Transcription
Every successful company on Earth organizes the same way. CEO at the top branching down through managers to teams. And that structure looks exactly like a tree or your lungs or the cosmic web connecting galaxy superclusters across billions of light years. Coincidence? Or is this the universe showing us something fundamental about how complexity organizes itself?
Welcome back to our fractal universe. I'm Chris Leato, and if you watched video one, you know we discovered something remarkable. The universe's fundamental structures from protons to galactic superclusters show consistent scale jumps averaging 10 to the 2.98, essentially 10 cubed. This pattern appears across 15 different structures spanning 42 orders of magnitude.
But why call this our fractal universe? I didn't start out believing that. Actually, I was just plotting the scale data from peer-reviewed sources, looking for patterns, and the numbers kept screaming fractal to me. First, I'll show you what fractals actually are beyond pretty pictures. Then, I'll prove you're already living in a fractal universe, participating in it every single day.
Fractals were formalized by mathematician Benois Mandelro just in 1975. So they're not that old. The word comes from the Latin fractice, meaning broken or fragmented. But the ideas do go back further. In 1904, Helga von Ko created the Koch snowflake. So you start with a triangle, add smaller triangles to each side, repeat forever, and you get an infinite perimeter in a finite space. And the pattern looks the same at every zoom. So that was in 1904.
In 1915, you have the Serpinsky triangle that was described by Waklaw Serpinsky. You remove the middle triangle repeatedly and you get a self similar pattern at every scale. And then we get to the most famous that's the mandelro set discovered in 1980 and it comes from one simple iterative equation and that's z n^2 + c. If the result stays bounded i.e doesn't escape to infinity then it's in the set. And so the colors that you see in the Mandlero animation, they show the escape speed. Zoom forever and new structures keep emerging. It's infinite complexity from simple rules.
And here's a key point of fractals is fractals have fractional dimensions. So more than a line, one-dimensional, but less than a plane, twodimensional. So a coastline might be 1.2 26 dimensional. So it means it's efficiently filling the space through repetition. Nature uses this everywhere for optimization. And here's what blew my mind when I started looking into this was that so do we.
The clearest proof that you're already participating in a fractal universe is from something humans build instinctively, companies. So think about it. One person can only effectively oversee five to 10 direct reports. Decades of research confirms this span of control. If you have too many people under you, there's bottlenecks really communication limits. Too few people then you have too many unnecessary bureaucratic layers, right? It's inefficient. So successful companies branch creating layers that repeat the same structure at every level. So if you zoom in to any department, it's a mini company. So you have self similarity across scales. This is textbook fractal. It's based on limits in communication. Basically physical limits at that scale.
But now we look at your circulatory system. It's fractal branching. We look at trees and water. cities, road networks. NASA's illustrious simulations show the cosmic web galaxy filaments following the exact same branching topology. So you have the same pattern every scale. Jeffrey West discovered power law scaling in biology, cities, and companies. So efficiency grows with an exponent around three. surprise. My cosmic scale data plots to slope 2.98. That's essentially three. And this comes from three-dimensional space. So in 3D space, volume scales as the length cubed. Fractal networks with an exponent around three efficiently fill that space. So that's biology, companies, cities, and the cosmos all around three. I don't think this convergence is a coincidence. I think it's how complexity scales optimally in our 3D universe.
I had a great comment from video one. It was a question basically if it's just base 10 bias if you change the base then the pattern will vanish. So basically because humans have 10 fingers we use base 10. And so the argument is this number three, this exponent three is just numerology, right? Except actually you get the same relationship if you use a different base, right? So base 10 you're going to get 2.98. What's the real expansion is 955. So it's around a,000 times more, right? That's your the 10 to the 3 is really about a,000 times. 955 times the original. If we use base 12 now it will be a different exponent 12 to the 2.76 but it's the same result 955. So base 8 you'll have a different exponent 3.3 but your end expansion will be around a th00and times bigger. Base e you're going to get e to the 6.86 again that's around a th00and so 955. So in this case the exponent changes but the physical ratio stays the same at 955 times the original length. And again that's based on cubing something. So that's what the actual ratio is. It's ratio of cubing. So the universe organizes in cubic volumetric scaling. Base 10 just makes it look clean to us but it has the same exponent that shows that this this isn't numerology. Okay. This is 3D geometry and about fractal efficiency.
So here's the hypothesis that the data suggests. If the same fractal principles optimize complexity from cells to companies to galaxies with consistent scaling and near zero error, then life and consciousness might be natural expressions of universal organizational laws. So now this doesn't mean that galaxies think or that stars have DNA but it does imply that the patterns of metabolism, reproduction, response to external stimuli and evolution could operate at cosmic scales in different substrates. So different forms of matter from what we understand as normal biological life. We build fractal companies because it works. The universe appears to do the same at all different scales. So, future data will test this. We'll expand on this in future videos, but the pattern is definitely worth exploring. I found some really mind-blowing relationships I can't wait to share with you guys.
Companies prove we're already living in a fractal universe. We just haven't seen how far it extends or at least internalized it. If this is resonating with you, please hit the like button. Does your workplace feel fractal? Let me know what points you have. This does help me draft and create the next videos. In the next video, we'll talk about cosmic octaves. So, perfect repeating patterns every 10 to the 24 m that look almost designed. It is really insane and mind-blowing. Again, I can't wait to share this with you guys. Thank you so much for watching to the end and listening. Have a great rest of your day. Welcome to our fractal universe. Peace.