Some Case Studies
The other day my friend was learning to solder and he asked an experienced hacker for advice. The hacker told him that because heat rises, you should apply the soldering iron underneath the work to maximize heat transfer. Seems reasonable, logically inescapable, even. When I heard of this, I thought through to why heat rises and when, and saw that it was not so. I don't remember the conversation, but the punchline is that hot things become less dense, and less dense things float, and if you're not in a fluid, hot fluids can't float. In the case of soldering, the primary mode of heat transfer is conduction through the liquid metal, so to maximize heat transfer, get the tip wet before you stick it in, and don't worry about position.
This is a case of surface reasoning failing because the heuristic (heat rises) was not truly a part of my friend or the random hacker. I want to focus on the actual 5-second skill of going back To First Principles that catches those failures.
Here's another; watch for the 5 second cues and responses: A few years ago, I was building a robot submarine for a school project. We were in the initial concept design phase, wondering what it should look like. My friend Peter said, "It should be wide, because stability is important". I noticed the heuristic "low and wide is stable" and thought to myself "Where does that come from? When is it valid?". In the case of catamarans or sports cars, wide is stable because it increases the lever arm between restoring force (gravity) and support point (wheel or hull), and low makes the tipping point harder to reach. Under water, there is no tipping point, and things are better modeled as hanging from their center of volume. In other words, underwater, the stability criteria is vertical separation, instead of horizontal separation. (More precisely, you can model the submarine as a damped pendulum, and notice that you want to tune the parameters for approximately critical damping). We went back to First Principles and figured out what actually mattered, then went on to build an awesome robot.
Let's review what happened. We noticed a heuristic or bit of qualitative knowledge (wide is stable), and asked "Why? When? How much?", which led us to the quantitative answer, which told us much more precisely exactly what matters (critical damping) and what does not matter (width, maximizing restoring force, etc).
A more Rationality-related example: I recently thought about Courage, and the fact that most people are too afraid of risk (beyond just utility concavity), and as a heuristic we should be failing more. Around the same time, I'd been hounding Michael Vassar (at minicamp) for advice. One piece that stuck with me was "use decision theory". Ok, Courage is about decisions; let's go.
"You should be failing more", they say. You notice the heuristic, and immediately ask yourself "Why? How much more? Prove it from first principles!" "Ok", your forked copy says. "We want to take all actions with positive expected utility. By the law of large numbers, in (non-black-swan) games we play a lot of, observed utility should approximate expected utility, which means you should be observing just as much fail as win on the edge of what you're willing to do. Courage is being well calibrated on risk; If your craziest plans are systematically succeeding, you are not well calibrated and you need to take more risks." That's approximately quantitative, and you can pull out the equations to verify if you like.
Notice all the subtle qualifications that you may not have guessed from the initial advice; (non-pascalian/lln applies, you can observe utility, your craziest plans, just as much fail as win (not just as many, not more)). (example application: one of the best matches for those conditions is social interaction) Those of you who actually busted out the equations and saw the math of it, notice how much more you understand than I am able to communicate with just words.
Ok, now I've named three, so we can play the generalization game without angering the gods.
Trigger: Notice an attempt to use some bit of knowledge or a heuristic. Something qualitative, something with unclear domain, something that affects what you are doing, something where you can't see the truth.
Action: Ask yourself: What problem does it try to solve (what's its interface, type signature, domain, etc)? What's the specific mechanism of its truth when it is true? In what situations does that hold? Is this one of those? If not, can we derive what the correct result would be in this case? Basically "prove it". Sometimes it will take 2 seconds, sometimes a day or two; if it looks like you can't immediately see it, come up with whatever quick approximation you can and update towards "I don't know what's going on here". Come back later for practice.
It doesn't have to be a formal proof that would convince even the most skeptical mathematician or outsmart even the most powerful demon, but be sure to see the truth.
Without this skill of going back to First Principles, I think you would not fully get the point of truly a part of you. Why is being able to regenerate your knowledge useful? What are the hidden qualifications on that? How does it work? (See what I'm doing here?) Once you see many examples of the kind of expanded and formidably precise knowledge you get from having performed a derivation, and the vague and confusing state of having only a theorem, you will notice the difference. What the difference is, in terms of a derivation From First Principles, is left as an exercise for the reader (ie. I don't know). Even without that, though, having seen the difference is a huge step up.
From having seen the difference between derived and taught knowledge, I notice that one of the caveats of making knowledge Truly a Part of You is that just being able to get it From First Principles is not enough; Actually having done the proof tells you a lot more than simply what the correct theorem is. Do not take my word for it; go do some proofs; see the difference.
So far I've just described something that has been unusually valuable for me. Can it be taught? Will others gain as much? I don't know; I got this one more or less by intellectual lottery. It can probably be tested, though:
Testing the "Prove It" Habit
In school, we had this awesome teacher for thermodynamics and fluid dynamics. He was usually voted best in faculty. His teaching and testing style fit perfectly with my "learn first principles and derive on the fly" approach that I've just outlined above, so I did very well in his classes.
In the lectures and homework, we'd learn all the equations, where they came from (with derivations), how they are used, etc. He'd get us to practice and be good at straightforward application of them. Some of the questions required a bit of creativity.
On the exams, the questions were substantially easier, but they all required creativity and really understanding the first principles. "Curve Balls", we called them. Otherwise smart people found his tests very hard; I got all my marks from them. It's fair to say I did well because I had a very efficient and practiced From First Principles groove in my mind. (This was fair, because actually studying for the test was a reasonable substitute.)
So basically, I think a good discriminator would be to throw people difficult problems that can be solved with standard procedure and surface heuristics, and then some easier problems that require creative application of first principles, or don't quite work with standard heuristics (but seem to).
If your subjects have consistent scores between the two types, they are doing it From First Principles. If they get the standard problems right, but not the curve balls, they aren't.
Straight: Bayesian cancer test. Curve: Here's the base rate and positive rate, how good is the test (liklihood ratio)?
Straight: Sunk cost on some bad investment. Curve: Something where switching costs, opportunity for experience make staying the correct thing.
Straight: Monty Hall. Curve: Ignorant Monty Hall.
Again, maybe this can't be taught, but here's some practice ideas just in case it can. I got substantial value from figuring these out From First Principles. Some may be correct, others incorrect, or correct in a limited range. The point is to use them to point you to a problem to solve; once you know the actual problem, ignore the heuristic and just go for truth:
Science says good theories make bold predictions.
Deriving From First Principles is a good habit.
Boats go where you point them, so just sail with the bow pointed to the island.
People who do bad things should feel guilty.
I don't have to feel responsible for people getting tortured in Syria.
If it's broken, fix it.
(post more in comments)