studiot

You should know by now that mathematicians like to make precise statements that are as general as possible and as vague as possible. So there is no limit to the nuggets of order, they could be large, they could be small. The mathematical phrase is 'at least' . Ramsey was not only active in this area, he was also active in developing applied variational theory and acting as a bridge between the era of Russell and that of Godel.

I suggest looking at Frank Ramsey's work. https://en.wikipedia.org/wiki/Frank_Ramsey_(mathematician)

Coulomb's law does not include c or mention time, though I grant you that r/c has the dimensions of a time. You have not answered my more important question as to which particle is which ie is the electron you mentioned the first or second particle. Without this vital information your two statements are just quotations from gobbledegook.

Please clarify which is the first particle and which is the second. Please also clarify why you did not mention force in the post I queried but now introduce it ? You actually said Which is the r I was asking about tending to infinity. Since c is finite but nonzero there is no division by zero and the ratio tends to infinity of time.

I am clearly wasting my time in this thread.

+1 What happens in this model as r tends to infinity since c is still finite ?

I can't buy into this. Energy is a property of something it is not a 'something' ie not a substance. Yes it is about a mathematical space which is an abstraction from 'real space'. I think that this space has also to be convex for the integrals to work (have meaning) in reality, though the subject of convexity is now a subject of much research. The surface or hypersurface referred to contain the variations, but modern terminology now refers to extremal principles rather than variational ones .

Although over 20 miles inland these wetlands are at sea level, some parts 1 -5 metres above and some a similar amount below. This reminded me that I haven't congratulated @beecee on his cricket teams performances lately. They deserved their victory. The point of this is to introduce a newly created wetland in the lower otter valley, in neighbouring Devon, is being returned to its natural state. in the late 1700s, the land was drained and protected from the sea by a barrier to create new farmland. But the land was always too marshy and prone to flooding, so became the Budleigh Salterton cricket club. The pavilion can be seen in the first video. The second video shows the valley in normal times, from 2 minutes in. The red rocks are the start of the 'Jurrasic Coast' with the old red sandstone low cliffs.

Looks an easy mistake to make. Thanks for explaining that. As to the flammability, the strongest (most concentrated) form of the acid is called glacial acetic acid, which is pretty reactive and some of these reactions can generate a lot of heat. I looked up its flammability and sure enough its vapour can form explosive mixtures with air above 39o C ICSC 0363 - ACETIC ACID (inchem.org) But you should never introduce glacial acetic acid at a primary school, and only with care at more advanced establishments. Glacial acid is about 17.4M so 0.1M will be quite safe. A couple of other thoughts. Sodium bicarbonate can act as either a base or an acid, depending upon what it is reacting with. Sodium or calcium carbonate is always basic. Chalk or limestone fizzes nicely and safely with various acids. You should be careful not to confuse strength and concentration and certainly not say anything to introduce such a confusion to primary pupils. I can remember half truths that were all to difficult to unlearn later from my school days.

Yes I was considering something like that. Recently someone posted a question about a homemade spectrophotmeter, can't remember the thread now. But looking at Ebay I found a complete monochromator from one for a couple of quid by typing in spectrophotometer. Anyway doogles' beef appears to be that he can't find any reference to people today measuring the absorbance of carbon dioxide relative to concentration. Od course all the constants for that is well documented today and he is asking the question backwards. Many institutes have been measuring concentration from absorbance for decades, for example this New Zealand agency. https://niwa.co.nz/atmosphere/facilities/baring-head/greenhouse-gas-analyses Perhaps we should be explaining that we know the relationship and are using it to measure the concentration, not the other way round, these days. Note there are also establishments using other methods such as mass spectrometry. All that is needed is to type into Google "analysis of atmospheric gas" to find lots of pages of folks doing this.

Lot's of queries here. 1) Where does the Methanoic acid, as trailed in your title come into it ? 2) 0.1M ethanoic acid contains 6 grammes per litre of acid. To be sold as vinegar the concentration must be at least 40g per litre. So 0.1M is very dilute. 3) Very strong ethanoic acid (glacial acetic acid) is certainly corrosive and unsafe. I have not heard of it being particularly flammable of itself. 4) There are brands of toothpaste based on sodium bicarbonate (baking soda) which would be alkaline to a suitable strength of vinegar.

@Doogles31731 You have not replied to the information (graphs) I gave you in my last comment or the comment itself about measurements on the atmousphere being better than laboraory measurements. You should look up 'extinction coefficients' and its relationship to 'absobance'. https://www.sciencedirect.com/topics/earth-and-planetary-sciences/extinction-coefficient One further comment. If we look at the graphs I posted what stands out is the large effect from a very small concentrations (in the range 300 - 360 parts per million) of carbon dioxide gas. This is the important lesson to be taken away, not the absolute values.

Glad someone found the article interesting.

You miss my point. I agree that further laboratory experiments are unneccessary. Spectrophotmetric experiments at varying concentrations are commonplace in Pharmacy and presumably Chemistry courses these days. But the point I was making is that because the Sun's rays are parallel and the Earth is curved, the distance travelled by a ray of light through the atmousphere varies with time of day and location. This has implications for the application of say Beer's Law to models. Also there are other particles in the air, particularly at lower levels, which also have an effect on the absorbtion and re-radiation process.

Image source, Historic England Image caption, The Sweet Track in Shapwick Heath National Nature Reserve is protected as a scheduled monument A 6,000-year-old wooden walkway over wetlands is no longer under threat thanks to conservation work. The Sweet Track, in the Shapwick Heath National Nature Reserve in Somerset, is set to be removed from Historic England's Heritage at Risk Register. The prehistoric track was built by the first farming communities in 3,806 BC and is the UK's oldest wooden walkway. BBC news article. https://www.bbc.co.uk/news/uk-england-somerset-60203225 What tickles me is the date it was allegedly built. 3806 BC. Not one year earlier or one year later ! Happy reading.

I am assuming your apology is more sincere than the recent one from our Prime Minister, so it is accepted. I would, like you, thank swansont for his observation. I must confess to not noticing it, probably like several other viewers. So the important thing is to learn and move on. Whilst this is true in one sense, it does not bring out an important issue appreciated in Tyndall's time and one of the reasons Piazzi-Smyth was sent to establish an observatory on Alta Vista. That is the effect of the curvature of the Earth's atmousphere on perceived sunlight spectra.

I wasn't the one quoting allegedly learned papers. I was originally responding to and commenting on such papers.

My point is that in the scientific section of a scientific website we should be scientifically accurate and correct (unlike the UK Prime Minister) common usage is not good enough for a basic scientific term with a very specific meaning. If the probabilities are not equal then it does not mean the process does not have a stochastic model. It means that something else is going on, ie that some additional factor is involved. That something else could be deliberation by outside intelligent agency or internal intelligent agency, but not necessarily. For instance calouses will develop on the hands and finger tips of archers and musicians. Or suppose you tested a die that was 'born with' two fives, but no six due to a manufacturing error. Your test, measuring the probabilities, would soon reveal both the extra 5 and the missing 6. I know these are not genetic modifications, but they clearly indicate the fact that other, non intelligent, agencies could influence the process.

Agreed. Yes, but it may not be the OP who is confused about the meaning of random. The notion of random is based on the proposition of equal probabilities for every possible outcome. This is mathematically equivalent to your null hypothesis comment. My definition of a random is therefore " A process is random when all possible outcomes have equal probabilities" The question then becomes How do we assess the process when the probabilities are not equal, perhaps for the reasons you have already mentioned or perhaps for other reasons ? For instance the outcome of a horse race is not random, even though every runner has a chance of winning, because the chances (probabilities) will not be equal.

This is (supposed to be) a scientific discussion. And in scientific discussions we are supposed to state explicitly, not imply. That is why I am searching for an unambiguous term. Random has already been shown to be inappropriate. It is also inappropriate because when used in a scientific manner it has an exact meaning that does not apply here without mathematical demonstration. Perhaps you might like to choose another word or phrase ? And no I did not mean accidental as the opposite of deliberate. I meant 'by chance'. Nor am I ruling out the possibility of deliberate mutation, but I do dispute that it follows that if the results of chance are not random then they must be deliberate.

I would like to thank both Arete and CharonY for several excellent posts apiece, extending my knowledge of the subject. It is really good to hear someone who knows their subject. My comment on the study. Random might not be the best adjective for the mutation process. Accidental might be better ?

Am I really in danger of poisoning from the NHS website as well as the Russian embassy ? More seriously, sorry to be a sourpuss, especially when my comment is sweet. One thing I discovered when island hopping in the Greek Isles some years ago. That was how much better cold rice pudding keeps than ice cream in warm weather or cold. A note to the OP, If you ever read manufacturer's instructions you will have noted that you are not supposed to put hot or even warm food straight into a fridge or (perish the thought) the freezer. So it is clearly OK to cool it off somewhere else. Of course the food concerned should be covered. The old fashioned practice of serving food in containers with lids and keeping them lidded after serving, bear witness to this. I find a good place to allow things to coolis in the oven they were cooked in. This will be a sterile cooling environment.

The use of the Beer-Lambert law is still modelling, albeit simpler than the billion tax dollar computer models currently promoted. I don't see how this would not still result in a model. Surely from a climate science point of view, only actual measurements on the actual atmousphere count ? Here are a couple of graphs of slightly older data, including references that might provide a starting point for you.

I should have added two things. The UK is one of the most camera monitored countries on Earth. We do not have so many traffic signals (lights) as they use in Europe. Most junctions are 'controlled'' by passive markings on the roads and signs mounted on posts, And of course the rules of conduct embodied in the Highway Code. There is even a section where these take over from lights,and tell the motorist what to do if the lights fail.

Patterns ? For m members and n selections it is a double product series of terms, one ascending, one descending In this case we have 1*6 + 2*5 + 3*4 + 4*3 + 5*2 + 6*1 6 + 10 + 12 + 12 + 10 + 6