studiot

What have you done so far ? Have you assigned any symbols to the variables eg Vg and Vl for the gas and liquid volumes ? Can you start to form equations as a result, using the rest of the information given ?

A volume integral is not a volume. If you can assign a value of some property to every point in a particular region of space that property is either additive so that you get a total if you add up the values at every point. Such a property is called an extensive property. If the region is a line (1 dimensional) the taking a line integral gives that sum If the region is 2 dimensions then taking an area integral gives the sum If the region is 3 dimensional then a volume integral gives the sum If the region is 4 dimensional then taking a hypervolume integral gives the sum Examples would be mass, energy. If the property is not additive it is called an intensive property. Examples would be temperature, gas pressure. Intensive properties can be converted to extensive ones by taking deviations from an average. The average then represents every point in the whole.

I would suggest beneficial. Although it would be even more benficial for humans if it died out altogether.

Glad it was helpful. To put things more simply I think Markus was referring to building one of your structures with his elements like building a brick or block wall with one brick stacked on top of another. Each brick corresponds to a 'volume element'. However I am concerned with apparent suggestion that you can string together any old set of axes and multiply coordinates on them to form a volume. Here is a simple example of the nonsense that could produce. Let there be 3 space axes, the Mercator projection grid lines and plot the coordinates of the capitals of the world on two of these axes. On the third space axis plot their respective elevations above sea level. Now introduce an axis measured in seconds ie a time axis. Plot on this axis the half lives of all the radioactive isotopes (in seconds). All these points will result in a 4D space for which the concept of hypervolume, or integration over some region of the space, has no meaning. Sometimes when you multiply two or more quantities together you get a new quantity with some significance in the physical world. Area and volume and work and energy are such products. But multiplying temperature by distance has no real world significance that I am aware of.

Not sure what you are looking for ?

I have heard the proposition that it is an unfavourable outcome for a virus to exterminate (or nearly so) its host. As a result more successful viruses evolve to be less pathogenic towards their hosts. I understand this happened in time with Spanish flu, and even the common cold.

Thank you both for staying on topic, a practice that seems unfashionable these days. +1 Yes you have the essence of the original difference between the two, though there is a lot more to it these days.

Thank you for your thoughts. The general public use the noun plastic to refer to materials which have the property of plasticity. Plasticity is the correct scientific noun which refers to a well defined property, which may or may not be invoked to the application of heat. Science uses the adjective plastic (as I did with my catchplate) to refer to nouns that have the specific property. The property is that makes a material plastic is a mechanical property of they way it responds (mechanically) to stress, not a thermal property per se. Plasticity is not the 'opposite' of elasticity, it is just one of many possible responses. The principle responses being, elasticity, plasticity and brittleness. Most materials exhibit all three at different stress levels and or stress time rates.

No worries, perhaps these sketches will help. Starting with only 2 dimensions and comparing two different figures. There are no volumes in 2 dimensions, only areas and lengths. In figure 1 one side is measured in seconds the other in metres. The region enclosed by the axes and the dashed lines is not an area. In figure 2 both sides are measured in metres and the shaded figure is inded an area. Moving up to 3 dimensions we now have areas and volumes (and lengths). In fig 3 we have two side lengths measured in metres and one side measured in seconds. This figure is not a volume. The base and top of the figure are measured in metres times metres ie is an area but the other faces are measured in metres x seconds, which is not an area. In figure 4 we have all three side lengths are measured in metres so the figure is a volume and is measured in metres x metres x metres. Also any of the faces are measured in metres x metres so all faces are areas. I can't depict 4 dimensions on a piece of paper, but the idea is the same and as you rightly say the next step up is a hypervolume. But the progression has the same characteristics. You can only have a hypervolume if all the sides are measured in metres and all the 'faces' are (3D) volumes. If one of the sides is measured in anything else then the result is not a hypervolume. So we can't use time directly. So I have ended with the observation that if we multiply time by a speed the times cancel and we 'convert' the time axis into a distance axis. Newton just used any old speed. Einstein introduced the idea of a special speed, c, the speed of light.

But a structure cube or whatever is not a point. Can you describe what you mean using only one space axis (x) and one t acts (ct) ? Do you understand why the other axis has to be ct ?

I think both these graphs are perfectly compatible, but they show different things. Swansont's graphs are specifically the relationship between infection and vaccination. That is one effect only, with other effects not included Mistermack's graphs are a composite of different effects. Yes the trend in the 7 day average new cases within 24 hours and deaths tracked each other pretty closely. And they still do. But they also show a dramatic of deaths suppression following significant mass vaccination of the population. Nothing wrong with either of them

In what way ? I am not sure of what use the hypervolume is to anyone anyway ?

Yes, but what is the letter of the law ? The UK advisory body has just advised that fully vaccinated for folks in the age range 12 - 15 should be increased from one shot to two. But it is not yet law. I think age grouping of data is another effect not properly spelled out in these summary charts.

I haven't checked the arithmetic but some practical comments may be in order. 1 How would you heat the water ? 2) How would you extract the energy from your supertank ? Assuming 50oC, as soon as you had extracted half the energy the tank water would be down to 25oC. If you simply ran water from than tank through a domestic radiator system the system would cease to heat the house at about this point. Radiators at 25oC are of little use. 3) Very large houses for very rich people in the past had 'ice houses' capable of preserving winter ice during the summer heat against a temperature differential of perhaps 30oC. With modern insulation we could perhaps contemplate the larger differential, but it would still ad considerable bulk to any installation. Not a prospect available to most.

I am using the AGA, as I think druS did, to represent cast iron ranges which often had/have a domestic hot water capacity as well, not to represent any particular brand. I should perhaps take this opportunity to note that building owners in the UK, have a statutory duty to inform Building Control if they change the form of heating (water and I think space) in their property. I had to do this when I changed from oil to gas and again from gas to an electrically driven heat pump.

I am not sure how much you will find about vectors in Bondi's book, but the Einstein train experiments chapter is worth thinking about. Here is another train experiment which shows some interesting things. A man holding two bricks is travelling in a glass train. (Glass so he can see and be seen) He holds them side by side, one just inside the carriage and one just outside by the window. As he passes another man standing on a station platform he drops them both together. It is illuminating to consider what each man sees about the paths of the two bricks.

I have that beef about the UK Inland Revenue and tax forms.

Thank you it is useful to be able to compare data standards. One thing immediately stands out from that. When do you become 'unvaccinated' after the one or two shots ? The UK is managing boosters for about six months and two weeks. But many mean fully vaccinated = after the booster.

It should be noted that data from all countries/regions contains considerable hidden unknowns. Also the methods used for recording the data are different in different countries, making comparison a bit tricky. The UK defines death from covid as "Death within 28 days of a positive covid test" It defines infection rates as "recorded by a positive covid test", not as presenting with covid symptoms But only a minor % of the population undergoes routine testing. Most only test if the have symptoms. Also what is meant by 'fully vaccinated' has never been clear.

Actually I was a bit overdramatic there because you can still install an electric AGA, its just the gas ones at the moment. Interestingly folks come from all over the world (even Oz) to visit the splendid country kitchen showrooms near me. You can see not only AGA, but many other European and American manufacturers rages there. Some of these are absolutely enormous. We sometimes take our visitors there as it provides a good half day out.

Shape is a very difficult concept to tie down. I don't know of any way to define it without involving boundaries. So far as we know, the Universe has no boundaries.

I wasn't asking for myself, but thanks for your links. I was gently referring to the invariance of 4 dimensional distance in spacetime. Distance or length in 4 dimensions is the invariant '4 squares quantity' No one measures it lengthened or shortened. 3 dimensional distance is measured as shortened by many observers (but not all) And , of course time is then measured as lengthened. But I'm sure you know all this. My point is that many others mix up which distance they are foreshortening.

If you weren't persistently so rudely aggressive towards others, I might be inclined to resume conversation with you.

I did have a chuckle about the large negative spike in the green (death) graph. Reincarnation and Resuscitation Rules OK ?

You may wish to expand on this statement as i think it is easily capapble of misinterpretation.