studiot

Good point, thanks. +1

Don't know why he couldn't post it, but apparently there is a website for the book. : https://www.cambridge.org/core/books/thermodynamics-of-the-earth-and-planets/D527F02CB15D79D9B59AA69CBA4AA0BD Thanks essay +1

Pauli is safe. These two extracts should clear it up. The plot of the radial distribution function in Fig9 of the first one shows quite clearly that the high density / high probability regions do not overlap. Extract 2 presents an alternaive view of the same thing. good luck.

For those who want solid Science can I bring to the attention of the Forum this recent book by Alberto Patino Douce Thermodynamics of the Earth and Planets and published by Cambridge University Press. This hefty book contains much discusion, modern data, Maple presentations and references all for the current subject and other appropriate aspects of planetary geophysics/geochemistry ranging between undergraduate and postgraduate level and linking them together in a coherent way.

Interesting examples Bender. +1

The irony of this is that I wrote a first post sympathetic to your 'outlandish claim', but not entirely supporting it. You chose the direction from there. First by asking "Can I tell you something...... " But since that something you asked for had altered my words in more than one way I had to answer No . I could have added I am unable to do so, but I did chose to suggest you reread my exact words so you could rephrase your questions. Instead all you have done since is attack me. So why should I help you realise that you are asking about the present and I deliberately set my society in the past. Furthermore you kept demanding countries, ( a word I did not use) whilst the society I talked about existed in a region of Africa that did not have formal countries at that time. Finally I mentioned the word surfeit, which is crucial to my examples since they had a surfeit of energy, which still exists today as I noted in the present tense.

I prefer my equations as I wrote them (unless, being human, I made one of those silly errors that John Cuthber so likes to point out) thank you. Perhaps you would be so good as to shown how this occurs?

Well this looks to me like a claim that money is being measured in camels somewhere. Can you really not see the difference between what I wrote and what you wrote?

Well that assumes inertial mass is the same as gravitational mass, and I know of no law of Physics that says this must be so. That is particularly poignant when you consider how many quantities include M in their dimension lineup. Yes convenience has dictated the amp over the coulomb, but you can have (theoretically) charge without current, but not the other way round. The dimension system we have today is very good and have seen development and improvement since Buckingham's day. But are you claiming it is perfect? For it is any imperfections this thread seeks to discuss. y does not appear in any of my equations so how can it have a value there?

I most certainly did not make the statements you attribute to me. I also answered the question you actually asked accurately, but made no such admission as you attribute to me.

No. It is a pity you did not read my post properly or you would not have asked that question, nor made the unfortunate second statement following it.

I don't think anyone is denying that dimensional analysis is an incredibly useful tool. But that is not reason not to reconsider it from time to time ( as was indeed done in the case of the move from cgs to MKS units ) A more fundamental move was of course the change from charge as a fundamental dimension to current or current density. The point is that the set L M t T I n Iv is not the only set we could use. Each possibility has its own pros and cons (apart from the clash of first letters). One of the obvious difficulties with M, L and t is that they are not immutable (They change in relativity for example one man's metre is not the same as another man's metre). Further there are so many types of mass - Proper mass, rest mass, effective mass, active mass, passive mass, inertial mass, gravitational mass.... the list goes on.

The terms money, wealth and currency are very very closly linked together, although each has its own links to other aspects of society. In economic modelling of societies I would also agree that the economic concept of money is linked to energy. However the money supply and the energy supply are different things and in some cases the link is much stronger / weaker than in others. For instance in societies where there is a surfeit of energy ( an example would be those where money was measured in camels) the link is extremely weak. In others; I recently went to some lectures at the University of Dundee studying the sadly delterious economic effect of the introduction of 'money' to societies in South Pacific islands where it had not perviously existed. So I would hope that modern socio-economics had moved on from (over) simplifications to more complex models capable of dealing with these types of society.

Where did he say it wasn't? He said it was incomplete. Indeed any more than adding the two distinct quantities both with the dimensions L2MT-2 makes sense, as I already noted before.

Yes you have emphasised my point that the Mathematics and the Science can be separated. So if you like you can add another separation by introducing a system of dimensions. Just as in the flower, fruit and veg market you have the horticultural system, the system of weights and measures and the Mathematics (usually simple arithmetic). All are quite independent of each other. I really don't understand this. What is y?

Is jumping over a hole a high jump? However you are right to point out that I need to be more careful with my choice of examples, thank you +1 Because it's true? Maybe swansont remembers and used these units, but anyway here are some tables. Note very carefully that certain quantities (as I mentions) have different units and dimensions in different systems. (The equations are also different )

No it doesn't. Did you do what I asked and substitute x = 100 into both equations. Were both sides the same in both cases? Here is a Physics question for you to chew on, since you eschew pure maths and chemistry ones. Why is inductance measured in Henries in the MKS system and centimetres in the cgs system Why is EMF measured in voltage in the MKS system and ergs in the cgs system since they are different physical quantities? What happened to the dimensions?

Thank you Eise for you input, which as alwys respects the material and views posted by others whether you disagree or not. I note you have picked up on several points raised by various others. Between say 1900 and 1920 the distinction would have been taught to a 12 year old in primary school. Until about 1960 this was pushed up the ladder to early secondary school at about 13 or 14. I am not sure what happened after that. The point is that the first of those expressions is an identity and the second an equality. The distinction as taught to 12 -14 year olds is that an identity is true for every x, an equality is only true for some x. At university deeper understanding is studied in the set theory of equivalence realtions. But it is far from unusual in Mathematics for words or symbols to perform multiple duties. Look in any Dictionary of Mathematics and you will see that many of the terms have multiple meanings and use. This is the place where 'context' is of use in Mathematics. Yes indeed multiple meanings. Actually you can add 2 to the vector (1,2). All that happens is that you move from the mathematics of a vector space to the mathematics of an affine space. One application of this has importantance in modern relativity. But the mathematical definition of a vector is very different from the one normally employed in Physics, and you have used here. So you can, for instance, add a constant (which is not a vector) to a vector in a Fourier series. Maybe so, but Physics is not the only Science and the question here was about Science in general. This is not an exercise in "Physik uber alles" That is a matter of opinion. The person who originally wrote that equation was a very famous Professor of Chemical Thermodynamics at the University of California, Santa Barbara. I used it because it is now standard and I did not measure the themochemistry part. So in short, some do some don't. The liberating part of Science is that, like the English Language, no one has domain over expression. Long may that continue. Well that is so as far as it goes, but it is woefully incomplete. What symbol is used for the electrochemical neutrality of a chemical equation? What symbol is used for a nonstoichiometric equation? for instance in the presence of excess of one reagent? If a reagent appears also as a product, can you legitimately 'cancel' part or all of that quantity, as you most assuredly can in a mathematical expression for example 2x + 3 = 6 + 3 yields x = 3 But if 3 is the concentration of a necessary reagent, what happens if you cancel it? Did you attempt the nonstochiometric question I asked Strange? You can extract 6 dimensionally correct equations from the nonstoichiometrical statement of the reaction and solve them for the 6 unknowns in a proper mathematical way. This is an example of Applied Mathematics in action, whereby the Mathematics is separated from the Science of the situation and solved, providing useful information about the Science of the situation. If you answered the chemical question I posted earlier

Once again thank you for the typographical correction. Yes 4 square metres would be better.

It must be your turn to explain what you mean, because I don't understand the question. Mathematics has no 'context'. The meanings are different. Period. I'm sorry the response was cryptic but I assume you understand enough mathematics to know that in one case the expression is true for all x, whereas in the other it is only true for two specific values of x and untrue for the rest of the infinite possibilities available. Why do you think I will answer your questions, when you do not answer mine?

Thank you for correcting that oversight, Of course I should have said Answer the height squared = 4 metres squared. However that does not invalidate the argument. I too have a degree in applied Maths. So what? What does your esteemed cousin say about this? What happens if he substitutes x = 100 into both expressions?

Of course. In the expression (x - 1) (x - 1) = x2 +1 - 2x the equals sign is used differently from its use in the expression x2 + 4x + 4 = 0 I have no idea about your trousers but your following exactly exemplifies my stance. There is mathematics and there are applications (or there are other disciplines that can use Mathematics however you like to describe it). And they are separate and distinct things. How high did he jump? Answer the height squared = 4 metres. Now as an invigilator in the high jump I can say there is only one answer viz 2 metres. But as a Mathematician I cannot pretend that -2 is not also a solution of the equation x2 = 4. Notice also this is entirely consistent usage As an invigilator I use units of metres - ie my 4 and 2 have dimensions. As a Mathematician no units are used - they are just numbers.

There are two approaches to teaching and learning Organic Chemistry. The traditional approach which I learned at school and many schools still operate. That is by grouping together and studying many similar compounds together via homologous series. So using alcohols as an example you learn the comparative properties of methanol, ethanol, butanol, propanol and so on. The automatic repetition inherent in this of the 'alcohol' part (-OH) helps fix the idea of an alcohol in one's mind, rather as others have said. When I got to university their approach was a big shock because they di things differently. Organic Chemistry was studied and classified under different heading. Those of reaction types and mechanisms - substitution - esterification - condensation - nucleophilic - electrophilic and so forth. These affect all types of homologous series so these were lumped in together and mixed up. this was the modern approach. So there you are, try getting an old fashioned textbook (one with chapters labelled aldehydes, ketones, alcohols etc) and reading it. BTW you didn't say what stage you are at.

Hi Butch, here is a quote to get your teeth into

Less strict than what? Mathematics itself employs the equality sign for more than one meaning. An assertion without proof. I do agree that much of dimensional analysis can be put into mathematical form, just as can much of other aspects of Science. But how is Science able to throw away part of the consistent maths in my example of selecting only the real part of a complete solution. In other words what are 5 i metres, or what is the arcsin of 3 ?