studiot

I will have to look closely at your references, but sorry I thought you would have no probs finding the plato article. https://plato.stanford.edu/entries/intuitionism/ As for 'information'. The mathematical theory of information is seriously limited to its domain of definition, which most of mathematics is of course. And people so often forget this limitation. Maths inormation is about subjects which are carefully specified. So there is no mathematical definition or description of indirect forms of information. As an example, I don't know if you have seen the pigeon advert for the Vauxhall Mokka - (I don't know what it is called in the US) - I don't know of any way of translating the advertising information into maths or logic, but they certainly get their message across to any human. Look forward to it !

Thank you for posting this +1. I would warn that intuitionism is in area of (mathematical) philosophy the Stanford Encyclopedia (Plato) is highy questionable about.

I can't possibly imagine why this post would have offended anyone, so I am adding a counterbalancing+1. Willem has actually told us about one of his limitations and, i believe, asked for help. I am not exactly sure what is meant by a shift operation, but I can guess. That would certainly be one way of putting. Not my personal favourite however because I am used to the shift operator being something from numerical analysis, not something defined by a programmer. But if my guess is correct then W is right.

I expect he means orthoclase, which is the softer of the two main minerals in granite.

I don't know how long is a long time for you, but do you remember old fashioned steam railway engines or steam powered traction engines, steam rollers or other steam propelled equipment, or have you seen pictures of them ? They had one thing in common, they were big and very heavy. All that machinery to provide steam propulsion is very bulky and heavy. And yet their makers knew about thermondynamics and mechanics and made them about as efficient as it is possible to be. With various grades of liquid or liquified gas fuels it became possible to use different and far lighter mechanics for the propulsion drive. Now that is where the internal combustion propulsion is at today. A far ligher drive mechanics meaning a far lighter chassis meaning far more efficient use of the fuel. Furthermore it doesn't require to carry either a large and weighty tank of water or additional weighty mechanics to recover the water from the steam and recycle it. And don't forget that some heat is extracted in cold countries to heat the passenger cabin. So yes, it is possible but just not practicable, there are better ways to use the fuels. Note also the even more and smaller engines such as racing car engines wear out far more quickly than engines designed for road vehicles. It is somebodie's law that says the more efficient and highly tuned a car engine is the more servicing it needs and the shorter its service life.

Yes +1 I would just lik to add to this part "in fact you could turn a ball into anything at all in this manner, no matter how big or small. " the following in response to the OP's assertion. You are right the the proposition works the other way round as well, but adding to Markus comment that it anything at all does not have to have the same shape as a ball and could have 'holes' in it. So no you don't have to exclude turning a pincushion into a pumpkin. It is true however that doing this topologically (ie continuously) means you can't make a doughnut into an apple.

Hello rufus and welcome. Good, well founded discussion is always welcome here. I can assure you that whilst many scientists and mathematicians are too busy in their working lives to sppend much time on the history, this is not the case with all of them. Some even make a career out of it and I can recommend some top notch material as a result. For myself, as a retired applied mathematician I understand fully the pressures of 'getting an answer' in the working world. It is called "shut up and calculate" But since retirement I have been able to look around at the History and Philosophy of Science and Maths which has enabled me to fill in many gaps and achieve a more rounded view of it all. edit. Please note (did you read the rules here?) that for your first 24 hours you can only make 5 posts - so use them wisely - This is a very effective anti spammer measure.

OK I'll accept that it is not homework. I do not see any essential difference between looking up on Google and asking a real person so Granite has a Moh's hardness of 5.5 - 6.5 and decays by chenmical weathering to clay, which was (and still is) used to make bricks and tiles and of course Hammurabi's famous clay tablets for writing cuneiform on.

What was the question ?

I have repeatedly said they do not separate. But I have also repeatedly said they were not mixed in the first place. Convection requires a source of heat. I did not say anything about heatng the bucket or having the bucket at 0oC. You seem hung up on diffusion, yet you ar starting to admit that other mechanisms and processes are acting. That is good. Now let us take the experiment a little bit further, remembering that my bucket was freely suspended in the open air, clear of walls, rooves and so forth. How quickly would the bucket of hydrogen empty compared to a bucket of plain air, noting that other air would diffuse into the bucket in both cases ? In the experience of every engineer I know said bucket of hydrogen would empty immediately and pretty well all the hydrogen would go straight up, the plume widening with ascent as Seth says. Whereas the bucket of plain air would take a long time to homogenize with the plain surrounding air. This is always provided that both the hydrogen and the original plain air in the bucket were originally at the same temperature and pressure as the surrounding air.

Hello, Roman, and welcome. I don't know if this is homework or not ? - but it really belongs in Earth Science anyway. We don't do people's homwork here, just help them find the answer for themselves. So a suggestion, I wasn't aware that there was any civilisation in what is now the Ukraine before the Babylonians, but I think the answer you are looking for can be found by looking up Hammurabi and how his laws were written. See what you make of this hint and tell us about the homework or source of the question please.

Yes I agree that a rising plume expands horizontally. But the ascent is much more rapid than the widthwise expansion. I agree that diffusion, without an additional forcing function tends to flatten the gradient. We have all agree these matters many times now. But consider a thermally conductive bar, which is being cooled at one end (the cold end) and heated with the extracted heat at the other end (the hot end) via a heat pump. Which way does the heat flow through the bar ? Here is a reference for the benefit of exchemist. I keep saying this but can't seem to get anybody to pick it up. Diffusion is acting, but it is not only the not the only active process it is not the principal process in the cases under consideration.

Of course there isn't. But the operative word is 'some'. This is a very very small fraction and is not accounted for by the dispersion equation. It is also the reason that concentration boundaries are blurred and gradual, even with only the entropic dispersion acting. It is accounted for by the kinetic theory. Clearly some of the hydrogen molecules in their upwards path will collide with molecules many times their mass and bounce back downwards. But in their downwards travel they will encounter a (very slightly) higher density of heavier molecules so will be even more likely to strike one and bounce back upwards again. It should be noted that this mechanism is not always availble in the dispersion equation. When the dispersion equation appears at 'the 'heat equation' the heat always flows in the direction from higher temperature to lower temperature. Thermodynamics laws forbid the sort of dynamic equilibrium that is established for momentum transport. But I'm sure you are well aware of all this. BTW plume was a very good term to use. Finally my commiserations to Ken for his team's loss in the World Cup. The Aussie soccer team doesn't seem to be of the calibre of their rugger teams.

Have you considered that is because they are not mixed ?

"'Weather' tends to keep the troposphere very well mixed as you suggest." Great statement. +1 Diffusion is a very slow and weak process. Weather is a very fast and strong process. In most cases there are no 'streams' of carbon dioxide or methane (or other unwanted gases), just intermittent trickles. So the words 'accumulation' or 'collection' appear again and again in most treatments. Of course, accumulation is the opposite of diffusion. Here is a simple experiment for your consideration. You have a bucket of hydrogen with a removable lid, suspended 100 feet up in the air. What happens when you remove the lid ? Ken seems to think that the hydrogen diffuses downwards towards the ground, as well as upwards and sideways. So what would be the distribution of this diffused hydrogen above, below and to the sides of this bucket if you measured it ? https://www.hse.gov.uk/pubns/gasdetector.pdf https://www.designingbuildings.co.uk/wiki/Ground_gas https://www.claire.co.uk/home/news/1149-british-standard-8485-code-of-practice-for-the-design-of-protective-measures-for-methane-and-carbon-dioxide-ground-gases-for-new-buildings-amended-and-updated https://www.gov.scot/publications/research-project-investigate-prevalence-co2-disused-mineral-mines-implications-residential-buildings/pages/15/ There you go from New York to Scotland to British Standards to................ Ther is just loads of supporting data all to be be had for the googling and reading.

Why go neither the HSE, the Soc of Environmental Health officers or the Association of Building ontrol Officers, nor I believe your bland statements, always qualified by non realistic additons. How would the gas be released as a stream ? It is randomly generated in small quantities underground and slowly percolates upwards through the ground. (methane and hydrogen will even get though a 300 deep concrete slab) there is moves quite rapidly upwards through the building air until it concentrates under the roof. No streams of gas are generally involved or the site cleanup has not been properly carried out. Concentrates is the reverse action from what you are describing. The gas remains getting more and more concentrated, until it either the supply stops or the gas ignites or it is let out. There is a giant ASDA in one town in Somerset that was built on an old rubbish tip and the disposal method was contolled occasional flare burning. Other methods have been used since on further retail development on the same tip. Eventually doors or ventilators will open causing natural air currents or there may be forced ventilation. Either way if the supply stops the gas will eventually dissipate by these processes, just as you say. But that could take a very very long time. The trenches were subject to considerable disturbing agents called winds. It was well known that the gas would 'hang around' much longer on windless days. Ken's thesis, and you appear to support it, is as far as I can tell, that there diffusion reduces the concentration gradient to zero. It is a requirement of the diffusion equation that no diffusion occurs unless there is a forcing function. The pre existence of a concentration gradient constitutes such a forcing function, but slowly subsides to nothing as the concentration gradient is reduced. So Ken is right in that if the cap is suddenly taken off a concentration gradient and nothing else is acting then the concentration will even out to nothing and then diffusion will cease. But that is not the case here as there are always other forces acting continuously and intermittently.

Don't apologise, +1, it was meant as a helpful comment/piece of information. We all have to learn these things somewhere along the line. A good example of dilatation is what happens when you walk on wet sand on the beach.

Tank you for that useful addition. +1 It is also what made these chemical agents so dangerous. Mustard gas has a molecular weight of 159 and phosphine 34. Compare with carbon dioxide at 44. That is my definition of an inhibitor, not a poison. But nevermind it will kill you all the same. Well I thought I had provided a pretty comprehensive answer, with several different parts to it. 1) A discussion as to the meaning of the words you guys used, notably stratification and a stement to the effect that there will never be a series of layers, each composed of one gas only, lying one above the other, 2) A discussion about what actually does occur, notably that a concentration gradient develops for all gasses, but the spatial distribution of that gradient varies with the molecular weight of the gas. 3) A discussion of the diffusion equation and the requirements for applying it in a gravitational field. 4) A mathematical outline of the kinetic theory mechanism for this. In what way was that insufficient ? You have still to answer the question why do lighter gases such as hydrogen and methane go straight up when released and collect in and under roofspaces ? Since you now have the maths, why do you need some nerd reference ? Why can you not check it for yourself ? Why do the building regulations require roof venting for this collecting gas and why does it continue straight up towards the stratosphere when it exits the vents ?

Do the maths. The diffusion equation describes the response of the particles to a forcing function. In this case gravity. It also requires the particles to be (1) non interacting and in the versions referred to to be (2) identical, and (3) have no significant disturbing function. What happens when a particle bumps into another, under condition 1 above, that is a) 22 times a heavy (hydrogen into carbon dioxide) ? b) 1.5 times as heavy ? (nitrogen into carbon dioxide) ? Well momentum and energy is preserved so if m is the mass of the lighter molecule and M the mass of the heavier; u and U the before and after velocities of the heavy molecule; and v=0 and V the before and after velocities of the light molecule then [math]Mu = MU + mV \Rightarrow M\left( {u - U} \right) = mV....................1[/math] momentum balance [math]Mu{}^2 = M{U^2} + m{V^2} \Rightarrow M\left( {{u^2} - {U^2}} \right) = m{V^2}..........2[/math] Energy balance Divide equation 2 by 1 V = (u + U) So the lighter molecule is greatly accelerated and the heavier one slightly decelerated. That is the kinetic processes of diffusion tend to speed up the lighter moelcules and slow down the heavier ones. Remember also that in the atmousphere there are very significant disturbing functions. So significant that our very climate depends upon really massive amounts of energy being transported from the tropics to the polar regions, after first being high into the air by rotational forces due to the Earths rotation. This energy effect was not realised until the mid 20th century.

Further explanation. Dilation is a general term in English meaning to get larger and applies to many different properties such as the size of an opening, the duration of a time period in relativity, and so on. Dilatiation is a specific scientific term for an increase ( or decrease if negative) in volume due to stress (mechanics) or other factors such as pore pressure (earth science).

Aha, two processes. Thank you, +1 I will read further. Agreed and this is why I said that prior information is also required by the observer. In your example this would mean there must also be some law akin to Pauli acting, stating that although either of us could pull out a coin at random, the other must then be opposite. This would correspond to the events not being statistically truly independent.

Thank you both. So why does do the lighter gases I mentioned not diffuse downwards to form a homogenous gas body inside a large commercial building (tin sheds I call them) ? I see that you have both avoided this question. The points I am making are 1) That the Earth's atmousphere is never perfectly still. 2) That 'stratification' fully developed into layering is not happening. However there exists a measurable concentration gradient for any gas in the atmousphere, depending upon the difference of its molecular weight and the average for air. In fact as we rise in the atmousphere there exists a concentration gradient for air itself (or its average). 3) A point I didn't make before, If we look high enough the concentration of very light gases like hydrogen will be changed by processes which change or even break up the molecules. 2)

Well I disagree. Let us look at it another way. If the gas was hydrogen or helium or methane what would happen ? The truth is that mixing will occur if there is sufficient activity in the gas body and then gases will keep remixing so appear to to remain unstratified. As you correctly point out, there is a lot of activity in the atmousphere. In perfectly still air there is no mixing. Equally in a tub of denser gas. with no disturbing flow activity the denser gas will remain in the tub. This is just the inverse of the lighter gases I mentioned collecting under roofspaces. I have measured this latter effect and designed buildings in danger of this to be safe. In Australia you have a large amount of spare space and no need to build on former rubbish tips. In the UK we don't have that luxury, but rubbish tips release methane and some much smaller amount of hydrogen, which are very dangerous gases if allowed to collect in upper spaces.

Thank you for your reply to my post the photos are the most useful informatuiom you have posted so far. Coin cell bateries may be housed in stainless steel, but there are lots of things on you Nintendo that are not and all, including that battery are subject to some forms of corrosion. Given the photograph which also shows failure of two decoupling capacitors, one showing serious leakage and lead corrosion I would question the history of your apparatus, rather than accusing your CR2032.. I can't identify the orange component next to the edge of the board by the battery, but that looks also to have suffered catastophically and may be the source of your issues.

If you do have corrosion or just general contact oxidation to clean off try a glass fibre pen. https://www.amazon.com/s?k=glass+fibre+cleaning+pen&ref=nb_sb_noss