Genady

Just want to share what the great man wrote about it:

"That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers."

(It stayed open for 250 years.)

8 hours ago, shivajikobardan said:

It takes me 45 minutes to read 3 paragraph and comprehend it at least.

If a research paper is good, this is about the right amount of time. Comprehending a good research paper should take time.

However, my experience is from different fields than yours, so maybe it doesn't apply.

3 minutes ago, studiot said:

Personally I don't think that's good enough support.

Can you not take one of these proposals and say what characteristic of emergence it matches and under what circumstances.

'Hocus Pocus' belongs on the Magic Circle website, not the Physics section of SF.

Sorry, no, I cannot. This is the only characteristic of emergence I assume: not to be a result of direct application of other laws, but to be a consequence of some elaborate and not obvious mathematical construction built upon other laws.

In the examples above these constructions are: statistics, Noether theorem, antisymmetry of fermionic wavefunctions, and Lorentz invariance of wave equations.

1 minute ago, studiot said:

You have put forward a large collection of phenomena as emergent.
So I look forward to your elaboration as to why they are emergent  in support.

They are emergent, according to the proposed approach, because they are consequences of some mathematical "hocus-pocus" rather than straightforward results of other laws.

No, I cannot clearly define "hocus-pocus" vs. "straightforward". Maybe these are not objective attributes, but rather how the things appear to us.

53 minutes ago, studiot said:

I think that 'cause' and 'scale' are extraneous parameters that do not bear upon 'emergence' or have at best only the loosest of connection to it.

I think so as well. I propose here a different approach:

A phenomenon appears emergent to us if it emerges as a consequence of some mathematical "hocus-pocus" rather than a straightforward result of other laws.

Such are all statistical phenomena: entropy, statistical distributions, blackbody radiation, Bose-Einstein condensate, superfluidity, superconductivity, ...

Such are conservation laws emerging, via Noether theorem, from symmetries of the system's Lagrangian.

Such is even a familiar phenomenon that solid materials do not collapse in on themselves or on each other. There is nothing emergent about it when it is erroneously explained by electrostatic repulsion of outer electrons in atoms. But it is emergent when viewed correctly as a consequence of Pauli exclusion principle, which in turn is a manifestation of antisymmetry of fermionic wavefunctions. 

Existence of mater and anti-matter is an emergent phenomenon too, because it is a required in order for quantum wave equations to be Lorentz invariant.

12 minutes ago, TheVat said:

A popular example is a mind having the thought to take some action - this is viewed, by strong emergentists, as thoughts having causal power with downward causation through lower levels (neurons, synapses, action potentials, etc.) ... I am not asserting any of this as valid, just (like you) exploring some implications.

Mind affecting brain would mean that atoms and molecules disobey laws of physics, unless mind is a new fundamental field.

(Exploring implications as well.)

1 hour ago, Peterkin said:

To me, the issue was the purpose of a school assignment. It's not that the teacher wants to see pictures of fishing boats and read articles from the National Geographic; it's that the student should learn about Atlantic fisheries. My teachers, back in the Dark Ages, held that I would retain more of the information if I hand-copied the illustrations and rendered the text into my own words. If there was an element of creativity involved, we got extra praise. There was a sense of achievement, too, that was missing from my children's school experience.

We've taught children how to cut out pictures by the time they graduate kindergarten. Why waste another 12 or 20 years educating them?

The same with math and physics. If one reproduces a derivation with their own hand, it gets imprinted in memory forever. In most cases, you don't need to memorize a formula - you can just quickly rederive it.

19 minutes ago, dimreepr said:

... part of the equation for evolution to predict the next branch of the tree ...

Is there a way to predict a next branch of the tree in biological evolution?

23 minutes ago, swansont said:

There’s nothing wrong with using pictures, drawings or passages made by others (sometimes it’s unavoidable) But you need to give citations for them, and not present them as your own work.

Absolutely right. However, one shouldn't get an A for compiling works of others, unless such compiling is a goal of the assignment, should they? 

The thread about wire black corals' chirality is done, but here is another picture I took back then:

1 hour ago, Markus Hanke said:

Well, this is what we assume (of course with good reason) would happen - but how can we show this?

G: ... 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.

M: Well, this is what we assume (of course with good reason) would happen - but how can we show this?

G: By building such a simulation, or an approximation, and let it run. There is a very successful computer simulation of the Universe evolution, with creation of filaments, voids, super clusters and such, with 2.1  trillion “particles” in a space of 9.6 billion light-years across for more than 13 billion years.

On 10/25/2021 at 9:29 AM, Yevgeny Karasik said:

Mathematics is the science about equal dualities. In other words, axioms of any mathematical theory can be replaced with another set of axioms, each of which asserts equivalence (or equality) of dual expressions. This fact has nothing to do with duality principles in various branches of mathematics. 

commercial linked removed per Rule 2.7

Wow! It's a small world after all. This person used to be a classmate of mine around 50 years ago.

11 minutes ago, Peterkin said:

When my daughter was in Grade 12, in the late 1980's, she had a history project. I insisted - in spite of tears and slammed doors - that she draw ever picture and write every word herself.  It turned out very well and she got a B. Later, I saw the A papers on the bulletin board in her classroom. Every one had paste-in pictures and articles cut out periodicals. Apparently, the teacher was already less clear on the concept and a lot more flexible in the definition of "original work" than mine had been a few decades before. 

Sad.

On the other note, my daughter was in Grade 12 in 1995... Now I'm starting to see why these forums are more interesting than some others.

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. 

37 minutes ago, swansont said:

The teachers did it?

To make clear: not the university profs, but the high school teachers who were students in the program.

36 minutes ago, studiot said:

The question of cheating is as old as education itself.

I do know that at least some universities have adopted methods of countering the latest wave via the internet either buying essays etc or just blatantly copying of the net.
However I won't detail any to avoid this becoming a cheat recipe book for casual readers.
 

Don't forget that the staff are also intellingent folks too.

I will relate a different form of cheating from 50 something years ago.
In my first year we did a lot of wet chemical analysis, using standard reagents prepared by the lab techs.
One such session I couldn't get my titrations to work out.

I chose to report my results as observed anyway.

The following week, after marking (that took longer back then), almost everyone except myself was marked down for haveing fiddled their readings to get the correct (expected) results.
I actually had appropriate results for the reagents actually supplied.
The staff had deliberately mislabled them becuae they suspected dreading s were being doctored on a large scale
 

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...

1 hour ago, joigus said:

OK. I see. Why didn't you just say that was your answer from the beginning, instead of giving it piecemeal?

You had this 'question' all ready with the answer and all. Then you ask a question pretending not to know the answer.

The answer is kinda obvious TBH. You can find about infinitely many possibilities to do that. I gave you one that's pretty obvious too. About as obvious as the fact that 2–√ is irrational, which you haven't proved either. Yes, that's a result in number theory too, and you're resting your answer on shoulders of giants.

(pi)^rational cannot give you a rational is pretty obvious to me too. Proving it rigorously is another matter.

You, though, for some reason, don't like the argument. You prefer yours, (which is to come pretty soon.)

You reappear then in intervals of less than one minute declaring that your answer is the answer, and it's simpler than everybody else's. Your answer in every step is, of course, flawed unless you provide the looping argument which is your final effect. Then you pull the rabbit out of the hat that you've been silent about for the whole conversation. 

Voilá! --Applause. 👏👏👏

To me, it's been a considerable amount of time down the drain. I have better things to do.

Cute.

Thank you.

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.

Just now, joigus said:

Not quite: If it's not, then it's rational. Then you use your algebra and you prove that some 'rational' you've found, raised to sqrt(2), gives a rational.

You need to prove that 2–√2√ is irrational in order to make that claim. See my point?

No, I don't. Here is why.

The question is: are there such irrational r and s that r^s is rational?

Consider two possibilities.

1. r=sqrt(2) s=sqrt(2) If r^s = 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 r^s is rational, answering the question.

Just now, joigus said:

How do you know 2–√2√ is irrational?

I don't. But if it is not, then we take r=sqrt(2)=s, and r^s is rational. Which answer the OP.

One of the two has to be rational, and this answers the question.

25 minutes ago, studiot said:

 

I didn't think of that.  +1

 

There is a more detailed discussion here.

I am not an expert on number theory, I find the minutiae rather boring after a while.

https://math.stackexchange.com/questions/823970/is-i-irrational

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 r^s is rational.

So, the answer to the OP is, Yes.

7 minutes ago, joigus said:

Ah, OK. Yes, that can happen. Studiot gave an important clue, I think. Think Euler.

I think you will agree that logπ2 is irrational. Take r=π and s=logπ2 . Then,

 

rs=πlogπ2=2

 

The fact that πx=2 cannot be solved with x rational should be easy to prove by contradiction.

Edit: Actually, I don't think it's 'easy', it's a somewhat elaborate result of number theory.

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 r^s is rational.

45 minutes ago, joigus said:

You said an irrational raised to an irrational. (-1)^-i is a negative integer number raised to an imaginary (complex) number. Both can be done. One is more sophisticated. Which one is your question?

For example, (−1)π presents its own challenge. Which one are you interested in?

It's better perhaps to tackle directly zw with z,w∈C .

The comment you refer to is a reply to an attempted proof above that:

1 hour ago, studiot said:

Can't see why.

e and pi are irrational (and also trancendental but that is irrelevant here).
i and 1 and 0 are all rational.
So proceed as follows

eπi+1=0            Euler

Rearrange

eπi=−1

Raise each side to the power -i

(eπi)−i=(−1)−i

Which is

(e−iπi)=(−1)−i

Which is

eπ=(−1)−i

Which is an irrational number raised to an irrational power expressed as a rational fraction of two rational numbers.

 

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."   

2 minutes ago, studiot said:

Are you referring to euler's identity ?

eπi+1≡0

 

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?