This is literally that scene from Schindler’s List where the Commandant sits on the balcony and snipes any prisoner below who isn’t laboring fast enough. And for years they were saying this was unrealistic and such crass cruelty could not have happened!

https://piped.video/watch?v=N0DqnUk90lo

There are even over 100,000 distinct chemicals in a banana. Probably over 1M. Horrified whenever I see somebody eat one. Only plastic food pellets for me please.

Ah, I can see OP’s line of thought now:

• you have a point A’ on a plane and a random point A
• you find a midpoint B and draw a sphere around it. A and A’ are now a diameter of the sphere
• pick two random points D and C at the intersection of the plane and the sphere
• by the “triangle inscribed in a circle/sphere where one side is a diameter” rule, such a triangle must be a right triangle
• therefore both angles ACA’ and ADA’ are right angles
• thus C and D both satisfy the conditions of the initial question (with all points renamed: A=P, (C or D)=H, A’=A)
• OP never defined what a projection is, it being “4th grade math”, but one of the requirements is being unique
• C and D cannot both be the projection, therefore the initial question must be answered “false”: just because AH is perpendicular to PH doesn’t make H a projection.

I like treating posts as puzzles, figuring out thread by thread WTF they are talking about. But dear OP, let me let you know, your picture and explanation of it are completely incomprehensible to everyone else xD. The picture is not an illustration to the question but a sketch of your search for a counterexample, with all points renamed of course, but also a sphere appearing out of nowhere (for you to invoke the inscribed-triangle-rule, also mentioned nowhere). Your headline question is a non-sequitur, jumping from talking about 4D (never to be mentioned again) into a ChatGPT experiment, into demanding more education in schools. You complain about geometry being hard but also simple. The math problem itself was not even your question, yet it distracted everyone else from whatever it is you were trying to ask. If you ever want to get useful answers from people other than crazed puzzleseekers like me, you’ll need to use better communication!

PH would be parallel to n

The question doesn’t posit that.

Spoiler alert: the image has no relation to the question, it’s just something OP picked to elicit that “3D geometry” feeling. There is a point A’, a point B, point C, and point D, but no point P or H or n.

quantum computing is revolutionary because it allows instant transmission of information across unlimited space

False and common misconception! In quantum mechanics there is even a theorem called the no-communication theorem that mathematically proves that no information can ever be transmitted by quantum entanglement. Sorry!

12:30 AM GMT 🤡

Gravity—the curvature of space-time—can’t stop changes in the curvature of spacetime from propagating outward.

This is false. If it were true, you could build a device to communicate from inside a black hole event horizon. By waving around a heavy ball you would create gravitational waves that a sensitive enough LIGO outside the black hole could detect. But this is impossible. You would create gravitational waves, yes, but they would fall towards the center singularity same as you, and will never penetrate and escape the event horizon.

The yyyy-mm-dd format (ISO 8601) is the only one that is unambiguous, because no one so far in history has ever used the yyyy-dd-mm format (at least until some xkcd-reading jokester probably will start using it just out of spite). I use ISO 8601 everywhere. It has the additional benefit that filenames get sorted correctly in lexographical order.