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The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

justinmath.com

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Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#11

Post by mmastrac »

This applies to code as well. I worked on an internal PostgreSQL protocol driver for work and I've been focusing on understanding the binary message format inside and out, then the server state machine and query behaviour, and only then building a driver.

Don't underestimate the value of time spent grinding the low levels for code that is fundamentally important to what you are doing. You come away with a much stronger understanding than if you just hack a solution, cargo culting some existing code and just shipping it.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#12

Post by bick_nyers »

joshdavham wrote: post #10

This was something that really lacked in my statistics degree. We were always learning different distributions, proofs and estimation methods but very rarely applied them to actual problems. I feel like you can kinda get away with this type of thing in math more, but in statistics, it makes things super hard to learn.

I kinda wish you could just take a course on a specific distribution. Like, here's the Poisson class where you learn all of its interesting properties and apply it to e.g. queuing problems.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#13

Post by danielmarkbruce »

aqme28 wrote: post #9

Yes. I think I did well in math/physics classes in college and grad school just because I found the most effective way to study, for me, was to grind out as many problems as possible. Go through the old homework, old exams, books, anywhere you can find relevant problems with solutions to check against.

It's not just for you. It's the most effective way. I know several people who all crushed college etc and only later realized maybe they aren't so smart, maybe they just stumbled into the right way(by an order of magnitude) to study... hell, I'd redo problems and find depth or nuance in the same problem that I didn't see the first time.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#14

Post by erikerikson »

The author is generalizing their preference here to say it's "right". Some brains need this, others need the abstraction before the examples provide the most benefit.

As noted by others this preference influences how one learns code effectively too. It's a pretty basic trait.

The author's stated preference is most common but it is not the only one.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#15

Post by pitched »

erikerikson wrote: post #14

The author is generalizing their preference here to say it's "right". Some brains need this, others need the abstraction before the examples provide the most benefit. As noted by others this preference influences how one learns code effectively too. It's a pretty basic trait. The author's stated preference is most common but it is not the only one.

Not sure I’m following here. Happen to have a concrete example of when abstracting first is more helpful?

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#16

Post by SilasX »

pitched wrote: post #15
erikerikson wrote: post #14

The author is generalizing their preference here to say it's "right". Some brains need this, others need the abstraction before the examples provide the most benefit. As noted by others this preference influences how one learns code effectively too. It's a pretty basic trait. The author's stated preference is most common but it is not the only one.

Not sure I’m following here. Happen to have a concrete example of when abstracting first is more helpful?

Not disagreeing, and I'm not sure if your comment was intended as a joke, but it's kind of funny what just happened here, if anyone missed it:

"They say you have to use concrete examples, but not everyone needs that."

'Can you give a concrete example of that?'

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#17

Post by dr_dshiv »

skobes wrote: post #4

Ironically, this post would benefit from showing some examples.

100%.

And why is it so hard to have math education based on good concrete contextualized examples, vs just rules and problem sets? Understanding the “why” behind the math is often lacking… and math doesn’t always need to be applied, that’s ok— but if it can be, it is so much easier to understand

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#18

Post by fiddlerwoaroof »

danielmarkbruce wrote: post #13
aqme28 wrote: post #9

Yes. I think I did well in math/physics classes in college and grad school just because I found the most effective way to study, for me, was to grind out as many problems as possible. Go through the old homework, old exams, books, anywhere you can find relevant problems with solutions to check against.

It's not just for you. It's the most effective way. I know several people who all crushed college etc and only later realized maybe they aren't so smart, maybe they just stumbled into the right way(by an order of magnitude) to study... hell, I'd redo problems and find depth or nuance in the same problem that I didn't see the first time.

I think a lot of people do college too young: if you can find a reasonable “real” job, a gap year or two will give you some life experience and a chance to mature a bit, which puts you in a much better place for actually learning.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#19

Post by erikerikson »

pitched wrote: post #15
erikerikson wrote: post #14

The author is generalizing their preference here to say it's "right". Some brains need this, others need the abstraction before the examples provide the most benefit. As noted by others this preference influences how one learns code effectively too. It's a pretty basic trait. The author's stated preference is most common but it is not the only one.

Not sure I’m following here. Happen to have a concrete example of when abstracting first is more helpful?

This question seems to bring a frame that implies there is an example that would apply to everyone. I'm claiming such an example doesn't exist but I will try (please note these are overly simplified).

Consider addition...

"We're going to learn addition today"

One approach: "it is combining two quantities into one. For example, 1 + 1 = 2, 2 + 2 = 4"

Another: "1 + 1 = 2, 2 + 2 = 4, you see, we are combining the quantities"

For some of us, getting the abstraction first gives us the mental framing that allows the examples to teach us the most and the alternative feels like noise.

For others, they're not sure what we're going on about until we have given them enough examples so that they can understand the abstraction. They want to generalize off of the examples they've seen.

Neither is inherently right but they have trade offs and we have preferences on this dimension that end up being strong and usually outside of our awareness. Frequently it can not matter if we jump back and forth between concreteness and abstraction.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#20

Post by erikerikson »

SilasX wrote: post #16
pitched wrote: post #15

Earlier quoted context omitted.

Not sure I’m following here. Happen to have a concrete example of when abstracting first is more helpful?

Not disagreeing, and I'm not sure if your comment was intended as a joke, but it's kind of funny what just happened here, if anyone missed it: "They say you have to use concrete examples, but not everyone needs that." 'Can you give a concrete example of that?'

Indeed, and both a reasonable desire and one of my systemic communication failures. :)
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