On Digital Extremities


More scientists.

It's always scientists who discover this kind of stuff.

"Are you looking at this? Mike?"

Professor Mike Murphy put his glasses on and squinted down from his vantage point on top of the domed roof of the forty-foot Medium Preonic Receiver, putting a hand out on a handrail to steady himself. There was still enough sun that he could clearly see the gazebo, the array of consoles plugged in semi-permanently underneath them, and even the screen his associate was pointing at, but he had difficulty making out what it was on the screen she was referring to.

"Yeah, but I can't see it. Is it working?"

"It had better be, for this much money," said (Jo)Seph(ine) Baird, who had astoundingly long hair and half a PhD. It had cost one point eight million pounds to build the MPR (and the same again to build its Transmitting twin brother in New Zealand), and they had both been nominally "fully built" for four months. Seph and Mike were among the eight physicists still on the UKAPL site, frantically trying to get their receiver working for the evening's experiment before it became too dark to see which nuts and bolts to turn. A-LAY communications were still at the literal nuts-and-bolts stage. "It's working weirdly. You see this jumping bit here? There?"

"No, I don't."

"Well come down and look, Mike."

"Is it worth it? I spent long enough getting up here and I don't have as much knee cartilage as I used to." Mike was sixty-three.

Seph sighed. "I'll describe it to you and you can tell me what you think. All the regular telltales are at nominal levels except ψ which is edging into amber. The irregular telltales are all amber. There's one red thing which I don't know what it means..."

"That's there because I'm still up here with the lids on the GEWR units open." Murphy disappeared from view for a while, then reappeared, eclipsing the setting orange sun. "Now?"

"Green. Great. But I still have this jumping thing on the M-squared-B graph."

"Is it jumping pretty regularly?" Seph nodded. "Under the console you're standing in front of there are a few knobs. Can you find the two that read 'X-scaling'? Fiddle with them until you can get the wave to stand still and then tell me the frequency."

Seph did so. This took long enough for Mike to fold his arms and lean on the railing, taking in the view briefly. The United Kingdom Advanced Physical Laboratory was in a reasonably undisturbed region of Lincolnshire, next door to a stately home on a hill which belonged to the National Trust, and which was lit a rather dazzling orange by the sunlight. An amateur photographer, Mike had already photographed a good quantity of the MPR's construction, for an unofficial record, but this was the first time he had seen the stately home illuminated so. He decided it would be worth the effort to fetch his camera. Despite himself, he headed for the nearest ladder and began to climb down.

"One hundred and ninety-five meg— no, terahertz. Mean anything to you?"

"Carrier signal, then. That must be NZAPL."

"That's what it looks like? They've started transmitting already?"

Halfway down the ladder, Mike Murphy checked his watch and mentally added twelve hours. It was heading for 8am in Gisborne. "They're over an hour early. Get them on the radio."

Seph was fiddling with the bulky radio handset as Mike stepped with care down onto the grass. He joined her under the gazebo and collected the old, worn case containing his camera from a pile of other boxes and backpacks of equipment. "I'm going to take a photo of the sunset."

"Mike," said Seph as he was about step onto the ladder and climb back up again. "Firstly, I thought you were having knee issues?" Mike grinned, and started to respond, but Seph interrupted him. "And secondly, NZAPL says they haven't turned on yet. They're still in pre-warm."

Mike stared blankly at his associate.

A-LAY communications had started out as a set of problematic particle accelerator observations and an equation which had been constructed to, if not explain, then at least account for them. To the dismay and annoyance of almost everybody who understood it, this equation had proved no less problematic than the observations: it had a leftover term, an extra "+δ" on the side which shouldn't have been there. The delta, though small, proved troublesome from both a mathematical and a physical standpoint, for, as the newly-discovered equation was installed into established ones, the delta grew and morphed and squared and never completely vanished and generally made a nuisance of itself without ever saying anything useful.

Constructing and implementing mathematical tools for dealing with the delta almost became its own minor field of study. Then, unexpectedly, a group of four mathematicians, Murphy among them, had pulled some magic out of the air and showed that the existence of the delta actually had some major implications. Real-world implications.

The mathematics was much, much too complicated for the layman, but P. Hood, A. Kosogorin, M.X. Murphy & J. Zhang's Generating Waveforms in Ambient Neutrality (2002) described it as a space which ran parallel to reality, like two water pipes running alongside each other underground. In theory, you could build machinery, real-world machinery, to "tap" on the other pipe, sending signals along it in both directions. In theory, you could send messages around the world; in fact, since the Ambient Layer was theoretically empty of physical obstructions, you could send messages through the world. And light speed in the Ambient Layer was unimaginably faster. It was actually less like a water pipe and more like a phone line; a phone line nobody was using, which could easily be tapped into.

To their credit, nobody involved in the study had immediately announced to the world that supralight "radio" would soon enable cell phones to operate under mountains and space probes to communicate with home in real time. The future had failed to arrive frequently enough for that to be a clear mistake. Instead, UKAPL had been quietly formed, had bought some land and had started to build something which looked rather like an upside-down radio telescope - a receiver for A-LAY communications, aimed directly at its transmitting twin in New Zealand, through the body of the Earth itself.

"We're receiving signals but they haven't started transmitting yet?"

"Zed says they can't be. Half of their stuff is still unplugged from last night."

Mike frowned, and walked across the grass and down some concrete steps to a door set in the bottom of the domed MPR structure. Opening it, he was able to crouch and see into the very wide circular room under the MPR receiver, in the centre of which most of the actual receiving equipment was stacked. Six more technicians were in here, fiddling with various bits of the scenery. The room was brightly lit, the ceiling semitransparent, and the walls all painted white, but, being partially underground with no real windows to speak of, it was nevertheless claustrophobic and Mike avoided going in if he could manage it, opting to be the designated Man On The Roof wherever possible. This was most of the reason why his knees had been giving him grief lately.

Mike sat on the steps just outside the door and said "Folks, we're receiving, anything to do with you?"

"We connected the last few dots up just a few minutes ago," said Dr Philip Hood, a bearded fellow with very thick-rimmed glasses who was almost as old as Mike. "We haven't tested anything yet but... Hugh?"

Hugh - fantastically short, dark-haired, side parting - didn't bother looking up from the panel he had two multimeter probes wedged inside. "We haven't tested every link in the chain yet but in theory it could be receiving already. Have NZAPL started early?"

"That's the thing, they haven't."

"What are we picking up? Static?"

"Sinusoidal wave on the M-squared-B range. I just thought it might be a test you guys were running."

Hugh pulled all his tools out of the panel he had been working on. "Nobody's been working on that part of the system. And there's nothing foreign in the sequence at all now. It should be running uninterrupted. If it is running."

"Check the GEWRs," said somebody else. There was a little laughter - it had become a running gag that any fault in the system was always instantly blamed on the most remote and annoyingly difficult-to-reach part of the Receiver, because everybody knew how much fun Mike Murphy had getting up and down the ladders each time. But this time around it also happened to be a valid suggestion, so Mike nodded, picked up his camera, hauled himself to his feet and headed back to the ladder.


An hour passed. Mike took his photograph, but the UKAPL team failed to find any kind of fault in their equipment and the NZAPL team continued to insist that they had not yet begun attempting to transmit. In fact, they later announced as the allotted time for activation came and went, they couldn't get their equipment working anyway.

Several more hours passed, after which the NZAPL team announced that their Medium Preonic Transmitter, now to the best of their reckoning in complete working order, was nevertheless continuing to fail to transmit anything.

Around 2am the UK team began to run out of enthusiasm. Everybody had turned in except Mike, Seph and Hugh, who all perched on the dome looking at the stars and slurping the day's final pot of coffee from Seph's thermos flask.

"Ambient neutrality is supposed to be empty, right?" asked Hugh.

"Metaphorically speaking, yes. Of physical obstructions," said Mike. "As far as I can make out, at any rate. But that's why we're doing the experiment. There could be stuff in there. There could be... pulsar-like objects. Or just objects in our space which naturally emit continuous signals into the A-Layer... stranger things have happened."

"Not much stranger," said Hugh.

"There is always room for another delta," said Mike. "The important thing is not to jump to conclusions. As I said whenever it was, the first pulsar was mistaken for evidence of alien intelligence by the people who first saw it. So assume nothing. Until we start finding prime numbers. Then you can politely tell me to shut up."

"I think we should try channel two tomorrow," said Seph.

"Not a bad idea, 'Sephine," said Mike. "Not bad."


Mike was the last to arrive the following day. People were already waving frantically at him as he drove up towards the small MPR car park. He was forced to roll down his window to let Philip Hood talk to him while he parked.

"What's happened?"

"Channel two. We tried it just now. It's making noise. And NZAPL's in bed, Michael."

Mike shook his head, turned off his engine, rolled up his window and climbed out of his car. "Noise?"

"This only happened about five minutes ago-"

"Mike!" shouted yet more voices as he got his backpack out of the car.

"Everybody calm down! I will be there in a moment! Nothing is this Earth-shattering."

"It's a pattern! It's repeating," said Philip.

"What's the pattern?"

"We don't know. You have to come and look."

Mike wound up at the front of the crowd of people crammed under the gazebo staring at the oscilloscope wave and its recorded duplicate on the computer monitor to its right.

"There's a carrier on the second channel just like the first," explained Phil. "Three-ninety terahertz. But the carrier's being amplitude-modulated. We didn't think we'd need to fix up our signal processing equipment so early so this bit of analysis is a bit of a rush job. It's a binary signal. It repeats every sixty-five thousand, five hundred and thirty-six cycles, the last half of which are all zeroes. Here's a printout of the whole thing," he added, handing over a few pieces of paper. Mike glanced at it. Ones and zeroes. They didn't immediately mean anything to him.

"What does it say?"

" I haven't figured it out yet," said Ching, a Chinese communications engineer who was best-qualified of all of them to answer that question.

"We're just... picking up something," said Mike. "Somebody's phone is interfering with our equipment or it's a short-wave radio station or a secret military thing which they've been using for decades. Like a numbers station or something. Or birds on the antenna."

"The antenna is underground," said Hugh.

"But you get what I'm saying? Let's just try to find out what it is. We've come this far. Obviously some part of this receiver works, which is a good thing. Get your coffee and get going."


Around mid-afternoon Mike heard an approaching clanging sound. Ching poked his head over the edge of the dome. "Mike? You got a minute?"

"Of course." Mike kicked the GEWRs closed and sat down on the nearest railing.

Ching climbed up and took a look around before perching on the railing opposite. He waved several sheets of lined paper covered with scribbled diagrams and calculations, meshed with a few computer printouts. "Been looking at that signal."


"Yeah..." Ching shook his head. "Nothing."

Mike sighed and folded his arms. "Is it encrypted? Or something like that?"

"Well, I don't know. I don't know if I'd expect half of it to be blank if it was encrypted. And it seems to make a kind of sense. Look at this sheet. It's four thousand and ninety-six bytes altogether. Look at the numbers. You get gaps and repeated patterns and things. I did a frequency analysis and it's not at all random. But it's not ASCII or Unicode or ROT-13 or anything obvious. It could be something more complicated. If the signal was a hundred times longer somebody could probably figure it out, but I don't think I have enough to go on. Sorry."

"No problem, Ching," said Mike. "It might not be intended to make sense anyway."

"I'll keep looking at it."

"No," said Mike. "Leave it for now. Concentrate on getting the proper signal processing modules up and running. I want to try channel three before the Kiwis wake up."

"Should I tell people? That we're trying channel three?"

"Yeah, let it be known. Wait, don't stand up yet. You've got the House behind you. Smile. Or hold up your work and look wry and interested or something." Mike pulled his camera out again.

Ching obliged. "Day one hundred and thirty," he narrated. "Mike Murphy And Friends randomly tune into Radio Moscow. ...Do that again, I think I blinked."


Tuning to channel three, as for channel two, involved altering a small, deceptively plain-looking dial to an integer multiple of its basic (channel one) setting. This, in itself, was a five-second process, but it took long enough for Ching and Mike to get everybody to stop working on the system that the team decided to break for dinner first. That, in turn, gave Ching time to get his signal processing equipment connected up.

Channel three turned out to contain another repeating pattern. This one was roughly 60 trillion binary digits long, and began with the prime numbers from 2 to 127, which were followed by a rough drawing of a circle, then what appeared to be some simple mathematical equations.

Things got a little hectic at this point.

"Somebody find the NZAPL website. I think they've got a webcam. Zed?" said Mike, directing this last word into a radio handset.

"Professor Mike Murphy!" It had been about a week since Mike had last spoken to this person, his friend, co-author and opposite number in New Zealand.

"Professor John Zhang. Indeed. Zed, any chance you could turn off your transmitter?"

"It's not on," said Zed.

"Zed, is it completely powered down?"

"It's seven in the morning, I'm the first one here, I haven't turned anything on yet."

Somebody tapped on Mike's shoulder and pointed at a nearby screen. The webcam was small, but it clearly showed a darkened shape in a darker field, with the clouds behind it only palely illuminated by the not-yet-risen Sun. The MPT didn't even have its interior lights turned on.

"Great, just checking. Talk to you later." Mike closed the conversation and turned away. "Alright. So it's not a practical joke. Doesn't change anything."

"Michael," said Philip Hood. "Dense energy amplifies A-LAY signals. We know this. If you want to send an A-LAY message across interstellar space you just have to point your antenna at the nearest star and start talking. We have to at least consider the possibility. And nobody on this planet's built A-LAY communications equipment before us."

"As far as we know," said Mike. "But our paper is available for anybody to read. And if we've built something, they could have built something. And they could have had a primer written and ready and waiting - for heaven's sake, they were working on stuff like this in the Seventies. If we wanted to make contact with aliens, this is exactly what we'd do. In fact, this is what we've DONE, with the Voyager probes. Send out a message, along with a universal guide for translating it. We can't start jumping... I think the only way to find out who is to just decode this dictionary or whatever it is."

"But it's huge," said Seph. "And we're not exactly the experts in this field. And we do, actually, have better things to do. As in, proper physics."

"Well... we could just put it online," said Hugh. "If nobody claims responsibility then at least somebody might solve it for us."

That seemed like a good idea.


Quite a lot of time passed.

UKAPL and NZAPL spent almost two more years trying to send signals to each other through the Earth, on a huge variety of channels, settings and intensities. UKAPL picked up nothing more interesting than total silence on every other channel they tried, while the carrier, short message and primer looped forever on channels one, two and three. NZAPL, meanwhile, never succeeded in transmitting a single signal. At length, it was discovered that their signals were simply being cancelled out, just a few tens of micrometres beyond the tip of the transmitter, for reasons which had Murphy, Hood, Zhang and Kosogorin scratching their heads. Eventually, the teams ran out of money and the experiments were shut down.

Zhang and Kosogorin along with most of the others were relieved to move on to less demoralisingly futile projects. Philip Hood saw mathematical potential in the "delta tools" he and his colleagues had developed and took an opportunity in Hull University's mathematics department to develop them further. Only Mike Murphy kept plugging away at the original problem on his own, continuing to discover and model more and more exciting theoretical phenomena, all of which were directly contradicted by experimental evidence.

"Mike! It's Ching."

"Ching. It's been a good while. How've you been?"

"Well, it's been pretty busy... You know I finished my PhD. After that, I went travelling around Asia for about a year. Last year I got married to Susie... aaaand now I'm working for Google. That's the ultra-condensed version, anyway."

"Good one."

"Thanks! How are you doing?"

"I, as I was last time we met, am still working on this delta, sad to say."

"Ah, a problem worthy of attack?"

"Proves its worth by fighting back, indeed. Yes, it's getting pretty heavy. It's not that I'm not making progress, it's just that," Mike laughed hollowly, "none of it fits our experimental data! It's generating interesting mathematics though. Phil Hood is still working with me from time to time. Applied maths side."

"I wanted to talk to you about this primer."

"Ah, yes? You put it online, I remember."

"Yeah. Hugh and I couldn't get any prize money together, and we were both hopeless at getting publicity so it kind of dropped off the face of the Earth. Nobody claimed responsibility, which, as you say, kind of doesn't prove anything. Also, nobody got more than a hundred thousand bits into interpreting it, and that was all maths, so as you can imagine people just got bored and gave up. Well, anyway, just a few days ago somebody sent me a solution. Not to the whole thing, but enough to decode the channel two message. He sent me this massive walkthrough, essentially. The first part is mathematics and mathematics is universal. He says it was like code-breaking. Really easy code-breaking. Once you get down far enough it gets through arithmetic to algebra. It gets to calculus. Differential equations. It develops all these symbols and gives bundles and bundles of examples as practice. But then, this is the mad part. Then it goes to diagrams. There are diagrams of atoms. It starts representing electrons jumping between quantum states, you know? It took him a long time to figure out, but he realised it was starting to define its terms. It defines units. Physics. Physical equations. Get this: four megabytes in, this guy - Jim - found E=mc2. He's found Maxwell's equations and Newton's equations - there are little bits of notes by this point, words like 'because' and 'therefore' and 'true' and 'false'. Bits and pieces, enough to start building a dictionary out of, right?"

"Enough to start describing atoms. And subatomic particles. I guess from there you could go to molecules."

"Right! And then, if it was us, you could describe structures and metals and cells and it'd take all the space in the primer that's left over, I think, but you could get to describe metabolism, and 'eating', and from that you can build up further still... like I say, he hasn't got a hundredth of the way through it yet, but I'm positive that's where it'll go. It makes sense! These tiny little blocks, they still use them later! There are 'therefore' signs all the way through, I did a frequency analysis! Isn't that amazing? But we haven't got that far yet. We're still lodged in the physics. And it's twisting my brain. It gets to Schrodinger's equations. And goes further than that. All of a sudden, this guy starts reciting your equations. I could swear I was reading your paper, Mike! Murphy's Preonic Theorem. ZHK spectra, although they don't call them that, they just have this squiggly symbol, but they have the analysis down right. And it keeps going. It explains the principles they use to transmit the message. Because that's the one other thing that the guy the other end will have in common with you, apart from mathematics. The principles behind the messaging technology."

"Ching, anybody could put Generating Waveforms in Ambient Neutrality into that format."

"But it keeps going! Maybe Jim is this genius author who originally wrote it, but whichever way you slice it, there's more maths! Stuff you haven't published even now. Stuff nobody has published."

"Well, there are better mathematicians than me out there."

"Well, be cynical if you want. Be a pessimist. I'll let you know when we reach the bottom, although I can't say I have any idea when that might be. I dare say we could end up building a working mass-energy converter out of paperclips and you'd just go 'I could have done that' or something. It doesn't matter. I said we translated channel two, and that's the main thing."

"Yes, and I'm not sure how you managed that. I rather think you'd need to be able to translate more sophisticated ideas than just numerical building blocks before 'Welcome, fledgling newcomers, to the Galactic Brotherhood of Light' made any sense."

"Yeah, well, that's not what it says. It says - and this is all dressed up in equations, remember - channel two and channel three will repeat forever. And every other channel and setting will remain absolutely silent. And any attempt to transmit on those channels will fail. As we know. That's part of the message - it's all boxed out - that's one thing that can happen if a certain parameter is below a certain threshold. If the parameter is equal to or above that threshold, then the other box 'happens'. Channel two and channel three repeat forever, but channel one makes... well, I think this bit here symbolises coherent noise. Likewise every other channel. Forever. And we can transmit freely. That's what the message says."

"So what's this parameter? Is it distance?"

"Well, that was what Jim thought at first. Like we were just in some dead zone, too far from the central transmitter(s). But that doesn't make much sense, because we were still picking channels two and three up fine, right? Our transmissions were being actively cancelled out. Besides which, 'distance' as a concept and a variable is already described pretty unambiguously in the primer and this isn't the right symbol for it. We think it's something else. The symbol isn't one I recognise, but it crops up quite a lot further down the primer in contexts which... almost make a mathematical kind of sense..."

"Ching, I'm waiting for a punchline here."

"Jim thinks - and this is purely conjectural at this point - the A-Layer might not be natural. He thinks it might have been built - installed - by some other species, thousands or millions or thousands of millions of years ago. He thinks, and I agree with him, that the symbol means money. And we think the whole message is saying we need to buy a more expensive broadband package."

Next: Power Of Two

Discussion (17)

2008-05-31 03:41:51 by Alexandru:

This is one of the best things I've ever read. Reminds of Contact (movie-tie-in-wise), but spears off with one of the greatest punchlines ever. Never saw it coming. Congrats.

2008-07-13 21:52:49 by Cyle:

I was brought here because of geocide two years ago, and have just started to read your fiction, this is simply wonderful.

2008-07-17 19:44:29 by Paradoxia:

Absolutely Awesome. That's all I can say. Every single story on this entire site. Awesome.

2009-06-19 16:02:13 by Paradoxia:

I'd just like to ask something, can anyone answer me (sorry if I'm being naive): How do you transmit a picture of a circle or a squiggly symbol in binary? I can understand 100101011010110101 representing something, but how do you get something which is drawn?

2009-06-30 00:42:38 by Rio:

Paradoxia: Here is a small circle in binary notation. 0110 1001 1001 0110 It's a bitmap graphic!

2009-07-23 20:28:02 by DaveB:

What exactly is a ROT-13 encoding in binary...? I thought ROT-13 only works on English (not even ASCII or alphanumerics, but *English*). Otherwise, awesome story, and a punchline completely out of left-field, I love it! Can't wait to get deeper into the series.

2009-10-25 20:01:26 by TimMcCormack:

@Paradoxia: Imagine that someone sends you a long binary string starting with 0s, and then you start seeing these runs of 1s embedded in it. The 1-runs get longer (and 0-runs shorter) until it is almost all 1s, and then the pattern reverses. You graph the length of the runs, and find it is half of an ellipse! Put this together with the "fixed width" (length of 0-run and length of next 1-run add to almost a constant), and you realize you are dealing with a raster displaying a circle.

2010-06-23 11:10:11 by YourNameHere:

Greatest story ever: starts off normal, gets deep, than BOOM! hilarity ensues.

2011-10-21 16:53:26 by Unclevertitle:

Awesome story. And a whole lot of build up for a hilarious joke.

2012-10-30 23:28:37 by Dave:

Arggghhh, a shaggy dog story we call it in US. but (like many shaggy dog stories), entertaining.

2013-06-13 20:17:25 by Eduardo:

Very good. And funny.

2013-06-30 09:31:39 by Eitan:

*Thousands* of millions?

2014-06-05 03:38:46 by Greg.B:

If this weren't written in 2004, it would come off as a joke about the net neutrality issue.

2015-11-27 03:34:55 by dx:

This is probably a meaningless detail, but what does GEWR mean?

2016-06-02 19:32:39 by Aimless:

@dx: Generating Waveforms in Ambient Neutrality. Mike's work (equations)

2016-06-02 19:33:49 by Aimless:

I fucked up.

2019-03-24 06:41:10 by blackpen:

@rio: You'd also want the picture to have dimensions that are primary numbers. Makes it easier to put together. If I get your circle picture as a long string of ones and zeros, I could also lay it out 8x2 instead of 4x4: 01101001 10010110 and then it's not a circle any more. But if you get a picture like this: 0001000 0110110 0100010 0110110 0001000 that's 7x5 or 5x7, can't slice it any other way.

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