studiot

No they are invalid criticisms as demonstrated by the wartime economies of Britain and Germany. There was great efficiency and great innovation on both sides.

I'm glad we are making progress. A plane figure is the perimeter only of a shape that lies all in one plane (ie flat not like the surface of the Earth). Such a shape may have any combination of curved or straight or straight sides, but it must be 'closed'. That is it must come back to its starting point and enclose some area, although the area does not form part of the figure. The only closed shape with a single side is a circle (note a circle is the perimeter only of a disc so it is the circle that has a circumference but no area and the disc that has the area). A lens or lenticular has a two sided perimeter Of course both lenses and circles have curved sides. A polygon is a many sided figure, with all the sides straight. (poly means many) So a rectangle is a four sided figure. If all the sides are the same length the figure is called a regular polygon and these are the sorts of figures we are considering. There is more but that's the bare bones of it.

I know its harder to study just out of a book or online because you can't ask questions of a book or pdf, when you come across something you are not sure of. So you are doing exactly the right thing because SF is exactly the right place to ask. +1 OK so there are no polygons with 1 side or 2 sides (can you say why ?) So in the expression (1-2/n) n must be 3 or more, that is greater than 2. so 2/n is always less than 1 and so the whole expression is always positive. Discussing this helps us since we now know you can understand the notation (brackets and algebraic expression) so keep it up. This was an example of mathematical reasoning. Butit does not answer you question. The answer comes from the proof of the formula. Here is a chatty version. We can do a formal proof if you like but you need understanding rather than formal instruction. Incidentally do you understand X - Y graphs ie plots with x and y axes on graph paper ?

To further your studies, have a look at this pdf and see wht you make of it. http://www.benjamin-mills.com/maths/Year11/dimensional-analysis.pdf Then look here at the other pdfs in this range (they are all free) https://www.benjamin-mills.com/maths/Year11/ In fact this little experiment is successful, there are lots of free pdfs for Physics - we can help you find some good ones. One good online resource resides at http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html But you may need to imbrush up your maths a bit.

You asked for a book. Try this one, it can be obtained very cheaply second hand. https://www.goodreads.com/book/show/1259850 Ferris is the editor , but the authors are all solid solid scientists saying their piece. The World Treasury Of Physics, Astronomy And Mathematics (paperback) £2.99

What the Dickens is that ? The challenge was Note that the poet is addressing the kittens (in the plural) with declensions of thou.

Thanks I have learned something here as I was considering the difference between singular and plural. +1 Apparantly we are both wrong since the addressee is plural (kittens)

Why so ? Though I agree it is just drivel. Was that meant to be in the style of Shakespeare or Browning ? Surely poetry competitions 'in the style of...' are just more plays upon words up with which we will not put - in the style of Churchill ? 😀

Well you have already taken the first two steps so +1 You have understood your current limitations and are looking in the right direction to overcome them. But take heart. We can provides some basic explanations here at SF. Your idea of a book is a good one because once found you can always refer back to it again and again. However first please give us some idea of your education since you cannot get far without some maths. Much of the requirement is or was on the school syllabus for instance have you done any algebra (secondary school) ? I deliberately introduced MLT to investigate your reaction to some very simple algebra of indices or powers, roots and reciprocals. You will come across this again and again so if you don't understand something - copy and post the part you need help with. Never bre afraid to ask in the manner you have. These questions are not silly at all.

Energy is not fundamental nor is it an entity or substance. Mass, length and time are fundamental properties of what we see today. Firstly I did not supply an equation. Combinations of M, L and T are special and complete in themselves. for example force is MLT-2 that is it is not energy. Acceleration has no mass term LT-2 I take it you are comfortable with the square cubes tc notation and the negative indices ? In answer to your first question. We simply don't know what was there or fundamental at the 'big bang', or even if there was a bang. It is really pointless trying to describe those conditions in terms of what we see today.

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.