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Everyone talks about the 4th dimension, BUT why is 3D geometry so hard for the average person compared to 2D ? (lemmy.ml)

submitted 6 days ago* (last edited 6 days ago) by zaknenou@lemmy.dbzer0.com to c/asklemmy@lemmy.ml

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I think 3D geometry has a lot of quirks and has so many results that un_intuitively don't hold up. In the link I share a discussion with ChatGPT where I asked the following:

assume a plane defined by a point A=(x_0,y_0,z_0), and normal vector n=(a,b,c) which doesn't matter here, suppose a point P=(x,y,z) also sitting on the space R^3. Question is:
If H is a point on the plane such that (AH) is perpendicular to (PH), does it follow immediately that H is the projection of P on the plane ?

I suspected the answer is no before asking, but GPT gives the wrong answer "yes", then corrects it afterwards.

So Don't we need more education about the 3D space in highschools really? It shouldn't be that hard to recall such simple properties on the fly, even for the best knowledge retrieving tool at the moment.

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[–] CanadaPlus 1 points 1 day ago* (last edited 1 day ago)

I would go seriously digging for the source for you, since a cursory search is full of modern stuff and I can't remember where I saw it exactly, but that would require non-glued fingers.

If you look at old (siege) engineering manuscripts, they're full of "take the square root of the armslengths and rewrite as dactyls"-type rules for everything. They didn't know much about mechanics, and often had funny ideas like momentum being self-dissipating if not sustained. but enough experimentation and basic calculating tools allows you to make rules of thumb anyway.

And, it's not like nobody could see how things moved through the air when launched or dropped. Basic principles about falling things go back to the 14th century at least, and the ancient Greeks thought so much about parabolas one must have at least noticed that's the trajectory of a thrown javelin, albeit without even algebra to start to explain why.

For example, we don’t need to know about ballistics to use a gun.

Sure, but you need to know about the trigger and where the bullet comes out of. And, if you don't know about the recoil, how to load it and where the casing is ejected you might not use it well.

Thinking about places like Europe and China, there's probably over a billion people that have never seen a gun operated in real life, so I suppose that's actually not really necessary, either. On the other hand, I have trouble imagining a modern person who's never needed to convey "perpendicular".

You can define knowledge as enablement to do things.