This reminds me of something from Sam Bowles's "Microeconomics":
Like the overnight train that left me in an empty field some distance from the settlement, the process of economic development has for the most part bypassed the two hundred or so families that make up the village of Palanpur. They have remained poor, even by Indian standards: less than a third of the adults are literate, and most have endured the loss of a child to malnutrition or to illnesses that are long forgotten in other parts of the world. But for the occasional wristwatch, bicycle, or irrigation pump, Palanpur appears to be a timeless backwater, untouched by India’s cutting edge software industry and booming agricultural regions. Seeking to understand why, I approached a sharecropper and his three daughters weeding a small plot. The conversation eventually turned to the fact that Palanpur farmers sow their winter crops several weeks after the date at which yields would be maximized. The farmers do not doubt that earlier planting would give them larger harvests, but no one the farmer explained, is willing to be the first to plant, as the seeds on any lone plot would be quickly eaten by birds. I asked if a large group of farmers, perhaps relatives, had ever agreed to sow earlier, all planting on the same day to minimize losses. “If we knew how to do that,” he said, looking up from his hoe at me, “we would not be poor.”
The key takeaway from that is the difficulty of social organization. The first proponent of early sowing will be viewed as seeking to gain some private advantage precisely because poverty creates an economic incentive to maximize private advantage. Some open source proponents overcame this reluctance in the 1980s with the Stone Soup metaphor.
That story makes no sense. If those farmers of Palanpur can not agree to plant all together at the right time, how come they manage it several weeks later, or ever?
> When farmers are planting at different times, pests can move from one field to another, but when farmers plant in synchrony, pests drown and the pest load is reduced.
The strategy is that if there are several fields planted for the same amount of bugs, each field receive less bugs than if it was the only one planted (on the contrary, if they were planted one after an other, the whole bug population would just jump from field to field).
Its actually that planting "in synchrony" reduced pests. Balancing that with limited water supplies resulted in the fractal pattern, which created close to an optimal yield.
I fail to see how the planting patterns are fractal. A fractal pattern is one which repeats itself at different scales. I realize that the repetition does not need to be exact but I don't see how there is any at all in this situation.
Actually, that is only one type of fractals. Perfectly self similar patterns like the Triforce or Sierpensky triangle are used as toy models for learning . Typically, fractals in nature are not self similar(Branching of your blood vessels for example) . Mandelbrot developed fractal geometry as a way to model nature that captures roughness. It was kind of a rebellion against calculus, where if you zoom in eventually you get smoothness.
It's funny that many people think that only self similar patterns are fractals when his desire was to get away from idealized models towards more pragmatic ones
EDIT: I'm actually just learning about fractals, so I'm certainly no expert, but I'm excited to share what I've learned so far.
Look at a line, square, and cube in 1, 2, and 3 dimensions respectively. If you scale down each by 1/2 in all its dimensions, you need to look at how much of the "mass" (for lack of a better term is scaled down
If you cut a line in 1/2, it's mass is scaled by 1/2 as it takes 2 one-half length lines to make the original line.
If you scale a square down 1/2 along all its dimensions, you break into/scale it down into 4 smaller squares, it's mass scaling factor is 1/4....scaling a cube down 1/2 along all its dimensions (1/2)^2 breaks it into 8 smaller cubes...it's scaling factor is 1/8 and you can see the progression here. (1/2)^3. (I imagine a tesseract/hypercube has a scaling of 1/16 as it is the 4D analogue of a cube) The exponent represents the concept of dimension and this is how you can have non-integer dimensions.
So, back to the Sierpenski triangle or triforce example. Let's scale it down 1/2. When we do that, we know we get 1/3 the "mass" of the original since there are 3 triangles contained in the larger triangle at each level. The dimensionality is then (1/2)^x = 1/3 where x is the dimensionality. We rewrite this as log 3 base 2 which gives it a dimensionality of ~1.585.
And that is the definition of a fractal, a shape with a non-integer dimension which gives the shape roughness at every scale. I don't quite understand the more technical definition, but hopefully this helps!
Note, you cannot use length or area as a measurment for a scaling factor, as the length would be infinite and area would be 0. Also, I say mass because the more correct concept is difficult for me to explain without a whiteboard, but basically, it has to do with putting the fractal on a 2d grid, scaling it, and seeing what the ratio of boxes touched is. See, told you I'm bad at explaining it :D
There's no One True Definition of what it means to be fractal, but a lot of working mathematicians use the criterion that a space's Hausdorf dimension is not equal to its topological dimension. Oftentimes (but not always), the Hausdorf dimension will be fractional, which is where the word comes from. Self-similarity is an easy way to satisfy that requirement in a way that's easy to explain, but it's far from the only way.
Something as simple as a contour map could be thought of as intrinsically fractal. It isn't as mathematically rigorous as the fractals we are used to seeing described as such, but it fulfils the criteria.
This looks very interesting from a regulation point of view, as a potential way to bring greedy self-interest into alignment with national/international social interest. I wonder what scenarios could be given a "pest tax", to alter the dynamic from a tradgedy of the commons to a cooperative/competitive optimum?
The classical solution to the tragedy of the commons for rivalrous goods is propertization. It's the logic behind contemporary land rights, some very successful commercial fisheries management (north west Atlantic), and emissions auctions in the US (SOx and NOx implementation - but notably not the proposed carbon, which has other wierd factors bolted on)
There's plenty of science against (20th century) top heavy / top down control. The issue seems to be: the current power holders admitting their model is flawed; and those being managed realized they'd be better off without "leadership."
That's an absolutely valid question that doesn't deserve to be downvoted. Generalizing these insights for deployment is absolutely a problem worth solving.
this is very interesting, wondering the principle applies to societal organization and current reversal trends on globalization (mono-culture) and weakening of international 'controlling' organizations.
Actually this depends on a monoculture as it is an adaptation to the life cycle of the rice (paddy) plant and its water requirements. If different farmers were growing different crops the requirements would vary.
[+] [-] chrismealy|8 years ago|reply
Like the overnight train that left me in an empty field some distance from the settlement, the process of economic development has for the most part bypassed the two hundred or so families that make up the village of Palanpur. They have remained poor, even by Indian standards: less than a third of the adults are literate, and most have endured the loss of a child to malnutrition or to illnesses that are long forgotten in other parts of the world. But for the occasional wristwatch, bicycle, or irrigation pump, Palanpur appears to be a timeless backwater, untouched by India’s cutting edge software industry and booming agricultural regions. Seeking to understand why, I approached a sharecropper and his three daughters weeding a small plot. The conversation eventually turned to the fact that Palanpur farmers sow their winter crops several weeks after the date at which yields would be maximized. The farmers do not doubt that earlier planting would give them larger harvests, but no one the farmer explained, is willing to be the first to plant, as the seeds on any lone plot would be quickly eaten by birds. I asked if a large group of farmers, perhaps relatives, had ever agreed to sow earlier, all planting on the same day to minimize losses. “If we knew how to do that,” he said, looking up from his hoe at me, “we would not be poor.”
[+] [-] anigbrowl|8 years ago|reply
[+] [-] std_throwaway|8 years ago|reply
[+] [-] SagelyGuru|8 years ago|reply
[+] [-] aetherspawn|8 years ago|reply
1. how they didn't have pest problems if they planted in fractal patterns
2. but they did have pest problems if they didn't plant at the same time
Could someone kindly explain that in a little more depth?
[+] [-] oelmekki|8 years ago|reply
The strategy is that if there are several fields planted for the same amount of bugs, each field receive less bugs than if it was the only one planted (on the contrary, if they were planted one after an other, the whole bug population would just jump from field to field).
[+] [-] positr0n|8 years ago|reply
[+] [-] livingparadox|8 years ago|reply
[+] [-] jcoffland|8 years ago|reply
[+] [-] FullMtlAlcoholc|8 years ago|reply
EDIT: I'm actually just learning about fractals, so I'm certainly no expert, but I'm excited to share what I've learned so far.
Look at a line, square, and cube in 1, 2, and 3 dimensions respectively. If you scale down each by 1/2 in all its dimensions, you need to look at how much of the "mass" (for lack of a better term is scaled down
If you cut a line in 1/2, it's mass is scaled by 1/2 as it takes 2 one-half length lines to make the original line.
If you scale a square down 1/2 along all its dimensions, you break into/scale it down into 4 smaller squares, it's mass scaling factor is 1/4....scaling a cube down 1/2 along all its dimensions (1/2)^2 breaks it into 8 smaller cubes...it's scaling factor is 1/8 and you can see the progression here. (1/2)^3. (I imagine a tesseract/hypercube has a scaling of 1/16 as it is the 4D analogue of a cube) The exponent represents the concept of dimension and this is how you can have non-integer dimensions.
So, back to the Sierpenski triangle or triforce example. Let's scale it down 1/2. When we do that, we know we get 1/3 the "mass" of the original since there are 3 triangles contained in the larger triangle at each level. The dimensionality is then (1/2)^x = 1/3 where x is the dimensionality. We rewrite this as log 3 base 2 which gives it a dimensionality of ~1.585.
And that is the definition of a fractal, a shape with a non-integer dimension which gives the shape roughness at every scale. I don't quite understand the more technical definition, but hopefully this helps!
Note, you cannot use length or area as a measurment for a scaling factor, as the length would be infinite and area would be 0. Also, I say mass because the more correct concept is difficult for me to explain without a whiteboard, but basically, it has to do with putting the fractal on a 2d grid, scaling it, and seeing what the ratio of boxes touched is. See, told you I'm bad at explaining it :D
[+] [-] zeroer|8 years ago|reply
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[+] [-] DanBC|8 years ago|reply
Here's some figures which might help with satellite image searches.
http://www.pnas.org/content/early/2017/05/31/1605369114.figu...
[+] [-] unknown|8 years ago|reply
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