studiot

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.

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

I am not sure if I proposed an atom bomb explosion as an emergent phenomenon back along but the echange at 'critical mass' is such a change. (Just fancied a change from my arch as a conversation subject)

Testing in the UK is far more complicated that this and has been subject to different rules at different times throughout. Further the government has just announced that the lateral flow chromatography will now be accepted instead of PCR, for the political expediancy that it failed to provide suficient proper tests which are now being rationed. I say proper tests rather than PCR because up to 1/2 million health workers and 1.5 million social care workers are regularly using an alternative to PCR - a saliva test - as a matter of course several times a week. This is still a laboratory test but results are returned much more quickly. Also the UK has remained very open to travellers in and out during the whole pandemic. This has been 'controlled ?' by a PCR testing regime, more stringent than for the general population at large. Finally some employers have been funding their own worker testing regimes. However the tests are conducted, the results are all supposed to be reported to the government, though not everyone does so.

Thank you for the replies. There is another more worrying possibility that is the reason I posted. I note no one has replied to my comment. We had a long period of level or slowly declining cases, hospitalisations and deaths until 3 - 4 weeks ago. Too many thought that meant it was the beginning of the end and began to relax. Then the case rates skyrocketed, but the hospitilisations did not go up. 3 weeks ago I watched the hospitalsations go through the 6000 barrier. Deaths still steady at about 50 per day. Then hospitilisations started rising fast but deaths kept steady. Last week deaths started rising into the low hundreds. 3 days ago we had 1000 deaths and are now in the higher hundreds. Furthermore we now have several treatment drugs in use that were unavailable in the first two waves. Looking at the small amount of current data I wonder and fear that omicron simply takes longer to work it harm.

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

Thank you. I also realise another characteristic of emergence I haven't mentioned. If you some bricks, you can build some sort of structure, even if just a pile. But unless you have enough bricks you cannot build an arch. In other words, the emergent phenomenon only emerges when all the necessary precursors are in place. The change from no emergence to emergent is sudden. This is consistent with the link to Catastrophe theory I referred to earlier in the thread.

Here are today's UK figures from the BBC Note how the hospitilisation and then deaths lag behind the cases, but they are now catching up.

I haven't used it for a while but Redo-Backup is free (open source project) and works really well. https://sourceforge.net/projects/redobackup/ You make a byte by byte copy of the entire or part of the hard drive or chosen partition onto other media such as DVD/USBstick/Hard drive (spare) etc. Then the backup software copies the other way when needed and handles wiping and repartitioning you hard drive automatically. Unfortunately it won't do servers.

Wow ? Is this an example civility left over from your defunct forum ? You referenced the Stanford Encyclopedia of Philosophy, to which I pay a subscription.