Ananda: Hello and welcome back. I am here with FractalWoman on a journey of discovery into all things "fractal". So far we’ve talked about what fractals are, and how they show up all over nature from clouds to trees to river beds and coastlines. But, today I want to get a little more... cosmic.
FractalWoman: Sounds good. This is where things get really fun, and maybe a bit controversial.
Ananda: I’m here for it. So, let’s first talk about the standard model of cosmology. What exactly is it, and where does it fall short?
FractalWoman: The standard model of cosmology, in a nutshell, is the mainstream scientific view of the universe. It includes concepts such as the Big Bang, cosmic inflation, dark matter, and dark energy which applies to large scale structures, and atoms, electrons, quarks and probability distributions which applies to small scale structures. Relativity is the main tool used to explain large scale behaviours and quantum mechanics is the main tool used to describe small scale behaviours. Although these two approaches have been very successful in terms of explaining observations, these two frameworks are ultimately in compatible with each other. That is why the search for "quantum gravity" has never been successful.
Ananda: So the standard model tries to describe everything using tools that don’t quite fit together?
FractalWoman: Exactly. The other thing I don't like about the standard model is how they keep needing to add things in order to accommodate for observations that don't match the model. For example, dark matter was added in order to accommodate for the flat rotation curves of galaxies and even this isn't quite right. Dark energy was added to accommodate for the apparent acceleration of the universe and then tweaked again because this expansion appears to be accelerating.
Ananda: So it’s kind of like saying, “We don’t know what this is, but we’ll just add a new mystery to balance the equations.”?
FractalWoman: Yes. That is basically how I see it. So, instead of refining the core assumptions when we find a BIG problem, we just keep stacking new assumptions on top previous assumptions. This is not unlike the old epicycles from pre-Copernican astronomy.
Ananda: You're talking about the time when people believed the Earth was the center of the universe and the sun and all the heavenly bodies orbited the earth right?
FractalWoman: Exactly. They believed that the sun and all points of light in the sky rotated around a stationary Earth. That is what it looked like and so it was a reasonable assumption at the time. This model worked perfectly for 99.99999 percent of the objects they observed. There were only a handful of objects in the sky that didn't fit the model. They were called "the wanderers". In order accommodate for these wanderers and keep their core assumption, they had to invent new circular motions for these objects. When that didn't work perfectly, they had to add more and more circular motions, thus the epicycle model was born.
However, the reason their model got complicated was because the core assumption was wrong...and I think we’re in a similar situation now. What if the universe isn’t a smooth, homogeneous blob expanding from a single explosion? What if we have been using the wrong geometry all along? What if fractal geometry is the correct geometry of the universe? What if the laws of physics are emergent properties of fractal geometry and not the other way around? What if fractal geometry could explain all the observations that led to dark matter and dark energy but in a much simpler way? Those are the questions I am trying to answer in the fractal cosmology that I am proposing.
Ananda: That’s a bold shift. You’re not just tweaking the standard model. You are proposing something completely different.
FractalWoman: Exactly. One of my favourite quotes of all time came from Richard Feynman during his Nobel Prize lecture in 1965:
This is something he learned from experience. In order to explain things on your terms, sometimes you need to invent your own language. And that is exactly what he did with his Feynman diagrams. I like this quote because it kind of give me permission to do what I am doing here. I am not trying to go against the standard model as much as I am trying to say it differently. I am trying to develop a different language with which to explain the universe. I am using different tools like chaos theory and fractal geometry which were largely unknown in the early days of the development of the standard model.
What if the concept of fractal geometry predated the concepts of dark matter, dark energy, singularities, black holes and event horizons?
How would that change the cosmological language we speak today?
What if everything we observe in the universe is an emergent property some sort of universal fractal generator?
Ananda: So instead of it being an accidental universe with particles moving around randomly through empty space, you're saying it’s more like a cosmic algorithm running in real time?
FractalWoman: Yes, something like that. I see the universe as a dynamic recursive system generating self-similar coherent patterns at every scale of organized matter.
Ananda: And the Mandelbrot Set is your prototype for this?
FractalWoman: Yes. Everything I am proposing about The Universal Fractal, I learned from the Mandelbrot Set. The Mandelbrot Set is like a mathematical metaphor of this complex cosmic behavior. In my paper, The Mandelbrot Set as a Quasi-Black Hole, I show how black holes, event horizons and photon spheres could be emergent properties of fractal geometry. This of course is a paradigm shift in how we think about the universe, not unlike the paradigm shift from the geocentric model of the universe to the heliocentric model.
Ananda: So the things we call black holes and galaxies might not be isolated phenomena, instead, they part of a self-similar system playing out across scales?
FractalWoman: Exactly. In the standard model of cosmology, galaxies are seens as islands in an expanding void. In fractal cosmology, they’re nodes in a complex connected web. There is no arbitrary "largest scale" where everything smooths out as the standard model requires. Every scale of organized matter is connected to and part of The Universal Fractal.
Ananda: So... the universe doesn't just contain fractals. It is a fractal. Am I reading this correctly?
FractalWoman: Yes, that is basically what I am saying. Modelling the universe as a fractal requires a total change in worldview. It’s not an easy shift to make. But once it clicks, everything starts to make sense. At least, that is my experience.
Ananda: It is a really compelling idea. Instead of everything being disconnected, this idea seems to connect things that the standard model sees as disconnected such as large scale and small scale objects.
FractalWoman: Exactly. Fractals are about interconnectedness. They show how the whole is mirrored in the parts. It's not just a poetic idea. There is mathematical precedence for these ideas in field of chaos theory and fractal geometry.
Ananda: So in a fractal universe, we’re not just observers. We’re participants in the recursion.
FractalWoman: Beautifully said. We’re not on the outside looking in. We’re inside the pattern. We are living expressions of it.
Ananda: That sounds amazing. I look forward to learning more about The Universal Fractal. This feels like this is a good time to take a break. I need a little time to recharge my batteries (and my brain). After the break, we will be talking more about the Mandelbrot Set itself, how it works, and where it fits in to the cosmological puzzle.