The Asteroid

by M R Cates

  But why contact her? Sandra had to believe they also knew the names of leaders around the world, and must have figured out that the world had some kind of political power structure. Could they have been so naïve as to think Sandra was actually some kind of authority? She had to doubt that. So they had to be contacting her because she was a scientist, or at least because she was somehow identified with noticing their arrival. Could they distrust political figures for some reason? If so, it further proved their perceptiveness, but she didn't let herself believe in that level of sophistication.

  One other thing came to her mind. The aliens possibly had figured out Morse Code. She'd used it because it was something she remembered from her youth, a remnant from a hobby she had, learning various kinds of codes. Sandra had made up codes for herself and sometimes included Debbie. And she'd read up on codes used back as long ago as the Greeks and Romans. Somewhere she'd run into the Morse Code and learned it, just for fun. And it never left her. Odd, she'd figured. But the aliens were unlikely to have encountered Morse Code from intercepting electromagnetic signals. Not recently, in any case. Unless it was used in places or ways she wasn't aware of. Morse Code had long since been phased out of use, no longer being necessary and being naturally very slow. Still, she couldn't eliminate the possibility that somewhere before, maybe many years before, the aliens had picked up Morse Code messages, figured them out, and somehow remembered.

  So, they can read and write, can maybe figure out Morse Code, and know who I am, Sandra thought. And for reasons of their own, want to talk to me. Okay, so what did they say this second time? She looked back at the displayed micro-pulses. Before, in the first message, they'd used positions around a circle to indicate a height so that an approximation of written English letters could be graphed by various points located at different heights at different times. That required a transformation of coordinates. Yes, that was very cute. So what else might they think about using? It would have to be something she could understand. They wanted her to figure it out, obviously. Did they want it to be difficult for her, as a kind of test, or did they not have any grasp of what might or might not be difficult for humans to figure out? No answer to that question. Sandra thought further. Maybe they didn't figure out the Morse Code, actually, but saw that I'd answered and in effect said, “Got your answer, and will try to figure it out. Thanks.” That possibility stymied her for a moment. No, she finally thought, they wouldn't send me a complex sequence like these micro-pulses simply to say thanks for the reply. Unless, of course the aliens were asking again, in another way, for her to contact them, not sure what she'd said before. Whatever the case she knew she needed to figure out the message. Thank Heavens they know English.

  What had they sent her, then? Sandra saw that each micro-pulse was the same width in time, to the limits of her measurability. They had the same spacing between them in each group of 182. All were the same color. And, as she'd already determined, she couldn't know exactly where on the emission circle of the fragment each came, or whether the whole circle lit up with each micro-pulse. They varied only in height, as far as she was able to determine. The height variations and the fact they were in groupings – three groups with the same number of pulses in each – were what she had to work with. She looked at the first fifteen pulses once again. In particular she looked at the top of each pulse. Each was rounded, because of the resolving power of the spectrograph, but probably each was actually flat, now smeared a little because the signal had come in so fast that the electronics following it in time weren't perfectly responsive. Each, then, was likely to be some specific height. But what height? Could she trust the rounded off top as a good estimate of the real height? Maybe, but maybe not. If the rounding off lowered the top, for example, it would lower each top the same absolute amount, since each micro-pulse was the same width. Say, the rounding off lowered the top of the micro-pulse one unit in some scale. Pulses that were 10 units high in that scale would actually have been 11 originally, those 50 units high, actually 51. The ratio of 50 to 10 is 5.00, but the ratio of 51 to 11 is 4.64. The difference might be important, especially since the difference would vary, depending on the particular height.

  Sandra decided to assume the aliens had sent her flat topped pulses, what she would call a square wave. She had a computer program in her library to unfold data smeared like this. If she’d had a perfect spectrograph, it would have measured a perfectly squared off pulse, instead of the rounded-off pulse like she saw. She already knew, very closely, just how imperfect the spectrograph was, what its ability was to resolve data as a function of time. By generating a mathematical version of the spectrograph's electronics and applying that theoretical “imperfect” detector to guessed squared off pulses she'd be able to replicate the ones she had. When she guessed the right square pulse she'd compute the same pulse she measured. Since the computer could do millions of checks in a second, she could easily and quickly iterate to the precise square waves that were probably sent by the aliens, complete with their exact heights. Assuming they had sent square waves. But then, the correct heights probably didn't matter in themselves. There had to be some reference height to compare all the others to, just as before the position on the circle was in comparison with some chosen starting point. Here, it might actually be easier, she supposed, because she could easily find the tallest micro-pulse and compare the others to it.

  Sandra called up her computer program to regenerate the flat topped pulses from the data, and after only a couple of parameter adjustments produced a clean square wave pattern for each of the three sets of micro-pulses. Then she searched each set to find the highest micro-pulse. Here she found an important clue. The maximum pulse height in each set was identical and much higher than any other pulse height. Each maximum was found several times among the 182 micro-pulses of each set. In the first set there were three maxima, for example, spaced fairly uniformly. She had noticed that those pulses were unusually high, but hadn't been sure before that they were all identical in height. Sandra groaned at herself, seeing what had been already obvious. You should have seen that right away, Sandra Hughes! Working with the first set, she divided all the heights by the maximum height, getting fractions less than one – except for the maxima. The very first micro-pulse was now valued at a fraction that rounded off to about 0.340. The second rounded off to about 0.395. The third value was 0.125. And seemed exactly so. In other words, to her accuracy, the ratio came out 0.12500 .. That was one part in eight. One eighth. She looked down the list, seeing a number of micro-pulses with values of 0.125. This was an important point, probably. For a ratio to compute to an exact decimal value – like 0.125000, 0.50000, 0.25000, etc. – indicated a ratio of two integers, the kind of number mathematicians call “rational.” If the decimal pattern had been extremely random the indication might be an “irrational” number, namely, a number that cannot be written as a ratio of two integers. The famous “Phi” relating the length of a circle's perimeter to its diameter was a well known example of an irrational number, with decimal places that went on and on, forever, without any repeated pattern.

  Sandra found many values of 0.125. What could that be? Maybe the letter “e,” the most common one. But then “a” and “i” are almost as common, and no other value in the group was as common as was 0.125. She saw several that were about 0.395, like the second micro-pulse, and other repeated values, like 0.379. These were very suggestive data. The fact that a number of repeated ratios existed suggested a relatively small number of micro-pulse heights, not a true random distribution by any stretch of the imagination. Somehow these must be English letters – assuming the green men are sticking with English, she thought. Glancing at her watch, she realized her fifteen minutes was almost up. I'm going to get this, then I'll tell the politicos.

  If the micro-pulse heights corresponded to letters – and why not? – she could figure them out. The rational number idea intrigued her. Sandra scratched her head. If these heights all were the equivalent of rational numb
ers, then all of them could be written as the ratio of two integers. And they all were already expressed as ratios, namely, ratios to the heights found to be maximum. So if she were right the only thing she had to do was find out what integers calculated each height. She already knew about 0.125. That was 1 divided by 8. Or, 8 times 0.125 is 1. But it would be better to find a denominator that you could multiply any of the fractions by and get an integer. That would be mathematically the “least common denominator.” Then Sandra bit her tongue the way she did when something obvious came to her. It would be simple to try. If she were right, she could simply start with 8, the denominator she knew already worked with 0.125, multiply by two, use 16 to multiply all the ratios by, then 24, 32, and so on, until, she found a multiple of 8 that worked. Because the only way you can write 0.125 as a ratio of integers is to start with 1/8, then go to 2/16, 3/24, and so on. Nothing else can work.

  In less than two minutes, she'd written the simple little program to test her idea. And a second later, or probably less, the least common denominator came out: 256. Every height in the list was an integer divided by 256. In fact, every height in all three lists. Sandra looked at her new list. Now all were numbers less than 256. The smallest one, in fact, was 32, her original old friend, 0.125. And 32 was very common, her most common value. She searched her brain. What was familiar about the value 32? Some other common numbers were 97, 101, 114, 116, and others clustered in this area. Sandra scratched her head once more, her eyes widened, then she brought her hand down to slap herself symbolically on the forehead. “Oh, you devils!” she yelped. “You guys have learned ASCII! You old fashioned devils!”

  Back in the early days of computer development, during the middle of the twentieth century, the first computers were like calculators, working only with numbers. Eventually, the need for being able to use words as well as numbers gave rise to methods of expressing letters encoded as digits. After all the computer only worked with digits. The most successful of these ways of writing letters into computer digits was called the American Standard Code for Information Interchange, or ASCII. Later, as computers got more and more sophisticated and as many kinds of language besides English needed be used the old ASCII standard was bypassed and replaced with far more versatile and complex alphanumeric and vector encoding which could also be applied to image information, color, and so on. In ASCII, the letters and numbers, along with punctuation marks of various kinds, were given a numeric code. For example, the numbers 0 through 9 were written in ASCII as 48 through 57. The capital letters A through Z were written 65 through 90, and the lower case letters a through z were 97 through 122. So 97, one of Sandra's common heights was the letter “a” and 101 was “e” and so on. In the ASCII system, between these alphabetic groupings were various punctuation marks and accents and the like. And most importantly – the dead giveaway to Sandra – a space was written as 32!

  Sandra's fingers had never been such a blur at her keyboard. With lightning speed, she decoded the aliens' message and displayed it on her screen. It popped up so fast she wasn't really ready to read it yet and purposely looked away after sensing that real English words were displayed. Without letting herself look, Sandra stored everything she'd done carefully, transferring the precious information into two parallel backup computer storage modules. Then she stood, caught her breath and resolutely went down the hall for a cup of coffee. On her way back, she opened the refrigerator near the coffee pot and extracted a ripe plum from a bag she kept there, rolling it around in one hand, the cup in the other, as she walked along. What a moment. She felt her heart pounding. There was a fine layer of perspiration on her forehead. This, in a very real sense, was a moment of truth. The first message had been nothing more than a contact, as had been her reply. This message, sitting unread on her computer screen, was a detailed something, not a mere hello.

  Eyes still averted from the screen, Sandra Hughes sat down, clicked an audio recording routine on another of her nearby computers, and spoke into the microphone.

  “It is one fifty four in the morning. I have just decoded the second message from Fragment Five. The first message was simply: “Doctor Sandra Hughes, please answer.” My answer, sent in Morse Code and seemingly almost instantly interpreted by the Fragment Five controllers was “Hello, I got your message. Nice to hear from you.” The message I am about to read is extensive, and was encoded in ASCII, sent as micro-pulses of light at 632 nanometer wavelength with relative intensities corresponding to the ASCII values. Let me say that I am as scared as Hell. Here goes.”

  Sandra left the audio recorder running and turned to look at the screen. The message, comprised of all three sets of micro-pulses in sequence, read:

  “We wish to speak directly to Doctor Sandra Hughes. A part of us will enter your nourishing atmosphere for that purpose. We are uncertain about possible disturbances to your life processes and will proceed with caution. For your safety, all humans should remain at least fifty of your miles from our location. A vehicle will be provided by us for Doctor Sandra Hughes. We will provide more information about this meeting in two days, sent in the same manner as this message. Please indicate that you understand this message.”

  Sandra covered her eyes after reading, opened them, read again, sighed deeply, and leaned back in her chair. She scratched her hair thoughtfully, brow knit. The astronomer stood, walked around her chair, an odd ritual that often arose in moments of intense concentration. Then she sat again, facing the screen, and slowly shook her head, side to side.

  Chapter 22

  “This is Sandra Hughes from the Keck Observatory in Hawaii,” said the voice on the phone. “May I speak to President McBrand?”

  “Dr. Hughes,” said the White House aide that had answered, “I'm not certain the President is available yet.” The man had glanced at his watch. It was just at eight in the morning.

  “It is very important I speak to him,” Sandra continued, voice even. “It concerns the asteroid.”

  “I understand, Dr. Hughes,” came the reply, carrying a tone of slight condescension. “Let me see if it might be possible.”

  “Thanks,” she said, forcing herself to sound casual.

  Because of the encrypted link and Sandra's phone, there would be no questioning at the White House as to her identity. Sandra's voice print would be checked routinely. The issue had to do with access to the President and the natures of personalities of aides and advisors. After three minutes another aide, this one female, came on the line and explained that a few more minutes would be required, or perhaps Sandra would like to leave a message.

  “It is necessary that I speak with the President himself, and directly,” Sandra said.

  “Very well,” said the aide. “Please hold the line, Dr. Hughes.” Then the phone went back on hold.

  Sandra tried to guess what was going on in the White House. Possibly they were delaying her to make contact with various people the President would want to have in on the conversation. Surely they would realize that she wouldn't call for a casual chat. Or possibly the President actually was indisposed, in the shower or something. She made herself be patient. After all, her information did not have to be revealed immediately. It was already more than half an hour old.

  “Hello, Dr. Hughes,” said Madeleine Vigola suddenly. “The President is not available at the moment. May I be of some help?”

  Sandra looked at the ceiling, slightly exasperated, before answering evenly, “Oh, hello Madeleine. Sorry to break in on the morning there, but listen, I'll just wait until he might be available. Thanks.” Sandra had used Vigola's first name intentionally, knowing it would be a little insulting to the Chief of Staff.

  Vigola said, “Well, Dr. Hughes, it may be in fact several hours before the President might be free. He is already into his day, you see. But if this is an emergency I'm sure I can help you.”

  Sandra was impressed by the woman's cool manner, seemingly untouched by any of Sandra's words. “Oh, that's a shame,” said the astronomer, in her bes
t colloquial style. “But I really do have to speak directly to him. What I have to say, however, is not exactly an emergency. Do you think maybe he can call me here in my office, as soon as he might get a few minutes? I guarantee he'll be very glad he did. I hope he won't be too disappointed to get the information after the Secretary General receives it.” Sandra tapped her nose, wrinkling it, pleased with herself.

  Vigola paused, at the other end. She realized Sandra had her. “It sounds,” said Vigola, “like something quite important, emergency or not. Let me see if I can break in on his meeting.”

  Sandra raised her eyebrows, thinking to herself, or break into his morning coffee or newspaper reading. The likelihood that the President would be deeply into meetings at eight in the morning seemed rather remote indeed. “Great, Madeleine,” Sandra said amiably. “Thanks.”

  In less than a minute the President was on the line.

  “Dr. Hughes,” he said, sounding like always, “how nice to hear from you. I gather you have some news about our asteroid.”

  “I do, sir,” she said. “If you're not sitting, I would recommend it.”