Comment by nvarsj | Hacker News Reader

Comment by nvarsj | Hacker News Reader

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"do you need to learn how the engine of a car works before you can drive it?"

No, but you'd be a much better driver if you did.

Understanding the basics of a science, especially math, is extremely important to fully grasp the higher level topics. I don't believe one can conceptually understand a topic without understanding the fundamentals that it builds upon.

Unfortunately I see philosophies as you describe in my local school system (Chicago Public Schools), especially in poverty stricken neighborhoods. High school kids are given scientific calculators and taught algebra/pre-calc when they can't even add or multiply single digit numbers. Similarly, there are pushes to move more "computer learning" into grade school, despite extremely poor reading and math proficiency.

I can draw parallels in my job as well - it's remarkable how poor most programmers' basic math skills are. Someone who can do the chain rule is regarded as a genius. With only a strong grasp of fundamentals, I feel that many engineers could be substantially more successful.

> No, but you'd be a much better driver if you did.

Agreed, but it might still be a good idea to change the order in which you teach them: first learn to drive, then learn how the car works inside. There is ample evidence that the human brain is better capable of understanding if it understands the big picture first (for proof see: "The pyramid principle" by M.Minto)

No, but you'd be a much better driver if you did.

And I think that the time is better spent learning to drive. That's just an unfounded opinion, but at least I can see it as such. Do you have any evidence that understanding engines makes drivers "much better"?

> No, but you'd be a much better driver if you did [learn how a car engine works]

Yes, but one simple computer animation could give you the same understanding of the engine as if you had built the engine yourself. Computers can give you an understanding of calculations in addition to doing the work.

> I don't believe one can conceptually understand a topic without understanding the fundamentals that it builds upon.

This is probably the biggest argument against using computers to calculate for you. However, if you haven't already, watch Wolfram's video that I linked to above as he clearly explains how this belief is not necessarily true. The very rudimentary basics will need to be learned by calculating, but anything above the fundamentals can be understood without the calculations.

> Similarly, there are pushes to move more "computer learning" into grade school, despite extremely poor reading and math proficiency.

I think this computer learning is different than the learning I'm talking about. Schools currently use computers as a medium to enhance the current education system. They use them to make calculating more interactive and fun. I think that computers should actually do the calculations, rather than "tricking" the students into doing the work.

> The very rudimentary basics will need to be learned by calculating, but anything above the fundamentals can be understood without the calculations.

Generally, I agree with this. But if everybody were to adopt that philosophy, eventually we'd get to the point where nobody could actually implement the calculations for those high level concepts. And then what happens when you need to update the software that's been doing all of that for you?

Does everybody need to know how to calculate? Probably not, above arithmetic and some basic algebra. But a lot of people do, and that needs to be included in their education somewhere.

You're probably aware of all that, but I felt it warrants making explicit.

I am aware of this, but still, thank you for bringing it up as it is an important issue. The software engineers and people who have to interact with more calculations than everyone else would at sometime need to learn them - as you said.

I think speleding is onto something, though: http://news.ycombinator.com/item?id=2213985

We all believe that calculations need to be taught first, but maybe it is not necessary. Learning the calculations after the bigger concepts has its own advantages. Everyone could start with general education, and those that need it could be taught the more advanced (or one might say, basic) calculations.

Relevant (but very basic) example of what I think you're describing: http://www.animatedengines.com/

It worked very well for me personally and gave me quite a few "A-HA" moments. I'm not sure it helped with my driving however ;-)

> Yes, but one simple computer animation could give you the same understanding of the engine as if you had built the engine yourself.

That must be one impressive animation.

I mean, to what depth do you really need to understand an engine in order to drive it better?

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