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On magic<br />
usually mentioned fields of mathematics, i.e., geometry, arithmetic, astronomy,<br />
optics, music, etc., but rather by its likeness and relationship to these<br />
disciplines. It is similar to geometry in that it uses figures and symbols, to<br />
music in its chants, to arithmetic in its numbers and manipulations, to<br />
astronomy in its concerns for times and motions, and to optics in making<br />
observations. In general, it is similar to mathematics as a whole, either<br />
because it mediates between divine and natural actions, or because it shares<br />
or lacks something of both. For some things are intermediates because they<br />
participate in both extremes, others because they are excluded from both<br />
extremes, in which case they should not be called intermediates but a third<br />
species which is not between the other two but outside of them. From what<br />
has been said, it is clear how divine and physical magic differ from the third<br />
type.<br />
To turn now to the particulars, magicians take it as axiomatic that, in all<br />
the panorama before our eyes, God acts on the gods; the gods act on the<br />
celestial or astral bodies, which are divine bodies; these act on the spirits<br />
who reside in and control the stars, one of which is the earth; the spirits act<br />
on the elements, the elements on the compounds, the compounds on the<br />
senses; the senses on the soul, and the soul on the whole animal. This is the<br />
descending scale.<br />
By contrast, the ascending scale is from the animal through the soul to<br />
the senses, through the senses to compounds, through compounds to the<br />
elements, through these to spirits, through the spirits in the elements to<br />
those in the stars, through these to the incorporeal gods who have an ethereal<br />
substance or body, through them to the soul of the world or the spirit of the<br />
universe; and through that to the contemplation of the one, most simple,<br />
best, greatest, incorporeal, absolute and self-sufficient being.<br />
Thus, there is a descent from God through the world to animals, and an<br />
ascent from animals through the world to God. He is the highest point of<br />
the scale, pure act and active power, the purest light. At the bottom of the<br />
scale is matter, darkness and pure passive potency, which can become all<br />
things from the bottom, just as He can make all things from the top.<br />
Between the highest and lowest levels, there are intermediaries, the higher<br />
of which have a greater share of light and action and active power, while the<br />
lower levels have a greater share of darkness, potency and passive power.<br />
As a result, all light in lower things, which comes to them from above, is<br />
more powerful in higher things. And also, all darkness in higher things is<br />
stronger in lower things. But the nature and power of light and darkness<br />
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