What Gears Teach Us About Thinking

When you solve a problem, do you use your imagination? Or do you use a mathematical rule?
The answer depends on what you understand about the problems you're tackling.
Gear problems involve figuring out what happens to gears in various configurations. And they tell us some interesting things about how we solve problems.
00:00 Introduction
00:31 Three Ways to Solve This Problem
02:05 Generating a Local Rule
03:01 Generating a General Rule
04:15 A Twist on the Problem
05:32 Lesson One
06:10 Lesson Two
06:52 Lesson Three
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The main inspiration for this video came from this gem from the mid-90s, though there are other pieces that discuss similar issues.
Schwartz, D. L., & Black, J. B. (1996). Shuttling between depictive models and abstract rules: Induction and fallback. Cognitive science, 20(4), 457-497. (available at citeseerx.ist.psu.edu/viewdoc...)

[@IPP133]

I just found your channel and I absolutely love your videos! I've already watched several, including one where you talk about not trying to watch too many educational videos back to back 😅. Excellent stuff!
This video got me thinking about how I approach problem solving. One thing that occurred to me with the second kind of gear problem was that I don't begin by imagining the specific problem with five gears in a circle. Instead, I picture it with three gears as a kind of "minimal case" from which I can develop the local and then general rules. I'm not sure you can say I really learned this from this video, because I have definitely picked up the rule from years of studying math to begin with the simplest case, but it got me thinking about it in a new way. Before watching this video, I don't think I would have explained this strategy as utilizing my imagination, which it is. The simplest case is the easiest to work with in many ways, but I didn't consider how much easier it is to imagine, especially visually. It's also easier to construct a model of the simplest case, which can be useful in using and improving imagination.
I find your videos very thought provoking and inspiring. Thanks for creating such great content!

[@ishrakmujibift4269]

When we are encountering a totally novel problem, we should go deep into it to figure out a solution. Based on that solution we then develop a local rule and furthermore a general rule. So when we encounter a similar problem we can use the general rule to find solutions faster. However, if the problem is a little bit modified then we should use the local rule to figure ot a solution. I guess that is something I do quite often but only realised it after watching the video. Thanks :D

[@maal124]

Reminds me of 3Blue1Brown's video on Alice and Bob

[@heej8748]

I learned that the 'big picture' thinking i was doing was a form of abstraction to form a 'general' rule.

[@shan504]

Very insightful! Good to know that there are videos like this out there.

[@samarthtandale9121]

So it's all about making right abstractions 😅
Guess that's what the ml models do as well by feature selection and correlation ...

[@iNeFFaBLeSaPiEN]

Thanks

[@KillerKatz12]

Omg I just realized he has those puzzle pieces with gears game/toy I mean toy.

[@GustavoSilva-ny8jc]

Math part blew my mind, it would have made sub and division look totally different and MUCH MUCH easier, i had a trash education.

[@kellymackeyjr.6319]

There are pros and cons to viewing and doing things certain ways

[@madhavav8432]

Imagination , Local rule , General rule.

[@technoworlddd]

I thought that exist only the imagination

[@unknown-10k]

Q: What causes learning disabilities and can they be cured?
I didn't want to look for that myself, because a lot of information on the internet is inaccurate.

[@benjaminkeep]

That's outside my area, sadly. I know very little about learning disabilities.

[@noxfelis5333]

For that you realy need to check on a case by case, as different people have learning disabilities for different reasons, some are inborn genetically whereas others are just having a hard time to learn due to trauma, be it physical, psychological or emotional. If you wish to learn more about it, you need to find someone who specializes in those fields and be more specific about what kind of learning disability you wish to talk about.