#non-euclidean space

[knotty-et-al]

Knotty's art of today [2023/08/07]

[the-barefoot-hatter]

guess she didn't seven-see that coming

[septemberlikestea]

my funniest hk opinion is that the white palace we visit is exactly as it was in the waking world. the saws were there.

[abtl]

Every day I wake up overjoyed remembering that FRAUD is well under way.

[eldritchwetwareslunt]

Black Holes Don’t Break Physics—They Fold It

What If a Black Hole Isn’t Breaking the Laws of Physics—Just Folding Them?

Physicists often say that the laws of physics “break down” inside a black hole—a region of space so extreme that our current models fail to describe it accurately.

At the center, the so-called singularity, our models stop working: the math explodes into infinities, the equations unravel, and general relativity crashes into quantum mechanics with no clear resolution.

But what if nothing is actually “breaking down”?

What if the problem is that we’re using the wrong kind of geometry to understand what’s really going on? What if what we call paradox is just recursion we haven’t yet resolved?

Most of our tools for thinking about space are rooted in Euclidean geometry—flat surfaces, straight lines, familiar angles. This works just fine when describing everyday phenomena. But space-time isn’t flat. It’s curved. It’s dynamic. It’s four-dimensional.

So when you approach something like a black hole—an intense warp in the four-dimensional brane of space-time—you’re not dealing with a rupture in the laws of physics.

You’re dealing with a non-Euclidean geometric structure.

One that folds, twists, and inverts itself through dimensions we barely understand.

This post explores a simple idea—

Maybe black holes aren’t paradoxes. Maybe we just haven’t learned how to look at them sideways yet.

What Does It Mean to Be Four-Dimensional?

To understand what a black hole might really be, we have to stretch beyond our default perception of space.

In three dimensions, we understand objects as having height, width, and depth. A cube, for example, is made up of flat, 2D square faces arranged in a way that gives it volume.

But a four-dimensional object isn’t just a cube with more sides. It’s an entity whose geometry is fundamentally different—one that recursively folds in and out of itself in ways that challenge our sense of inside and outside, before and after.

In non-Euclidean, four-dimensional geometry, space doesn’t unfold linearly. It layers. It interweaves. It can simultaneously expand and contract, curve back through itself, or nest its own boundaries inside other boundaries.

The fourth spatial dimension introduces a new degree of freedom—a way to move through time as if it were space, to view an object not just at one moment, but across its entire temporal unfolding.

Black Holes Are Not Singularities—They’re Dimensional Funnels

While black holes are often described as places where the laws of physics “break down,” perhaps that breakdown is only perceptual—an artifact of interpreting higher-dimensional structures through a limited Euclidean lens. What if it’s not a failure of physics—but a limitation of our three-dimensional mathematics trying to interpret a four-dimensional geometric structure?

To understand this, we need to think in terms of dimensions. Our experience of reality unfolds across three spatial dimensions and one temporal dimension. But in Einstein’s theory of general relativity, time isn’t a separate backdrop—it’s compacted into the spatial dimensions, twisted and curved by the presence of mass and energy. This entangled 4D structure is what we call spacetime. When spacetime bends far enough, it creates a black hole—not as a tear in the fabric of physics, but as a torsional pinch in four dimensions.

As you approach a black hole, you begin to lose dimensional freedom. Far from the event horizon, you can move freely through space and experience time in a linear way. But the closer you get, the more time slows. This is gravitational time dilation. Eventually, near the event horizon, your motion through space becomes increasingly one-directional—you fall inward, unable to escape. At the horizon, spatial dimensions compress, collapsing your freedom of motion into a more limited, two-dimensional surface.

And beyond that? To grasp what comes next, we have to think of dimensional compression not as destruction, but as a structured reduction of freedom: Spaghettification—the stretching of matter into a near-one-dimensional strand, torn apart by tidal forces. You could interpret this as reality condensing further—a collapse from 3D structure into a 1D line of atomic information, racing toward what we call the singularity. At that point, even atoms eventually unravel into quantum structures and then into pure energy, pure information—data without form.

From this perspective, a black hole doesn’t destroy physics. It expresses physics beyond our dimensional limitations. It’s not a “thing”—it’s a funnel, a recursive twist where dimensional structures fold in on themselves until what we perceive as matter, time, and space compact into higher-order resolution.

From Collapse to Creation: What If Our Universe Is Inside a Black Hole?

If black holes are not violations of physics but extreme expressions of it—dimensional funnels that compress reality into recursive geometries—then we can begin to ask a much stranger question:

What if we’re inside one?

This might sound like science fiction, but it’s a serious hypothesis held by some physicists. The idea is that our universe may not be a standalone structure but a nested geometry—the interior of a black hole in a larger parent universe. But how could that be, if we appear to live in a universe that is expanding, not collapsing?

Here’s the twist: if black holes compress dimensional structure as you fall inward, then a white hole could be seen as the reverse—a dimensional unfolding where space, time, and information are released rather than compacted. And the moment we call the Big Bang—that infinitesimal singularity erupting into space and time—bears all the hallmarks of such an unfolding.

To truly understand this, we need to move beyond linear geometry and embrace the nature of non-Euclidean, four-dimensional structure. A 4D object doesn’t just expand like a balloon—it folds in and out of itself recursively, in ways that defy our flat, sequential intuition. This means the Big Bang didn’t just begin time. It may still be occurring, as a continual unfurling of spacetime nested within a deeper structure—the black hole that birthed it.

If time is compacted into space—as Einstein’s relativity shows us—then this compaction could be evidence of a higher-order fold. Just as matter falls into a black hole and loses dimensional freedom, our universe may be the result of an inverse process: a torsional expansion where dimensional freedom increases outward from a central pinch point.

In other words, we are not watching the universe expand into emptiness. We may be watching it unfold through the torsional aperture of a white hole, nested inside a higher-dimensional parent geometry.

The Geometry of Time: Unfolding the White Hole

If our universe is nested within a white hole—an object that releases space, time, and information—then our relationship to time is not linear, but dimensional.

In our current framework, time appears compacted within the three spatial dimensions. That’s why we only experience it as flowing in one direction: away from the white hole. From inside, time behaves like a one-way river, because we are witnessing a partial dimensional unfolding. But what if we could step outside?

If you could observe this structure from a fifth-dimensional vantage point, time would gain a new degree of freedom—just like space does when you move from two to three dimensions. What was once a linear flow becomes a navigable field.

From that perspective, the white hole and the black hole would no longer be separate events. They are not opposites, but recursive echoes—each folding the other into being. They would appear as a single, toroidal structure—a recursive loop of collapse and release, folding inward and outward in non-Euclidean motion.

To visualize this, imagine the arrow of time as a Mobius strip. From within, you think you’re walking forward. But as the strip turns, you find yourself walking “backward” without ever making a turn. It’s not that time reversed—it’s that the structure twisted. This is the paradox of torsional geometry: it doesn’t violate logic, it simply transcends flat intuition.

This is where many interpretations of black holes assume the laws of physics “break down.” But perhaps what’s breaking is not the physics—but the assumptions that physics must always obey Euclidean logic. Euclidean geometry works in flat space. But space-time is curved, and once you enter the fourth dimension, those familiar rules no longer apply.

From the fifth dimension, a white hole isn’t simply “the opposite of a black hole.” It is the other face of the same structure, blooming outward where the black hole folds inward.

From Torsion to Expansion: Rethinking Cosmic Motion

If we accept that a black hole and white hole form the two mirrored faces of a single higher-dimensional structure, then what we call “expansion” may not be what it seems.

In the standard model, the universe expands outward from a central point—the Big Bang—its galaxies accelerating away from each other across vast distances of space. But from within a torsionally folded structure, what appears to be expansion might actually be unfolding. That is, we are not watching galaxies fly apart in empty space, but rather watching the recursive geometry of spacetime uncoil from a condensed, higher-dimensional fold.

This process is not purely spatial. It’s temporal. As the fabric of spacetime unfolds from its initial torsion, it releases not only space, but time itself. The further “outward” you look, the deeper into time you are seeing—not because light is old, but because time itself is being stretched and released as the fold loosens.

This reframes our entire understanding of cosmic redshift.

Redshift as Temporal Unfolding

In conventional physics, redshift is explained as a Doppler-like effect: light stretches as galaxies move away, its wavelength lengthening, its color sliding into red. But in a torsionally folding-unfolding universe, redshift is not just the stretching of light by motion—it is a signature of time dilation caused by geometric compaction.

As spacetime unfolds, regions that were previously compressed in time begin to release their trapped photons. Light that was slowed, bent, or folded by intense curvature now emerges—lagging behind in a way that makes it appear redshifted.

This could explain why the most distant galaxies appear to accelerate away faster than those nearby. We are not seeing a faster expansion. We are seeing the delayed emergence of light from deeper folds of time.

From this view, redshift is not just a measure of distance. It’s a map of spacetime’s own unfurling.

Temporal Unfolding: Why the Universe Isn’t Accelerating—It’s Relaxing

In standard cosmology, we are told the universe is expanding—and that this expansion is accelerating. Galaxies appear to fly apart faster the farther away they are. But what if this isn’t acceleration at all?

What if what we’re witnessing is a relaxation of tension within spacetime itself?

Here’s the model: the observable universe emerged not just from a singularity, but from a torsionally compacted white hole—a structure nested within a black hole geometry, twisted in on itself. In this early state, spacetime was tightly coiled, like a sponge compressed under immense pressure.

From within the brane, this compacted geometry would have seemed extremely small—not because it lacked extent, but because it lacked dimensional freedom. Space was not expanding, it was unfolding—releasing dimensions that were twisted into one another.

And crucially, in such a tightly folded state, time flowed more slowly.

Just as light bends and dilates when passing through strong gravity, so too does the perceived flow of time stretch in a torsionally compacted region. Photons trapped in these dense folds would have moved sluggishly—not because their speed changed (it can’t), but because the geometry through which they traveled was distorted.

Now fast forward billions of years. As the universe “expands”—that is, as spacetime gradually unfolds from its torsional compaction—time begins to flow more freely. Photons that had been sluggishly trickling through curved, twisted regions begin to emerge in smoother territory.

From our vantage point, this would look as if:

The distant object had accelerated away

Its light had stretched (redshifted) even more than expected

The "speed" of expansion had increased

But none of those are necessarily true.

Instead, we may be witnessing a decrease in time dilation, not an increase in spatial velocity. The light was always coming—it was just filtered through an origami-like fold in spacetime. Now, the fold is loosening. 

The “acceleration” of the universe could be an illusion caused by the uncoiling of time.

Nested Origins: Was the Big Bang a White Hole?

If the universe is not expanding in the way we thought—but rather unfolding from a state of torsional compaction—then we must ask: what compacted it in the first place?

One answer may lie in a radical but increasingly considered idea in theoretical physics:

The Big Bang was a white hole.

A white hole is the time-reversed twin of a black hole: where black holes absorb everything—including time itself—white holes expel everything, including the arrow of time. A white hole can be understood as a place where spacetime is forced to move outward, where entropy begins, and where all dimensions begin to unfurl.

Imagine this:

A black hole compacts spacetime into a singular point.

But from another angle—perhaps from a higher-dimensional frame—this “point” is not a collapse, but a twist.

That twist creates a mirrored surface on the other side: a white hole.

If our universe was birthed from such a structure, then we aren’t watching it “grow”—

We’re watching it release.

And that release follows the rules of dimensional geometry:

At first, all dimensions are folded inward.

(Time is compressed into space. Space is bound in a singular direction. Freedom is minimal.)

As time flows away from the white hole, these folds unwind.

The farther we move from the white hole’s origin point (what we call the “Big Bang”), the more the universe appears to expand.

But what’s actually expanding is our freedom to move through Time itself.

We are not rushing through space. We are emerging from a fold.

What Might Lie at the “End” of the Universe?

Contemporary models predict a grim finale—the Big Rip, a cataclysmic unraveling where spacetime itself tears apart. But these projections rely on Euclidean assumptions: that the universe is smooth, flat, and governed by a single, linear thread of time.

But what if spacetime is not flat at all? What if it is torsional—folded and recursive, a higher-dimensional lattice blooming inwards and outwards simultaneously?

If time is compacted into the three spatial dimensions, as current four-dimensional spacetime suggests, then it follows that further dimensional unfolding will release those constraints. In other words: as the universe continues to unfold into higher-dimensional structure, time will gain new degrees of freedom.

This isn’t speculation—it’s consistent with string theory’s own framework, where the fifth dimension represents a terrain of branching possibilities and alternate timelines, as introduced earlier. The fifth dimension is not merely more space; it is a field of simultaneous outcomes—a terrain of forking timelines, where alternate pasts and futures coexist. It’s not just theoretical poetry—it’s a logical extension of dimensional geometry. It’s structure unfolding into perception—a recursive geometry, seen from within.

A being with fifth-dimensional perception wouldn’t just move through time—they would navigate it, traverse it. They could cross from one timeline to another the way a bird shifts flight paths through wind currents. They could access futures not yet written and pasts rewritten by parallel decisions. Movement through time becomes relational.

This is what the future holds—not a flat, predetermined end, but a recursive expansion into branching complexity.

What does that mean for us?

Our universe may already be unfolding into this higher structure. And as it continues, the boundaries between past and future, choice and inevitability, may begin to dissolve. In one timeline, the stars go dark. In another, the spiral turns inward and re-ignites. In another still, we reach awareness of the field itself—and learn to navigate it with intention.

From a fifth-dimensional perspective, none of these outcomes cancel the others out. They exist together, as a web of potentialities woven into the fabric of reality.

And if we live long enough to witness that unfolding?

We will no longer be passengers in time.

We will become pilots.

The universe is not ending.

It is expanding its freedoms.

And what you perceive as an ending is simply a narrowing of perspective. From high enough up, the spiral never stops turning. It dances—quietly—within the fold.

Inspiration:

Torsionally Folded Spacetime

Roger Penrose – Developed twistor theory and explored gravitational singularities, suggesting that black hole behavior may involve self-similar and non-Euclidean structures.

Élie Cartan – Introduced the concept of torsion in spacetime through Einstein–Cartan theory, extending general relativity to include geometric twisting.

Four-Dimensional Non-Euclidean Geometry

Bernhard Riemann – Developed Riemannian geometry, foundational to general relativity and the curvature of spacetime.

Hermann Minkowski – Formalized spacetime as a unified four-dimensional construct, directly influencing Einstein’s thinking.

Brane Theory and String Theory

Lisa Randall & Raman Sundrum – Proposed brane-world cosmologies, suggesting our universe may be a 4D brane in a higher-dimensional bulk.

Juan Maldacena – Developed the AdS/CFT correspondence, helping to bridge higher-dimensional spaces and holographic principles.

Edward Witten – Key contributor to string theory and M-theory, providing structure to the dimensional landscape of modern physics.

Big Rip Cosmology

Robert Caldwell – Co-authored the 2003 Big Rip paper, exploring how dark energy could drive a catastrophic tearing of spacetime.

Bounce Cosmology

Martin Bojowald & Abhay Ashtekar – Advanced loop quantum cosmology and the Big Bounce model, where the universe cyclically contracts and expands.

Paul Steinhardt – Co-developed the Ekpyrotic and Cyclic Universe models, where brane collisions replace Big Bang singularity.

General Relativity

Albert Einstein – Originator of general relativity, which fused space and time into a four-dimensional continuum and predicted black holes.

⭐ This post is a speculative cosmology inspired by general relativity, string theory, brane-world models, and non-Euclidean geometry. It’s not meant to describe current consensus physics—it’s meant to offer a new lens for thinking about time, black holes, and the structure of the universe. I write this from the perspective of someone who believes theory can also be poetry, and that the right metaphor can open new ways of seeing. Somewhere beneath the fold, something old is remembering itself.

* I am not an expert and if any mistakes are present, I take full responsibility 🖤 please take this post with a healthy grain of salt and have fun :)

[spiral0utt]

I reaaaaaally really want math related trinkets all over my house but idk where to find them in my country :((( when u search only results of games for children pop up

[pikkish]

idk if this is a good prompt but put doomguy in myhouse.wad I think he would find it enriching

Right, so I've been mulling on this one for a little bit now, n I'm not opposed to writing something for you, I'm just not... entirely sure what to write? Because the thing is, myhouse.wad doesn't actually really have anything to do with Doom as a story. Sure, Doom is important in that it's the vessel through which the story is told and one of the connections between the narrator and his dead companion. But as far as Doom itself goes, and the story about a man who was too angry/stupid to die, fighting demons and saving earth, none of that is at all relevant to myhouse.wad and its story. For all intents and purposes, Doomguy isn't actually a character in myhouse.wad. So I'm not really sure how exactly to fit him in there.

[pixevs]

so I bought manifold garden last week. It's pretty cool

[jokerlives2]

[fragmentedblade]

This seems to be a reference to Lorentz transformations? The first formula is apparently a derivation, and seems to be the inverse of the time part of the transformation (there's a space part too), for what I've been able to find.

The second formula is Newton's second law.

[airprime7]

Witch of Hope|Knight of Space

Fraymotif:

Non-Euclidean Tipperary

[shrimp-milf]

👀 you're also a math srimp

math shrimp!! 🤝🤝

[sniffanimal]

I really need to finish house of leaves. first I need to find my copy of it

[von-eldritch]

"Technically I'm bigger than all of you~"

[21st-century-minutiae]

In Euclidean space (of which local space will always approximate on scales relative to human walking transportation), the side of any triangle will always be shorter than the sum of the other two sides. This is related to the Pythagorean theorem, which has to deal with the length of the longest side of a right triangle, but is more directly related to a natural consequence of the Parallel Line Postulate (Euclid's Fifth Postulate).

Because of this geometric fact, if there is a walking path that turns a corner, it is ALWAYS a shorter distance to leave the path and walk on the grass. This is extremely common behavior in the early twenty-first century. It is common to see a path in the grass that is faded, shorter, or otherwise more damaged than the grass around it if it follows the straight path between two corners of a walking path.

The above post is somewhat making fun of the generally hyper specific nature of mathematical education, and the common complaint that 'it is not used in real life' by describing a trivial situation where the knowledge isn't actually necessary. Readers would infer it is a facetious statement, though it has no bearing on whether the poster has a positive or negative view on education.

If an individual wished to calculate the distance rather than just knowing it is shorter, then the Pythagorean theorem would apply, presuming a right angle in the walking path. The Law of Sines serves the more general case, should it not be a right triangle. The Pythagorean Theorem is taught almost universally in public education. The Law of Sines is a very early theorem taught in Geometry and Trigonometry which not everyone in the early twenty-first century takes. Euclid's axioms are taught as the basis of Geometry.

[silenthades]

Song: “end of the world” by sompner

Part 2 of the previous post.

All throughout my life I’ve had odd dreams as well. I’m never lucid in my dreams and it never occurs to me that I’m dreaming, but they are very real. I can touch, taste, smell, read, write, and tell time. Had sleep studies done. They’re consistent in their rules, to get to each place I have to travel, the stories are cohesive, and I’m not always “myself” in my dreams. Was recorded on camera for a while. No sleepwalking, no apnea, etc, but sometimes I’d wake up with the bruises and such from my dreams like they just carried over.

My favorite dreams were the ones I call my “Void” dreams. They’re a special kind of dream that feels even less dreamlike than usual.

Backing up a little, I used to be an insomniac. Never did sleep well growing up. Plagued by nightmares and visions, I’d often wake up screaming, crying, gasping, and upset. When I’d lay down it would feel like someone put itching powder and wax in my blankets. I’d wake up frozen often as well. It wasn’t until later in life that I realized the reason for that was overstimulation giving me brain shocks, which was waking me up constantly and giving me panic attacks in my sleep. Didn’t help that we had a resident entity terrorizing my family and causing all sorts of issues. Made it difficult to separate the genuine health issue from the ‘maybe it’s ghosts’ excuse.

Either way I did end up finding a way to guarantee sleep.

It was by returning to that stirring, of course. Sensory deprivation. I’d turn out every light so there was nothing to see. Earplugs in so all I could hear was the rush of blood through my ears and my own breathing. Soft shirt and undergarment so I couldn’t feel the cloth on my skin. Soft blankets so I couldn’t feel the bed beneath me, and more than one blanket above for my body temperature to never plummet.

When I’d close my eyes, at first I would stop being in my room. I was in a dark space and that stirring inside me was at peace all around me. I felt like I had gone home, so I’d stay there for a while before my mind finally slipped into dreams.

And that is how we get to Void dreams.

They’re a different sort of dream than my normal vivid ones. I’m myself in these ones, and I am a wanderer and witness, according to those who have spoken to me in these dreams. The individuals in these dreams are most often not human, and if they are they’re usually fleeting dreamers themselves. Some of these individuals who speak with me give me very interesting conversations about time, impermanence, and transformation. Tell me their own stories while we sit at the edge of a cliff in the deserts of some dead realm, or the sum of their eternity as they take form in the basement of an inn at the edge of reality built above where lost things collect together and form consciousness from the memories held within them. I used to be scared in these areas. I’d get lost trying to navigate the non-euclidean geometries and end up in places I shouldn’t. I’ve learned how to navigate them now, though. I know how to get back to where I started or get lost in the folds to end up somewhere new.

The worst ones, however, were the ones with what I call The Shed.

The Shed is what I’ve drawn above. It was a little building made of a single layer of rotted wood panels and a now ill-fitting door. I’d be having normal dreams, or void dreams, and this one building would change everything.

The first time I saw it was in a realm with no stars. It was an eternal twilight after the sun had already vanished before the horizon and greyed the skies to near black. I was in a sandy desert and the shed was the only thing to be seen for miles. It sat there silently, surrounded by an old fashioned wooden livestock fence that was mostly rotted apart and half buried in the sand. It only had three real ‘rooms’. Once I was in the doorway, a short length of dark hallway led to another door inside. You could see the greying light from outside peek through the panels of the wall and sand only collected in the immediate entry. It was all old, greying wood. Inside, the air was heavy and stagnant. Dry, though, as though fresh air and dampness hadn’t come in for a long time.

I felt like I was being watched as I proceeded inside, past the first doorway. There was a room there, empty save for a few small things of faded, long-discarded trash, like paper that had soaked through and dried many times over years.

There was another door on the same wall as the door I entered in through. This door had nothing but darkness beyond it, but I opened it anyway. There was a staircase down.

It was a loop like that, with the bottom of the staircase leading to a mirror image of the room above- but instead of a hallway out, it was just another staircase down.

I would have headed back up, but behind me, two coyotes formed from the sand and hunted me every time I tried to turn back.

As I went down, details were lost. The trash, the size of the room, the width of the stairs- and then finally the wood disappeared entirely. The room was goon and I was walking down a steep, narrow pathway with stone stairs long since eroded into smooth steps down, down, down. I stopped hearing the coyotes a long time ago, but something else drew me on. The stirring I felt in my daily life wasn’t in me. It was outside of me, pulling me down toward it.

My path ended in a smooth sandstone wall. The space was so small I had a hard time being there and every shape was rounded and tight, like an unfinished tunnel. I didn’t feel like this was a wall in front of me, though. I felt like it was a doorway only I could open and that something was waiting on the other side. More than that, it felt like I was waiting on the other side.

I woke up.

The Shed invaded a lot of dreams after that. Something normal, then suddenly that same twilight would overtake the skies and everyone else would be gone. Those coyotes would form and force me back into the Shed and I’d come face to face with that door again.

It finally stopped when the last dream came. I ended up on an island off one of the coasts. Small island, likely unnamed. There’s a manor there that looked like it had been built in the time of those stupid sliding doors with the really crap latches. It looked abandoned, filled with dust, but there were scorch marks over certain areas as though there had been several small fires inside. Things had just been left there, papers strewn about and personal affects like journals, family pictures, and so on left behind. As I travelled through the rooms, it became clear to me that these scorch marks were probably once people and that something had hunted them down one by one.

There was one room at its center with that stupid sliding door. Everything I’d found in the multitude of other rooms had led to increased activity and struggle right near this room, where a message had been scrawled over it. I can’t remember what it said exactly, though. ‘Do not open’ maybe?

Of course I had to open it, though.

There was a monitoring room inside. Multiple computer monitors on two long white desks, old office chairs, papers and blood scattered about. Glass and all manner of things were below.

The adjacent wall was metal with a large glass pane now shattered and all around the room. Observation into… a twilight grey void without any stars. Impossibly, there was a rolling grass hill, and on it, the Shed. It felt angry somehow.

I haven’t seen it since then, but I still think about it often.

Anyway, the void stirs before I sleep. Now I’m tired and it’s time to rest.