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.
How often do you think most people need to know the advanced mathmatical properties of 3d space?
I think it is a shame that I’m a math student in university and needed to verify about such a thing. And if we’re talking about people doing physics it might be even worst if they suck like me at 3d geometry.
Math students in university need to verify basically everything, that’s a lot of what the career is about. I remember being humbled when asked to prove something as familiar to everybody as -1 * -1 = 1
hhhh abstract algebra and proof writing courses.
I mean, we live in it. It comes up in practice fairly often.
We use plenty of simple geometry everyday, sure, but you don’t need to be able to even understand what OP’s example says to engage with the world. Like you don’t need to provide a mathematical proof to put a shelf up properly.
Besides understanding what a projection is, I’m actually going to say that’s all pretty important stuff to know. A point, forming a line between points, how to describe a plane and what perpendicular means.
If you want to do graphics projections suddenly become very important, but sure, you can explain carpentry without it. Although if you want to draft the solution first the concept will be at least relevant.
Kind of a separate issue yet. Even with OP’s example, you can explain the solution in natural language pretty easily, but the obvious way to formally prove it would be with linear algebra.
How many people do you think are working in computer graphics? It’s specialised knowledge, exactly the kind of thing that should be taught at university to the people it’s relevent to.
It’s not about how you phrase the solution, it’s about needing the solution at all.
Yeah, agreed, but like I said most of this is not advanced or specialised.
Let me guess, you’re the kind of person who thinks we need to understand gravity to make use of it.
I really wish people like you could just have their mouths taped shut and their fingers glued together.
That’s pretty mean, bro/brah/other.
Even in the days of catapults, rough formulas for the effects of gravity made them work a lot better. Knowing “it goes down” can do a bit, but not everything. If you somehow didn’t even know that it would be useless.
Your misunderstanding comes from the type and amount of people that needed to have that knowledge.
For example, we don’t need to know about ballistics to use a gun.
Do you have a source for this? I’m genuinely curious, considering Newton didn’t show up until the 17th century.
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.
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.