A group of frogs secedes from the Swamp Union and starts their own frog country in a neighboring pond. After some political turmoil and the beheading of any frogs that wished to go back to the swamp, Ugly Frog gathers all the remaining frogs and says they need to make a list of rules. First on the list is "no associating with foreigners." Squeaky Frog asks, "what exactly constitutes a foreigner?" After beheading him for speaking out of turn, the rest of the frogs contemplate this question and decide that a foreigner is anyone who lives outside the new pond. The ghost of Squeaky Frog then remarks that if they send frogs to infiltrate the Swamp Union as sleeper agents, these agents would count as foreigners, and if the Swamp Union sends agents to the pond, those agents would not count as foreigners. The frogs exorcize the ground to destroy all remnants of Squeaky Frog and then begin a furious debate over the definition of "foreigner."

After hours of physical and verbal fighting, two dominant sides emerge, with a few smaller groups. The first side holds that all frogs currently outside the pond should be permanently dubbed "foreign," and all frogs currently in the pond should be permanently dubbed "non-foreign." The second side thinks frogs should count as "foreign" or "non-foreign" based on where their current allegiance lies, and not on any geographical position. They are both determined to shame and ostracize all foreigners, and not listen to their ideas or opinions.

Both of these sides share some common goals. They both want Funny Frog to be a "non-foreigner" because he is beloved by nearly all frogs and brings life to every frog party you can imagine. And both sides also want Hairy Frog to be a "foreigner" because his hair is so un-amphibian that it disgraces their entire species. In fact, both sides are so adamant that these two frogs stay in their respective categories that any definition which did not satisfy this requirement would be seriously frowned upon, and the proponents would be beaten to death in ditches. For example, one of the smaller factions claims that all frogs in the valley should count as "non-foreign," and that only the frogs of the mountains should be "foreigners." But this definition allows Hairy Frog to be a "non-foreigner," so it's rejected by most of the frogs. Another small faction is telling everyone that only the original proponents of the secession should count as "non-foreigners," and that all the rest of the frogs that only joined at the last minute should count as "foreigners." But of course, this definition makes Funny Frog a "foreigner," so it's also rejected by most of the frogs.

If the ghost of Squeaky Frog still existed, he would be drawing a map (neatly labeled "thing-space" on the back) consisting of hundreds of dots, some centered around the bottom left and some around the top right. He would be explaining that each faction is trying to draw lines around these dots when they talk about the definition of the word "foreigner." In particular, they want to draw a circle around the dots in the bottom left and label them as "non-foreigners" and then lump everyone else into the enormous glob of "foreigners." He would label one dot as Hairy Frog and one dot as Funny Frog and explain that these dots are Schelling points, perhaps even as "the last defensible Schelling points" such that, if these points are abandoned, all hope of a coherent definition is lost (to most frogs; some smaller factions might be perfectly happy with the result). 

Squeaky Frog would further state that every faction wants the lines that they draw to either be straight or at least uniformly curved. Drawing a straight diagonal line that divided the two collections of dots would be ideal, but drawing a mathematically perfect circle around the lower-left frogs would be suitable. Any definition like "frogs that are within a kilometer of the pond, are at least 6 centimeters tall but no more than 7 centimeters tall, have an odd number of warts, and ribbet in either baritone notes or can hit a high c," creates a line spanning too many dimensions, looking too much like swiss cheese, or making too many corners, to be appealing. Definitions like "Bouncy Frog, Dirty Frog, Zippy Frog, Weird Frog, and Moist Frog are the only non-foreigners" simply draw a series of individual circles around seemingly unconnected dots and are not appealing either.

Lastly, Squeaky Frog would state that each frog in the group probably has a different private picture in their own mind about the precise position of each dot on the map, and about which dots are Schelling points and which aren't (most frogs probably consider their own dot to be a Schelling point, but know that other frogs won't see it that way). This means that two different frogs may have a different opinion on how straight/uniformly curved a particular line is as it weaves between dots (again, because they disagree on where the dots are), and they may disagree on whether it stops nicely at good Schelling points.

When questions are simple, like How Young Does A Frog Need To Be To Swim In The Tadd Pool, the Schelling points (1 year, and to a lesser extent, 6 months and 3 months) allow the rules to settle on a neat number. But when rules need to deal with multiple Schelling points spanning different dimensions of thing-space (Funny Frog is currently in the borders of the pond and has a strong allegiance to the pond, but he wasn't an original proponent of the secession), the rules get insanely complicated to cope, and sometimes people start wanting to drop Schelling points. For example, the English grammer and spelling system (and those systems in countless other languages) have the strain of millions of words and phrases that they need to explain away as "correct." But sometimes this becomes so convoluted that people actually end up changing the words themselves to fit with the rules they're making up. And Schelling points like the Star Trek quote "we boldly go" get abandoned by some as the straightness of the lines becomes more important than the territory they surround. In other words, it's sometimes more important to people to be consistent than it is to hold on to every preconceived notion. Way to go, people!

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1 comment, sorted by Click to highlight new comments since: Today at 10:39 AM

I think "support vector" makes more sense than "schelling point" in this context. The actual schelling points here are the boundaries themselves.