In the Divine Comedy, Dante obviously just made a slight error in scale. Dante thought he was traveling through the center of the Earth and into the Earth's heavens, but he was actually traveling through the whole galaxy.
The Unthinking Depths is Hell, of course. (Though the upper levels of Hell, such as Limbo, might have been just outside the Depths.) Dante placed Hell inside the Hemispheres of Earth and Water, but he didn't realize he was traveling not through the Earth's center, but through the galactic center.
The Slowness is both Purgatory and the Living Earth. This makes sense because Earth is in the Slowness, and Dante's travels began there. Dante places the Earth's surface in Sphere of Air, whereas Purgatory reaches up into the Sphere of Fire, but in actually he was moving though the Slowness. As with Dante's spheres, the Zones of Thought are determined more or less by density. As Dante rose higher and higher in Purgatory, the density got lower and lower until Dante believed he'd crossed into the Sphere of fire (which is the lightest classical element). But he was just higher up in the slowness.
The Beyond is Heaven. You'll notice that there are different levels of the Beyond (The Below, the Middle Beyond, the High Beyond, and so on) just as there are different spheres in Heaven. Dante correctly realized that he was traveling further outward, but due to his error in scale he interpreted this as the Ptolemaic spheres of the planets.
And of course, the Transcend is the Empyrean, the location of the most blessed people, the angels (and we'll note that at least one rank of angels is called Powers), and God.
It was established in A Deepness in the Sky that the On-Off Star of the Spiders and the fossilized nanotechnological cavorite were at least Beyond-level technologies despite having originated in what was now the Unthinking Depths of the galactic core. The implications being, that the Unthinking Depths weren't always like that. Furthermore in A Fire Upon the Deep, the Old One's Countermeasure against the Blight reduces vast areas of the High Beyond to the Slow Zone, demonstrating that superweapons that reduce the maximum toposophic levels possible under the local laws of physics are possible and that they're the weapon of choice for Powers to kill each other.
Originally, the entire universe was at least Transcend, but fighting has since rendered large portions of it inhospitable to Powers and lesser sentient creatures and unless stopped, will eventually render it inhospitable to all life, or at least all life smart enough to invent the technologies for toposophic level reducing superweaponry. It's unclear if humans qualify under that criteria and therefore if the final state of the universe will be Unthinking Depths, or if we don't, in which case it'll be Slow Zone.
