Consciousness is clickbait, and quantum consciousness is mega-clickbait, so I usually avoid it, but fractal quantum consciousness? They got me.
Image credit: Fractal Forums, 2018
First let's talk about fractals in real life.
I have the same thing happen in my dreams that you do. I'm trying to leave the house, and I forget something, and now I'm on a side mission to get that thing, but then I forget something else I need for the side thing, and now I'm on a side-side mission, but then I forget something else, ... and it repeats until I wake up. (I never make it out of the house.)
This happens in real life, at least in New Jersey it does -- you're on a main road and need to make a left, but you have to first make a right, in order to get on an overpass (like a jughandle, aka Jersey left). But when you make the first right, you realize you can't turn from there to the overpass; you instead have to make another right, onto a road parallel to the first main road you were on, but now going in the opposite direction. But even still, you find you can't make a left off this road, so you have to make another right, ad infinitum.
The trajectory of your quest has collapsed into a fractal dimension, from which you might never make it back.
This year, the recursive nature of consciousness is showing up in some interesting studies. It's beginning to look like those psychedelic images of the Mandelbrot set aren't just a good visual metaphor, they might underlie actual brain patterns, and get us closer to understanding what consciousness is.
Fractal brain networks support complex thought
Oct 2021, phys.org
A Dartmouth study has found a new way to look at brain networks using the mathematical notion of fractals, to convey communication patterns between different brain regions as people listened to a short story.Researchers show that brain networks organize in a similar way: patterns of brain interactions are mirrored simultaneously at different scales.When people engage in complex thoughts, their networks seem to spontaneously organize into fractal-like patterns. When those thoughts are disrupted, the fractal patterns become scrambled and lose their integrity.The study shows that when people listened to an audio recording of a 10-minute story, their brain networks spontaneously organized into fourth-order [fractal] network patterns. ... However, this organization was disrupted when the story's paragraphs were randomly shuffled."The more finely the story was shuffled, the more the fractal structures of the network patterns were disrupted,"-Lucy Owen, first author and graduate student in psychological and brain sciences at Dartmouth, link""
And it works just like you think it would:
The results show that the smallest scale (first-order) interactions occurred in brain regions that process raw sounds. Second-order interactions linked these raw sounds with speech processing regions, and third-order interactions linked sound and speech areas with a network of visual processing regions. The largest-scale (fourth-order) interactions linked these auditory and visual sensory networks with brain structures that support high-level thinking.
via Dartmouth College: High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns, Nature Communications (2021). DOI: 10.1038/s41467-021-25876-x
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| 3D Fractal w Fragmentarium - Adam Majewski on Fractal Forums - 2018 |
Can consciousness be explained by quantum physics? Research is closer to finding out
Jul 2021, phys.org
The Penrose-Hameroff theory of quantum consciousness argues that microtubules are structured in a fractal pattern which would enable quantum processes to occur.
First they created a quantum fractal by arranging electrons in a Sierpiński triangle. But now they're using photonics to watch the electrons move in real time. And this means that quantum fractals behave differently than classical fractals. So now they think it's time to revisit.
via Cristiane de Morais Smith and Xian-Min Jin at Shanghai Jiaotong University: Xu, XY., Wang, XW., Chen, DY. et al. Quantum transport in fractal networks. Nat. Photon. (2021).
Now that you've been primed on the potential fractal nature of consciousness, it's time to enter the n-dimensional world.
This next study should make your head spin, literally --
New research finds that collective neural activity is shaped like the surface of a doughnut
Jan 2022, phys.org
We already know about grid cells, they were discovered not long ago. Grid cells are the types of brain cells that map where you are in space -- your brain keeps a map in your head that's compressed by a layer of hexagonal grid coordinates.
But now, they found that the grid itself is not a never-ending expanse of hexagons that surrounds us in two dimensions. Instead, it's a grid superimposed on a toroid (but you might call it a donut). That means the map is not two-dimensional, but multidimensional.
This is because the grid cells do not form as a result of our motor activity as we travel over the two-dimensional surface of the Earth. Instead these cells form based on their own innate tendencies to arrange in a way that represents a toroid more than a flat grid. Note this is the shape of the data we're talking about, not the shape of the cluster of cells themselves. It's the way the cells interact, not how they're actually laid out. (Kind of like thinking of the difference between actual distance and Hamming distance.)
The big deal though, is that it hints to us how the brain orchestrates all these subregions, coordinating together to create the complexities of higher-order functioning (the kind referenced above as "4th order"). It lies in the network structures, and in this case, those structures are part of continuous attractor networks. (They did get a lot of help from a new tool called Neuropixels, which allows access to raw output from neurons from all over the brain, all at the same time.)
So network theory will become a bigger part of understanding how the brain works. And meanwhile, we can just trip out on the idea that even when walking in a straight line, our brain is superimposing that data on a toroid model.
Tl;dr -- The brain thinks the landscape is a toroid. (Even in your dreams; or especially in your dreams).
via Norwegian University of Science and Technology's Kavli Institute for Systems Neuroscience: Richard J. Gardner et al, Toroidal topology of population activity in grid cells, Nature (2022). DOI: 10.1038/s41586-021-04268-7
Further Reading:
Isaac Asimov's Robot Dreams -- a robot named Elvex (LVX-1) is updated with "fractal geometry" because the offending young scientist though it would "produce a brain pattern with more complexity, possibly closer to that of a human". The robot begins to dream about self-preservation, in direct opposition to the Laws of Robots, and is subsequently killed ("killed"?).
Maertens, James W. , Donald E. Palumbo. "Chaos Theory, Asimov's Foundations and Robots, and Herbert's Dune: the Fractal Aesthetic of Epic Science Fiction." Utopian Studies, vol. 14, no. 1, winter 2003, pp. 244+. Penn State University Press. https://www.jstor.org/stable/20718595
The Hyperbolic Geometry of DMT Experiences at the Harvard Science of Psychedelics Club in the year 2020, with Andrés Gómez Emilsson from the Qualia Research Institute
Quantum Fractals, 2019
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