something simple, something it would already know:
|||| | ÷ || = |||
Now you. The Indigenous wiped its board clean, and after some scrawling, presented a pip followed by the null sign – ten in base-6, right – three pips stacked in an inverted pyramid, two pips, a solid inverted pyramid, and three pips. He put it down in his notebook, noting the relationships between it and multiplication. Just like with addition and subtraction – same sign, mirror-reversed for opposite operations.
But before Adam could demonstrate fractions, the Indigenous wiped its board first, then did some writing. Something new in mathematics? What am I going to learn? Then it turned the board around – it had a rod with a circle on one end, which was pointing at itself, along with a script he had never seen before. I could swear it’s an alphasyllabary, but how does it work? Then the Indigenous used its chalk as a pointer, and sounded out each part of the script, very slowly: [ɑ̃ːː ... tiːːɹ ... l̩ːː ... sɑːː ... pɑːː] Then it pointed the chalk at itself: [ɑ̃ˈtiɹ l̩sɑˈpɑ].
Ah, that must be its name. “Ahn-teer Ullsapah?” he cautiously sounded. The Indigenous smiled and nodded its head – its name, for the time being at least, was Antir. He started jotting down the odd-looking shapes, as closely as he could to what was presented, along with an IPA transcription. I’ll figure out a better way to Romanize that. Eventually. Wait, did I just assume the meaning of its body language? Antir didn’t seem to mind – at least, no sign of aggression could be found. Or maybe it’s more subtle than I thought.
Nevertheless, he copied for once – he wiped the board clean, put an arrow that would point to him, and wrote his name: ADAM SOMERSET. Just like Antir, he used the pen to sound out each letter: “A-dam. . . So-mer-set.” Then, pointing at himself, “Adam Somerset.”
[eˈdem zɤmɹ̩ˈzed] it echoed back. An interesting corruption, he thought. It could just as easily have called me Etem. But maybe there’s something about the walls of the lander that muffles the noise. Eh, whatever. It did get the O in my name rather close, I’ll give it that.
Adam looked over its shoulder, on a whim, and found that, at some point, most of the other Indigenous had left the landing site. Perhaps the novelty wore off so soon? Or did they grow bored of interspecies communications? I wouldn’t blame them for the latter. After all, the day had just begun, and they shouldn’t slack off with. . . whatever it was they did.
What else could I show it? Antir once again took initiative, clearly enjoying itself with newfound knowledge of another world, and after some drawing showed him. . . a series of circles. The leftmost one was enormous, followed by a tiny one, a medium-sized one with a nearby small one, and further away, a large one with a line through it. The second circle in the line had another rod-with-circle symbol, again with the circled end pointed where it wanted to indicate. Wait. . . that’s the local star system, Adam realized. We’re on the second planet, Rhysling, just like that symbol points at, there’s another planet we didn’t know about, and there’s that gas giant Einstein also spotted. No moons around it though. Maybe they haven’t found any? Maybe its orbit is perfectly clean? Or it just wants to keep it simple? It’s also obvious they have a heliocentric view of the universe. Should make it easier to represent our Solar System.
So Adam did just that. Once he copied down its diagram on another page, including the previously-unknown planet, he took longer to draw out the Solar System, since it was a lot busier than theirs, and he wanted to be sure to include every planet. There’s the Sun, Mercury, Venus, Earth – I’ll put an arrow there – and the Moon, what the hell – Mars, Jupiter, Saturn, its rings, Uranus, Neptune, and Pluto. Somehow all the bodies fit on the whiteboard, without him erasing everything. Nice. He turned around to show the Indigenous – whose jaw dropped at the sheer scale of the Solar System, compared to its local star system.
Something called out to Antir. It turned around and shouted something back, but of course he couldn’t catch it. Then it turned back to him, raised a hoof, pointing its frog straight at him. Then its horn lit up. Adam didn’t have time to close the shutter before a loud pop! intervened in a flash of brilliant violet light – then Antir was nowhere to be found.
But never mind that – what the hell kind of phenomenon was that? he thought. Was that radiation? I hope my life isn’t any shorter for it. . . even if I have the feeling that’s the case anyway. I should probably ask. . . .
He capped his pen, got up, shut the shutter – far too late to prevent anything – stepped away from the window, and headed back to the radio. “Zulu-Alfa, come in,” he opened. “Over.”
“This is Zulu-Alfa,” Louis replied. “Any new developments? Over.”
“As a matter of fact, yes,” Adam said. “I have good news and bad news. Good news is I have a decent grasp of their counting and mathematics. Bad news is I may have received a high dosage of an unknown radiation. Did you detect anything of the sort earlier? Over.”
“De quessé!” Louis yelled loud enough to startle Adam. “Are you okay, l’ami? Do you have a headache, any starry vision? How did that even happen, anyway? Did the Indigenous tamper with the power supply module? Over!”
Uh. . . huh. Nothing like that, actually. “I’m fine, if that’s all I have to worry about,” Adam answered. “As for how it happened. . . TPRU-1 still has power, so the power module is intact. I believe the Indigenous possess some unknown ability or technology. It’s hard to describe, but one of them was able to levitate objects with some sort of device on its head. It used the same device to. . . teleport, or something. I honestly don’t know how it works. Over.”
“Well, it’s possible it might not have an effect on the human body. If you were looking right at the device and haven’t gone blind, you should be good.” Louis sounded relieved to be able to say that confidently. “In any case, well done with the mathematical notation, even if it’s not something we’ll be using at all times.” Really? “At your desk is a camera wired to Tango-1’s transmitter – just snap pictures of your notes, and they’ll be transmitted to up here. Our high- and low-gain antennas are standing by, Somerset. Transmission will be slow, but that’s what the data tape recorder is for. Zulu-Alfa out.”
Didn’t get to tell them about their exponent triangle. Adam sighed, then shrugged. Oh well, they’ll see it soon enough anyway. Now where is. . . oh. Right there in the corner it laid, attached to a flexible metal arm on stiff joints. The shutter button was not on the camera itself, but wired to the base of the arm. So it won’t become blurry when I snap it. Perfect.
He flipped to the first page, which had most of everything he’d jotted down from the mathematical exchange. He brought the camera over, carefully positioned it to capture as much of the page as possible in what he hoped was a readable resolution, then pressed the button. Click-click. No flash, no further action, but he knew the exposure was on its way up.
He turned the page to the exponent triangle, feeling giddy at such a perfect unity of three related concepts. After placing the notebook precisely where it was before, he hit the shutter button again. Click-click. Here’s to you, Dr. Marshall.
Last was their view of their star system. Click-click. Here comes the freakout, Adam thought. I’ll just sit by the radio and wait for their inevitable reaction.
And come it did – after a minute of radio silence. Louis sounded much more calm than he expected – did he need that time to compose himself? “Just got everything, Somerset,” he announced. “Mon dieu, it’s sparse at first glance, but it’s definitely not lacking in information. Any purpose behind the first planet in the third image? That object isn’t there. Over.”
“I’m sure if you look again, you’ll find it transiting the star,” Adam shot back. “It orbits much faster than Rhysling, in case you haven’t noticed. There’s no indication of how far away it is from us, so you’ll just have to look for it with your eyes, as dangerous as it sounds.” Aren’t the windows and telescopes polarized for that exact purpose anyway? “Over.”
“Copy, but what’s with the triangle on the second page, though?” Louis asked next. “I was never very good at math, and Anton is just as lost as me, and neither of us are willing to thaw out a mathematician just to answer this. Over.”
How do I explain this? Hmm. . . . “It’s basically a three-in-one tool,” he started. “You input two numbers in each corner, then you have to figure out the third missing one, whether it’s an exponent, a root, or a logarithm.” Dunno how much more clear I can make it. “Over.”
“. . . I see. I’ll keep them here for now and transmit back to Earth at our next opportunity,” Louis said. “Anything else we should know about, Doctor? Over.”
Internally, he debated over whether he should tell them about their equine nature – but ultimately he concluded they wouldn’t believe him, and then he’d be here all day convincing them. “Nothing else, Commander,” Adam closed. “Tango-1 out.” He set down the receiver and looked over his notes again. How fine their civilization must be, he thought, if their mathematics are this well-developed. No, not just well-developed – there’s a sort of elegance that looks like conscious control over their functions, eschewing older symbology in favor of something that’s easy to remember.
And that’s to say nothing of the obvious – that they have writing as well. A way of transmitting information not just across space, but across time as well. Their numerology, while senary in nature, allows division into halves and thirds with ease. Not quarters, but that probably never really bothers them. He shrugged. But what would they do with the symbols they’ve made? Surely none of them are just solutions waiting for problems. A lot of those are really good for architecture and logistics. But that’s something I have to leave the lander for, of course.
Besides. . . . Once again Adam picked up the radio. They’re getting real sick of me talking, aren’t they? “Zulu-Alfa, this is Somerset again,” he opened for what felt like the hundredth time since he landed. “Is it possible for me to leave the lander? Over.”
“Yes you can,” Louis said. “I think it’s time you stepped into your brand-new suit anyway – you’re burning daylight as it is. You’ll find it mounted outside the lander; just step in from the back, sterilize the backpack, and off you go. Couldn’t be simpler.”
Well, I could’ve told you that! “Copy that, Commander. Somerset out.”