by Larry Niven
I thought of these things as I sat on the saddle and took the helmet from Silver. “Now let him find out what there is to be known, while I check upstairs for something,” Silver told the crew, and winked at them. I suppose they thought he was going to bug this place as he had the first tower, and maybe he was. He had some parting words for me which came with a certain menace: “And Peter, no declaring what ye’ find until I be back, d’ye hear?” Then he left us.
I could at least do that for him, I supposed. I wasn’t prepared to lie, but I didn’t have to blurt out the truth either.
I chose a bar at random, placed it in the indentations in the table and then put the helmet on. The cables flexed and must have connected, although I couldn’t see them. I could almost feel them sucking information out of the bar.
The usual blue light came on, so everything was working still; I set the age setting to egg to make it as simple as possible, and skipped the standard introduction. I went too far and had to go back, what I saw was just incomprehensible. The word at the top looked like the symbol for what I had decided was mathematics. This was promising, but it surprised me a bit. I had noticed that the emotional stuff had been what we met up with first, and as we had travelled east, it had become more austere and abstract. I had expected to find this was music. Well, it was and it wasn’t. I vaguely thought there would be no sound with mathematics, since it is a written language, not a spoken one, at least in human and kzin. But the beings who had made the technology on this world didn’t seem to think that. It was puzzling. There was something like music; it had to be. At the egg level it was just like drum beats. The pace was much, much slower than I was used to. They say that the basic drum-beat frequency is an approximation to the human heartbeat, which explains why kzin drumming is usually slower, but much more variable than human music. It is also much quieter because kzin ears are incredibly sensitive, save when they dance on drums in wild ceremonies or before battles.
Marthar and I had sometimes played duets together, I on my guitar and she on drums, which were really more like a wooden xylophone than human drums. I don’t say it was good, but it was fun. Once Marthar and I had gone to a concert, where Dimity Carmody had played the solo part in the Elgar ’Cello Concerto. It had moved me to tears, and Marthar to a long silence. Then the orchestra filed out silently, and Dimity had moved forward and played one of the unaccompanied Bach ’Cello Suites. It was received well, but with more subdued applause than the Elgar. She then explained that she was going to finish with a work of her own, called On a Theorem by Kelangor. Kelangor, she noted, was in the audience, and she indicated a hulking great kzin with a rich black pelt. If you think mathematicians are delicate souls, you should have seen this one.
I suppose if you take a line from the Elgar to the Bach and kept going for a few light-years, you’d get to her own composition. There was a dead silence for two minutes after she finished. She rose, holding the neck of the instrument in one hand and the bow in the other, and gave a barely perceptible bow.
And Kelangor howled.
It started as a moan which ravaged the auditorium, and rose to a tortured scream, as of a whole wolfpack in anguish. There was a brief flash of compassion across Dimity’s face, then she put down the instrument and the bow, turned and walked off. People started climbing to their feet, still silent. The humans who walked past the still keening Kelangor were plainly embarrassed, the kzin gave a respectful nod to him and passed by.
Afterwards we sat together in a shop that sold drinks for both our species and talked of the concert. Marthar had said in a forlorn little voice, “I could never do that, could I?” and she had looked at her paws with the claws on the ends. I suddenly realized she was not just forlorn, she was grief-stricken. I tried to comfort her. “I expect they could make a special thing like a ’cello for you,” I told her. She nodded, somberly.
“It wouldn’t be the same,” she said, still hurting.
We had gone on to discuss why so many mathematicians had an interest in music and she explained it to me: “It’s all about patterns, seeing them and making them. You realize I won’t be able to do any algebra for a month now? Some of that music will be running through my head, and I won’t be able to see anything else while it is.”
“Perhaps it will be good in the long run,” I told her. “It might be good if the part of the brain which does both gets a rest from one and plays with the other for a while.”
She cheered up. “Yes, maybe that’s why Dimity does it,” she decided. “Different sorts of patterns may be a good idea. And you don’t need hands and fingers to do mathematics, thank the stars. You know, you are quite a clever little monkey, aren’t you?”
“Why did Kelangor howl?” I asked her.
She looked down. “He was expressing an emotion you humans don’t have a name for,” she explained. “The grief you feel when you realize you have omitted to do something very important, because you didn’t see it until it was too late.”
“I don’t understand,” I admitted.
“I think Dimity showed him something in his own theorem he had not realized was there.”
I thought about it. “I suppose it has something to do with us all living much longer these days. In the old days, you couldn’t master music, even one instrument, in less than a lifetime. The same with mathematics. But now it’s possible to master much more, because we stay young for longer. And Dimity has lived a couple of lifetimes already. If you keep on learning, you could learn an awful lot, I guess.”
Marthar looked at me bleakly. “Yes, you are a clever little monkey. But you haven’t thought it through, have you?”
I never really fathomed what she was getting at there.
I was reminded of that conversation by the weird stuff I was seeing now. It looked as though these creatures didn’t cut the world up the way humans and kzin did. They were more like the Jotok, who also didn’t see mathematics the same way at all. They could do it, and they could understand ours, but I don’t think many human beings could understand theirs, though I bet Dimity could. But this stuff looked like some weird combination of mathematics and music all together. And the mathematical part of it was different too.
I didn’t know much mathematics, as I’ve already admitted, and certainly a lot less than Marthar. We’d done the basics of course. I knew about groups and metric spaces and measure spaces; I guess everybody does that in primary school. We’ve known about those things for centuries. And q-groups and q-manifolds, which aren’t commutative, and which you need to do any serious Hard. But I knew I was not going to be well equipped for the really tough stuff I would need for Soft, but then, I was going to be using it, not really understanding it, which is a whole lot easier. I mean, you can train yourself to follow the rules without understanding how people had worked them out. Just as well, or I was doomed.
The thing about mathematics is that it is basically natural language only with very high precision. So you get strings of symbols coming up, and rules for rewriting one string to another; even stupid old early computers could do that without any understanding of what the strings meant. But these creatures didn’t seem to use strings, they used networks instead. There were lots of little circles with symbols, and lines joining them in different colors, with flags on the lines and symbols on the flags. And you could trace a path through it, and hear music of some sort. I turned up the age from basic egg to something slightly more advanced, and the sounds and the networks got hideously complicated. Not that it made much difference: I couldn’t even understand the egg-level material. They somehow transformed the networks according to some sort of rules presumably, but I never found out what the rules were. Perhaps the rules were encoded in networks, too. It was hard to see how to get started.
I had been puzzling over these things for a long time when Silver came back and asked how I was progressing. I told him I didn’t know for certain, but thought I was halfway between music, mathematics and a sort of algebra done with networks instead of s
trings. He left me to get on with it, but I think it cheered him. If I was right, this definitely counted as treasure. If nothing else, the Jotok would recognize its value, even if many human beings and kzin were too stupid to see it. I didn’t envy his having to convince the crew that this was valuable. They knew computers were important, but they probably thought computers could do mathematics. Well, maybe some of them can these days, in a routine sort of way, just as they can compose tunes and paint pictures. But they still aren’t very good at it compared with an expert human being or kzin or Jotok. It’s not like chess or Go. Computers can beat any human being or kzin at those things, but they don’t even do it in an interesting way. All the important part of the program is just stolen from a living brain anyway. And nobody has figured out how to do that with music or painting, still less mathematics.
At last, after three hours or more, I gave up. This was much too hard for me. Marthar might have got somewhere, but I couldn’t; I just wasn’t smart enough. I took the helmet off and sighed as I uncrossed my eyes. Concentrating for that long wears me out. Marthar can do it for a whole day at a time, and Dimity Carmody can probably keep it up for a week without sleep, but I’m just an average sort of person and I know my limitations.
“Well, what is it this time?” Rraangar demanded. He was not in a good mood.
“It’s some sort of mathematics, I think.”
He roared with rage. “That’s no use,” he growled at me and Silver alternately.
“Rraangar, you are an ignorant fool. How can you expect to understand an alien technology without it? This is the key we have in our hands. Maybe we should sell it, and maybe we should save it for ourselves so that any technology we find has to pass through us; a nice way of steady earning even if others find this world and loot it. Their loot will be useless without the key, and we hold the key, right here, ye damned eedjut.” For kzin, this was about the mildest insult in their vocabulary.
The crew looked at each other. They wanted to believe they had something valuable, but they suspected Silver was fooling them and taking advantage of their ignorance.
“The humans on Earth would give trillions for this,” I told them positively. More positively than I felt, actually. But if I was right at all, it was true. The possibility that it was some art form halfway to mathematics, but without its utility, haunted me a bit. I could recognize structure and pattern when I saw it, and anything with that amount of structure had to have some kind of value, surely?
The crew seemed to have more faith in me than in Silver. I don’t know why.
“I need something to eat,” I told them. “That sort of brainwork uses a lot of energy.” This is true, the brain uses more energy than all the muscles put together. On the other hand, it’s a lot easier to use muscles; we haven’t really evolved to use our brains a whole lot. Not for thinking, anyway. It definitely hurts the head, which is why most don’t do it, I suppose.
They argued a bit with each other, but weren’t too sure of what to do, and in those circumstances, anyone with a clear idea of what they want tends to get it. So we all went out into the plain outside the tower. It was barely any darker than it had been when we went in, so it was light enough for them to go hunting.
“Well done, young Peter,” Silver whispered to me. I suspect he felt I had made it all up, and that it was really something useless that I had found. He’d put a good spin on it all the same.
“I didn’t lie about it,” I protested. “It isn’t much like our mathematics, but it’s more like it than anything else. I’m fairly sure that there’s something pretty much like mathematics in there somewhere.” Of course, if aliens came to Wunderland and looked at a music score they might jump to the same conclusion. Not that there were many old-fashioned music scores around these days. It was impossible to make a synthesizer follow one of them, they left too many gaps which a human being could easily fill but a computer program could not.
“No, no, I’m sure you wouldn’t lie,” Silver soothed me. “It were a good job o’ work though, makin’ sense o’ the malarkey.”
We were interrupted by the crew, who came back with some animals they had killed, and they threw me one of the smaller ones, of which I managed to eat at least a little. While gnawing at their prey, they had been arguing with each other about the possible value of mathematics as treasure. I think they would have been happier with lumps of gold.
“Silver, if what ye say is true, then we need to fill up a pinnace wi’ these here bars, and get back into space. So we wants to know, how are we to get the pinnace?”
“Let’s be taking a look at the discs, then, me hearties, and see what we can be makin’ o’ them. One flight up, so it is, and afore too long we’ll be out of here.” He radiated optimism, but there was something strained about it, I thought. And the kzin were much better at reading each other than I was. They looked at each other with something savage in their glances.
We all trooped up the stairs, Silver and I in the lead, and we entered one of the rooms. Silver flashed his phone at the wall.
“Ah, we’ve had no visitors, not since I put the bugs up. At least, not from this room. Let’s try the others.”
We went from room to room, and none of them repaid the effort. The crew began to mutter.
“Let’s try to see if we can fall back on another plan,” Silver said with a cheer I was almost certain he didn’t feel.
We returned to the first room, and Silver walked around looking at the discs, motioning me to accompany him. The crew were half in the room and half out.
“Now there be writin’ on these discs, which will tell us where ’tes we are headed for, should we step on them, I’m thinkin’. And we have a man-kit here can read the heathen tongue, so we does. Now if he can tell us where the place is on the planet where we came from, I thinks we can return the quick way, and save ourselves a deal o’ time and trouble, and when we get there, why, we can discover whether someone has been since we left, which I’d take to be like enough, and we can follow her back whence she came; follow her enough and she’ll lead us to the pinnace, I’ve no doubt of it.”
It was an ingenious plan, and might have worked but for one thing.
“But Silver,” I said, “I cannot read these things. I’ve no idea what they mean in terms of location, and no way of finding out. I suppose if there is a geography tower it might be possible to learn it, but we’re in a mathematics tower. There’s no way I can help.”
I had said it in a loud, clear and definite voice, and I saw Silver crouch into himself, suddenly looking old and hunched. It took a second for the crew to absorb what I had said, and then they snarled with a blood-curdling ferocity.
“Ye ha’ lost us, Silver, ye ha’ been the death of all here!” But ye shall lead the way to the mist demons, damn yer eyes!” Rrangaar shouted and drew his wtsai. Silver drew his cutlass in an instant.
“Aah, ye’re after promotion once again, are ye, Rraangar? ’Tes a pushing kind o’ kzin ye be, to be sure. Why, which o’ ye has the stomach to face me down, then?”
But it was all of them, lending each other courage; seven of the huge beasts came forward, wtsais raised. Some would fall, but Silver couldn’t stand against the lot of them, and then it would be all over. What they were doing was not intelligent; they were maddened with rage at being lost, and someone had to die for it.
There was only one thing to do. The Doctor had said to cry out when we needed help, so I did, at the top of my voice: “Marthar! Help!”
And Marthar flashed into existence on one of the discs, a blaster in her right paw and a needler in her left. She took one look and blasted Rraangar into gas and bubbling gobbets of cooked meat, then took a narrow look at Silver and decided to save him until later. Silver prudently moved behind me and sheathed his cutlass. Marthar gave a scream that echoed around the room and jumped forward. She used the blaster twice, and the remaining crew fled. Bengar appeared on the same disc she had left, and stepped after her, then Orion also appeared and
looked around, then the Judge and finally the Doctor appeared and advanced into the room. Everyone was armed to the teeth. They all looked at Silver.
“Well done, Heroes and others! Well met, again, Miss Marthar. Ye got here just in time t’ save young Peter and me from a bloody end, I’m thinking.” He looked as unconcerned, as amiable and as friendly as he ever had.
CHAPTER TWENTY-NINE
“Bengar just shot up halfway to space before I could get after you,” Marthar said. “He saw Silver and decided to get me away, and I suppose it was the sensible thing to do really, though I was a bit mad at him at the time.”
“How did you know to come when I called? It was like magic,” I said.
“We’d been listening on your communicator, which happily you kept around your neck. So we knew where you were and that Silver was hunting for the pinnace. At least, we had an idea of where you were, until you walked to the third tower. We had to do a bit of work there to find how to get to it by disc, but Bengar soon worked it out for us. I was planning to get you out as soon as we could, without giving Silver another disc to use.”