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How can Bob produce novel things when he lacks the skills to do even trivial things? I didn't get to be a senior engineer by immediately being able to solve no
by troupo 7mo ago
How can Bob produce novel things when he lacks the skills to do even trivial things?
I didn't get to be a senior engineer by immediately being able to solve novel problems. I can now solve novel problems because I spent untold hours solving trivial ones.
- stavros 7mo agoBecause trivial things aren't a prerequisite for novel things, as any theoretical mathematician who can't do long division will tell you.
- troupo 7mo agoAh yes. The famous theoretical mathematicians who immediately started on novel problems in theoretical mathematics without first learning and understanding a huge number of trivial things like how division works to begin with, what fractions are, what equations are and how they are solved etc. Edit: let's look at a paper like Some Linear Transformations on Symmetric Functions Arising From a Formula of Thiel and Williams https://ecajournal.haifa.ac.il/Volume2023/ECA2023_S2A24.pdf https://ecajournal.haifa.ac.il/Volume2023/ECA2023_S2A24.pdf and try and guess how many of trivial things were completely unneeded to write a paper like this.
- stavros 7mo agoSeems that teaching Bob trivial things would be a simple solution to this predicament.
- sumeno 7mo agoThat's what the program he just took was supposed to be for, learning not output. You've just reinvented the article from first principles, congrats
- HauntingPin 7mo agoSometimes I wonder how deeply some people actually read these articles. What's the point of the comments if all we're doing is re-explaining what's already explained in such a precise and succint manner? It's a fantastic article. It's so well-written and clear. And yet we're stuck going in a circle repeating what's in the article to people who either didn't read it, or didn't read it with the care it deserves.
- deleted 7mo ago[deleted]
- thepasch 7mo ago> That’s what the program he just took was supposed to be for, learning not output. If you send a kid to an elementary school, and they come back not having learned anything, do you blame the concept of elementary schools, or do you blame that particular school - perhaps a particular teacher _within_ that school?
- deleted 7mo ago[deleted]
- Folcon 7mo agoThere's a difference between needing no trivial skills to do novel things and not needing specific prerequisite trivial skills to do a novel thing
- sgarland 7mo agoI would love to see someone attempt to do multiplication who never learned addition, or exponentiation without having learned multiplication. There is a vast difference between “never learned the skill,” and “forgot the skill from lack of use.” I learned how to do long division in school, decades ago. I sat down and tried it last year, and found myself struggling, because I hadn’t needed to do it in such a long time.
- ipaddr 7mo agoMost people learn multiplication by memorizing a series of cards 2x2,2x3.. 9x9. Later this gets broken down to addition in higher grades.
- throawayonthe 7mo agoi have never heard of this, multiplication was definitely introduced to both me/my peers and my siblings as "doing addition n times"
- Jensson 7mo agoMost people learn multiplication by counting, it has been in basic mathbooks since forever. "1 box has 4 cookies. Jenny ha 4 boxes of cookies. How many cookies do Jenny have?" and so on, the kids solve that by counting 4 cookies in every of the 4 boxes and reaching 16. Only later do you learn those tables.
- sgarland 7mo agoThat’s definitely not how I learned it, nor how my kids have learned it. I vividly remember writing out “2 x 3 = 2 + 2 + 2 = 3 + 3.” I later memorized the multiplication table up to 12, yes, but that was not a replacement of understanding what multiplication was
- acuozzo 7mo ago> but that was not a replacement of understanding what multiplication was You're conflating an algorithm in N or Z with inherent meaning. Let's shift over to R: Expand e*pi to repeated addition. Think exponentiation is "repeated multiplication"? Try 2^pi.
- Warwolt 7mo agoThat's not a good analogy. A good mathematician isn't necessarily dealing with calculations, i.e. long division, but rather with proof. No-ones becomes a good mathematician without first learning to write simple proofs, and then later on more complex proof. It's the very stuff of the field itself.