Image is from:
I stand at the railing and
watch the sky -- stars, dust and rock fall inward in total silence.
The woman is standing next to me. How long has she been there?
“Look out towards the boundary,” she points. “It’s coming together and the shape is just right.”
“Infinitely improbable,” I laugh.
“Inevitable”, she smiles.
We have lived together in and around this starship for over a billion years. There are others here too. Before that there were other ships, and their names recede backward in my memory to a past that thrills me with its adventures and terrifies me with its pain. It’s been a long road, and it’s about to end … if I choose it.
Suddenly I’m confused. If I choose it? Who am I? I’m out there – a strange evolution of consciousness that even now directs the forces that shape the end of this universe. And yet I’m also in here as a much simpler being that has been resurrected just for this event.
“This belongs to all of us,” the woman says. “We are all invited.”
In my present form I can’t retain all the memories of my past. Most of my memories are kept elsewhere, but I can ask for them at any time. I ask for them now.
We brought the lander down near one of the water vents, and we built the habitat on light gray formations of rock positioned between a long wall of translucent, crystal ice and a fracture that plunges deep into the moon’s surface.
Along this ridge the underground ocean has risen to within a few kilometers of the surface, and our drill is anchored to ice above a bubble of water only a few kilometers below.
The rest of the team has taken our mother ship closer to Jupiter and its shrinking Great Red Spot (GRS). I can see that strange being riding the storms in Jupiter’s southern hemisphere through the diamond window in my living quarters. It peeks out from the side of the ice wall, a cyclone of activity 17,000 km across and straddling the boundary between a stripe and zone in Jupiter’s upper atmosphere.
We are looking for yet other forms of life to supplement our list for Earth, Mars and (apparently) Jupiter.
I stand up from my small desk and open the partition. I hear conversation that grows louder as I walk down the narrow corridor into the operations center. It’s a big day because, in a short time, the laser drill will likely penetrate the ice into the slush and water below. We know roughly what we’ll find – the remote probes were quite good in their preliminary analyses. Those analyses brought us here. Nevertheless, what happens now, and what happens with the crew watching Jupiter may soon change our perspective on almost everything we know.
Carmen is at the white board in shorts and tank top, and she is evoking images and equations by waving her hand over its surface. My wife is sitting nearby and monitors drill progress from a tablet in her lap.
Carmen is reviewing the biology for the engineers in our crew, but with my arrival the entire crew is present. “The question has always been whether or not life started on Earth or was transported to Earth from elsewhere. The primitive life forms we’ve found on Mars have the same nucleic acid and protein chemistry that we do. Indeed there is an almost 20 percent homology between the DNA codon sequences for life on Mars and life on Earth. For specific proteins the homology is sometimes over 60 percent.
“This makes sense,” she continues. “Early comet and asteroid impacts on Mars ejected a good deal of surface rock, and some of that rock landed on Earth as meteorites. Some of these meteorites contain small carbon-containing tunnels similar to those created by rock eating bacteria on Earth. It’s easy to imagine primitive but robust life forms hitchhiking a ride to Earth and then evolving into us.”
Abdul broods in a more formal uniform from a perch near the coffee maker. “The Europa probes found organic compounds in the surface ice, even some phosphorus containing sugars, but was there anything big enough to contain a sequence.”
“Big enough, yes,” answers Carmen, “and possibly organized into linear strands. However, the probes lacked the capability to do any real structural analysis.” She pauses and then continues, “That’s why we’re here.”
My wife interjects. “We’re almost certain to find carbon-based life here, but it’s an open question whether it will be carbon-based life like ours or something entirely different.”
A radio transmission from the mother ship announces its presence on six tablets at once. Everyone jumps and then quickly look down to read it.
First the abbreviated envelope:
Received: by 10.107.10.29.143.66 with CMTP id u29csp154447ioi;
01082035 16:37:11 -0800 (JST)
Subject: Final GRS Message? 00A3EF
Thread-Topic: GRS Messages
And then the video attachment:
A sea gull flies out from a beach over the ocean.
Commander Harcourt’s face then replaces the video.
“We think it means, goodbye,” he says.
Years ago an unmanned probe first detected an ordered sequence of laser pulses coming from the GRS. We almost didn’t catch them because they were very brief and they were aimed away from Earth into the interstellar night. It was initially thought to be a glitch in the probe’s electronics. The GRS was believed to be an anticyclone accompanied by strong convection currents and massive thunderstorms, but closer examination revealed a complex internal structure that included signaling pathways not unlike neurons in the human brain. A laser on the probe was repurposed and a series of pulses of two different durations were beamed at the GRS.
Long Short Short
Long Short Long
In this way the probe counted up from 0 to fifteen in binary numbers, paused for a while and then repeated.
The response came back very quickly. It was an image in PNG format of Gottfried Wilhelm Leibniz from the art collection in the Royal Society in London.
The engineers on Earth thought they understood the message. It seemed that the GRS knew about us; it knew our communication standards and it knew our history. In 1679, Leibniz had written the pioneering paper on binary arithmetic Explication de l'Arithmétique Binaire. The GRS was talking to us, and it was talking to us in a way that conveyed an enormous amount of information in a very brief transmission.
Later it was suggested that there was an even deeper message in the reply. Leibniz had first become interested in binary numbers after being introduced to the I Ching by Joachim Bouvet, a Jesuit missionary to China. Leibniz saw an affirmation of his Christian faith in the I Ching hexagrams, and he saw binary numerals as symbolic of the Christian idea of creatio ex nihilo -- creation out of nothing.
“Goodbye?” We’ve only just arrived. A large part of my current sense of purpose is built around the GRS and Europa. I feel myself falling into confusion as my wife walks over and stands next to me.
“Alhamdulillah,” she says. “Perhaps its existence is the main message.”
Her tablet buzzes -- the drill had penetrated into the slush that separates the surface ice from the ocean below.
I raise my tablet, confirm the penetration, and then activate the machinery that will return slush and ocean samples to the surface. The other four members of our crew look up and smile. “Dios es grandioso,” Rodriguez winks at my wife as he reaches for his own tablet, and triggers the startup sequence for the nanolaser microsensor that we will need shortly.
We continue to talk about the meaning of the seagull image as we don our biohazard suits and walk through the airlock into the single, large laboratory module of our habitat. The analyzers are arrayed along the inner wall of this room and the outer wall has three work areas that look out over the surface of Europa. There is also a large isolation hood that extends a narrow bridge of polymer track from the lab to the drill. The center of the room has two large tables with plain, dark gray surfaces and a few apparently random pieces of equipment.
I look out one of the windows and watch as a small cylinder ejects from the drill and moves slowly toward the lab. After a few minutes it pops from a small lock into the isolation hood and is grasped by a gray, plastic frame.
As I walk over the isolation hood, I move an icon between two locations on my tablet. Chemically inert fingers extend from the frame and plug into preordained locations on the cylinder.
Inside the isolation hood is a camera mounted optical microscope. A sample of ocean water is sandwiched between a microscope slide and a thin glass coverslip. The assembly is placed beneath the objective of the microscope, and a focused image appears on all of our tablets. Cellular structures, cilia, motion. There is life on Europa!
Another sample of ocean is taken from the cylinder and placed in a small, hermetically sealed container that is moved to the inner airlock of the isolation hood. The outside of the container is sprayed and irradiated before I remove it and walk over to Rodriguez who is waiting by the microsensor.
Behind me a small, wire-guided submarine begins its journey down the drill hole into the dark ocean below.
I watch Rodriguez as the living components of Europa’s ocean are separated from the water, homogenized, treated and fed into the tiny tube that forms the recognition component of the microsensor. Some substances will bind at different locations along the microsensor surface where they will activate tiny nanolasers whose light will signal the presence of those substances for which that region of the microsensor has been tuned. For the moment, the device is configured for elemental analysis.
We’re waiting for the first results when another message comes from Jupiter. “False alarm,” reports Commander Harcourt. “It’s still with us. There appear to be two different approaches to translating the seagull image.”
Conversation with the GRS is a curious affair. It seems to know who we are and what we are doing, but after that first binary transmission it has never responded to our queries unless they are framed as images. We try to keep our images focused on a single topic, but the GRS often responds with images that contain multiple levels of meaning. We will be exploring, interpreting and misinterpreting these images for decades to come.
We have software that assists with the translation, but it usually returns a prioritized list of possible meanings. Often this list consists of minor variations on a single theme. Other times it contains multiple lists with varying translation themes. Harcourt is telling us that the seagull image appears to have at least two possible interpretation paths. One is goodbye. The other seems to be an invitation to “watch carefully”.
“We’ll get back to you with more as we get it,” Commander Harcourt continued, “For the moment, you folks are center stage.”
My tablet beeps and I look down to see the results from the microsensor:
Elemental Analysis By Weight:
“As we expected,” Carman says as she looks over my shoulder. “Now let’s try for the big one.”
While we wait for the results we continue talking about the GRS.
Jamal reminds us that the GRS has been shrinking for a very long time. He put the numbers on a white board.
“In the 1800’s it was estimated to be 40,000 km in length across its long axis. In 1979 the length was 24,000 km. By 2012 its rate of shrinkage had increased to almost 1,000 km per year and it was changing from an ellipsoidal to circular shape. It would be gone by now but the shrinkage stopped after our unmanned probe talked to it. Now that we’ve arrived it’s shrinking again very rapidly – it’s 17,000 km across and, at it’s present rate of shrinkage, it will be gone within a decade.”
The next set of results comes in:
Component Analysis By Weight:
Nucleic Acids [0.0%]
Long Chain Fatty Acids [0.0%]
Long Chain Carbohydrates [0.0%]
We all look at each other in shock and excitement. “It’s not us! This is a totally different form of life. No DNA; no protein!” Carmen is almost shouting.
We send the results to Jupiter and we get an answer quickly. “Extraordinary,” says Commander Harcourt. “Great work. I wish that I could say we were making similar progress here. We’re trying to get a common foundation for math, science and technology. We sent images of Newton’s geometric proofs in Principia and we got back an image of Pietro Longhi’s painting of an alchemist pointing to a flask. We sent an image of a Feynman diagram and we got back an image of The Labyrinth of the Cathedral of Chartres.”
Abdul interjects, “The responses of the GRS trigger something that seems right in me, but the ‘rightness’ isn’t logical, it’s psychological. Surely the translation software recognized that Newton was also an alchemist. What translation path did that generate?”
Harcourt answered, “Weak correlations to chemistry and a stronger correlation to Newton’s metaphysical beliefs; but we need to keep our feet on the ground; we need keep our conversation grounded in reality.”
“Why?” my wife asks while looking at Harcourt’s image on her tablet. “Perhaps it doesn’t want to talk about physics and chemistry. Let’s find out what it does want to talk about.”
Harcourt looks both confused and interested at the same time. “How would you do that?”
“Rorschach tests,” Rodriguez suggests. “Respond with whatever comes to mind first. … Let it guide us.”
We all look at him. “This being obviously thinks very differently than we do, but it seems to understand a bit of our psychology. Why don’t we accept its mood and respond the same way?”
I look at Rodriguez. “It sent us a picture of an alchemist, what was the first thing that came to your mind?”
Rodriguez blushes, “I remembered the priest in my village parish mixing sacramental wine and water during the Mass.”
Abdul looked up, smiling. “In retrospect, can you trace the association?”
“Well, oddly,” says Rodriguez, “I’ve been reading a psychology text about alchemy. Last night I was reading about an experiment in which an alchemist pours consecrated wine into a wooden bowl of clear water. It’s a reference to creation.” He looks down at his tablet and calls up a reference. “… take a drop of the consecrated red wine and let it fall into the water, and you will instantly perceive a fog and thick darkness on top of the water, such as also was at the first creation. Then put in two drops, and you will see the light coming forth from the darkness.”
“Intriguing,” I say. “The first message we received may have included a veiled reference to creation – the mystical treatment Leibniz gave to binary numbers -- creatio ex nihilo.”
“Anyone else?”” Harcourt asks.
I answer. “When I saw the Labyrinth of Chartres, I immediately pictured a Tibetan sand mandala.”
My wife smiles at me, and winks.
Harcourt’s tablet image looks away for a moment, his expression becomes confused, and then he looks back at his tablet camera. “You want us to send images of priests and mandalas?”
“That’s a possibility,” I answer, “But why don’t we try being as obscure as it is.”
I’m a bit embarrassed by the laugh this generates.
“Let’s see how well it knows us? Send an image of a drop of wine spreading in a container of water, or Picasso drawing a painting on the sand below tideline.”
“Why Picasso?” My wife asks. “Where did that come from?”
“An old Bradbury story about the transience of created things,” I grin. “Let’s start talking to it the way it talks to us; at least, to the degree that we can.”
Harcourt looks a bit unhappy. “I’ll get back to you,” he says shortly, and signs off.
“Time to call it a day,” I suggest. “We’ll talk over dinner and make plans for tomorrow.”
It’s morning, and as we finish breakfast another message arrives from the mother ship.
Commander Harcourt speaks immediately. “We sent the image of a sand drawing at the tideline. The GRS responded with an image of the Borobudur Temple in Central Java.
“We then sent an image of wine slowly mixing with water and it came back with a picture of Europa itself.” This just isn’t making any sense. “We’re beginning to wonder if the GRS is simply a data repository with an alien search engine and unusual indices. Perhaps we’re reading too much into the responses that we are getting.”
We talk a little more about messaging strategies and then my wife and I watch our four colleagues don biohazard suits and enter the laboratory module. While they continue to analyze the ocean samples, we will explore the ocean depths using the small submarine waiting in the dark below the ice. Two small closets set in a wall of the operations center contain VR kits designed for piloting the submarine.
I enter one of the closets and sit before a small table containing a joystick and a small control panel. The high backed chair is quite comfortable and even contains a seat belt to help restrain a body that’s about to think that it’s somewhere else. I put on 3D goggles and a high quality audio headset and, after a few moments, I find myself floating in an all-encompassing darkness broken only by the joystick and the small panel of controls before me. The microphones are on but there is total silence except for an occasional crack from the ice above.
Suddenly, my wife appears next to me as an avatar sitting before her own control panel. In addition to an audio connection there are ranges of expressions that can appear on the avatar’s face – a quick “emoticon” method of communication offered by a simple list of icons on our control panel.
The submarine is anchored to the hard ice adjacent to the drill hole. It’s about 10 cm in diameter and 60 cm long. It includes buoyancy tanks and steerable impellers both front and back. Microphones and video cameras are swivel-mounted mid-body along with both lamps and speakers. Three control cables offer triple modular redundancy and exit the rear of the submarine to run up the drill hole.
We retrieve the anchors and change the buoyancy of the submarine as our impellers drive the submarine through the slush and into the ocean below.
We keep our lights off and navigate by sound; our sonar pings return no echoes except for a thermocline 100 meters below. There is nothing to find even after an hour of swimming through the night. Finally we turn on our search lamps and gaze into an ocean that is crystal clear but empty.
I look over at my wife’s avatar and see a raised eyebrow in return. I respond with a grin.
The control cables of the submarine have a total length of five km. That gives us two kilometers of range beneath the ice. We have sufficient cable length to support a journey below the thermocline, and so I turn off our light and adjust impellers and buoyancy to begin our descent. … As we descend below the thermocline we are suddenly in a different world. We have found beings on Europa.
Large creatures, perhaps the size of a walrus, float vertically in the water. They maintain their position with gentle motions of several flipper-like appendages. They seem to be organized into some kind of ordered array that spreads out both horizontally and vertically, but the nature of the pattern eludes me. Flickers of light in different colors appear on their skins and evoke a response from their nearest neighbors. And there is music. These creatures seem to be singing in a chorus.
In our VR gear we are floating weightless in space, surrounded by both light and sound. The music and light patterns are quite alien, but compelling. Indeed, we both seem to fall into the music and become lost in the moment. We hover for a very long time – motionless beneath the thermocline – embraced in light and sound.
It takes considerable effort to force myself back to knowledge of the submarine and its controls. Attempts to signal these beings with both light and sound are ignored. Finally, I take the controls and we descend slowly though the chorus into the open waters below.
We seem to pass through yet another kind of barrier and the music and light disappear only to be replaced by … chaos.
Smaller Europans dart through the water like children in a game of tag. Their skins also emit colored light patterns but the displays are more sporadic and less ordered than those of the adults above. And sounds! Is it laughter? The entire scene evokes a sense of joyful play as they spiral about us and occasionally stop to poke a snout into one of our cameras.
And then, suddenly, they’re serious and some of them gather into a group that swims deeper into the ocean while occasionally glancing back at us. When we don’t follow they return, swim in circles, and then dive again. The invitation is obvious and so into the depths we go.
We follow our guides toward a cluster of lights and sounds that finally resolves into a group of Europans – one large and a dozen small. It seems almost like a school. The larger being is humming in a single tone:
Hum Hum Hum
Hum Hum Hum Hum Hum
Hum Hum Hum Hum Hum Hum Hum Hum
My wife and I look at each other’s avatar in surprise. Fibonacci?
In graduate school, both of us had taken the usual mandatory math courses. The Fibonacci series consists of the sequence of numbers obtained when each new number is generated from the sum of the previous two numbers.
1 + 1 = 2
1 + 2 = 3
3 + 2 = 5
5 + 3 = 8
8 + 5 = 13
The Fibonacci series is often used as an introduction to number theory and to the extraordinary depths of formal, abstract mathematics. Something tugs at me from the back of my mind; something about the GRS image of the Borobudur Temple. I try to follow that tug but then the larger Europan ceases humming, the smaller creatures begin to “sing” Fibonacci by assigning a note on a musical scale to each number. At first they all sing the same ascending notes, but then some members of the chorus start a new voice by singing the notes at a different pitch while others sing at a different tempo. Somehow they make this work by emphasizing and de-emphasizing certain notes and syncopations. At first the music is a strict canon, but then it becomes playful and appears to vary more loosely in a fugue. As the music becomes increasingly complex some phrases are sung backwards in complex counterpoints that hint at things I am unable to grasp. Slowly, then, the music simplifies into a single voice and comes to a gentle and very satisfactory halt.
The smaller Europans then swim silently in spirals around our vessel, peek into our camera lenses and then form up in two vertical lines, almost as if preparing to take a bow. But that’s not it at all; rather, the performance continues.
The teacher, for clearly that is what it is, sings Fibonacci very slowly and the two vertical lines of students teach us a lesson. With the first two notes the two lines are of identical length. At the third note the right-hand line expands to twice the length of its partner. At the fourth note the ratio of the two lengths is 3/2. With each subsequent note the ratio of the two lengths change to 5/3, 8/5, 13/8, and the ratio of the lengths converge on what we assume is close to 1.618, ϕ, the golden ratio.
In a dramatic finish, the shorter line of students rotates to form a horizontal line extending from the left side of the top of the longer line. A swarm of students we hadn’t seen earlier swim swiftly in to close the rectangle – the golden rectangle.
Suddenly it comes together in my mind! I look over at my wife’s avatar and she’s looking at me with a raised eyebrows emoticon. Both the Fibonacci series and the golden ratio ϕ are prominent architectural features of the Borobudur Temple. The temple is a layered structure with five lower, square terraces and three upper circular terraces. The total number of layers is eight. Three, five, eight are numbers in the Fibonacci sequence. Furthermore, the ratio of the dimension of its square base to the diameter of its largest circular terrace is close to 1.618, ϕ.
“The GRS and the beings on Europa are collaborating in their communication with us.
We both sit there stunned. We were looking for life, but we’ve found a civilization. The teacher swims up to the front of its students and rests there in the water, waiting.
I look over at the avatar of my wife and she’s displaying the emoticon for “your turn”. Of course! And I know exactly what to do. I remove my VR goggles and reach for my tablet on the table in the small closet. Pulling up a file, I transfer it to the memory of the submarine, and then return to my virtual presence.
I aim the two speakers to project in different directions and then I play the music file – Bach’s Crab Canon.
The left speaker of the submarine plays the notes of the canon front to back on a harpsichord. Then, from the right speaker, the harpsichord plays the notes in reverse – from back to front. Finally, the harpsichord plays two voices simultaneously – front to back (on the left speaker) and back to front (on the right speaker) at the same time. It is the genius of Bach that it works!
As the canon plays, the creatures before us quickly form two circles, one behind the other, and then the circles break in adjacent places and cross-connect to form a Möbius strip. Different colored lights on these creatures simultaneously move clockwise and counterclockwise along the single surface of this strip -- colors and movements in perfect time with the music. 
My heart is racing – almost exploding in my chest – my mind expands into regions of pure thought – a gift from creatures with a different biology and a different mind.
As the music stops, the lights on the Europans dim but don’t extinguish. Our vessel floats in a night that seems to extend infinitely in all directions, and we are surrounded by creatures that float motionless in the dark -- a subdued pattern of lights beat in time with the now departed music. We embrace this silence and then notice that eight small Europans surround our craft and are slowly rising beside us.
I change our buoyancy and rise with them, up and past the barrier that separates this school from the larger creatures floating motionless just below the thermocline. The larger creatures are now silent, but their lights are beating in time with the memory of Bach’s canon. Europan and human are united in a language of music and number theory that simultaneously thrills and terrifies me with its implications.
We pass the thermocline and return to … silence … night.
We turn on our lamps but there is nothing in any direction but clear water. There is no hint of the community below. Although I keep our ascent rate slow, it’s inevitable that we finally float below the slush that separates us from the surface ice. I halt our ascent and we both sit there in the night for almost an hour. We seem unwilling to take those last few steps toward home.
Just as I reach once again for the ascent controls we hear tones in an octave so low that they are felt more as vibrations than heard as music. The notes seem to come from the very core of this moon, and they play the Bach canon one last time – back to front, front to back, and then both directions simultaneously. The notes are so deep and so faint it’s hard to know if they are real or imagined.
And then, once again, there is only silence and an infinite black.
I return the submarine to the drill hole and anchor it to the adjacent ice. Slowly, reluctantly, I remove my 3D goggles and headset and open the closet door into my own world. My wife is already standing there, as stunned as me.
Our crewmates are celebrating around a table in the ops center and Abdul and Rodriguez each grab a plastic cup of fruit juice and almost dance over to us.
“Hydrogen peroxide,” Rodriguez laughs. I stand there confused.
“Hydrogen peroxide,” he laughs again. “Hydrogen peroxide is generated by the radiation in Jupiter space. That’s the energy source for life here. And the structure of the macromolecules, it’s …”, He pauses and looks carefully at our faces.
“You found something!” he says. It’s not a question.
Suddenly the entire room is silent. My wife and I smile at each other, and we tell them.
It’s been three weeks and it’s time to go home. As our lander ascends toward our mother ship, I watch Europa recede into a ball of ice loosely wrapped in red-brown twine. Beneath the ice the beings of Europa sing their thoughts and seek their future deep within their minds. Although they are clearly speaking with the GRS they show no other interest in the outside world. Deep beneath the ice they have never seen the Sun, planets or stars. Their frontier is in their minds and they travel to places that seem incomprensible to us. Newly aware that companions await them above the ice, however, their songs contain new voices that slowly grow stronger – odd mixtures of Bach and Mozart, Armstrong and Coltrane, Maxwell and de Broglie.
We’ve accomplished so much, and yet I feel more overwhelmed by mystery than at any time in my life.
Years ago a colleague had suggested to me that there is a geography to knowledge. Prior to 1492, my friend suggested, the mapmakers of Europe had drawings of 90 percent of their world. When Columbus returned from the Americas these mapmakers knew more than they had known before, but their drawings now described a far lower percentage of that same world. “The more you know,” my friend quipped, “the less you know as a percentage of what you can know. And what does that mean for the future?” 
Life on Europa does not compete. An economy of abundance is guaranteed by complex molecules saturating the slush beneath Europa’s ice, and by the oxygen released into the oceans by the hydrogen peroxide generated by Jupiter’s intense fields of radiation. I wonder how the aggressive creatures of Darwin’s Earth and the gentler creatures of Europa will co-exist, and which will rise in a competition?
The GRS remains an enigma. Unlike the Europans, the GRS looks outward, and frequently transmits laser pulses into universe beyond our solar system. Recently, it has increased the rate of those transmissions even as it shrinks toward apparent oblivion. A summing up? To whom?
So here I sit, strapped into a vehicle that will rendezvous with the ship that will take me home. I know that, as a species, we are outward bound. Who will we meet there? Until now they have been silent. Why? Will we be welcomed or sent home?
I look over at my wife and she shares my ache. Our part is done.
 C.G. Jung, Psychology and Alchemy (Princeton, Princeton University Press, 1980), 246.
 I saw this idea in a remarkable rendition of the Crab Canon by Jos Leys, https://www.youtube.com/watch?v=xUHQ2ybTejU
 I owe this idea to an untitled, unpublished manuscript of Daniel E. Atkinson (University of California, Los Angeles)