For the lazy guy accusing me of "trolling"...read this...

- In mathematics, a
** self-similar** object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically **self-similar**: parts of them show the same statistical properties at many scales.

What if that's true for the Universe? That there is some form of pattern of

** Self Similarity**?

Next, read this...it's the transcript of that TED video...and the explanation of scaling...

Despite the fact that this is the most complex and diverse system in the universe, there's an

**extraordinary simplicity** being expressed by this. It's particularly astonishing because each one of these organisms, each subsystem, each cell type, each gene, has evolved in its own unique environmental niche with its own unique history. And yet, despite all of that Darwinian evolution and natural selection,they've

** been constrained to lie on a line.**
7:22Something else is going on. Before I talk about that, I've written down at the bottom there the slope of this curve, this straight line. It's three-quarters, roughly, which is less than one -- and we call that sublinear. And here's the point of that. It says that, if it were linear, the steepest slope, then doubling the size you would require double the amount of energy. But it's sublinear, and what that translates into is that, if you double the size of the organism, you actually only need 75 percent more energy. So a wonderful thing about all of

**biology is that it expresses an extraordinary economy of scale**. The bigger you are systematically, according to very well-defined rules, less energy per capita. Now any physiological variable you can think of, any life history event you can think of, if you plot it this way, looks like this.

**There is an extraordinary regularity.** So you tell me the size of a mammal, I can tell you at the 90 percent level everything about it in terms of its physiology, life history, etc.

8:25And the reason for this is because of

**networks**.

**All of life is controlled by networks** -- from the intracellular through the multicellular through the ecosystem level. And you're very familiar with these networks.That's a little thing that lives inside an elephant. And here's the summary of what I'm saying. If you take those networks, this idea of networks, and you apply

**universal principles, mathematizable, universal principles, all of these scalings and all of these constraints follow**, including the description of the forest,the description of your circulatory system, the description within cells. One of the things I did not stress in that introduction was that, systematically, the pace of life decreases as you get bigger. Heart rates are slower; you live longer; diffusion of oxygen and resources across membranes is slower, etc.

9:19The question is: Is any of this true for cities and companies? So is London a scaled up Birmingham,which is a scaled up Brighton, etc., etc.? Is New York a scaled up San Francisco, which is a scaled up Santa Fe? Don't know. We will discuss that. But they are networks, and the most important network of cities is you. Cities are just a physical manifestation of your interactions, our interactions, and the clustering and grouping of individuals. Here's just a symbolic picture of that. And here's scaling of cities.This shows that in this very simple example, which happens to be a mundane example of number of petrol stations as a function of size -- plotted in the same way as the biology -- you see exactly the same kind of thing.

10:09

**There is a scaling.** That is that the number of petrol stations in the city is now given to you when you tell me its size. The slope of that is less than linear. There is an economy of scale. Less petrol stations per capita the bigger you are -- not surprising. But here's what's surprising. It scales in the same way everywhere. This is just European countries, but you do it in Japan or China or Colombia, always the same with the same kind of economy of scale to the same degree. And any infrastructure you look at --whether it's the length of roads, length of electrical lines -- anything you look at has the same economy of scale scaling in the same way. It's an integrated system that has evolved despite all the planning and so on. But even more surprising is if you look at socio-economic quantities, quantities that have no analog in biology, that have evolved when we started forming communities eight to 10,000 years ago. The top one is wages as a function of size plotted in the same way. And the bottom one is you lot -- super-creatives plotted in the same way. And what you see is a scaling phenomenon. But most important in this, the exponent, the analog to that three-quarters for the metabolic rate, is bigger than one -- it's about 1.15 to 1.2. Here it is, which says that the bigger you are the more you have per capita, unlike biology -- higher wages, more super-creative people per capita as you get bigger, more patents per capita, more crime per capita.

11:46And we've looked at everything: more AIDS cases, flu, etc. And here, they're all plotted together. Just to show you what we plotted, here is income, GDP -- GDP of the city -- crime and patents all on one graph.And you can see, they all follow the same line. And here's the statement. If you double the size of a city from 100,000 to 200,000, from a million to two million, 10 to 20 million, it doesn't matter, then systematically you get a 15 percent increase in wages, wealth, number of AIDS cases, number of police,anything you can think of. It goes up by 15 percent, and you have a 15 percent savings on the infrastructure. This, no doubt, is the reason why a million people a week are gathering in cities. Because they think that all those wonderful things -- like creative people, wealth, income -- is what attracts them,forgetting about the ugly and the bad.

12:46What is the reason for this? Well I don't have time to tell you about

**all the mathematics**, but underlying this is the social networks, because this is a

**universal phenomenon**. This 15 percent rule is true no matter where you are on the planet -- Japan, Chile, Portugal, Scotland, doesn't matter. Always, all the data shows it's the same, despite the fact that these cities have evolved independently.

**Something universal is going on.** The universality, to repeat, is us -- that we are the city. And it is our interactions and the clustering of those interactions. So there it is, I've said it again. So if it is those networks and their mathematical structure, unlike biology, which had sublinear scaling, economies of scale, you had the slowing of the pace of life as you get bigger. If it's social networks with super-linear scaling -- more per capita -- then the theory says that you increase the pace of life. The bigger you are, life gets faster. On the left is the heart rate showing biology. On the right is the speed of walking in a bunch of European cities, showing that increase.

Now, could the mathematics of scaling possibly apply to planets and suns? My guess is "yes". As I said earlier in the thread, it's all about the math.

50,000,000,000,000,000,000,000,0000 possible planets that are habitable in the universe.

1,000,000,000,000,000,000,000 stars in the universe.

That's not trolling, it's math.