Questioning The Prime Directive

Pi in the Sky?

Should we be listening for a beacon from the clouds in the language of mathematics? It has long been offered as a prototypical communication sent from one advanced civilization to another, that the first message will encode the ratio of a circle’s circumference to its diameter, or pi (3.142…). In Carl Sagan’s book, Contact, and the movie it inspired, the signal beacon was the mathematical sequence of prime numbers, those which are divisible only by itself and one. Similarly, in Steven Spielberg’s film, Close Encounters of the Third Kind, a dialogue is struck in the language of music in a quick action lesson in mimicry and translation.

The history of what type of signal might qualify as a signpost of intelligent broadcasting has traditionally been a choice subject to contention. From the 1960’s, with the discovery of pulsars, or stars that blink on and off naturally, the notion of a lighthouse beacon from nature has had to evolve and change. As the SETI Institute’s Seth Shostak writes: "since [pular discoveries], SETI researchers have expended considerable neural energy in considering what type of radio emissions would unequivocally qualify as artificial". In SETI discussions, the idea has been to separate cleanly the artificial from the natural, with artificiality as one key to understanding another broadcasting language and ultimately, intelligence itself. Can our own mathematicians differentiate between what signals from deep space might contain wise intelligence or the witless noise of a galactic dust cloud.

According to Nobel Laureate, Herbert Simon,–widely considered the father of artificial intelligence–, this distinction is central to what might be interpreted as a detection event: "Symbol systems solve problems by generating potential solutions and testing them, that is, by searching…We must be careful about equating ‘biological’ with ‘natural’. A forest may be a phenomenon of nature; a farm certainly is not…Unfortunately the term ‘artificial’ has a pejorative air about it that we must dispel before we can proceed. Our language seems to reflect man’s deep distrust of his own products. My dictionary defines ‘artificial’ as, ‘Produced by art rather than by nature’."

Stephen Wolfram, founder of Wolfram Research, author of A New Kind of Science
Credit: Wolfram Science

The new book, A New Kind of Science, by the esteemed founder of the software company, Mathematica, and MacArthur Award winner–Stephen Wolfram–addresses the wisdom of considering whether any natural process can spawn the sort of radio signals that previously have been regarded as one definitive SETI signature of an intelligent transmission.

Shostak continues to frame the question that has occupied both SETI researchers and Wolfram alike: "An obvious suggestion – and one that well-meaning folks the world over love to send me in e-mails – is to search for a signal that is branded with a mathematical label. For example, maybe the aliens will tag their transmission with the value of pi. That would clearly bespeak a middle school education, and would prove that the signal comes from thinking beings, rather than witless neutron stars or some other cosmic oddity. More numerate correspondents try to improve on pi. Perhaps the extraterrestrials will preface their message with a string of prime numbers, or maybe the first fifty terms of the ever-popular Fibonacci series. Well, there’s no doubt that such tags would convey intelligence. But what if the prime numbers are only broadcast at the start of a 100-hour interstellar screed, and we tune in somewhere in the middle? We’d miss the label."

Can the inanimate or unintelligent spawn a sequence of primes, those numbers divisible only by one and itself, like 2,3,5,7, 11 and 13? The excerpt that follows from Wolfram’s A New Kind of Science details the arguments for why Wolfram believes pure computation and natural phenomena can emulate most previous mathematical signatures of an intelligent broadcast. In other words, simple rules can fool the sky-listening algorithms currently wired for detection of another civilization’s beacon.

Stephen Wolfram was born in London and educated at Eton, Oxford, and Caltech. He received his Ph.D. in theoretical physics in 1979 at the age of 20, having already made lasting contributions to particle physics and cosmology. In 1981 his work was recognized by a MacArthur award. In the early 1980s he made a series of classic discoveries about systems known as cellular automata, which have yielded many new insights in physics, mathematics, computer science, biology, and other fields. In 1986 he founded Wolfram Research, Inc. and began the creation of Mathematica, now the world’s leading software system for technical computing and symbolic programming, and the tool that made A New Kind of Science possible. Over the past decade Wolfram has divided his time between the leadership of his company and his pursuit of basic science.

We have seen a great many examples where data that appears to us quite random can in fact be produced by very simple underlying rules. And although I somewhat doubt it, one could certainly imagine that if one where to show data …or the digit sequence of pi to an extraterrestrial then they would immediately be able to deduce simple rules that can produce these.

But even if at some point we were able to find that some of the seemingly random radio noise that we detect can be generated by simple rules, what would this mean about extraterrestrial intelligence?

In many respects, the simpler the rules, the more likely it might seem that they could be associated with ordinary physical processes without anything like intelligence being involved.

So is there then any kind of signal that could be sent that would unabiguously communicate the presence of intelligence?

wolfram science
A New Kind of Science sample page, rich with drawings of natural patterns simulated by relatively simple computational rules
Credit: Wolfram Science

In the past one might have thought that it would be enough for the production of the signal to involve sophisticated computation. But…such computation is quite common in all sorts of systems that do not show anything that we would normally consider intelligence.

And indeed it seems likely that for example an ordinary physical process like fluid turbulence in the gas around a star should rather quickly do more computation than has be most measures ever been done throughout the whole course of human intellectual history.

In discussions of extraterrestrial intelligence it is often claimed that mathematical constructs–such as the sequence of primes–somehow serve as universal signs of intelligence.

Sounds of Earth
On the chance that someone is out there, NASA approved the placement of a phonograph record on each of the Voyager spacecraft. The recording, called "Sounds of Earth" fits on a 12-inch, copper disc containing greetings from Earth people in 60 languages, samples of music from different cultures and eras, and natural sounds of surf, wind and thunder, and birds, whales and other animals. The record also contains electronic information that an advanced technological civilization could convert into diagrams, pictures and printed words, including a message from President Carter. Credit: NASA

But from the results in [A New Kind of Science], it is clear that this is not correct.

For while in the past it might have seemed that the only way to generate primes was by using intelligence, we now know that the rather straightforward computations required can actually be carried out by a vast range of different systems–with no apparent need for intelligence.

One might nevertheless imagine that any sufficiently advanced intelligence would somehow at least consider the primes significant.

But here again I do not believe that this is correct. For very little even of current human technology depends on ideas about primes. And I am also fairly sure that not much can be deduced from the fact that primes happen to be popular in present-day human mathematics.

If one identifies a feature–such as repetition or nesting–that is common to many possible systems, then it becomes inevitable that this feature will appear not only when intelligence or mathematics is involved, but also in all sorts of systems that just occur in nature.

So what about trying to set up a signal that gives evidence of somehow having been created for a purpose? I argued above that if the rules of a system are as simple as they can be, then this may suggest the presence of purpose. But such a criterion relies on seeing not only a signal but also the mechanism by which the signal was produced.

So what about a signal on its own? One might imagine that one could set something up–say the solution to a difficult mathematical problem–that was somehow easy to describe in terms of a constraint or purpose, but difficult to explain in terms of an explicit mechanism.

But in a sense such a thing cannot exist. For given a constraint, it is always in principle simple to set up an exhaustive search that provides a mechanism for finding what satisfies the constraint. …For as we have seen, many systems that just occur in nature actually end up doing more computation than typical systems that we explicitly set up for a purpose.

Can one perhaps use a signal that is a representation of actual data in, say, astronomy, physics or chemistry?

The more direct the representation, the more easily an ordinary physical process can be expected to generate it, and the less there will be any indication of intelligence–just as, for example, something like a photograph can be produced essentially just by projecting light, while a diagram or painting requires more.

Digital cave painting has been part of signals sent into deep space as indicators of human perception and representation
Credit: SETI Institute/Arecibo

But as soon as there is interpretation of data, it can become very difficult to recognize the results. For different forms of perception and different experiences and contexts can cause vastly different features to be emphasized. And thus, for example, the fact that we can readily recognize pictures of animals in cave paintings made by Stone Age humans depend greatly on the fact that our visual systems still picks up the same specific features.

So what does all this mean about extraterrestrial intelligence?

My main conclusion is rather similar to my conclusion about artificial intelligence: that the basic issue is not finding systems that perform sophisticated enough computations, but rather finding ones whose details happen to be similar enough to us as humans that we recognize what they do as showing intelligence.

If we require something that follows too many of the details of us as humans there is already evidence that it does not exist. For if such intelligence had ever arisen in the past, then extrapolating from our own history we would expect that some of it would long ago have colonized our galaxy–at least with signals, if not with physical objects.

But I suspect that if we generalize even quite modestly our definition of intelligence then there would be examples that can be found–at least with sufficiently powerful methods of perception and analysis. Yet it seems likely that they will behave in some ways that are as bizarrely different from human intelligence as many of the simple programs in [A New Kind of Science] are different from the systems that have been traditionally been studied in human mathematics and science.

"A New Kind of Science", by Wolfram Media, Inc. Copyright is held by Stephen Wolfram, LLC, 2002

Related Web Pages

Prime Pages
A New Kind of Science