A Theological Fantasy

I'm a litle puzzled by the way Lewis deals with convergence. In his preface to TGD, he rejects the image of radial paths converging on a point, favoring that of infinitely ramifying paths. Is he saying only that "God is where you find him," or what am I missing? OTOH in Ch. 1 it's the people in hell who're spread out over vast distances, taking great care to keep themselves remote from all others. Can you reconcile this?

Forgiveness, especially the forgiveness for which Christ's mother continually begs for mankind, is the theme of a classic Orthodox iconic grouping, the "Great Deisis." Possibly the most famous Deisis is the one recovered last century in the church of Hagia Sophia in Istanbul. Flanked by his mother and John the Baptist is a grave and compassionate Christ - glorious yet approachable, and attentive to supplication. It's unquestionably the greatest representation of Christ anywhere, ever.

Forgiveness is a timely topic.

Just now, Christians in America are learning a bitter lesson in forgiveness. Having so recently acquired a first-hand experience of just how hard it is to forgive one's enemies, it's rather a shaming thing to acknowledge how much we count on receiving forgiveness for our own offenses.

As far as I'm concerned, the spiritual significance of September 11 is that, having been thrust into the role of the aggrieved party, we're in a better position than ever to discover a spirit of repentence and decent humility respecting our own transgressions. We're in a better position than ever to acquire a true appreciation of the mercy of God who so readily offers forgiveness for what we've done to Him.

This wonderful and terrible God who wants us to know him expresses this desire for unity by imposing upon us the divine office of forgiveness. "Forgive us our trespasses, as we forgive those who trespass against us." This is far more than ethical culture for a polite and orderly life. It's a call to theosis, perfect order, cosmic order -- not to an obliteration of human will and identity, but to an accord between man and God that mirrors the perfect accord of the Trinity. The Peace of Christ is not the peace of this world, not the peace that consists in the absence of war or even a nicely calculated balance of I-Thou reciprocity. The peace of Christmas is the composed, orderly, and perfect accord of the Trinity, and the mystery of forgiveness is our ticket to the life of that perfect communion.

(The Great Belaborer) rejects the image of radial paths converging on a point, favoring that of infinitely ramifying paths.

This mathematical analogy may be of interest; it was big stuff among the ancients.

Visualize a plane tangent to the south pole of a sphere (Picture).

It appears that the plane is infinite, "riding madly off in all directions", and the sphere is finite. It can be shown, however, that there is a one-to-one mapping between the sphere and the plane, with the exception of the point at the north pole, which corresponds to infinity on the plane. No matter which direction you move from the tangent point on the plane, you are moving towards the north pole when the plane is mapped to the sphere.

Some of the ancients felt the north pole of the sphere corresponded to God.

What a delightful little thread.

patent

I can visualize a unique mapping of every point on the sphere to a unique point on the plane, but since both sphere and plance contain an infinite number of points, I'm not sure what "one-to-one" means. But it's a helpful model all the same (even if it fails to address the dispersed "initial state" in hell).

There are different levels of infinity (for example, there are more real numbers than rationals, even though there are an infinite number of both). A one-to-one correspondence is used to demonstrate whether two infinite sets are at the same level. One might think that a sphere, which is bounded, has "less points" than a plane, which is unbounded, but it isn't so. There are lots of unintuitive results along these lines, e.g., there are the same number of numbers between zero and one as between zero and two.

even if it fails to address the dispersed "initial state" in hell

True. Far be it from me to model hell precisely; I leave that to economists or those global warming guys. My thought was only that it may be difficult to tell, either in mathematics, physics (in our non-Euclidean universe) or theology when things are moving together or apart.

There are lots of unintuitive results along these lines, e.g., there are the same number of numbers between zero and one as between zero and two.

Or between zero and infinity, agreed. It was not the availability of an infinite number of points, and thus unique paths (each for a unique soul?) that I found uncongenial; it was the "one-to-one" business. Anyway, it's not important. Don't think of me as quibbling; even if incomplete the model you proposed is imaginative and helpful.

Sorry for bringing this thread off-topic, but since I already have, let me try to clarify.

In mathematics, there are orders of infinity; some are bigger than others. There are more irrational numbers than rational numbers even though they are both infinite (the irrationals are more dense on the number line).

The one-to-one mapping is used in number theory to determine if two infinite sets are of the same size. Roughly speaking, if each point in infinite set A can be mapped to a unique point in infinite set B, and vice versa, then they are the same order of infinity. Otherwise, one set is bigger than the other.

Every point between 0 and 2 can be mapped to a unique point between 0 and 1 (and, obviously, vice versa), so they are the same order of infinity.*

Each rational can be mapped to a unique irrational, but every irrational cannot be mapped to a unique rational; hence, they are different orders of infinity (there are more irrationals than rationals).

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* Given a point between 0 and 2, divide it by 2 to get a unique point between 0 and 1.

the irrationals are more dense

Figures.

barak