studiot

It records radio programs (or auxiliary audio inputs) directly onto an SD card, and provides a pause-the-radio-to-answer the-phone function or a listen at another time function. The set normally runs off the mains, but the batteries are handy to take it into the garden. Roberts, the makers, didn't think to make it rechargeable. In fact all the DAB radios I have seen have suffered clumsy and inept design. DR is digital broadcast radio. DAB is the format used in the UK

I am going to start this instalment with a quick look at the modulus function. There is a difficulty at x = 0 where there is a sharp corner. There are two tangents. If we approach from A the tangent is AA' But if we approach from B the tangent is B’B The function y = |x| is not differentiable at 0 because of this. Functions which are not differentiable at some point are not smooth. In topological terms y = |x| is a 1D manifold, but not a differentiable manifold. When we step up through the dimensions we want differentiable manifolds. This is important because tangents and radii of curvature define perpendicular lines and we cannot accept competing tangents and radii. Note that as we step up through the dimensions tangent lines become tangent planes and ‘tangent’ solids and…… also called tangent hyperplanes. So what sort of manifold do we want, stepping up to 2D surfaces? A football surface or a brick surface? Topologically speaking the football surface are equivalent to the brick surface. The surfaces are each 2D manifolds that can be seamlessly converted into each other in true blue topological fashion. Note that I did not say that the football or brick themselves are 3D manifolds – We will examine that next time. Whilst the surface of the football is differentiable at every point and therefore smooth, the edges of the brick act like the origin in the modulus function. So the brick is not a smooth manifold and must be excluded from consideration. OK so now it s time to get out your stamp collection to examine the football more closely and then step up to Fig7. Fig6 is a 2D boundary round a 3D object in 3D space. Fig7 is a 3D boundary around a 4D object in 4D space. So are your stamps licked and ready? The stick one onto each rectangle on the football, until you have covered it entirely. Each stamp is a small segment of 2D space that can be stuck on to form an impenetrable barrier surrounding the ball in 3 space. There are no gaps, although overlap is permissible. The inside of the ball is now disconnected from the outside and this surface is curved in 3 space in such a way that it can be detected by 2D ‘flatlanders’ living on the ball (Newcastle United players?) This is intrinsic curvature – which we will explore in detail next time. In just the same way we as can surround (a portion of) 3D space with a 2D surface we can surround (a portion of) 4D space with a 3D hypersurface, if we follow the same rules. We have achieved you first goal which is to reach 4D space so I think this is a good place to stop and get into print. Next time we start to look into the more serious mathematics of 2D curvature in 3D and see how we can step it up to 3D in 4D.

This thread was inspired by jingori's recent thread about English writing, but is oof topic there so I have opened a new discussion thread. Hidden in this weekend's sensationalist trash, this article from the BBC presents a balanced survey of answers to the question round the world. Most interestingly it also offers measured evidence that teaching joined up writing improves joined up thinking and reading in later life. http://www.bbc.co.uk/news/world-us-canada-41927258

Thanks for the reply, Capiert. For all I knew Dr Turner might have been a doctor of divinity, which title is still due respect. For instance Professor Michael Heller is one such and has written some useful stuff about differential manifolds that I am drawing on in another thread. https://en.wikipedia.org/wiki/Michał_Heller

They came out of my digital(DAB) radio recorder. This is the only model I know of that records DR, expensive but it does have design issues.

Though meant as a jocular pun that at least one other understood, wasn't a fortuitous accident, but +1 for the peacemaker post. I don't see how asking for the credentials of someone makeing such sweeping claims is unreasonable.

Bullying? All I have asked you to do is follow the rules of this forum and answer a politely put question.

Have you actually tried this experiment? It is very instructive and proves Ed correct +1 Here are two photos of actual measurements. I am using slightly exhausted 1.2 volts cells so their combine voltage only adds up to 3.5 volts The first has all three batteries in series in the same direction. I have reversed one of the batteries for the second shot and you can see the voltmeter reading just under 1.2 volts.

Surely both require a change in medium? But you are right, in that I assumed a change in medium because of the question. I think SJ has identified what question should be. No, reflection takes place entirely within one medium which the the photon never leaves. Yes of course it occurs at a medium boundary. Refraction does not occur until the photon has entered the second medium. Of course the second medium may simple be a variant of the original, perhaps colder air or water. That's a bit like asking in a unverse that is empty apart from one single gas molecule, does that comprise a gas? You don't get wavelike properties until you have a stream or repetition of (many) photons in the plural.

Firstly, Jingori, let me say welcome and observe that I to chafed at the choice of study subjects imposed from on high for the good of my soul. In defence let me say that they have to select material that will cover everybody's needs and of course everybody is different. But they do try to include selections so that everbody will find at least something to gain from. Does you course include a 'Use of English' or Use of Language subject. We did that in my day a senior school level. Yopu might like to look out this book, published by the UK Institution of Civil Engineers Communication for Professional Engineers (2nd ed) By Bill Scott It is a masterpiece of clarity.

Three posts and lots of wild claims, but not one word of evidence or support. (You did read the rules of the speculation forum?) I also asked a valid question since you use the title Dr. I will repeat it for your convenience Yes your Facebook says you are a dentist. In UK law that alone does not entitle you to use the title Dr.

Yes indeed a photon can change direction - it is called reflection (not refraction, that requires a change of medium sorry Strange). But what it can't do is spontaneously change direction for no reason. That would contravene momentum conservation as John says.

Magnetic focusing was traditionally used in cathode ray tubes (CRTS) for televisions, unlike CRTs for oscilloscopes which use electrostatic focusing.

I'm afraid that the Wiki article is one of the easiest I have seen, which is why I chose it. Keep at it and hopefully enough will come clear. Very quickly affine is what happens when we add a constant to linear and arises from the difference between linear and straight line. The definition of linear is that for any function f(x) multiplied by a constant af(x) = f(ax) If we add another constant to x this is not satisfied. My sketch shows this is equivalent to moving the origin to a point C Look at my diagram and try a few straight lines and sketching in the effect of y = a(mx + c) and y = m(ax) + c When we move the origin to a new point c it is an affine transformation

No there is nothing wrong with the question, it is a good one. Further I do have you intended goal as the ultimate destination (hopefully over the weekend). Topology is concerned with the next step connectedness and also the continuity of mappings. However not all are differentiable and we need to select manifolds that are differentiable. That is why topology is too wide as it includes those. I hope you liked the method of studying the simpler lower dimensions and extending both the results and differences to higher ones. Meanwhile this Wikipedia article is more accessible than most on the subject. https://en.wikipedia.org/wiki/Real_coordinate_space

What sort of doctor did you say you were? Are you pulling my leg or pulling my teeth?

Thank you for the clarification. I understand you to be saying that Since there is no current standardisation of the tumour delineation I (we?) have compared (the region? volume? described by? ) the 50% of SUVmax isosurface the 41% of SUVmax isosurface etc etc to measure the MTV. I don't see the use of threshold as quite appropriate?

Perhaps I should make it clear I have merely addressed the headline question in the thread title. That is 4 spatial dimensions. Strange has already done an admirable job of addressing Dan's subsequent ramblings about Time and pointing out that the term he should use is space-time.

Well I don't like the word 'isocontour', since that is saying the same thing twice. I suppose the choice will depend upon the purpose of the procedure. Is this for standardisation or to set a baseline for future measurements/treatments?

A long time back (ha ha ) I posted a method of marking time that does not involve a clock, in a thread about the existence/nonexistence of time. So no I have not said (I hope) that time is not observable.

A friendly well thought out response, Prometheus. +1

Nice point. +1

Was this question aimed at my post? We are working towards an answer to this in geordief's thread here Feel free to contribute.

Definitely snappier. Solution:- Replace IPB with a Dave.

This is Engineering not Physics or Chemistry?