Bernoulli's test for non random design
Bernoulli used the fact that the orbits of the planets about the sun fall into striking patterns. They are roughly in the same plane, and they circle the sun in the same direction. It is highly unlikely that this is due to mere coincidence and Bernoulli rightly concluded that the planetary orbits are far from random.
This fact that the orbits are far from random was highly significant for Bernoulli. He argued strenuously that this proved that the solar system was formed by a single cause. One problem with Bernoulli's logic is that a design can be far from random and yet nonetheless highly variable. In other words, the test for non randomness is not very precise.
Indeed, in later years the many variations in the planetary orbits would require a number of causes to be hypothesized. In order to create the various oddities in the planetary orbits, as well as our moon, cosmologists were hypothesizing a cosmic game of billiards with celestial objects careening and crashing into each other. Long gone was Bernoulli's single cause even though the solar system still passed his test of non randomness.
Immanuel Kant makes the metaphysics explicit
Another problem with Bernoulli's proof was the underlying metaphysics of naturalism. This became explicit twenty years later when the great philosopher Immanuel Kant reiterated the argument. The solar system must have evolved via natural laws, concluded Kant, because if God had designed the solar system it would not have the patterns we observe:
It is clear that there is no reason why the celestial bodies must organize their orbits in one single direction. … Thus, God’s choice, not having the slightest motive for tying them to one single arrangement, would reveal itself with a greater freedom in all sorts of deviations and differences.
And after Kant the great French mathematician and scientist, Pierre Laplace repeated the argument. Laplace and Kant are, to this day, credited with elucidating the foundational thesis of the evolution of the solar system. They both were quite certain their reasoning had led to a new truth. This was no mere hypothesis or theory.
Darwin's use of non random design in biology
Like astronomy, biology also reveals many patterns. And like Bernoulli, Kant and Laplace, Darwin proved his theory of evolution to be true using random design as the null hypothesis. Darwin cited patterns that revealed biological designs are not random. Echoing Kant, Darwin rhetorically asked, “Why should not Nature take a sudden leap from structure to structure?” For Darwin biology revealed consistent patterns. “We never find the bones of the arm and forearm, or of the thigh and leg, transposed.” This was his null hypothesis: unconstrained, random design. Its failure and the patterns in biology left non evolutionary explanations “hopeless.”
Following Darwin, evolutionists continued to interpret patterns in biology as proofs of their theory. Everything from blood immunity data to chimp-human DNA comparisons are, for Darwinists, mandates for common descent, regardless of evidential difficulties. The important point here is that evolution is viewed as the only alternative to random design. That is a metaphysical claim.
And as with the theory of the evolution of the solar system, the theory of biological evolution also had to be substantially patched due to the many variations of designs. In other words, yes biological designs reveal patterns that are far from random, but the many variations in those designs defy evolutionary explanations.
Other star systems not so orderly
In recent years planets circling distant stars have been detected. Many of them seemed to defy our understanding of how star systems would form (based on studies of our solar system). Now, new research is showing that the evidence is even more defiant as a substantial fraction of these distant planets are found to have non standard (more random) orbits about their sun. As one astronomer explained, the new findings represent “a spectacular upheaval of the standard view of close-in planet formation … and probably indicate instead catastrophic encounters between several planets.”
So star systems can be chaotic after all. The orderly, non random, solar system of Bernoulli and Kant now appears to be anything but the norm. They argued that such orderliness was proof of evolution, but now we see that evolution accommodates chaotic designs as well. It turns out that such orderliness was not so crucial. It was the motivation for the original argument from non random design, but as usual nature has turned out to be more complicated than evolution expected.