An engineering student at Northwestern University.
aaq
Karma: 272
(Reinventing wheels) Maybe our world has become more people-shaped.
Call for resources on the link between causation and ontology
I would picture them as rectangles and count. Like, 2x3 would look like
xxx
xxx
in my head, and for small numbers I could use the size of it to feel whether I was close. I remember doing really well with ratios and fractions and stuff for that reason.
For larger numbers, like 8x8, I would often subdivide into smaller squares (like 4x4 or 2x2), and count those. Then it would be easy to subdivide the larger one and repeat-add. I would often get a sour taste if the answer just “popped” into my head and I would actively fight against it, so I think there was a part of me that really just viscerally hated the idea of letting ‘mere’ memorization into my learning at all.
Incidentally, my past memories are saying that’s why 6x7 and 7x7 gave me such trouble in particular; there was no “easy” way to decompose that in my head, it just looked like a square and another almost-maybe-a-square.
Agreed. I’m a big fan of spaced repetition systems now, even though I have a long way to go towards consistently using them.
[Question] Have you experienced a purity norm around learning “from first principles”?
For your specific situation, may I recommend curling up with Visual Complex Analysis for a few hours? 😊 http://pipad.org/tmp/Needham.visual-complex-analysis.pdf
On a more general note, I find that anyone who says they “learned it from first principles” is usually putting on airs. It’s an odd intellectual purity norm that I think is unfortunately very common among the mathematically- and philosophically-minded.
As evolved chimpanzees, we are excellent at seeing a few examples of something and then understanding the more general abstractions that guide it on a gut level; we have an amazing ability to arrest form from thing, but our ability to go the other way around is a lot more limited.
I think most of your intellectual idols would agree that while eventually being able to build up “from first principles” is a great goal to shoot for, it’s actually not the pedagogy you want. It’s okay to start concrete and just practice and grind until the more abstract stuff becomes obvious!
Take it from a guy who leapt off the deep end this quarter into abstract algebra, real analysis, signal processing and probability theory at the same time—there is no way I would be performing at the level I am in these classes if I didn’t force my abstraction-loving ass down to ground level and actually just crank out problem sets until the abstractions finally started to make sense.
{Math} A times tables memory.
I always like seeing someone else on LessWrong who’s as interested in the transformative potential of SRS as I am. 🙂
Sadly, I don’t have any research to back up my claims. Just personal experiences, as an engineering student with a secondary love of computer science and fixing knowledge-gaps. Take this with several grains of salt—it’s not exactly wild, speculative theory, but it’s not completely unfounded thinking either.
I’m going to focus on the specific case you mentioned because I’m not smart enough to generalize my thinking on this, yet.
First let’s think about what design patterns are, and where they emerged from. As I understand it, design patterns emerged from decades of working computer programmers realizing that there existed understandable, replicable structures which prevented future problems in software engineering down the line. Most of this learning came out of previous projects in which they had been burned. In other words, they are artifacts of experience. They’re the tricks of the trade that don’t actually get taught in trade school, and are instead picked up during the apprenticeship (if you’re lucky).
If I were designing an SRS deck for the purpose of being able to remember and recognize design patterns, then, I think I would build it on the following pillars:
1. ” the name of the pattern on one side and the definition on the other”, as you suggested. These cards aren’t going to be terribly helpful right now, until I’ve gone through some of #2, but after a week or so of diligent review, their meanings will snap into place for me and I’ll suddenly understand why they’re so valuable.
2. ” names and examples ”, as you suggested. I am on the books as generally thinking there’s a lot of value in generating concrete examples , to the point where I’d say the LessWrong community systemically underrates the value of ground-level knowledge. (We’re a bunch of lazy nerds who want to solve the world-equation without leaving our bedrooms. I digress.)
3. motivations and reasons for those names and examples. Try taking them and setting up scenarios, and then asking “Why would design pattern X make sense/not make sense in this situation?” or “What design pattern do you think would work best in this situation?” You’ll have to spend more than a couple seconds on these cards, but they will give you the appropriate training in critical thinking to be able to, later on, think through the problems in real life.
Hope some of this was food for thought. I might change this into a genuine post later on, since I’m on a writing kick the last couple days.
[Productivity] Task vs. time delimitation
[Math] Vision problems
[Health] [Math] Proofs, forgetting, and an eldritch god
Aaaaaaaaaaaaaaaaaaaaand now I’m thinking I know what’s wrong with me.
https://deponysum.com/2019/04/28/ocd-what-i-learned-fighting-mind-cancer/
[Math] Proofs vs. documentation vs. “it’s trivial”
Everyday belief in diminishing returns is resistant to diminishing returns
Nutrition heuristic: Cycle healthy options
Nutrition is Satisficing
Fear as fossil fuel
Set up for Success: Insights from ‘Naive Set Theory’
I very much doubt anyone else will care much about this post, so I will give my reasoning.
Please vote before you read my reasoning. :)
This is the only post I’ve ever read that actually convinced me to do something with substantial effort, that is, actually read Naive Set Theory. I really, really wanted to practice kata on sets before I attempted a math minor and I still look back on that as the best 3 weeks of last summer.
Reading NST the way I did taught me a lot about how not to read a math book. Don’t try to memorize everything. Don’t try to get every detail on the first pass. And definitely don’t copy the book almost verbatim into a spaced repetition system ending up with over 8,000 cloze deletion cards which you then practice for 6 months. There is a really good reason why we learn math through proofs, problems, and puzzles.
Also I like the tradition of having several smart people read the same classic book and give their slightly different spins on it. The information is mostly redundant, but my all-too-human memory is thankful for it.
Causality seems to be a property that we can infer in the Democritan atoms and how they interact with one another. But when you start reasoning with abstractions, rather than the interactions of the atoms directly, you lose information in the compression, which causes causality in the interactions of abstractions with another to be a harder thing to infer from watching them.
I don’t yet have a stronger argument than that; this is a fairly new topic of interest to me.