ἀγεωμέτρητος μηδεὶς εἰσίτω
The Mandelbrot Set
The Mandelbrot Set, defined by the equation zn+1 = zn2 + c, is plotted on a two-dimensional complex plane. The set itself is two-dimensional, as it occupies a finite area. However, its boundary exhibits fractal behavior and has a Hausdorff dimension of 2.
At first glance, this seems counterintuitive. A circle, for example, is a simple shape on a plane with a smooth, well-defined boundary. Its edge is one-dimensional, even though it encloses a two-dimensional region.
The Mandelbrot set behaves very differently. Its boundary is infinitely complex: no matter how far you zoom in, new layers of structure continue to appear. Unlike the smooth edge of a circle, the boundary never becomes simple or regular at any scale.
Key Takeaway: The Mandelbrot set is 2D, but its boundary is so infinitely complex that it also has a dimension of 2.
What Do The Colors Mean?
In the Mandelbrot set, each point is a starting value and the colors show how its behavior unfolds over time under iteration.
Black (inside the set)
- These points never escape
- Their iteration stays bounded forever
Colored regions (outside the set)
- These points do escape to infinity
- The color tells you how long it takes
At the boundary between black and color:
- Numbers are on the edge of stability
- Tiny changes in c = huge differences in behavior
The true Mandelbrot set is infinitely detailed and continuous.
What you see on a screen is a finite-resolution sampling of it.
Coloring adds an extra interpretive layer, escape time → color.
So the digital version is a projection + approximation + artistic mapping of a deeper mathematical object.
Dimensions
Humans use mathematics to define and explore spatial dimensions.
Zero Dimension (0D): A point is considered zero-dimensional, as it has no length, width, or depth, it simply exists as a location.
One Dimension (1D): A line is one-dimensional, characterized by length alone.
Two Dimensions (2D): In the second dimension, we introduce a new axis, width, forming a flat plane where closed shapes like polygons and circles can exist.
Three Dimensions (3D): Moving into the third dimension, we add depth, represented by the z-axis, allowing us to describe volumetric forms like cubes, spheres, and all physical objects as we perceive them in space.
When it comes to dimensions beyond the third, we run into a cognitive limit. Visualizing a fourth spatial axis, one that is perpendicular to the three we already know, is beyond the capabilities of our spatial perception. We can infer the existence of higher dimensions mathematically or symbolically, but these higher dimensions are not bounded by time, and we cannot fully visualize them in the same way we understand length, width, and depth.
In physics, the concept of a fourth dimension takes a different form. Rather than introducing another spatial direction, the fourth dimension is understood as time. By combining the three spatial dimensions with time, we form what is known as spacetime, where every event is defined not only by where it occurs, but also when. Unlike spatial dimensions, which we can move through freely, time appears to flow in a single direction, making it fundamentally different in how it is experienced.
A rotating tesseract: the 3D projection (shadow) of a 4D cube, morphing as it turns through an unseen dimension.
Mathematically a fourth spatial dimension can be defined; just as a cube extends a square into three dimensions, a four-dimensional shape, such as a tesseract, extends a cube into a higher spatial dimension. While we cannot directly perceive such objects, we can represent them through projections and analogies, offering glimpses into how higher-dimensional space might behave. In this way, the fourth dimension sits at the boundary between what we can experience and what we can only describe, mathematically precise, yet intuitively out of reach…
Or is it?
Loki’s Tesseract symbolically represents higher-dimensional access, using “space” as a power source to open portals.
Violations of Linear Spacetime
The “boundary” of your human world is not a hard edge, it’s a limit defined by what you can observe and interact with. Your “dimension” is basically: 3D space + time (spacetime). There’s no wall around it, but there are limits. The closest thing to a real boundary is the observable universe. It’s the farthest distance light has had time to reach you. Beyond that, you cannot see or receive information…
Or can you?
Within our bounded world, we still experience phenomena that hint at interaction with something beyond it. Things like:
Remote Viewing
Declassified CIA programs like Project Stargate used trained psychic spies to perceive distant locations, including targets across the world and even different points in time, implying access to information beyond normal space-time constraints.
Near-death experiences
Reports of timeless awareness or life review suggest consciousness operating outside normal time flow. In the book Dying to Be Me, Anita Moorjani, dying of late-stage cancer describes leaving her body, experiencing a state of expanded awareness beyond space and time, and then returning, after which her body rapidly healed, with medical documentation showing the disappearance of her cancer.
Telepathy
Direct mind-to-mind communication implies information transfer without physical signals, effectively ignoring spatial separation. In the work of Diane Hennacy Powell, there are documented cases of non-speaking autistic individuals identifying hidden objects, responding to unseen prompts, or communicating complex thoughts without verbal language.
Past-life Memories
Cases like James Leininger a child who described detailed memories of a WWII pilot, are often cited as examples of consciousness accessing information beyond a single lifetime.
Ghosts, Apparitions, Orbs, etc.
Mediumship
Psychic Intuition
Astral Projection
Déjà Vu
Unexplained Synchronicities
These aren’t just strange occurrences, they’re violations of linear space-time. How is that possible? Does our consciousness have access to higher-dimensional information?
Remember the simple formula behind the Mandelbrot set contains not just the solid region, but the boundary, the infinite detail, and infinity itself. It’s all encoded in one compact expression: zn+1 = zn2 + c
Could our reality be described by a similar equation? Could reality be defined by an equation? Fuck yeah it can.
From 1D → 2D → 3D → nD
1D: y = x^2
2D surface: z = x^2 + y^2
3D+ (higher dimension): w = x^2 + y^2 + z^2
Mathematical equations maintain the same structure – as dimensions increase, more variables or axes are added. So a higher-dimensional equation is just a rule relating many variables at once.
The brain itself is a fractal system, with recursive structures in its neural architecture and activity patterns. Under psychedelics, the brain’s default mode network which usually keeps our experience grounded and predictable becomes disrupted. This allows for a flood of sensory, emotional, and symbolic information to surface. In that altered state, one may begin to perceive non-linear patterns, seemingly impossible geometries, or even entities that exist outside of time.
Reality is an Illusion
Reality is less like a window into the world and more like a carefully designed user interface. In The Case Against Reality, Donald D. Hoffman argues that evolution did not shape our senses to reveal objective truth, but to maximize survival. Through models of Natural Selection, he suggests that the probability of perceiving reality as it truly is effectively ZERO. Instead, what we see, hear, and feel are simplified symbols that guide adaptive behavior. Reality is a survival-driven projection that helps us navigate the world without ever showing us what’s actually there.
TLDR: Your reality is a user interface your brain renders just well enough to keep you alive, not to show you what’s actually there.
Control is an Illusion
Studies on Sleepwalking show the brain can run full motor behavior with no conscious awareness. Under Anesthesia, signals still move through the brain, but they don’t integrate into conscious experience, pointing away from any single “control center” for awareness. And in cases of Split-Brain Surgery, the two hemispheres can act independently, even producing conflicting actions. Watch Your Brain: Who’s in Control? and see how your brain makes decisions before you even realize it.
TLDR: What feels like deliberate control is often just awareness arriving late to a process your brain has already executed on its own.
Can We Rewire Our Brain? Can Code Write Itself?
Your experiences shape neural pathways, and those pathways can be reinforced, weakened, or overridden over time. This is called neuroplasticity. Old patterns can become less dominant, overwritten, or decoded.
The Newest Sacred Geometry: The Amplituhedron
Spacetime has been challenged by physicists Nima Arkani-Hamed and Jaroslav Trnka when they discovered the amplituhedron in 2013.
The amplituhedron is a geometrical framework that lives entirely in a higher-dimensional space. By observing projections or slices of the amplituhedron physicists can
is not a shape; I know it sounds like one, but it’s not. The amplituhedron is a revolutionary discovery that allows for the immense simplification of studying particle collisions. Traditionally, physicists use what’s called Feynman diagrams to predict what will happen when particles collide under certain conditions. However, these diagrams can result in hundreds of pages of mathematical equations, taking physicists days to compute, And its important to know what to expect when smashing particles together because any deviation from expected scattering amplitudes could indicate new physics (such as extra dimensions or unknown particles).
So previously we assumed particles move through space time so we used Feynman diagrams to track those movements or possible movements. The amplituhedron gets rid of space and time and predicts particle interactions using pure geometry instead.
This suggests that spacetime might not be the fabric of reality, but a useful way we interpret the deeper, geometric principles underlying the universe. Instead of space and time being the starting point, they could be emergent properties of a more fundamental structure, just as temperature emerges from the motion of atoms or a rainbow emerges from the bending of light.
Just like when you see a smiling emoji, you immediately know it means happiness. Geometry, in the case of the amplituhedron, works the same way. It’s a universal shorthand that conveys the answers to physics problems faster and more intuitively than equations.
The amplituhedron shows us that underneath all the complexity of the universe, there’s a beautiful, simple truth—captured in geometry.
So just as Plato used the platonic solids to describe the elements and the building blocks of reality, we are finding hundreds of years later, more underlying geometry, that explain our physics better than we ever could’ve using spacetime math. Geometry is not metaphorically the language of the universe, it is literally the language of the universe, and we are just a byproduct of all that is happening, we are the rainbow that appears when light is bent.
The truth doesn’t exist in one place, its scattered across many religions, schools of thought, and fields of science.