One Moe on Fractal Universes, But It’s A Little Bit Silly
I know, I know, i said i was done with the topic, but here i am writing about it one more time. So what got me going yet again?
I going back to the original article
Recall our use of an image that showed a 3D printed sculpture that cleverly demonstrated how a curved higher-dimensional object can project a seemingly flat, uniform grid pattern in a lower dimension?
A powerful visual metaphor for some mind-bending concepts in geometry and physics:
Back to the key ideas:
- The 3D sculpture has a curved, distorted grid pattern on its surface.
- But, when light shines through it, the 2D shadow it casts looks like a perfect, evenly spaced grid.
- This illustrates how a curved space (the 3D object) can appear flat when projected to fewer dimensions (the 2D shadow.)
- It suggests our seemingly flat 3D universe could actually be a projection or “shadow” of a curved 4D spacetime.
Confirming the mathematics behind it:
This demonstration relies on principles from differential geometry, topology and general relativity. Here’s a step-by-step explanation of the key mathematical ideas:
Intrinsic vs Extrinsic Curvature
A classic example, imagine a 2D creature living on the surface of a sphere. Locally, their world feels flat — parallel lines seem to stay parallel, triangles seem to have 180° angles, etc. But globally, we 3D beings can see the sphere is curved. This is the difference between intrinsic curvature (what geometry feels like from within the space itself) and extrinsic curvature (how the space curves within a higher dimensional space it’s embedded in).
Curvature and Parallel Transport
One way to detect curvature intrinsically is through parallel transport. On a flat plane, if you move a vector along any closed path, it comes back unchanged. But on a curved surface, a vector transported along a closed path comes back rotated. The amount a vector twists when parallel transported around a small loop is directly related to the intrinsic curvature of the space, captured in the Riemann curvature tensor:
The Γ’s are Christoffel symbols that describe how vectors twist and turn in the space.
Projection and Dimensionality
Now imagine a curved 3D grid, like the one on the sculpture. Even though it’s warped, at each point you can still define a little flat plane tangent to the surface. As you shine a light through this object, each point projects onto a corresponding point on a flat 2D plane. This projection is like a coordinate mapping between the curved 3D grid and the flat 2D shadow. Mathematically, if the curved 3D space has coordinates (u,v,w) and the flat 2D space has coordinates (x,y), the projection is a map: P: (u,v,w) -> (x,y) This is analogous to how a curved 4D spacetime could project down to our perceivably flat 3D space.
Coordinates and Metrics
To do geometry in curved spaces, we need a way to measure distances and angles. This is the job of the metric tensor g_μν. In the curved 3D space, the grid is described by a curved metric g_uv, but when projected to 2D, it looks like a flat metric δ_xy. This means the actual distances in the curved 3D space get hidden or encoded when flattened to the shadow. It’s like a distorted map — the shapes on the map aren’t the true shapes on the curved globe.
Einstein’s Field Equations
This idea of curved space projecting to flat space is at the heart of general relativity. Einstein’s insight was that matter and energy curve spacetime, and this curvature is what we perceive as gravity. The Einstein field equations relate the curvature of 4D spacetime to the amount of matter and energy in it:
Here G_μν is the Einstein tensor describing curvature, Λ is the cosmological constant, and as g_μν is the metric, T_μν is the stress-energy tensor encoding the matter and energy content.
These equations tell us that the more matter/energy in a region, the more spacetime will curved there. A black hole is an extreme example — a single point of infinite density that infinitely curves spacetime around it. So in our universe, massive objects like stars and galaxies curve 4D spacetime, but to us 3D creatures, we just experience it as the force of gravity in our seemingly flat space. It’s just like how the curved 3D grid projects to a flat-looking 2D shadow! Conclusion This sculpture is a stunning visual metaphor for some of the most profound ideas in modern geometry and physics. Just as the curved 3D grid projects to a flat 2D shadow, our apparently flat 3D universe may be a projection of a vastly more complex curved 4D spacetime.
The mathematics behind this, from differential geometry to Einstein’s general relativity, gives us a framework to understand these higher dimensional phenomena and how they manifest in our perceivable reality. Of course, directly visualizing 4D spacetime curvature is impossible for us 3D creatures, which is why demonstrations like this sculpture are so powerful. They give us a tactile, intuitive sense of these otherwise abstract mathematical concepts. I hope this explanation helps reveal some of the deep insights hidden in both that beautiful artwork and the reality were living in!
- What really got me stewing was, the concept of where does the ‘light’ projecting the shadow on the lower dimensional surface shine from?
- And what is the particular form that this light takes in our case?
That is, what exactly is this mysterious kind of ‘hyperluminous ether’ necessary to project our dimension as reality from a ~5D universe ‘above’ it and where would the source of this ‘hyperluminous ether’ projecting our universe onto it’s lower dimension as we perceive be? i.e. would it be center of Menger sponge cube? Out side it, evenly distributed? Or somehow from an angular incidence point? Or what?
To consider where this “hyperluminous ether” might originate in a Menger sponge fractal universe model, we need to think about how higher-dimensional projections would work in this conceptual framework — the question of where the “illumination” comes from in our hypothetical fractal universe is fascinating and profound. In the original article, this hyperluminous ether was assumed as the 4D equivalent of light that projects the higher-dimensional fractal structure onto our 3D reality — analogous to how light projects the 3D grid sculpture onto a 2D shadow in the example above.
This gives several possibilities for the source of this projection:
From the Center: If the projection originated from the center of the Menger sponge, it would create an interesting radial effect. The center of a Menger sponge is actually empty after the first iteration (a hole), which creates an intriguing pos sibility — perhaps the projection emanates from the emptiness at the center, similar to how some cosmological models place the Big Bang as occurring everywhere simultaneously. This central projection would mean that our 3D universe is a kind of radial projection outward from this central void, with the fractal complexity increasing as we move away from the center. Gravity might increase toward the periphery in this model, as we’d be moving “down” the fractal stack away from the central void.
From the Exterior: Kinda the easy default beause for the majority of people i’d guess this is the inuitive default to imagine derived from how we see our universe generlaly. If the projection came uniformly from the exterior of the sponge, it would be more like how we typically think of illumination — light shining in from all directions outside the object. This would mean our 3D reality is the result of all these projection rays passing through the fractal structure and creating interference patterns. In this model, we might be experiencing a kind of “shadow reality” within the sponge itself, with the projection source being some kind of boundary condition of the overall fractal structure — perhaps analogous to how the holographic principle describes our universe as a projection from information encoded on a distant boundary.
Distributed Throughout: Perhaps the most sophisticated possibility is that the projection source is not localized at all but is distributed throughout the entire fractal structure. In this case, each point in the Menger sponge would be both projecting and receiving projections simultaneously. This aligns with how quantum field theory describes particles and forces — as excitations in fields that permeate all of spacetime. The hyperluminous ether would then be a kind of fundamental field that exists at all points in the higher-dimensional fractal, with its fluctuations and patterns creating the projection that we experience as our 3D reality.
From an Angular Incidence Point: The idea of an angular projection is curious because it introduces asymmetry — if the projection comes from a specific angle rather than uniformly from all directions, it could explain certain asymmetries we observe in physics, such as the slight imbalance between matter and antimatter in the universe. An angular projection would mean that different “sides” of our reality might have subtle differences, depending on their orientation relative to the projection source. This could potentially manifest as variations in physical constants across vast cosmic distances or as preferred directions in space — something that cosmologists have occasionally found hints of in the cosmic microwave background.
Physical Implications Regardless of the source configuration, this model suggests some testable predictions:
This brings to mind Wheeler’s “It from Bit” concept, suggesting that all physical reality might ultimately be informational in nature — but with the fractal dimension adding a new layer of complexity to how that information is structured and projected across dimensions.
let’s ponder the implications of the ‘it from bit’ concept here a little more — if the single bit structure is the lowest level — the hot, high gravity, fine Planck constant bottom level, just strings/fields/(whatever single bit data may be stored as), then how complex and information rich would they become by the time we reach the top?
Ok, so, in our fractal universe model, starting from the simplest level and scaling up through the fractal hierarchy:
At the Bottom; The Single Bit.
The very bottom of the fractal stack — at the high gravity, Planck-scale level, we’d have the simplest information structures possible: single bits. These fundamental units might be:
The First Few Levels;
Emergence of Complexity. As we move up just a few levels in the fractal structure, these bits would begin to organize into more complex patterns:
Middle Levels;
Familiar Physics Emerges. Continuing upward, we’d reach the realms of familiar quantum physics and then classical physics:
Our Level; At our position in the fractal stack, the original bits have organized into astonishingly complex structures:
- Information is processed through brain networks containing billions of neurons
- Consciousness emerges as a way to model and predict increasingly complex bit-patterns
- Societies and civilizations represent collective information processing systems
- Scientific theories are effectively attempts to reverse-engineer the bit structure beneath our reality Before you protest, remember — our reality contains an immense amount of information.
Consider that a single human genome contains about 3 billion base pairs, equivalent to about 750 megabytes of data. The human brain processes about 11 million bits per second through our senses. The observable universe contains roughly 10⁸⁰ atoms, each representing numerous bits of information about position, momentum, charge, etc. @.@
Approaching the Top; Transcendent Information Complexity.
As we move beyond our level toward the top of the fractal hierarchy information complexity would continue to increase exponentially:
At the Top; Maximum Information, Minimum Constraint.
At the hypothetical “top” level of the fractal structure, we might find:
So i’ve been thinking real hard about the implications of the Menger Sponge structure here. Taking a lil’ sidetrack for a moment, lemme take you deeper into the weird world of the Hausdorff dimension than we’ve previously delved. At approx. 2.7268, let’s consider what it might mean for the “size” of the fractal universe.
First, let’s make sure we’re on the same page about what this dimension represents. In fractal geometry, the Hausdorff/fractal dimension is a measure of how the complexity of a structure changes as you zoom in or out. In other words, for a normal 3D object like a cube, if we double its size, its volume grows by a factor of 8 (2³). But for a Menger Sponge, if we double its size, its “volume” (really its fractal measure) grows by a factor of only ~6.5 (2².7268).
This fractional dimension arises because the Menger Sponge is “holey” at every scale — as we zoom in, we keep finding more and more holes, right? so it doesn’t quite ‘fill up’ space like a solid 3D object would — in a sense, it’s caught between being a 2D surface and a 3D volume, just as its dimension is caught between 2 and 3. Ok, now, what does this mean for the “stack” of universes in the fractal model? Well, if each universe is like a “slice” of the 4D Menger Sponge, then the dimension suggests that there are “more” universes as you go “down” the stack (towards smaller scales), *but, not quite an infinite number.
Think of it like this: if the universes were stacked like sheets of paper, you’d expect the number of sheets to (what? …yes,) double every time you halve the thickness (dimension 2).
But for the Menger Sponge stack, the number of “sheets” grows a bit faster than doubling, but not as fast as it would for a solid 3D stack (dimension 3).
Ok, i admit, it’s a lil’ counter intuitive — the Menger sponge stack results with more n’ more universes getting crammed in as we move down the “stack”, just not quite as fast as they would be increasing in ‘density’ if they were in a fully solid 3D stack.
If it’s still awkward, perhaps instead thinking of the number of universes you can fit in getting less as you climb the stack? /shrug.
But… but.. but., what does this mean you wail, sinking in the math a lil?
Look at it like this.
In a sense, the Hausdorff/fractal dimension is telling us that the multiverse has a kind of “sub-infinite” size — it’s unimaginably vast, but not quite the same as a never-ending stack.
That’s not too bad is it? all we’re saying is we can conclude from the fact a Menger sponge isn’t fully of fractal dimension 3 but in fact 2.7268-ish is that as a result, the stack of universes making up the multiverse isn’t in fact infinite — there are, somewhere, limits to it’s size.
There is a top and a bottom of the “stack”!
What’s more, this correlates nicely with the ‘it’ from ‘bit’ hypothesis — that there is a bottom, ultimate coarse grained, as low as it gets, ‘binary’ kinda universe; and, a top opposite state ultimate high resolution universe!
Whoa! Stop. Pause. Wait.
Something’s been bugging me here. I mentioned, amongst other fundamental values which have to be juuuuusst right to cook up our particular universe as it is, the Fine Structure constant.
It’s one that fascinates me:
The fine structure constant (α) is approximately 1/137, or more precisely about 1/137.036. It’s a dimensionless physical constant that characterizes the strength of the electromagnetic interaction between elementary charged particles.
From the fractal universe perspective I discussed in the original article, we can infer several interesting possibilities: I’m definitely smelling something — in the article I mentioned that the Menger Sponge has a fractal dimension of approximately 2.7268. The inverse of 1/137 is… (yes i’m tappa tappa tappa’ing into ChatGPT because it’s the first calculator that came to hand and my mental arithmetic sucks) …ok, i’m loathe to admit how long that actually took, but nevertheless — they do say trust your gut:
3^2.7268 ≈ 137.03
(near as damnit), close enough to really get me cookin’ (3 = recursion base of menger sponge; 137.03^-1 is the finestructure constant; and 2.7268 is ofc the Hausdorff/fractal dimension of a Menger sponge).
Isn’t that some number fun?
Ok, so, the inverse of the fine structure constant ( approximately 137) doesn’t match the fractal dimension of aMenger sponge directly, but in a fractal universe model, surely it’s conceivable that fundamental constants might emerge from the geometric properties of the underlying fractal structure, …right?
Furthermore, in the original article I ever so briefly danced near the concept of a “fractal gravity ratio” and suggested that our universe might be in a “fractal stack” of universes, increasing in dimensionality going ‘up’ and lower dimensionalities ‘below’; (Now, work with me a lil’ here)
If there’s an ‘up’ and a ‘below’, and our demonstrated reasonable theoretical ‘bottom’ (‘it’ from ‘bit’ hypothesis, keep it in mind!) and ‘top’ then we (our universe) is somewhere in the range between max and min information/gravity/squished to Planck vs. (near?) totally unconstrained. After all we know we’re not in a pure binary, total squished-to-plank-length universe, and we know we’re not in a near-zero gravity universe (after all, we have gravity, and in fact we know we have, although not a ridiculous top-of-the-stack nothing, at least lightly present amount.)
So; If we know:
- ‘Bottom’ is the most coarse resolution information/maximum gravity/most ‘data’ squished.
- ‘Top’ is the most high resolution information/lowest gravity/most ‘data’ sparse.
- We know the approx. avg. …ah. oh. info density? not yet./gravity? check!/ degree of data compression? again no.
Cool! we got one out of three — that’s still something to work with!
we have a max, a min and our ‘location’.
Still with me?
(Hehehe — ok, not gonna lie, i’m goin’ waaaaay far off anything remotely sensible now but this is great fun…) Time for some real crazy:
Let’s assume if gravity grows weaker/stronger depending on the place in the “fractal stack” (from here-on i’ll call this our “Fractal Address”), then as I said, we have demonstrated there are top and bottom limits to the “fractal stack” — i.e. zero or 100% of that possible, and hence, by plotting gravity from 0–100% and where we lie upon that scale, then we could, theoretically, gain an insight as to our own particular ‘fractal address’, no?
C’mon — just for fun let’s see if we can develop it into a potential method for estimating our place in the fractal universe!
First, let’s consider what the extremes of gravity might look like in this model:
Minimum gravity (0% on my scale): This would correspond to the “top” of the fractal stack, where the recursive depth is smallest.
- Here, spacetime would be nearly flat, with only the tiniest quantum fluctuations hinting at the fractal structure beneath.
- Matter would barely interact gravitationally, and,
- The universe would expand very rapidly, as there’d be little to slow it down.
Maximum gravity (100% on my scale): This would be the “bottom” of the stack, where the recursive depth is greatest.
- Here, spacetime would be extremely curved, with the fractal “holes” at the Planck scale dominating the geometry.
- Matter would be crushed together by the intense gravitational force, and,
- The universe would be very small and hot, as the strong gravity would prevent expansion.
Now, let’s think about where our universe might fall on this spectrum.
- We know that gravity is relatively weak compared to the other fundamental forces — electromagnetism, strong nuclear force, weak nuclear force. (In fact, it’s about 10^-39 times weaker than the strong force!), but not fully zero either — this suggests that we’re probably closer to the “top” of the stack than the “bottom”, right, still with me?
- However, we also know that gravity is still strong enough to hold together large structures like planets, stars, and galaxies. It’s not so weak that matter doesn’t interact at all. This suggests we’re not at the very “top” either.
So, based on these observations, we might guess that our universe is somewhere in the “upper middle” of the fractal stack — far enough down to have noticeable gravity, but not so far as to be dominated by it.
To get a more quantitative estimate, we could try to calculate a “fractal gravity ratio” (FGR — oooh, fancy new term coined! yay!) — the strength of gravity relative to some fundamental “maximum” set by the Planck scale.
Here’s a rough sketch of how that might work:
Starting with Newton’s gravitational constant G, which characterizes the strength of gravity in our universe, in SI units;
The Planck units define natural scales for length, time, mass, etc. based on fundamental constants. The Planck mass m_P is about 2.18 × 10^-8 kg, and the Planck length l_P is about 1.62 × 10^-35 m.
We can use these to define a “maximum” gravitational constant
where t_P is the Planck time (about 5.39 × 10^-44 s).
This sets the scale for the strongest possible gravity.
Our FGR would then be the ratio of the actual G to this maximum value:
So in this very rough model, our universe has a gravity strength that’s about 10^-60 of the theoretical maximum.
This puts us quite far up the fractal stack, but not at the very top (which would have FGR = 0).
Of course, this is a VERY (over?)-simplistic calculation, and there are MANY details we’d need to fill in to make it rigorous.
Amongst other things, we’d need a more precise definition of G_max based on the actual fractal geometry, and we’d need to account for quantum effects, which become REAL important at small scales. Nevertheless, it does illustrate the basic idea — by comparing the strength of gravity in our universe to some fundamental scale set by the fractal structure, we can get a rough estimate of our “fractal address” in the supposed Menger sponge multiverse. The weaker gravity is, the higher up the stack we are.
How much fun was that!? hard to resist, eh?
Amongst various (slighly naughty) thought experimentations we’re playing with here, this is an enticing possibility to entertain because it means the fractal universe model makes possible testable predictions! (I know, i know — i really shouldn’t — such ridiculously approximate calculations and so many assumptions — but a i repeat, yet again, just for fun, roll with me!)
For example, if we could measure G and the Planck scales to high precision, we could calculate our FGR and compare it to the model’s predictions. If the numbers match, it would be strong evidence for the fractal structure of spacetime. It also suggests some intriguing possibilities for cosmology.
If our universe is indeed in the “upper middle” of the fractal stack, what does that mean for its long-term evolution?
Will gravity eventually become weaker and weaker, leading to a “Big Rip” scenario where even atoms are torn apart?
Or will the fractal structure itself evolve, shifting our universe’s position in the stack?
These are open questions that would require much more research to answer. But they show how the fractal universe model could lead to new insights and predictions about the nature of reality.
The fractal universe may be vast and complex, but breaking it down piece by piece would be how we could slowly map its intricate structure.
Of course, I’ll bet that you, like me have already gone as far as… this begs the question:
How many divisions of the fractal stack are there above us, to go from ~10^-60 to 0?
Is there any way we can predict, especially since the divisions likely do not progress in a linear fashion? I’m loathe to answer my own question, but it’s really hard not to think about once you’ve let it cross your mind, so, let’s go ahead and try to answer it. We’re gonna need to consider the nature of the fractal structure and how it relates to the strength of gravity. Let’s break it down step-by-step:
First, recall that in a fractal like aMenger Sponge, the structure is self-similar at every scale. This means that as you zoom in (moving “down” the stack), you keep finding the same pattern repeated over and over.
Now, yes as we’ve already said, although, in principle, as far as a fractal is concerned this process could continue indefinitely — i.e. there’s no inherent limit to how many times you can subdivide a fractal, however, in the context of a physical universe, there are some natural scales that come into play — the most important of these being the Planck scale, which is set by the fundamental constants of nature (the speed of light, Planck’s constant, and the gravitational constant);
The Planck length, at about 1.62 × 10^-35 meters, is thought to be the smallest meaningful size in physics — below this scale, the concept of “distance” itself may break down due to quantum fluctuations.
[NOTE: this is where I’m going real deep into absolute wild assumptions — it’s utter supposition from here, as emphasized by the big, fat bold emphasis of the word assume, when it rears its ugly head]
So, for want of anything better, we’ll go with the assumptions that while the fractal structure itself may be infinite, our physical description of it likely cuts off at the Planck scale.
This suggests that the “bottom” of the fractal stack corresponds to the Planck length, and, shall we assume the “top” corresponds to the size of the observable universe (about 8.8 × 10²⁶ meters). (/shrug, you gotta start somewhere…)
Now, how does this relate to the strength of gravity? In the fractal universe model, gravity is an emergent property of the recursive structure of spacetime. The more “levels” of the fractal you traverse, the stronger gravity becomes, as the curvature of spacetime accumulates with each iteration.
[KEY TO REALISE] The exact relationship between fractal depth and gravity strength would depend on the specific geometry of the fractal. [KEY TO REALISE]
But, for the sake of illustration, let’s assume a simple exponential model (sorta reasonable for a fractal of the dimension applicable to a Menger sponge…):
Each “level” down the stack increaseing the strength of gravity by a factor of, well, i rather like ‘e’ — about 2.72
(again, c’mon — it’s so elegantly irresistible, right?);
Under this model, moving from our universe’s FGR of 10^-60 to the maximum of 1 (at the Planck scale) would require about 138 levels of the fractal (since e¹³⁸ ≈ 10⁶⁰).
So in this rough picture, there would be around 138 “divisions” of the fractal stack above us.
Wait, you yell — and you’d be absolutely right — the progression is unlikely to be linear.
Since The fractal structure of spacetime could be much more complex, with the strength of gravity changing in a more intricate way as you move through the levels, it’s possible that the relationship is logarithmic, or follows a power law, or has some other form entirely.
To really answer this question, we would need a much more detailed model of how the fractal geometry relates to the emergent physics. This would likely involve complex mathematics from the fields of fractals, general relativity, and quantum mechanics.
We might need new theoretical tools to fully describe the recursive structure of spacetime and its implications for gravity.
That said, there are some general principles we can apply:
- One is the holographic principle, which suggests that the amount of information in a region of spacetime is proportional to its surface area, not its volume — in a fractal universe, this could translate to a limit on how many “levels” of the stack can be physically meaningful — at some point, the amount of information needed to describe each additional level would exceed the information capacity of the universe itself!
- Another relevant concept is renormalization, which is a technique in quantum field theory for dealing with infinite quantities by absorbing them into the definitions of physical constants. In the context of the fractal universe, renormalization could provide a way to “smooth out” the infinite levels of the stack and arrive at finite, measurable quantities.
These are just some initial thoughts, and MUCH more work would be needed to develop them into a rigorous model. The key point is that understanding the relationship between fractal depth and gravity strength is a complex problem that likely requires insights from multiple areas of physics and mathematics.
But that’s what makes it such an exciting question!
By probing the structure of the fractal universe, we’re really asking about the deepest nature of reality itself.
We’re trying to understand how the very fabric of spacetime could be woven, and how that weaving gives rise to the forces and phenomena we observe. It’s a grand cosmic puzzle, and every question we ask, every model we build, every calculation we do, adds another piece to another possible picture. The fractal universe idea is still in its early stages, but I enjoy its potential to revolutionize our understanding of a physics and a cosmology.
Wanna keep goin’?
We can try to quantify the information scaling too:
If each level increases complexity by a factor related to the fractal dimension, then by level 138 up from bottom, the complexity increase would be approximately:
(2.7268)¹³⁸ ≈ 10⁶²
That’s a factor of 10 followed by 62 zeros!
To put this in perspective, there are estimated to be about 10⁸⁰ atoms in the observable universe.
By the time we reach the hypothetical top level at around …276 levels (if we assume symmetry), we’d be looking at complexity on the order of:
(2.7268)²⁷⁶ ≈ 10¹²⁴
Hmmm… This is an incomprehensibly large number, far exceeding the number of atoms in the universe or even the number of possible quantum states in the observable universe!?!? Anyone else starting to feel something went wrong somewhere?
Waiiiiit — i spot my big fat error: If we’re approx. 138 down from top supposedly, but near top — yup, assuming symmetry was erroneous.
Ooop — assumptions, as ever, are tricksy lil’ gotchas… (when you make an assumption you make an ‘ass’ out of ‘u’ and …’mption’?) so this implies the numbers work out different, no?
Right. I erred bigtime!
From the top then;
If we’re supposed to be approximately 138 levels from the top, (but not necessarily from the bottom — no symmetry), redoing the math:
Last known good point, we had the Fractal Gravity Ratio (FGR) of approximately 10^-60, and said:
“So in this very rough model, our universe has a gravity strength that’s about 10^-60 of the theoretical maximum. This puts us quite far up the fractal stack, but not at the very top (which would have FGR = 0).”
and:
“Under this model, moving from our universe’s of 10^-60 to the of 1 (at the Planck scale) would require about 138 levels of the fractal (since e¹³⁸ ≈ 10⁶⁰).”
What have i highlighted and why?
I got it upside down! (yeah, i know — fell for that self-same unintuitive ‘denser as you go down’, upside down seeming situation Iexplained ‘so well’ earlier…).
Since It’s 10^-60 of maximum of 1;
this places us about 138 levels ‘below’ the “Bottom” (quotes, quotes, quotes) of the MAX of the stack, (it’s flipped over, the Planck scale with minimum gravity is top!!!),
also, rmembering, not 138 levels above the bottom as for a symmetrical fractal address in the “stack”, only 138 levels down from MAX at the top.
This completely changes our position in the fractal hierarchy.
A revised version of our position:
If we’re 138 levels from the top of the stack at max ‘resolution’ (the region of minimum gravity), this means:
- We are much closer to the “bottom” (high gravity, Planck-scale region) than I previously analyzed
- Most of the fractal hierarchy extends above us, not below us
- We’re in a relatively information-dense, gravity-strong region of the fractal structure
Information Complexity in This Revised Model
Let’s reconsider the “It from Bit” concept with this corrected understanding:
At the very bottom (maximum gravity, Planck scale), we would have the highest information density and complexity. This region would be characterized by:
- Extremely dense information packing
- Maximum computational capacity per unit volume
- Highest possible bit-encoding efficiency As we move upward in the fractal hierarchy (toward lower gravity regions), information becomes less densely packed, more “spread out.” This creates an interesting inversion of my previous analysis.
Starting Point: The Information-Dense Bottom The bottom of the fractal stack (which we’re relatively close to) would be characterized by:
Moving Upward: Information Diffusion As we move up the stack (away from our position and toward the top):
Our Position (~138 Levels from the Top) Being relatively close to the bottom of the stack would mean:
The top of the stack (138+ levels above us) would represent:
The Mathematical Implications If we’re using the same exponential scaling model with the fractal dimension, then moving from our position to the top would involve a decrease in information density by a factor of approximately:
(2.7268)¹³⁸ ≈ 10⁶²
This means the information density at the top would be about 10^-62 times what we experience — almost vanishingly small.
(sidenote:
This revised understanding also changes the metaphysical implications:
Rather than seeing spiritual enlightenment as moving “up” toward greater complexity, it might be seen as moving “up” toward greater simplicity and less constraint. The top of the fractal stack would represent something like:
- Maximum freedom from physical constraints
- Minimum information requirement
- Spacetime approaching perfect flatness
- A state of minimal interference patterns
This resonates with certain spiritual traditions that view enlightenment as a process of simplification, letting go, and returning to an unconditioned state — rather than accumulating more complexity or information. Interesting huh?)
The revised math creates a completely different picture of the fractal universe model and our place within it — the “It from Bit” concept still works, but in this version, the maximum bit density and complexity would be at the bottom (Planck scale), with a gradual diffusion and simplification as we move toward the top of the hierarchy.
It’s also striking that this number (138) is very close to the inverse of the fine structure constant (137.036).
Might this be deterministic? Perhaps the fine structure constant is related to our universe’s “address” in the fractal hierarchy…
The FSC as Emergent from Recursive Structure: If our universe is a projection of a higher-dimensional fractal structure (as the original article suggested), then the fine structure constant might not be truly fundamental, but rather emergent from the recursive geometry of spacetime. The strength of electromagnetic interactions could be determined by how recursive patterns at one scale project to another.
Implying It Varies Across the Fractal: The original suggested gravity might vary in strength depending on position in the fractal stack. By extension, it’s possible that the fine structure constant might also vary across different “levels” of the universe. This could have profound implications for our understanding of physics, as it would mean that what we consider fundamental constants might be locally constant but globally variable.
Information Encoding: The original artical discussed how information might be encoded in the fractal structure of spacetime. The precise value of the fine structure constant (1/137.036) might encode important information about the overall structure of the multiverse or about our specific position within it.
Implications for Physics: If the fine structure constant is indeed related to the fractal structure of spacetime, this would suggest;
Information Transcendence
What’s fascinating about this model is that it suggests a kind of “information transcendence” as we move up the fractal stack. Each level doesn’t just contain less information — it represents a fundamental shift in how information is organized and expressed.
Under this model, moving from our universe’s FGR of 10^-60 to the maximum of 1 (at the Planck scale) would require about 138 levels of the fractal (since e¹³⁸ ≈ 10⁶⁰).
This “It from Bit” fractal hierarchy gives us a fascinating framework for understanding how the apparently simple foundation of reality could give rise to the rich complexity we experience, and hints at even greater complexity in levels beyond our own.