studiot

These are much more cojerent thoughts. But what makes you think this hasn't already been done in mathematics? Is this the problem? It is a fact that all members here are communicating using real material electrons chips that can only provide a different answer to that sum.

So let us look at some examples using my definition of a distance function. [math]d:X \times X \to {\Re ^ + } \cup \{ 0\} [/math] So my first example is as follows 1 Let X be the set of all binary words of length 3 characters. Thus there are 8 members of this finite set { 000, 001, 010, 100, 110, 101, 011, 111 } Then if x, y are elements of this set define d(x,y) as the number of digits in which x and y differ. It can easily be seen that for each x there are 3 ys that differ by one character Thus each x has 2 ys at a distance of 1 from it . d = 1 similarly there are 3 words that are at a distance of 2 characters from each. And there is 1 word that is at a distance of 3 characters 2 Let X be the set of all real numbers and d(x,y) be be the modulus or abs function. [math]d(x,y) = \left| {x - y} \right|[/math] 3 [math]d(x,y) = \sqrt {{{(x - y)}^2}} [/math] Again it is easy to see that all three examples satisfy the requirements [math]d(x,y) \ge 0[/math] [math]d(x,y) = 0if\;and\;onlyif\;x = y[/math] [math]d(x,y) = d(y,x)[/math] [math]d(x,z) \le d(x,y) + d(y,z)[/math] The distance function in Example 1 is discrete The distance function in Example 2 is is continuous but it is not differentiable over the entire domain. The distance function in Example 3 is both continuous and differentiable, which is why it is often used to replace the absolute value function. So in order to do calculus with our metric we must further limit allowable distance functions, which has clear implications for relativity.

[math]d:X \times X \to {\Re ^ + } \cup \{ 0\} [/math]

Yes and you are asking us to respect your imagination. Do you think you have shown due respect to the short piece of help I offered ? Only you don't seem to have read it very well.

You could of course see if Euclid's method for finding the HCF can be combined with your proposal, to find factors, as it already seems to be a modification of it.

Before we disappear down an einstinian rabbit squabble hole, I'm pretty sure he did say something like the quote, though I am not sure those were his exact words. Einstein was renouned for his intuitive understanding of Physics, a skill which greatly assisted his progress. He did say something like get the Physics right and the Maths will follow, though I haven't got the exact quote to hand. But then he was also wrong sometimes and had the grace to admit it. indeed (General) Relativity started out without the lambda term, but that is another story.

Thank you, agreed. As to the cautionary tale of the sea mile that no one seems interested in, A few hundred years ago we could determine latitude pretty well but not longitude. At that time we had a properly spherical model of our globe. Maritime nations, in particular England, introduced the 'sea mile' or 'nautical mile' as a measure of distance ... at sea where the surface of the model globe was considered uniformly spherical. The sea mile was defined as 'One minute of arc, measured along a meridion of longitude'. Although they did no know which meridion, they assumed all segments of all meridions were equivalent. They chose meridions of longitude because they were all supposed to be great arcs, whereas the equator is the only parallel of latitude that is a great arc. Mixing these up still leads to some unfortunate descriptions (particularly when AI is asked) about the arc being one of latitude to this day. The point is that they did not know the flattening of the Earth distorts these great arcs of longitude, especially near the poles. This was sufficient for the 'metric' to vary from place to place, a most undesirable requirement. Subsequently an average was agreed internationally, but it still means that the sea mile still does not conform to its original definition anywhere.

There are such things as non stochiometric compounds, https://en.wikipedia.org/wiki/Non-stoichiometric_compound These are still made of atoms and or other particles.

That's the way. Did you notice I did not include either quantum or field in my basic list ? What did you make of the list ? I don't know what you think a field is but in Science it is a name for a region of space in which some property ( or collection of properties) has specific values at every point in that region. The value may be zero and , of course, a field where the value is zero everywhere is not very interesting. The field may be real like an electric field or a magnetic field or it may be totally abstract as in a direction field. Obviously in order to specify values we must have a way of referring to each point and equation(s) telling us the value at that point. If these equations fail at a few points the we say there is a singularity at that point and we cannot then determine the desired values. Now the point of knowing all this is that a field, for example a magnetic field, can interact with other objects, in particular material objects. For example magnetic materials will align themselves with a magnetic field. It may be that the equations that describe these interactions yield discrete or stepped solutions. This is called quantisation. So it is the interaction between the field and something else that is 'quantum' and leads to quantum theory. There is no such thing as a 'quantum field' by itself. I mentioned 'principles' and energy because our understanding of The Principle of Least Energy is what underlies quantum theory and much else of the processes of the universe.

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.