studiot

I suggest a better way to think of the maths/physics of these matters is to understand that we recognise three basic quantities, which we call dimensions, that can be combined to explain, describe and work with what we observe in the universe today. These are Mass, Length and Time , given symbols M, L and T. Very simple combinations are length squared, (written L2) which gives us area. and Length cubed (written L3), which gives us volume. Energy can be described in this way (written ML2T-2) Notes There are a couple of other basic 'dimensions', which I won't introduce at this point. The use of the word dimension in this way is perhaps unfortunate as it is quite diferent from common perceptions of dimension but it is well embedded in Science.

Yes but 'scientific progress' is patchy. It proceeds at different rates at different times and in different places on Earth. And sometimes it goes backwards and stuff is lost.

OK so I have obtained the original article, which for the benefit of other readers is Finite Elastic Waves in Rubber P Mason Proceedings of the Royal Society of London: Series A, Mathematical and Physical Sciences March 19th 1963 pages 315 - 330 I agree the diagrams are a bit odd, but In the first 5 pages Mason clearly describes the meanings of the variables v, u, λ1 and λ2 ; It seems that the 'wave' referred to is a single unloading pulse which travels back towards the fixed point faster than the material itself. Different parts of the rubber are travelling at different speeds. That is how is is contracting.

A good idea to stick to the OP. One topic per thread is preferred at SF. My aim is to encourages participants to look much further back in history and much mor widely geographically when discussing progress of Science. I think the picture looks very different from an expanded point of view.

So can you advise on this question please ?

I was only a child when I read those stories. I had a quick look on the net but can't find any of the stories I remember - even the names are spelled differently now. However the 'solution' to the story was that the hero was slain in a doorway - neither inside nor outside the house. The fact remains that first order logic is unable to resolve the issue as it is based on absolute (usually binary) non intersecting classes in all cases. It is also interesting the the mythology of the four 'home' nations is quite different from the mythology in Europe, Russia, China and the middle East which have much commonality.

Yes it is, but I do not think you mean linear, I think you mean sequential. Yes I agree but not only is it not linear it is not always in the forward direction. Have you heard of the dark ages ? Interesting comment and welcome. I see from your postings that you have a wide interest in the Sciences, so with respect; When you say "This likely occurs" it is not very scinetific unless you adopt the scientific rigour ot backing up you statistical assertion with some facts, references or reasoning.

Thank you for posting this update, +1 I note that right at the beginning the authors acknowledge difficulties with solid-penetrating radar and later introduce ulltrasonic tomography. I too have had better reliability and accuracy. looking into solids with ultrasonics than with radar

If and only if you are genuinely interested in discussing this you will have to work harder yourself. Yes swansont says this (ie some) statement is a tautology. So what ? Under what system of logic, propositional (first order) or predicate (second order) or what? Since I consider examples are really helpful I have given you several, and again you have not responded to any of them. Why not ? swansont also said to which you responded Well I suggest to you that 'how?' is answered by providing an example for discussion. Here is an example of a first order logic being defeated by a second order answer In Irish Mythology there was a superhero who was apparantly invincible. So magic was cast so that he could not be killed either inside a house or outside one. Yet he was eventually slain. Would you like to discuss how and is his invincibility a tautology ?

I am away for the w/e Try the following articles. Ogden R W (1972) Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids Proc Royal Soc London A326 565 - 84 Ogden R W (1972) Large deformation isotropic elasticity - on the correlation of theory and experiment for compressible rubberlike solids Proc Royal Soc London A328 567 - 83

Yup, but only after considerable creation, organisation and optimisation effort by humans. Which is why they are so useful for repetitive drudgery, once that spadework has been put in. Edit I did mean to ask why noone seemed interested in my debunking the AI wave height measurer, but then I discovered that the thread wqs moved to trash so I could not post there anymore. Considering the current debate is no one interested in my comments there ? My back of envelope calculation suggests that the deflection angle of the horizontal for an instrument set up 1000m from the wave is about 36 seconds of arc which makes the height error 0.2 m. aft5er that the error grws rapidly with distance.

Does this address any of my comments on so called AI ? If so how please ? for example

Are you sure it was a short circuit failure ? https://academy.gs-yuasa.eu/wp-content/uploads/2019/03/Battery-Failure-Modes.pdf

My question was a rather tongue-in-cheek oblique reference to the long running row between the opponents and proponents of bayesian statistics as a way of highlighting the fact that, to the best of my knowledge, no AI yet constructed has ever discovered anything by itself nor had an original 'thought' of its own. How could it , when it is programmed to weigh up the most probable response to any given text string, based on what has already been written (usually in English) ? In other words at the higher level you are talking about student were (and I hope still are) taught by people who have actually discovered (new) things.

If the AI has never read the early work of the Reverend Bayes, but only been trained on Pearson and Fisher and Gosset what would it teach ? After all this thread is entitled statistics in science.

That still has to obey energy conservation.

That would not work well due to the Law of conservation of Energy, assuming the panels were optimally laid out in the first place.

And did you ask Chat GPT why this method would yield fallacious answers ? AI 0 ......... Surveyors 1

Here is some explanation that may help. The Earth is not 'all there is'. In other words there is space and time along with contents and the stuff that makes it all up beyond or outside the Earth. However the Universe is defined as 'all there is'. In these circumstances both space and time may be part of this 'all there is'. We don't know if either space or time are finite or infinite. We don't even know the nature of this infinity if it is there. We do know of other infinities which which have no boundary but yet can't be reached. For instance absolute zero of temperature. As you approach AZ it becomes harder and harder to take the next smaller and smaller temperature step towards it such that it can never be reached. Another example, if you know any maths, is exhibited by numbers. Take any real or rational number you will find there is no such thing as a nearest number to it. You can always find a nearer number than any propest 'nearest' and can go on indefinitely getting closer and closer to the proposed number, without ever actually reaching it. So if our finite is bounded in space, why not also finite in time ? Nature has shown itself more varied and unwilling to fit into our human conceived boxes and is therefore constantly suprising us with new stuff.

Your question - A good one - seems the sort of question that might (should) pop up in class when you have all the background of the course and its notation. So it is a very good idea to give as much information as possible about where you are coming ffrom and where you want to go. We normally like to place replies into the body of a thread, to benefit any member who might be interested. There is nothing confidential abolout this. The honest answer is that we are looking for solutions to Airy's equation. There is no pat answer as with say linear differential equations, each solution must be worked out for the specific situation. Airy's original was an inspired guess as are pretty well all other known solutions. This is the drawback for this method and the reason it has never proceeded very far. Complex analysis and conformal mapping techniques have largely replaced it as an analytical technique. Anyway here are a few pages from a book that is ideal for engineers studying stress analysis. It works from an engineering point of view and explains, when it comes to it, that we 'guess' the form of the solution and back substitute to check it fits the equations of constitution and discusses this for several example cases. Are you familiar with the idea of the equations of constitution and compatibility ? For Constitution either the equations of equilibrium or the equations of motion may be employed, but these alone will not give enough equations to produce a solution. That is where compatibility (or configuration or constraint) come in. Advanced Strength and Applied Stress Analysis R G Budynas

Is the 'Gap' getting smaller ? I invite you to explore this report on a computer closing the gap. Note this is only one of a line of bionic implants. Is the computer-brain one an advance on the well established computer-heart one ? https://www.bbc.co.uk/news/articles/ckgn49r069wo

I caught you previous howl of anguish over my previous post, but it is taking a few days to prepare something simpler. I had hoped that by pinching someone elses' drawing I could offer a quicker answer. Never fear, we will get there.

Not sure if you want a physical or mathematical explanation. The physical one is easier so I will start with that. When you integrate the differential equations you get many or infinitely many solutions that differ by an arbitrary constant. (actually since you should be using partial derivatives for this, you get an arbitrary function). Physically what we want is for that arbtrary function to affect all parts of the region and its boundary equally. Then its effect may be discounted. Finding a suitable function requires differentiating ande substituting the derivatives into the proposed stress function as you have indicated. The only way for the arbitrary part to affect all parts equally is for it to a constant function or at most a linear function, whose derivatives are zero or constant.

Well I am not claiming that there is a single object, but a simple example would be a shadow.

Given that the building blocks of life are molecules, it seems reasonable to assume that life arose from molecules in a "primordial soup". Well I agree with Luc on this. But only partly since he has made the basic mistake of trying to combine two separate statements, each with their own independant veracity, "Arising from molecules" is about source. "In a primordial soup" is about place.