5min chapter

Simplifying Complexity cover image

The sand pile model

Simplifying Complexity

CHAPTER

The Self-Organized Criticality of Per Back

Per back called this self-organized criticality. Can you talk about what he means by that? It's not like there's one DEO sand particle that's saying, okay, everybody around me do this and the ones at the bottom stay there. No, the system is kind of organizing itself. And in many ways, you can imagine something like a heart. For example, the heart is fed energy by the body. Doesn't feed it. Just feeds it energy. Yet it manages to organize itself into some kind of regularity.

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Speaker 2
So you've got your sample and you drop in your sand and history matters and information matters in this sample as to what happened in previous steps and the slope that you drop the piece of sand on and all that sort of stuff. And per back called this self-organized criticality. Can you talk about what he means by
Speaker 1
that? So this brings us to the second part of the genius of per back because on the one side he was saying that systems of history dependent more fine. Maybe that just means that we're already those depending on what happened and nothing really exciting is going on. But the second part is related to this self-organization because going back to this sample, imagine we're just dropping them the pieces of sand on the top. This is controlling all these pieces of sand. It's not like there's one DEO sand particle that's saying, okay, everybody around me do this and the ones at the bottom stay there and we'll have this next little avalanche here. No, the system is kind of organizing itself. So the natural way to describe this is it's self-organizing. And it clearly is because I'm dropping in just sand particles in some random way, which is not interesting. There's nothing interesting going on. I'm not causing it to have these kind of sporadic clips of sand. In other words, these avalanches, but it is self-organizing itself to produce them. And in many ways, you can imagine something like a heart. For example, the heart is fed energy by the body. Doesn't feed it. Just feeds it energy. And yet it manages to organize itself into some kind of regularity. Again, the genius of her back was to realize that although this self-organization, this sample, which is producing these kind of slippages of sand, which she calls avalanches, which is a good word, and they were of all sizes because sometimes there may be five grains of sand and sometimes there'll be 5,000 grains of sand. But you wouldn't expect that many big slippages. You'd expect lots and lots of little ones, less kind of medium-sized ones, and then a few really big ones. You know that one just before you leave the beach and go home when you think, oh, I give up. If you keep doing that, if you had infinite patience and somebody allowed you to stay at the beach, you wanted to stay at the beach all night and keep doing this, and you were to take the sizes of the number of particles that fell in each slippage. You'd have to stay up all night, a lot of cups of coffee, just measuring the size of these slippages like you would kids in a class of their heights. And now we're going to plot out now not the number of kids of a certain height. We're going to plot out the number of avalanches of a certain size, where size is the number of particles, sand particles that fell. It's hard to count and we might be off by 20% or 30% it doesn't matter because we're actually asking a question about the system at the system level. So we don't need it to be that precise. But the remarkable thing is, and people have now done this, wanting out not now a histogram of like number of kids in her class, which would be nice kind of peaked kind of upside down U-shape so-called bell curve, what how that knew was that the date of that distribution would not be like the bell curve because he knew that when you even just think of the simple sandbar problem, there are moments effectively have the equivalent of the 600 foot chart. In other words, you drop stand on the sandbar and there are moments when there will be a slippage, which is almost the size of the number of particles that you have. Whereas a lot of the time the slippage is a tiny fraction. So you know that the smallest slippage might be five pieces of sand and the largest might be five million. And so you've got this huge scale of possible behaviors. Whereas we know from distribution's typical distribution, so-called normal distribution or the bell curve distribution that you don't have all the sizes of kids in a class. Thank goodness. You know, it goes from I-R-O, we could take adults, just take adults. You know, it goes from five foot to seven foot, something like that. It does not go from a fraction of an inch to three miles tall. And yet the sandbar slippage is
Speaker 2
due.

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