studiot

Sorry but I think you have only answered one of my 4 questions. 1) is the most important and not the same as 3 It is still not clear what words or symbols that are on the page are discarded and what words or symbols are used to form a list from which one in 5 is then chosen. So I have reproduced number 2 of the words on my earlier list - note you originally rejected all of them, but the attachment contains every word associated with what I call the head word - dabble- in this case. Now I have asked and received directly conflicting answers to this question do you just consider Dabble as a candidate word or all the words in my attachment , for example are Mitchell, moisten, or, soil counted??

I can see you are having as much trouble understanding me as I am understanding you. Yes I have the OED, but unfortunately not the supplement so I don't know what the layout is for that part. As regards my other questions I have annotated the page in question. 1) Are you only choosing from the head word as I noted, 1,2,3,4,5 all in red? (These are different words not from the same stem.) 2) Where the word appears multiple times as a head word as I have underlined dab several times, how many times does it count? 3) If you are only choosing head words you will never see the abbreviations they are in the body of the text, as ringed. 4) if you are including the body of the text in the count, note the many standard abbreviations as arrowed in red. How are these reckoned?

Definitely there are some misunderstandings. And yes I remember your other thread. The problem is lack of precision. What do you mean by bias? Selection bias Self selection bias some other process And as to the sampling technique. Just opening the OED at the letter D shows imprecision of definition. I had assumed that you had not included in your 'every 5th word' all the text associated with each entry. But you seem to include all the text. If you stuck with the main entry heading eg dab, dabble, dabby, dabchick, dabitis being a sequence of 5 entries Then all abbreviations are listed at the beginning under abbreviations, which is a sub heading under D,d (the first entry in the D section) As such no abbreviations so listed at the beginning would be picked up. So the word 'dab' has five separate entries. How many would you count or reject? The text associated with entries usually includes abbreviations that are repeated many times eg v.t. ; colloq ; adv ; f.

You should look up Generalised Coordinates Degrees of freedom Which are used in many areas of science an engineering Thermodynamics and statmech - Gibbs Formulation Mechanics - Hamilton - Lagrange dynamics

Imatfaal is right, you need to put some meat on the bones and demonstrate that you follow the answers you are receiving. In particular I am concerned that you will use the sampling in a statistically unsatisfactory manner. Let us say that 10% of the picked out words are abbreviations Do you understand that it is unsatisfactory to simply say 10% of the words in the dictionary (or this section of the dictionary) are abbreviations? Because you are comparing two different distributions - the sample and the original population you also need to estimate the probability that you are right (or wrong). That is what confidence intervals are all about.

Being present in a frame is not the same as being present at all (significant) events. I say significant to distinguish between events of interest and the rest of the points in spacetime since an event is a point in spacetime. Your original claim was that all clocks were present at all events as well as in all frames. For any observer, Spacetime has timelike zones at which it is possible to be present at both events and spacelike zones for which it is not. So in the twins, significant events are P leaving Earth Q turning around R return to Earth The rocket clock is present at all three P, Q and R The Earth clock is only present at two, P and R. This is just a more formal way to explaining the asymmetry than my original offering which was essentially, the rocket went somewhere, the Earth did not.

I was about to say that I will leave it to swansont to discuss routes through spacetime and geodesics with you, but I see he has already replied. +1 you are nearly there with this question, but think about this. Think of a globe. The lines of longitude are the shortest paths between two points, but they are all of the same length and there are many of them. They are given a special name - 'geodesics'. By contrast only one parallel of latitude (the equator) is a shortest path. Every other parallel is longer than a great circle (geodesic) between these same two points. If there are multiple shortest paths, why can there not be multiple longest paths? Another thing about paths. The paths assume no 'wiggle'. A wiggle is a deviation or detour in some sense from 'straight on'. So a trip from London to Edinburgh via Leeds is (more or less) straight on, but a trip via Cardiff incorporates a wiggle and via Dublin a bigger wiggle. Wiggles are not possible in one dimension, but as soon as you get two or more dimensions they become longer paths than a direct one in the same way that the sum of two sides of a triangle is always greater than the third. However I regard this question of yours as a diversion or wiggle so I will leave it to yourself and swansont to carry on. When you are ready to go back to the twins, let me know.

It takes students studying this about 12 weeks to make their way through a basic course. And those students are already au fait with a good deal of Physics ie they are Physics students. Yes my offered analysis, that nobody seems to want, contains some simple arithmetic but it is perfectly possible to perform graphical constructions with gamma/lerontz built in to avoid even this. Russell shows a simple one in his elementary ABCs of Relativity. In fact graphical construction was once de rigeur in most engineering design offices for many tasks we now undertake by calculation. I have some old books that show how to extract roots, solve algebraic equations, perform graphical integration and differentiation etc etc.

Alfred, have you checked up on Latin Squares? They are not difficult to understand. Remember I said the question is like them, not exactly the same. Personally I don't think it is possible to develop a single mathematical expression that covers all possible cases with the front loading described. You would have to chop up the word count range and perhaps the % of abbreviations as well into segments and develop a separate formula for each.

Yes I was including Michel in the 'you guys'. (Would I ever exclude him?) The problem with those diagrams is that, whilst they are an excellent summary to someone familiar with this stuff, they contain a lot of information and there is no explanation as to where any of it comes from. Hence all the toing and froing about this in the posts. Thanks for the vote.

The (linear) wave equation in one dimension is given by a differential equation [math]\frac{{{\partial ^2}y}}{{\partial {t^2}}} = {v^2}\frac{{{\partial ^2}y}}{{\partial {x^2}}}[/math] With (one) commonly used solution [math]y = a\sin \frac{{2\pi }}{\lambda }\left( {x - vt} \right)[/math] As As you can see it connects space and time. The standing wave obeys the differential equation but has a solution [math]y = 2a\sin \left( {\frac{{2\pi x}}{\lambda }} \right)\cos 2\pi nt[/math] This separates space and time so for any time t you can plot the value of y over x. Edit Doing this with the wave equation is the beginnings of quantum theory by the way.

I honestly think that the diagrams you guys are bandying about are far too complicated for first understanding. In particular they run for way too many years. A few years are sufficient to establish the principles.

Yes he has miscopied. +1 mark please review your first post and correct it.

For a large word population I don't think it matters what distribution you assume; sampling every 5th word will divide it into uniform blocks, a bit like Latin Squares, and the result will tell you what the distribution is. This assumes all blocks are equally treated according to the distribution function. in the seeding of abbreviations. But this population is being compared to a second circumstance where the first bock or few blocks are treated differently from the rest. And the question was essentially which circumstance will lead to a better answer? The answer to this is that neither will always lead to a better answer. For very small word populations putting the abbreviations first is more likely to lead to a better answer. For very large word populations putting the abbreviations first is more likely to lead to a significantly worse answer, but will only be definitely worse for an infinite word population. The actual crossover point depends upon the actual populations.

I have to say that spacetime diagrams help some and hinder others. They are not necessary to understanding or working things out.

Yes the theorems variously attributed to Gauss, Green, Stokes are much used in Engineering and Physics to generate working equations. Green's other theorems are also used to help with some integration. They are also used in applied maths (numerical methods) to convert finite element to boundary element methods. Normally we do not used such a generally shaped volume of integration (It must be the mathematician in you that wants to be so general) because it is too difficult. The volume is generally a box, cylinder or sphere so we can use appropriate coordinates to simplify the calculation and is called the control volume. The control volume may be infinitesimal ie dx, dy, dz or it may be large but finite eg a reservoir. As to time independent functions you can integrate over the region in question potential functions are good. (Is R the best variable to use to describe your function ?) Scalar potentials - eg potential energy are much used in thermodynamics. Vector potentials can demonstrate static fields. So you need to expand your description of what you want to do. In general you either integrate a variable which is a function of position over some region to obtain the total amount of that variable (eg potential energy) in that region That is [math]\int {U\left( {{x_1},{x_2},{x_3}} \right)} d{x_1}d{x_2}d{x_3}[/math] Which gets you a sum total. But this is not integrating an equations, which you also mentioned. For this you (may) need Greens functions or Fourier transforms etc. For suitable equations that define functions this will get you another equation defining another function. A good example of this is integrating slopes, loads and moments on beams

+1

Sorry, Tim, I see what you mean. Try this. Actually, Tim, the frame of the clock(s) is of vital importance which are most certainly not present at all events in all frames, which they would be (could be) if they were present in all frames. I was not referring to Einsteins paper but the paintball games posts in this thread. In a way it is a shame that this thread had been split from another since it seems to have killed its progenitor. The twins offer a good opportunity to simply work through both time dilation and length contraction. In neither thread is anyone prepared to work properly through this. Furthermore the example I quoted above is the commencement of a simple analysis where the numbers drop out very easily. It also shows what happens to both clocks, only one of which (the rocket clock) is present at all important events. (Do you know what an 'event' is?) It is the sad fact that so many published 'explanations' of the twins tells less than half the story that IMHO confuses so many people. (I have to own to a bit of this myself in my very simple explanation of the asymmetry) I thought Mordred had already explained why you mistakenly think one clock 'ticks' faster and how you were misinterpreting spacetime diagrams, but obviously I was wrong since you persist in this view.

Actually, Tim, the frame of the clock(s) is of vital importance and most certainly not present at all events, which they would be if they were present in all frames. Michel, There is a big difference between length contraction and time dilation. An example for both of you. A rocket ship (observer A) leaves Earth (observer B) and take with it a clock and an one metre rule, marked off in 1cm graduations (0 through 100) and travelling at 0.8c. Both A and B will always 'see' the one hundred and one graduations on the ruler at all points in the journey. But they will differ in their assessment of the length of that ruler. As to the clocks, say A sends back a light flash every year, A will not see anything in the first three years, that is A's first flash will arrive at B when B's clock reads 3 years. The rocket clock is no longer in B's frame and B cannot measure on it.

Paste function not working. Clocks don't loose some ticks, they just never make them. A big source of confusion is identifying which frame a clock is in and not trying to take time differences between clocks in different frames.

Since you have visited the forum a couple of times since last posted, do I take it that you have lost interest in this thread of yours?

Was there something in my post you did not understand? It was a direct response to the OP assertion that the Earth has no (classical mechanics) connection to the plane. It was not an exhaustive analysis of all the forces acting, real or imaginary.

There is no simple anser to this, it is going to depend upon the sizes of the abbreviation and other word populations. Say there are 6 abbreviations and 30 words ( a short section). If you lump all the abbreviations together at the beginning you are guaranteed only 1 hit regardless of the subsequent number of words, but your accuracy will decrease as the number of words increases as you will never get another hit. If however the abbreviations are distributed it is possible to either get them all or miss them all depending upon the size of the rest of the word population. With 30 or greater as I offered you could get none or all six.

Robin, this question of yours has spawned at least one more thread and become very messy, which is why I originally avoided it. I did make a couple of posts containing questions designed to help you find the right view, But you have avoided answering them. When contemplating these questions it is very important to keep track of which clock is where and which system you are measuring in. A wrong placement here leads to embarrassing paradoxes and misunderstanding. In particular you should always find out which clock is at all the events - There will in general be only one of these. If you are interested I will work through the Twins using largely logic, although a little easy maths will be needed. The main thing to get the correct time differences, is to know which reading on which clocks can be used directly and which have to be transformed. Logic is need for this, not maths. But I will only do this as a discussion as I am not prepared to do all the work here. So In the Twins there are no clocks in the Earth system that are present at every event. Can you say which clock or clocks are at all the significant events in the the history? We will also be following this from swansont as it is a highly significant hint. +1

Please confirm the following with reference to my diagrams attached. Sorry for the quality of the hasty sketches. 1) Mark off an interval, ab, along the x axis shown by lines through a and b parallel to the y axis. Draw in y1(x) and y2(x) as the bounds in the xy plane. This defines a surface (area) in the xy plane. 2) Erect a z axis perpendicular to the xy plane showing the bounding area we are working in. I have shown this hatched. 3) Erect rectangular columns over this area from xy plane to the bonding surfaces given by z1(xy) and z2(xy) This defines the volume we are working in now for your function R The general wave equation is a connection between time and space which introduces an extra variable we have not catered for (time) To take time into account we have to account for the flux of R crossing the volume boundary as defined above, as well as the waves already within the volume. A more restrictive wave equation is the time independent equation of standing waves. If the waves are standing there is no flux across the boundaries so time may be discounted and a simple spatial volume integral employed.