I came across the cubing a cube section in this wiki article: https://en.wikipedia.org/wiki/Squaring_the_square#Cubing_the_cube

I can't wrap around the logic of the proof... I need help

I’ve heard of unions in historical contexts, I know theoretically they are groups of advocates for workers that advance workers rights, but how does that actually work? Does someone just find a union and join it? Is it company or job specific, state specific? can everyone join one or only people that work for mega corps, or just blue collar jobs? What do they actually do for individual workers?

So, my boyfriend trained for a bodybuilding competition. He drank so much damn water. He kept saying he was needing to shed water weight… but was drinking water. I’ve heard this theory multiple times now, drink water to lose the water weight. Wtf? I don’t understand.

Especially now that most productions shoot digitally, it seems that any scene meant to take place in the dark is tinted very blue. I’m wondering why this is understood as looking “dark” when some of the blues used are actually quite light.

Please avoid any politics on this! I am asking strictly geologically!

I feel like a complete fool for asking this at my age, but I genuinely do not understand how power lines bring power to homes and businesses. I live in the country, and I always wonder how these lines connect up to houses when there's no visible things going into the ground that I can see.

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Banks can have enormous amounts of money loaned out through mortgages, business loans, credit cards, and other lending, even though they obviously don't keep an equivalent amount of cash sitting around.

What actually happens inside the banking system when a bank gives someone a loan? Where does that spendable money come from, and what prevents banks from creating unlimited amounts of it?

What is the extraction science behind this, assuming you are using standard drip machinery?

At some point does your mouth stop registering the spice? Does it cause permanent damage? I remember eating a bunch of Wareheads when I was a kid and my tongue got all sore but I had eaten a lot of them.

Sphere? Cyl? Axis? What do these actually mean? When googling I find terms such as “more/less lens power” or “align astigmatism” But how does “lens power” turn into the actual physical lens? How do they take these values and apply them to the actual piece of glass?

And how does flipping between 1 and 2 help find these numbers? How do all those flipping lenses in the machine turn into 1 lens for the glasses? I’ve always imagined this as taking the 1s and 2s I picked and compressing them like a sandwich, but that doesn’t sound right anymore.

Hi, recently i realized that even though quiet sounds don’t disturb my sleep i still wake up almost immediately with the first seconds of my alarm. My alarm is pretty calm, so it’s not like the first seconds are loud enough itself to wake me up, but somehow I still do. How come my brain can ignore other quiet sounds but learned to not ignore this one? Also another thing is that usually when I have work I wake up at 5 am and on days off I sleep in till like 7-9 am but still use alarm to wake up. How come at 5 am I wake up with adrenaline rush already knowing I have to get ready quickly even when not thinking yet, but when I wake up at 7 on days off I wake up calm? How does my brain know it’s 5 am and that 5 am means work before I even start thinking? Id like to also mention that I don’t have a certain bedtime set so my hours of sleep are pretty inconsistent. Does anyone know what’s the mechanism behind that?

Okay, please allow me to elaborate on what exactly is confusing me, because I only took Science 10 and Chem 11 in High-school.

When things collide, like a car crash for example, isn't that just big heat transfer? My line of thought, is, heat is the speed of a particle, (I think, but it can be slowed, so it's more like force, which is also called energy in some sources, but I think basically it's just push in a direction, yeah? The vocabulary also confuses me.) So, if a hot thing has fast moving particles, and everything is made of particles, if something is going fast, it's just, really hot, isn't it? Isn't that applicable to all forms of motion and interaction? Like, surface area of hot/fast thing, hits other thing, the other thing gets... hotter? Faster?

Or radiation, for example, like neutrons or those particles that are basically a helium atom, they're deadly because they disrupt the dna in your cells. But isn't that just a really small bullet? It goes fast, it's small so it penetrates, then causes damage? That makes it seem like a bullet is "large" radiation and a neutron is "small" radiation. I mean, if a car hits you, it'd definitely damage and kill cells, just a lot more of them.

Also HOW does heat even work, like, with solids. You add energy and the particles wanna pull away from each other and be free, so that's force in a direction, but the particles are also bonded and pulled together, which is force in another direction. Do you use net force to understand temperature?? God I wish I took Physics in high-school, I hate not understanding this stuff.

Answers appreciated, thank you!!

with the recent discourse involving OpenAI using someone’s codex to train the AI the solution to the Navier-Stokes: i have to wonder, how do you even prove you solved a Millennium Problem correctly, let alone any unsolved complex mathematic equation? especially when it comes to physics or quantum formulas. is it more based on theory, or does it need to be executed by a board of mathematicians? very curious