studiot

Well that would make all mathematicians plagiarists. But then I suppose we are very fond of plagiarizing the phrase 'if and only if'

Can't see why. Swansont has already told you the essence of how to do it, collect enough energy from the wind. As an observation he also said So a 'lighter than air' balloon would make the collection burden easier.

Personally I'd be more worried about the chemicals allowed in bottled 'beverages' than either salt, soap or vinegar. More especially if you drink a lot of them.

Lots of great comments here. +1 I will add to just two of them. 1) Dry suits can come with weighted boots, especially those meant for fixed air lines. 2) I had to drop my weight belt once in an emergency. It was an expensive exercise. However if you are multiple diving diving a fixed site (perhaps with a line) you can leave your weightbelt on a line or for others to haul in or even have a system of hauling up bottom sourced weights with each dive, and dropping them back again at the surface.

Is this a genuine puzzle/brainteaser or is this a genuine physics question ?

What aspect of GR makes it a field theory ? In other words what properties specified and used in GR form this 'gravitational field' ? It should be noted that when GR was published in 1915 it described no such properties and did not conform to the then still developing definition of a Field Theory formalised by Kellogg in his 1929 book "Potential Theory". This definition was in use for most of the 20th century. In order to turn GR into a Field Theory it is necessary to modify both GR (via a non linear Lagrangian) and the definition of a field (theory). Quite a lot of progress has been made towards this in the last few decades and there are postgrad lectures on the subject at MIT, including youtube lectures and padf papers. https://www.google.co.uk/search?q=Donoghue+effective+field+theory&source=hp&ei=SGfdYZDOCbyEhbIP06GW8AI&iflsig=ALs-wAMAAAAAYd11WKFROtIycqoYvDENHbw-KziO8FkI&ved=0ahUKEwiQktPJyan1AhU8QkEAHdOQBS4Q4dUDCAg&uact=5&oq=Donoghue+effective+field+theory&gs_lcp=Cgdnd3Mtd2l6EAMyCAgAEIAEELEDMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDILCC4QgAQQxwEQrwEyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEOgsIABCABBCxAxCDAToOCC4QgAQQsQMQxwEQowI6CAguELEDEIMBOg4ILhCABBCxAxDHARDRAzoLCC4QgAQQxwEQowI6CwguEIAEEMcBENEDOggILhCABBCxAzoICAAQsQMQgwE6CwguEIAEELEDEIMBOggIABCABBDJAzoFCAAQkgM6DgguELEDEIMBEMcBENEDOgUIABCxA1AAWJ5jYP5maABwAHgAgAGmEogBuDSSAQkwLjQuOC0yLjGYAQCgAQE&sclient=gws-wiz A new term "Effective Field Theory" has been coined, but note the caveat (from Wikipdia) it is an approximation to the real thing. @geordief you have +1 for one post, have +1 for the other as well for being brave enough to ask rational questions. Edit I should add that Effective Field Theory is not quite there yet, nor is it (yet) mainstream. But it does answer Markus' points about scale, local v global variables and quantum considerations.

So just as I said Lecture 1 contains many things, including analysis and synthesis.

Yes, and when I do (it's nearly one hour long) I will not misrepresent what he (or anyone else) says, and I would expect to learn something I did not already know, even though it was only lecture 1 of 30. I have already said that it seems a good course, and its also free. I note from the transcript that both analysis and synthesis are defined and contrasted.

Studiot Genady This most definitely appears to contradict my comment yet Stanford I have underlined the relevant words in the topics list appearing under lecture 1.

I did indeed state that fourier transforms are applied maths. You have contradicted that statement more than once now. I have also pointed out that the very words in the link you provided state explicitly that fourier trnasforms are applied maths. I even quote the passage from that link. Yet you seem to maintain that fourier transforms are not applied maths. Have you ever studied fourier transforms at all ?

Then you were not clear enough.

So you disagree with the quoted statement from your own link ? It refers to manynthings. Please don't sidestep the issue by implying that there it refers to only one matter. Did you ever take this course ?

In an affort to stay on the topic of emergence, I looked carfully at the Wikipedia entry on emergence. https://en.wikipedia.org/wiki/Emergence It looks like other members have also looked there since I note several terms (words and phrases) that have been mentioned here. Two things stands out. A) Apart from also discussing emergence in non scientific contexts, Wiki offers several ancient and also very modern contradictory accounts and definitions of emergence in the the Sciences. B) About the only characteristic of these different emergent characteristics seems to be the notion of emergence being the result of a combination/interaction of parts which do not themselves possess this characteristic. This second point begs the immediate questions How many parts are required? Is the process reversible? That is can the emergence disappear if we revert to a collection of the parts? Can we actually revert to or recover the original parts? However though Wiki is rich in general statements, it is poor in detailed examples. So taking my exples of an arch and an atom bomb and comparing them I note For the arch the answers are Minimum 1, no upper limit Yes the parts may be deconstructed and reconstructed as many times as required Yes For the atom bomb Many parts are required. The actually number is statistically detemined. No No The actual parts are destroyed in the emergence

I don't think anyone suggested they are applied maths. Fair enough, not me then. Now how about properly addressing my points and making a discussion of it ?

Well I think you implied that in your words, so I highlighted the word 'pure' - which you did use - in my reply. Pure Maths, by definition, does not include Applied Maths, which you also referred to in relation to 'concepts'. I don't think I defined anything so I am not sure about your last line but taking your second line I would say that vector spaces are the "pure maths", and fourier transforms are the "skillfully operating with it to get deep and rich theorems" In other words the applied maths. Thank you for this reference, I expect it is an excellent course. Edit A quick look at this course suggests that it is pretty comprehensive. It also states in so many words that this is an applied maths subject, firmly based in StanfordEngineering Everywhere no less. Lecture 1 refers to 'analysis' and 'synthesis', a subject distinction you to seem to wish to avoid. When I studied the Integral transforms in general I was following a part of my math degree called 'Linear Analysis' which had both pure and applied components. The pure componet was represented in the course texts by Nering and by Hoffman and Kunze. The applied component was represented by the text by Keider, Kuller, Ostberg and Perkins. Needless to say the integral transforms came in the applied component. However my main objection to your 'rule based' approach is that it is 'static'. Adopting this therefore precludes the study of process in Mathematics, process being a dynamic object. This approach is therefore akin to studying only statics in Mechanics, and ignoring dynamics and all that dynamics introduces. Finally another member recently tried to categories the parts of Mathematics, you may wish to look at their thread.

Yes, I do. So why did you list the Fourier transformation as a fundamental concept ? It is simply a skillful operation of the vector space concept.

A vector space is certainly a mathematical concept. Do you know what one is ? I'm sorry but I can't go along with this rule based approach you seem to have to everything in Science, including it seems, Mathematics. It has its place, no more no less. But there are plenty of other aspects that are not rule based. The Ancient Greeks thought all of Maths was founded in Geometry and this view prevailed until recently, although it was steadily eroded by other branches in the last couple of centuries. In the early 20th century there was an attempt by certain sections to regard Algebra as the foundation, with everything being expressed in terms of Algebra. Developements in the second half of the 20th century showed how untenable such a goal was.

Very interesting and perceptive comments added to the discussion. +1 The Principle of Reversibility. Can you also incorporate the Reciprocal Theorem somehow ?

+1 Well I hope you recover better than this 9 year old girl. https://www.bbc.co.uk/news/uk-england-somerset-59842304 GET WELL SOON.

+1

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.

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.

Sure. Two members of my family are engaged in that routine so we have a pretty good idea of what goes on. The response and efforts by properly trained technical staff in the UK NHS has been oustandingly good. The support provided by the politicians has been considerably less effective, even to the point of getting in the way sometimes. Just before last Christmas, I had an operation at a specialist clinic that had been set up some years a go as a public- private partnership that has been outstandingly successful. The clinic, some 50 miles from me, was set up to relieve pressure on routine operations being displaced by emergencies at local general district hospitals. The regime at the clinic is even stricter, and they proudly told me they'are a green site' which means they have no covid, nor have they ever had any. In order to be allowed through the entry door I had to drive to a temporary shack just ouside ( a bit like a bus shelter) just for them to take a PCR sample. They would not accept anyone else taking or processing the sample. I then had to wait 3 days for the results (they actually came in 2) and self isolate whilst I was waiting so that the were sure I was clear on the day of the op. Needless to say their careful procedures extended to the op itself which went smoothly according to plan.

I disagree. Even in the best achievable system, some data will go astray. But in the NHS the standard is to undergo their test twice a week for non frontline staff and up to daily for sharp end covid staff or they may not/cannot go into work. The sample kit is collected from the hospital/clinic/surgery with a serial number and attributed to a particular staff member via a scanned QR code or similar, which then attaches to that staff member and test. The log goes automatically to the controlling system. The staff member cannot 'not submit' for very long before action is taken. So the amount of data going astray will be very small indeed, rather than 'often' as you portray.

I would like to draw out a few points being made in different ways by members and add some comments to them. Firstly I think it is important to distinguish between plagiarism at school and plagiarism at college or university. This is because at school pupils are forced to 'study' many subjects they have little or no interest in or use for. Once at college most (though not all) are studying for something they need, not something they want, in order to earn their living. To take the college situation first, one way to counter plagiarism is to separate the college exams from subsequent state exams that allow them to actualy practice their chosen profession. As a for instance, you can spend 3 - 5 years getting top marks (by cheating) pursuing a Batchelors or Masters in Pharmacy at one of several Universities in the UK. But you cannot practice until you have passed your 'registration' exam (which has a significant failure rate first time around). This exam has a rigorous anti cheating format including specifying a specific non memory, non programmable, calculator, no mobile phones, offsite exam centres etc. Essays are not required in this exam it is a test of competency. At school a pupil might have little knowledge, virtually no skill and absolutely no interest in a forced subject for example Music. Yet that pupil needs to obtain some minimum score. So is it little wonder they will take any route to gain this score, including cheating if the opportunity presents ? This situation has been present in schools since time immemorial.