studiot

https://books.google.pl/books?id=V7IR6tFfaAEC&pg=PA65&lpg=PA65&dq=non-differentiable+space&source=bl&ots=sual_23EI-&sig=wNszgl3QdvymNGBICd0KNhfH9nI&hl=pl&sa=X&ved=0ahUKEwj19q2UuKHaAhUQJlAKHcdYAZ4Q6AEIiQEwCQ#v=onepage&q=non-differentiable space&f=false "The theory of scale relativity [14) is an attempt to study the Of giving up the hypothesis Of space—time differentiability. One can show [14] [15] that a continuous but nondifferentiable space-time is necessarily fractal. Here the word fractal [12] is taken in a general meaning, as defining a set, object or space that shows structures at all scales, or on a wide range of scales. More precisely, one can demonstrate [17) that a continuous but nondifferentiable function is explicitly resolution-dependent, and that its length C tends to infinity when the resolution interval tends to zero Well I assume that twaddle is a result of improper translation to English since your original was in some other language, that I can't read. To be fair it does confirm what I said that functions are differentiable, although it starts off with something that is clearly mistranslated. The whole point about functions is that they are a two part mathematical object. And that's what makes them differentiable, because differentiation is a two part process. When I learned calculus we always had to write as justification something like ""differentiating .Y. with respect to X" as justification. This definitely brings out that two- part nature containing both that which is being differentiated and that with which the differentiation is being performed. This is especially important for the sort of mathematics you have already invoked here using cycles and frequency ie the wave equation. That is because you differentiate one side with respect to distance and the other with respect to time. The object being differentiated is of course the wave variable, which is a function of both space and time. Thank you for the link about fractals. I am aware of the nature of fractal sets. Do you understand measure theory and Hausdorf dimension theory? These are needed to handle fractals.

Not sure where you got that graph from but do you understand what you are talking about? [math]y = \sqrt x = \sqrt 0 = 0[/math] is perfectly well defined. But so what? What does this have to do with the differentiability or otherwise of a space? [math]y = \sqrt x [/math] is a function, which is indeed not differentiable at x=0 because it is not defined for x<0 It is functions, not spaces that are differentiable or not. Stating that a space is or is not differentiable has no meaning, which is why I asked what you mean by such a statement.

Will you just answer my question since it concerned your words not any one else's?

Well, if his theory, deserves Nobel Prize, then maybe I also deserve somekind of prize I made an extension to his theory, without even knowing about it... But what I was asking was were you even stating his theory correctly, let alone understanding it? I will ask my question again. What does it mean to say a space is or is not differentiable?

Really? What does this statement mean please?

Are we both reading the same thread? Or are you just being funny?

Look at the two blocks you have labelled 'pure cyan' They appear different. The one on the left appears to be pure cyan plus grey to me. The one on the right appears to be a fair pure cyan The two you have labelled pure yellow are more different and I think, though I may be wrong, that they are pure yellow plus some other non grey light left and pure yellow (right). I apologise, I now realise that they are your original colour blocks, I was too hasty.

What are you doing there? These are not the colour blocks you originally posted. I didn't make clear that the "other light in the beam" ias not necessarily grey. One of the colour models uses the neutral grey to adjust the apparent brightness of the pure colour. I think this is called the Hue Saturation Brightness (HSB) model. A % grey can be added to any pure colour this way. But that is a restriction of what can be added to any pure colour. Adding any other mixture but the grey alters the received appearance of the colour ie changes the colour.

But I am challenging that that is the case. Therefore, and if I am right, Yes?

But it doesn't, as I have tried to explain. You are mixing up situations. The way to see the colour of additive light sources is to shine them on a common area on a white screen or paper. You don't stare into the beam. What you then see in your two different situations looks different because it is different. That is because the illuminated spot you see is giving off two different lights. One is the pure narrow bandwidth called yellow. The other is the agglomerate of all the other light in the beam, which is what I meant when I originally asked how much grey there is in the left hand sample.

I like it. +1 @thoughtfuhk The beginning of the tile presupposes there is only one purpose? Why can't lots of different 'purposes' be served at the same time. Perhaps 'evolution' tries out lots of different possible progressions at once, some bear fruit, some do not (there is a biblical parable about this) But perhaps all those trials are just in case or are just like a drug manufacturer haveiong a row of test tubes with (slight) variations on a theme.

I suggest you restudy the difference between additive and subtractive colour systems. Since we have been dicussing the colour of light in this thread we are discussing the additive colour system, whereby you sart with no light (black) and add light of various colours, each time changing the result colour until you have added light of all colours when you get the white (or the near white broad spectrum (not necessarily continuous that is a different thing) of your halogen lamp. This is how colour projectors work. The alternative is the subtractive system where you start with white and remove particular colours either by filtering or by reflecting from a coloured object that removes the desired colour. The end result of this is of course, no light or black. This is how mixing paint colours works. http://www.worqx.com/color/color_systems.htm

You made claims fundamentally opposed to conventional thinking about tides. Please respond to my comments as required by the rules of this forum instead of listing the names of some water bodies in the northern hemisphere. I would agree that mathematically a tidal wave is also called a soliton, but as I pointed out there is more than one mechanism of generation for these in hydraulic bodies.

I don't think so. (Issue underlined). What do you think might be the physical mechanism for this to happen?

Einstein was not a world class Mathematician, although no one surpassed his standing in Physics. His liflong friend Grossman helped with much of the maths. Willian Clifford , on the other hand, was one of the leading Mathematicians of his day ( a differential geometer to be precise just like our own ajb) and made many advances in his field. Clifford algebras are named after hime and concern differential forms, the exterior calculus and stuff, which is only these days coming into its own in Physics and Engineering. He, in his turn relied heavily on the pioneering work and insights of Riemann whos efamous Doctoral lecture kicked the whole thing off. Gauss before hime had some insight, but didn't publish it all so we don't know how much he knew, but he was responsible for the original work on the geometric curvature of curves. Poincare added his own theoretical work including the famous Poincare Conjecture, only recently proved by Perelman, in non-Euclidian geometry and the Poincare disk, which is one way to contain 'infinity'.

Did you read the Konica-Minolta document I linked to? It really is an excellent presentation. And it offers 'official' answers to your questions plus some that you haven't asked but need to.

It wasn't Poincare anyway. Strange is correct they all did their bit, from Gauss to Riemann to Clifford I have emboldened the relevant phrase.

The point to remember is that the Uncertainty Principle refers to any determination of the values concerned. This includes, but is not limited to, direct measurement, deduction from other data, calculation of the physical variables involved. Possibly the simplest way to understand this is to follow the reasoning behing the broadening of a spectral emission line. Such reasoning is used all the time in Spectroscopy.

Indeed they are and it is 20 years+ since I threw out my (then) old university notes on Environmental Engineering including illumination. I have been trying to think of a simple one paragraph explanation of the role of grey. Hasan, it is good to have someone interested in the subject, especially as the last persion wanting to 'discuss' colour perception was a troll. So here goes. Illimination and the visual perception of illuminated object a very complicated subject because of the interaction between the the source, the light itself and the illuminated objects. This is not helped by the fact that the relationships change with the intensity (and sometimes other parameters such as direction) of the illuminating light. So first off there are standards to refer to. One of these is the CIE 'Standard Sky' https://www.google.co.uk/search?q=CIE+standard+sky&ie=utf-8&oe=utf-8&client=firefox-b&gfe_rd=cr&dcr=0&ei=aIbEWpesJo-Btgfb56fIBQ When we (or a recording machine such as a camera) view an illuminated object we see two separate aspects of the incident light. We see the level or intensity as a measurement we call the Luminance and The perceived colour or Chrominance. These are not independent and at very low levels of light we can only see the Luminance. That is we cannot see colour. The Luminance property by itself allows us to create a monchrome or greyscale model of the image, point by point. This is how early fax machines, photocopiers, the silver screen at the cinema and old fashioned 'black and white' television work. The luminance is a simple single numerical value that specifies the light density. The chrominance is much more complicated and is not a single value but has to be represented by a collection of several numbers that indentify it on a two or three dimensional chart. This is further complicated by the fact that there are several different charts schemes available and each includes a different overall range of the light spectrum, known as the (colour) gamut. So some colours appear in one scheme but not in others. But having chosen the scheme it does not end there because we see with two eyes and each of our eyes sees a slightly different colour emanating from each point on the object in view. This is because the light is affected by shading and other effects from nearby points and perhaps also from the light source itself. Amazingly our brain is able to filter out these differences and assemble a coherent unique colour value for any point on the illuminated object. Here is a good semi technical introduction to the subject. https://www.konicaminolta.eu/fileadmin/content/eu/Measuring_Instruments/4_Learning_Centre/C_A/PRECISE_COLOR_COMMUNICATION/pcc_english_13.pdf

No because the appearance of brightness depends upon the response curve of the eye. The point I am trying to make is that pure colour (monochromatic light) has a very narrow band, perhaps even narrowere than your 570-590 nm. Grey is a mixture of certain proportions of all the primary coulours (I forget the proportions but they could be looked up). Grey is also regarded as the universal neutral colour.

I'm quite sure the " Institute of Geography of the Russian Academy of Sciences. " can do much better than this. I'm also sure it can get its terminology correct. Russia is, after all, one of the two nations on Earth that attempts to produce charts of the entire World Ocean. So Terminology. You need to distinguish between 'currents', which always flow one way and are part of the basic thermally driven movement of water in the world ocean. and 'tidal streams' which are the horizontal movements of water due to tidal action. Unlike currents, tidal streams reverse once or twice a day. Are 'Tidal waves' proper terminology? Do you mean a Tsunami, born of tectonic activity or a hydraulic jump like the Severn Bore, born of rapidly changing bottom gradient?

Did you miss my question or did you not understand it? There clearly is a difference between narrow band light and wideband light, which includes some of the original narrow band. Further the statement "this is also aceptable.... etc" makes no sense. So please restate you question and premise.

Don't the colours on the left have added grey?

Good morning and welcome. You will need to be more specific as to your requirements. Here is a recent report with data, standards to compare against to follow. https://www.epa.ie/researchandeducation/research/researchpublications/researchreports/EPA RR 183 Essentra_web.pdf

Yes exactly V = IR is the problem. If you plot a graph of voltage against current (or better the other way round) the above relationship is a straight line through the origin, so beloved of schoolboy Physics "Please Miss I got a straight line through the origin for my practical" These are known as transfer curves and, like the rest of more advanced Physics life is never that simple. The simplest step up is of course "what if it's affine?" That is V = IR + C, but still a straight line? In fact the ratio R = V/I is the slope of this graph at any point and the inverse ratio (called the conductance) is perhaps better used and we have that current is some function of applied voltage, I = f(V). We can then do calculus on this. JimS should remember something called transconductance, appropriate to valve (tube) circuitry and FET circuitry these days. For a junction transistor, the function f(V) is too complicated to write as an equation so electronic manufacturers publish graphs showing families curves for their products. Next up the transfer curve ladder comes what statisticians call the Gompertz curve or the S or Z shaped curve which allows switching activity to be created in a circuit. Then we have devices with negative resistance regions such as tunnel diodes (available in the 1960s) that have more that one solution for the equation. This allows the creation of oscillator circuits vibrating back and fore between the available states represented by alternative solutions. It can also lead to circuits with chaotic behaviour. I mentioned oscillators, which introduces other variables - time or frequency. Temperature is another one. Ohm's law is an idealisation, just as the Gas Laws, but we abstract ideal transfer curves for all the more complicated situations. Ohm's Law then becomes just the simplest possible idealisation in the form V = IR. But in the form R = V/I it can be used to define resistance as the limit of ratio of the voltage to the current at a point.