studiot

This question and the subsequent discussion depends crucially on what the participants consider a dimension to be and also what properties it posses and its relationships to any other dimensions included in the discussion. Is a dimension more than just a succession of numbers?

Has anybody considered the implications of rotation first v translation first ? There is more than one possible solution to the question as posed in the title. Some of these solutions lead to unfortunate consequences if attempted in the real world as opposed to the abstract world of mathematical manipulation. For instance consider a spacecraft docking with the spacestation or a supertanker docking with a jetty. I would suggest it is better to line up (rotate) your craft before attempting the final docking manouevere (translation).

Here is your initial error. This incorrect ve is relative to the rocket, as correctly stated in your own reference. Did you understand the derivation of 'The rocket equation' given in your reference and in particular the significance of setting the condition that delta t tneds to zero? This is necessary to achieve an inertial frame (which is your observer "at rest" ) by a Galilean tansformation, given by in your reference.

I was interpreting the OP word 'move' That is why I quoted from the title, not from the body text of the post. Note that in 3D space (as required) the ( 3) coordinates cannot fill out a 4 x 4 matrix.

This cannot (in general) be accomplished with a single operation. It requires one or more rotations followed by a single translation. The rotations are required to bring the plane of the polygon parallel to the required plane. The rotated plane can then be brought into coincidence with the required plane by a single translation.

Gagging order received and understood. Goodbye.

I have reported personal experiences only. I do not like to be called a liar, especially not by a moderator. Post reported. I have reported personal experiences only. I do not like to be called a liar, especially not by a moderator. Post reported.

Unfortunately some of the younger generation want to do exactly what the worst of the older generation does. Tell me what to think. The Brexit referendum is the first and only opportunity I have ever had to say what I think. Other than that I have only been offered a list of people with stated polices few to none of which I support.

But you were stopped? Once is once too many. How many times have you been stopped on th M1 or M25 by men with guns? Schengen had not been 'invented' when I was promised that. It was written into the original treaty Heath signed (but never enforced). But yes, I have been pleasantly suprised how easy it is these days to travel between Ulster and Eire. Long may that continue. There is no need of a border of any description. Of course the border issue is another source of misinformation over the Brexit argument. It is completely untrue that it would be the only 'free' border' between the EU and another state if only the politicians both in the UK and the EU would. I remember well going into France with friends living in Switzerland (not in the EU) just to go to the supermarket. There was no border in sight. Again a visit from Geneva to Yviore (and back), for lunch No visible border to be seen. But the powers and term of office are vastly different. The EU is being dragged back to the Napoleonic system. A total anathama to anglo saxon virtues. "No one voted to make Theresa May PM ", certainly not me, I never wanted her. Edit It is hard to say where she was more incompetent. Her time at the Home Office, the remain campaign she was part of or the leave 'agreement' she didn't negotiate. The only 'rag' I have ever subscribed to was the Saudi Gazette. And a far better example of journalism that either of those you mention. As to the insulting comment, I knew it would end in tears when I obtained and went through the entire Maastricht agreement, some years ago now. Do you know what it says?

No there was never a public vote to join. The government of the day under Edward Heath decided to join and took us in. There was a later referendum, heavily biased in its wording about remaining in. (1975) The 2016 referendum was the first plain and simple in or out question and Cameron deserves credit for that simplicity. Both official sides of that debate ran totally incompetent campaigns and many half truths, statemetns of wishful thinking or ignorance and outright lies were made. This have never been unusual in British politics. One such untruth was the statement "The UK would be the first country to leave." This is just not so., although I believed it until I found out that in fact Iceland had left many years earlier. Another half truth was the idea that the European Union of 2016 was the same as the European Economic Community the UK joined in 1973. It is nothing like. The EU is an entirely different, non democratic political organisation. I have never been allowed to vote for its 'president' - unlike the USA. It was created without democratic reference to its people during the time of Major. As an oldster I can remember the days before the UK became a member of the EU. Personally I cannot point to many benefits I have seen. Things were definitely better in 1965 than in 1975 or 1985 and I do not think they have improved since. In particular I was promised the right to freely (ie without let or hindrance or question) travel to other parts of the EEC/EU as though it were all one big country. This has certainly never happened. I still cannot 'pop over' to visit relatives in Rotterdam as easily as I can those in Rochester, Without men with tommy guns demanding my papers and reason for visit and so on and so forth. Of course the same applies when I come home.

Thank you for this detailed reply. Here are my initial thoughts, more detail to follow as it is late here. The point I am making is that entropy increases when you consider the entropy of the system plus the entropy of the surroundings. System B is (by definition) part of the surroundings to system A at the beginning of your process, since it is not part of system A. System B is also isolated from system A. During the process systems A and B amalgamate to form system C, which is again isolated from the rest of the universe. This is therefore not the system you started with, unless you choose to so adopt it, instead of system A. This approach has the advantage that isolation (of system C = the system) is maintained at all times. But the volume of system C does not change so ln(V2/V1) = 0 and classical thermodynamics is upheld. Alternatively you can start with system A alone as the system. In this case you loose the isolation the moment you remove the barrier between system A and some of its surroundings. If you calculate the number of microstates in the enlarged system from Boltzman's Law then you will find that the increase in W more than compensates for the loss of entropy in system A alone as a result of the mass efflux.

Yes but a scale of mass is not very complex. There are other far more complicated objects around.

Such dramatics are not requested. Yes I realised that I missed out making it clear I was referring to your idea so I added those words as an edit. I'm sorry if that threw you. The idea I'm referring to is the idea that Yes I think they, like many other 'object' I have tried to talk to you about do not inhabit spacetime. So I think you are right there. But you also say because of their size and I disagree with this part. I think they belong in another framework because of their complexity. They do indeed have a common point of intersection between their world and spacetime. But the two 'worlds' only touch at one common point. That is how they interact with each other.

I don't understand what you mean.

And yet you repeated your idea at the beginning of this thread. Why do you think it was wrong? Wouldn't it be better to ask what idea of yours I thought, and think might be (nearly) right?

You have had a good idea. Good because most people don't notice this. However your idea is not quite right and the consequences that you attribute to it do not flow from it. Your consequences are thus wrong. The last time I tried to help you understand (and develop) this idea of yours you were quite rude, and then stopped talking to me.

Perhaps if you took other people more seriously you might make faster progress.

What exactly in what I wrote leads you to think this might be the case?

A pity you are not talking to me since you are both right and wrong here. Part of you problem is you start talking about non particulate things, like spacetime for example, but then switch to particles for your discussion. Why do you do this, it makes no sense.

What other salts are there besides metal salts? Would you prefer Ammonia?

Don't forget there are several Nobel prizes for different things, so your scientist could be involved in one of a variety of sciences. Various Jedi talked of feeling a 'disturbance in the Force' Considering the dustance involved both hyperdrives and feeling in the Force must be translight. Perhaps your scientist discovers a connection between them?

Translating this to Joules the average kinetic energy of one single air molecule at room temperatures is of the order of 10-21 Joules. The lowest ionisation energies are around 10-18 Joules per electron. So you can see that even if the air molecule lost all its energy colliding with the wall this would be 1000 times too small to liberate one electron. There are phenomena that convert mechanical energy directly to electricity but the amout available is very small for similar reasons. Triboelectricity (generated by friction) Piezoelectricity (generated by stress/strain) are often offered as generators in fanciful green energy schemes. Any form of work or work equivalent generation also suffers from the thermal efficiency formula [math]{\rm{Efficiency = }}\frac{{{{\rm{T}}_{{\rm{hot}}}}{\rm{ - }}{{\rm{T}}_{{\rm{cold}}}}}}{{{{\rm{T}}_{{\rm{hot}}}}}}[/math] As you can see there will be a very small temperature difference between the wall and the air ( perhaps less than one degree) which leads to a hoplessly inefficient generator. A final comment Chlorophyll extracts energy from photons not air molecules. Photoelectricity is an entirely different ball game.

It would help if you explained what you are trying to do. Are you trying to obtain an estimate of the derivative from the finite differences? You realise that you need multiple points to obtain the second and higher difference, you don't square the first differences? For numerical differentiation it is normal to use forward differences at the beginning of a table (where you have tabulated values below you) backward differences at the end of the table (where you have tabulated values above you) central differences in the middle of the table where you have tabulated values (both above and below you)

I wouldn't recommend it since the dx2 in [math]\frac{{{d^2}y}}{{d{x^2}}}[/math] means something slightly different than h2 , ie not the same as (dx)2 would be.

Polling in yet another election closed a few minutes ago. In fact it was so cold I saw a politician with his hands in his own pockets. .......?