This was the Weird Bannk, the shortest of all the Bannks, with the shortest of all the teclads and those growing shorter still. The sun, never above shoulder height this Bannk, was now sinking fast toward the horizon. After three months of failing to climb even halfway to the zenith, the snail-paced orb had decided to retreat quickly, unhesitatingly, monotonically toward the Patra. The temperature of the air in those slanting rays followed the curve of the sun, falling with it now, quickly, also unhesitatingly, monotonically toward the Patra.
Stringer was sure that the sun was now moving so fast that night would come at any moment. For a second he cursed his imagination, wishing time would fly and carry his life nearer to its end; then he forced himself to concentrate on what to do next.
He set about collecting wood for a fire. He wasn’t sure if he needed one yet, but Pike had told him that it was the first thing you did when stranded. He ignited the wood with his graser and basked in the added heat of the faintly visible daylight flames.
He heard a rustle behind him and swiveled around just in time to see a small two-legged sauropod scurrying into the woods. He ran after it, tripped twice, and cut his arm. He finally caught up with the animal as it ducked into a hole in the ground. It shrieked as he killed it with a quick blast. Then he felt around in the hole. He couldn’t reach to the bottom but imagined that it was deeper than the Patra. No wonder, then, that he had seen only small animals, except for the grask, brought by the Polkraitz themselves. Burrow under for the Patra. Save yourself. Stringer didn’t think he could fit into the hole, so he stood up and headed back into the woods.
At the fire, Stringer opened the plastic sack that, thankfully, Benjfold had thrown overboard and took out his knife. He began cutting up his catch, whose skin smelled strongly of glycerol, into small portions. That done, he emptied the sack onto the ground and mounted the bag itself on a tall pod-tree branch. If he were lucky, somebody would come by within a Patra-Bannk or two and see his frozen body as well as his distress signal. Glintz, clearly, was too far to walk to; there was not even a chance of his getting there. Would the insulated plastic tent last the Patra? Stringer laughed.
He finished his dinner, sighed, and glanced at the contents of his sack scattered over the ground. He picked up his rodoft, hardly damp thanks to the waterproof bag, and began picking at the strings. A dull twang released itself. Stringer found the bow lying across his kalan, picked it up, and dragged it across the strings. A squawk and a screech pierced the air. He sighed again and spread out a fingering chart Uslid had given him. He began to sort out the notes, testing the sound at each placement of his fingers. That was better. A thirty-one-tone scale. The Tjenens had already demonstrated the flexibility of their voices with their sing-song language; their ears must be equally sensitive, if not more so, to distinguish the close-packed frequencies of the subtle scale. And as another screeeech emerged from the sounding gourd, Stringer was sure that he would never master it.
For hours or telclads, Stringer sat on the beach playing the rodoft. He set up the tent, searched for shelter and more food, then went back to playing in the open under the cloud-filled sky. That was all he wanted to do. He glanced across the water at the dim outline of the sun. The sun was laughing at him for sure.
The water lapping around his ankle made Stringer conscious of something he had noticed on the trip south and earlier on the beach. The impression that had continually impinged on his retina and immediately evaporated could now be verbalized: the ocean was experiencing tides. Even with the waves, that was clear; every few hours the water would creep up on the beach, then recede.
Stringer looked up into the sky. But Patra-Bannk had no moon; at least he hadn’t seen one. Every child knew that tides were produced by the moon. Or by the sun. Stringer thought for a moment. No, he didn’t think the sun explained anything, either. Patra-Bannk rotated so slowly that he doubted solar tides would be so easily noticed. So Stringer reasoned against the tides and decided he was seeing some other long-term wave phenomenon. At least that explanation had the advantage of being untestable, whereas his tide theory seemed to be disproved.
After watching the water recede, Stringer searched a new area for shelter. Finding none, he returned to the beach. The wind wrapped his cowl around his neck and distorted the sounds of his rodoft. The wind was not always south any more, but was beginning to gust and veer, changing direction at whim. Stringer could taste the forest fire moving closer, borne on that wind, and he remembered that his was not the only life in danger.
As he sat there bowing the rodoft, he felt the first drops of rain whipping into his face. It had rained once or twice at Ta-tjenen, but now it was late Bannk, so this must be the start of the late-Bannk rains that Taljen has mentioned. Bad weather was on its way, and the bad weather would not let us before Bannk’s end. Stringer went back to his instrument.
He wasn’t sure what made him look up at the precise instant that he did, but he was sure that if he hadn’t, it would have been too late. Oars dipping into the water, a ship was making its way north, straining against both wind and waves. Stringer jumped up and shouted:
Here! Here!
He plucked his bag from the pod-tree and waved it high above his head. Here! Can you see me?
The ship wasn’t far off shore and Stringer was quickly spotted. In a few minutes, after some trouble in the surf, the craft had beached itself. Stringer gathered up his things and ran to the small vessel.
This is a strange place to be near Bannk’s end,
said one of the oarsmen as he helped Stringer over the edge.
It’s a strange place to be at any time,
Stringer answered.
The oarsman was tall and dark, with face almost the same shade as hair. Stringer knew what that meant.
You speak with an accent. Where are you from?
Far away…very far away. Tell me where you are
going.
Back to the Center. Where else is there to go?
Stringer nodded heavily, and the boat once again took to the water. They tacked the coast, angling in and out like a sewing needle, doing their best to avoid sailing into the wind. It was a long process, and the ten oarsmen did not seem to help greatly.
Stringer watched the sail for a moment and then stretched out on the deck. He slept soundly for the first time since the start of the fire. He was awakened by heavier drops of rain falling on his face than those he had felt before. He got up and turned to the cabin.
You can’t go down there,
said the same oarsman.
Why not?
The Time Keeper is hard at work.
Stringer balked, but only for a moment. I think he
would like to see me.
He pushed the other aside and opened the cabin
door. Two or three steps down, he entered a room that was cluttered with
parchment lying on the floor and scattered over the single desk. On that
desk was a blank white ball with some black marks scribbled over its
surface.
A short little man with silvery hair and very black eyes paced the cabin, kicking up the papers with his shuffle.
Come in! Come in! I thank you. Who are you? Come
in!
the man continually exclaimed with a squeak in his voice.
Stringer stepped forward. My name is Stringer.
You are not from Ta-tjenen or Glintz, no, that is
obvious.
The silver-haired man studied Stringer closely.
No, I’m not.
Good, then maybe you will listen to me. I have made
a great discovery. The results are here. I have made runs in previous
Bannks, but no one listens. So I did it again and again. I still have to
compare these figures with those taken at Ta-tjenen this Mid-Bannk. But I
am sure—
What have you found out?
The world is round!
Spherical? Like a ball?
Precisely as this one here. Isn’t that exciting?
The little man chuckled in obvious delight.
Stringer leaned against the wall and sighed. I
thought I was mad when I told Taljen and she wouldn’t believe me.
You know already?
The silver-haired
man’s voice betrayed disappointment.
Stringer nodded. I am not from this world but
another. I knew already. But don’t worry, the discovery is still yours.
The older man smiled. I thank you. An Alien, that is
interesting. Polkraitz?
He studied Stringer closely again.
Do I look like one?
I wouldn’t know. But you say you have talked to
Taljen?
You know her?
Yes, of course—very well, in fact. Who in Ta-tjenen
doesn’t know her?
That seems to be true.
But she was my assistant also and should have been
taking measurements for me while I was gone. Was she?
I don’t know. She may have been. For the first
teclad I was there, I was not very conscious of what she was doing. You
mentioned Mid-Bannk. I arrived after that, about a teclad after, I
think. But it is good to know that I am not crazy. How stupid can Ta-tjenen
be, not to realize that the world is a ball? Taljen just couldn’t believe
me—or you, I guess.
This has been a standing argument between us and has
gotten to the point where she doesn’t like to talk about it at all. But, I
ask you, why should Taljen believe you or me? She is a bright girl and
believes what she sees. Why should she listen to us? If you lived on this
planet all your life, what would make you believe it wasn’t flat?
Stringer gave his standard answer: Ships on my
world gradually sink below the horizon. That wouldn’t happen on a flat
world. They would fall off and suddenly disappear.
True. But do you think you could see this ship on
the horizon? Not unless you had eyes like a solofar. We usually don’t
travel that far, anyway.
Why not?
Where is there to go but fishing? Glintz is the
closest town to Ta-tjenen, and that is almost two thousand kilometers, and
we have just come from Godrhan, the next town, twice as far as
that. Besides, the Bannks are hot and the wind is usually south. Sailing
back north is cumbersome; that is why we tried coming back now, when the
wind shifts to the south-east. However, I see we may have waited too
long.
Hasn’t anyone sailed around the world?
Stringer,
the silver-haired man chuckled, are you serious? With the heat of Mid-Bannk and the
Patra, and the size—
Yes, I suppose that was silly. I had
forgotten. Didn’t your Polkraitz leave any records? Maps?
Not that I know of. Any more questions?
Hmmm.
Stringer thought for a moment. Once somebody told me that you can see the roundness
of other planets and the—
For the first time Stringer realized that the
Tjenens had no word for moon.
Do you see any other planets?
Well,
sighed Stringer, it looks as if the right thing to ask is, why do you
believe the world is round?
A good question, and it took me a long time to be
convinced of it, I’ll not tell you wrongly. I’ll show you the first
evidence that got me thinking.
The old man ducked under the table and
brushed away some of the parchments lying about, to reveal a metal box
about half a meter long, handsomely made of brass or something very
similar. He motioned Stringer to the door, and they went above, taking the
box with them.
Ah, it’s raining, and the sun has begun to put on
fur. But it isn’t fully clothed yet, for the moment, and we might still see
something. Look here.
Stringer peered through the hole that was cut into one side of the box and saw an image of the cloud-streaked sun projected along an inner wall.
Do you see those little black specks on the sun?
Stringer nodded, barely making out a single sun-spot.
I keep a record of their positions. They travel
across the sun. The bigger ones I can see get distorted, disappear around
the edge, and in less than an average teclad come around to the other
side. The sun, at least, acts like a ball, don’t you think?
Stringer thought that was clever. Do you have any
other evidence?
Yes,
said the little man with that curious
squeak in his voice. After all, I
thought that if the sun was a ball, maybe the world was too. But I couldn’t
figure out a way of testing that, and my head ran itself around in
circles. Finally, one beclad in the market, I spotted my own shadow being
cast on a rather large melon. The shadows were the key, it came to me in
that instant. But that was only the beginning. After beclads of
excruciating thought—and this I can’t underestimate—I eventually decided
that if the world was flat and the sun traveling above it, then the sun’s
rays would strike the ground at the same angle whether you were north or
south. Indeed, this requires the assumption that the sun is small and far
away and that the rays can be considered parallel. You might object that I
have no justification for making that assumption unless I know how far away
the sun is—which I don’t—and I would say you’re right. Nonetheless, it was
the simplest assumption to make—I would agree with that myself, and
somebannk when all the answers are in, I am sure I will be borne out.
On the other hand, and under the
same assumption, if the world was curved then the angle of the sun would
change depending on where you were. It took me a long time to figure that
out; after all, I’m no geometer, am I not? My father was more the
mathematical type but I hate the stuff. Does it, I ask you, give you any
feel for real things? Have you ever seen a perfect triangle in nature? Or a
semi-infinite half plane? Geometry is really very fictitious, especially if
the world truly is a ball. In that case, I ask you further, does it make
any sense to talk about plane geometry at all? Certainly not. You can’t
make real triangles on a sphere. Whoever invented plane geometry was living
in a world of his own.
Anyway, not to digress, this was all four or five
Bannks ago. What I did then was to take two big rods like so
—the Time
Keeper held his arms outstretched—and go out onto the beach with an assistant. We planted
the first rod in the sand, making sure that it was quite straight, and then
I ran down the beach with the second rod, doing the same thing. At my
signal we both measured the length of the shadow cast by the sun. To my
profound disappointment, I’ll be truthful on that, we saw no difference in
the lengths of the shadows. Absolutely none. At first I thought that the
world was surely flat but, after some thought, I decided to try bigger
poles. We repeated the experiment, hoping that taller posts would make the
difference in shadow lengths easier to see. The only result was that I got
tired from running up and down the beach. Finally, and this was a curious
thought, I conjectured that perhaps the world was bigger than I had
expected, and so I sailed down the coast for a few dozens of kilometers. We
thought we could trust our clocks for that short amount of time to make
sure we took the readings at the same instant, although, on afterthought,
that turned out not to be so crucial; the sun does move very slowly, as you
can see. So we did it. Again nothing. There was absolutely nothing.
By this time, you can be sure that
I was about to give up the whole project. However, I was possessed by the
idea and vowed to go all the way to Glintz the next Bannk. Now, I shan’t
tell you falsely that no one ever goes to Glintz, especially just to
measure shadows. So I got a number of rods—taking many poles and averaging
data would offer more reasonable results, don’t you agree?—and left some
behind at Ta-tjenen and sailed south to Glintz. Because our clocks wouldn’t
be useful after such a journey, we were especially careful to get there
before Mid-Bannk, when we would take most of the readings. When we got back
to Ta-tjenen, my assistants and I compared measurements. Once again I felt
my heart freezing, because the first readings taken on the way south showed
nothing definite. Oh, there were small differences in shadow lengths,
hardly readable, I tell you, but some showed the longer shadow on the
northern pole and some showed it on the southern. And I’m afraid it can’t
be both at once, whether the world is flat or round.
Finally we reached the measurements taken at Glintz
itself. Again, on the shorter poles where reading anything is difficult,
only small random fluctuations showed up. At last, on most of the taller
poles we got results that were big enough to be read, and some of those
agreed as closely as might be expected. It wasn’t much to go on, but enough
to convince me. It convinced no one else, I can tell you that.
Why not?
Ah, Stringer Not of Ta-tjenen,
when I got my results back and showed them around, people said,
Why,
that’s only a few centimeters’ difference in the length of a shadow, not
even a finger’s length. And if your measurements were not made at the same
time, then everything is meaningless. And of course, you have no way of
telling that the measurements were made at the same time.
And I replied,
No, you’re quite
wrong. That’s why we took lots of measurements at Mid-Bannk, when the sun
was moving the slowest—and that is very slow indeed. Certainly, by taking
measurements every few belclads, we could be sure to find the shortest
shadow, even through the haze if we were lucky, indicating that the
measurement was taken precisely at Mid-Bannk.
And then I went on to
explain that we wanted local Mid-Bannk wherever we were, be it
Glintz or Ta-tjenen, and it didn’t matter if the two towns were directly
north or south, which would make the Mid-Bannks at the same time. This went
totally over their heads, and I gave up trying to explain it to them.
Still, they wouldn’t be
silenced.
And how do you know how far it is to Glintz?
they
asked. You can’t measure the distance with a ruler; you can only guess
at it from your travel times and estimated speeds. What if you’re
wrong?
That,
I replied, would
only change the size of the world and not the shape, so your objection is
irrelevant.
No sooner had I made this devastating rebuttal than
they raised the objection that the measuring pole had to be perfectly
vertical or the results would be wrong. Was that ever dirt in the eyes!
When I calculated the error that a slightly tilted pole would cause, and
estimated the accuracy with which I could make a pole vertical by eye, I
realized that the experiment was at best questionable, at worst totally
useless. In fact, I am sure those random readings and wholesale
disagreements I spoke of were caused by just this phenomenon: poles tilting
in the wind. What is even sadder, it seems that by increasing the height of
the pole to make reading the results easier, one just increases the error
by the same percentage. So tall poles do not decrease the error, only
enlarge it along with the
true
result. Thus, my tall-pole readings
at Glintz may have simply made my readings of a systematic error more
accurate, and the world could still be flat.
Stringer could only shake his head now, not in derision, but in the realization that he would have given up long before then.
The Time Keeper continued: I
resolved to go back to Glintz the next Bannk with better apparatus, which I
did, making sure that the poles were perfectly vertical, which, to be sure,
is no mean feat in the wind. To my great and overwhelming satisfaction, I
got the same results, or close enough. Still, the same objections were
raised when I returned. After all, would you change the shape of the world
because one shadow is half a finger longer than another two thousand
kilometers away?
Well, at this point, I sent a ship out onto the
ocean and watched it all the while with my telescope, hoping to see it
sink, which, as you suggest, occurs on your world. I wanted to show the
others that proof, too. But after looking and seeing little more than a
blur—and that only if I was being optimistic—I knew I wasn’t going to
convince anybody.
And yet you still believed?
Stringer asked in
admiration.
I did begin to doubt my results again, especially
when I used them to compute the size of Patra-Bannk. It’s two million
kilometers around! How could I believe it? You ask about sailing around the
world—and I tried to measure shadows running up and down the beach! What a
comedy of errors!
But you’re right,
said Stringer softly.
However, the old man didn’t hear.
So,
the other went on, sighing, nobody believed me and I hardly did, either. When I
suggested that my theory predicted that the sun would look higher in the
south and therefore the south should be hotter than Ta-tjenen, just as the
Long Bannk is hotter than the Short, everyone laughed. That’s when I
decided to take an expedition to Godrhan, which, as I’ve said, is more than
twice as far as Glintz. And the angle so measured is more than twice as big
as the ones I have measured before. I’ll bet on that without having seen the
latest data from Ta-tjenen. Furthermore, as the sun is lowest this Bannk,
the error due to any pole tilt will be lessened, I will so argue.
He
paused for a very long time. Maybe Ta-tjenen will
believe me now, maybe they won’t. It’s a few questionable shadows versus
the obvious.
Would you go past Godrhan to get more of a change
in the shadows? That might convince them.
The Time Keeper started involuntarily. But beyond
Godrhan is the Edge of the World.
Stringer eyed him closely, and under his scrutiny the Time Keeper chuckled, perhaps a little nervously.
Does it really matter to Ta-tjenen whether the world
is flat or round? Ta-tjenen is its own world; it has to be by necessity,
and no one can blame them for that. Perhaps somebannk it will be different,
but I doubt it.
Stringer laughed at the matter-of-factness of the last statement. If it makes you feel any better, you’re right.
The silver-haired man shrugged. I knew I was.
Tell me,
Stringer said, drenched, back into
the cabin, why do they call you the Time
Keeper?
Because that’s supposed to be my job. It was passed
on to me over generations. All the previous Time Keepers had the regimen
worked out fairly well, so all I had to do was learn it. It isn’t much of a
job any more, not unless I can discover a better way of keeping time. And
you can be sure I haven’t been able to do that.
But I don’t understand why anyone has to do
it.
How else would you keep track of how long the Bannk
is?
But can’t you do that by looking at the big
sundial?
And how good is that? Better than most of the
clocks, actually. But who is to say which Bannk we are on?
I’ve heard they change.
Most certainly! This is the Weird Bannk, so called
because, as you have seen, the sun travels almost horizontally across the
sky, hardly up at all, and even the sunset seems too long—
Not long enough!
It is the shortest of all the Bannks, and the
temperature is pleasant.
It is?
You saw the sun this Bannk? A trifle. It never finds
its way into the sky. Wait ’til next Bannk, the Killer Bannk, which is the
longest of all, and, I’ll not tell you wrongly, the sun climbs twice as
high as in this Bannk. The teclads are long and almost all activity
stops. But before then is a Short Patra, longer than this Bannk, coming
shortly, as you can see—
Yes, I can.
The Killer Bannk is followed by another Short Patra,
which is in turn followed by another Weird Bannk. After the Weird Bannk we
have a Long Patra and a Long Bannk, each as long as the other but not as
long as the Killer Bannk. Following the Long Bannk is a Weird Patra, so
called because it is as long—or as short—as the Weird Bannk, thus making it
the shortest of all the Patras. On its heels comes the first of the Short
Bannks, which is not as long as the Long Bannk but is longer than the Weird
Bannk—
Why do you call it the Short Bannk if it is
not?
Because the shortest Bannk already has another name:
the Weird Bannk. If we changed it, then we would have to find another name
for the Short Bannk. But to continue—the Short Bannk is followed by the
Deep Freeze, equally as long as the Killer Bannk. The Deep Freeze precedes
another Short Bannk, as short—or as long—as a Short Patra, which is
followed consecutively by a Weird Patra, a Long Bannk, a Long Patra, and
then the cycle starts all over again with the Weird Bannk after seven
Bannks and seven Patras. So the sundial must keep track of seven Bannks,
and we have not even discussed what to do in the Patra.
If there are seven Bannks to keep track of, then
how come the sundial only shows four scales? I should think there would be
seven.
If you were counting, there are only four different
types of Patras and Bannks, although the cycle is seven Patra-Bannks
long.
How long is a Patra-Bannk, if they’re all
different?
Either that question is meaningless or the answer is
obvious. But let’s not digress. We are talking about the Time Keeper. Of
course, my duties don’t stop with just deciding which Bannk we are on,
which the sundial does, anyway. There is the Golun calendar as well, and, I
ask you, what about the Parlztlu? Of course, there is the additional task
of keeping track of how long the beclad is at any given time—
How long a beclad is? Do you mean all the units
change?
No,
the Time Keeper replied. The clad itself, which goes by in the flap of a
solofar, is too short to bother changing, as is the belclad. But telclads,
beclads, and teclads all change noticeably. Telclads only on the best
clocks. Otherwise—or even in that case—the error usually swamps the actual
change. So beclads and teclads remain to worry about.
But how can the larger units change and not the
smaller?
If you change a large unit—make it larger, for
instance—then I’d say you can either increase the small units
proportionally or just put in more of the small units into the large.
What if they don’t fit?
Do you mean, what if there’s not an integral
number?
Right.
As I’ve said, the clad is quite small, so there is
always an integral number in, say, even a telclad.
Not theoretically.
I’m not talking about theory, am I?
That sounds like cheating to me.
No, it’s just a matter of how accurately we want to
bother defining the units. I quantize them. That makes it easy, I’ll say
truthfully.
If that makes it easy, why bother with any of
this?
Stringer asked, throwing up his arms. What good can changing the units do?
Well, let’s think about it, should we not?
Obviously, the Bannks and Patras all differ greatly in a highly
asymmetrical fashion, and it is hard to remember exactly how—as you’ve just
seen. Time between Mid-bannk and sunset varies between each Bannk as well
as from sunrise to Mid-bannk. But what Ta-tjenen is interested in is simply
when to come Above and when to go Under. So it is just as easy to keep
everything nice and even, let’s say six teclads for each Bannk and each
Patra. I think that’s reasonable.
Okay, then you have to change the size of the unit
from Bannk to Patra. That seems fairly reasonable, even though on my world
I’ve never heard of such a thing. But to change them during the Bannk seems
absolutely outrageous.
Well, I suppose that depends on how you define a
teclad, don’t you think? We define it as the time it takes the sun to move
one-third of the way up or down the sky. And of course that changes. You
see the sun move quickly at first, then slow down as it approaches its
maximum, and then speed up again on its way back down.
What a ridiculous system! No wonder no one in
Ta-tjenen ever knows what time it is!
How would you define a teclad?
Why not just a sixth of a given Bannk?
And how do you determine how long that is?
With bad clocks, it’s easier to measure the angle of the sun. But, in
concession to your views, I was toying with the idea of keeping the teclad
constant and changing the angle in the sky which the sun moves during its
traversal. However, that bothered me a little.
I should hope so.
It does seem that the size of an angle should remain
fixed.
Why not the size of a beclad or a teclad? Are they
any less real?
As I’ve asked you before, how do you define these
terms? Not only is it hard to conceive of what a teclad might be, once
that’s decided, but it is hard enough to measure, so you might as well
change it if we need to. I admit, though, I balked at changing the angle in
the sky.
I’m at least glad for that.
At any rate, no matter what system you use, or what
system I use, building a clock that keeps good time on Patra-Bannk is
difficult; there is so little to check it with, especially during the
Patra, when there is nothing to check it with. I do have one of our best
here.…
The silver-haired man opened a cabinet door, and Stringer saw a
beautiful device that had seven large dials and two smaller ones. The
calibrations, like those on the sundial at Ta-tjenen, were uneven on the
seven larger scales. The whole was mounted in brass and inlaid with
polished gems.
Why are there seven scales here and only four for
the sundial?
If you remember, there are only four different types
of Bannks and Patras, as I told you, but the cycle is seven Patra-Bannks
long. This clock counts them separately.
So why does the sundial have only four?
Why do you see with your eyes? Because a shadow
can’t tell the difference between two Bannks that are the same, that’s
why. My grandfather built this, or my grandmother, I’m not sure which,
although I’m told that the jewels are from the Polkraitz themselves. We
have few enough now.
Tell me one more thing: What is the Golun-Patra?
It keeps following me around and I don’t think I like it.
The Golun-Patra occurs once every ninety-seven
Patra-Bannks.
Why is that?
Because the Golun is ninety-seven beclads long,
whereas the Patra-Bannk is one hundred forty-four.
Stringer shook his head. How Tjenens always answered the wrong question! But what is a Golun and why is it ninety-seven
beclads?
The elder man scratched his head. Well, the Golun is
one-third of a Parlztlu, why I can’t say exactly. But if you start off the
Golun and Patra-Bannk together, they don’t coincide again for another
ninety-seven Patra-Bannks, one Golun-Patra. This is the twelfth Golun-Patra
since the revolt, a special anniversary because it is the twelfth.
And does it have something to do with the return
of the Polkraitz?
I don’t know. Does it have anything to do with
that?
Stringer stood up angrily. Sarek or
Verlaxchi—whichever is in charge around here! That old woman Kenken Wer,
who tried to kill me, and most of Ta-tjenen seem to think it does.
Kenken Wer, yes. The Great Cackler. Well, I can’t
speak for her.
Stringer gritted his teeth and threw up his arms once more. I think I need some more fresh air.
Stringer went above and stood in the rain. It was, even now, heavier than when he was last on deck. The boat was approaching a part of the coast where the great fire had done its work, and the damage was clear to see. The forest, not dense to begin with, was scattered with burned-out stumps and charred fern-moss. It wasn’t a pleasant sight, but one that went well with this planet.
The Time Keeper then noticed the forest. Verlaxchi!
What happened?
There was a great fire just before the rains. Most
of the forest is in ruins. You will not be returning to a happy city, Time
Keeper.
Do you know if there is fuel enough?
For this Patra, at least, I was told. If I were
Ta-tjenen, I would start being like most worlds and begin using oil.
Oil? Certainly there isn’t enough oil in all the
grask in Ta-tjenen to do that.
No, I mean oil from the ground.
I’ve never heard of any of that.
Curious maybe, maybe not. But then there seem to
be a few curious things about this planet. The gravity, for instance.
Humph. I never could understand it.
Neither could I, but something is certainly wrong
on Patra-Bannk.
The old man’s eyes lit up. Really? The world is
always much more interesting when something is wrong with it. Tell me.
Let me get it straight. I think I finally
remembered the exact expression. The weight of an object on a planet is
proportional to the mass of the planet divided by the radius squared—
Amazing! Is it always true? Everywhere?
Yes, as far as I know.
Incredible! Go on! Go on! Aha…
The little man
went dancing around the deck in the rain, falling several times as the boat
pitched.
Now, see if I make sense. On my planet, which is
about one-fiftieth the diameter of this one, I weigh about the same as I do
here—
I see! That means the mass of Patra-Bannk is about
twenty-five hundred times that of your world.
Stringer was glad to be talking to someone who understood him. But don’t you see how ridiculous that is? The volume
of Patra-Bannk is one hundred twenty thousand times that of my world, so
the mass can’t be twenty-five hundred times that of my world unless the
density is fifty times less than on—
Two-Bit didn’t translate. If the density was the same or even nearly, I should
weigh about fifty times more than I do.
Amazing.
The older man turned to the captain of
the boat. Put us ashore a minute, would you?
In this weather? Are you sure?
Yes, yes, go ahead. Don’t mind the waves. Go
ahead.
After having some trouble in the rugged surf, the boat was beached and the
Time Keeper hopped to the ground with a box of odds and ends he had taken
from the cabin. Within a few beclads he had constructed a crude but
admirably serviceable balance and began measuring out equal volumes of
sand, rock, and water. He put a bit of dirt on the balance, then emptied
the dish and filled it with water, placing that on the balance instead. Is your world made out of dirt?
A lot of it is. I don’t know how much. A lot is
water, too.
Well, Stringer Who Asks Odd Questions, if that is
true, then I would guess that Patra-Bannk would float on water—if you found
an ocean big enough.
If! But that’s what I thought,
said Stringer
as he climbed back aboard.
Are you sure your gravity is right?
asked the
other as he gathered up his toys.
Absolutely. Everybody learns it when they’re
ten. I forgot about it until I got here; I never had any use for it. But
I’m sure that’s the formula.
Surely you misremembered. The observations show you
are wrong: you are standing on your own two feet.
No, I am sure I am right.
I am certain you are wrong. How does one figure it
out? I’d like to check it.
Stringer shrugged. That I don’t know—
But that is what is important to know.
What do you mean?
It seems to me that it is more important to know how
to verify what you say than to know the fact itself, don’t you think,
especially since you’re so obviously mistaken?
I’m not sure. All I can tell you is that it has
something to do with measuring the positions of the planets against the
stars in the night sky—
Something suddenly struck Stringer. Of course you wouldn’t know; you’re always
underground at night.
But I have seen stars. Once in a great while, if my
clock is off enough so that I go out to find the sunrise much too early, by
a few beclads, I can see one or two. I’m not sure what they are, perhaps
balls of ice, parts of the atmosphere frozen.
Stringer smiled. Not balls of ice, and I don’t
think one or two would be good enough. Somehow you have to observe the
planets and figure out how they go around the sun—
What do you mean, go around the sun?
That’s what I mean.
Stringer then remembered
his discussions with Taljen. Don’t you believe
that Patra-Bannk goes around the sun?
No, should I?
Do you mean to tell me, Time Keeper with the Bad
Clocks, that you have decided the world is round and yet you still believe
the sun and the stars—all two of them—move around Patra-Bannk?
I don’t see what one thing has to do with the
other. Anyone with eyes in his head can see that the sun goes around
Patra-Bannk.
Stringer laughed aloud, but it was at himself. You’re right. Absolutely. Well, I wish you luck, Time
Keeper Who Asks the Right Questions. I can tell you it took some of the
greatest minds in history to figure out gravity, and I certainly am not one
of them.
Who is?
Stringer laughed again and was happy.