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Dreaming is a process of organizing thoughts in new ways. Memories get consolidated, and it happens while our normal connection between our brain and our body is “severed” ... much like our normal connection to time while we dream can be discarded. I don’t believe we see the future in our dreams. I believe instead that our conscious mind struggles to make sense of these more unconscious processes and so applies narratives which DO make sense to us. These narratives are not tied to specific events and so are not anchored to chronology in the normal way our daily experiences are. These narratives and insights and feelings are essentially intuitions that we selectively remember at a later time (“hey... this pattern I’m seeing right now IRL is incredibly similar to that pattern I experienced all those weeks ago in my dream!”). We then call this feeling deja vu or mistakenly describe it as precognition. Its a pattern, and humans are incredibly good at finding patterns even where none exist. Note: This is my own conjecture, not necessarily a representation of the most current research. Apologies for inserting a speculation into a non-speculative thread. Could be both. Hit the quote button.

You have to stop eating fried foods, or drinking coffee, before bedtime, Strange; you have some pretty disturbing dreams. ( I still dream about women )

Yes it helped and I got my answer.

One way of defining cosine is as proportional to the horizontal projection of what you call B in your figure. The segment B would be the one that sweeps the angle. That's why it's zero. The sine of 90º is 1, on the contrary, because the vertical projection of B is just B. The post does answer your question, although it may be difficult to see because it's moving. Take a look at the horizontal projection of the triangle when it goes through 90º.

! Moderator Note The discussion has been going off-topic a fair bit. As such it is closed. If a more focused discussion is desired, a new thread may be a better home.

The ones around our own Gas Giants do tend to have some decent resources or novelties so similar exomoons would definitely be of interest. Realistically travelers would have to be living in space already to reach that far. One that shared a similar atmospheric composition might even be forbidden from inhabitation as that could harm future research into native life.

Photons between conductors have to form a standing wave, so not all wavelengths are allowed, unlike free space. So? The “vacuum” label is there to tell you it’s there even when you have nothing. You generally don’t care about the walls of a vacuum, anyway. The Casimir effect is something that tells you zero-point energy is a real phenomenon. The Casimir effect itself is not the vacuum energy, it’s one result of it.

The actual thermal equilibrium temp of the Earth is -18 degrees C. In other words, without the Greenhouse effect of the CO2 in the atmosphere, The average temp of the Earth would remain below freezing. In addition, an ice ball earth would reflect more Sunlight back into space, reducing the effectiveness of solar heating. Your "evidence" is fatally flawed, as it is based on the false assumption that the Sun alone would provide enough heating at the Earth's present distance from the Sun to keep it above freezing.

This shows lack of proper consideration. How I wish folks would give some proper consideration before they posted rather than just looking in the mirror after one too many pina coladas. Very clearly if the Earth was captured from somewhere else then it was formed somewhere else, before it was (could be ) captured. So this thread is not about the origin of the Earth but about a conjectured later event in its history. Please think before you post.

I'm not a monotone speaker, although one of the best teachers I had at university was a real drone. I mostly use some mime to teach, as a visual aid. Very general teaching tips those you're giving me. Can be applied in lots of cases, me thinks. Although I once had a student who suffered what was announced to me as some kind of geometric dyslexia. I'd never heard of such a thing. We had to circumvent anything that was visual. I can hardly remember a more difficult teaching experience than that. I don't think I did very well TBH. Going back to my student, which I will name A. A couple of days ago we started dealing with optimization problems. We got stuck, as the problems require separation in two very different steps. The 1st one for insight (setting the problem's variables, relating them and writing down the function in terms of one final variable); and the 2nd one, more mechanical, taking the derivatives and solving for the stationary point, etc. Now, there came my mistake. I should have paid more attention to @iNow, because I didn't chose the problems very carefully beforehand, which should have been in a progression from less to more difficult, especially when it comes to insight, which is the most difficult part. Unfortunately both problems were also "mechanically" difficult. Something quite amazing then happened, because A told me after having been pointed out by me what the mistake and the reason for his confusion were, that we'd better turn page and go for another problem (without having properly finished them at all!!!) I said to myself "what the hell?" But then what @iNow and @naitche told me must have resonated in my mind, because I suddenly relaxed about it, thought "what the hell!" and offered him two more problems, much better suited for a warming-up stage. It worked wonders! I just wanted to tell you, people, that your advice has been priceless. Thanks a lot. And A thanks all of you too, I'm sure. It's as if A were telling me: 'don't you remember what these people have told you, you idiot? All your contributions are helping me a lot. As A would say, Follow meeee?

Really? "I submit that much of society has been collectively misled into believing that global CO2 and temperature are too high when the opposite is true for both." (Nice crossover the with racial language thread here as he preempts accusations of "denialism" by claiming that is an ad-hominem.) It is not at the expense of the ecosystem. The current ecosystem has evolved to (something close to) the current (well, recent past) CO2 levels. Global warming (plus ocean acidification[1] due to CO2) is a contributing fact in, for example, the dying-off of corals. [1] "It's not 'acidification', it's 'less-alkalinisation'" they say. What, so it doesn't matter then? I gave it a more accurate title, initially. Then decided I should be polite. The title is "Split from ..." because it is off-topic (and pretty nonsensical).

That's what I think. Art and/or symbolism certainly imply intelligence. But I would make the further qualification that first hints only too reasonably come later than the real thing. The excavations of Homo naledi (335,000–236,000 years ago) at the Rising Star cave in South Africa have shown that, very likely, a stray cousin of ours that looked very much like an upright ape and didn't use tools or made any kind of art, seemed to go to the trouble of carefully placing their dead in an almost inaccessible dead end of a cave where no other fossils of animals have been found. My suspicion is that some "human" attributes go farther back than we dare to postulate. Cautiousness is mandatory, of course.