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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 21 hours ago* (last edited 21 hours 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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[–] zaknenou@lemmy.dbzer0.com 1 points 10 hours ago (4 children)

ChatGPT is trained based on forum discussions and pretty likely pirated books. If it found the idea in a previously established text it would have answered correctly. That's why I DO think it is representative of what the average good student was taught (not how smart, or good at problem solving they be). What's funny is that after reasoning it found the right answer, which is counter intuitive, since ChatGPT is supposed to be good at retrieving information, not at reasoning!

[–] calidris@hexbear.net 1 points 8 hours ago (3 children)

I'm trained on pirated books and I do alright.

Believing forum shitposts would definitely poison the well though.

[–] zaknenou@lemmy.dbzer0.com 2 points 8 hours ago (2 children)

when I say forums, that includes math.stackexchange, please don't call it shitpost, people there are really something to say the least.

[–] calidris@hexbear.net 1 points 7 hours ago (1 children)

I didn't say they were all shitposts. Just that it likely consumed shitposts.

[–] zaknenou@lemmy.dbzer0.com 1 points 6 hours ago

https://www.youtube.com/watch?v=7rkiwtQjlVI