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Maybe an old ACE sci-fi novel (Maybe one of the ACE Doubles) But I am not certain it was an ACE Book.

Basiclly a poor boy on a scrap planet, eventually leaves the planet, adopts a small kitten, meets a young woman in trouble and helps her. (The possible princess) In aiding her, he takes on larger and larger forces until eventually he defeats the great evil, but dies in the process.

Specific events I recall:

  1. In the beginning he is scavenging in a scrap yard(?) (it might just be he was taking a short cut through the dangerous scrapyard) but the old security guard catches him and leads him out. (They are acquaintances(?), or she has been catching kids in there many times before. Not angry just old and tired.)

    She tells him to stay out, it's to dangerous in there for his simplex-mind. [There are 3 terms she uses to describe intelligence, I think they were Simplex, Complex, and Multiplex.]

    He asks what she means and she describes the following which is the event I recall.

    She tells him to look up at the night sky and tell her what he sees. He sees stars and blank areas. [There is a bridge above them and the blank areas are the girders, trusses, and crossbeams to support it] She tells him that's a simplex-mind describing what's there.

    She tells him to start walking, and he says he sees some of the stars winking off and on in different spots, and something is blocking the stars. She tells him that is complex-mind thinking as he knows something is blocking the stars.

    She tells him to run and he tells he he can see the stars are in the same place as they always go off and on in the same spots in the sky as they go behind and reappear from behind what is blocking them. She tells him that is multi-plex thinking as he can recognize that the stars are in a fixed position and not randomly winking on and off as something blocks them.

    About that time, since he was looking upward as he ran, he trips over something and falls flat on his face. She tells him that can happen when a simplex-mind tries to grasp a complex or multiplex idea.

  2. He stows away aboard a large spaceship, finding a cleaning gear room and puts a fake sign on the door saying it's a restricted access room and uses it for his hideaway. (The people on the space ship live in a rigid society, they obey orders and don't question them.) I believe it is aboard this ship he encounters the girl in trouble and assists her (maybe sharing his hideaway with her)

  3. The kitten he found may have also been on the ship, it has some (mental?) power, and over time grows much larger (size of a mini-van?) near the end of the book he might be the size of a bus and eats the leader of the great evil empire.

  4. The three of them leave the ship and have various adventures and encounters during the book always struggling against the great evil.

  5. They may end up going through a blackhole/wormhole/portal/time machine to escape. He dies and she is transported back in time. Where she eventual grows older and settles on a scrapyard planet where she is a security guard. (The same woman we meet in the beginning of the story)

  6. I think after the boy and girl go through the blackhole, leaving the cat behind is when the cat eats the evil leader defeating the evil empire.

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This is Delany's Empire Star (1966). The conversation happens exactly as you recall it. Quoting from the plot summary on Wikipedia:

As the narrative opens, we meet Comet Jo at eighteen years of age. He has spent his entire life in a "simplex" society on Rhys, a satellite of a Jovian planet orbiting Tau Ceti. (At first it might seem that "simplex" means "simple" or "unintelligent," but after Jo's encounter with the "Geodesic Survey Station" at the latest, it will be clear the notion is much more complicated.) Jo comes upon the wreckage of a spacecraft and encounters two survivors. The first is quickly dying and asks Jo to bring an important message to Empire Star moments before dying. The other is a lifeform known as Jewel. Jewel is a tritovian in crystallized form, and in that state can easily view situations from several points of view, thus enabling narration from the point of view of the omniscient observer.

The first publication was indeed in an Ace Double, though because of its short (novella) length, it was frequently published with other works, like The Ballad of Beta-2 and Babel-17.

The bit with the bridge:

Charona laughed. 3-Dog ran back and rubbed her hip with his head.

"Perhaps I can explain it in purely metaphorical terms, though painfully I know that thou wilt not understand until thou hast seen for thyself. Stop and look above."

They paused in the broken stone and looked up.

"See the holes?" she asked.

In the plating that floored the bridge, here and there were pinpricks of light.

"They just look like random dots, do they not?"

He nodded.

"That's the simplex view. Now start walking and keep looking."

Comet started to walk, steadily, staring upward. The dots of light winked out, and here and there others appeared, then winked out again, and more, or perhaps the original ones, returned.

"There's a superstructure of girders above the bridge that gets in the way of some of the holes and keeps thee from perceiving all at once. But thou art now receiving the complex view, for thou art aware that there is more than what is seen from any one spot. Now, start to run, and keep thy head up.

Jo began to run along the rocks. The rate of flickering increased, and suddenly he realized that the holes were in a pattern, six-pointed stars crossed by diagonals of seven holes each. It was only with the flickering coming so fast that the entire pattern could be perceived—

He stumbled, and skidded onto his hands and knees.

"Didst thou see the pattern?"

"Eh... yeah." Jo shook his head. His palms stung through the gloves, and one knee was raw.

"That was the multiplex view."

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