Genady

I have tried several projects in Zooniverse. Was not impressed by a depth of their science. Simple surveys of images. I wonder if there are published research papers where the authors acknowledge citizen scientists' contribution or even specifically Zooniverse.

To make clear: not the university profs, but the high school teachers who were students in the program. Nice trick. And good for you. But this is a relatively innocent cheating. What I saw was steeling and getting credit for other people's work. Some plagiarism was just ridiculous, like copying stuff from Wikipedia. But some other was "ideological". E.g. a woman was caught copying paragraphs from published papers on biological evolution. It was so bad, that she was expelled. In her last message on the board she said that she doesn't care because she doesn't believe in this bs anyway. 50 something years ago? Looks like we are about the same age.

There is no question here, but I'd like to see comments. It is about my unpleasant experience in an M.Sc program in one of the US universities. Not an ivy league school, so relatively inexpensive. I was an out-of-state student, I guess it was even less expensive for the in-state ones. About half of the class were regular kids while another half were high school teachers who needed the degree to be able to teach in a higher education. I didn't have any prior experience in US schools, so maybe I'm not going to say anything new, but it was completely unexpected for me. The program was good, the professors were excellent, but the students... many of them routinely plagiarized in their work. In the beginning of the program everyone got a paper with explanation of plagiarism and expected degrees of punishment. I guess, the school knew about the problem. Everyone signed a statement of understanding, but they plagiarized anyway, and some actually were caught and punished. Not all, though. So, if teachers did it, it is to be expected from their students. And it is to be expected to spread out and to become a part of the culture...

It was not my answer, unfortunately. Somebody has shown it to me, and I was curious to know, how easy it is to find it.

No, I don't. Here is why. The question is: are there such irrational r and s that rs is rational? Consider two possibilities. 1. r=sqrt(2) s=sqrt(2) If rs = sqrt(2)sqrt(2) is rational then this answers the question. 2. If sqrt(2)sqrt(2) is irrational, then r=sqrt(2)sqrt(2) s=sqrt(2), and rs is rational, answering the question.

I don't. But if it is not, then we take r=sqrt(2)=s, and rs is rational. Which answer the OP. One of the two has to be rational, and this answers the question.

The following answer doesn't require number theory, Euler, or complex powers, just algebra: r=sqrt(2)sqrt(2) , s=sqrt(2) Either r is rational or rs is rational. So, the answer to the OP is, Yes.

Yes, it answers it. If we know that logπ2 is irrational. I got a simpler proof, without that knowledge: r=sqrt(2)sqrt(2) , s=sqrt(2).

I am interested to know if there are two real irrational numbers r and s such that rs is rational. The comment you refer to is a reply to an attempted proof above that:

OK. I just don't see yet that (-1)-i is a rational number as per definition "a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q."

I thought about it, but I don't know if πi is rational or irrational. To make it well-defined, let's stay in the real numbers.

Can the thing in the title be rational?

This is exactly what math is -- investigation of such features which do not depend on implementation of a system. This point seems to connect back to another recent thread. Perhaps, Navier-Stokes equations are not derivable from the molecular level, but a system behavior that these equations describe is. As if we had a gigantic computer which could simulate evolution of a system of billions molecules of water, a macroscopic behavior of water would appear in the output.

A state of two quantum-entangled particles is irreducible? unpredictable? novel? emergent? The question marks are to indicate that I'm not certain in meaning of these terms. However, I'm certain in the meaning of terms "state of two quantum-entangled particles".

I wonder, is it in fact useful? When? Where?

This is correct. Approaching a neutron star, there would be a similar but less intense curvature. Moreover, approaching any star (or anything else for that matter) there is a similar, but much less intense curvature. The gravity in empty space around any radially symmetric mass has the same shape and only differs in intensity.

Yes, it would be the same gravitationally. Same with the black hole, too.

(1) THE SHINING (1980) - "All work and no play makes Jack a dull boy" [HD] - Bing video jk However, Computer Engineering? It is better than accounting, but still... Did you consider that may be this subject is not your forte? or your bliss?

In fact, it is overexplained. There are many different explanations, sometimes overlapping, sometimes inconsistent. My OP generated a small survey of what some members here pick as their favorite explanation. It turned out to be a subset of explanations existing "on the market."

First of all, thank you for the correction. I like it. And, yes, I also think that it (something being emergent) refers to phenomenon rather than to our description of it, including all the circumstances that the said phenomenon needs in order to occur. Then, the criteria of a phenomenon being or not being emergent should not depend on how we describe it and what we know or need to know to describe it. In other words, the criteria should be about the phenomenon and not about us.

Thus, there are things which are emergent as per less specific criteria but not emergent as per the more specific one.

Now I see where all (my) confusion in the earlier discussion came from -- I never seriously related to the word "unreasonable" and saw it just as metaphoric. In the article Wigner talks only about unexplained effectiveness.

So, this criterion is different from:

Does a phenomenon become 'emergent' after we find a way to describe how it emerges? If a condition for a phenomenon to be emergent is to "be described without knowing or needing from what they exactly emerge", and the evolution of a wave function is a phenomenon that is "described without knowing or needing from what they exactly emerge", how come that this phenomenon does not qualify as being emergent?

Do 'regularity' and 'existence and uniqueness' mean the same?