studiot

Why would they wish to burn their product? Surely the industrial buyer has gas pokers?

What industrial use would this be? Gas pokers are usually used to promote rapid combustion industrially so this has never been a problem.

Any half ways decent Engineering course will incorporate the necessary Maths and Physics as a matter of course (pun intended). Most have 'common core' subjects with many different branches of Engineering. Remember to concentrate on the underlying basics / fundamentals. This is because of the pace of change, particularly in your chosen area. Water will still boil at 100oC in one hundred year's time, but I doubt that the OPV302 laser diode will still be around, except in museums. Go well in your future studies and career.

Yes. +1

A few paragraphs. Considering the first one ( or should I now say 0/0? ) in the OP are you encouraging more? Gulp! Allkey, please take a breath (preferably many) and approach this a bit at a time. You have too many concepts mixed up with too many non standard usages of words for people to read and respond too. I will take only one of your points and one of your words. What makes you thing the old sailors' meaning of cardinal as applied points of the compass is the same, or even related to, the very specific meaning of cardinal in mathematical number theory? The mathematical expression 0/0 is neither 1 nor 0. It is indeterminate without context and maybe not even determinate then. Please also be aware that zero and nothing are not the same in mathematics, although colloquially they are. So discussion based on mixing these is fruitless. I am giving you a balancing upvote so you can start with a clean sheet to try and save your thread before the moderators close it altogether.

You should read this book The attacking Ocean by Brian Fagan I see it can be obtained very cheaply second hand or perhaps your local library will have it.

This nicely embodies my comment, which is not about the general correctness, but about the detail or presentation. I prefer the phrase "for every point in that small region." I think it can be confusing for many to be emphasising the thermodynamic idea of a state function which is a single representation for a whole system, and then considering something like a tensor function which varies from point to point within a system and has no overall single representation. Indeed zero may feature as an overall average. I know this and you know this but... Sorry to be so pedantic.

But as you pointed out elsewhere, we work with continuous manifolds which means there are no boundaries between the points. So all your 'systems' have no boundaries and are therefore ill defined as systems.

No of course not. Have you not considered open systems or quasi closed systems?

Only 500 hundred years? Caeser came to Somerset over 2000 years ago, for just that purpose, and he wan't the first. We have had many more since.

This tensor (like all of them) is a point function/property so isn't it stretching it a bit to call a point a system?

But I wasn't speaking of 'indeterminate'. It was concerning the relative bit. Our units and plus/minus sign convention is just that a convention. Somewhere else they will use different 'units' but these will still be the same multiples of their fundamental units of charge as ours, in any given situation.

Hello Steven and welcome to SF. I take it this was an artificial scenario constructed for instructional purposes. Have you thought about the sampled population ? Two things stand out a mile about it.

No, charge is absolute. The field lines radiate outwardly from what we call a positive charge and inwardly for what we call a negative one. Note it is one of the physical properties unaffected by relativistic transforrmations. I'm pretty sure we have mentioned all this before.

Well I offered you discussion and you chose to reject it. Thank you for the lecture, it is clear that you only wish to push your own views. I'm sorry you will never know the correct Physics definition for the words Power and Energy, which unlike some words, have only the one meaning all across the different Sciences. And nowhere is it equated with a force, though that is a very common beginner's error.

Edit this bit about probabilities belongs in the other thread. Sorry. Here is a good discussion of combined probabilities https://math.stackexchange.com/questions/72589/whats-the-probability-of-at-least-and-exactly-one-event-occurring I don't favour the use of 'curled' dimensions. The use of 'curled' runs into the same problem as the use of warped or curved in the question of 'where does it curve/curl/warp into? Far better (IMHO) to use the notion of non linear dimensions which do not have this issue.

Fine, now please show mathematically how you can correctly add the probabilities of finding each spearately to get a value greater than unity. You are suggesting that if I take a control volume, V and introduce two balls sequentially into it, bouncing about at random then The probability of finding the first particle in a specific part is therefore [math]\alpha V[/math], and the second [math]\beta V[/math] where alpha and beta are some fractions, less than or equal to unity. Clearly if the control volume fraction of V is greater than one half then alpha plus beta will be greater than unity. This is because the combined probability for your either ball in the volume is not simply alpha + beta. Can you provide the necessary statistics?

I have been watching this thread from the sidelines as you have some interesting and valid points to make. But mockery through hyperbole is not the way to argue. We build standard houses from standard bricks. Sometimes special bricks are needed for a particular architectural feature or situation. These 'specials' are usually specially made to order. Marcus said that he wanted to work with continuous manifolds, I presume because he wanted to use calculus. However calculus of a sort is available for discontinuous manifolds, indeed the original calculus was discontinuous, and is still used under the term finite differences. So how about a mathematical refutation of a mathematical requirement?

Rather than remove it - improve it Just as you stated in the last line of the quote as underlined This last paragraph refers to the title, but unfortunately shows a basic misunderstanding of the scientific term power. The use of machinery does not change the amount of power or energy required to perfom a task, as you imply. Have you heard the Philosophical definition of a machine? "A machine is a device for putting work in a convenient form" ?

Thank you Arete for providing this balanced view and analysis and introducing pertinent material from Biology theory to us in general and me in particular. +1

Ken is my middle name ( though I don't use it)

That's a good point, John. However the process can go too far the other way. What was wrong with Webers per square metre or Newtons per square metre? I think that to be somewhat more demonstrative than the nonsense they have nowadays.

Yes they are equally fundamental. Have you heard of the mathematical phrases 'necessary and sufficient' ; necessary but not sufficient ? There is that sort of relationship here. Both are necessary but neither are sufficient by themselves, combined they become necessary and sufficient. Let us take some simple examples. Consider the burning of gases. First the burning of some fuel gas, say methane. This illustrates the probabilistic factor quite nicely. The chemical reaction (burning) cannot occur unless the fuel and oxygen molecules bump into one and other. It is reasonable to suppose that the more fuel and the more oxygen molecules there are the greater the probability of such a collision. So the greater the probability the faster the buring proceeds. However now consider the burning of argon or helium. Is this still true? Clearly the answer is no, and a good demonstration is given in the use of this fact in MIG welding processes. You have a very high concentration of inert gas that does not burn. So there is a deterministic factor in play which in this case acts as an on/off switch and determines whether burning takes place at all. This is the mathematical energy equation for the reaction process which shows that burning fuel emits a lot of energy, burning inert gases takes in a lot of energy, if it happens at all.

Yes, of course there is. Both can be found in consideration of the process of a chemical reaction.

Yes you are quite right. Thanks for pointing that out.