The title gives the news. I’m aiming to post something substantial at least once a month and hope for once every two weeks—at least occasionally.
Why am I writing posts less frequently?
For now the main reason for fewer posts is my various efforts to gain new knowledge and to think new thoughts in dealing with a very difficult problem which will be introduced next week in a posting—though it’s a line of thought I’ve dealt with in a more general way in past years. The difficulties are leading me to learn or re-learn a bit more mathematics and it’s usually fun, sometimes to the point of distraction from my goals. Again, for much of the thinking we need to do to establish a new Christian civilization (or any other sort of well-ordered civilization), we need to deal in more intelligent ways with the knowledge of empirical reality which has been gained in recent centuries by historians as well as physicists.
I think the proper way to do this is by using various branches of abstract mathematics which have proven so powerful in the works of Einstein and other theoreticians, that is, so powerful in describing certain realms of created being. It is so powerful largely because it has been abstracted to the level of relationships (abstract created being) which are primary and which create and shape the more concrete forms of created being which we can perceive more directly.
But we need to abstract further to levels of relationships which are not necessarily at all quantitative and, though sharing in the discipline of mathematics, aren’t necessarily formal in quite the way of geometry and algebra as most people understand (or don’t understand) those fields of human endeavor. Relationships of more specific relationships are the way to head and may be the true key to it all. So far as I can figure from very slight knowledge of the field, category theory is heading in this direction.
One way to start thinking about the nature of modern mathematics is to learn about the difference between great mathematical thinkers of, say, the early 1800s and more recent decades. Gauss, arguably the greatest of all mathematicians to now and also a great physicist and something of a great technologist, loved to do calculations which would be repellent to any current mathematicians. Gauss maybe needed to be that way since he worked such problems as the development of least-squares curve-fitting and its application to plotting orbits of planets and asteroids; and he had no computers. In any case, we are educated in ways nowadays so that the brighter minds are usually horrified at any hint of having to spend hours calculating a constant of mathematics or physics out to many places of accuracy. Gauss seemed to enjoy it as much as he enjoyed doing high-level number theory.
The minds of serious mathematics thinkers of the West in our day are shaped differently than those of Gauss and Newton; those minds, and our more ordinary minds in slightly different ways, are shaped to the current (or perhaps just past) needs of our civilization. As a thinker who is a devout Christian and also convinced of the dire situation of the West, convinced of the need to reform or rebuild Western Civilization, I’m heading in the same general direction as the more recent generations of mathematicians and theoretical physicists. Mathematicians, even more than physicists and biologists and engineers, have been extremely successful at responding to our world and producing new ways of understanding this world and what lies beyond and above and below this world. We who work in other fields should be learning from the most successful of modern thinkers rather than continuing to walk along the ruts first formed in the early generations of the Modern Age.
And so it is that I’m about to make a more serious effort to deal with the truths expressed by various forms of dualistic thought but to deal with them in a way consistent with our modern knowledge of empirical reality. This could even feed back into mathematics and physics and other fields of human thought, correcting the dualistic tendencies to, for example, see mathematical truths as being somehow independent of the world and all that which lies beyond and above and below it. This creates the dualistic paradox of creatures knowing truths which aren’t somehow manifested in realms of Creation—to put it in Christian terms.