Genady

Right. Back of a very tiny envelope calculation shows that to have a drop in acceleration 1% over 10 m the radius needs to be 1 km. Here comes the real question: How do I type Greek letters here? I wanted to put 'omega' for the angular velocity...

What my question (see above) relates to, can be found in a variety of sources. A "simple", Feynman-style explanation on how the principle of least action emerges in the path integral picture, is in his book "QED: The Strange Theory of Light and Matter". On pp.42-45 he applies this picture in an example of reflection of light and "derives" the principle of least action, in this case. He concludes, "And that’s why, in approximation, we can get away with the crude picture of the world that says that light only goes where the time is least" (p.45). More generally, on p.123, "This brings us all the way back to classical physics, which supposes that there are fields and that electrons move through them in such a way as to make a certain quantity least. (Physicists call this quantity “action” and formulate this rule as the “principle of least action.”) This is one example of how the rules of quantum electrodynamics produce phenomena on a large scale." More formal derivation is in Zee, A.. Quantum Field Theory in a Nutshell. On p.12, "Applying the stationary phase or steepest descent method ... [to a path integral] we obtain ... the “classical path” determined by solving the Euler-Lagrange equation ... with appropriate boundary conditions." (I've removed the math expressions.) Edit: After re-reading these sections in the books I got the answer to my question. Thus I don't have any more open questions in this thread.

Thank you very much for a very good explanation of what the principle of least action is. Unfortunately, it doesn't relate to my question. But it's OK. You don't necessarily know what my question relates to.

I remember that stationary action "emerges" from the Feynman path integral. Doesn't QM "explain" it?

Do you mean a station is spinning to create 1G at the circumference? Then, acceleration of a circular motion is v2/R. Equate it to 1G and find R for a given v.

I think it does. Why do you think it's weird?

You never need to quote. You just say something like, "Since the process is irreversible [4], ...", where [4] is in the References at the end of your manuscript, directing a reader to the source of this clause.

Scientific journals, at least in this field, also discourage authors from submitting manuscripts with unnecessary quotes.

I've noticed this alien looking "thing" slowly drifting along the reef at the depth of about 10 m. It was about 4-5 m long, 30 cm in diameter. A flexible, hollow tube, so one could put an arm into it. Which I did. Here are more pictures, with a dive buddy of mine for a scale, and some closeups: It took me a while to find out, what it was. Egg mass of a diamondback squid, Thysanoteuthis rhombus.

It sure is. Good luck!

Plants evolved from organisms which were not plants. The not-plants also evolved from organisms which were not plants. The bottom line is, not-plants did not evolve from plants.

No, it has not. Plants split off early from the rest of life. Schematically, so:

Expanding on and paraphrasing the @MigL's statement above: As a mathematician, "I'm not overly concerned with the 'why' of a paradigm, or set of rules, only its 'function'." "Math is simply a tool for describing/investigating the world" of absolute truths, which are independent of the world around us and thus hold and can be trusted when investigating new, unfamiliar worlds.

If I remember correctly, we have an area in the brain which is activated for basic counting - small quantities, comparing sizes, amounts, etc. This area is separate and removed from the language areas, and the two get activated independently in different situations / tasks. This does not support the view that math is at the basis of language. In addition to this, the quantifying systems and languages come in a variety of sophistications in different cultures. In some, language is very rich and complex, while counting is very limited. In others, vice versa. Again, not a refutation, but doesn't support the hypothesis.

I wonder how it is in fishes? E.g. in this Flying Gurnard I saw (in spite of being "Flying" it is a fish, not a bird )

Gerard ’t Hooft has created this website for you: How to become a GOOD Theoretical Physicist (uu.nl)

Don't 'we' understand the difference between a phenomenon and an equation?

@joigus is correct. However, would you elaborate on your question and on how it relates to that quote?

It looks like concepts in geometry are idealizations of perceptions and intuitions about space, concepts in algebra are idealizations of perceptions and intuitions about counting, and concepts in analysis are idealizations of perceptions and intuitions about acting.

Yes, I did. It has a beautiful and appropriate name, Voluta musica. Here is Wikipedia article about it. BTW, this article doesn't list "my" island in their distribution. Also, it appears that my specimen was especially large, and at a more shallow depth. Voluta musica - Wikipedia (att. @StringJunky)

What do you mean, Humans are important: All humans are important all the time All humans are important at some time Some humans are important all the time Some humans are important at some time ?

On top of that, having many quotes, even with citations, was discouraged. Not as a plagiarism, but just as a sign of laziness. You better interpret and say it in your own words., with reference to the source.

Zee, A.. Einstein Gravity in a Nutshell: "the equivalence principle leads us directly to an understanding of the gravitational field as a manifestation of curved spacetime." (p. 280) "the gravitational field and curved spacetime are effectively the same thing." (p. 285) "We could say that there is no such thing as gravity, only curved spacetime. But you could say with equal justification that spacetime does not exist; there is only the gravitational field. To me, it is just a matter of words, and the only relevant issue is which language you find more useful to think in." (p. 285) "In Einstein’s theory, the gravitational field is equivalent to curved spacetime." (p. 302) And so on.

Yes. And my picture, being made with an unprofessional equipment, doesn't convey the whole beauty. Plus, the real thing has an extra effect being in fact three-dimensional. I was watching it until I ran out of air. (No problem at 3 m.) They were crawling see floors long before Minoans. Hmmm... They are very rare now. For an obvious reason, I think.