studiot

That would seem to be at variance with the history I grew up with. The experiments that led to the expanding universe predated the 'steady state theory' So any proposal of steady state had to account for the lack of mass density change.

So why did Bondi and Hoyle propose 'continuous creation', if not because the universe was known to be expanding ? Surely that would lead to a steadily increasing mass density, which equally surely can't be called 'steady state' ?

So should we all move to Antarctica or Greenland ?

Everything we do rests on things people before us did. For instance if someone had not already 'invented' calculations of what use would a calculation engine be ? I would imagine that the abacus was known to Babbage, but so what ? and Why would his knowledge of that be suprising ? He would probably also know that surveyors of his time measured by a physical chain. Each time it was laid along its length the survey would pick up a small stone and put it into his pocket. At the end of the survey he could then count how mainy chains he had measured. So a pocket full of stones is a sort of calculation device. In fact it is a sort of primitive memory.

Thank you. I haven't kept up with cosmology, standard or otherwise, for many years, decades even, as theories seem to change almost as frequently as I change my socks. I had understood that the original reason for (now discredited) ' the continuous creation of steady state theory' because the mass density did not appear to be going down, despite inflation.

Yes, if it worked. Here is a simple (and very cheap) experiment to test it. Even in the UK we have rivers where there are weirs with substantial falls. Nothing like the Victoria or Niagara falls but enough for must test experiment. Where there is a reasonable flow of water tumbling down a few tens of feet there is usually to be found a substantial fine upward rebound spray zone. So take a humidity meter and measure how quickly the humidity drops off to ambient away from this zone. This would provide a crude assessment of how much and how far the 'climate' is affected by such a spray zone. River gauging information would give an idea of how much water you would need to pump.

The probability that the electron (or any quantum particle) exists at a specific point on a space axis is exactly zero. Yet all those zero probabilities can be summed to exactly 1 over the entire space axis. There are many counter intuitive results in Maths like this.

This must be a record, I have agreed with John Cuthber 5 times in a row. +1 for that post. Almost every time we have well publicised strikes the tired old argument about the nature of "the strike weapon", imflamatory language in my opinion is repeated ad nauseum. If employers say " the cost of raw materials, rent, utilities etc is going up so this must reflect in higher prices in the shops". Why can employees not say "the cost of rent, utilities, food etc is going up so this must be reflected in a higher cost of labour" ?

In fairness I don't think conventional mass density 'dilutes' with expansion either, but please correct me if I am wrong about that, I am not a cosmologist. However +1 for the calculations first half of your post.

Perhaps our north american members might remember this short story I read in Analog or Gollanz around 1966. Can't find it even on this site https://sf-encyclopedia.com/entry/black_holes But the story was about three voyagers who literally fell into a black hole in their spaceship and their respective viewpoints. One voyager was an altered human, one was an AI robot of some sort. I will post more if I remember the name of the story.

Professor ? Thawne Tachyons and TNT, an unusual scattergun combination of questions. Did anyone say this is dangerous ? Here is an old picture from ICI to demonstrate this Have a nice day.

Did you actually read the article you linked to ? Charles Babbage died in 1871. No one has suggested that Babbage's engine was the first - How about the Jacquard Loom controller from 1801 ? Or the abacus that certainly predated the Greek device

Yes, my mistake. Chad Orzel.

Thanks for your continued interest and more considered responses than the previous responder's wild posting. You mentioned rive gradients, I don't know if there are equivalent maps for Australia but here are some figures for the British Isles. There are some key comments in your post notably That is so true almost everywhere. +1

Thank you, so there is scope for this type of thinking. though problems to be overcome. +1

Update Interesting thing about beavers, doing exactly the Harappan thing and the Yeomans thing, in the continued drought. Beaver dams in east Devon create area of wetland amid drought https://w ww.bbc.co.uk/news/uk-england-devon-62662909

Thank you for this elaboration. How are these of equal shape ? It would be a very good idea if you could label your points (as in geometric points) so that issues can be discussed.

Thank you for posting your solution to the question, I am still thinking about it but +1. Four line segments, yes not four lines. Did you read the extract from Durrel ? You also mentioned area, do you include the diagonals as part of a tetragon ? Thank you for your contribution. Can you explain what bearing it has on my comments ?

Do you understand what this is all about and can you relate it to the thread topic of prime numbers and Fields ?

Members might find this distinction between a quadrangle and a quadrilateral enlightening. It is from one of the many textbooks from that master of Euclidian geometry, C V Durrell, entitled Modern Geometry (from 100 years ago). You might find the definitions in the first page useful.

That's not what I said. There are seven variables involved. Four of these are the independent driving and controlling factors and three are the dependent variables describing the results. The three resultant or dependent variables are 1) The max and min heights of the tides at any particular location and day. 2) The shape of the wave peaks and troughs, plotted as tide height against time at any particular location. 3) The timing of these peaks and troughs at any one location. (That is the relationahip of the timing from one peak to the next and its variation, which is what you are asking about.) The independent driving variables are A) The gravitational pull of the Moon. B) The gravitational pull of the Sun. The independent modifying and controlling variables are C) The local topography. D) Meteorological modifications. That is changes to any or all of the above dependent variables due to the local weather. These vary from day to day and are not cyclic. The Moon's gravitational pull causes a bulge in the water surface that is dragged round the Earth as the Moon orbits. As MIgL has already said if the Earth was a perfect smooth spherical water world this would result in a 'clockwork tide'. The height of this bulge above the mean level would be high water and travel round the earth at a regular daily rate. However this height is modified by the interaction of the Sun's gravity which results in a periodic monthly variation of this height called 'spring and neap' tides. But the story does not quite end there because the lunar orbital month is just a little bit shorter than the solar month, which means that the timing of the the interaction varies as the Earth-Moon system travels around the Sun. In other words the the Moon does not make a whole number of orbits of the Earth in the time it takes for the Earht to orbit the Sun. This basic pattern is called 'the equilibrium tide' and is nearly sinusoidal in shape. But the equilibrium tides faces two additional 'controllong' factors. The local topography is neither smooth nor part of a perfect sphere and varies in depth. This changes the general nearly sinusoidal shape to a more irregular pattern. But any modification to the timing is repeated daily as the topography does not change from day to day. It does not induce the cyclic day by day slippage of the high tide around the clock over about a fortnight, that is generated by the phasing difference between the Moon's orbit and that of the Earth. Finally, the weather (mostly wind) can hold back or push forward the timing of high tide by quite a few minutes and also hold its height down or pile it up. This is a random day to day affair that has no cyclicity.

Yes I think there is a small solar component but I haven't done any harmonic analysis of tides since the 1970s. But the result of the elliptical orbits of both the Earth rond the Sun and the Moon around the Earth is that the 'passing velocity' varies as the bodies go round. Kepler's laws say equal areas swept out in equal times. Not constant cvelocity around the ellipse. The 'equilibrium tide' therefore is not driven by a constant passing velocity gravitational pull. However you are quite right to observe that local topography has a great influence on the actual wave that is observed at any tidal station. Waters partly enclosed by land are subject to resonance and standing wave effects, just as the water surface in a bathtub laps back and fore. Southampton (the Solent) for instance has a 'double maximum' and the North Sea slops around just like the bathwater.

The shape of the Moon's orbit is an ellipse with the Earth at one focus. So the actual Earth - Moon distance varies over that orbit by about 13%. https://oceanservice.noaa.gov/education/tutorial_tides/tides06_variations.html

A small point; Technically, the figure offered by OldChemE is a re-entrant quadrangle and the one you offered is a crossed quadrangle. Neither is a quadrilateral. A quadrangle is not a quadrilateral unless it is also a polygon. Your figure might actually be a pair of triangles with a common vertex. I can't tell from the sketch.

How many sides does this figure have ? As to the original question for a quadrilateral, any figure, even a disconnected one of several parts and/or curved lines, a line can be drawn the make the area on one side equal to the area on the other. For some figures the two sides may be congruent figures or they may not depending upon the symmetries. I do not know enough about the topology of quadrilaterals to answer this - it is certainly the sort of question Martin Gardner likes to ask and there is a five sided version in his book on this subject, but observe that if a dividing line can be srawn to from two congruent halves, also quads, then the process can be repeated to yield an answer.