studiot

Stand next to it and smile please - you are being photographed. 🙂 +1

The diffusion equation is not only impossible to solve, it is actually meaningless without the boundary conditions, (and I include initial conditions in this). The link Amy provided pays attention to this and describes in some detail some of the possible circumstances including multiple sources and/ or sinks both time and space and the possibility of both diffusing and transmission media interacting. It is true that the simple quadratic formula it calculates refers to a single source with no sinks and and an unbounded transmission medium. Thus it is a very simplistic formula (It is not the diffusion equation) which simply comes up with a rough estimate of how far (x) a diffusing medium would get in time (D), all other things being equal. but it depends upon these conditions which are part of the diffusion equation, not something separate from it. To see how diffusion can lead to chemical oscillation read this

@chenbeier @exchemist Surely you should also consider the boundary conditions. Even the simple diffusion equation has periodic solutions with the right conditions. There are plenty of learned maths papers on the subject. eg Diffusion equation if f and φ are periodic the solution is also periodic - Mathematics Stack Exchange Periodic solutions in reaction–diffusion equations with time delay - ScienceDirect The point is to find out from Amy what she is trying to do as I still don't follow this and she hasn't responded to my last post. Again a medical example, with more complicated conditions is the calculation of the rate and size of periodic dosing to achieve a 'steady state concentration' in the body. This also happens when considering Fourier solutions to the heat equation, which is a form of the simple diffusion equation. So @amy1vaulhausen, please, Why are you working with a physiological calculator and why are you measuring distance in light seconds ? What conditions are you setting

1) So you are saying there are only countably many positions in this first universe ? 2) Surely this depends upon how you define 'distance'. How does that work in a universe where distance is defined as the length of the peano curve between two points ?

We can all quote Cantor.

So would you like to explain this further ?

I have to say I am, like swansont, puzzled by your usage. I don't know a great deal about physiology so it is new to me that they measure distances in light-seconds (300,000 kilometres). What sort of organism incorporates those distances ? I further agree with swansont that you need to model a repetitive (not necessarily cyclic) phenomenon, such as the one I mentioned earlier. For instance in medicine, the half life of a drug in a body is given by Half life, t0.5 = 0.693* Volume of Distribution / Clearance = 0.693/kc where kc is the elimination rate constant (a form of diffusion constant) This half life models how much drug is eliminated by the body every time period.

Indeed so but periodic does not necessarily mean wave like. It means that something happens every specific time interval called the period. In the case of a chemical or nuclear reaction this means this something refers to the consumption/ concentration of decaying reactant. But I was really inviting Amy to provide more detail as to what she was really after, not wishing to engage in a semantic discussion. That way we could help her more successfully.

Yes indeed it makes a difference. Because there is more than one infinity.I will use the word infinity / infinite to follow you. There are an infinity of counting numbers - 1, 2, 3, ...... and so on. Each one is a whole complete package. But there is a more numerous infinity of real numbers - 1, 1.1, 1.11, 1.111 and so on. We say that this greater amount is the infinity of the continuum. Aah! the continuum. So is the Universe granular ie made up of lots of individual, indivisible pieces of space (eg the Planck length or whatever) or is it actually infinite as the real numbers ie indefinitely divisible? Because if it is granular we can count the total number of grains, even if they are infinite. But if it is continuous we can't. Incidentally be careful of genady's suggestion. Bounded v unbounded are not quite the same as infinite v finite. Didderent combinations of these two qualities are possible.

Hello Amy, I don't think you mean diffusion rate, perhaps you mean diffusion half life. The diffusion equation can be as complicated as you wish ut the simple one can be modelled with a half life (measured in seconds or milliseconds etc) Of course 'frequency' is the reciprocal of seconds. see here How to model mass diffusion with half life - Physics Stack Exchange

Yes I think the surge equation is a good way to approximate it. +1

Good point. +1 I just don't buy the fireball hypothesis. The water pressure at titanic depth is around 400 atm and the volume of the titan is around 4 cubic metres at 1 atm To compress this to 400atm would reduce its volume to 0.01 cubic metres. The only way this could happen would be if the remaining 4- 0.01 cubic metres was replaced by inflooding water. This would surely crush and or drown the occupants ? I said in my first post that connections between dissimilar materials should be carefully examined and the reports today seem to indicate that failure occurred at these places. A further consideration is that no one has mentioned shear failure. Carbon fibre composites rely on shear stress to tranfer the load from fibre to fibre. Further swansont has already pointed out that although the outside loading is triaxial compression, the shape of the titan induces shear and bending stress due to unbalanced normal loads. Squat objects subject to polyaxial compression fail in shear.

Whether or not you interpret such writing correctly (you don't), they have no bearing on the mathematical proof called CDA. I was beginning to wonder if this thread was actually anout the diagonal argument or a character assassination of Cantor. Thank you for exposing this point so simply and clearly. +1

I don't think anyone has a full handle on AI so thank you to all members who have added their piece. +1 to Ghideon for a particularly cogent offering. I have certainly learned many things from this thread, including how many 'Turing Machines' or variations thereof there are. I was only thinking of the most basic one when I started this. I do feel there is plenty more good mileage left in this subject yet.

Dear oh dear. Whilst I accept that much of what you are trying to say is in principle correct, you don't seem to be explaining it very well. I'm sorry but several members from different English speaking countries on diverse continents have all told you that they understand that when rays of different colours that are initially combined into a single ray, start going in different directions from some point or other in their path separation is said to occur from that point. Yes I agree you could also say they diverge or use yet other terms, but you cannot discount all of us who use the term separation. The equation you quoted (which I agree with) D(n) = n*180+2A - 2(n+2)B is purely geometric and does not rely on Snell's law. It is true that you can substitute for B as a function of A but this remains true regardless of whether that function obeys Snell's law or not. In other words the above equation is geometry, Snell's law is physics. Swansont nailed it when he said to you There is no difference, except how the colors are formed. If we could create an array of small prisms suspended in the air, and all aligned the same way, we would see a linear band of spectrum (i.e., not quite the same as rainbow) colors across the array. The image project from one is the same as the image seen in the array. Then say we have a screen, with a hole cut in it so that we can shine a bright beam of white light through it. Place a spherical flask of water in the beam. It will reflect a white circle of light onto the screen, with rainbow (i.e., not quite the same as spectrum) colors around the rim. Something like this:+ The point is that the reflection from one, and the image from an (aligned) array, are the same. Please note this picture you posted breaks the condition I already poste as in the quote below yours. The image on the screen is on the same side of the simulated water drop as the light source. (that is the wrong side for a rainbow). In particular it is a real image. The sky image of a rainbow is a virtual image. Your screen corresponds to the retina of the eye or the plate of a camera system. The real image on the retina or camera is caused by the optics of the eye or camera focusing the virtual image of the rainbow itself. The real image is not the rainbow. As I said in my first post it is very complicated, and this is still not the whole story because the red and blue etc do not come from the same drops. So in that sense we do not see a split of the red and blue from the same drop, we see red from a drop at a certain altitude and blue from a drop below it, brought to the same focus on the retina.

Good question +1 Thanks for the link, but there is more to it than that I think. As far as I know Canto never used the term infinite, despite the above translation. Instead he invented the term transfinite. I am given to understand by Wikipedia that this was because he realised he was talking about something different from the ancient greek infinities. In the German in the paper you refer to he used the word unendliche. But just as Rome wasn't built in a day, the theory of infinite aggregates took 10 to 15 years to develop, with more work going on after that and to this day. In volume 1 of his "The Theory of functions of a Real Variable", Hobson claims the first English language exposition of Cantor's theory, as opposed to a translation. Hobson keeps with the terms aggregate and transfinite, which were current at the time.

Hi Mordred, who were you addressing in this post ? I think we are all aware of Snell's law, and that it applies only to refraction. The equation I was querying refers to reflection.

Perhaps you would prefer the phrase partial separation ? And I described it. It determines the angle B in the equation D(n)=n*180°+2*A-(2n+2)*B, where A is the angle of incidence of an incoming light ray, n is the number of (not total) internal reflections, and D is the total angle thru which that light is deflected. Since the primary and secondary rainbows are both seen when looking away from the sun, often this is subtracted from 180° and put in the range 0° to 180°. That's 4*B-2*A for the primary. I would be interested in finding out how Snell's Law is applicable to that equation (which refers to reflection) I wonder if you are trying to offer some form (possibly transverse) of chromatic aberration as the mechanism for the rainbow colours formation, as in the pictures from Wikipedia below. Ring 3 perhaps on the first one ? Chromatic aberration - Wikipedia The second one shows purple fringing on the donkey's ears. This discussion on Physics forums lends some support to that description, in some circumstance. Exploration into the Physics of Rainbows | Physics Forums

There is nothing wrong with Cantor's argument. It is called diagonalisation because it is usually presented in grid format. But this format is not necessary, The issue arises because the set of all sets of positive integers in not enumerable. That is it cannot be put into one-to-one correspondence with the set of all positive integers.

Well yes and no. Since Bayes theorem gives a conditional probability, that is a probability given so other result, it is necessary to start with a value and apply the condition. Conventionally in the absence of any other information (you called it belief) we start with P = 0.5. There is one other point to mention about Bayesian searches. The Scorpion was travelling basically horizontally The Titan was travelling basically vertically. Here are some thoughts as to the the failure. First I must stess that at this stage we really don't know, we must just draw up a list of factors to investigate. 1) The carbon fibre issue may be pointing the finger in the wrong direction. 2) Yes carbon fibre is very strong and does not fatigue appreciably. 3) But the fibres are embedded in a matrix which is a different matter and this may easily creep, although the sub was lass than 10years old. I remember the 1960s fibreglass kit cars, the Fairthorpe in particular. A fellow student was killed in one in those days where the body shell had crept appreciably over its mounting points. 4) This bring me to another point. It is all very well having superstrong materials, but it has to be mated with other parts and so may fail at the union. I understand that an intact titanium nose cone has been found. 5) I remember also similar problems besetting the RB211 Rolls-Royce aero engine, the first with carbon fibre fan blades, eventually leading to shortened life and a couple of disasters. The blades were eventually replaced with metal ones. So was it a material failure or a naval architecture vessel design failure ?

Definitely not. You mentioned 'spacetime. I had meant to point out that one particular quadratic expression is preferred over other (emerges). When you look at it is seems very reasonable and is what we would prefer it to be since it is easier than most. But we have no theoretical basis for saying that it must be this way. Most emergences seem to be beneficial as for instance in the shakedown theorem. Some are just interesting ad pretty vas in the B-Z reaction.

Emergent is a very slippery concept, especially in a diswcipline that tries to 'nail things down'. I would offer the idea that emergence is a way of selecting one particular response of system to input/stimulus/configuration or whatever. That response nedds to be special, perhaps unique, in some way when counted amongst the many possible responses. So In a physics sense think the calculus of variations, the shakedown theorem, plasticity, This definitely does not make it some sort of mystic woo. But it does not necessarily make it predictable either. Sorry for rambling, ask again about anything that is not clear.

For those who might be interested there is an interesting paper free here. (PDF) An indirect measurement of the speed of light in a General Physics Laboratory (researchgate.net) The indirect method this this paper discusses involves separate measurements of permeability and permittivity and the calculation of c from them both by themselves and some other workers.

Wood based translational materials science with a medical flavour ? Wow. You could try the following. There are a number of government and industry organisations that hold univeristy status and also have a publishing arm. COFI Council of Forest Industries | Forestry for the planet. Forest products for the world. (cofi.org) Wellcome Trust Home | Wellcome spring to mind. Also some universities with a strong materials dept also have publishing departments eg in the UK Exeter and UMIST Also some professional bodies publish occasional papers in their field. Try talking to the Technical Officers for these organisations. I used to answer questions like yours when I was Technical Officer for the IHT - an inappropriate body for your subject but the principle is the same.

You are right, after carefully only specifying reflections and distinguishing between total internal and internal and external an unwanted total slipped in. However I think for everyone's benefit we should review some basic optics and its terminology since your excuse for claiming diffraction should read refraction, which you also seem claim does not occur. However hopefully we are now agreed that the is no periodic structure that can cause diffraction. So we can rule out diffraction. Refraction is then the only mechanism that can bring about the observed colour separation. In particular reflection of the light in your bubbles example is white just because reflection alone cannot bring about colour separation. , One difference between refraction and reflection is that for reflection the light remains in one medium, whilst refraction requires two. Both the website I linked to and the one you linked state state quite clearly that the formation of a rainbow requires both refraction and reflection. This is because the actual mechanism is more complicated. If the colours were not split the observer would see only white light as with your air bubbles. The split occurs at the first refraction, that occurs as the light enters the raindrop, somewhere on the incoming sunshine side. Subsequently the red and blue etc paths are different in the passage of the now split light. So when the red and blue rays strike the surface on the opposing side of the drop, they will not strike at exactly the same place. When they do strike, as you say, some will be reflected back into the liquid water, to pass through it a second time. As you also said, this turning light away from where it was originally travelling to necessarily darkens that area. Again some of the light will pass out of the drop on striking the surface a second time. This also the difference spatial between the blue and red strike points will increase. Refraction then occurs at the exit interface for both red and blue rays. The upshot of this is that some of the blue light is directed out of the top of the observer's field of view and some of the red light out of the bottom. So you are correct there is not the fully developed fan of pure colours as with a prism.