studiot

It's a little more than that as it also includes charge conservation, which you need sometimes to gather the right number of equations to complete the set for solving.

It would also be useful to understand the meaning of 'singularity'. But it's rather technical and I don't think the definition as 'a point where a function ceases to be analystic' will help much until you know quite a few more supporting technical terms.

+1 Here is some of the knowledge you need :- Essential The difference between an Hypothesis and a Theory. An outline of the Scientific Method. The difference between proof in Law, Mathematics and Science. The difference between Axioms in Mathematics and Principles in Science Desireable The meaning of energy and probability.

I do not really want to discuss religion at all. But you seem to want to drag religion into the discussion. For your information we have a member who after teaching himself advanvance theoretical Physics , became a buddhist monk. He successfully manages to combine the two, without letting one subvert the other. If you want to know some Science or are looking for a simple rundown on some part the simply you only have to.... ask. Do not commit the error of two and half thousand years ago where they thought that everything could be discerned from the comfort of a slave supported armchair and notions of 'how things ough to be'. And please do not preach Science to Scientists, any more than I would dream of preaching religion to a Bhuddist. Here is an example of what I am referring to.

Yes I agree and I was beginning to fear that no one else except the redoubtable MigL and myself were interested. So thank you +1 Interestingly since the time you posted this is the first time I have seen your post in full and I was going to say that I cannot correct your Tex. But I see that some fairy godmoderator has done it. There is lots to say about a metric, not the least that we should not only concentrate on distance functions but also ask about area/volume/shape/ direction/angle. Further we should be careful when defining our base manifold. Are you aware of the story of the sea-mile ?

How would you feel ? What would you think ? If I walked into your Bhuddist Temple and started spouting Shiva this and And Vishnu that to the monks there ? I fear your speculation is not going to reach the standard required here. But this been a civilsed, not unpleasant, discussion.

If if was clear I wouldn't need to challenge it. What do you mean by this. ? Potential has a very specific meaning in science.

Just a sample of your nonsense statements. Why is this not self contradictory ? You say your 'field' has no defined characteristics, yet you already specified two -- quantum and primeval. This is just chucking big words about for effect.

I don't usually answer this OP since they refuse to enter discussion. However I would point out for the benefit of others who may read this that There is no such thing as a forward equilibrium constant or a backward equilibrium constant. That would be a direct contradiction of terms. As @sethoflagos has already pointed out at equilibrium the reaction is not proceedijg; It is going nowhere. This follows from the definition of equilibrium. As shown in this thread there are two competing reactions, a forward reaction and a reverse reaction, both of which are proceeding. Each of these have their own reaction rate constants, which are not and cannot be equilibrium constants, by definition. Yes agreed the reaction rate constants do not play a part in the calculation., even though the equilibrium constant is their ratio, and therefore a pure number. Thanks also to @swansont in the other thread for referencing the full test of the source material, which I agree is clunsily drafted.

I I asked you (politely) to follow the rules here. These rules require you to provide suitbale references to your claims.

This is the only accurate thing in your post, so I'm glad you mentioned this. Perhaps you would provide some verifiable references to your other claims ?

Hermann Bondi was a significant scientist, though his version of the steady state theory has fallen by the wayside. His 'Common Sense' relativity book contains nothing contrary to current explanations of Lorenz or Einsteins additions of relativistic velocites or why it is not possible to travel faster than light. Indeed he has chapters explaining mainstream theory on all of these. So please do not invoke this book as backup for your way out propositions.

I have posted my replies in a new thread since this one is in speculations and might easily be closed at any moment and the subject of a metric is really off topic here.

This thread is in response to questions in the Speculations forum about exactly what a metric is and this level of detailand discussion is neither speculation nor really on topic for the older thread. I am posting it in Physics as most instances of metric at SF are connected with coordinates. Also Maths is rather dry with its format of "Let us state an axiom or axioms and see what we can do with them." Physics can be more chatty. First a little backgorund. Yes indeed a set with a notion of distance between its elements. But we really need more than a notion, so let us examine the sort of things we want 'distance' to do for us or not do for us. As so often in maths we gather togther all the objects we want to find a distnce between and put them in a set. Voila we have a basic manifold or space. We will call the set X and the elements x1, x2 x3 etc Note these elements may be coordinate points in some coordinate system in which case our distance is coordinate distance. Or they may be binary strings or actual words in characters in which case our distance is known as the Hamming distance. So what do we want from our notion ? Well here are some suggestions. Our first notion of distance is that it is between two elements. So our set must contain at least two elements. We do not want any elements to be 'left out.' That is our distance determining function (D) must apply between each and every pair of elements (xn , xm) That is we we do not want the distances to be undefined or undefinable between any pairs of elements. We do not want any distance to be infinite (or do we?) Ideally we would like the distance to appear as a number that we can append a physical unit to. The function, D, must allow repeat values of distance from all different to all the same and everything in between. We want the distance from xn to xm to be the same as the distance from xm to xn. We want the distance to be zero if xn and xm are the same point or element. That is D(xn, xm) = 0 But we really do not want to cope with negative distances so we specify that D(xn , xm) is greater than or equal to zero. These can all be written very compactly as a couple of mathematical axioms, but I am going to add one further dersire that is very useful, but not essential. We want our D(xn , xm) to be the shortest or least value and that any distance via an intermediary point is greater than this. These conditions form the basis of Riemannian Geometry (and thus Euclidian Geometry) For Relativity we need to relax the restriction on negative values. I think this has rapidly swept through the questions in the anti-time thread so next time will be for examples and further answers along with clearer maths.

Why is that a problem ? We both sprang from a traceable common ancestor so have some common genetic material. But when push came to shove HS proved more adaptable than HN so outcompeted them.

Current thinking in anthropology actually proposes the opposes of this as the reason why H. Sapiens superceeded the more numerous H Neanderthalis. The last episode of the recent BBC series Human made this point most emphatically.

This is actually a very good question +1 and @TheVat has given a good shortform answer +1 If you like to explore this further the mathematics is extremely simple, yet reaches into most corners of the subject from classical mechanics to relativity to geometry to cryptography to error correction codes to statistics to topology to.... This all hinges on what is meant by 'distance' that is what we want from our 'tool'.

Thanks +1

Do you have a quotable source for this information ?

If you are going to quote the originator of the Butterfly Effect, then you should take note of what he actually said and / or wrote in his paper or his book. So read that instead of quoting rubbish garbled up by some experimental program. What was actually said is interesting because Lorenz said that if we are going to consider the scenario that s small sensitivity in the initial conditions such as the disturbance caused by a single flap of a butterfly's wing could cause a tornado, we should also consider that on another occasion a similarly small disturbance could prevent a tornado. As the implications of that are profound because unless you have reason to think that disturbances pushing in one direction are more numerous than disturbances pushing in another such disturbances should balance out and merely change the order of events. So can you control it ? Well the nature of the problem depends upon the deterministic equations involved. For instance autonomous first order differential equations cannot be controlled. But there are other equations that admit a form of control. (Not those to do with weather)

If you want to discuss your claim, then discuss it. But, when presented with a counterexample, please do not pretend you are the sole arbiter of nomenclature in such an offensive way.

Well the op certainly seems to have been frightened away, if that was your objective. As far as I know most students start with the definition a vector is something that requires both a magnitude and a direction. My treatment is linked to that and is designed to develop from there.

OK so you read a short paper which didn't tell you any of the back history leading up to this. Professor Millikan (famous for millikan's experiment with electrons) was a very careful and thorough worker and indeed justly famous for the work he did on the electron and its properties. But he also did a lot of work in Cosmic Rays. Not only was he a careful worker but he also documented his work in papers and in a book what was revised several times, starting in 1917 and called the electron. My 1947 revision is a model of how to report basic research, methods, results and conclusion and is now called electrons (+ and -) , protons, photons, neutrons, mesotrons and comic rays. It is the mesotrons that are the same particles we now call muons. The book also documents and correlates the work of other scientists in this field. The actualy work took place over a period 1917 to the early 1940s. It was published by Chicago University Press (and also by Cambridge University Press in England) On page 519 ff , you will find all the detail you want carefully explained with photographs, graphs, and more.