by Oliver Yu
Here was that example distribution of test scores:
When you look at the data and there are irregularities or non-smoothness, you're looking at some human intervention... some manual action that does not comport with the natural order.
Have a look at this visualization. It's apparently the average monthly premiums for insurance plans under the Affordable Care Act for each county. Dark blue are plans that cost $250/mo. Dark red are plans that cost $1,250/mo... so the more red, the more costly.
What's most interesting to me is that you can see the shapes of Virginia, Wyoming, South Dakota and New Jersey pretty well on this map according to the price of ACA insurance premiums. Some guy living in Montana is paying $500/month; cross an imaginary line into Wyoming and now it's $1,000.
When you see something like this, you can infer that a non-natural phenomenon holds the true explanation (e.g. state law). There's a step-function here and step-functions aren't found that often in nature.
Now have a look at New England: here, there's a gradient... the farther northeast you go, the more costly the insurance. Likewise in Wisconsin... the closer you get to Minnesota, the more expensive the premium. Gradual changes or smoothness is what we can expect for nature. And a lot of information can be inferred by just looking.