As I read books on mathematics and science, I’m always thinking of issues in theology and metaphysics and politics and history. My inclination, whatever works I produce as byproducts, is to absorb knowledge as if it were background knowledge for a novelist. This doesn’t mean ‘research’ that will produce reliable historical novels but rather the reshaping of my mind that I might tell a particular story which describes some true aspect or aspects of this world.
As I review discussions of coordinate systems in the science and mathematics books on my current reading list, I’m thinking about ways to speak of human knowledge in a unified sense as being made of knowledge-units, so to badly speak for now, which can be seen as states of being situated at specific points defined by a very complex system of coordinates which are defined by the various aspects of the issue under discussion. I’ll give a specific example later. (See the freely downloadable book, Four Kinds of Knowledge for my general views on the nature of knowledge.)
This much seems to be clear: modern forms of rationalism assume the world, Creation if admitted as such, consists of different realms describable by different forms of knowledge. Let’s simplistically but usefully think of these forms of rationalism as being both Spinozean and Cartesian. From Spinoza, we learned to think of the world in terms of realms of being, each with its own realm of knowledge. From Descartes, we learned to think of those realms of knowledge as being orthogonal to each other — in a manner of speaking. Moral philosophy and physics deal with the same reality but x-morality and y-physics meet at point (x,y) without really affecting each other. Changes to our understanding of man’s moral nature don’t affect our view of our physical world and vice versa.
Despite the potential, or even likely, complexity of this Spinozean-Cartesian way of thought, simplicity was the order of the day. Then again, as much simplicity as possible, but no more, is the rule for most thinkers exploring new ideas, else, they would soon be lost in many-dimensional mazes. Simplicity demanded that, at all points of contact between reality and a way of thinking about realms of knowledge, we should try to see simple geometrical objects — points or lines or planes. To make the system manageable, and to advance to a better system, thinkers had to — mostly — implicitly assume that those orthogonal knowledge-objects have flat surfaces and follow the rules laid down by Euclid. The entities and path-events we see in our world seem fantastically shaped to us, quite mysterious they be, partly because we expect to see the structures and movements suitable to an erector-set world. To be fair to Spinoza, a powerful and brutally honest thinker, and Descartes, a similar thinker with the added skills of a great mathematical thinker, they couldn’t have gone directly to ways of thinking about knowledge that are as sophisticated as what are now possible because of the explosion of geometric knowledge in the 19th century which resulted in, amongst other advances, Einstein’s view of spacetime.
The structures and movements, and the relationships between structures, are what they are and our efforts to understand their world — which is also our world — produce some sort of approximation to reality. Gradually, we can move towards a better approximation so that I can even say our minds can be shaped to encapsulate this world. Once it was necessary to see the physical stuff of the world in terms of Euclidean geometry. This fed into the philosophical systems of the Classical Greeks and related thinkers. Then we had the much richer world of the Newtonian-Libnizean calculus in (sometimes unfriendly) alliance with Cartesian analytic geometry. This fed into Kant and the British empiricists. The thoughts of all these schools of philosophy and science were greatly shaped by Spinoza’s fragmenting of the world into realms of being, realms of knowledge, but modern science developed in a certain way partly because of Cartesian schematics and Spinozean fragmentation. Could the advance have happened so rapidly otherwise? I don’t know.
In any case, the thinkers of the Age of Discovery were not only astronomers and mathematicians but also geographical explorers and even proto-anthropologists and proto-zoologists who enriched human thought by bringing samples or at least word and drawings of the exotic creatures and human cultures outside of Europe, but that didn’t seem to have led to any questioning of the fundamental nature of the stuff of this world. But why should all specialized levels and fields of human knowledge advance together?
To complete this whirlwind summary of human intellectual history, we have more recently had such oddities of thought as positivism which seemed to have taken Descartes’ skeptical methods and made those means into ends as well. These latter developments seem to have been also distortions and misuses of the tremendous advances in mathematical rigor in the 19th century or so. One line of advance was the explorations by Riemann, Klein, and others of more abstract systems of geometries in research papers, which papers were used by Einstein and his friend Grossman to develop systematic techniques of differential geometry and tensor calculus for use in Einstein’s description of world with a curved geometry of spacetime.
Our world is what it is and it’s a bit twisted and curved to our perceptions and cognitions. We can think of it in analogy to Einsteinian spacetime where the three dimensions of space and the one dimension of time can be best described in terms of coordinate axes which are generally skewed, not at right angles. This provides mathematical ways of describing, say, the bending of both time and space at the horizon of a black hole, ways which can be labeled as ‘natural’. Coordinates are handled, that is, in ways that are natural for the aspects of physical reality which are being explored, such as the problem of measuring a 12 inch ruler on a spaceship passing you at 10,000 miles per hour and another passing at 10,000 miles per second. The second spaceship is traveling, relative to you, at a small but significant percentage of the speed of light — 189,000 miles per second — and the ruler will be relatively shorter by your measurement than the ruler on the slower spaceship.
At the same time, we should note that these measurements of reality, in fact — reality itself, are governed by certain invariants. The most important for this example is the speed of light which is the maximum speed of communication between entities in this universe — after all, light or electromagnetic energy in general is the medium which carries communications in this universe.
Let me take a very simple commandment as an invariant for human communities:
You should honor your mother and your father.
The problem is: how are we to care for our parents, including all those of the earlier generation in our community? For communities reasonably stable over a small number of generations and also in the concrete relationships between individuals, there is usually a traditional solution to the problem and it can be accepted, even accepted as an ‘absolute’ solution by those rigidly bound to one set of attitudes and thoughts. For example, the Puritans of Colonial Massachusetts took care of most of their elderly and others needing help within families or local congregations. At the same time, the Colonial government, and the Massachusetts government for several decades after the War of Independence, mandated that all local political communities provide shelter and clothing and food for those in those local communities without someone to care for them.
More directly in line with the problem of caring for the elderly: those who had built up farms or trade businesses, or had maintained or expanded inherited productive property, would turn those over to one or more children in return for care over their remaining years. There was no highly liquid economy to provide even an illusion of independence for the elderly from their children. The productivity of those children and their willingness to honor their commitments to their parents founded or ill-founded the security for those parents in their elder years. The parents prospered or suffered, all else being equal as economists say, from the competence or incompetence, luck or ill-luck, of their children.
Right away, we can see a more complete description of this problem would involve a complex set of coordinates dealing with the economic structure of a particular community and the larger communities of which it’s a part and also a complex set of coordinates describing the relationships between generations. The aspects of economic structure to be considered would include the ownership of productive operations (corporation/family), the level of liquidity (cash-transactions/barter), the ways of setting up offspring in life (“communities setting up other communities in the ‘Amish’ way”/”send the kid off to the mills at 12 or to college at 18 in the liberal/individualist way”), and so forth. This isn’t an inclusive list and the possibilities in the parentheses are merely examples. Already we can see a complication and complexification — the list of aspects of economic structure includes “the ways of setting up offspring in life” which is also an important aspect of the coordinate system describing relationships between generations.
What can I conclude at this point? First of all, I’ve failed at a very basic level — that of setting up a way of dealing with the complex moral surfaces we form in our community lives. This is a well-known failure — some moral-social conservatives were in opposition to Social Security from the beginning because of this particular issue of the interaction between economic structure and the relationship between generations, but those conservatives had no way of speaking that was compelling. In my terms, they feared that an effort to deal with the care of the elderly using a tax-based, cash-based pension system would itself tear American families and communities apart by altering the relationships between generations, but they came across as being simply Scrooges uncaring about the starving elderly. Action, especially that as dramatic as altering the care of the elderly and disabled, changes the shape of the surfaces we move on as moral and social creatures. That action is also very difficult to describe and, for now, beyond being describable to any but sophisticated thinkers — which doesn’t necessarily mean those with doctorates or even those with college degrees. In any case, even those philosophers and social-scientists who are sophisticated thinkers haven’t any convincing ways to describe these problems to each other.
In general, competent historians and economists have been dealing with these issues for a couple of centuries or so, some of them in very competent and articulate ways, some of them in prose much easier to understand than that I’m producing as I suggest new ways to look at our individual and community lives. The problem remains that their prose is that of traditional thinkers, embedded in ‘Euclidean’ worlds or perhaps ‘Spinozean-Cartesian’ worlds. They don’t think or write in words and concepts more natural to the sophisticated problems of abstracting from concrete and particular human societies and of describing societies much more complex than those of pre-modern times.