Riddles and mental models

I’ve been thinking about some assorted cognitive processes over the past week, trying to remove the mysterious/magical feel to cognition. I have no idea if my observations reflect the cognitive science literature, I don’t know if what is true of my mind is true of others’, and I haven’t done any actual serious testing of my guesses, but as long as the ideas described are a possible description of reality, they should work as an acceptable basis for doing AI, which is the main purpose of cognitive science anyway.

Observation: thoughts are wordless

People often describe their thoughts in words, and often insist that their thoughts are in the form of words mentally. This is obviously false, because (1) words need to be rooted to some notion of meaning, and (2) you need to already know what the sentence you’re about to think is before you think it, or you won’t get into the right grammar, etc. 

So “thoughts”, whatever they are, are not words. So what are they? Let’s think about some example thoughts one may have, in the form of words:

• “I’ll find carrots tastier than cucumbers, so let me eat it.”
• “Alright, let’s focus on this for now.”
• “It’s sunny, let me close the curtain.”
• “What are thoughts?”
• “Saying the words What are thoughts? won’t help me progress on the question.”
• “What will help me progress on the question?”
• “What thoughts am I having right now?”
• “I need to develop a stronger intuition for this”
• “Wait, I thought thoughts weren’t words, what’s this?”
• “Stupid question, never mind, but I should add that clarification to the sentence above.”
• “Ah, stupid spelling mistake.”

I think that they key abstraction here is the idea of mental theories and models. Thoughts are beliefs and reasoning about implications between mental models – i.e. a very model theoretic concept. This is true for thoughts about how things are, thoughts about decisions to make, introspective thoughts (these are just self-referential sentences), whatever.

One may consider these model theoretic sentences to be generalizations of linguistic sentences – a sort of language that every conscious being naturally has and vividly imagines, lives in. It is not necessary to talk about how your brain attaches meaning to sentences in these models – associates them with reality, because your brain lives in these models, that is its reality, it is the source of all meaning. One of these mental models is the very visual picture you see of your surroundings.

Observation: riddle solving.

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There are two kinds of riddles – one, the ancient Greek kind, like “what has four legs at dawn, two legs at noon, three legs at dusk, one foot stuck in its skull, and zero legs after time-traveling back to dawn?” and “what comes first? the chicken or the egg?”. These are stupid and pretentious, and have nothing interesting to tell us.

Two, the kind of riddle that people scoff at as childish and uncultured, and is therefore actually somewhat interesting. Some examples:

• A bus driver was heading down a street in Colorado. He went right past a stop sign without stopping, he turned left where there was a “no left turn” sign, and he went the wrong way on a one-way street. Then he went on the left side of the road past a cop car. Still - he didn’t break any traffic laws. Why not?
• Samuel was out for a walk when it started to rain. He did not have an umbrella and he wasn’t wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How could this happen?
• A pet shop owner had a parrot with a sign on its cage that said “Parrot repeats everything it hears”. Davey bought the parrot and for two weeks he spoke to it and it didn’t say a word. He returned the parrot but the shopkeeper said he never lied about the parrot. How can this be?
• The 22nd and 24th presidents of the United States of America had the same parents, but were not brothers. How can this be possible?
• What goes place to place yet stays in one place?
• What is harder to catch the faster you run?

(Source: Riddles.com, a site I frequented as a kid.)

(There’s also a third kind riddle, having to do with pattern matching, like What did the _ tell to the __? and Why did the _ _?)

When you hear about the riddle about Samuel and the rain, your brain immediately infers a particular mental theory from the problem text – and very quickly ends up at a contradiction (or confusion), something that eliminates all possible models. In a sense, riddles are all about the art of noticing confusion – about identifying the axiom you subconsciously assumed in your reasoning. You subconsciously assumed that the bus driver was in a bus, that was included in your mental picture, but was not implied by the form of the question itself.

The last two appear different, but are based on the same principle of being able to infer multiple possible theories and evaluate their consequences.