Masters of the Arches

by Mandil

Chapter 12

The first thing that they noticed when emerging in their new surrounding was the brightness of the light. Whereas a second or so before they had been standing in a relatively dimly lit room, they now found themselves in a very sterile and bright place.

The room resembled a gymnasium in its emptiness as well as its height. In one corner of the room stood Nika. She had not yet recognized them and her arms were outstretched while her knees were bended as if she was getting ready to fight them.

When she did recognize them, her facial expression changed from one of half anger and half fear to one of joy as well as surprise. She immediately rushed toward them with tears in her eyes. It took the three of them a couple of minutes before they could overcome their emotions and as soon as the hugging and kissing was over, they began to ask her questions.

Her story was very simple. Once she had been captured by the birdmen, they took her to their village that was many miles to the south. Once there, she was placed into a wooden cage. As a measure of security, they also tied her hands behind her back and although she could walk in the cage, she couldn’t use her hands at all. Nika remained like that for five days. Her hands were untied twice a day when she was fed and also when she had to attend her body needs.

On the fifth day, she knew that something special was going to happen since the whole village was very excited and she could see them making preparations for a celebration. In mid-afternoon, they took her out of her cage, then every man, woman and child was made to touch her as she was forced to parade throughout the village. Later she was taken inside the mountain through large carved doors.

Once she was in the depth of the mountain, she discovered that she was in an immense room with hundred of people assembled there. She soon realized that she was going to be offered as a sacrifice in front of a very tall statue of a bird. But when she saw the arch near the statue of the bird, she then knew what her fate was going to be.

The fact that she already knew that the arch was evil did greatly help to boost her resistance, but at last, the physical strength of those holding her was too great and she was thrown on the plate of the arch. She then found herself in this room where they were now. All of this had happened just a few minutes before Vincent and Verla appeared.

Once the joy of being reunited was no longer new and after they had listen to Nika’s story, they began to pay more attention to their surrounding. The room they were in was large indeed and light was being diffused somewhere from the ceiling high above their head. Some light was also coming from the higher portion of the walls. They could not actually see the light sources since it seamed to be coming from the paint or the colors of the material of itself.

There were two doors or panels in the far wall, while close to the opposite wall where they now stood, was the receiving end of the arch. Both doors at the other end of the room were shut.

They slowly walked to the two doors and  examined them. Both doors were identical except for one small difference. On the door to their right there was a small hole in the middle while there were no such hole in the other door. A distance of at least thirty feet separated the two doors and except for the small hole in one of them, there were no other marks whatsoever on them.

To Vincent who was familiar with doors, and also judging by the rectangular cracks along their contour, it was evident that they were made to open somehow, either pivoting on hinges or sliding into the wall somehow. But no hinges or knobs could be seen.  They did try to push on each one of them and  they also tried to slide them using the friction of their hands, but it felt as if the doors were part of the wall and they didn’t even begin to move.

After many long minutes of trying all sorts of ways to open them, they gave up and they focussed their attention on the rest of the room. On the wall opposite to the two doors, behind the arch and near a corner, was a table-like altar made of the same material as that of the walls and floor of the room. Resting on the table was a rectangular transparent box.

As soon as Vincent approched the table, he discovered that the table top in front of the transparent box was covered with small round buttons arranged in many rows. Each button was about half an inch high and they were arranged in a triangular pattern.  One button in the first row then two in the second and so on, up to twenty- two rows with twenty-two buttons in that last row. Inside the transparent box was a turquoise rod about a foot long and it was made of what appeared to be glass with an intricate design at one end and a flat portion at the other end.

Vincent noticed that the round end with the intricate design could probably fit into the hole of the door. It thus became apparent to him - since he was familiar with doors on his world - that this was the key that would open that particular door. The only problem was that they couldn’t open the lid of the box where the key was. Even when he hit it with the butt of his rifle he could not break the glass-like material. After a while he ordered the two women to stand behind him and he fired two shots at it.

When he examined the box afterward, there wasn’t even a mark on it. The material of which the box was made was transparent, but it was certainly not glass or plastic since none of these would have resisted the penetrating capacity of a 303 high speed slug and worst still without even sustaining a scratch.

Vincent next focused his attention on the round buttons arranged in rows. When he pressed one, it did depress half way into the table and a soft musical note was heard coming from the box. It was a sound very similar to that made by a touch -tone telephone on his world. Then after what he estimated to be eight or nine seconds, the sound stopped and the depressed button lifted itself to its initial position. When he pressed another button, the same thing happened but a different note was emitted. He then tried pressing two or more buttons simultaneously. But each time he did that, only one note was heard; it appeared that the button that had gone in first, would be the one to emit its corresponding pitch. Pressing on any other button while this one was emitting a sound did not change the pitch of the note in any way. Finally he looked at both women and he said.

"It is some kind of code to open the box. The only problem is that we don’t know what button to press and also what sequence to use."

"Why do we need to open the box?" Said Nika.

She had probably never seen a key before and Vincent though that her question was very logical.

"You see the rod inside the box, it will open one of the doors if we can get it."

"Then why don’t we press all the buttons one after the other, then we are certain to get the right one?" Said Verla.

"No this will not work, I think that we are allowed to use only a certain number on button and they must be the right one."

"Then only a person that knows which one to press will be able to get the rod inside?"

"Yes this is the purpose of it. I think it was placed there as a sort of a test. After all, if the builders of this place wanted to kill us they could have done it in a much easier way than starving us here. Beside, there are no bones here and I am sure that these birdmen that pushed Nika on the plate of the arch are frequent senders of unwilling visitors here."

"You mean," Nika said in surprise, "that the birdmen capture people only to push them through the arch? But why do they want to do that?"

"I wish that I knew the answer to that, but it seem that this is exactly what they are doing. It could be part of their religion or belief or something else."

"But what is preventing us form going back the same way we came here?" Said Verla.

Vincent realized that she had a good point, but deep inside he felt certain that this arch would not work both ways. To test this, he took one of the knapsacks and he threw it on the plate of the arch. Nothing happened even after a ten seconds wait. He then stepped on the plate and still the arch didn’t work. He then looked at both women and he said to them in a low voice.

"The only way we are going to get out of her is by breaking the code and using the key in the box."

For many hours after than, they took turn in trying different sequences with different rows of buttons, but the lid of the box never opened. At last Vincent thought of something.

"I think that I know why the box and the key were placed there. The person or group of persons that built this place wanted to be sure that one of the doors would be opened only by someone that came from a culture that has a sophisticated degree of technology, that is why a proper combination is needed to open the box."

"But anyone that knows the right order could press the buttons." Said Nika.

"Yes, but that is the point, we don’t know the right sequence and I am sure that this sequence is such that if you have the proper scientific background you can figure it out."

Nika stared at him for a second or so then she said.

"You do have such a background, you have all sort of machines where you live, I have seen some of them when I went to your house, so you should be able to open it then."

Of course Vincent knew that she hadn't met this as an insult, but like most of the people of her world she was used to say what was in her mind and he didn't take any offence because of her last remark. But deep down he knew that she was right. If any of them could break the code he was the one since he had the necessary background, and this tremendously increase the pressure on him. He had to solve this puzzle; he knew that their life depended on it.

He decided that they all should take a break for a while so that they could proceed later to examine the problem in a new frame of mind. They ate a little then they stretched on the floor for a couple of hours. Food and water were not a problem yet; they still had a few days supply left. But Vincent had a feeling that they should leave the place as soon as possible. The fact that there were no traces of the previous visitors was proof enough that someone or something did come into the room once in a while to remove these visitors or whatever was left of them after a fix length of time. He was perfectly aware also that if he, with all of his background from his so called more advanced civilization, - advanced at least compared to what he had seen on this world so far - could not solve the problem of the code, then it would certainly be impossible for any native of this world to do so.

He had a deep feeling that their time in this room was limited and if they did not solve the problem soon they would be forced out of the room somehow. That second door, the one without the hole, the one that could not be opened with the key, was most probably used for this purpose. He didn’t bother to tell this to the women of course since there were no reasons to scare them, but still the faster they were going to get the door open the better it would be for them.

While he was having these unpleasant thoughts, Nika and Verla were busy pressing different buttons in front of the table and trying different sequences so as to get the transparent box open. Slowly Vincent walked toward them and while he was approaching them, the answer or at least part of it came to him.

Yes, he could see it now. Those rows of buttons represented numbers. All he had to do was to choose the row that contained ten buttons. He tried to explain what he had in mind to the women but since they had no notion of written numbers they had much trouble to follow his explanations.

"You see, that row of ten buttons here is for us. There is no use trying the other rows because we will never get the right combination using them."

"But why were they put there then?" Protested Nika.

"If they don’t open the box then they are not useful?" She went on to add.

" They certainly could open the box, but we will never succeed with them since there is no way for us to get the right sequence with any of them. You see, different civilizations use more or less units as the base for their numbers. All the numbers then use a combination of these units. Where I come from we use the same number of units as there are fingers on both hands, which is ten. All other numbers are then written as a combination of these fundamental units which are 0 to 9. If your world is ever permitted to develop a technology, the chances are that they will also adopt ten units for their base numbers since like the people of my world you have ten fingers in both hands. But there is no reasons to suppose that other beings from another world will have ten fingers like us, they could have two or eight or even twelve. This is why there are different sets of buttons with different number of buttons in each set."

He doubted very much that they could understand what he was trying to say, but they both seemed to be listening with great interest. Vincent then went on to explain.

"The builders of this place must have been expecting beings from different worlds, this is why they set up many rows with set of buttons. Since we use numbers based on ten units and multiple of these, we will concentrate our efforts on the row with ten buttons."

Verla looked at him for a second, at last she said.

"Why bother with only this row if any row can open the box?"

"True, any row will open the box but for us it will be much easier to figure the right sequence if we keep on trying on that row of ten buttons. The fact that we have already solve the problem of choosing the proper row for us, mean that we have already overcome half of the difficulty."

They both looked at him with a strange expression on their face and he could tell that they weren’t convinced at all, but they seemed willing to accept his decision.

"It also means," went on Vincent, "that whoever made this place is not interested in anyone from a non-technical civilization. In other word only those with a mathematic oriented background will be able to open the box and thus leave this place."

"What happen to those that can’t unlock the door?" Said Verla.

"Frankly I don’t know. But I think it will be much preferable if we were to open it."

Then talking more to himself than to his companions, he went on.

"Let me see, the sequence must be a series of numbers that anyone from a relatively technically oriented civilization must know. Something such as the speed of light maybe."

Since there were no markings at all on the buttons, he had to choose one end of the row and suppose it had the value of zero while the button at the other end would be nine. He pressed on the ‘one’ then the ‘eight’ and ‘six’ then on the ‘zero’ three times so as to represent the speed of light in a vacuum, which is 186,000 miles per second. Nothing happened. He then tried the same thing starting from the other end. Still nothing. Of course, he told himself, why should it work? Why would the unit of a mile and the length of time of a second work? This test had been prepared so that any intelligent specie could pass it and not only people from Earth and those that were using the mile as the unit of distance at that. No it had to be a number that had no unit and that was universal. It had to be a constant.

By now, Nika and Verla were watching carefully what he was doing, both knew that he was in deep concentration and they didn't try to interrupt his train of thoughts by asking questions. All of sudden, Vincent saw something in the box that gave him a clue. The key was resting on a flat surface covered with circles of all sizes, it occurred to him that the number that they were looking for, probably had to do with circles. His heart then began to beat faster. Yes, there was such a constant based on circles. It was the constant 'pi'.

He could still remember from his high school years what his mathematic teacher had proven to the class one day using a length of string, a ruler and different cardboards circles. In fact he could still recall the words of his teacher saying - if you divide the circumference of any circle by its diameter, you will always get the same constant and the value of this constant is represented by the Greek letter 'pi'. That number ‘pi’ was an infinite sequence and thus it had an infinite number of digits after the decimal. Vincent still could see in his mind, how his teacher had written on sections of cardboard placed around the classroom, a couple dozens of digits after the 3 and the decimal representing the value of that constant. He now could even remember the first four digits after the decimal.

That value of ‘pi’ was 3.1416... but that did creat a new problem. What about the decimal? How could he represent a decimal in the sequence using only the ten buttons? He told himself that he would just forget about the decimal and press the buttons without bothering about the cumbersome decimal.

Beginning from the left, he thus proceeded to press the buttons in the sequence corresponding to the value of ‘pi’. Nothing happened. Could it be, he told himself, that he needed more than five digits? Vincent certainly hoped not since he didn't remember more than the five he already had. He therfore tried the same five digits but this time starting from the other end of the row.

As soon as the last button was depressed, he expected the note to stop but this time it persisted until he saw the cover of the transparent box slide slowly until there was just enough room for his hand to reach inside for the key.

By then both Nika and Verla seemed mesmerized by what they were seeing and neither of them could move or speak. The transparent key was much lighter than he would have imagined it to be. As Vincent slowly walked toward the proper door with the key held in front of him as if it was a trophy, both girls were eagerly following him.

Before inserting the key in its proper place he looked at Nika then at Verla, he had a very serious expression of apprehension on his face. Then before actually pushing the key into the proper receptacle in the center of the door, he told the two women to pick the two knapsacks as well as their weapons. Then with his riffle in his left hand, he slowly pushed the key into the hole. He didn’t have to turn it, the instant if was inserted properly, he heard a low humming then he felt the door vibrate and slowly it retracted into the wall.

( end of chapter 12)