Thinking With Models

Language is the first model so I wonder how people manage to disparage models without using a model!

Outperform how?

re: 4 “model-free thinkers tend to be more fox-like.”

You don’t think actual foxes use models? Foxes just apprehend reality directly? How does that work? (In your explanation, eschew the use of models, please.)

Slightly off-topic, but I just finished an animated model for macroeconomics:

http://www.youtube.com/watch?v=7RBfBTIFs6o

I would argue that this is better than a mathematical model, for the purpose of introductory understanding.

In particular, the next few mini-vids will argue for gov’t stimuli.

1. “Evidence shows that people who think with models consistently outperform those who don’t” – Scott Page.

2. “There is no way to think without models, they’re structures of assumption.” – an adult.

3. “You don’t think actual foxes use models?” – Jeffrey Davis.

If 2 and 3 are correct, then 1 can be true only in the sense that “people who think with models consistently outperform those who don’t think”. I have no argument with that conclusion.

re: 9

My reaction is complicated since that hedgehog is trotted out every time some somnambulist right-winger says the same thing twice.

My point was simply that all thought is a model.

#14: Isn’t the general pro-fox propaganda that the fox has a collection of models, and is happy switching from one to another as seems appropriate, whereas the hedgehog has one model that he/she is too much in love with?

Counter-recommendation: Emanuel Derman’s Models.Behaving.Badly: Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life

20: What is the contradiction between Page’s quite proper reasoning about models and a title which argues against “confusing illusion with reality”? To the extent that people take thought experiments as representatives of reality, then clearly they are in error. But they would equally be in error to neglect any sort of formal structured reasoning which allows the brain to spot connections between seemingly different problems; i.e., the reasoning of game theoretic equilibrium applies to a broad class of situations with social interactions.

Can anyone see what kind of time commitment (hours per week) is involved in the course? I could not see anything obvious at the sign up page.

Page means mathematical models, right?

I found Evidence shows that people who think with models consistently outperform those who don’t odd, too – not because it’s impossible to provide an appropriate sense of ‘model’ under which some people do and some don’t think with them, but because such a sweeping yet nebulous claim, appealing to generic ‘research’ with no hint of a citation, makes the thing read like a newspaper ad for some dodgy ‘improve your memory’ or ‘secrets of winning investment strategy’ course, which is distinctly off-putting.

…I feel like I see substantiation of Evidence shows that people who think with models consistently outperform those who don’t in every exam I give. The folks who ace the thing outright seem to have a pretty good overall picture of what their tools can do.

In particular, ‘thinking with models’ helps you to spot wild and weird claims, especially your own wild claims. I’ve seen plenty of exams on which a student obtained a result, realized it didn’t accord with their general sense of what kind of answer would make sense, and backtracked to discover an error. I don’t mean, like, a minus sign error, which is more an issue of basic awareness; people without models can spot that form of error probably just as well as the model folks. Sure, students leave answers that can’t possibly make sense (for any variety of reasons, e.g. running out of time).

The model-vs-nonmodel difference shows up when students attempt methods that can’t possibly make sense. What I mean is, a realization that their whole approach to the question they want to answer can’t possibly make sense, because the computations they’ve attempted or considered attempting can’t possibly produce the desired information. A model provides a strong sense of what information is connected to (or should be connected to) what other information. The kind of error the models folks tend to make is ‘invent a way to solve this that sort of makes some intuitive sense, but turns out to have a fatal flaw in reasoning that they didn’t catch.’ Awkwardly, given {exam time pressure} + {exam rule prohibits asking someone to review their idea}, quite a lot of model-oriented folks . But when they see their own work returned, their reaction is often something like “oh sheesh duh why did I think that?” — they have a strong sense of nonsense and can assess “sheesh, why did I think this was related to that?”

My favorite quote on models-vs-procedures was from my undergrad days: “You shouldn’t have to find the answer in order to know what the answer is.” (You can replace the ‘is’ with a ‘should be’ and tack on some sort of statement like “You have to find the answer in order to check that you have it” if you prefer less pithy statements.)

{models}{rules} and {models}{procedures} are both really neat nontrivial Venn diagrams.

“In particular, ‘thinking with models’ helps you to spot wild and weird claims, especially your own wild claims. I’ve seen plenty of exams on which a student obtained a result, realized it didn’t accord with their general sense of what kind of answer would make sense, and backtracked to discover an error.”

I don’t know if and how this is related to models but you are addressing a very important issue. I see students give nonsense answers apparently without giving any thought to whether their answers make sense, and I would love to hear any ideas about how to teach them do better. This reminds me of course of the old “how old was the captain” joke. The way many students are exposed to Mathematics leads them to believe that numbers are meaningless abstractions. Their task is to perform meaningless arithmetic manipulations and come up with some sort of response. At that point they seem to stop without giving any thought to what their answer might mean. I try to counter this tendency by using only real-world examples with real-world data in my exercises but still the results often drive me to despair.

I don’t know if and how this is related to models… / Nor I.

Well, heck, possibly nor I, I guess. I was loosely interpreting ‘model’ as a characterization of relationships between objects of study, providing a plausible description that enables us to make predictions because it generalizes previously observed phenomena in a plausible way. So a mathematical model is a sense not only of how some particular quantities are related to each other, but also of what it means for quantities to be related, and some intuition about what should be true about those relationships even when available data is incomplete or ambiguous.

Perhaps that’s nonsense; it’s just a definition I derived ad hoc from:

Models help us to better organize information – to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures.

I’d be happy to hear alternative characterizations of what ‘model’ means in this context, and I’m looking forward to hearing more from Scott Page about it.

OT, but — Did anyone else notice and appreciate the sort of beautiful point/counterpoint of Henry’s two posts? I like that Scott Page (who wrote an intelligent, careful, measured, and fairly reasonable book on diversity) was implicitly contrasted with Andrew Sullivan (who expressed support for a fallacious, irresponsible, immoderate, and daft book on diversity). That was meta-cool.