studiot

Vitalism, as it was called flourished and then declined in the 17th , 18th and early 19th centuries until it was finally laid to rest with the synthesis of urea from purely inorganic sources in 1828 by Wohler. I seriously suggest you read the history for interest and direct your efforts to something that has reasonable propect of success in this modern world.

Thank you for deciding to participate in the discussion. +1 Hopefully now you have taken the first bite of the apple you will have aquired the taste of posting here at SF. Meanwhile I was interested in the line above concerning Bayesian methods, which are semi-empirical. Can you provide more detail? It is interesting because my view of GR is that our use is in a similar state to late 19th and early twentieth century Physics in many areas. If you read texts from that era much was made of more and more accurate experimental determination of many coefficients in a wide variety of physical equations, well ahead of any theoretical interpretation or links (for example the Lennard Jones potential). I'm not saying this was not very good work, because it was. Just that the Einstein Field equations conntain quite a few such coefficients, the values of which make enormous differences to the outcome solutions. So I would be very interested to see how Bayesian guesswork ties into this. (nor is this a condemnation of Bayesian methods which has some spectacular successes over more traditional methods and also offers a fine example of establishment blocking of significant work and theory)

So did you catch my point about the different terminology used by different mathematicians? This would be important to you since English is not your first language. I have basically been restricting my input to try to help you make sense of what others are telling you.

Yes that's good, and thank you for the next extraction, but I can't aks for all 55 pages. I tried copy and paste in to my old Word, but didn't get very far. Anyway I have some thoughts about the axiom vector field to make. It is a pity ajb is not here as he was the only one I have ever got to understand this point about vector fields. Even Modred didn't fully appreciate it. Unfortunately those pesky philosophers were right insofar as there has been all to much blocking and obstructionism by some established figures in the past. Although we like to think we are better today still scientific fraud still occurs (cold fusion and certain skeletons comes to mind). So open mindedness coupled with vigilance is the watchword.

Let's be fair. An well respected, but junior mathematician at the univesity of Kazan wrote Geometriya in 1823. This was the mathematics that paved the way for GR. It was blocked by the Progfessor of Applied Mathematics (Ostragradskii) and not publish until 1909.

+1

Thank you for extracting the 'abstract' (various puns come to mind) I was struggling with this. How did you achieve it? I ask because I want to extract the postulates and discuss them. they are interesting.

But I'm not wrong, though we do seem to have a difference of opinion. Differences of opinion occur in mathematics as well as other disciplines, as noted in part of my recent post. https://www.quora.com/What-is-the-difference-between-a-countable-and-a-denumerable-set Whilst I have already agreed that what I said was ill thought out and therefore amounts to balderdash, that was no reason to pour out vitriol. You could have discussed more like I did with taeto's slip. However since the OP is indifferent to my help I see no purpose being served in my further presence in this thread. If you wish to discuss Russell and the set of all infinite sets of numbers properly, then this should be done in another thread, should you wish to start one.

This is a good answer https://www.quora.com/What-is-the-difference-between-a-countable-and-a-denumerable-set Yes that was a bad description. I tend to think in pictures, not algebra. I have no trouble with universal sets in pictures. So go take a cold shower before you overheat.

Forgive me I should have said "the appropriate universal set", since there term as a relative one. In this case the universal set is the set of all entities possessing the properties of finiteness and nonfiniteness. This has nothing to do with Russell.

Yes a good thought. +1 But we should remember that our proposed curve between the points, straight or not is just a model. I think this is also what swansont was indirectly alluding to. Taking this model idea further, we should not say These are the measured points, this curve or straight line fits them so that is the correct reality. but These are the measured points. Whatever this curve measures does not deviate anywhere from the curve by more than X, which is an acceptable model between the points. Obviously straight lines, and therefore direct proportion, are generally the most preferable and often provably accurate enough. But here is a straight line conundrum. The height of a brick wall is given by the staight line function H = cN Where H is the height, N is the number of courses and c is the course size. Given that the standard course size is 75mm how many courses are needed to build a 5m wall? Well 67 courses will give you a wall that is one inch too tall and 66 courses will provide a wall that is two and a half inches too short. So what's to do?

Not necessarily. First there is the question of how one measures 'fit'. for example MiniMax or Least Squares. Then there is the question of curvature (and even perhaps higher order derivatives). This is particularly true at the endpoints, where the curve may have to fit smoothly into something else. Even straight lines, (and not everything is a straight line especially with 'end corrections') Curvature fitpoints are also used to generate additional equations to solve Physics situations. For example zero at the bottom of an elastic curve and a min or max in some energy consideration. And what about pulse measurement? All the wobbles are at the corners. And even the sags and slants from a stright line are significant. The schoolboy "I got a straight line through the origin sir" only works for Nigel Molesworth.

He's just stamping his foot because no one is taking him seriously any more. (and thanks for the spelling correction in an earlier post)

Seven words. Wisdom often fits into small spaces. Normally it is the other way round, the 'fit' is used to calibrate the curve.

Yes, as I said there is a whole extensive and sophisticated theory so that you can find bounds for any error, which you can make as small as you like, consistent with the actual precision of the data points. This is one of the underlying principles that allows finite element analysis to be so successful. BTW, it's nice to discuss the actual topic with someone.

The OP is right to be concerned about that. It is very very important in Science, which is why such an extensive theory of interpolation and extrapolation has been developed. In Physics we are lucky that in general the 'pathological' mathematical functions that make it difficult or even impossible to check this do not appear. The only exceptions to this I know occur with cellular automata, fractals and Gibbs Phenomena.

It doesn't help to chose the opening example from a discipline he has insufficient knowledge of.

To add background to the excellent definitions from wtf and uncool: Cantor chose the word 'transfinite' instead of infinite since he developed several different infinities. The point is you divide the universal set into only two parts and define one part as XXX. Everything else is then in then in the other part not or non XXX. The trick is to chose the right part for the definition. @taeto, did you get your X and Y mixed up?

I have already agreed with the sentiment, but perhaps the English could read a little more in line with what you actually meant next time. The thought of going down to the automation mart for a pound of nuts and bolts to fry up for dinner doesn't appeal.

I have already pointed out that no sine curve fits the data as drawn. The simplest equation to produce the sketches is f(x) = {Ax + Bsin(x)} This is not a sine curve for a numebr of reasons.

Was there some reason for not publishing the abstract? And perchance a comment? That would make your OP comply with SF rules. There are 55 pages in the article, which seems well put together at first glance, but it will take some reading. But definitely worth discussing. I was particularly interested in his distinction between 'vector' and 'tensor' (midway down the abstract) so my first task is to find out what he means by this, as tensors are technically vectors but only some vectors are tensors and GR relies on this.

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I think this explanation of undeterminism is pretty self explanatory. I also think it sometimes holds true. But I take issue that it is always true. So what is the relationship of this to Science? Well it suggests there is usually more than one answer / method of calculation / consideration etic. Do the philosophers really think scientists don't know this, live with it everyday, and have developed sophisticated techniques for handling the situation? Why do they think more than one method of solving quadratic (and other simple) equations is taught in elementary school? What more is there to say on the subject?

Fair question and yes I agree sufficient evidence can lead to proof. I think that the answers are being made too complicated. Evidence is material (data etc) which does not contradict the hypothesis. ( but may contradict some other competing hypotheses) Evidence does not preclude the validity of all other hypotheses. That is the job of proof. Proof contradicts and therefore eliminates alternative hypotheses. Does this help?

One thing we know about in Somerset is all things apple. Somerset is known as the apple county and along with the Wyvern, the apple is our symbol. Cider, scrumpy to those in the know, is of course our tipple. It is not necessary to fly drones to harvest apples. Special machinery straddles the trees, planted in appropriately spaced rows, and harvests the fruit in tonnes ( as Raider notes). Some apple farms are going back to the past experimenting with grazing animals between the rows for environmentally friendly reasons. When I moved to Somerset was the first time I saw the sign up on a billboard "Sub Contract Orchard"