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A Scientist's Notebook
by Gregory Benford


The central images of the 1968 classic film, 2001: A Space Odyssey revolve about a mysterious message left in the form of a monolith buried on our moon. It had been waiting for millions of years for us to show sufficient ability to uncover it.

Soon after the space program began, scientists proposed sending messages aboard spacecraft. It's easy see that a long-term message can survive in the high vacuum and isolation available beyond Earth---deep space equals deep time. But what should be the medium? And what should be the content of this message in a bottle?

The first concerted attempt to send a material message beyond Earth rode upon the first spacecraft to leave our solar system, Pioneers 10 and 11. Launched in 1971 and 1972 to fly by several outer planets, each has support struts carrying a six- by nine-inch gold-anodized aluminum plaque, which bears an etched drawing that describes some facts about our civilization. A sketch of two nude humans, greeting the infinite with a hopeful wave, became its best known feature.

In 1977 NASA launched the Voyager missions to the outer planets, each bearing an Interstellar Record created by a team including Carl Sagan, Frank Drake, and Jon Lomberg. The metal phonograph record carried both sights and sounds of Earth, from Gregorian chants and seagulls to Chuck Berry, and set the standard for broadly based, information-dense messages. Other small messages -- a microdot of inscribed names on the Viking lander to Mars, and an honorary plaque on the failed Russian Phobos mission to Mars -- added nothing new.

More than a decade passed before another substantial attempt. A CD-ROM disk flew on the Russian Mars '96 mission, which failed at launch and splashed into the Pacific Ocean.

I worked on the Mars '94 disk, bringing me into close touch with Jon Lomberg, a major player in the Voyager markers. His paintings adorn many books and exhibitions; his astronomically correct rendering of our galaxy greets visitors to the National Air and Space Museum.

Lomberg had an idea: put a message on the Cassini spacecraft bound for Saturn in 1997. This and my next two columns deal with designing such a message.

Lomberg had already enlisted the help of Carolyn Porco, a professor of astronomy at the University of Arizona, who promised to get such a message on the spacecraft. Porco was a brisk and efficient woman, a principal investigator on the Cassini imaging camera team.

Cassini was to be an anthology mission, with eighteen separate scientific instruments. It also carried a lander which would drop through the soupy atmosphere of Saturn's largest moon, Titan, and radio back data from the surface. A duplicate message might also fly aboard the Huygens Probe lander (named for the discoverer of Titan), built by the European Space Agency. At 5,562 pounds the Cassini spacecraft would be the heaviest unmanned package ever launched into the solar system, except for the failed Mars '96 craft. With fuel, it weighed 12,470 pounds and was the last of the dinosaur generation of spacecraft, having accreted more experiments as the planning spiraled through many years. Under Daniel Goldin, NASA's approach had reversed to favoring "lighter, faster, cheaper" missions, and Cassini narrowly averted cancellation.

Including staff salaries and assuming it survives for five operating years in the Saturnian system, Cassini will cost 3.5 billion dollars. It is surely the last multi-purpose mission to which teams of scientists glued their hopes and hardware as the mission consumed their careers. Astronomers exploring the outer solar system must deal with long flight times, but the repeated delays of Cassini meant that some of them would have only this single opportunity. After Cassini, missions will be quick, light, cheap--and politically stronger. NASA's extreme sensitivity to Congress grew from years of narrowly getting Cassini past their skeptical eyes. The agency became risk-averse as launch date approached, a fact that came to have great significance as the drama of the Cassini marker unfolded.

While we were working on the Cassini marker, the Mars '96 mission ended up in the Pacific Ocean. It failed to reach orbit because the Russian Proton booster misfired in its fourth rocket stage. Again, the craft was so heavy that a fourth stage was essential. Many experiments were lost, the Visions of Mars disk with them. There was some consolation that the disk may fly on a later Russian Mars mission.

Cassini is an implausibly fat spacecraft, so heavy that it has to undergo two gravity-assist flybys of Venus, and one each of Earth and Jupiter. Arriving at Saturn late in 2004, it will fire an onboard rocket to brake it into the first of some six dozen orbits during its planned four-year tour. Shortly after arrival, the Huygens lander will separate and plunge into the chilly, hazy-brown atmosphere of Titan.

Apparently Titan has at least one continent, perhaps jutting up from chilly seas of liquid hydrocarbons like ethane. Organically rich, its atmosphere is thicker at the surface than Earth's, but at temperatures around -170 Centigrade. No one has any good idea of what such frigid chemistry could produce, over the four billion years Titan has orbited Saturn.

In November of 1994 Lomberg and I wrote to the Jet Propulsion Laboratory (JPL), who were assembling the spacecraft. As with Mars '94, we suggested attaching an existing small package, the Microelectronics and Photonics Exposure experiment (MAPEX), plus a message. Lomberg thought adding MAPEX might make the marker more saleable. We tried to hawk the idea with the usual positives:

"* increasing public awareness of the mission, as the Pioneer plaque did, through an optimistic, imaginative goal.

* educating a broad public about the lander, Titan's strange chemistry, and the problems of communicating across long timescales."

The eventual audience could be humanity centuries hence, or on a far longer time scale, any lifeforms that evolve in the organic soup of Titan. We would not imply that Titan bears life now, but would allow for later evolution. We sketched out the plausible readers, ranging from our distant heirs (1000 to 100,000 years) to aliens, including possible Titanians, on scales of a million to billions of years.

Porco came to UCI and we three spent days brainstorming design ideas over lunches and dinners. Much scientific work proceeds like this, sighting in on the critical problems, then using the skills of each team member to attack them. Such free-for-alls are one of the best aspects of scientific collaboration, spirited and enjoyable. They are quite the opposite of how other creative people work, as in the classic image of solitary, agonized artists.

Labor and material costs were to be kept low. We thought the message-bearer should probably be an "artificial fossil" embedded in hard glass which could survive Titan's weather. The message would thus outlast the lander by far.

Unlike the wandering Voyager strategy, we could shape our message for a specific place, Saturn and Titan. We could include information about the present solar system (which cannot be seen in visible light through Titan's thick atmosphere) and our place in it. Communicating this in clear, unambiguous ways promised to be an imaginative intellectual exercise, raising interwoven cultural and scientific issues of wide interest. We would aim to be "understandable, optimistic and awe-inspiring."

JPL said they would submit the idea through the usual channels; Carolyn Porco promised to hurry it along.

Mulling over the huge time scales a week later, I realized that Titan's frigid weathering and the lacerating forces the orbiter would meet around Saturn suggested a message medium of great durability.

Engineers estimated the orbiter would remain intact in orbit for roughly a century, while the Huygens lander could be buried by the flows of sluggish, cold fluids within decades. These were very crude projections, given Titan's unknown weather. In both environments, diamond would preserve a message against abrasion better than metals.

To me the best candidate appeared to be a thin, single-crystal diamond disk to write upon. Using a jewel to carry a message across a billion years could delight the mind, as well.

Manufacturing a disk bigger than a nickel would be expensive. And how to write on the hardest of all substances? At first I thought of using writing processes I knew, such as a layer of boron inside the sheet, laid down using a template and chemical vapor deposition.

The utility of this approach lay in its simplicity, readability, and the unequalled rugged properties of single diamond crystals. Diamond is robust, strong, inert, and resists abrasion. Only very high temperatures and aggressive oxides can damage it. Further, it is transparent in the visible spectrum and a broad range of the infrared. Many spacecraft use diamond windows for their infrared sensors and its space-rated properties are well known. On Titan, infrared is probably the preferred range for best visibility. Diamond has no known chemical reaction with substances in the Titan atmosphere.

Construction of the marker would begin with purchase of an industrial diamond plate, polished, about one mm thick. My discussions with the leading diamond firm, DeBeers, proved this was not a routine request, but they could make such diamond disks for about $5000 each. Since cost scales quickly with size, maximum diameter would be at most a few centimeters.

Writing a microscopic message into the planes of a diamond would probably be attractive to the general audience, I thought, much as the gold-plated Voyager disk proved eye-catching. Indeed, DeBeers seemed interested in the jewelry angle as a possible new market: wear the Cassini Medallion! At perhaps $30,000 or more, this would be a very high end item.

Lomberg, Porco, and I visited JPL and spoke with the flight engineers and managers, with Porco fielding this proposal in Europe. The jewel message notion seemed to catch the attention of even skeptical engineers. We had approval within a month. The European Space Agency also liked the idea and agreed to carry a diamond disk on the Huygens lander.

Word came to me late in the evening, by telephone from a jubilant Lomberg. I walked outside and viewed the stars, thinking of the marker as a sort of memorial for all the scientific community, and indeed, for our era. The sheer joy of it made it difficult for me to speak. I remembered that awe is a blending of wonder and fear, and realized whence my fear came. The time scales of astronomy imply the mortality of those who study it. No less does designing a message which could not be read until all its designers are dust. The night sky filled me with a chilly awe in a way it never had before.

I went back inside and set to work. Soon enough, consultation with DeBeers converged upon a disk 2.8 centimeters across, a millimeter thick and weighing 4.3 grams. Each spacecraft would carry the same message. Though we had two years until the diamond disk had to be attached to the spacecraft and lander, there were myriad engineering and conceptual issues to resolve.

We wished to build on the Voyager experience, extending their thinking. As with Voyager, NASA reserved the right to veto us or even drop the marker entirely. When Voyager design ideas leaked to the press in 1977, NASA's official posture was that they had made no final decision on the project at all.

Still, this did not protect from public vitriol the makeshift team making the Voyager record. Shadowy rumors emerged at the United Nations, when they tried to get diplomats to record verbal greetings to go on the record. Some felt Voyager should carry depictions of war, poverty, and disease, and that a best-foot-forward approach was a sunny half-truth.

Early on the designers had decided to avoid explicit depiction of religion, lest they ignore some. Afterward, others questioned whether the team's belief in the scientific method and use of it to convey much of the message was not itself a sort of ideology. Editorials in the British press had demanded that any future messages be crafted by a large international ecumenical assortment of scientists and nonspecialists alike.

We three had no liking for such an unwieldy opera of interests. NASA agreed; we would design and deliver a disk, following solely our own judgment and paying the cost ourselves.

Before beginning, we had to assume that our future readers could indeed read. Brains often must decipher the visual world from ambiguous, ill-defined data. Like many other animals, we make educated guesses about what lies behind our sometimes chaotic environment. Evolution has shaped our brains to create models of the world that mesh well with our learned reality.

At least a third of our approximately hundred thousand genes are exclusively involved in brain function, and many of those relate to sight. We use a strategy of storing a perception across many neurons, much as TV sets break images into pixels.

This method is like the great Rose Bowl prank of 1961, when Caltech students stole the coding sheets for the University of Washington's mass card display. The students then doctored these and returned them to the hotel safe where they were stored. No Washington fan knew the message beforehand, so none could tell that anything was wrong. Each Washington fan knew only to hold up his white or black card, following written orders handed out at the game. When the stadium crowd held aloft their cards, they spelled CALTECH. The next image in this little half-time entertainment was of the Caltech beaver, not the Washington Husky.

Like the fans, our neurons know nothing. But parallel processing of their individual minute signals, carried up through hierarchies of neural organization, eventually constructs a model of what the eye is seeing. The brain uses this image in making evolutionarily effective calculations and decisions.

For example, if we paint dots on a hollow glass cylinder and view it with one eye, it looks like a random set of two-dimensional dots. But turn it and—aha!—the three dimensional shape of the glass pops out, a whole three-dimensional picture. Our brain generates this from a mere bit of motion, a talent of great use in the African veldt long ago. Similarly, stereo vision enables our brains to take the small differences in the angles that objects make and decode them into distance estimates.

All this processing plays out behind the sets of our internal, unitary world. We had to assume our future audience would have such abilities as well, but perhaps not exactly ours.

Voyager's messages had embodied the idea that the aesthetic properties of human art (especially music, since they were sending a record) emerged from physical constants and nature's mathematical harmonies. Intelligences of the far future, springing from physical circumstances at least partially shared with us, might well appreciate underlying ideas based on natural order. Lomberg speculated that highly ordered structures like fugues and geometric constructions might come through best.

Conventions of perspective and the entire problem of interpreting two-dimensional representations loomed large. Even those humans whose cultures do not use perspective have to learn how to see it. Dogs never do learn. What of humans evolved in a far future? Or even aliens?

It had always seemed to me that evolutionary mechanisms should select for living forms that respond to nature's underlying simplicities. Of course, it is difficult to know in general just what simple patterns the universe has. In a sense they may be like Plato's perfect forms, the geometric constructions such as the circle and polygons, which supposedly we see in their abstract perfection with our mind's eye, but in the actual world are only approximately realized. Thinking further in like fashion, we can sense simple, elegant ways to viewing dynamical systems, calling forth ideas of the irreducibly elementary.

Imagine a primate ancestor for whom the flight of a stone, thrown after fleeing prey, was a complicated matter, hard to predict. It could try a hunting strategy using stones or even spears, but with limited success, because complicated curves are hard to understand. A cousin who saw in the stone's flight a simple and graceful parabola would have a better chance of predicting where it would fall. The cousin would eat more often and presumably reproduce more as well. Neural wiring could reinforce this behavior by instilling a sense of genuine pleasure at the sight of an artful parabola.

We descend from that appreciative cousin. Baseball outfielders learn to sense a ball's deviations from its parabolic descent, due to air friction and wind, because they are building on mental processing machinery finely tuned to the problem. Other appreciations of natural geometric ordering could emerge from hunting maneuvers on flat plains, from the clever design of simple tools, and the like. We all share an appreciation for the beauty of simplicity, a sense emerging from our origins.

In an academic paper, R. Lemarchand and Jon Lomberg had argued in detail that symmetries and other aesthetic principles should be truly universal, because they arise from fundamental physical properties. Aliens orbiting distant stars will still spring from evolutionary forces that reward a deep, automatic understanding of the laws of mechanics.

Many things in nature, inanimate and living, show bilateral, radial, concentric and other mathematically based symmetries. Our rectangular houses, football fields and books spring from engineering constraints, their beauty arising from necessity. We appreciate the curve of a suspension bridge, intuitively sensing the urgencies of gravity and tension.

Radial symmetry appears in the mandala patterns of almost every human culture, from Gothic stoneworks to Chinese rugs. Perhaps they echo the sun's glare flattened into two dimensions. In all cultures, small flaws in strict symmetries express artful creativity. As Lemarchand and Lomberg note, the universe itself began with a Big Bang that can be envisioned as a four-dimensional symmetric expansion; yet "without some flaws, so-called anisotropies, in the symmetry of the Big Bang, galaxies and stars would never have appeared."

A less obvious mathematical underpinning expresses itself in forms as diverse as the chambered nautilus, flower petals and galaxies. Draw three diagonals in a pentagon, and the intersections divide the lines in a ratio, 1/2(1+51/2) = 1.61803... The ancient Greeks noticed that this "Golden Section" in geometry emerged in many strikingly different ways. The human eye finds its echo pleasing in our own buildings; the Greeks used this.

When its pediment was intact, the Parthenon fit exactly into a rectangle with this ratio of sides. This proportion was first discovered by the Greek mathematician Pythagoras 2500 years ago; the sculptor Phidias used it. The United Nations building in New York City is proportioned as three stacked Parthenons.

Natural philosophers noticed that this number also appears in a famous sequence, the Fibonacci series (0, 1, 1, 2, 3, 5, 8, 13, 21...), which nature favors as well. Arrived at simply by summing the previous two entries in the sequence, this pattern appears in the branching pattern of trees, in the number of petals in the iris, primrose, and daisy, and in many other flowers. Pinecones, pineapples and sunflowers display overlapping clockwise and counter- clockwise patterns, their florets in the ratio of successive Fibonacci numbers, such as 21:34 in the sunflower. The Golden Section emerges when one takes the ratio of two successive terms; the higher these terms are, the nearer their ratio to 1.61803...

The Golden Section emerges from spirals by drawing perpendicular lines connecting different parts of the curve. The ratio of the lengths of adjacent lines is a close approximation to 1.6180... The spiral of the chambered nautilus follows the Golden Section, as do the curves of seashells and animal horns. Apparently the necessities of strong structures built from minimal materials force such underlying choices to emerge from the pressures of evolution. Growing in a fixed proportion does not shift the center of gravity, so balance problems do not develop.

Quite different physics generates the spiral waves in galaxies, yet in many these curves too express the Golden Section, sometimes also called the logarithmic spiral. The Golden Section lives in flowers, trees and galaxies, giving pattern to our entire universe, yet known only to a few of us hominids.

To those who have not had their sense of mathematics squashed by the mechanical drills of elementary school, the subject can burn with a peculiar rich intensity. Would aliens (or even further evolved humans) "see" the same mathematical underpinnings to our universe?

Strategies for the Search for Extra-Terrestrial Intelligence, SETI, have assumed this since their beginnings in the early 1960s. Many supposed that interesting properties such as the prime numbers, which do not appear in nature, would figure in schemes to send messages by radio. A case for the universality of mathematics is in turn an argument for the universality of aesthetic principles: evolution would shape all of us to the general contours of physical reality. The specifics could differ enormously, of course, as a glance at the odd creatures in our fossil record shows.

Our prospect was daunting. Many mathematical paths beckoned. For example, was there a way to embed in our message the compact equation


which links the most important constants in the whole of mathematical analysis, O, 1, e, pi and i? The equation looked beautiful to me, a "math type" as my wife dryly noted, but such types comprise a tiny audience even among humans.

What's more, we could not even find a clear way (independent of many assumptions about notation) to write the equation. Any writing scheme called upon human symbols. Such points stumped us. After all, philosophers of mathematics have argued over whether a mathematical object, like "9", is independent of human thought, or not. Some hold that it is neither external nor internal but social. This means mathematical ideas arise from our interactions with each other. Then a theorem known solely to its inventor does not in some sense even exist as mathematics until someone else understands it. Plates are round, an objective fact, but mathematical roundness is a human construction.

Perhaps. But all three views--mathematics is objective and real; it arises from an internal set of preconceptions; it is social--ignore biology, which brought about humans themselves through evolution. How general were our adaptations to our world?

How to decide such fundamental points? Our imaginations yearned to soar but momentarily stalled. In the end, we retreated to our sense of beauty.

Further difficulties arose in areas I had naively thought were straightforward. How to depict our solar system? To use mathematical universals, even once identified? How about the data processing assumptions behind recovering three-dimensionality through two- dimensional projections? How universal could be the use of scientific diagrams, our design of mathematical symbols, and the use of photos of humans?

All involved standing at a conceptual distance from ourselves, reaching for a more general way of seeing the world. But how firmly could we believe arguments from our own sense of beauty?

Comments and objections to this column are welcome. Please send them to Gregory Benford, Physics Department, Univ. Calif., Irvine, CA 92717. email:

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