studiot

1)First, please note I didn't carte blanche tar everyone with the same brush. Second, your own words here seem to be encouraging further negative scoring! Go check the continued hostility from one poster here in particular, who keeps up a barrage of negative commentary yet without incurring any negative scoring on his part. Interesting - no? 2)Now, wrt your 'axioms' issues, on checking back to your first post here, I note you stated the following: "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." 3)That has it backwards - vectors are a rank 1 subset of tensors. I note on p2 here you complained: "So no response to my vector field question then, and we still have to go offsite to read any replies?" 4)But I found no earlier specific question just a vague appeal for discussion on it. If the well structured manuscript itself is not sufficiently clear for your needs, consider emailing the author directly for further expert clarification. I'm a layman btw not claiming expert understanding of it's content. 1) But you continue to complain about a 'negative response'; I looked back and confirmed that not only did I welcome warmly your first post, but you received several upvotes for it. 2 & 3) I am an applied mathematician, not a cosmologist so I am more interested in the maths behind it than the cosmology itself. I would have thought that someone who is 'new to this' would have asked what was meant when someone who has been studying and applying maths for more than 60 years made the comments I did. Certain (mathematical) events stand out in that time. Several times I have had to unlearn what I was taught as 'gospel' in order to progress to more advanced Mathematics. Vector theory was one of those times. Physicists are prone to deploy a very simple version of mathematical vector theory, and neglect to say that their theories mostly need to be extended to affine spaces to be of any real use. Integrals are vectors, continuous functions are vectors, and yes tensors are vectors. Which is why the tensor - vector- scalar heirarchy is an unfortunate classification. A vector is a member of one the two sets that are needed to make up a minimal vector space. Useful vector spaces also often contain extra structure, by way of adding extra sets along with perhaps a few extra axioms. It is this extra structure that distinguished one vector space from another. Relationships between the members of the two or more sets in the vector space conform to a basic set of between 8 and 10 vector space axioms. 4) I am sorry if you found the quoted question vague, I thought it simple and direct.

Hello, You video is quite a good one - if you understand some basic facts so I will tailor my comments to the video. But first try this experiment. Take a book of heavy sheet of carboard or wood and see how fast you can wave it through the air. You should have not trouble feeling the air resistance. And the harder and faster you wave the greater that resistance. It is this air resistance that is the key to the operation of both the turbine and the compressor. Rotating turbines and compressors have two basic modes or types of operation. Fluid (air) can enter or leave at right angles to the disk of blades, along or parallel to the shaft. This air is then directed outwards by the action of the blades against the air resistance. As you found out in your experiment the greater the speed the greater the effect. That is why the blades need to spin so fast. This action turns the air flow through a right angle so it is now moving at right angles to the spinning shaft and parallel to the disk of blades. The blades themselves are specially shaped to facilitate this. The air then leaves or enters the casing at a hole in the outer edge into a pipe. Note I said the air can enter or leave and then it leaves or enters. You video shows this very well, can you identify which way the air is flowing in the turbine and the compressor parts? Hint they are opposite directions. This type of turbine or compressor is called a radial flow machine. The other type is called an axial flow machine. Here the air enters parallel to the shaft and does not change direction. It remains flowing parallel to the shaft and so enters the machine at one end and exits at the other. This type of compressor is used in jet engines.

It would be helpful if you could fill in more detail since neither of these subjects are suitable for beginners. Both these reactions are currently the subject of intensive and secretive research for commercial and national economic/ security reasons. Hence much remains unpublished about the subject. Do you know enough electrochemistry to understand the potentials involved and catalysis theory to support efforts? Where exactly do you want to start?

I haven't distorted anything. In fact I have repeated offered you discussion about fundamental assumption or 'axioms' proposed by Svidzinsky Discussion which you have steadfastly avoided. Added to attitude like that displayed in the above quote you are likely to receive negative responses anywhere. Further I observe that many of my earlier posts in this thread welcomed both the OP (who has now let us) and the subject here for adult debate, not playgrund catcalls.

And what would the Beta i be?, Edit and the w?

OK as so often happens Wiki gets bogged down in detail. Here is an untangled version. Formally the rapidity alpha is a quantity associated with and derived from a velocity V. [math]\alpha = {\tanh ^{ - 1}}\left( {\frac{V}{c}} \right)[/math] Note this is an observed or apparent velocity, not a relative velocity. As you observed this is the so called hyperbolic tangent. The justification of this term is that it give an easy way (formula) to compose (add) velocities to find their resultant. For two velocities V and U the vector addition yields [math]W = \frac{{U + V}}{{1 + \frac{{UV}}{{{c^2}}}}}[/math] However we may simply add the rapidities thus [math]{\alpha _W} = {\alpha _U} + {\alpha _V}[/math]

Thank you for that explanation. It means that your defining expression is not an identity (for your purpose) and therefore cannot be used as a definition. This is because one or more variables are limited in extent and you have not shown this.

Well the underlying theory of Chemical Kinetics (the time rate of progress of a chemical reaction) is found by considering the probability of the reactant species meeting, since they can't react without meeting. Boy meets girl stuff you know. However many chemical reaction are not simply A plus B meet and go straight to C plus D This is a single step On many occasions intermediate temporary products are formed which finally turn into C and D. This is multistep and only one of these may depend upon chance. Let us say the reaction is such that when A & B meet they form AB first. The composite AB then breaks up into C & D. The first step is probabilistic (chance) the second is guaranteed so deterministic. Does this help?

Thank you Strange. What is 0.2V in Steve Upson's reply? Is capital V a new variable or what? And is this a reply to Strnages question in the preceeding post?

I seem to have missed both of them. Can someone please identify them. Thanks.

Yes what about them? Remember you have 5 posts in your first 24 hours, so don't waste them - after that it is unlimited.

Chance and the multiverse. Perhaps your view of both chance and the multixxx is to simplistic? If you look at some chemical kinetics you will see another (more complex) viewpoint of both subjects. For instance you are assuming a single step in your use of the word chance. What about multistep?

I expect your error is that the calculator see the division by 10-23 as division by zero, since it cant hold such a small number. Have you tried cancelling all the powers of 10 first.

Thank you for the interesting link, Geordie. One thing I immediately noticed was the following The author replaces time as the fourth dimension, with a fourth space dimension, for his analysis. That's all very well but he still admits only four dimensions. Yet he goes on to talk about motion and velocity in his four dimensions, without apparently allowing time to have a status.

I see you are back again Q-rrrus. but I still can't see a response to my question to you from two pages back. This was about one of the 'axioms' stated in the paper you provided.

Interesting. I think there is some fault movement and minor quaking in N. Carolina generally. And far down is that water table? Is the water warmer further down? But of course if the water is already that warm how would Ken store more heat in it?

I'm not quite sure how many times (I think it was three) Einstein fundamentally changed the equations of GR and 'experts' are still arguing over which version is 'correct'. Note I don't mean the solutions, I mean the equations themselves.

Perhaps only a poet can answer you so here is Samuel Taylor Coleridge on Mathematics

Thank you for the information, though I think we still have a very long way to go in grappling with this subject. IMHO we are still trying to extrapolate far too much from far too little information. So the process of 'refinement' will go on.

Yes and they can reach boiling in certain tributories of the Amazon and places like Iceland if there is local tectonic activity. I should have been more specific and specified stable ordinary ground free of such. Discussion goes better if you read what I wrote more thoroughly.

Thanks for all the replies, too many to comment on individually, but the thread has provided an opportunity to air different views and experiences. I will pick out a few comments. I presume the survey you referred to was an EU survey not a forum one. Either way this is the first I have heard of it so I didn't respond. That's exactly it " no one told me" +1 Mman. The annoyance has only been happening for a few days. Unfortunately cookies, though they can be used in a benign manner, they are like visitors to my house. Some behave themselves properly, some don't want to follow my house rules and some are simply there for no good. So to avoid the latter I wonder in simply banning cookies is the answer.

Hello, Geordie, haven't you asked this question before, or perhaps it wasn't you? The answer depends in part on whether you are talking to a Pure Mathematician or an Applied Mathematician. A Pure Mathematician might say that Geometry is the branch of Algebra that deals with congruence. Since (Pure) Mathematicians set out in the early 20th century to recast the whole of geometry in algebraic form. These same Pure Mathematicians might also say that Topology is the algebra of similarity And that wider, since similarity includes congruence as a special case, geometry is a branch of the more general topology, where a beer glass and a football are considered to have the same shape. This arises because you can only define congruence (and congruent shapes) when you have a definition of distance. For instance corresponding sides of congruent triangles have the same length. Thus is this Geometry. But if your triangles only have the same angles, but different coresponding lengths of sides they are similar but not congruent. Completely on the other hand an Applied Mathematician would say that yes, Geometry is the Mathematics of Shape and Form. Indeed I have several important textbooks with that or similar names. So a Pure mathematician might say to you The equation of a general inverted Catenary is [math]y = \frac{\alpha }{2}\left[ {2 - \left( {{e^{ - \frac{x}{\beta }}} + {e^{\frac{x}{\beta }}}} \right)} \right][/math] Where alpha and beta are coefficients. But an Applied Mathematician might say, "That's no good" or "That's no fun" "But if you put apha = 1.030 and beta = 1.322 you wil have the equation of the St Louis Arch, which ahs featured on television recently.

Why do I have to be pestered with this cookie nonsense every time I look on the forum now? Surely accepting the cookies once should be enough. And is anyone going to tell us about the changes to the site. Who knows some of them might actually be useful to users.

If it's only an approximationhow can the show that they have found the longest line? See also my edit above.

Nice one Cyril. Nice one Son +1