Ever read Surely You’re Joking, Mr. Feynmann? Plenty of the stories in there involve someone (or an entire student body) not really understanding extremely basic things about what the hell they were talking about, despite having memorized some formulas and being adept at manipulating them.
Examples include:
Students who can recite the formula for Brewster’s angle but don’t realize what that would have to do with polaroids and light reflecting off of water,
Stedents being able to calculate the displacement of a ray of light shined through glass but thinking that if a book is rotated underneath a glass table that the image would rotate by twice the angle
Students that can recite the definition of diamagnetism but that can’t actually name a single diamagnetic material.
A bunch of engineering students who clearly didn’t understand that the derivative of a curve is the slope of the tangent line.
An assistant to Einstein that could not answer a simple question (whose result should’ve been well known to him) about length minimizing geodesics when phrased in terms of a rocket path that takes the least time to go up and back down again (aka the meaning of (a special case of) ‘length minimizing geodesic’)
a man adept at calculating cube roots with an abacus that had to use the device to confirm that 2^3 = 8.
To paraphrase from memory: Most people’s knowledge is so fragile!
Yeah, knowledge, especially specialized knowledge, seems tragically fragile. I did read the book many years ago and recall enjoying it. Do you think in those cases:
It is a problem that the specialists’ specialized knowledge is fragile?
The knowledge fragility is caused by some perverse incentive to focus on the technical rather than practical?
The fragility of the specialized knowledge could have been avoided if the perverse incentive issue was fixed?
The problem is not specialized knowledge. All of these examples are basic and fundamental to the subject. Except for the geodesic example[1], I am confident that the other cases are cases of never actually learning what the hell they were talking about, and instead of focusing on that fundamental gap of understanding they instead focused on memorization and rote algebra.
Partly this is perverse incentive of current schools. But I suspect that even if schools didn’t actively encourage these problems that you’d still see this, that you need some way to actively fight back. Unfortunately I’m not sure what the key is, here.
Some guesses:
If you actually, like, try to understand what the hell the things you’re doing mean, maybe you’ll succeed? This is good advice even if Feynmann’s examples are easy for you: often relatively more complicated formulas have some intuitive meaning, even if it’s not as standard to explain.
Maybe, try always coming up with simpler and more concrete examples for everything? This is similarly good advice, but also despite not doing enough of this for a while I wouldn’t have nearly so bad a problem as Feynmann describes, which suggests this is less load bearing for me. Possibly, it’s compensated by me understanding the abstract thing more by itself than most?
Maybe, try actually applying or operationalizing the knowledge? If on the first day that you learn about “polarization” you buy a polarizing filter and then just go look at a bunch of stuff (surfaces that shine at a grazing angle, phone screens, a couple other polarizers, an oil film, plastic objects, the sky, a rainbow, a laser, bright lights) you’ll learn a bunch (e.g. brewster’s angle, liquid crystals, malus’s law, thin film interference, photoelasticity and stress polarimetry, rayleigh sky model and the vikings, more direct demonstration of dipole radiation in the air being polarized at near 90°, the polarizer being worse at higher frequency). Again despite not doing this for a while I ended up as me, even if doing so was fun and taught me extra bonus things.
Try… caring? Someone who cares may care to understand and to operationalize and to me concrete and to answer the questions they’ve always had about X.
I myself didn’t immediately know the answer to that one. However, it had been a while since I was looking into general relativity, and I had not gone that deeply, so I forgot the fact that the (spacetime interval version of) arc length of an observer’s path is the proper time of the observer (just because the observer’s not moving in their frame) and had to refigure it out (though by then I had read Feynmann’s answer).
I anticipate that the assistant would’ve been able to tell you that fact without connecting it to rocket flights; and I anticipate that I would’ve, and even that if I had taken the time to write down the problem that I would’ve had a good chance of figuring out the necessary fact. Why am I like this, when the assistant wasn’t?
I think it might be about specialized knowledge, because I see indexing and cross linking things as it’s own kind of specialized knowledge. It seems like all of your examples are focused on creating bigger denser networks of cross domain indexing. I think that is great, and I love trying to do it myself! It’s highly useful. But is it possible to be useful without it? I can hypothesize that a few people on a team with that skill could make other people that don’t have that skill useful...
For example, maybe my co-worker might not understand what Brewster’s angle actually means, but if I can rely on them to do the calculations correctly than I can use them to get more work done than I could do alone (hypothetically). If situations like that exist, or are common, then it is actually ok that most students (and employees) are not that interested in actually understanding what the symbolic manipulation they are doing means.
But there are two potential flaws. (1) We are creating more and more capable artificial general intelligence, and doing so may make the people who didn’t understand what they were doing deeply enough no longer useful. This is bad under the current prevailing social systems. (2) It might not be the case that schools are actually teaching students anything that is actually useful if the students do not understand it deeply with cross indexing.
(1) is a more general problem… and honestly I’m more worried about misaligned ASI then economic impact, but it is still a pretty important concern.
(2) Is definitely true in some regards. It seems like education does function as a shit test to sort people into social strata, but insofar as it is actually teaching skills that get used, it may be better if emphasis was shifted away from “practice applying specialized skill” and towards “learn dense indexes connecting specialized skills to their applications”, trusting that people can look up and reference the specialized skill if they need to apply it, but are much more likely to benefit from knowing which skills exist and where they are useful than to have a bunch of skills that they will forget because they don’t understand how those skills connected back to anything real at all.
But I must confess I think (2) is happening somewhat implicitly through the way different communities of different specialized knowledge produce specialists that connect into cross domain teams. I think it would benefit from being made more explicit, but that is probably the sort of thing that sociologists and business management students learn about… I would like to learn more about sociology.
Ever read Surely You’re Joking, Mr. Feynmann? Plenty of the stories in there involve someone (or an entire student body) not really understanding extremely basic things about what the hell they were talking about, despite having memorized some formulas and being adept at manipulating them.
Examples include:
Students who can recite the formula for Brewster’s angle but don’t realize what that would have to do with polaroids and light reflecting off of water,
Stedents being able to calculate the displacement of a ray of light shined through glass but thinking that if a book is rotated underneath a glass table that the image would rotate by twice the angle
Students that can recite the definition of diamagnetism but that can’t actually name a single diamagnetic material.
A bunch of engineering students who clearly didn’t understand that the derivative of a curve is the slope of the tangent line.
An assistant to Einstein that could not answer a simple question (whose result should’ve been well known to him) about length minimizing geodesics when phrased in terms of a rocket path that takes the least time to go up and back down again (aka the meaning of (a special case of) ‘length minimizing geodesic’)
a man adept at calculating cube roots with an abacus that had to use the device to confirm that 2^3 = 8.
To paraphrase from memory: Most people’s knowledge is so fragile!
Yeah, knowledge, especially specialized knowledge, seems tragically fragile. I did read the book many years ago and recall enjoying it. Do you think in those cases:
It is a problem that the specialists’ specialized knowledge is fragile?
The knowledge fragility is caused by some perverse incentive to focus on the technical rather than practical?
The fragility of the specialized knowledge could have been avoided if the perverse incentive issue was fixed?
The problem is not specialized knowledge. All of these examples are basic and fundamental to the subject. Except for the geodesic example[1], I am confident that the other cases are cases of never actually learning what the hell they were talking about, and instead of focusing on that fundamental gap of understanding they instead focused on memorization and rote algebra.
Partly this is perverse incentive of current schools. But I suspect that even if schools didn’t actively encourage these problems that you’d still see this, that you need some way to actively fight back. Unfortunately I’m not sure what the key is, here.
Some guesses:
If you actually, like, try to understand what the hell the things you’re doing mean, maybe you’ll succeed? This is good advice even if Feynmann’s examples are easy for you: often relatively more complicated formulas have some intuitive meaning, even if it’s not as standard to explain.
Maybe, try always coming up with simpler and more concrete examples for everything? This is similarly good advice, but also despite not doing enough of this for a while I wouldn’t have nearly so bad a problem as Feynmann describes, which suggests this is less load bearing for me. Possibly, it’s compensated by me understanding the abstract thing more by itself than most?
Maybe, try actually applying or operationalizing the knowledge? If on the first day that you learn about “polarization” you buy a polarizing filter and then just go look at a bunch of stuff (surfaces that shine at a grazing angle, phone screens, a couple other polarizers, an oil film, plastic objects, the sky, a rainbow, a laser, bright lights) you’ll learn a bunch (e.g. brewster’s angle, liquid crystals, malus’s law, thin film interference, photoelasticity and stress polarimetry, rayleigh sky model and the vikings, more direct demonstration of dipole radiation in the air being polarized at near 90°, the polarizer being worse at higher frequency). Again despite not doing this for a while I ended up as me, even if doing so was fun and taught me extra bonus things.
Try… caring? Someone who cares may care to understand and to operationalize and to me concrete and to answer the questions they’ve always had about X.
I myself didn’t immediately know the answer to that one. However, it had been a while since I was looking into general relativity, and I had not gone that deeply, so I forgot the fact that the (spacetime interval version of) arc length of an observer’s path is the proper time of the observer (just because the observer’s not moving in their frame) and had to refigure it out (though by then I had read Feynmann’s answer).
I anticipate that the assistant would’ve been able to tell you that fact without connecting it to rocket flights; and I anticipate that I would’ve, and even that if I had taken the time to write down the problem that I would’ve had a good chance of figuring out the necessary fact. Why am I like this, when the assistant wasn’t?
I think it might be about specialized knowledge, because I see indexing and cross linking things as it’s own kind of specialized knowledge. It seems like all of your examples are focused on creating bigger denser networks of cross domain indexing. I think that is great, and I love trying to do it myself! It’s highly useful. But is it possible to be useful without it? I can hypothesize that a few people on a team with that skill could make other people that don’t have that skill useful...
For example, maybe my co-worker might not understand what Brewster’s angle actually means, but if I can rely on them to do the calculations correctly than I can use them to get more work done than I could do alone (hypothetically). If situations like that exist, or are common, then it is actually ok that most students (and employees) are not that interested in actually understanding what the symbolic manipulation they are doing means.
But there are two potential flaws. (1) We are creating more and more capable artificial general intelligence, and doing so may make the people who didn’t understand what they were doing deeply enough no longer useful. This is bad under the current prevailing social systems. (2) It might not be the case that schools are actually teaching students anything that is actually useful if the students do not understand it deeply with cross indexing.
(1) is a more general problem… and honestly I’m more worried about misaligned ASI then economic impact, but it is still a pretty important concern.
(2) Is definitely true in some regards. It seems like education does function as a shit test to sort people into social strata, but insofar as it is actually teaching skills that get used, it may be better if emphasis was shifted away from “practice applying specialized skill” and towards “learn dense indexes connecting specialized skills to their applications”, trusting that people can look up and reference the specialized skill if they need to apply it, but are much more likely to benefit from knowing which skills exist and where they are useful than to have a bunch of skills that they will forget because they don’t understand how those skills connected back to anything real at all.
But I must confess I think (2) is happening somewhat implicitly through the way different communities of different specialized knowledge produce specialists that connect into cross domain teams. I think it would benefit from being made more explicit, but that is probably the sort of thing that sociologists and business management students learn about… I would like to learn more about sociology.