One of the other desk attendants laughed at me when I told her that Ye Interesting Person set off my Genius Kid Detector. I wish I could explain better how that worked. I can usually pinpoint the look or comment that set it off the first time, but explaining why that set it off is much more difficult. I have an imperfect record of setting out my case without using words like "timey-wimey ball".

I also told her that something he'd done tipped me off to the fact that he'd taken a lot of math. She told me she thought I was reading too much into it. Nuts to that -- I'm right on that stuff orders of magnitude more often than I'm wrong.

Inductive reasoning about other brains is fun stuff. It relies on having a vast store of patterns, both of behavior and of the characteristic thinking styles that go with a wide variety of specializations, to compare and contrast. It also impresses the hell out of everybody, except the other people who have worked out the same trick. They usually smile, but are not all that surprised, and I've rarely if ever had another sherlock-y person ask me how I got to a conclusion.

Ye Interesting Person runs a weekly group class thing, and has sense enough to show up early, check which room he's in (the studio books first come, first serve), and stick a sign on the front of our desk. He's done this every week so far, and judging from everyone else's reaction, he's probably been doing this for months already. The class group also seem to have been showing up for a while, at least most of them -- we do periodically get people who don't appear to know what it's called, but most of them just come in and ask after him by name.

A couple of weeks ago, he turned up and did his usual sign routine, and skedaddled upstairs to his booked room. His group started wandering in. They looked at his sign, looked around -- for him, for other notices, for divine inspiration, I don't know -- then looked at the sign again, paused, and hesitantly asked me, "What studio are we in tonight?" For like half an hour, counting the people who were late. I began to wonder if all of his students were illiterate.

Eventually I just got up and walked around the desk to take a look at the sign. Which of course explained everything. Including, inadvertently, the part about the math.

Assumption one: People do not intentionally post unhelpful signs. It's his class, he likes them, he wants them to show up. He take the time to write things legibly on paper and tape it up. So he thinks that whatever he has put on that sign will help to get his group to where they want to go. Moreover, he didn't give any special instructions to us at the desk about it, so he also thinks it's sufficient to get his group to where they want to go.

Assumption two: His students are not morons. It's Cambridge, half of them probably have PhDs. It's normal for a person or two to miss a sign or just forget to think it through, but almost all of the group members had to ask. So his assumption about what comprises necessary and sufficient information in this case is off somehow.

What this sign said was that his class would be in studio "2 or 4". As soon as I saw that, I knew exactly how he'd gotten there, and why it wasn't helping. What he was putting on the sign was that he knew he would be in studio 2 XOR studio 4 with a probability of 1. Not 3, not 6, not 1, and 5 is right out. When you have the kind of brain that's entertained by 5-minute mysteries and books of logic puzzles, this is useful information. It eliminates all but two testable hypotheses, which is much more manageable than checking every studio in the building, and as it happens you have to walk right past 2 to get to 4 anyway. (I was up there later, and he had indeed stuck a sign up on the door of the one he was physically in; he expected people to take the information he gave them and just come up to look, whereupon they would find his helpful confirmation.) It's a very math-y approach to things -- it's about one and a half steps away from the joke about the mathematician who wakes up to find his bedroom on fire, sees a sink, sees a bucket, realizes there is a solution to be found, and goes back to bed.

To other people, this sign does not provide information. This sign reflects uncertainty. It gives an "or" option, and doesn't give any instructions on how to resolve the ambiguity yourself, so effectively it just says 'this sign doesn't know the answer! find someone who does!' The sign he stuck up on the door of the studio was upstairs and not visible from the desk, so people who came in had no idea that he'd already figured it out, and that the answer awaited them farther into the building.

I've seen him socialize in the lobby, and he reads people like he's got the captions on. What we have here is not a general disconnect, but a failure to accurately assess how much processing J. Random Dancer is going to apply to what they read on the sign. He's mis-located the line between "things people will put some thought into" and "things people expect to be strictly declarative". His students were expecting a pointing arrow that didn't require interpretation; he accidentally gave them something that was not as pointy an arrow as he thought it was, and everybody's brains hiccuped.

Assuming that people will automatically apply logic to things they expect to just be outright giving them directions is a classic gifted-kid thing, and it drives other people bonkers. It comes from using yourself as a starting point for predicting the behavior of others -- sometimes it works, sometimes it doesn't. You'd go through those extra two steps of reasoning and figure out what was going on, but other people think you're mental for expecting that. The base error is the same one all the other humans are making (i.e., "other people think like me"), but you happen to be weird in the logic-puzzle regard, so you make it in the opposite direction, and inadvertently confuse everyone.

The other desk attendant stopped laughing after I told her that I'd asked him already, and I was right. Actually, what I usually do is make statements. It impresses people more and invites less spluttering. As a bonus, when I am wrong, people who will give a flat 'no' to a question will often instead correct a statement, which gets me yet more information.