When I discovered that the modern paradigm in neuroscience is viewing the brain as a dynamical system, something very different from a machine or a computer, I quickly realized how much mathematical background was required to really understand the fascinating topics of our time. The way I understand it is this: much of the technology developed during the last few centuries has been enabled through reductionist methods.
What is this made out of? Why is that? How come that happens or this occurs? Deducing, analyzing, reducing the world to its constituents.
But now the perplexing phenomena are emergent ones: mind, life, weather, etc. Is it even possible to understand, given the exapted abilities we have? (meaning, cognitive abilities originally evolved for one set of purposes becomes the ability to invent, create, build, etc.) For instance, Yann LeCun raised the example that we are not able to percieve structure in the motion of molecules of gas (the entropy or heat in a volume of space) even though there may exist such a thing, because our eyes and brains did not evolve to see it.
Granted I am just a dabbler in this knowledge, but it almost seems that there are two possibilities. One, that the above in fact is not possible and we are already at the upper echelons of scientific progress. That, though intelligent life may have sprung up in the galaxy many times, or in the universe a countless number, all civilizations and beings ultimately reached a similar maximum level of technology.
Or two, that just as the scientific revolution ushered in new ages that brought first the sailing of worldwide seas and international trade, then modern medicine, industrial production of chemicals and mechanization, then ultimately nuclear power, space flight, the biotech revolution, and the information age we currently live in, some fundamental shift in paradigm would occur as studying emergent phenomena necessitates new mathematics and science, and that there are unknown ages to come.
After all, over the last two decades thousands of exoplanets have been discovered, and the next generation of ground and space telescopes will be able to directly image other Earths, around other stars. Could the structure of reality be such that humans would be able to see other Earths but never be able to construct the spacecraft to visit them? Would the structure of reality be such that humans could create art and music, but not have the technology to survive natural and cosmic events (global warming, asteroid impact, etc.)
I do have some of my own thoughts, that are more qualitative than formal. For instance, I seem to notice that many things are structurally similar at different scales. So, as a notion of beauty, if there are multiple explanations and one fits that principle, that (to me) could be viewed as more beautiful.
https://www.goodreads.com/book/show/18554985-the-systems-view-of-life
