A number of traditions, in The Ancient City and elsewhere, hold that each species of animal has a so-called "group soul" rather than the individual souls that humans have. Thus all animals of that species are part of one being which may also be part of whatever god watches over the species.
One group takes this idea farther. They believe that the souls of all creatures, including humans and minor deities, are part of one Supreme Being.
Humans appear to be distinct beings but are really part of the One Soul, just as fingers are part of the hand even though they appear to move independently. And as fingers are part of the hand while the hands are part of the body, there is a hierarchy of being, from the lowliest insect up to the Supreme God. Humans, they say, are part of some mid-level deity which is in turn part of some higher one, and so on up.
Why do humans appear to be so distinctly separate? Because there are degrees of closeness of the connection. Long thin fingers have more individual freedom than short stubby toes. And humans are more free than even the thinnest fingers. The proper analogy is closer to that of an animal on a leash. The connection may in some cases be invisibly thin, but it never breaks.
Some of the sects holding this belief use a mathematical construct known as the "Mandelbrot Set" as a symbol. This is the set of those numbers that remain finite no matter how many times a certain operation is repeated on them. Numbers that are not part of the Set sooner or later grow to infinity.
A graph of the Set looks vaguely like a heart with a circle grafted onto the pointed end, with other much smaller circles stuck on all around the edges. And it is what the math people call "fractal": No matter how much you magnify it, you can find areas of ever finer detail, ad infinitum.
(Most of the circles are slightly distorted. But let's call them "circles" for the moment anyway.)
In most pictures, areas near the Set but not actually part of it are often colored according to how quickly the number grows to infinity. This makes it easier to search for certain details. And it looks pretty.
In math texts the Mandelbrot Set is usually shown with the "V" of the heart on the right and the pointed end to the left. This is because they follow the standard way of arranging graphs of numbers. Most Fractal-God sects, however, prefer to depict the Set pointing upward, like a tree or a tower.
If you look closely at one of the small circles along the edge you will see that it has even smaller circles along its edge. And these have even smaller circles on their edges. There is no end to this progression of ever-smaller circles on the edge of larger ones.
If you look in the right places just beyond the edge of the main Set you may find a tiny replica of the entire Set, perhaps slightly distorted. Each of these tiny copies of the Set is connected to the main Set by a thin filament. It may be too fine to see, but it has been proven mathematically to be there. All parts of the Set are connected. The Set is One.
And each of these tiny copies of the Set is fully as complex as the main Set itself. Each in turn has its own even tinier satellite copies, all connected by filaments too fine to see. Since the detail goes to infinity, the normal rules of counting do not apply. There is no such thing as "getting near the bottom" of the detail.
This aspect of the Set holds more symbolism. If some tiny people were living on one of those satellite Sets, they could look downward with their magnifiers and see no end of detail. But they might not be able to comprehend the vastness of the larger Set theirs is tied to. They might be able to map one or two levels of larger Sets above theirs, but what if they were thousands of levels from the top? Millions?
And what if they did not look closely enough to see the filament connecting them to the next higher level? They might think themselves on the main body of the Set when in fact they were not. Even if they knew themselves to be on a satellite Set, they might well find the task of mapping the route to the top level to be never-ending.
And so it is with souls. Humans are believed to be the children of, and part of, one or a few specific deities. But what are those deities part of? And do all the connections eventually lead to some One Supreme Being that all souls on all possible worlds are one with? Does the Mandelbrot Set analogy still hold there?
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