studiot

Is that so? I wonder how you deduce this ? Or is it one of the many claims you are going to make without evidence. Have you ever heard of the cuckoo? Both the cuckoo and the target bird can count to at least 5. It is really quite sophisticated, but not as sophisticated as the fractions you seem to claim animals can cope with.

But that's what proof testing is. Suppose you have loading sling. You will want to know that it will perform up to and beyond its rated lifting capacity. You obviously can't test it to destruction to find out what its ultimate capacity is so you test it to a 'proof' level, which is greater than it will be called upon to lift in normal working (its rated capacity), but not great enough to break it or even damage it. In the UK lifting devices have to be proof tested every year like this. You pictured a bridge. I have proof tested hundreds of bridge deck beams in this way before installation. That is measured the performance at a load less than breakpoint, but higher than working. There is reams of theory about this.

We have proof testing because tests to destruction can never be repeated, but when made ultimate results are never rejected. But you did make some other good points.

In the absence of further comments from ydoaPs I can only go by what he said. Please quote where he said precisely the above. This quote has an entirely different meaning from your version.

From your response I assume that you regard counting as mathematics, although you didn't specifically answer that part of my question. In respect of your comment, as far as I can tell, it is only humans who compare counting methods. Animals are not that advanced. But were the earliest human counters that advanced either?

It is well known in biological science that some animals can count, I'm sure one of the life sciences members could tell us which birds can count eggs and chicks. So is counting mathematics and does it have to be a human invention?

I believe it has been tried, though I don't know the result as I don't know much about the maths of economics. The applications of the FFT are much wider than just electrical engineering, I last used it to analyse the vibration frequencies of a spinning aircraft propellor, from the wind noise generated. The FFT requires the data to be present in a specific format for analysis. There are several schemes.

What do you mean a timeseries and what is it for? Well you need to organise your question in the light of the information below. Fourier series and transforms are a way of representing the original function of time as the sum of a series of functions of frequency because they may be easier to work on than the original function. In the case of the FT you also need the inverse transform when you have done calculating. Fourier series only apply to periodic functions Fourier transforms can also apply to non periodic functions There is also the fast fourier transform (or finite fourier transform) , FFT, which is different again and is used to work with XY data as opposed to analytical formulae. Over to you

Quickly a multiply connected curve crooses or intersects itself, a simply connected curve does not. Figure of eight. - Multiply connected Circle - simply connected. Parabola simply connected.

I think you have it bass ackward sir! Measurement is in the title, the introduction and specification of this thread. Distance is not. It only appears amongst a collection of examples presented by ydoaPs. I can;t see how anyone reading post1 can take anything other than measurement as the focus. This said, the rest of your reasoning falls.

Do you not differentiate between the measurement situation for a continuous variable where values arbitrarily close to zero are permissible and variables where only certain values are permissible?

Hello pavel, If you genuinely feel that zero resultant is the same as no force, try this experiment. Go and stand in the middle of an empty horse park, where there are no forces acting on you (except gravity and the ground reaction). Now obtain two equal on opposite horses, stretch out your arms and hitch a horse to each one and shout giddyup. Do you still feel that they are the same?

Well I think there is a difference and zero is not always arbitrary. Pavel asked a wider question than his charge example so I will addres that. Sometimes zero or not present make no (practical) difference. But would you describe absolute zero of temperature as an arbitrary reference or zero being the same as the absence of temperature? Some physical qwuantiies have continuous values that reduce to zero in certain circumstances, which may be very important. For instance the resultant of a system of forces is always present and zero is neither arbitrary or equivalent to no forces being present at all. I am rushing this because I see swansont hovering, maybe more later.

All too many books for science follow the stuffy 'lecture at the audience' approach. Even those with the most amazing graphics that are really showy. This makes the reader passive, except perhaps for forced 'exercises'. This sort of thing is fine for those who are already interested but will not stimulate those who are not. Science is about doing. 8-10 year olds are about doing. So I suggest you use this fact to create a book that they can do with, and learn some scinece along the way. Perhaps a bit like the National Treasure films (But with real science). Perhaps a crime mystery withs lots of CSI But present them with problems and take then through solutions, and choice of solutions. Old fashioned science teaching often promoted the idea that there is only one solution. So I am suggesting you create a theme or challenge to work through. This could be the basis for a series of books if the idea turns out successful.

I really don't know what to make of this last response. Are you moving away from polynomials? The fixed point methods referred to on page 22 of your latest link is a posh name for the method I offered back in post2 to solve your original example. The classic reference work for what you have just outlined (it contains all the programs you could possibly want as the authors set out to code every numerical technique in an encyclopaedic fashion) is Numerical Recipes Flannery, Press, Teukolsky and Vetterling Cambridge University Press There are disks of the computer programs also available. Two books you might get for next to nothing since they are outdated (in Basic) Basic Numerical Methods Further Numerical Methods in Basic Both by R E Scraton They contain excellent presnetations of both the necessary underlying math theory and the computing theory needed to turn these into practical (Basic) coding. I'm sure that a competent C programmer could reuse these. There are many worked examples to act as benchmarks

Well sort of, but not quite as you imagine, but +1 for having the idea. Driving a reaction by applying electricity is called electrolysis. However that does not let us reach new reactions, it only works on reactions that might happen anyway. It can do two things. 1) It can accelerate actually occurring reactions and/or drive the equilibrium further in the direction of products. 2) It can overcome activation energy requirements in the form of potential barriers.

I am suprised that you found the formalism expressed in the Harvard pdf simpler than the question and answer expressed below. Through this thread I have noticed something (this is an observation, not a criticism). That you seem to concentrate on and work from abtract theory and the most general to the particular. So all the references and quotes you are bringing up are about abstract theorisation and generalities. Numerical methods is basically the one part of mathematics that works the other way round. The whole raison d'etre for numerical methods is to obtain an answer, by any trick in or out of the book. If you can later generalise this to more situations so much the better. You originally asked about numerical methods for solving (= finding the roots of) polynomials and provided an example for discussion. This was a good idea as we began to explore the application of numerical methods to a problem we could readily solve exactly by applying a formula. Comparison with the known is always a good way to explore new techniques. Somehow that discussion became diverted before that exploration was anywhere near complete. in particular we did not look at why the numerical method I offered would produce one root but not the other one, or how to ensure we get to both roots or at least to the one we want. Working through that traditionally provides invaluable experience in the study of numerical methods. But we got diverted to generalisations. I suggest you need some hands on experience as to what happens when we try to use particular polynomials in particular circumstances which will show why there are so many different techniques available. I will try to post some sketches which will answer, explore and illustrate bothe these questions and the comments made in your quotes above, if this is of interest? The second quote seems to echo much of what I have said, (or been trying to say).

Yes most technical subjects have a plethora of jargon and abbreviations to make thing easier for the experienced and harder for the beginner. How did you get on with my link to extrapolation, interpolation, collocation and stuff?

You are not the first in this thread to deny this as a measurement, although I have to wonder about substituting 'quantification'. Neither you nor the others who don't like my measurement of area (can you offer a direct single quantity measurement to replace length times breadth) have offered any definitive definition of 'measurement'. So here are some more thoughts to ponder. Consider a single photon approaching an atom or molecule. It is, or is not, captured by the molecule. Is this a measurement? Well yes it's is a definiteve measurement of the energy level of the capturing electron - it either fits the energy gap or it doesn't. This is the same as granny using a hole gauge to measure her knitting needle or a mechanic to measure a drill size. They either fit or they don't. Again these new examples show something interesting. Measurement as a non mathematical technical process. Here is another. I have a telephone socket tester that displays coloured lights depending on the connection of the wiring., reverse or correct and other functions. It measures wiring polarity correct, ringer operation and within range voltage.

Beware of jumping ahead too quickly or you will find yourself increasingly tangled up. I identified that you misunderstand the word linear ( a very common misunderstanding, shared with the author of your last reference). A function, f(x), (including polynomials) is linear if and only if 1) For any x1 and x2 f(x1 + x2) = f(x1) + f(x2) 2) For any x and any coefficient a af(x) = f(ax) Try this with f(x) = 1+x and see if it works. You will find it does not. f(x) = 1 + x is called affine not linear. If you add the constant to a polynomial it changes things. I did suggest you need to look at linear mathematics and also offered some links about basic terms in numerical mathematics. Did you look at them?

Neither I nor the OED can agree with you there, since epistemic can apply to gradations and you are only putting a binary case.

Hello angus, do you know what plasma is? Plasma is a state of matter where the atoms have (nearly) all lost their outer electron(s) so they are ionised.

That's true and harnessing the 'power' is already achieved in flourescent light tubes. The gas inside is in the plasma state.

Until you can do us all the courtesy of providing a proper specification. I am going to suggest you study MHD and fusion containment vessels.

Those 'professionals' closest to the money somehow see the most of it.