In my last three essays I posted, Mathematical Models of Human Communities: Parts and Wholes, Mathematical Models of Human Communities: We Live in Narratives, Not in Models, and Mathematical Models of Human Communities: Randomness, I acknowledged the usefulness and potential truthfulness of mathematical models but claimed we need to consider wider aspects of this world and of all of Creation; mathematical models have to be put into a greater context, a belief also seemingly held by Weidlich, the author of the book I was responding to. In particular, I discussed in the first of those essays, very briefly, the ways in which many complex systems, those of physical spacetime and—with near certainty—those of human social relationships, have global properties which don’t fully come from summing up local properties. In the second essay, I discussed, with equal brevity, the nature of one of those global aspects of complex systems and especially human communities—they are stories or narratives with the properties which we expect in novels or tales and which don’t come from mathematical models as such. In the third essay, I presented a very preliminary discussion of the true nature of randomness (more or less—factuality) in this context of mathematical models.
In this essay, fourth and last in this series, I’ll respond to the same quote that I responded to in the third essay. In Sociodynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences (Wolfgang Weidlich, Dover Publications, 2006), the author writes on page 155:
Historical and/or social phase-transitions are by definition revolutionary events in which the macrovariables of the system change their whole dynamical mode. A necessary concomitant circumstance of such a phase-transition is the appearance of critical fluctuations. These critical fluctuations are crucial for deciding the question which direction the path of the system will take at the cross-roads. In our case they are decisive for the question whether the political system will remain a liberal democratic one or whether it tumbles into the new totalitarian phase.
However—and this is the essential argument—the critical fluctuations are of random nature and are neither predictable by the research of historians, nor by the macroequations of any mathematical model! At best the full set of macrovariables and (not predictable) fluctuating microvariables which both together are causative for the concrete course of historical events at a phase-transition can be recognized by historians only retrospectively.
Therefor the general conclusion must be: In the rare cases of historical phase-transitions fluctuations become decisive (in contrast to smoothly and continuously evolving situations). These fluctuations consist of thoughts, decisions and activities of one or a few persons in key-positions in a global situation on the verge of a possible phase-transition.
This does of course not mean, that the continuous—to a high degree “calculable” and therefore predictable—macrovariables would be unimportant. In the contrary! They lead to the “revolutionary situation”, i.e. into the vicinity of a destabilizable situation where “everything can happen“. However, at the phase-transition these macrovariables are insufficient to make the further course of events predictable!
It’s hardly surprising that we can’t predict which of, say, five major paths a country might follow as a crisis approaches. I’d claim, and perhaps Weidlich would agree, that it’s worse than that—we can’t really even lay out the landscape in which possible paths lie.
As Weidlich says: “the concrete course of historical events at a phase-transition can be recognized by historians only retrospectively“. I’m currently reading a mainstream and apparently well-regarded book: A History of Russia by Nicholas V Riasanovsky. It reminds me of what I’ve read before: even Lenin, a remarkably competent actor in real-time whatever we might think of his ideas and actions, was improvising and adjusting his ideas to justify those ad-hoc responses to a rapidly changing situation. Ahead of us lies the fog of war and of other crises, ongoing or concentrated in a short period of time.
When I was younger and playing regularly in pickup basketball games, I also couldn’t see the position of all the players on the court let alone see their positions a second later the way that Larry Bird and a few other great playmakers could. They have mental skills, talents for geometric imaging, which are not found in many; they are inborn but highly developed by way of doing.
Suppose that there are also mental skills, cognitive and imaginative, which could allow us to see the possible futures ahead of us; this form of seeing would be abstract; it wouldn’t be likely we could visualize these possible futures in terms of discrete possibilities as is true on a basketball court. These would be high level mental skills, more like the highly developed skills of a mathematical physicist than those of a great playmaker on the basketball court.
But, as John Polkinghorne—theoretical physicist and then Anglican priest—pointed out: physicists haven’t learned how to think in this way. (See Shaping Our Minds to Reality.) As a one-time professor of physics at Cambridge University, he wrote of the difficulty in convincing (presumably elite) physics students that a vector is simply a mathematical object which obeys certain rules of transformation. It took about a year for the students to accept what they were told by Professor Polkinghorne and then they apparently couldn’t imagine they’d ever believed anything different. Polkinghorne also noted, in my terms, that physicists were still trying to make quantum physics conform to the preconceptions of reality they had brought to the study of advanced physics. We are all still, in a strong but constrained sense, opponents of Galileo. Galileo himself was not so flexible of thought as some renderings of his story would have it. A human being fully flexible of thought would be forever chasing will-o’-the-wisps.
More importantly for now, we need to recognize that scientists and philosophers aren’t so progressive as they claim to be; that is to say, they haven’t really reshaped their thoughts to conform to a coherent understanding of reality. Even the last sentence is inadequate, not nearly radical enough, as could be probably said of Polkinghorne’s ways of expressing the problem.
We don’t need new thoughts for our existing minds. We need new minds, that is, new relationships to reality. We need to encapsulate our best knowledge of Creation, the best knowledge from physics and mathematics and evolutionary biology and neuroscience and engineering and history; we need to encapsulate that knowledge in our brains as understandings capable of holding this knowledge in a coherent way. Even better: we need to encapsulate that knowledge in our brains as images of reality, in its concrete and abstract levels. We need minds which are mirrors of Creation, that is: mirrors of certain thoughts the Creator manifested as created being.
If we succeed in such a task, or more plausibly—succeed in helping future generations to form minds proper to our world, even all of Creation, as we now know it, then we will no longer feel obliged to pour our new knowledge into an inherited understanding of the world, though perhaps patched-up. We’ll be at peace with the world, until something happens to bring to light some major aspects or levels of Creation which are new to us—and thus seem to be alien to the purposes of our God.
I’m most certainly not claiming we’ll be able to see the future in the sense of knowing what will happen or even to be able to propose, in all cases, a set of all possibilities along with a probability of each of those possibilities being realized. What we will be able to see is some overlapping possibilities somewhat like a collection of quantum wavefunctions. From there we can get to work by returning to the forms of reasoning more appropriate to the concrete world. I wrote of my own efforts to work toward a better understanding of Creation, way back in 2009, in the essay: Defining Landscapes and Possible Paths, Not Determining Paths. This is the sort of general analysis which applies in the small as well as the large, applies to our efforts to understand the emerging relationships between East and West in our period as well as to our efforts to understand the emerging relationships of Creation at its fundamental levels—the emerging relationships which will allow richer and more complex understandings of rocks and stars and our own human natures. And also richer and more complex understandings of algebraic relationships and of transfinite numbers.
In the previous entry in this short series ended by the current essay, Mathematical Models of Human Communities: Randomness, I wrote: “[I]n the 14th century or so, long division was coming into use and was considered to be a topic for mathematical geniuses, well beyond those even of more normal high intelligence. Nowadays, we start learning long division in mass education elementary schools, though many still have trouble with it and some can never master it even to the point of figuring how much per pound a roast costs if 4.5 pounds cost $25.”
There are other transitions in history, one perhaps being the birth of the mind in the sense of an entity which can deal with abstract forms of being as well as concrete forms of being. Many there are who seem bright but see “true being” as the single level of concrete, thing-like being. Many there are who can use formalisms, such as those of mathematics or logic or common-sense of various types, in trying to see the “rules” of concrete being. Few there seem to be who can see abstract being as being such. It takes certain developments of the cognitive and imaginative regions of their minds; many there might be who are capable of such but few seem to have developed such.
Back in 2008 and 2009, I wrote some early essays on the issue of the human mind as being an encapsulation of what lies around it, in the sense of what can be perceived and conceived and imagined in a particular cultural and physical setting: What is the Role of Philosophy in an Age of Science?, What is Mind?: Can Inadequate Formation Mimic Mental Diseases?, and Preliminary Thoughts on the Evolution of the Human Mind.
Since that time, I have not concentrated on this issue—in this particular explicit form. As it turned out, my early feelings seem more and more correct: the human mind in a particular place and at a particular time reaches its peak, and then most noticeably in its communal form, when it accurately encapsulates as much of Creation as can be `reached’ at that place and time. We expand our individual and communal minds, enriching and complexifying, by using our existing minds to do this reaching. We explore. We measure and build quantitative models. We struggle to reach greater qualitative understandings. We reason and we imagine. We enlarge and complexify our own minds to some extent and those of our children to a greater extent.
In this sense, we modern men, including Christians, have poorly developed minds. We can’t see the cloudy futures because we don’t have a good understanding of spacetime, of matter, of human nature. Our weak understandings of Creation, of particular forms or aspects of created being, are sometimes good enough to see the past in an intelligible and intelligent way, but seeing possible futures for, say, the United States is even harder than trying to see what it was that the Founding Fathers really did. Even our vision of past and present will clarify and provide for more intelligible and intelligent understandings if we simply come to a better understanding of the world, including the evolutionary and developmental aspects of human nature and also including the somewhat similar aspects of the nature of brute matter and energy.
Back to seeing future possibilities: we need to truly understand blurriness as it shows up in complex statistical situations and in quantum physics—with an underlying measure-theoretic understanding of probability, these are similar problems and problems of a world which generates facts rather than a world generated by some pseudo-mystical mathemagic. I can’t even say what it might mean to visualize such aspects of reality, just as the greatest of ancient mathematicians, Greek and Indian and Arabic, couldn’t say what it might mean to visualize the quantitative aspects of shapes or movements in symbolic forms. Yet, they worked, however unknowingly, toward algebra and it’s now taught in most high schools and some higher-quality elementary schools. Some precocious youngsters even learn it at an age before most are learning to read or write.