In terms of science, applied science, leads pure or natural science. This is why we still have to do experiments to verify any theory, with experiments connected to applied science. The mistake that is being made, in terms of life elsewhere in the universe, is this is based on science, placed before applied science experimental proof. We have never seen life of any kind outside the earth, yet science tries to predict there is, all without hard applied science data?
The significance of this premise; applied science comes first and pure science second, explains how something like the Pyramids were built at a time, before modern science. Their understanding of the modern laws of science were primitive, yet they could design and build what still challenges modern science explanations. This was advanced applied science, consistent with modern science, but applied at a time, before much was known in pure science. History would still need to develop tech, to help fill in the earlier blanks; telescope and optics, before the Pyramid applied science can be known.
As a modern day example of this hierarchy of science, consider the iPhone. If we only use the known laws of modern pure and natural science, and statistics, what are the odds of the iPhone, appearing naturally on earth; grow on trees or hatch from eggs? The odds are close to zero, even though there is nothing about the iPhone that exceeds the laws of science we know. What are the odds of millions of iPhones appearing in nature, on earth, by natural laws? Applied science is not based on the randomness principles, used by pure science ,since it can defy these natural odds. Pure science is a subset of applied science, since many innovation that obey natural laws, do have natural odds for appearing. Humans create them even before they are thought about. However, bad quality control can introduce the need for the science math subset of QC statistics. Applied is more sure thing even of natural law is modeled with odds.
In modern times, our catalo of pure science has been developed, from applied science experiments, from the past. We now have a large pure science theoretical complex and data base. Theory that derives ew science from existing science, tends to be based on odds; life on other planets, even without any hard experimental data from applied science. This science from science approach leads to science fiction, sold as genuine science, since science that evolves, not by its itself and proof, but from odds. However, the principle of applied science is not limited by statistics or natural odds.
A good case in point was the BB theory seemed to be a done deal based on randomness assumption; BB, and science from science. Recently, applied science experiments have discovered fully formed galaxies from very early in the BB universe. This applied science observation is too deterministic, and not predicted by the experts; science from science and odds, who tried to extrapolate science from science with odds. Now Physics has a major redo.
This is why I fight against statistical models, since they are more of an artifact of science from science theory without applied science leading. Ironically, the prestige in science culture is more about science theory and less about engineering proof. This is backwards in terms of the natural hierarchy of science. It leads to illusions in science.