*by* Gaianne
*Wed Jan 2nd, 2008 at 01:31:29 AM EST*

Of course you will be wanting me to justify or defend this title. So perhaps I had better admit at the outset that I cannot. Nobody knows what the coming age will be, nor what metaphysics it will either accept, or require. Nonetheless, that is where I would have us turn our minds, for consideration and speculation.

This is, obviously, a heat-generating topic. Metaphysics is like religion, indeed, as it is concerned with the fundamental structure and meaning of the world (or of life) it IS religion, where religion exists. And where religion does not, metaphysics takes on the religious passion.

But I would have us consider it anyway, because whatever we believe, it is likely to change. Circumstances alone will see to that. My goal here is not to seek agreement, but to find possibilities--more important than what is precluded (although some notions will be being shed) is what is allowed.

I write as a progressive who no longer believes in progress. This is an embarrassing thing. But progressivism was born in the apparent abundance of rising empire, and in the idea that if wealth is plentiful, then it OUGHT to be shared out (rather than horded by a few), but as abundance visibly disappears, the spiritual aspects of progressivism (to me, the most important part) lose their material support. Now what?

I should also admit at the outset that I am an apostate from science. I indulge some personal history to explain what that is and how it came to be:

I grew up, as a child, in a context of intermittent violence and pervasive lying (and lying about the lying) so that it was natural and inevitable that I was drawn to mathematics, where the truth was both knowable and provable. This became both a career and an emotional anchor.

The irony, of course, is that unbeknownst to me, a century earlier the idea of truth had already run into trouble. The problem was the parallel postulate of Euclidean Geometry, which has several equivalent forms, but is readily visualized as stating that through any point outside a given line, there is exactly one line through that point parallel to the given line. For centuries mathematicians had thought that postulate should be a theorem, proved as a consequence of the other postulates, but had failed to find the proof.

In the middle of the 19th century, in something like desperation, mathematicians decided to reverse their approach, to try assuming the postulate false, and see what kind of geometry would result.

Riemann became known for postulating that there are NO parallel lines. The result is a Geometry quite unlike Euclid's, but nevertheless completely consistent. All doubt about the validity of Riemann's work was perforce dispelled when a "model" of his Geometry was found:

Let a "point" be defined as any pair of antipodes of a sphere, and let a "line" be defined as a great circle on the sphere (a circle on a plane that passes through the center), and then Riemannian Geometry becomes equivalent to Spherical Geometry, which had already been being used by navigators for several centuries.

The alternative contradiction was also tried, and, skipping over the issues of theft and precedence (the practice of mathematics is truly a catfight), what was found is that you could construct a Geometry ("Hyperbolic" Geometry) assuming that there are INFINITELY MANY parallels through the given point. This can be modeled in several ways. My favourite way makes use of a hyperboloid of two sheets:

t sq - x sq - y sq = 1

under the (non-Pythagorean, non-Euclidean, specifically) Minkowski metric for arc-length

dx sq + dy sq - dt sq = ds sq.

This is a hyperboloid of revolution and is the natural analogue of a sphere. We use great hyperbolas on the surface of the hyperboloid (hyperbolas that lie on planes that pass through the center) to be the "lines" while again antipodes are the "points."

This is the natural environment for Einstein's Special Theory of Relativity.

If it is hard to visualize, project it onto a disc: "Lines" become circles cutting the edge of the disc at right angles, and "points" become points inside the disc. This mapping is "conformal," meaning angles are preserved. (Distances are another matter; never mind about distances.) This mapping is the basis of several beautiful lithographs by M. C. Escher: "Heaven and Hell," "Circle Limit I," and "Circle Limit III."

The point of these models is that they show non-Euclidean Geometries are as logically justified as Euclidean Geometry. But because they are all different, they CANNOT ALL BE TRUE. This was the problem.

The solution was to retreat FROM truth TO consistency. All three Geometries are consistent. Only consistency is real; truth is a matter of convenience (within consistency, please!).

Worse was to come.

Not only the new Geometries, but also difficulties in Calculus (among other things) had led to a desire for a more careful description of Logic itself. The idea was that Logic should become like Arithmetic--a matter of pure calculation--and this was epitomized in the program of Hilbert to convert the whole of mathematics into funny little symbols that would be manipulated according to formal, rigid rules. Leaving aside that the result can in no way be described as human-friendly (the resemblance to low-level computer code is more than accidental), the program seemed to be working: Mathematics was now on a reliably consistent (if unreadable) footing.

And so it remains--sort of. The problem is that already in the 1930s Goedel showed this formal system was necessarily too small, "incomplete." There are true theorems of Arithmetic that can be stated formally, but have no formal proof. If Arithmetic is itself consistent--AS WE ALL BELIEVE!!!--it's own consistency is one of those theorems.

Arithmetic is consistent if and only if its consistency cannot be formally proved. (Head explodes.)

This is no joke.

Now, it is not like two and two are suddenly going to start adding up to five. But for a system obsessed with consistency and proof, Goedel's Incompletenesss Theorem is a bomb planted right at the foundation.

By the time I was up to speed with this, several decades had passed, and as it happened, my own career was falling apart. (Also my mind.) Mathematicians paid no attention--no, had DECIDED to pay no attention--to the trouble at the foundations of their subject, an attitude I found increasingly difficult to live amidst.

Logicians did not feel the same freedom to put their fingers in their ears while singing loudly--it was their own subject, after all. Many (not all) were becoming very interested in Taoism, and this was not an accident. It was beginning to occur to them that their field might not be rooted in the Solid Rock of Certainty, but was rather floating on a Fog of Mystery. For centuries the Taoists have been teaching that you can trust that Fog.

What other choice do you have?

In my own case, this led me to Zen Buddhism, which is a very concrete spiritual practice, based on trusting the Fog. But nothing in Buddhism requires one to be apostate from science, so let me explain further:

Mathematics was not the only field finding limitative results, for example, physics was simultaneously going through wave after wave of them. First, Relativity set boundaries on available energy--vast, vast boundaries that, tantalizingly, we have no idea how to reach--yet boundaries they were. Then Quantum Mechanics set boundaries on what is knowable.

Worse, Quantum Mechanics directly contradicted our notions of how the physical world works. Nick Herbert in his book *Quantum Reality* has described eight different approaches to possible (mutually incompatible) world-views that are compatible with quantum mechanics. None are compatible with the Western mind.

So now I get to how I became apostate: Both mathematicians and physicists have chosen to turn away from the import of their own discoveries, in a sort of mental cowardice. Not the least of the many ironies of our time is that these various limitative results have created rich possibilities, especially for creating clever toys, and the attraction of the toys has served to mask the underlying difficulty.

Which is that the world absolutely does not work the way we think it does.

How does the world work? Nobody knows. Some OTHER way. Scientists have abandoned the field, clinging to solutions they already know are inadequate.

So I am apostate. What of it? All it really means is that I can expand my field of inquiry a bit. To wander off a bit. There is nothing in this that implies an ability to CONTRADICT science, just a recognition that science is missing a lot.

This brings me to what I was thinking was my real point: Even as we are reaching the limits of what the Western mind is willing to contemplate, the circumstances of peak oil, climate change, biosphere destruction, and consequent civilization collapse are going to require an utter rearrangement of that mind.

What rearrangement? I make vague guesses. I try to find what we can know or learn about people who lived sustainably. What did they think? How did they think? Example here and here. Surely this example is not reachable by us, being too fragile under external hostility, which is one constant of modern life, but it can at least open our mental field. Also, note how childrearing is key.

Then again, we are unlikely to reach sustainability soon. A preceding period of catabolism is likely, and Archdruid considers some possibilities.

**Update [2008-1-2 7:7:56 by Gaianne]:** Sorry about that last link. When you get there, you have to click on "show original post."

What is worth saving? There are aspects of Western Civilization that I am sure we would like to save; I am equally sure we would disagree on what they are. But CAN they be saved? How?

Some things are certainly going to go. The cancer-mind drug-binge we call capitalism (aka debt-based money aka empire aka taking without giving back) is one of them, though whether it goes before or after planetary destruction is a very intense and anxious question. Are there any direct ways to bail out of this one? I know that some folk here on ET have thoughts--can they be represented in a way that we can assess and utilize?

I should say for myself that I have moved on a bit from Zen Buddhism--though it is surely a good practice--finding it a bit austere. For several years now I have been mucking about in paleo-astronomy: This is a vast and interesting subject that includes, firstly, the cycles of the sky--ignored and forgotten by the modern mind--and secondly their relationship to the rhythms of life. Though, seemingly, these rhythms were thought to be given by the Gods (not a bad approach, really) it was always an active process to bring them into one's daily life, and the key point is that living in those cycles CHANGES MIND. It is one key to a sacred life. That this is an important key to sustainable mind seems likely.

CODA:

When I was learning musical counterpoint, after I had (finally) learned what a melody was, I was surprised at how many (real) melodies could be written to a given melody (cantus firmus) to make a harmony. In a class of twenty students no two were ever the same. Sometimes I was envious (and sometimes not). But within the constraints, the possibilities were all valid.

Metaphysics itself grew up as part of the philosophy of the Classical Greeks, at a time when faith in the Gods was collapsing. So it sought a different basis of support--logical argument. The study of Logic has been so successful, however, that it is now clear a strictly logical support of a metaphysics is not possible--we cannot even do as much for a technical study like Arithmetic! But, in truth, logical support of a metaphysics is not really necessary. It must SURVIVE Logic, but beyond that it can be whatever it wants to be and circumstances allow.

What will circumstances allow?

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