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After Beatrice's lesson, Dante gives a warning to his readers. Comparing us to passengers in a ship following his (Dante's) ship, he warns us to "turn back to see your [our] shores again" because otherwise we might lose sight of him and thus be lost at sea. In other words, because Dante is so talented, writing about unknown phenomena, we might not be able to understand his poetry. He urges readers who are not ready for the theological theory of Heaven to "turn back" and reread the first two books of the Divine Comedy.
Our poet says that his ship, unlike ours, is guided by Apollo and the Muses. So only those who understand (the "few who turned your minds in time unto the bread of angels") should follow in Dante's wake, where the waves are smooth because Dante is there to explain what's going on. The rest of the sea is tumultuous, making it hard to navigate.
Those worthy of following me, Dante asserts, will be more amazed than the Argonauts when their leader, Jason, tamed a pair of fire-breathing bulls.
Now back to the story. Beatrice again gazes upward.
In an instant, the travelers reach a wonderful place, which—Beatrice announces—is the "first star." Well, we wouldn't think of it as a star; it's the moon.
It's a beautiful place. Dante describes it with jewel-like imagery: "It seemed to me that we were covered by a / brilliant, solid, dense, and stainless cloud, / much like a diamond that the sun has struck." He compares the light to the reflection of light on water.
Dante is amazed at how he and Beatrice can enter the moon without displacing any mass. The explanation has to do with God, and His command of the universe. Their entrance into the moon shows "how God and human nature were made one."
We readers have to take this miracle on good faith. Dante, though, observes it firsthand. (This general rule applies to the entire Divine Comedy: what mortals have to believe on pure faith, Dante knows from experience.)
Dante thanks God, then asks Beatrice why there are dark marks on the moon's surface.
Beatrice smiles knowingly, saying that the human senses cannot possibly come up with the correct explanation for the moon's spots. She asks Dante his opinion.
Dante answers that the moon spots are caused by denser concentrations of matter in certain random areas.
Beatrice says this is incorrect. Dante's explanation would suggest that some stars simply have more matter than others. This would mean that a single power (in Italian, virtù) governs them all, manifested randomly as greater here and lesser there. But, Beatrice argues, this is wrong. Different appearances must originate from different powers.
Furthermore (ready for some serious physics?), if the moon spots were indeed caused by denser and rarer matter, this would mean that the entire moon would have spots totally devoid of matter, or that their density and rarity would alternate in stripes. The former theory is wrong because during a solar eclipse (when the moon is directly between the sun and the earth), sunlight cannot be seen through the empty spots of the moon. The latter is incorrect because the dense stripes of the moon would not allow light to pass through, but instead reflect them.
Here, she anticipates Dante's argument—that a reflected beam of light from far away will be dimmer than a reflected beam from a nearer source. But, if you actually do an experiment and place three mirrors at different distances from the light source, all three reflections will have the same brightness (though not the same size).
Now, she continues, let's learn the correct explanation, by returning to the concept of the different powers. The Eighth Heaven of the Fixed Stars receives the undifferentiated power from the highest Heaven and has the job of distributing this power to the various stars, as God sees fit. Those closer to the highest Heaven receive more power, and thus spin faster, than those farther from it. Just as each organ within the human body has a different power, each star is "inspired by the blessed movers." These "blessed movers" are different intelligences, commonly known to man as angels. So within each star, there is an intelligence (angel) which causes it to revolve in its path around the earth and shine forth in gladness for God.
This, Beatrice proclaims, is the correct explanation for the moon's spots. Basically, nothing in the universe (not even matter) is random, as Dante thought; each thing has its proper place in relation to God.