ET, phone home

This post also concerns the "intelligent design" controversy. See related posts below.

Let's think about the signal detected by SETI researchers in the fictional Contact scenario, an example given by intelligent design proponent William A. Dembski.

The signal from deep space was a sequence of sets of beeps, with each subsequent set holding the number of elements equal to a corresponding prime number. That is, the SETI team had detected a sequence of the first primes under the integer 100.
What are the chances of that? statistician Dembski asks. Obviously quite low. Detection of such a signal points to a sentient mind, he argues. Similarly, detection of a very low-probability pattern at the microbiotic level points to an intelligence behind the pattern, he says.

Suppose we don't consider the fact that the prime sequence is a well-known discrete climbing curve and we wished to know whether it significantly differed from a true random discrete curve. How would we go about detecting a difference?

Obviously, the SETI curve must differ from a fully random curve because it climbs from one value to the next, whereas a fully random curve would be likely to have an averaged out slope close to a horizontal line. So then, we must require that our candidate curve be random within constraints that require that the curve always climb. What would be the constraints? Clearly the constraints are the deterministic part of the curve.

What we find is that any computable climbing curve will do for constraints, with a set of random choices set between two values. A recursively defined curve (including a chaotic output recursive) would also do for a constraint, with the end value being randomly selected between f(x) and f(x+1). Or we can use two computable climbing curves and randomly choose a value that falls between the two curves.

For example, we might require that a value be chosen randomly between 2x and 3x. In that case, with enough values, the slope should tend to approximate [D(2x+3x)]/2, or 2.5.

Now we might check the SETI curve (up to the value received) and see what the average slope is. Even if the curve is actually composed of values of, say, p+7, the curve will map onto a known computable curve, of course. And we would suspect intelligence because we are unfamiliar with such a deterministically chaotic curve in nature.

However, it is conceivable that energy might be continually pumped into some system that results in a deterministically chaotic radio emission that shows ever-increasing numbers of bursts. Hence, we could not claim a designer was behind the emission merely on the basis of the constraints, unless we knew more about them.

Still, most processes in nature are deeply influenced by quantum phenomena, meaning a hefty degree of true randomness is injected into natural radio emissions.
So, if one could show that a radioed pattern was sufficiently deterministic, that would suffice to strongly indicate an intelligence behind the pattern. However, without knowledge of natural curves, we would have a tough time distinguishing between highly deterministic but chaotic climbing curves and truly random curves within constraints.

But, if we kept the constraints quite simple, that decision would influence how we categorize the suspect radio pattern. We would check the suspect slope and see whether its constraints (boundary slopes) are simple. If not, we would suspect full determinism, with any randomness being simple noise during transmission.

Now I don't suppose we expect constraint curves to be very complicated, probably following known climbing curves, such as supernova luminosity. That is, the slope average would conform to known natural phenomena, even if the specific patterns did not. So lacking such a slope, we could feel that we had either uncovered a new natural phenomenon or that we had encountered intelligence.