studiot

It helps to finish your sentences. It also helps to answer the questions of others if you want your own answered. Since I still don't know where you are coming from; I suggest you read the standard Oxford University text at this level for half a century. An introduction to the Infinistesimal Calculus by G W Caunt Oxford University press Chapter 3 Differentiation of simple algebraic functions In general and section 24 pages 64 to 67 in particular Differentials and Orders of small quantities.

But you still misread my statement and all else that you posted was based on this misreading so is therefore void.

So the source is destroyed whilst a field is still at least partially intact. So what? You would not have the field without the source and youadd another body as a detector. It's been a long time since we learned that source and effect are not instantaneous in a field.

Oliver Heaviside at a Royal Society Dinner, when the famous mathematicians of the day refused to accept his operational calculus because his proofs were not up to their standards.

Have you ever had a baby? Then you would know that human first teeth don't arrive until a few (maybe 6) months after the baby is born. Further your own teeth experience must have shown you that humans have first and second teeth. So what does it matter what happens to first teeth enamel?

It's not the way I usually try to explain it, I was trying to follow what I admit I am guessing is 113's approach by answering direct questions and correcting some notational errors. There is an old saying "Never ask an Irishman for directions" Because they will always say, "If I was going to XXX, I wouldn't start from here" My usual explanation is to start from the idea of an expression giving specific values (eg y = x2 say when x = 0) Then to move on to the idea of a function as a whole entity in itself so y = x2 for all x and then introduce the idea of the derived function - which is also a function in its own right. But my ever hopeful bottom line is that I don't (want to) see 113 as one of that merry band of folks dedicated to disproving, Cantor, Leibnitz Reiman et al, come what may.

Well I am sorry, Rob, that you have been put to producing such a long screed on a false assumption. That is not a correct or literal rephrasing of what I actually said. However I must take some blame for your misreading as I see from your extracted quote that I was not clear enough and I apologise for that. I did not say that anyone deliberately attempted to measure something other than what they set out to measure. What I did say, rather unclearly, was that if the results of their measurement did not accord with their prediction it might be as a result of faulty measurement for some reason.Then I gave a couple of possible reasons, known to have occurred in practice. Of course this in no way precludes the possibility that there was actually nothing wrong with the mesurement, it was the theory (Feynman's guess) that was faulty. IOW I was pointing out that Feynman was tacityly assumeing an experiment that was not faulty, in say it was 'right'. I have already offered my 'brick' experiment as an example for discussion. This has the merits of being much better defined than ramblings on the fringes of Science, even if it is less sexy.

I can see you are trying to point 113 towards more advanced and more coherent thinking I just don't think he has enough mathematics to take all that in. My point of departure is simply that until 113 tells us where he is coming from any attempt to help is only guesswork, so I have tried to be open about what I am guessing and the context in which I am pitching an explanation. I am not a teacher, but judging by the many textbooks on the subject I have seen, 113's questions are very common and nothing to be ashamed of.

Well I have to differ here on several counts. 113 is not using terminology exactly for instance Clearly misusing the term finite difference, which is a term concerning real numbers. I think 113 meant 'non zero difference' here. The approach I described was in use in grammar schools in England from at least 1880 to the mid twentieth century, for the subject of Pure Mathematics, my introduction to calculus was done that way in the mid 1960s. As I said, university analysis revisited the whole issue much more rigourosly. Throughout the twentieth century there was much discussion as to presentation and the use of infinitesimals, various delta x s, a small quantity h, various greek letters and so on. As I said fashions change. The bottom line was, and remains, that when pupils start this subject there are a great deal if disparate subjects within the discipline to get their heads around very quickly. So corners are always initially cut somewhere. We had become proficient in differentiation within the first term ie between September and Christmas in my 1960s A level. To do that we had a substantial amount of new more advanced algebra (sequences, series , limits ) and new trigonometry to get through at the same time. Integration came after Christmas.

A very good approach, probably the best one if your development of geometry has reached congruent triangles by this stage, but I fear that the OP has long gone. +1

I take it this is your reply to my attempts to engage in discussion with you. Where exactly did I do any of these alleged things? In particular where have I described you as an idiot? The quote above shows that I try to pick out statements from you that I agree with, but It's the (mis)use you put these statements to I don't. My main complaint is that you repeatedly fail to respond or show contempt as perfectly exemplified by our brief unfinished discussion about my brick experiment. I note that yet again in your latest post you have not made any reference to my posts, answered any of my questions or attempted to move any of aour discussions on, whilst pontificating at great length about the posts of others. As to your presentation of Feynman, Yes, absolutely, but you entirely miss the point. Interestingly my brick experiment, that you steadfastly refuse to discuss, if a prime example of a guess. And the story of the experiment a prime example of Science in action. His remark is predicated upon the experiment actually measuring the subject of the guess and not something else. If you actually measure something else, either by accident, or by failure to take account of some intervening factor or for some other reason, then your experiment offers little or nothing about the validity of the guess.

With that amount of money you don't want to loose any so risk is a big issue. Are you lucky? I know litttle of the Polish system but is there anything equivalent to UK premium Bonds? https://www.nsandi.com/premium-bonds?dclid=CIPj4saQ_t0CFdDW3godRCUH-Q You can't loose your money, and on average they pay out an amount equivalent to current interest rates. However that is not evenly distributed so some get much large amounts (two get £1million every month) And any return is tax free. A good place to start.especially if you are a lucky person. Are you a Dyson? To succeed like he has done you need to be a good businessman as well as a good inventor. Most are not. So if not, don't try it. Too many loose all that way. Some make money by finding something valuable and selling it, for instance a lost old manuscript, painting, antique etc. You need the interest and the right sort of 'eye' for this. I know someone who makes a good profit 300% + (but in small sums) because she has a good eye for trends. For instance she bought a collection of soft toys and kept them in tip top condition, then sold them a few years later at vast profit when they became collectable. Taklksing of soft toys I have an aquaintance who was a former sales manager with British Telecom. He made more than his salary by buying soft toys and selling them at (outside) conferences and exhibitions. If you visit exhibitions you will have seen such people. It is a risk but get the right products and the rewards are good. Have you ever helped with a local activity in its fundraising? We used to run the Somerset Rural Music School 'tuck shop' which made a modest but steady and respectable break time profit. Really good training into what sells and what does not, and how much to stock so as not to overstock.

Yes inded it does. So the next step is to find an expression for f(x+dx). Using taeto's example we have f(x+dx) is (x+dx)2 or x2 + 2xdx + (dx)2. Now you need to take a very important step in this method or route to the derived function. If dx is a very small quantity then (dx)2 is insignificant and may be ignored so we have the top line of your fraction is f(x) - f(x+dx) = x2 - (x2 + 2xdx) = 2xdx. So [math]\frac{{dy}}{{dx}} = \frac{{2xdx}}{{dx}} = 2x[/math] Now this is an example of 'starting somewhere' and glossing over certain parts of the derivation. It justifies the use of the notation y = f(x) as the above can get very clumsy. It is normal to use [math]\delta x[/math] not dx and take a limit as [math]\delta x[/math] approaches zero, before limits of ratios have been properly studied and quickly say as [math]\delta x[/math] and [math]\delta y[/math] tend to zero [math]\mathop {\lim }\limits_{\delta x \to 0} \frac{{\delta y}}{{\delta x}} = \frac{{dy}}{{dx}}[/math] But this has gone out of fashion.

How much can you warm the polyurethane parts with say warm air? I assume your release agent is some sort of silicone grease. So can you warm it up and wipe it off? (polyurethane material is good to 100oC Alternatively you could try some liquid siloxane http://dept.harpercollege.edu/chemistry/msds/Silicone oil Fisher.pdf Either way use proper ventilation and safety techniques.

Here he is again

But Reg is always right - even when he's wrong. Which is my way of noting that he often states plausible, even sensible lines many of which I can agree with. But then he uses them to argue ex extremum. He seems to either think he is or wishes to be the only person with anything worthwhile to say on a given subject. Several times I have picked out a particular line of his to agree with and give hime credit for. I have never noticed a reciprocal action.

Was that Nicola?

That is why so much else would come crashing down if relativity was disproved. But what does disproved mean? It means showing that Einstein's formulae and equations generally and consistently give the 'wrong ' answers ie inconsistent with observation. Indeed SR does this, but has theory been disproved? No it was recognised from the outset that SR does not include gravity. So we have GR, with SR as a special case. There are very few hypotheses (theories) that have been disproved and discredited Noye's Fludde come to mind here.

Well I have no idea who Popper is or was but I am not drawn to bother from your summary. Again I have no idea who Kuhn is or was but I find his views no real improvement. But enough quoting others who are not here. This is a live debate forum so here (appears to me) the view according to Reg Prescott. Yes indeed this happened many times, but how often was this for the reasons you give? I can think of one instance, that of Berzelius, who held up the development of chemistry by half a century for reasons of personal aggrandisement. Another major reason for obstructing progress came in the late 18th and early 19 centuries when many clergymen became avid geologists with the intention of providing a scientific underpinning of Noye's Fludde. Nor are many scientists themselves very good at history (many are too busy with Science itself). Some who can manage cogent works are John Buckingham in Chemistry G I Brown in Chemistry (His book the Big Bang - a history of explosives is good) Ian Stewart in Mathematics Jon Butterworth in particle Physics Fred Hoyle in cosmology Michael Benton Geology Donal Oshea Relativity Mathematics Non Scientists of note include Brenda Maddox in Geoscience William Berkson Philosophy of Physics

Avoided? This has been a main theme of my arguments/non-arguments/specious arguments since Post #1. Well it was the principal point of my one and only post (at that time) in your thread and you made no reference to it. I'm glad to hear that you do appreciate it and would be pleased to learn why you only consider the very very few examples that lie outside this category?

Thank you for this. I'm not really very interested in your continued argeuments with others that never seem to get anywhere. Surely the one important point to your thread that you have avoided was that Science is by and large mundane? Thank you for responding to my question. Yes of course it will cool down unless kept warm. However the important thing from the point of view of the investigation, which was a ministry programme lasting several of decades, though not for me as I just joined the team between school and university. It was my first introduction to true scientific investigation with a purpose, is that the fresh bricks absorb moisture. This is significant because they swell as a result. So the project was all about the effect of this swelling on brickwork built with fresh bricks after cooling. The following rhetorical questions, though I will supply details if you wish. How much did the bricks expand? How long does this process go on for? What does that mean for brick walls and expansion joints? A subject (though boring to most) of great importance to mankind around the world.

Wait don't you mean tangent? I thought the radius unit vector would be the normal. I said normal, you said normal he she or it said normal, what's the problem? Yes the tangent is orthogonal to the normal and is another vector.

Once again I asked a very simple straightforward question, this time about a scientific investigation I have personal experience of. Once again the silence from Reg Prescott was deafening or drowned out by specious arguments with others. Do you have any personal experience of scientific investigation ?

By aiming only at the really big discoveries of Science you are deceiving yourself as to the nature and activities of Science and scientists. There are only a handful of such really big discoveries a century, the rest of Science is prosaic and mundane. Perhaps what has been said this gives you the idea that (we think or you think) that all scientists are sitting at their desks doing nothing but challenging what they already know. Nothing could be further from the truth. I have made a few very small discoveries/innovations, but have never had the need or opportunity to challenge the basis from which I was working. Can you tell me what happens to a new brick, fresh from the kiln? Well I spent some time researching this question because the answer is of interest in the building industry. By far the most of Science and scientific activity is of this nature. So it is against this background that you should be discussing your question.

I am not quite sure what you mean by an 'angle vector' can you provide an example? Meanwhile consider this. Much use is made in field and potential theory of 'shells' of the quantity of interest. The three variables, [math]{\rm{r,}}\;{\rm{\theta }}\;{\rm{and}}\;{\rm{\varphi }}\;[/math] specify a point on such a shell. The theta and phi specify the direction of the outward normal at that point. As Timo has already pointed out integrating over all space will give a flux through that shell so we can applu Gauss' theorem The thing is that we often wish to go further than this and place an active (test) particle at the specified point. By active I mean that it interacts with the flux passing through the shell so it may have momentum, a magnetic moment or whatever. This interaction needs to be described with another vector, different from the outward normal. (This interaction includes the case of zero net action for a second vector orthogonal to the outward normal.) Differential equations in the three variables [math]{\rm{r,}}\;{\rm{\theta }}\;{\rm{and}}\;{\rm{\varphi }}\;[/math] can often be solved by the method of separation of variables, leading to Legendre's equation for instance. This applies most particularly to Laplace's equation which leads to spherical harmonics when the separation is applied.