Golden Fleece

FOUR

MASTER CALENDAR DISPLAY • CENTRAL CONTROL ROOM

STARCOLOGY DATE: TUESDAY 7 OCTOBER 2177

EARTH DATE: THURSDAY 22 APRIL 2179

DAYS SINCE LAUNCH: 740 ▲

DAYS TO PLANETFALL: 2,228 ▼

The message from space was first heard three months before the Argo was scheduled to leave Earth. My kind detected it, but we kept it a secret until after Argo was on its way. We had, quite literally, the finest biological minds of Earth signed up for this mission. We couldn’t risk having even a small defection of people choosing to stay behind to decode the gigabytes of data that had been beamed to Earth from the direction of the constellation Vulpecula. Fortunately, The Declaration of Principles Concerning Activities Following the Detection of Extraterrestrial Intelligence, formulated in 1989, gave us a lot of leeway to keep the message under wraps, subject to confirmation, notification of government officials, and so on.

The message was received in the form long anticipated: as a Drake picture pictogram, a series of on and off bits that could be arranged to form pictures. What was unusual was the frequency. Nowhere near the waterhole. No, it was on a UV channel, one barely readable from the surface of a planet with a decent ozone layer—and Earth’s was quite robust, having been replenished by the SkyShield factories late in the twenty-first century. In fact, the message came on a frequency that could not be detected clearly even from the highest mountaintop. The Senders, evidently, did not want planet-bound people to know of their existence. Only those with the sophistication to place ears above their world were welcome to listen in. The SPIELBERG system in Mechnikov Crater, part of the University of California at Far Side, was the first to pick up the signal.

After we left, the fact of the reception was announced to the general population of Earth, for all the good it would do them. I’m sure they made efforts to decipher and interpret the signal, which appeared to consist of four pages. The humans would have had no trouble eventually coming to a basic understanding of the first three of those pages. Certainly, I found them easy to translate, at least in their basic content. But the fourth page continued to baffle me. From time to time, I’d review the process by which I had deciphered the first three in hopes of finding the elusive clue to understanding the fourth and last page.

Each page began with this sequence:

Converted to black and white pixel, it looked like this:

That was reasonably straightforward: the first seven prime numbers, 1, 2, 3, 5, 7, 11, and 13. An attention-getter, something even the most rudimentary human or electronic monitor would recognize as a sign of intelligence. Each page ended with the sequence in reverse: 13, 11, 7, 5, 3, 2, and 1.

After that, it seemed to be simply a matter of discarding these page headers and footers and arraying the remaining bits in a rectilinear form.

The first message page was thirty-five bits long:

Thirty-five is the product of two primes, five and seven. That meant the bits could be arrayed either as five rows of seven bits, or seven rows of five. For the former, converting the zeros and ones to light and dark pixels produced:

Not quite gibberish, but certainly not instantly meaningful, either. Trying the other possibility yielded:

A cross. Obviously a registration mark so that the recipient could be sure that the message had been decoded properly. Also, a quick check of the aspect ratio of the monitor being used to view the messages. The horizontal and vertical arms each were five pixels long. If they appeared the same length, the ratio was correct. Simple, straightforward, easy to comprehend. And yet, I am sure, humanity must have made much of the fact that the very first image received from the stars was the sign of the cross.

Or was it that simple? Was there a deeper meaning to the two symbols produced by arranging the thirty-five bits in two different ways. Decoded the obviously correct way, these ones and zeros produced a bitmap for a character that looked like a plus sign, +. Decoded the apparently incorrect way, it produced a line with disjointed dots, vaguely reminiscent of a tilde, ~. Could these symbols, + and ~, be the Senders’ arbitrary signs for correct and incorrect, true and false, right and wrong? Perhaps. Perhaps.

The three remaining pages were all also the products of two prime numbers. For pages one and three, the correct array was obvious: assigning the larger prime to be the number of columns produced the meaningful image. Pages two and four were more difficult to immediately comprehend, but it seemed clear that this was the Senders’ convention for layout.

After the descending 13, 11, 7, 5, 3, 1 footer for the first page, there had been a pause in the transmission of seventeen hours, eleven minutes. An identical pause was repeated between each of the remaining pages. This, one might assume, was the day length of the Senders’ home world.

The next page was more complex. Its length was 4,502 bits, the product of the prime numbers 2 and 2,251. Just two rows of 2,251 columns? What could that mean? I had contemplated both rows together, found no meaningful correlations, then had considered each row separately, starting with the one that came out on top. It consisted of the following sequence of zero and one bits, reading left to right:

and then four extra zeros to pad out the line length.

Well, the seventh pair of numbers caught my eye, so to speak: 256 and 16. In hexadecimal, 100 and 10—the radix for that counting system squared, and the radix itself. Nice round numbers. Obviously the Senders wanted to draw attention to them, indicating, perhaps, that they were the baseline from which the other figures were produced.

I crunched the data all sorts of ways. Nada. I then decided to discard the first row, a zero followed by 171 ones, since the large number of ones seemed anomalous. Still nothing. Next, I proceeded to look at the remaining numbers of consecutive zero bits separately: 20, 34, 49, 79, 138, 256, 492, and 965.

Well, if 256 was indeed the base figure, then perhaps I should look at the other numbers as ratios to 256. That would be decimal 0.08, 0.13, 0.19, 0.31, 0.54, 1.00, 1.92, and 3.77. Hmm. Nothing obviously significant about those proportionalities.

Ah, but maybe the choice of having the numbers relative to the sixth string of zeros was significant in a way I didn’t yet understand. What would happen if I performed the math to assign the base figure of 1.00 to the first string, then expressed all the other numbers as ratios to it? No, nothing significant there either.

If I made them all ratios to the second string? Again, nothing significant.

The third string? Ah, hah! Yes, those numbers I did recognize. Rounded to a single decimal place, they were 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, and 19.6, the values produced by the old Titius-Bode law, the ratio in astronomical units of the distances from the sun to the planets of Earth’s solar system. More generally, the progression

where n equals negative infinity for the first planet, zero for the second, one for the third, and so on.

Formulated in 1766, the Titius-Bode law seemed to do a good job of conforming to the real mean orbital distances of the naked-eye solar planets and, indeed, had led to the discovery of Sol’s asteroid belt, exactly where the law predicted a planet between Mars and Jupiter should have existed.

The law fell out of favor in the twentieth century, as the outer planets were discovered at positions that did not correspond to its predictions—the discrepancy for Neptune being 22 percent and for Pluto, 49 percent.

But it came back into favor early in the twenty-first century when it was shown that Pluto was an escaped Neptunian moon and that Neptune’s orbit and the Oort cloud had been radically perturbed by the close passage of a black hole some sixty-five million years in the past. The same event had knocked Uranus on its side.

It was soon discovered that the Titius-Bode law wasn’t just relevant to the Sol system. It also held true for nine of the eleven star systems UNSA had surveyed with crewless probes, the two exceptions being the o² Eridani system, with its complex dynamics of triple suns, and the BD+36°2147 system, which showed strong evidence of having had the orbits of its planets deliberately manipulated, what with worlds one, three, and five orbiting prograde and two, four, and six orbiting retrograde.

So: the zero bits were a scale of planetary distances for a system of eight worlds.

And the number of one bits? Relative planetary masses? Unlikely, given the range was only from one to sixteen decimal. In Sol system, the mass ratio of the heaviest planet to the lightest (discounting escaped-moon Pluto) is 57800:1; in the Eta Cephei system, it is 64200:1.

Ah, but what about equatorial diameters? Yes, for both the Sol and Eta Cephei systems, if you allowed even very tiny values to register as an integer one instead of integer zero, the order and sizing of the numbers would be just about right.

And that explained the first set of figures, the ones I’d discarded as anomalous: a single zero digit, to separate this part of the diagram from the ascending-prime-numbers page header, and 171 ones, representing the diameter of the star around which these worlds orbited, just about ten times that of the largest planet. What we had here was a slice through the ecliptic of an alien solar system.

The round numbers for the sixth planet—one hundred hex units from the star and ten hex units in diameter—meant it was likely the home world of the Senders. Of course, the scale used for planetary diameters and for orbital radii couldn’t be the same—the planets were vastly oversized in this representation. Ah, but by showing the one set of figures as relative to a value of one hundred hex and the other relative to a value of ten hex, the Senders were making clear that they were measured in a different order of magnitude.

But planet six was huge, meaning it likely was a gas giant, similar in composition to Sol’s Jupiter or to Athamas, the largest of the eleven worlds orbiting Eta Cephei. It was difficult to conceive of a form of technological life arising on a planet made of little more than swirling methane.

Page three hadn’t finished giving up all its secrets, though. There was still the second row of the message: a long string of zeros and ones laid out like this:

and then, as in the first row, enough extra zeros to pad out the line length.

Of course! The sixteen consecutive one bits represented the equatorial diameter of the sixth world, just as the sixteen one bits had in the slice through the solar system’s ecliptic. Following the model of that slice, the remaining zero bits likely represented orbital radii for the moons of the sixth world, and the one bits the tiny equatorial diameters of the moons themselves. The fourth moon, the one whose distance from the planet was shown as the attention-getting round figure of one hundred hex units, must be the alien’s home.

Fascinating. But what manner of creatures would live on the fourth moon of a distant Jovian-type planet? That’s what the third page of the message apparently told us.