Last weekend we had OnlyConnect, and it got me thinking about the semantic structure of making connections. The 2 pictures in the first box were clue#1, which got me nowhere, and the 2 pictures in the second box were clue#2, of which the lightning picture led me almost instantly to the right answer, after which the other pictures were merely verification tools, a very neat delineation between P and NP.
As always with a connection question, in hindsight everything looks elegantly obvious and staring you in the face and we rush to the same 3 conclusions, a) I could have got it at the first clue but I didn’t think of the right connection b) Every clue adds a unique element waiting for that one piece that lets everything else fall into place, like the keystone that holds up the arch. This makes sense under my usual framework to think about semantics: of vertical layers, from most abstract at the bottom to most specific at the top. In this model, a connection is one layer of abstraction below the set of particulars, clues that all co-habit the same semantic layer. Each clue adds a different facet or strengthens the same facet of the property being abstracted out. Like an armchair, easychair, patio chair, each adding equally to the abstraction of platonic chairs. But this doesn’t explain the neat delineation between P and NP nature of clue 2a vs the rest. In the chair example, these would all be elements of an inductive model, 2a might make the pattern more apparent, but only in conjunction with the other clues, as a sequence. With totally independent clues, this is less obviously the correct semantic model.
Using this Q as the cognitive experiment, I’m considering an alternate model of pattern recognition. The difference I’m trying to explain is this —
Clue 1a connections sparked in mind: Catan, Boardgame, Dice, Resources, Trade, Monopoly, Ore/Sheep/Wheat/Brick/Wood/Port, Settler, Settlement, Area, Pioneers, Award Winning
1b: Rock Paper Scissors, Fistbump, Knuckles,
Abstraction route at clue 1: Chance, Probability, Dice.
1c: STORM. Lightning, Weather, Tornado, Thunder, STORM.
1d: Buffet, Meal, Food, Spread, Dessert, Cutlery
Abstraction route at clue 2: Storm, food: cook up a storm. A dark and stormy night. Stormborn. Storm of Swords -> Solved. Other clues for verification: Game of Thrones, Clash of Kings, Feast for Crows.
Why was 1c so superior a clue to the others? Using my vertical semantics model, I see that for the other clues I start connecting upwards, towards even more specifics (aspects of Catan, particular games, particulars of meals), and only for 1c do I go downwards to storm. I could assume that lightning is easier to abstract downwards to storm or weather than the other clues, but why should that be the case? The most telling pair is Catan — Lightning, with Game being just as easy an abstraction from Catan is Storm is. I was thinking of connections with Catan as the center, whereas I should have been thinking of that center for which Catan is a connection, which is what the question-setter was doing, with an answer in mind seeking connections to set as the clue. But why does Storm and Lightning work without this reversal of perspective?
I wonder if this has something to do with the lack of transitivity in human choices and organization of ideas. We used to believe our ideas of comparison could be likened to physical distance, that we compare two entities by drawing a line connecting them and measuring that line. So the line from USA to Europe is longer than from USA to India, so USA is more like Europe than like India. But this line should imply transitivity, that Europe is like USA as much as USA is like Europe. This is not the case. We think Vietnam is like China, but China is not like Vietnam. We think 103 is like 100, but 100 is not like 103. Our comparative frameworks are not transitive. So while Catan is like Game, Game is not like Catan. Yet, while Storm is like Lightning, Lightning is also like Storm. Why the transitivity here?
Here I depart from my vertical semantics model to a nodal network. Game and Catan are two nodes, each with a host of connections. Usually a more abstract node has more connections, but not always. Here, game has more connections than Catan, so the relationship isn’t transitive. In an intransitive relationship, given a start node Catan, do I look for the strongest connection (Game), or the connection for which my node is the strongest connection (resources, trade, settlers). Lightning and Storm each have a similar number of connections and the connection is more transitive. They each also have fewer connections in general, so I’m less able to shuffle through the deck of cards in my mind looking for one that strikes me as particularly strong. I settled on Storm almost immediately, and could explore its own connections farther from there instead of trying to decide between different connections like with Catan. It isn’t just about my limited vocabulary for adverse weather phenomena, but the inherently limited elements in the set.
This reminds me of a study that found that we all believe we’d have more friends and be more popular if we were more extroverted, but among our friends we prefer the more introverted ones. Is this a paradox? If we like the introverts, surely we must assume that others also prefer the introverts and therefore it is better to be introverted if our goal is to be liked and popular? As somebody with 25 friends, my bond with a friend who has 625 friends is deeply intransitive. My bond with someone with 5 friends likely enjoys higher recall than the 625 one? Even though as far as utility of connection goes, it serves me better to think first of this supernode network hub? As the Catan node, I am better off thinking of Game, with all its generality, intransitivity, and inexclusivity, than resources, settlers, and dice. Why am I not better at this, given how functionally superior this strategy would be?
At the other extreme, we have a couple, Lightning and Storm, each with almost no other connections that don’t point to each other. They’re excellent for a very specific narrow band of connection, offering the stability and confidence required to actually build a hypothesis. To test the hypothesis though, we need the nodes with larger number of connections. The situation is reversed in NP problems of verification, here we want a very low probability of getting a particular positive result, a needle in the haystack. I’m evaluating the hypothesis based on the probability of getting a true negative thereby falsifying my idea. With the lightning storm, I cannot falsify my hypothesis of Song Of Ice and Fire because there are not enough elements in the set. But once I test the Catan clue, there are 1000s of feasible connections, almost all of which will return negative for common ground with my hypothesis. Any positive result that connects my network hub (Catan) with my introvert (Storm) enjoys a high degree of confidence of being the correct answer.
I’d love to have the patience to analyze a variety of OnlyConnect questions and abstract out rules for both setting and answering questions that involve connecting ideas, once the initial stage of identifying the clue itself is crossed. It’s not without menace that it appears our minds are organized like a Google backlinked ranking algorithm. What exactly are we better at than computers? If only someone could write a program to finish George Martin’s books on his behalf while he’s still alive to allow us the comforting delusion that he might have had a hand in it somehow.