A few weeks back I asked about Babylonian mathematics on
Grim's Hall, in reply to a post there. I'd only read (in a book comparing Egyptian, Babylonian, and Greek mathematics) that the Babylonians had found ways to solve certain classes of quadratic equations, but not the general case. Grim recommended
The Idea of Nature as a start.
The library copy was originally stamped "3 hour loan," which is a bit humiliating since it took me a bit longer than that to read it.
It is a history of the philosophical idea of nature from the pre-Socratic Greeks to Whitehead. He admits it isn't thorough, only touching on representative (i.e. well known by the author (That's what he says)) philosophers in three main categories: ancient Greek, Renaissance to 18'th century, and modern.
Rude and crude thumbnail of the imaginative environment in which philosophers worked in each era: Greeks thought of the world as alive and that motion was a sign of life and acting toward some purpose. The Renaissance brought in a materialist and mechanistic idea of the world, including a mechanistic idea of biology. Modern philosophers hear of relativity and quantum mechanics and the resulting fuzziness and duality.
I'm afraid that when the author began his admittedly amateur explanation of modern physics I was tearing what little hair remains and scribbling in the margins. (If the librarian does not approve of the value added, the additions are in pencil...)
From the get-go people were trying to figure out thorny questions like why is there miscellaneous but similar stuff, where did it come from, what is the relationship of mind to matter, and where do the non-material things fit into the scheme of things. Some of the goofy-sounding ideas (everything comes from water) turn out to be less loony than meets the eye. What was meant by "water" wasn't really H2O but unknown primordial material that needed a handy name.
With (probably) Pythagoras proposing that what made matter and things from the primordial whatever was geometry came some new trends. FWIW, mathematical symmetries are all the rage among physicists today--searching for them and their consequences has been very fruitful.
The author skips over Christian philosophy and finds Renaissance philosophers in reaction to Christianity proposing a materialist universe.
Scientifically speaking, on the other hand, materialism was from first to last an aspiration rather than an achievement. Its God was always a miracle-working God whose mysterious ways were past finding out. The hope was always cherished that with the advance of science we should find them out some day; so the scientific credit of materialism was maintained by drawing very large cheques in its own favor on assets not yet to hand. ... a statement such as this, that the brain secretes thought in exactly the same way in which the gall-bladder secretes gall, might pass as a dogma of religion, but scientifically speaking was simple bluff.
From within that kind of framework it is hard to find an origin for mind, and there seems to have been a lot of ink wasted on worries about how much of the world is created by the observer.
With Darwinian ideas about evolution the older ideas about the striving of organisms to reach their full nature (bud into leaf, etc) fell out of fashion in favor of mechanical models.
Most of the modern philosophers he discusses are more interested in matter as activity, which is more in line with the approach of the physicists.
None of the philosophers satisfy the author, and he ends with a suggestion that they are starting with too small a base of suppositions. To understand science, you need to understand history, because science is based on history. Nobody does every single experiment; they rely on records.
I found it quite interesting and learned a lot--though not about Babylonian math.
It may have been the author's intent to convey that impression, but I got the sense that people were mixing up categories rather badly. Science works by creating models of how parts of the world works, abstracting away those things that clutter the measurements to be made. That "clutter" is absolutely essential in understanding everyday life; which is complex. Because it is outward focused and abstracting, it does not address the obvious questions involved with "whence came this I that is observing?"
Anybody who's had a pet dog or cat has had the opportunity to discover that they don't act like machines. Some in the AI crowd have been claiming that human intelligence emerged spontaneously from complexity, but that doesn't address the I. In any event, making a model of human reactions may look convincing, but so is a life-size photograph. The map is not the territory.
I haven't thought it all through, but just because I have a sense-based model of the operations of the world (that seems reliable enough to trust with my life) does not mean that the only kind of knowledge I can have is sensory. That living things can sometimes be modeled as machinery doesn't mean they don't have some telos. Where I come from complexity generally results in fragility, not robustness, and a small change in a program can sometimes change the output completely. That mental activity can be imitated by other intellects doesn't explain where it came from originally. And the moral realm is a whole other story.
I think our design is irreducibly complex.
Read the book.