studiot

Hello Col and welcome. +1 for a good start, I look forward to further worthwhile contributions. I've been a member since 2012 and in that time I have seen many threads started discussing the question, "What is space ?" So it is indeed apressing question. So pressing that in fact we now need to separate what is meant by a physical space and what is meant by a mathematical space. Defining a mathematical space is easy. You need a set containing at least three (perhaps four) sets of objects. 1) A set of mathematical objects you wish to work with. 2) A set of coefficients you wish to apply 3) A set of axiomatic relations between these objects 4) Perhaps if you want to be complete then a set of results (theorems lemmas etc) you can deduce from these. Hi Markus, I think you have this the wrong way round. Mathenmatical structures are models of physical reality, rather than physical reality being a model of mathematics.

Anyone wish to own up ? https://www.bbc.co.uk/news/business-55738540

This claim is not meaningless it is just plain wrong and arises from a basic misunderstanding of celestial navigation with a sextant, where the term 'arc of the sun or arc of other celestial body arises' It is not the altitude (which is the arc measured in degrees) but the plane from which is it is reckoned that changes with altitude and with altitude and other factors which have to be corrected for. This plane is called the true horizon and is not directly available to the observer so various 'observable horizons' are employed - marine navigators use the water horizon, aerial navigators use an 'artificial horizon' (yes aircraft still carry sextants for emergency navigation when the more modern electronic systems are broken). Clearly these calculations are correct since navigators do arrive at their destinations using them. The calculations and sight corrections can be quite complicated, here is a simple explanation. https://knowledgeofsea.com/correction-to-sextant-altitudes/

Generally an excellent explanation, +1, but your examples need updating somewhat. Both these examples were used in 1930's electrical equipment but have long since been abandoned as wasteful of power and potentially dangerous as they result in the excessive generation of heat. https://electronics.stackexchange.com/questions/252352/setting-heat-on-electric-stove Electronerd, are you sure you meant a bridge rectifier ? There are many sorts of bridges, but a simple bridge rectifier is not directly comparable to a rheostat. A bridge is a particular sort of circuit configuration containing four circuit components arranged in a 'diamond pattern. Some bridges are used for power control. This application would be comparable to using a rheostat for this purpose, but much more efficient. Such a bridge would be called a 'controlled bridge rectifier' and contain at least one, probably two or four silicon controlled rectifiers (SCR) or TRIACs If you have been reading about bridges for power control are you sure you don't mean this sort of bridge rectifier ?

Several countries have tried using Bluetooth to measure soical distancing distances. None (to my knowledge) have found a successful method. So what are the problems they are facing ?

Yes, yes and yes. +1

OK so I will try to discuss communication of Mathematics, rather than principle of Mathematics. I can't see where you have mentioned any basic Maths, computer code is hardly basic if it is indeed Maths at all. However I beg to disagree with your outright rejection of History. Perhaps your experience of History at school was of the sort "History is a list of dates of battles, deaths and treaties to be learned by heart and regurgitated for the examiner". History actually offers many lessons for those that care to peer into them. Not the least being concerning computer code. Coding languages have a very short lifetime; I have seen them come and go and stopped bothering to learn the new fashion decades ago now so I have little idea of the meaning of your example. The last serious program I wrote was PFortran TRIP (Trigonometric Intersection Program). British schools went through a phase of demanding that every child learn 'programming'. This mean resources were wasted on teaching first, different versions of BASIC, then PASCAL, then some early scripting. None of which are current today. History also tells us that the basic mathematical operation of counting is at least as old as writing, probably much older. Now schools used to teach using the old fashioned balance scales. Good schools would actually get the pupils to set up pretend shops acting as customers and shoperkeeps. They would weigh out amounts of materials, say potatoes or sand and also practice with pretend money. This allowed a method of counting by the custemr presenting say a half crown coin and the shopkeeper saying That's one and fivepence and then making up the one and fivepence to half a crown with coins to provide the change. Instant communication of arithmetic and fractions. For those who were a dunce at school arithmetic there was the joke, you say you can't do maths but you can still instantly recognise that you need a treble eighteen, double top and single nineteen to finish in a darts match when you are on 113! Would these be the sorts of examples you are looking for ?

Well thought out and presented answer +1

Is it? I wasn't aware of this. A detailed explanation of what I mean would be off topic in this thread so I will start another one for that purpose. I will let you know when I have posted it.

Swedish scientists use slowmo videography in a wind tunnel to confirm 1970s hypothesis of the aerodynamics of butterfly flight. https://www.bbc.co.uk/news/science-environment-55719955

To add to this. Mathematical continuity is defined in terms of the inverse functions, not the functions themselves. This has implications for any calculus you choose to adopt.

Ok. As a little tip - conventionally, writing (t,x,y,z) will imply Cartesian coordinates to most readers; if you want to indicate a general coordinate basis, it is better to use the notation x0,x1,x2,x3 , as it is less ambiguous. @Anamitra Palit I would like to add to this my comment to the OP. "(t,x,y,z) could represent coordinates of four dimensional space in a general manner" No they couldn't. t has the wrong physical dimensions to make this a physical space of four dimensions. You can only make an abstract 'space' (in the mathematical sense) with mixed dimensions on the coordinate axes. It is important to always keep this distinction in mind.

Reviewing your opening post I see that I did not give enough prominence to your actual question in my answer. Which is just how much of our NHS resources are being diverted by C-19 because of how long those patients who need hospital spend there All this week the BBC news cameras are following events in the Royal London Hospital, where they also went at the start of the pandemic. The RLH is a small 500 bed distict hospital in the middle of the East End of London. In normal times they have 40 odd intensive care beds, counted into the 500. Yesterday (Monday) it was reported that of the 500 beds over 490 were occupied by a 'high dependency' covid patient. Some of these will still be there months later. So what about the other 450 odd displaced would be patients ? This phenomenon also affects your interpretation of figures. The figures I was quoting were the daily new infections set against the daily deathis within 28 days of testing positive for C-19. This gives a good estimate of your chance of dying from C-19 if you caught it today. It would be false accounting to count in the number or % in the population with C-19 at any one time since the condition lasts a long time and you do not catch it every day. Here are some figures on that just released by the Office for National Statistics. https://www.bbc.co.uk/news/health-55718213

I wasn't and the OP stated You misunderstand although you posted a fair description of the partial working of a condensing boiler, it is a pity you have to always contradict me. The situation is much more complicated, for instance there may be no 'return' flow to a boiler running in DHW mode. But certainly if the inlet water is 100oC or greater then the output water would scald you. In fact it would scald you at a much lower temperature. The point is that the inlet water temperature is not fixed. But the output temperature will be set (there are often adjustable controls in a boiler for this) for both DHW and CH mode for efficiency purposes.

A statement on a UK death certificate is neither an assumption nor a model. There will always be some human errors, but the incidence of these is miniscule.

I feel sure that in a mature regular society somone will have done the research. We know the population we can poll the average number of colds/flu bouts each person has and we can compare this with the number of case of death where either of these conditions are recorded on the death certificate as a major cause. I am also sure that digging out this data will reveal just how low the incidence of death from these causes really is.

Seems to me you are trying to be sensationalist about it. Here are some (published and easily verified) facts. Over the last week or so the number of cases of C-19 in the UK has been running about 36,000 per day and the death rate at about 600 per day. So the death rate at the moment is about 1.5 - 2 % of those contracting the condition. What do you think the death rate for those contracting the common cold or influenza is ? Secondly the medical care required for these patients is such that the stay in hospital is longer than for most conditions and, of course, most influenza/cold cases do not require hospitilisation. The combined effect of these two factors mean that they have displaced treatements for other conditions, eg cancer, so that this time last year there were 150,000 outstanding hospital treatments, today there are 60 million. (reported in the last few days on the BBC) That figure is consistent with UK published figures. The result of my last comment leads to the count of so called 'excess deaths', which has been running between 150% and 200% of the recorded C-19 deaths.

Does anyone have a solvent recipe for cleaning the works of an Epson or Brother inkjet ? I found this website that has some interesting suggestions, but more are welcome. http://www.northlight-images.co.uk/inkjet-printer-cleaning/

Every degree above the optimal represents wasted heat and possibly dangerous conditions. Do you like being suddenly scalded in the shower ?

I think it is rather more complicated than that. The lower the input temperature the more heat you need to raise the water to the fixed output temperature. It also need to be considered whether the boiler is running in DHW or CH mode. But it is good to discuss these things to gain understanding.

Thank you for your reply, and the graph which does not display the quantity you asked for and I said was meaningless. You asked for You also wanted to be 'scientific' and cast various nastertiums about this forum. Your graph does show temperature (but not condensing temperature) but it does not show heat gained (which is the meaningless term) it shows efficiency. I was going to offer you some real world discussions, including practical facts and figures, from a 'plumber's' site - actually a very valuable resource, But it is important to actually be scientific and understand what you are talking about. It would be more profitable to discuss the science of condensing boilers, particularly in relatation to your excellent graph (+1 for that), rather than continued sniping. In particular your graph show boiler 'efficiency' falling dramatically with rising water inlet temperature, which begs the question of what is meant by efficiency?

But you are asking for a graph of a meaningless term.

Well I hope you got something out of it for you did not ask a silly question at all. It was a perfectly reasonable question for someone starting to study these matters. You didn't say whether you read my first post, at least you didn't answer it. Do you still want answers to your questions ? The short answer to your headline question is Yes it is one dimensional in that it acts along a specific line. But there is a lot more to the subject which your other questions suggest you haven't yet understood.

swansont was (correctly) quoting actual thermodynamic theory. unfortunately boilers such as condensing boilers can appear to havve efficiencies greater than 100% (according to advertisers and politicians) due to the way they measure it. The correct name for this term is COP (for Coefficient of Performance.)

I don't know much about gauge conditions, but having 'one' EM field assumes homegenity does it not. Otherwise epsilon and mu become tensors in their own right. I hope this discussion has not frightened off the OP as the level is way above his presentation as I have already pointed out.