(highlight:: Trees: An Example of Self-Similarity in Complex Systems
Key takeaways:
• The neural network is fractal-like and repeats itself as you go down through the network.
• The tree is self-similar and keeps repeating itself as it branches out, similar to the neural network.
• Self-similarity is technically called a fractal.
• Human beings are also considered as fractals.
Transcript:
Speaker 1
The network is fractal like, that is something that repeats itself over and over again, as you go down through the network, just in the same way as you look at a tree and you recognize intuitively That the tree is sort of self similar. It just keeps repeating itself as it branches out, so much so that if you took a branch, some branch halfway up the tree and you cut it off and you took it away and you plunked it on the ground, It would look like a little tree. And it would in fact be a little tree. In fact, you could take a photograph of that little tree and blow it up and it would just look like the big tree from which it came. That's called self similarity and it's technically called a fractal. And you and me are fractals.)
- Time 0:11:51
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(highlight:: 3 + 1: The Apparent Dimensionality of Living Things as Complex Systems
Key takeaways:
• The scaling of a system can be mathematically worked out based on its size.
• The four in the scaling equation comes from the fractal and network properties of the system.
• Fractals add an additional apparent dimension to the system, effectively making it four dimensional mathematically.
Transcript:
Speaker 2
So that's where the scaling comes from that we're able to actually mathematically work out how the system changes with size. But the three quarters are the this magic number four comes from the manner in which the scaling happens. And that's a network property or more importantly, it's a fractal property. So go for it. What is a fractal?
Speaker 1
Yeah, so I cryptically said the four is actually three plus one. And the three, if you just sort of go back through the mathematics, is actually a manifestation of the fact that we live in three dimensions. So if we lived in eight dimensions, that number would have been eight, the three I mentioned would have been eight. And the plus one comes from a very special property of fractals, and that is that they effectively, especially when they're optimized as the way I just talked about, they increase the Apparent dimensionality of the system. They add a whole other dimension to the system. And it's a bit like if you take a sheet, a sheet of paper or a bed sheet, you normally think of that as sort of two dimensional, it's just a two dimensional piece of paper or two dimensional Sheet of real bed. But if you crumpled up, it becomes a volume and you crumpled it up and crumpled it up, it becomes more and more volume like, and that is indeed an analog of what you are doing with your network. You're making something that is actually three dimensional. And by making it optimal, you are effectively adding another dimension. And the fractality adds another dimension, which is this plus one, which makes it four. So mathematically, the system, the network system and therefore the scaling acts as if we're four dimensional and not three dimensional.)
- Time 0:13:25
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(highlight:: Why Bigger Animals Live Longer: The Relationship between Size, Energy, and Longevity
Summary:
The larger an animal is, the more efficient it becomes in terms of energy consumption.
This is because the self-similar fractal structure of larger animals allows them to save energy. Bigger animals require less energy proportionally to run their bodies due to the massive amount of tissue per gram or per cell.
As a result, bigger animals experience less wear and tear and live longer than smaller animals.
The reason for less wear and tear is that bigger animals use less energy and create less damage, reducing entropy.
This principle can also be observed in machines, where those subjected to less stress and driven at lower revs per minute tend to last longer.
Transcript:
Speaker 2
So that's why we don't need to double our metabolism when we double our weight. It's that fractal like self similarity that allows us to get these essentially efficient savings in the amount of energy we need. So it's better to be bigger, isn't it? Because you don't need as much energy proportionally to run yourself. Correct.
Speaker 1
So you need massive tissue per gram of tissue or per cell. You need less energy, the bigger you are. And by the way, this has huge consequences throughout all aspects of biology and life. And maybe one just to tie it back to the beginning of this discussion where we started out by talking about aging and mortality. This means that the bigger you are, the less hard your cell is working. The bigger you are, there's less wear and tear the longer you live systematically. So this is the origin of why bigger things live longer than smaller things.
Speaker 2
And why is there less wear and tear if you're bigger?
Speaker 1
You're using less energy and creating less entropy. That is you're creating less damage the bigger you are because simply you're using much less energy if you have an engine, an automobile and you insist on racing it at 10,000 revs per Minute every time you drive it, I can assure you that car will not live as long as a car that's driven by a little old lady or a little old man like me who keeps the revs at about two or three Thousand revs per minute. So you know, cars and machines last much longer, the less stress you put on them.)
- Time 0:15:41
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