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## Transfinite Beings

The White Light

The top of the verse, and the focus of Rucker’s first story. Does more stuff than expected for a supreme being.

Any continuous piece of space is called a continuum. A line segment, the surface of a balloon, the space inside your head, the endless universe—all these are continua. Cantor discovered that viewed as sets of points all continua have the same degree of infinity, which he called c. The degree of infinity of the set of all natural numbers is called alef-null, and the next larger degree of infinity is called alef-one. In 1873, Cantor gave the first proof that c is greater than alef-null. Even if you lived forever and a day, you would not be able to assign a natural number to each and every point in space. The Continuum Problem is to decide how much greater c is than alef-null. Cantor thought c should be alef-one, the next infinity. But no one knows if he was right.

Explaining alephs

My thoughts turned to the Absolute Infinity. That was bigger than alef-null, bigger than alef-one—bigger than any conceivable level. I was supposed to go to Cimön and climb a mountain Absolutely Infinite in height. I wished I still had that pamphlet from Sunfish. Who had put it there for me? Probably the Devil, to lure me out of my body again

Description of absolute infinity

”That’s called the Reflection Principle.” “Please elaborate. This is new to me.” “The Reflection Principle is an old theological notion which we use in Set Theory. Any specific description of the full universe of Set Theory also applies to some little set inside the universe. Any description of the Absolute also applies to some limited, relative thing.” Franx made a disappointed noise. “You’re just saying that the Absolute is unknowable. That’s the most elementary teaching of mysticism.”

Via negativia

”This is only the beginning of the second number class. Beyond lie all the alefs. And beyond that is the Absolute, the Absolute Infinite where, where…” He stopped speaking and stared into the sky.

God = Absolute Infinity

”Of course I knew about the tunnel. There’s lots of tunnels to alef-one, and if you’re willing to chance going into the Desert you’ll find tunnels to alef-two, to alef-alef-null, to the inaccessible cardinals—I’ve seen them, I’ve peeked up God’s skirts like the others—gawked and gone home unchanged.” He sighed heavily. “At least I really climbed alef-one. At least I have that.”

Inaccesible Cardinals exist in the cosmology

Franx was talking again. “I’m scared of the White Light. I love myself too much to dissolve like that. None of the people on Mount On wants to get to the top. That’s why they go there. For the people who really want God, there’s an easy way. Beyond the Dump. Off the edge.” His lips were twitching and his hands ran up and down his body like live insects. “I don’t want that, I don’t want that—” He began sobbing. I looked away.

Dissolving people who see it

“Yes, but I still don’t think you see how it applies to Mount On. When you go white, and you are no longer really there, then there is no individual, and no conception of the Absolute. But the situation is unstable. The Absolute divides, tries to get outside itself, and wham, there’s a beetle looking at alef-one.”

Transduality stuffs

“YOU WHO,” the couch called as I fell back into it. There had been an instant, right when I moved through the center—an instant when I had been able to see the One, the Absolute, to grasp that YES is the same as NO—that Everything is Nothing.

Nonexistence physiology? Or at the very least, more evidence of transduality.

That covers the most important stuff in the original book specifically, but it is mentioned/does stuff outside it

And that’s when the creature came for me—all the way from the place where zero and infinity are the same.

This one alien is implied to have come from and be an avatar of the white light

“You are a pattern in the potentially infinite computation that is the universe; and I am the actually infinite end of said computation. I am all space and all time. The world you live in is happening; my essence is what comes before and after your mundane time.”

“How long is the program that starts it all?”

“Two bits. One Zero.”

“What about all the details?”

“You’d call it ‘screen wrap.’ Patterns grow out and around and come back over themselves and make fringes. It adds up over the billions of years, especially when you remember that each point in space is updating the computation each instant. Each of those points is me; I’m the rule that runs it all; and looked at the other way, I’m all the past and all the future.”

Some interesting things said by same character

Faint shapes wafted around me, and then a long luminous beaker of yellow was in my hand. I sucked greedily at the pure energy fluid. This was the kind of rest I deserved after all that mindbreaking hacking: always shifting bits left and right to make bytes, masking the bytes together into register-sized words, generating lookup tables, finding room for the tables in RAM, feeding the output into the color display ports…I drank and drank, and my glass was always full.

Data Manipulation?

On my bike ride I stopped in a small stone church on a hilltop and had a kind of vision of god. “I made all of this,” the white light seemed to say. “It’s all biology, all part of a whole, and my divine Light is in each and every fiber of everything there is.”

Directly speaking telepathically

Everything is reaching out to each other, the plants the water the rocks the animals the air and even mankind, we’re not spoilers, but thinkers and pattern makers, the plants are pattern makers the rodents peeping and darting are pattern makers…but why and wherefore? What causes and what senses the patterns? I scan and reject my outgrown fads of physics and math, which are only human beauty fern flower grow, no, math is not the answer, math is only part of the pattern that is the question: Why? I ponder this down the boulder rodent stag water air moss shrub grass soil-filled Rudy-Jr-found ramp towards The Fort and our campsite. I’m chuckling internally over an anti-Christian joke I’ve just made up. Some guy who lectured to us at an Episcopal Young Churchman meeting when I was a boy said “Gospel means good news. The Gospel is good news that stays good news.” And now coming down from the high lake having looked the raw nature-god in the face I think, “Christianity is bad news that stays bad news.” And like chuckling nervously a little, but really knowing it’s true, like what does a statue of a man being tortured to death have to do with this Nature or with this Yosemite? Like, hey dude, take your losses and lighten up, I mean species-wise, man, like why not worship a crushed ant or a funky crystal? So why why why? Here is all this fabulously interlaced organic god-like beauty of nature and why? I turn and stare at the sun, close my eyes, raise my hands, and— LOVE. Love is the force that grows the world. Love and the web of existence. Everything is beautiful because everything loves to be beautiful. All of us in the web love each other, we love to churn out better patterns for the others in the web to love. GOD IS LOVE.

Possible transcendence over mathematics? And embodies the concept of love.

# Harna

“It’s not really smelling. For us nothing’s so far away, you know. Your whole notion of space and distances is…a kind of flat picture? The folk are much realer than that. We live in full fractal Hilbert space. You think like a flat picture, but the paper, if you’ll just look, is all bumpy like a moonscape of bristlebushes covered with fuzzy fleas. There’s no fixed dimensions at all. Does it feel good when Alf and I do this?

Higher dimensions are more real than lower ones

# Saucer Aliens

Time doesn’t stop for me. The aliens can make my time axis run perpendicular to regular time. We get into what I call paratime. Here, let me draw you a picture.” He took my pen and began to draw on my pad. “Think of all space as a point, and think of human time as the line going up the page. Now suppose that at each instant of our time you can find a different time direction that goes off at a right angle. A perpendicular paratime axis for each moment of human history.

Infinite time dimensions?

## Misc

“Contradictions are logically impossible,” I explained. “A universe containing contradictions cannot exist.”

“Glub gazork,” said the mermaid. And then she did something very strange. She lifted up her arms and…didn’t lift up her arms. At the same time. She winked/smiled at Harry/me. The sprite pinched my cheek with both hands. Yet at the same time she was tickling Harry.

“You see?” said the gnome. “Who are you to tell the universe what it can do.”

More transduality?