Fractal criticality

Fractals at all scales

Episode Transcript

(00:00):
All right, so get ready, because today we're taking a deep dive into a world where you

(00:04):
can find connections between things like heart cells and AI and even bird behavior.
Oh, yeah.
All pointing to kind of a hidden order.
And that is the world of fractals.
Exactly.
You sent over some really interesting research.
And I'm really curious to see what we uncover here.
Yeah, it's amazing, you know, these self-similar patterns, these repeating structures that

(00:25):
you see.
Yeah.
These are popping up everywhere.
And what's really intriguing is what this could reveal about how our brains work, the
nature of reality.
And even the future of technology.
Okay, so let's unpack that a little bit.
For those who might need just a really quick refresher, fractals are like those images

(00:46):
you see of a tree branching out.
Or maybe like the jagged edges of a coastline, where the same pattern kind of repeats itself
no matter how much you zoom in or out.
Exactly.
And we're going to explore how these patterns are not just beautiful to look at, but they
might actually hold the key to understanding how complex systems function, adapt, and thrive.

(01:07):
I love it.
Okay.
So the first study that you sent over looks at mitochondria.
Okay.
These tiny powerhouses.
Yes.
Inside ourselves that turn food into energy.
So what's the fractal connection here?
Well, researchers found that the way mitochondria cluster together forms fractal patterns.
And here's the kicker.
The more organized these clusters are, the better they are at managing energy, especially

(01:29):
when the cell is stressed.
It's like nature has found an incredibly efficient way to pack a lot of power into a really tiny
space.
So it's not just randomly jumbled together.
There's this underlying order to it.
There's an order, a fractal efficiency to how these energy factories are arranged.
Yeah.
And this efficiency isn't limited to just the microscopic world of ourselves.

(01:52):
Another study that you sent over looked at the movement patterns of quails and found that
those exhibit fractal organization as well.
So from their tiny steps to like their daily cycles, it's like there's this pattern of
self-similarity that helps them conserve energy and adapt to their environment.
Absolutely.
It's like nature is speaking a language of fractals.
Using these patterns to optimize for survival and adaptability across all scales.

(02:16):
And then you know what gets really interesting?
Yeah.
This fractal language seems to be bridging the gap between the natural world and the
artificial systems that we're creating.
So large language models, those AI systems that power things like chat GPT are also showing
signs of fractal organization.
That's right.
Wait, so you're telling me that the way AI processes information could be similar to

(02:40):
how a flock of birds moves.
Or how our cells manage energy.
It's definitely mind bending, but researchers are finding that LLMs can process information
more efficiently when they divide it into regions that resemble fractals.
And this could be a game changer for developing AI that's not only more powerful, but also
uses less energy.
So instead of just mimicking the human brain, we might be uncovering this deeper, more universal

(03:05):
principle of information processing.
Yeah.
Like a fractal code that underlies both natural and artificial intelligence.
Exactly.
That brings us to a crucial concept called criticality.
Okay.
Imagine a sand pile.
You add too much sand and it avalanches too little and nothing happens.
Criticality is that sweet spot right in between where the system is poised for change, but

(03:27):
still stable.
So are you visualizing the sand pile?
I'm visualizing it, but how does this relate to fractals?
Well, there's a specific fractal dimension, 1.58, that seems to pop up in systems that
are at this critical point.
One study found that this dimension marks a transition point in mitochondrial oscillators,
which are the parts of the mitochondria that help regulate energy production.

(03:50):
So 1.58 is like this magic number for achieving that optimal balance between order and chaos.
It seems that way.
And what's fascinating is that this critical dimension isn't limited to the microscopic
world.
It might also play a role in how our brains function, particularly the hippocampus, the
area responsible for learning and memory.

(04:11):
So are you saying that our brains might be operating near this critical fractal state
for optimal information processing?
That's what some researchers are suggesting.
There's evidence that cognitive control training, which strengthens connections in the hippocampus,
could push the brain towards this 1.58 dimension, enhancing learning and adaptability.
Hold on.

(04:31):
So you're saying working out your brain could be making it more like a fractal?
Kind of, yeah.
That's a workout I can get behind, but what does that even mean for how we learn and think?
Well, it suggests that achieving this delicate balance between order and chaos, this fractal
sweet spot could be key to unlocking our cognitive potential.
A brain that's closer to this optimal dimension might be able to process information more

(04:54):
efficiently, learn new things faster, and adapt to new situations with greater ease.
Okay.
My mind is officially starting to feel a little fractally right now.
So far we've seen how these patterns show up in ourselves, in bird behavior, in AI, and
even in the way our brains function.
Yes.
But where else do we find this fractal signature?

(05:17):
Believe it or not, even pure math isn't immune to the allure of fractals.
So there's a study that looked at something called elliptic curve murmurations.
Elliptic curve murmurations.
Math isn't really my strong suit.
But I'm intrigued.
So what are elliptic curves?
And what do these murmurations tell us about fractals?
Even a landscape with hills and valleys, that's kind of a simplified way to think of an elliptic

(05:42):
curve, these murmurations are repeating patterns found in these mathematical landscapes.
And what's fascinating is that they exhibit fractal-like behavior with self-similar structures
appearing at different scales.
So even in the abstract world of math, we see these patterns emerging.
Exactly.
And it gets even weirder.

(06:02):
These murmuration patterns resemble formations that we see in nature, like flocks of birds
or schools of fish.
It's like there's this deeper connection between math, nature, and maybe even how our
brains perceive and understand the world.
This is blowing my mind.
Are we saying that these fractal principles are somehow baked into the fabric of reality

(06:24):
itself?
It's a bold question.
But one that researchers are starting to explore.
And it gets even more meta because there's a study that looked at how our brains and
artificial neural networks, despite being vastly different systems, seem to organize their
understanding of the world in surprisingly similar ways.

(06:45):
So AI and our brains are more alike than we thought?
It seems that way, especially for easily recognizable stimuli.
Both systems seem to organize their understanding around similar axes, suggesting a shared principle
of efficiency similar to what we see in fractal dynamics.
So we're seeing these fractal principles pop up in nature, in math, in our brains, and

(07:07):
even in the AI systems we're creating.
Everywhere.
It's everywhere.
Yeah.
And it leads us to, I think, a pretty fascinating question.
Are fractals merely a way to describe these complex systems?
Or are they actually the underlying blueprint for how they work?
That is the question.
That's a great question to ponder.
We've covered a lot of ground already from tiny cells to complex AI.

(07:29):
A lot.
But before we dive into that next study, let's take a quick moment just to let all this sink
in.
Okay, so we're back.
And it's really striking how these fractal patterns seem to be popping up everywhere
we look.
Yeah, everywhere.
But there's one study you sent over that I think takes this idea of fractals being everywhere
to a whole new level.

(07:50):
You're talking about the analysis that used a reverse thinking protocol to evaluate the
very logic of the research itself.
Yeah, exactly.
It's like holding up a mirror to a mirror and seeing an infinite reflection.
What's fascinating here is that even the analytical process, like the act of thinking about these
connections, seem to mirror the recursive, self-similar patterns that were found in the

(08:11):
studies themselves.
It's like our brains naturally gravitate towards this kind of fractal thinking when we're
grappling with these complex ideas.
That's fascinating.
But I'm having a little trouble wrapping my head around how thinking about fractals can
actually make our thinking fractal.
Okay.
Can you explain that a bit more?
Sure.

(08:32):
Think about how we approach a complex problem.
We often break it down into smaller parts and then we look for patterns and connections
between those parts.
And those parts might have their own subparts and so on.
It's a very recursive process.
Much like the self-similarity that we see in fractals.
Okay, I see what you mean.
So it's not that our thoughts literally become fractals, but the way we analyze and organize

(08:56):
information might naturally follow these fractal principles.
Precisely.
Our brains might be wired for this kind of pattern recognition and recursive thinking,
which could explain why we're so good at connecting seemingly unrelated ideas.
That makes sense.
So are we saying that this ability to think in kind of a fractal way is what allows us

(09:17):
to make sense of complex systems, whether it's the human body, the stock market, or
even the universe itself?
It's a compelling idea and it leads us to another fascinating study that explored how
AI is being used to predict chaotic systems like weather patterns or turbulent flows.
Have you heard of GLED?
GLED.

(09:37):
That rings a bell, but can you refresh my memory?
Okay.
GLED stands for Generative Learning of Effective Dynamics.
It's all about simplifying complex systems without losing crucial information.
And it does this by reducing them to a smaller representation that captures the essential
dynamics.
It's kind of like creating a simplified map of this vast and intricate territory.

(09:58):
Okay, so it's like finding the signal and the noise.
Exactly.
Extracting that underlying order from the apparent chaos.
Exactly.
And the way GLED achieves this is by finding these lower dimensional latent spaces that
somehow manage to retain the core patterns of the original system.
And here's where that fractal connection comes in.
This process of reducing dimensionality while preserving essential information is very much

(10:23):
aligned with the principles we see in fractal systems.
So we're seeing this same fractal efficiency at play in the way AI is learning to make sense
of these complex chaotic systems.
Could this be a key to developing more accurate and efficient models for predicting things
like weather patterns or even climate change?

(10:44):
Absolutely.
Imagine being able to forecast extreme weather events with greater accuracy or optimize energy
grids based on real-time fluctuations and demand.
The implications of harnessing these fractal principles in AI are potentially huge.
Okay, I see how fractals could be revolutionizing these fields like climate modeling and energy
management.

(11:05):
Can you bring this back down to earth a bit?
Sure.
You also sent over this study about metacognitive therapy or MCT, which is used to treat depression.
Right.
So how do fractals fit into that?
This one might seem like a bit of a leap at first, but bear with me.
MCT focuses on changing negative thought patterns, especially rumination.
Okay.
Where people get stuck in these loops of negative thoughts.

(11:26):
Right.
Instead of trying to change the content of your thoughts, it's more about changing your
relationship to them.
Exactly.
How you think about your thinking.
When the connection to fractals comes in, when we consider that these negative thought
patterns can be seen as this kind of chaotic state, this lack of cognitive control, it's
like the mind is trapped in a fractal loop, repeating the same negative patterns over

(11:49):
and over again.
So MCT is like using a fractal lens to understand and treat depression.
In a way, yes.
What MCT aims to do is disrupt these negative fractal loops to help people shift their thinking
towards a more stable, less chaotic state.
By understanding the fractal nature of these thought patterns, therapists can help patients

(12:10):
develop more flexible and adaptive ways of thinking.
This is incredible.
We've gone from the microscopic world of cells to the vastness of AI and now to the intricate
workings of the human mind.
It seems like these fractal principles are connecting them all.
It's truly remarkable how this concept of fractals, once considered just a mathematical curiosity,

(12:31):
is now illuminating our understanding of biology technology and even the human mind.
We're only just scratching the surface.
Speaking of scratching the surface, we've got one last study to unpack.
It delves into the world of artificial intelligence and a concept called Turing completeness.
All ears.
Okay.
Okay.

(12:51):
So we're back and ready to tackle this final study that you sent over.
It involves AI and something called Turing completeness.
Okay.
I've got to be honest.
I'm not really familiar with that term.
So think of Turing completeness as kind of a measure of a system's ability to perform
any computation that a traditional computer can.
Oh, okay.
It's like a benchmark for computational power.
So we're talking about the potential of AI to solve any problem.

(13:13):
Exactly.
And this study focused on something called prompting in neural networks.
Okay.
Essentially, it's about giving the AI a set of instructions, a prompt, that kind of unlocks
its ability to solve a wide range of problems.
Okay.
It's like giving it the right tools and then watching it go to work.
So it's not just about the size or the complexity of the AI, but about how effectively we can

(13:36):
actually communicate with it.
How we guide its thinking.
How we guide its thinking.
And this is where fractals come in.
Remember how we talked about fractal systems being incredibly efficient?
Yeah.
Achieving a lot with relatively simple rules?
Yeah.
Well, it seems that the same principle might be at play in these AI models.
Okay.
The ability to handle a wide range of tasks through prompting could be linked to a fractal

(14:00):
like organization of knowledge and processing power.
So by tapping into these fractal principles, we could create AI systems that are not only
incredibly powerful, but also remarkably efficient.
Absolutely.
It's like finding that elegant solution in nature and applying it to the world of technology.
It's a really exciting area of research and it suggests that understanding these deeper

(14:21):
principles of organization, these fractal patterns that we see throughout nature and
now in AI could be the key to unlocking the next level of artificial intelligence.
Wow.
We've covered so much ground today.
We have.
It's incredible how these fractal patterns are popping up everywhere we look.
Everywhere.

(14:42):
From the microscopic world of ourselves to the vastness of mathematical concepts and
now to the cutting edge of AI.
It's truly mind-boggling.
We've seen how these patterns are linked to efficiency, adaptability, and resilience.
And biological systems, artificial intelligence, and even in our own thinking.
It's like we're uncovering this hidden code, a blueprint for complexity and intelligence

(15:04):
that kind of permeates the universe.
Yeah.
What does this all mean?
What can our listener take away from this deep dive into the world of fractals?
Here's something to ponder.
If fractal patterns are so widespread and fundamental, could they be a key to understanding consciousness
itself?
Could they help us bridge the gap between the material world and the realm of subjective

(15:25):
experience?
That's a profound question.
And it really highlights how these seemingly abstract mathematical concepts can have real
world implications.
Touching on some of the biggest mysteries that we face as humans.
Exactly.
So keep your eyes open for those patterns.
They're everywhere.
From the veins on a leaf to the structure of a galaxy, the more we understand these fractal

(15:48):
principles, the more we might understand about the universe and our place within it.
That's a great note to end on.
Thanks for joining us on this deep dive into the world of fractals.
It's been a pleasure exploring these ideas with you.
Until next time, keep those fractal eyes peeled.