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> “Mike said, ‘Justin, you’re going to get me thinking about this problem again and I don’t want to do that,’” said Gilmer. This is a very relatable feeling. I often find myself getting trapped into thinking about problems I am unlikely to solve.
> “Mike said, ‘Justin, you’re going to get me thinking about this problem again and I don’t want to do that,’” said Gilmer. This is a very relatable feeling. I often find myself getting trapped into thinking about problems I am unlikely to solve.
I have this problem as well. The most disturbing thing is retracing old paths to dead ends without realizing it. Here I mean internal mental models, but also applies to previously known results I just wasn't familiar with, and don't turn up unless specific phrases are known.
Earlier quoted context omitted.
We can thank the academic system and Goodhart's Law for that. We measure students with tests, but all we get are people good at taking tests and rote memorization. Maybe if we had a better way to access actual learning but are teachers even paid enough to truly care?
Tests have their place though. The more rigorous maths exams I took in school were some of the most intellectually challenging things I did in school. If written correctly, they require you to apply the things you've learned in novel ways, or to combine the topics you've studied in new ways. Problem is, IME there's very few professors/teachers qualified and devoted enough to develop those sorts of exams, and as soon…
In many other disciplines applying what students learned to things they’ve never seen before isn’t really possible.
For example, you can teach students what factors were needed to start the Industrial Revolution and why, but then, to answer “why didn’t the Industrial Revolution start in the 1750s in South America?” students would have to know about South America in the 1750s. If they don’t, all they can answer is “it must be because not all of the prerequisites foo, bar, baz, … were available, but I wouldn’t know which one(s)”.
Because of that, that question isn’t better than the dull “why did the Industrial Revolution start where and when it started?”, the answer to which can be learned by rote learning.
> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said. Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone. Rings of the Einstein quote: “[I do not] carry such information in my…
I think it's the first place I ever saw the "Information Diagram" (https://en.wikipedia.org/wiki/Information_diagram) which is a Venn-like diagram that really helps to remember all these relationships.
Always cool to see unexpected applications of information theory, especially outside of probabilistic contexts. A related toy example that comes to mind is the puzzle where you're given 12 metal balls and told that one of them is either heavier or lighter than the rest. You're then given a balance/scale and instructed to figure out which ball is different and whether it is heavier or lighter using the balance a maxim…
I once made a cool solution to this problem using information theory, in particular coding theory. The usual solution uses the fact there are 3 places to put items: left scale, off scale, and right scale. Then those solutions do if/then cases to juggle items around to find the mis-weighted ball. My solution numbered the balls in base 3, then did four weighings with no if/thens,. The weightings each gave a base 3 resu…
Earlier quoted context omitted.
I find it's a cruel trick people, usually inadvertently, play on me at work: "when you've got a sec can you look at x?" There's a portion of my brain that's immediately hijacked and starts thinking about the problem whether I'm actively working on it or not. Happens to me for work problems outside of work, too. I'll just be chilling in the shower or something and suddenly I'm thinking about a work problem. Maybe one…
The obligatory XKCD https://xkcd.com/356/
Always cool to see unexpected applications of information theory, especially outside of probabilistic contexts. A related toy example that comes to mind is the puzzle where you're given 12 metal balls and told that one of them is either heavier or lighter than the rest. You're then given a balance/scale and instructed to figure out which ball is different and whether it is heavier or lighter using the balance a maxim…
I once made a cool solution to this problem using information theory, in particular coding theory. The usual solution uses the fact there are 3 places to put items: left scale, off scale, and right scale. Then those solutions do if/then cases to juggle items around to find the mis-weighted ball. My solution numbered the balls in base 3, then did four weighings with no if/thens,. The weightings each gave a base 3 resu…
Always cool to see unexpected applications of information theory, especially outside of probabilistic contexts. A related toy example that comes to mind is the puzzle where you're given 12 metal balls and told that one of them is either heavier or lighter than the rest. You're then given a balance/scale and instructed to figure out which ball is different and whether it is heavier or lighter using the balance a maxim…
The 12-ball problem is a fun one and IMO the key revelation is that you do not need to determine whether the ball is lighter or heavier (which isn’t possible anyway). Just which ball is different than the rest. It’s a great exercise in decision trees as you change your strategy based on total information, not just the most recent step. It’s also fun to scale the problem from 3 balls up to see how the solution evolves…
> “Mike said, ‘Justin, you’re going to get me thinking about this problem again and I don’t want to do that,’” said Gilmer. This is a very relatable feeling. I often find myself getting trapped into thinking about problems I am unlikely to solve.
I find it's a cruel trick people, usually inadvertently, play on me at work: "when you've got a sec can you look at x?" There's a portion of my brain that's immediately hijacked and starts thinking about the problem whether I'm actively working on it or not. Happens to me for work problems outside of work, too. I'll just be chilling in the shower or something and suddenly I'm thinking about a work problem. Maybe one…
> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said. Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone. Rings of the Einstein quote: “[I do not] carry such information in my…