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TIME: 10.5 million years in the future.

PLACE: Outer space, aboard an alien cosmic-junk retrieval vessel tasked with clearing the inter-planetary pathways of debris and derelict spacecraft.

SCENE: Along a corridor of their vessel. aliens Alpha and Beta encounter each other.

ALPHA. Hey, Beta! The retrieval crew just tractor-beamed aboard another spacecraft of unknown origin. Delta tells me this one also has some kind of cultural-artifact recording on it.

BETA. Not again! That makes it five so far this month. I hope this one won't be as undecipherable as the others because something important was left out. They all try so hard but come just short. Well, maybe we'll be lucky this time. Let's go take a look.

ALPHA. Delta's already waiting in the quarantine bay. (Both exit.)

SCENE: The quarantine bay, where the spacecraft known to the long-vanished civilization of Earth as Voyager 1 is being disassembled for examination by various alien specialists. On prominent display is the spacecraft's gold-plated LP recording containing music, voices and images from Earth.

BETA (admiring the disc). Well, well. What have we here? Yet another gold-plated copper disc with a continuous engraved information track.


The Sounds of Earth Record Cover - GPN-2000-001978



612px-The Sounds of Earth - GPN-2000-001976


DELTA. Yeah, that's why I wanted you two to come down here, you dudes being analog-recording buffs and all. It's funny how vastly separated cultures always use such a primitive solution to the ultra-long-term space archiving problem.

BETA. Analog recording is extremely primitive I admit, and not of the greatest fidelity. But for preserving signals for a very long time in outer space, it's hard to surpass an engraved-metal information track, especially one coated with corrosion-resistant gold.

ALPHA. The disc itself will withstand the physical stresses of the launch process and there are no carbon-based chemicals or plastics that degrade with temperature extremes, time, radiation exposure or from the occasional chemical gas cloud the spacecraft may pass through. In space, a metal disc's information content will last essentially forever as long as the information-containing surface remains intact and unscratched.

DELTA. Yeah, Retrieval Services got your memo on how not to grapple a spacecraft on board after those previous discs they scratched. I wonder why everybody puts their precious cultural heritage recordings on the outside of their spacecraft?

Vgr 0002


Vgr 0001


ALPHA. To make sure we don't miss them?

BETA. Not likely. They must realize that anybody capable of retrieving derelict spacecraft spacecraft would also want to look inside and would be capable of doing so. Just like we're doing now. No, I think they're on the outside because it makes for better pre-launch publicity images.

DELTA. Speaking of images, the cover of the disc has some images on it. I bet they're there to help us decode the information groove on the other side, just like the last two derelicts we picked up.

ALPHA. Yeah, it looks like the circles on the lower right are yet another version of the hydrogen resonance frequency intended to give us basic time-period and distance units. Frankly, I'm getting a little bored by the lack of originality here. It's high time that one of these discs used some other time unit than 0.7 nanoseconds and some other basic distance unit than 21 centimeters.

737px-Voyager Golden Record Cover Explanation.svg


BETA. All the spacecraft we've picked up recently have used those units derived from the hydrogen resonance-frequency while ignoring other potentially useful elements, like the cesium we used in our primitive atomic clocks. You remember that hydrogen-chauvinism greatly hindered our first attempts at detecting interstellar radio transmissions. Our scientists came up with all sorts of arguments as to why we should be looking for transmissions at the hydrogen resonance frequency. Boy were they wrong.

DELTA. Especially when it turns out that the first alien transmissions we detected were at frequencies useful for normal planet-centric communications that happened to “leak” out to interstellar distances. What was the name of the planet with those first signals?

ALPHA. Hold on and I'll look it up. That was millions of years ago and I'm terrible at ancient history. But I do remember that the first things we picked up were the radio distress calls of a water-ocean ship called the Titanic. Yup, the archival database confirms that its inhabitants called it Earth.

DELTA. Ah yes, Earth. I wonder if the spacecraft we have in pieces in front of us came from there?

BETA. I'm ahead of you. I just ran that spikey pulsar map on the disc through the stellar-cartography database and the spikes triangulate best to the archival coordinates we have of Earth, or at least to the general area that Earth was in when its transmissions petered out and the Earthlings probably went extinct.

ALPHA. Since it's a pulsar map like we've seen before, I trust what looks like binary numbers are the pulsar rotation rates measured in hydrogen-resonance time units and that by comparing the rotation rates labeled on the disc to what those spinning stars have slowed down to now we can deduce when the spacecraft was launched.

BETA. Exactly! I see the stellar-cartography database has returned a launch date of around 10.5 million years ago give or take few tens of thousands of years.

DELTA. Wow! That makes this spacecraft the second oldest object any of our spaceships has picked up. This one is definitely going into a museum. Now I'm doubly glad I called you two down here since full and accurate decoding of the disc's information track must now take top priority.

BETA. Like I told Alpha right before we came down here, that depends on whether the Earthlings provided enough information for us to do the job. Let's take a closer look.

DELTA. I see that the Earthlings have provided binary numbers for the rotation rate and a diagram of the rotation direction of the disc. At least the binary numbers for the rotation rate don't seem to have been damaged like on that disc two derelicts ago. Funny how a nick that looks like a binary “one” can easily double or quadruple the recommended playback speed.

ALPHA. That's the danger of using ultra-simplified sans-serif-font symbols for your number system. One nick masquerading as a digit can throw all the numbers in the diagrams completely off. It took our scientists more time than it should have to figure out the correct rotation rate for that one.

DELTA. It looks like the Earthlings have also provided a stylus transducer [i.e. phono cartridge] for the groove on the back of the disc. That's rather thoughtful of them, though I'm pretty sure the laser playback system we have in the xeno-engineering department can also easily play this recording.

ALPHA. The transducer seems to be of the piezoelectric [ceramic] variety with a diamond stylus.

BETA. A ceramic stylus transducer is a good engineering choice, since a more complex design like the moving-magnet or moving-coil cartridges audiophiles of old used to debate about usually contain flexing plastics [elastomers] to restore the stylus position and those probably would degrade in space after a few thousand years, let alone a few million. But do you see any information on whether any recording pre-emphasis is used? If it is, we need to generate the necessary de-emphasis frequency response curve.




ALPHA. Alas! I see no indications of that here.

BETA. Have the Earthlings left this off their craft?

ALPHA. They could have written down the necessary specs.

BETA. In the basic time units they themselves had specified.

ALPHA. Alas! But these are lacking too.

BETA. We cannot ever get the necessary frequency response!

ALPHA. Hi-fi playback now may be impossible.

BETA. Just one test tone would mean we could succeed.

ALPHA. Perhaps the Earthlings have provided such a tone.

BETA. I see no waveform of such signal on the disc.

ALPHA. Alas! We may not get the audio we want.

BETA. The eternal gods are arrayed against our quest!

DELTA. Enough with the short-phrase stichomythia already! You audiophiles get so over-excited about these things. But since you raised the issue of calibration I wonder if there's enough on the disc for proper decoding of the images. I can see a scanning-pattern reconstruction diagram like others we've encountered. And unlike a couple of the others, the Earthlings seem to have provided a reality-check test pattern of a circle.

ALPHA. Yes, but is there a test pattern for image gamma?

DELTA. Are you talking about that cute assistant to Captain Omega?

BETA. No! He's referring to the way image data is interpreted when turned into an image on a display. It effects the perception of brightness and contrast. Without playback gamma matching the inverse of the recording gamma, you'll get shifts, particularly in darker portions of an image, that may make some items in the image invisible.

ALPHA. I once saw a demonstration of this effect in one of the ancient LCD televisions in the Central Technology Museum. Adjusting its gamma control greatly affected what the image looked like. Hopefully there is an image that can be used to determine proper image gamma.

ALL THREE. We now look to our labs to tell us if we have the signals that we need!

(Pause, during which it is understood that the ship's labs have returned a full report of the disc contents.)

(Enter Messenger from the labs.)

MESSENGER. The labs have determined that there is no test tone among the audio signals recorded on the disc that will enable accurate determination of the de-emphasis frequency response necessary to undo any pre-emphasis applied during recording. The labs, if directed, could attempt to determine such a frequency curve by the studying the spectra of all the sounds on the disc, making guesses as to each signal's original frequency balances and by averaging the resulting differences to produce a composite estimated de-emphasis curve. But without knowing for sure the original frequency content of any of the audio signals—as would have been provided by, for example, a 20 Hz to 20 kHz frequency sweep test signal and its corresponding waveform being illustrated in the disc “instructions”—such efforts are limited in their ultimate accuracy.

A similar problem arises with the determination of a suitable reproduction gamma for the image signals, and if there is indeed only one suitable gamma setting for all the images. While there is a geometrical reality-check test pattern (the circle depicted in the engraved instructions), there is no test image provided that would provide an accurate determination of the encoding gamma, or gammas. Hence we will always be guessing as to exactly what the images were supposed to look like, even to the Earthlings who created them! (Exit Messenger.)

ALPHA. It is just as we feared. The Earthlings encoded their precious cultural legacy using encoding conventions not completely and accurately explained by the decoding information they provided. And this is on what is likely to be one of the longest lived artifacts their planet ever produced. We've seen this before and it's always sad, very sad.

BETA. I agree, unfortunately. Even in our much more advanced age some basic aspects of signal encoding are so deeply embedded in the technology as to be almost unnoticeable to even those familiar with that technology. Encoding standards for things like gamma, color and audio pre-emphasis are derived from a combination of basic physical and biophysical principles combined with agreed-upon engineering conventions. And both the basic principals and the engineering conventions should be explicitly transmitted in order for us to decode the signals correctly.

ALPHA. Gimme that stylus transducer, I'm going to analyze it to see if it can answer at least some of our audio questions. (Alpha starts running out of the quarantine bay.)

DELTA (calling out after him). Careful where you run with that thing!

BETA (also calling out). Yeah, you might trip and poke your eyes out!

(Exit Beta and Delta to music selected from among the tracks recorded on the Voyager disc, but with the bass greatly rolled off and the treble greatly boosted, creating the grossly bass-shy and overly sibilant hissiness of an LP recording played without de-emphasis.)

Scholarly notes:

 1. Timothy Ferris, original producer of the Voyager discs, confirmed to me in an email that the phono cartridges carried by the Voyager spacecraft were of the piezoelectric (ceramic) variety. There is speculation on the Web that NASA custom made them, which I find unlikely due to time, cost and expertise limitations. Jon Lomberg, who worked with Frank Drake on the image portions of the disc, told me in an email that the make and model number of the cartridges are buried somewhere in his (Lomberg's) papers, which are in storage. At least this pretty much nails down the cartridges' commercial origin. In another email Lomberg estimates that each cartridge, which is shielded from such things as dust impacts (unlike the instruction-surface of the disc cover) might last as long as a billion years! While a stylus assembly might well endure for ages, let's hope the plastics widely used in the housing and other ares of a phono cartridge also hold up that long—or that the aliens who find the discs have perfected non-contact groove-recording playback systems, unlike the Earthlings who are still struggling with that problem. 

 2. Ferris, in the same email mentioned above, said: "We used RIAA equalization. Otherwise we'd have to had to equalize the recording in advance to make the bass playable. We felt that the RIAA curve could be induced from the data, if it came to that." What I've tried to show here is that reverse engineering a pre-emphasis curve is difficult without at least one suitable reference signal. A single constant-level sine-wave frequency sweep of a few seconds would have sufficed.

3. The Colorado Video system used to encode the Voyager images was not patented. Nor is there enough technical information about the system available on the Web for me to draw any conclusions as to whether anybody involved in the process thought about image-gamma issues. The list of the images on the Voyager discs includes no gamma test pattern nor do any of the real-world images I've seen easily lend themselves to such a function. There are similar issues of untransmitted encoding assumptions revolving around the reproduction of the color images on the Voyager discs. I'll talk about these in my next posting, because such encoding issues will still be relevant in the next proposed attempt to send a recorded cultural time capsule. 

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PayPal's recent accidental crediting to the account of one Chris Reynolds of $92,233,720,368,547,800.00 (that's more than 92.2 quadrillion dollars, in scientific notation $9.22 x 1016) attracted worldwide press attention. The Huffington Post was probably not alone in using "astronomical" to describe the sum. And indeed, if you could travel one mile with each of those dollars, your trip would reach 15,689.7 lightyears, a little more than halfway to the center of our galaxy. And if each of those dollars were a year, Reynolds' number (not to be confused with Reynolds number) would be 6.7 million times the present age of our universe (13.77 billion years). If you spent one Reynolds dollar every 5 seconds since the Big Bang you'd still have around a half quadrillion left, almost enough for a down payment on a studio apartment here in New York City.




Even the tired old analogies give impressive results. A stack of 92.2 quadrillion dollar bills, each dollar being 0.0043 inches thick, would be 6.26 billion miles high. That's 67.3 times the distance between the Sun and Earth (that is, 67.3 astronomical units or AU). That stack of dollars would reach way past Pluto into the orbit of the dwarf planet Eris. A beam of light would take 9.33 hours to travel from one end of the stack to the other. Amazingly, the lowlyand at $865 million ($8.65 x 108), far less expensiveVoyager-1 spacecraft, launched in 1977, has gone nearly twice this distance (around 126 AU) and has just left the Solar System (or not, depending on how you interpret the data we're getting). If instead of making a stack of bills you placed each dollar end to end, light would take 555.3 days to travel from the first to the last bill since they would extend to 1.5 light years. Impressive as that sounds, it isn't even halfway to the next nearest star (Proxima Centuri at 4.24 light years). I'll have more on Voyager-1 and its attached LP record in a future post.


Considered as actual currency, $9.22 x 1016 is way more dollars than have ever been, anywhere in the Solar System. And since it's quite unlikely that any aliens are using units called "dollars," by extension PayPal's accident is more dollars than have ever been on any class-M planet in the Alpha Quadrant (to lapse into Star Trek terminology) or indeed on any planet in the entire Milky Way. And this very likely holds true all the way up the scale of cosmic structure, to the Local Group (of galaxies) up through the Virgo Supercluster and all the way up to the entire observable universe. PayPal's mistake is 18.4 times the $5 quadrillion total value of Earth, so $92.2 quadrillion is pretty much an impossible figure to obtain by any conceivable financial transaction on Terra Firma. This alone should have set off alarm bells at PayPal.


PayPal Destiny


Maybe an examination of Reynolds' number itself might provide some clues as to what went wrong. I'll ignore the fact that his PayPal account statement was in both dollars and cents, and I'll just discuss the whole-dollar amount, which is a 17-digit base-10 integer. There is no obvious pattern in the digits, as if somebody were typing in a phone number to spell out a message. And I also find it unlikely that those digits were obtained by somebody accidentally leaning on a keyboard. The chance of a computer coming up with this number at random is at best 1 in 92.2 quadrillion; you are around 5 billion times more likely to win the PowerBall lottery. Then again in both cases the odds might be considerably improved if the random number algorithm has been subverted by the NSA (more on them in another upcoming post). [Yo! NSA compuers scanning this! Sup in Fort Meade?]


Examining the number as a number and not merely a set of characters, it ends in zero and so is even and not a prime number. But discovering its prime factors using web-based tools is tricky since some of the on-line prime-factor calculators that come at the top of a Google search for can't handle 17-digit numbers. And at least one of the calculators seemingly accepts 17 digits but then gives an incorrect answer. Factoring large numbers is inherently difficult, a fact that is taken advantage of by cryptographic systems in widespread use. Appropriately enough, the first correct factorization I got (2 × 2 × 2 × 3 × 5 × 5 × 7 × 21960409611559, a disappointingly dull result) was obtained from a Java applet that uses some of the same "elliptic-curve" techniques employed by modern cryptosystems, including some using algorithms approved by the NSA.


Humans can get all excited about prime numbers, but typical computer hardware could hardly care less (though it's a safe bet that the NSA's codebreaking processors do care, a lot). All that the circuits know about are voltage levels signifying binary numbers, prime or otherwise. Pehaps conversion of Renyolds' number into binary digits might prove enlightening: 101000111101011100001010001111010111000010100011111011000. Or maybe not. Lets try the even more geeky hexadecimal (base-16) notation often used by programmers, where 0 to 9 decimal equals 0 to 9 hex, and 10 to 15 decimal is A to F in hex. Decimal 92233720368547800 = hexadecimal 147AE147AE147D8.


Wow, a pattern! (In retrospect, you can detect it in the binary.) Let me quickly point out that this pattern is not nearly on the transcendent level as the numerical revelation at the end of Carl Sagan's Contact (the novel, not the movie). At least I don't think it is. It could be nothing but a coincidence (remember I ignored such possibly relevant factors as the digital representation of cents). Nonetheless, duplicating bit patterns, or moving them from side to side within a binary number, is something digital computers can do easily, since such functions are literally built into the fundamental instructions of a computer (the processor's microcode). So a Reynolds-type error could come from a programming error or even a circuit error caused by the processor or memory chips being hit by subatomic particles from a nuclear decay or from cosmic radiation. Or perhaps the number was mistakenly shunted to Reynolds' account from a buggy version of the recently-launched Pay-Pal Galactic system, which will enable off-planet transactions (including paying for travel on PayPal's retro-looking space ship pictured above) and which probably should allow transactions into the quadrillions. This would be especially important when buying and selling whole planetsand when dealing with the Ferengi.


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