studiot

No I don't think you did answer either my questions, nor those of swansont. Anyway the OP picture 1 is purely Newtonian. GR is not involved. The curvatature is in the values of Newtonian gravitational potential. It is a depiction of a Newtonian gravity well. There is a similar picture of the Schwarzchild solution in GR which with which it should not be confused. @pmourad This New Zealand teaching website offers a really good explanation and some interesting material to play with. https://www.sciencelearn.org.nz/image_maps/76-exploring-physics-concepts-with-a-gravity-well

L-12 does not equal L-6L-5

Hi Markus, thanks for your reply. I'm sorry but that's too one sided. It's not true to say that the laws of Physics are scale dependant per se. It would be better to say that physical structures formed from interactions and combinations of these laws may be scale dependant. Some structures may only form at certain 'scales', such as colloidal suspensions, critical fission masses and black holes. It is true to say that different laws obey different variation relations with distance and/or or time This results in different laws predominating at different distance or time separations. I define 'local' as within a given region of space containing the subject(s) of interest. So clearly different physical structures can arise depending upon the size or extent of the 'locality' Exceptions to this might be regions with a huge extent in one dimension,but a minute extent in other dimensions. So shape is also significant.

Everyone is entitled to thir opinion, including those that can't or won't back up their assertions with detail.

Yes of course a marble would roll down the fabric of the trampoline. But the fabric of the trampoline is woven so there is a mesh with fine holes. This is fine so long as the holes are much smaller than the marble. But what would happen if we rolled successively smaller and smaller marbles until the marble was smaller than the holes ? If this is so then you can sketch the real curvature of space in the 1D and 2D cases. I look forward to your sketches. Again let us see a sketch, employing only a single axis. It is only possible if you have a non linear function that maps points on one (part of) the x axis to another part of the x axis. This is exactly the type of relation I described to those new philosophers who have recently joined. Which is why it is a bad analogy. It is allegedly gravity that gauses the 'curvature' in both cases. Nothing else. Just gravity. Yet your description of the rolling marble has normal reactive forces acting. It's not the stress - energy tensor you need but the Riemann tensor, if you must use tensors. But nobody mentioned them. In another thread Markus mentioned an alternative to curvature - torsion. This model (analogy) does not suffer from the difficulties of R . But these are way above the level this thread is pitched at. @pmourad Do you understand the idea of 'length of arc' of a curved line, that is distance as measured along the line (not the mathematical formulae involved) ? This is the same as what I meant by land surveyors' through chainage.

Simple but really cool. +1

These misunderstandings show why I dislike this analogy. 1) If it is meant to represent paths of objects (which is a very vague and ill defined statement) not the curvature of the fabric of space why is the picture so named the curvature of (the fabric of) space ? It can't be spacetime as there is no time axis. 2) If it is a representation of a path of a real object then why does that object not follow the direct line towards the COG of the Earth ? 3) The top picture implies that we start with an two dimensional model grid (whatever the grid represents), flat and empty of matter. We then place some matter (eg the Earth) onto this grid and it is displaced somehow into the third dimension by 'bending of a grid', whether the one in the picture or another grid. Now extend that up one dimension so we have a 3D grid, that implies, of necessity a 4D universe for this displacement to occur. 4) if you prefer start with a one dimensional line. If this line is one dimensional it cannot be curved, the term cannot be invoked and maintain the one dimensionality of the universe containing that line. In differential geometry in order to give rho and kappa maning you must invoke further orthoganal derivatives. Land surveyors are familiar with this one dimensional version under the name 'through chainage', which works basically as I have tried to describe it for pmourad as I seem to recall said they have only basic high school algebra. 5) We are talking about 'distortion' due to gravity alone. Surely you are not suggesting some additional force ?

Yes Linda is not recorded as having returned since before I posted my original erroneous reply. And yes you are correct in assessing a difficulty with the original statement in the OP about the concentrations of A and B. That is why I started with the chemical equation AB = A + B This is what is implied in the OP It is also implied that the equation could not be for instance A2B = 2A + B. So unless there is an unknown source of A and/or B, or some further reaction involving A or B, the concentrations of A and B must be equal as the only known source is AB. Of course the OP is at variance with this so has not been properly formulated. So it may well be as you suspect since this is a biochemical reaction.

I can agree with that, except for the 'hence' since I don't agree with the premise of scale. Davy_Jones has also agreed that there is more than one 'reality' or if you prefer, two versions of reality can both be true. I will come back to Davy in a moment, but first to complete my comments about Markus' post. Consider a brick wall. In my reality the wall, the bricks and the mineral particles that make up the bricks and mortar are all simultaneously real. Indeed one could not be real without the other. But what you (and Davy) said about contextuality is spot on. Yes you must alway qualify many things about the ground in which you are working. Hmm, does not seem like a problem to me. No doubt there are difficulties with the concept; this doesn't appear to be one, though. Isn't this like saying, The coin has two sides: one heads and the other tails. Our concept of reality is a mess"? When one side of the planet is illuminated, the other is not. When it's summer in Canada, it's winter in Australia. Where's the problem? In the philosophy of language, they talk about indexicals (words such as "I", "now". "here". etc.), that is, certain statements are indexed according to the person, time, place, etc. of utterance. Therefore, taking indexicals into account, there is no contradiction between the statements "It's hot here", when uttered by yourself, and "It's cold here" when uttered simultaneously by me. Both can be true. Thank you for your reply and most importantly thank you for including this most important statement. Far more important than the squabble over reality and truth, which we all now seem to accept need further qualification to make sense. The philosophy of language. Yes indeed you have just qualified 'philosophy' , as I have said to you several times now and you have always side stepped. I repeat that both Science and Philosophy need qualifying, just as we have all noted that truth and reality need qualifying. So many needless and pointles arguments ensue when that qualification is missing.

Yes and I wish they wouldn't do that as it is a bad analogy. Yes the Earth appears sitting on the fabric pulling it down as if it were a heavy ball on a trampoline. That is the trouble, a heavy ball on a trampoline pulls the fabric down into what ? Space where there is no 'fabric' whatever that is supposed to mean. Where did that space come from ? And the pulling it down - well a heavy ball only pulls down the trampoline because the earth is 'underneath it' pulling on the ball with gravity. And the lines on the fabric are stretched and distorted. But distorted from what ? Aren't they supposed to be the correct gridlines of the fabric ? How can they be distorted ? +1 for recognising it. Here is a better one, soor no pretty dagram at the moment. Say you are a road runner that can only travel along the road. Now say you are standing at 5 West Street on a grid pattern of roads where the sides are completely built up with buildings. And say you want to get to 5 North street. Well you can't cut through the corner of the buildings, you have to go first along West street to the intersection of North Street and West Street. And then you have to go up North Street until you reach number 5. These are the 'rules' of this grid pattern of points. Furthermore this route is the shortest possible route for a road runner. This is an example in 2D, that works without invoking the 3rd dimension at all. Now suppose we scale this up to 3D. Again we have an arrangement of point, just now in 3D. And we have rules either of travel between these points or equivalently the way these points are laid out. This time there is no need to invoke a 4th dimension (ignoring time for this). The (mathematical) rules are pretty complicated, but that basically how General Relativity works.

We are agreed then. Let's go down the pub and forget it all

Was the underlined part a question ? Yes I think it is wise to explore every avenue towards an improved life for all. But I fear that neither of yours are attractive. Population control is Nature's way, using the tools of war, pestilence and famine. It's very effective but do we really want this way ? Cloud control is a drop in the ocean (excuse the mixed metaphor). We need fundamental, root and branch, changes to our society, with proper respect for and contributions from all sectors. That is certainly not happening at the moment. Which is a great pity because nearly all would benefit from such change.

I don't see how any of this disagrees with anything I have said.

I do think the discussion about reality has failed to demonstrate the flaws in the concept. Last night (to me) or yesterday afternoon to her, along with millions of others I watched Radacanu win the US open (congratulations to her). So whose 'reality' was correct ? Was it really yesterday afternoon or last night ?

Sure. In my view, admittedly coloured by the fact that I am a mathematician, I hold that Theories operate on Principles, in a way similar to the way in which theorems operate on axioms (which Physics does not have) in Maths. The view I have been promoting here in several ways is that Philosophy deals with the Principles of any subject not the detail. It could even be said that the subject itself is the detail. I also hold that it is a 'good thing' that we have an independent process or discipline scrutinising the Principles.

So what ? I have never seen the bottom of the Pacific Ocean or the Higgs boson. Does not make either of them unobservable, although until recently no one had seen either of them. Although I wonder is some philosophers might not argue that since the Pacific Ocean does not drain out onto the turtles beneath it must have a bottom.

Another case of the conclusion does not follow from the antecedant. Just because Newton (or anybody else or even everybody else) says that they could not observe something does not make it unobservable. Not even in Philosophy.

It is worth noting that theories and models are not the same. It is also worth noting that they are secondary (ie not primary) in the domain of rational thought, subdivision Science. finally @Davy_Jones it is worth noting that I don't believe you have mentioned the word 'principles' (or a synonym) in any of your posts. And I hold that the main (call it real if you like @dimreepr) difference between Philosophy and Science occurs in the Principles of those two disciplines and in particular in the history of those Principles. Copernicus and Galileo were considering Principles, not theories.

And who might the you be in the 'your' ?

Thanks +1 Told you I was in a rush, don't know now where that + idea came from. So the top is p2, not 2p. Moral never rush. 😳

I'm rushing here as I won't be back tonight, but here is a start. Let the initial concentration of AB be q and the concentration of A be p then Equilibrium equation is [math]AB \leftrightarrow A + B[/math] Dissociation equation is [math]{K_d} = \frac{{\left[ A \right] + \left[ B \right]}}{{\left[ {AB} \right]}}[/math] Also [math]\left[ A \right] = \left[ B \right] = p[/math] and [math]{\left[ {AB} \right]_{initial}} = q[/math] So [math]{K_d} = \frac{{2p}}{{\left( {q - p} \right)}}[/math] Now I think this is right but I'll check again later unless Babcock or CharonY call in with a better idea first.

Well I did look it up because I had not heard about this. Thank you for the reference, it adds to my store. +1 I found this description https://www.quantumdiaries.org/2011/11/18/a-tale-of-two-tables/ Which I thought rather offensive towards the man. It seems that Fermilab features highly. It dismisses his main scientific achievements with an airy wave of the hand. I would suggest that the two tables analogy (Eddington did say it as an analogy) is a version of what so many members here have been telling you. Science works with models. Models only ever cover part of the subject they are modelling. None are perfect or exact in every respect, except the subject itself. Models are subject to continual revision and refinement. Do you have any idea of the number of scientific models that were developed this way during the period 1890 - 1935 ? I can tell you it is a very large number. Some of these we still find useful today, some have been developed further others have been discarded That is Science. But to denigrate that man as the linked site does is unforgivable. It almost has the air of those quack sites designed to spread deliberate disinformation. But thank you again to bringing it to my attention. I will leave it there in this thread, but would be happy to discuss your and the comment under the Fermilab banner further in another. Thank you for your response to my question to theVat. I am aware of this process, but it is not an answer to my question about probability. I would also like to see a response from theVat himself. Again this may be an interesting side issue to discuss in another thread. In this case I would have to disagree with both Wiki and yourself (as Wiki is misleading). Falsifiable literally means 'capable of being falsified or refuted. if it is contradicted by an observation that is logically possible does not mean that the observation has been carried out or will ever be carried out or that it may sometime be true and sometimes false depending upon circumstances. The proposition "you can't get a quart into a pint pot" can be 'proved' with two suitable beer glasses. But wait How many 'quarts' of oxygen from the air can I get into an oxygen cylinder ? It may also be that the 'falsification' is impossible to carry out.

I'm not trying to make them hard to answer, just relevant. Good thinking on your part, both the repetition and the gallantry dimension. +1 Quite different from what I had in mind, but certainly not wrong and worth saying. I was envisaging that in the time, even before the stone age, primitive Man would have witnessed natural fires. Perhaps he was drawn to them because of the warmth and yes as you say he may have then discovered that other animals kept away (Science). Perhaps he saw a natural fire from a distance and just wondered (Philosophy). At that time his tools/weapons would have been sharpened sticks or heavy wooden clubs. Somehow one on his sharp sticks got into a fire but was charred a bit rather than burned. Perhaps he pulled it out again. And then he found the charred end of the stick was harder and stronger than the original. Or perhaps it did catch fire and he was attacked whilst pulling it out and discoverd that waving a burning stick at a predator drove it away. There was a lot of perhaps or maybe in that tale it's really all supposition, but palusible. So the Science made him think and the thoughts led to better Science, which led to better thoughts... Or was it the other way round ? Or did they develop together ? Other thoughts are welcome which is why I said it would be a good topic for another thread.

Yes we have discussed that aspect before. But who did the first science or philosophy ? What did the first man to wonder what fire was and the perhaps to try to make use of it (by experiment). Was he doing Science or Philosophy , even though he probably could not speak to say the words then ? And would this question be abductive thinking or what ?

Thank you for this answer. Now I know why I am not a philosopher. Your quote uses the words "Most likely". Quite unspecific. What, exactly does this mean in the realms of Philolosophy please ? Or if you prefer here it is as a mathematical statement. The probability of X , P(X) =1 ? I would warn you this statement has at least 3 possible mathematical meanings. PS I do like you flea/dog comment that's now in the trash can.