Jeff Carreira: Can you give us an introductory explanation of what the fourth dimension is and then tell us why you have devoted so much of your time to exploring and elucidating the idea?

Rudy Rucker: I first heard about “the fourth dimension” in science fiction stories, and I thought it sounded cool. I remember an anthology that had a 1929 story by Miles J. Breuer called “The Captured Cross-Section.” A four dimensional being’s body intersects with our 3D space, and the people in the story see a shifting, flailing ball of meat, with maybe a tooth or a claw on it…and they drive a long crowbar through the meat, and anchor the ends in concrete and supposedly that keeps the 4D creature from getting away, although why would you want it to stick around?

Right away I knew the fourth dimension was cool, and I wanted to know a lot about it. By the way, as a boy, the other big mathematical topic I wanted to know about was infinity. And somehow my life worked out so that I published books about the fourth dimension and about infinity. I’ve been lucky; my dreams came true.

So what is the fourth dimension? The first thing to understand is that “fourth dimension” can be used in various ways. People often say that time is the fourth dimension and leave it at that.

But I want to talk about a mathematical, geometric fourth dimension. A point is 0D, a line is 1D, a flat square is 2D, a cube is 3D. So what about a 4D hypercube? Well, it’s sort of like two cubes connected at the corners—maybe you’ve seen an image like that, and it’s often called a tesseract. But the slanting lines between the corners shouldn’t really be in our space. How do we imagine a direction that’s not in our space?

The traditional method is to reason by analogy. You think about a 2D being who lives in a plane, and wonder how this being could imagine the third dimension. We get this approach from Edwin Abbott Abbottt who wrote a wonderful 1884 tale called Flatland, featuring a character called A Square.

(Just in passing, isn’t it great that Abbott has the same middle and last name? And two T’s in each of those. Like the two cubes we’re trying to connect to make a hypercube. And note that his publication date’s digits are kind of like that too. Two 8’s and 8 is two times 4. Mathematicians notice things like this. Numbers speak to us..)

A Square slides around in Flatland, and he can’t imagine the third dimension because it’s a direction completely different from any direction he can point to or move in. And that’s where we’re at relative to the fourth dimension. We can’t move in that direction, but even so it exists.

I’m not going to give a full recap of Flatland here, but you ought to read it.

Jeff Carreira: Tell us about your own books on the fourth dimension.

Rudy Rucker: The first book I ever wrote was Geometry, Relativity, and the Fourth Dimension, in1976. I was a long-haired thirty year old math prof at a small college in upstate New York, basically a hippie with a wife and three kids, and about to get fired for not being square.

Dover Books paid me a thousand dollars for the book, and at this point I think they’ve sold nearly half a million copies. They’re a little embarrassed about it, but not embarrassed enough to pay me more money. I love them anyway. They gave me my start.

Oddly enough, this first effort of mine was the most successful book I ever wrote, with about forty more books to come—science books and science fiction novels. And I wrote another 4D science book, The Fourth Dimension.

If you’re curious, you can read all of my science books for free online here.

Why would I post my books for free online instead of making people buy them? Two reasons. Mainly, I think the information in these books is important, even life-changing, and I want people to read it. I want to infect their minds. Secondly, if i give books away, it builds my brand, and recognition is an author’s lifeblood.

Jeff Carreira: And how about the fourth dimension in physics?

Rudy Rucker: In the special theory of relativity we speak of time as a fourth dimension. In general relativity, we explain gravity by saying that 4D spacetime is curved in still higher dimensions. Cosmologists suggest that the universe as a whole might be a 4D hypersphere. Or that possibly it’s “negatively curved” like a saddle, and it’s infinite. The popular notion of a multiverse speaks of alternate parallel universes stacked in a higher dimension. Particle physicists suggest that our space might have a slight 4D hyperthickness. And string theorists talk about using ten or eleven dimensions—although they pretty much waste all those nice dimensions by curling them up into tiny loops. Vermin dimensions, as my science fiction friend Bruce Sterling calls them.

As a mathematician, I have limited sympathy with the speculations of physicists. I almost want to say that they’re bullshitters who make it up as they go along. But, oops, that’s what science fiction writers do. But we don’t get all pompous and claim that what we say is really true. And, seriously, modern physics is less than two centuries old, so how could they be near the final answers?

My sense is that you’re more likely to find the truth if you look into your own mind.

Jeff Carreira: I find the fourth dimension a valuable way to understand my spiritual experience. Can you talk about that?

Rudy Rucker: Higher reality has many higher dimensional aspects. We can go all the way back to Plato’s allegory of the cave. He speaks of a group of people in a cave, watching shadows move on the cave’s rear wall, and never realizing that the rich, true reality is the world of objects behind them. The great P. D. Ouspensky wrote about this.

Sadly, Plato’s cave people resemble what we’re turning into, all of us staring at our phones, even as we walk around outside. Portable caves!

Despite my rant a few lines back, I do in fact like physics quite a bit, and it’s useful to imagine the world as a 4D spacetime pattern. Philosophers of science call this the “block universe” model. The past isn’t gone, it’s “underneath” us. And this is a weak form of immortality. “We’ll always have Paris.”

My beloved wife Sylvia died in January, 2023, and immortality is much on my mind. And it is indeed soothing to look back on the shape and the particulars of the life we had together. Not only does she live on in my heart and in my mind—she lives on in spacetime.

But I’m lonely, and I want something more than a pattern in spacetime. Among nineteenth century spiritualists it was common to say that ghosts live in the fourth dimension. It’s convenient. They can hover just above you, up in the fourth dimension, and suddenly dip down into your zone. I wrote a section about the history of this idea in my book The Fourth Dimension.

I like going to the bluffs in Santa Cruz, and watching pelicans fish. They glide along over the wrinkled surface of the sea and then, spotting something, they rise up, and then plummet down, beak first, grabbing a fish. For a fish in the sea, the surface looks like a mirror. What a shock to have a pterodactyl-like beak come spearing in.

Not always such a good thing to have a ghost pop into the room! This brings us back to Miles Breuer’s “Captured Cross-Section” a little bit.

Jeff Carreira: Do you think our physical bodies might have a 4D hyperthickness?

Rudy Rucker: In Flatland, the hero A Square travels up out of his 2D Flatland, and he moves around in 3D space.

In 2002 I wrote a 4D version of Abbott’s story: a novel called Spaceland. My book is about a Silicon Valley middle manager who travels into the fourth dimension and meets the beings there. At the end he finds a way to create wireless antennas that project out into 4D space so that their signals aren’t hampered by buildings. (Kind of a joke ending.)

A point I get into in Spaceland is that if you were in fact able to go up into 4D space, your body would need to have a hyperthickness to it, and some hyperskin, otherwise your guts would fall out on the open sides.

And our universe would divide hyperspace in half, with “heaven” on one side and “hell” on the other. It was fun writing about this. Trying to imagine now what a 4D eye would see was especially hard. But I don’t seriously think my book is true. I’m not a physicist. ☺

So, no, I don’t see there being a bunch of 4D ghosts or guardian angels or evil spirits hovering around our space. It’s a popular notion in horror stories, but I feel reality is so heavy handed and obvious. Nature is subtler and more graceful.

But if we don’t have 4D ghosts, is there any hope of immortality? How about this: the ghost of a lost loved one is literally living in your heart and mind. And this isn’t meant as a platitude. The ghost is a living pattern that’s in your system. It’s like a thought, or a memory, or a dream, or an emulation—and it’s not under your control. An autonomous entity who, if you’re lucky, loves you. And if you’re unlucky, they don’t.

And here we face the old options of guardian angel vs. mean devil. All our traditions tell us that you want to be on good terms with your ghosts. Your ancestors, your lovers, your friends. All those who live within you. Honor them. Make offerings to them. And if you’re hosting a demon, boot it out. Or starve it with lack of attention.

Jeff Carreira: Can you talk about how this relates to spirituality and mystical states?

Rudy Rucker: So many possibilities. I’m intoxicated by my word hoard. Having fun. Thanks for asking all these good questions!

For me the key spiritual or mystical thing is to view the world as a cosmic unity, and to be in touch with this One. To get a sense of the whole, with my mind melds into the minds of the objects around me, merging with nature, empathizing with people, dimly sensing the moon and the stars…moving outward to the all.

(Not that, of course, it has to be the One. It can just as well be the Many. Two sides of the same coin. You know the saying: a great truth’s opposite is also a great truth.)

In either case, One or Many, I want to merge —and find peace. I want respite from my weary frame, discarding my fears and my remorse. At one with god.

Think of the universal mind as a huge higher-dimensional mollusc that pokes out little tendrils. The tendrils are the people. And each tendril has an eye. Like puppets held by a puppeteer with a zillion hands. Each puppet has an eye, looking at the others. “Hi, it’s me.”
God seeing god.

Jeff Carreira: What would it mean for us to expand our thinking to higher dimensions?

Rudy Rucker: When I want to go fully ape with higher dimensions, I talk about Hilbert space, a mathematical construct invented by David Hilbert. Hilbert space has infinitely many dimensions.

It’s a little like the inside of your mind. You don’t really think in terms of a mere three or four dimensions. You’re layers and patches of overtones melding like paints on a palette.

Recently I was thinking a lot about the Hilbert space mind, trying to bring it to life for some scenes in my most recent novel, Juicy Ghosts. As always when I’m writing a novel, I know that at some level it is indeed bullshit. But while writing it, I have to believe that it’s true. It’s a type of thought experiment.

Certainly our minds are more like Hilbert space fractals than they are like feeds from surveillance videos. And, while in iconoclastic mode, let me point out that we don’t really think logically. We don’t sit around deducing things.

Thought is all about feelings. A process of free association. A stream of consciousness. “What does this remind me of?”

The latest AI flavor-of-the-month is ChatGPT, a type of “large language model.” It’s all about emulating our process of free association, and it does this so well that the outputs seem almost human.

Bringing the topic of dimensions back in, these models have billions or even trillions of dimensions, assuming that we associate each tweakable parameter with a dimension. How can we possibly tweak so many params? The models are self-tweaking; they use a process similar to evolution. Exploring Hilbert space.

The weirdest, most incomprehensible theory of the world is quantum mechanics. And the full quantum mechanical model is shifting pattern in—where else but Hilbert space?

4D is for lightweights, dude. Hilbert space is where it’s at. Glowing brain goo.
Are you high yet? That’s what a rap like this is for.
We don’t have to get high. We are high. All you have to do is notice.
We’re patterns in Hilbert space, and nothing matters.

And now another commercial interruption. I wrote a novel The Big Aha about a type of mindware high. I was thinking about the Sixties, and about Tim Leary in Millbrook and William J. Craddock in San Jose, and wondering. These guys were taking acid nearly every day, and it seemed like an interesting zone to explore.

Not that I’m at all an acidhead. I really only took it once. But I saw the white light, and that was enough, and I remember.

In The Big Aha it’s not a garden-variety psychedelics that they use, no, it’s a telepathy-inducing quantum wetware called qwet. I thought that if I used this angle, I’d avoid being pilloried by the puritans, but that didn’t really work out.

Jeff Carreira: In addition to being a writer, you had a career as a professor of mathematics and computer science and have written about what you call gnarl. What is gnarl and what did your exposure to it teach you about life?

Rudy Rucker: Surfers say a wave is gnarly if it’s very richly patterned and intense. Foods or situations can also be gnarly. “Gnarly, dude.”
Originally a gnarl is the part of a redwood or on oak tree at the base or at a knot, where the wood is all warped and twisted around, and if you polish a piece of that, you see these really intricate curves and folds.

In 1974 I got my Ph.D. in the mathematics of infinity, and that was pretty gnarly for sure. The proofs were insanely complex. I wrote about what that’s like in my novel Mathematicians in Love. The best analogy I could find for math proofs was Dr. Seuss drawings.

When we moved out to San Jose in 1986, I switched from teaching math to teaching computer science at SJSU. All my life I needed a day job as a professor, I never made enough money from my books to support our family of five.

I really liked doing computer science. My thing was generating gnarly graphics from relatively simple mathematical formulae. Fractals are a well-known example of this, particularly the celebrated Mandelbrot Set. And I discovered a multi-dimensional Mandelbrot Set that I looked at a lot. I called it the Rudy Set. If you Google it you can find it.

Seel the Gnarl!

As it happens, that personal slogan of mine is now engraved with my name on the granite gravestone that stands by Sylvia’s grave. I’ll join her there in a few years. Her slogan is there too: Carpe Diem. Means “Seize the Day,”

Chaotic processes are another source of mathematical gnarl. You take what seems to be some simple rules for how a dot on the screen will move, and it gets into never-repeating oscillations and layers of intricate patterns. Flocking algorithms and cellular automata are rich sources of computer gnarl as well.

But never mind the computers. Over time I’ve learned to see gnarl all around me. Right there in nature. Particularly in clouds, the wobbling of leaves in a breeze, and above all the ocean.

In a general way, if you don’t pay attention, the ocean is always pretty much the same. But it’s a gnarly chaotic process. The details are always different. You could watch waves hitting a rock for a hundred thousand years, and it would never be exactly the same.

Before fractals and chaos theory, people didn’t used to grasp that gnarl is good. It’s not a flaw, or an error, or a defect. It’s what there is. Chaos is health.

Jeff Carreira: You write fiction in a style you call transrealism. What do you mean by this, and how do you see your fiction as a vehicle for expanding consciousness into four dimensional thinking?

Rudy Rucker: I feel that science fiction needs to have realistic human characters to be fully engaging. So I very often base my characters on myself, my family, my friends, or even people that I know only casually. That’s a thing that the Beat authors used to do. If you want to bring dimensions into it, you might say that my transreal stories are an overlay on reality, slightly displaced into the fourth dimension.

Jeff Carreira: You’ve lived a fascinating life exploring some of the most progressive edges of thought, can you tell us about some of the people who have most influenced your own thinking?

Rudy Rucker: Try Kurt Gödel, Martin Gardner, William Burroughs, Allen Ginsberg, Robert Shekley, Ivan Stang, Bruce Sterling, William Gibson, Benoit Mandelbrot, John Walker, Stephen Wolfram, Ken Goffman, Eileen Gunn, Faustin Bray, Sylvia Rucker, Terence McKenna, and Tim Leary.

But I’m too tired to fill in the details. You can read about some of these characters in my Collected Essays. And others in The Lifebox, the Seashell, and the Soul. And still others in my autobiography Nested Scrolls.

Or try the online search-engine model of me that I call Rudy’s Lifebox.

Seek and ye shall find.
Thanks for interviewing me.
Stay high.