studiot

Ok so a set is just an imaginary container we use to collect together itmes/objects of interest. The simplest mathematical set is just a list of the (mathematical objects in it. Since some sets are very large indeed (even Infinite) the list can be very long or even never ending. The next step up (mathematically) is to collect together objects with some property to cope with this because if we can specify the property we only need this specification to specify the set. We can do without the list. For example { The set of all even numbers} We write the set in between curly brackets. But mathematicians prefer formulae to words so we write {x : x = 2n where n is an integer} To read this we say to ourselves (The colon means 'such that') "The set of all x such that x = 2n where n is an integer" In fact we can shorten this using the set of all integers which is given the symbol Z {x:x=2n,∈nZ} Note some authors use Note some authors use a vertical line instead of a colon. [math]\{ x|x = 2n, \in nZ\} [/math]

Just a little bit of help here. Charmap Many of the symbols used, including the square root sign, are not available on the ordinary keyboard but can be obtained using charmap if you are using Windows (any version) In later versions just type charmap into the query box and press return. Boxes like these should open up. https://www.bing.com/search?q=charmap+symbols&form=WNSGPH&qs=SC&cvid=0f0cbd2b7805469e9dcdfe1e8cfc51c4&pq=cgarmap&cc=GB&setlang=en-GB&nclid=74D28496F4DE45C06BECB76344916980&ts=1731258460021&wsso=Moderate You can then scroll up and down. Select a particular character Copy it and paste it into your text. Extra hint It often pays to select several special characters and paste them in and add one more step Delete the ones you don't want at any one place.

Did you also catch the bit about the forcing function ? A vibration can 'bang between hard stops, for example a car bonnet or a door or other fixed panel can bang in the wind again its restraints, alternately hitting one then the other. On oscillation reached the end of its travel naturally as it runs out of one energy (the energy of motion or kinetic energy) because the oscillation is transferring the KE to potential energy. In a system with not losses that cycle is repeated endlessly PE → KE → PE → KE...... In a system with energy losses, often due to friction, (called damping) the energy gradually leaves the system. Newton's cradle is not relly a simple oscillation it is actually quite complicated as one side is free to go as far as it likes, but the other side has a nearly hard stop.

Please make up you mind and also revise your terminology. x, y and z are not parallel they are orthogonal variables. That is why they are independant.

I wasn't suggesting you go self study those subjects, I was offering help with that. However it is laudable that you took the interest to look these up and also to indicate where I should start. +1 I have some apple trees to prune this afternoon ,but I will make a start when I have done that.

I don't think either the untimely demise of either Galois or Abel stopped their genius flowering. They had both achieved much before that. There were plenty of Frenchmen who started well but lost in one of the many french wars. I agree with that, But not this Depending upon your POV, rampant poverty is still true today.

Actually (pun intended) both were 'low church' middle class and fairly well to do. De Morgan studied under hamilton and Airy from at Trinity College Cambridge from the age of 16 whose main interest was economics (though Wiki has not picked up on that) Bayes main interest as a church minister.

Or simply went on to other things than Science, as with Bayes or DeMorgan. Of course there have been evil geniuses in the past like Cardinal Richlieu or Rasputin.

I think the point of my statistical comment was that without a proper statistical study you could be deceiving yourself.

You need to delve into set theory and group theory to discuss this. Are you ready for that ?

"Cometh the Hour Cometh the Man" you mean ? +1 However I counter you For every 'persuction' you could name i reckon I can match with an equally vile persecution from history that did not throw up (edit I should really say was not followed by) a Newton. For Instance the persection of the hugenots and the Cathars in France, the persecution of the general populace in ancient China that led to "The Water Margin", the persecution of the native americans following the advent of the europeans ...... But also a mathematical observation. Statistical variation would expect there to be 'clumps' of the occurrence of genius, not a continuous steady rate of incidence.

Somebody moved UK's oldest satellite, and no-one knows who or why https://www.bbc.co.uk/news/articles/cpwrr58801yo

Thanks. +1 That may work but not sure if my router will always assign the same local IP to the Nas unit.

Yeah it's suddenly all working perfectly again. No idea why though.

It has been working perfectly since around then. ~Except that I don't use firefox for this Why would I ? Here are a couple of screenshots from Windows explorer firstly the med on nas is indicated in the network places but reprts and error Attempting to open via the workgroup reports a second different error The account I am using is an administrator account but I have forgotton how to get the service or services running again or even which ones.

In what way do the foundations of Physics apply to Life ?

Thanks for the links and the interest. I have since found this but have not managed to fix it yet. https://www.gaasen.com/gaasen-blog/nas-servers/51-readynas/50-loss-of-access-to-readynas-admin My ReadyNas is the older type (NV+) as in the bottom two in the picture which is from the article.

Perhaps I should offer a translation guide in advance ? As you know I am trying to connect theory with everday experience and also keep looking back at what we have already done. Vibration, Oscillation and Wave Motion. When we talk about vibration we usually mean the whole (or most of) object or system shaking in some way. For example The reed in a reeded musical instrument such as a clarinet vibrates when you blow on it. Depending upon your skill this may produce a pleasant sound or a scratchy unpleasant sound. So there the same object or system can undergo different types or modes of vibration. Sometimes we talk about a car shuddering and shaking and vibrating as is passes over a bumpy road. This type of vibration may vary considerably in the pattern of movement as compared to the more regular and predictable pattern of the clarinet reed. Vibrations are normally subject to a 'forcing function' that makes the the object or system follow a particular pattern of vibration. And the vibration normally ceases with the ceasing of the forcing function. When we talkabout an oscillation we normally mean a much smoother more rhythmic activity such as the swinging to an fro of a pendulum. Here the same pattern of activity is repeated over and over again and called oscillation. Further, rather than a continuous forcing function being applied only a single impuls is given to start the oscillation off and perhaps subsequnet small impulses at suitable regular intervals. Remember my teach with the knotted handkerchief ? The system is then oscillating at what is known as a natural frequency and as already described this is called resonance. A particular feature of this type of activity is that the oscillation occure regularly about a mean or fixed point (think of the pendulum) Cue Mordred and his Simple Harmonic Oscillator. Now another simple harmonic oscillator is a weight suspended on a string. If we hang one such spring oscillator on a fairly taught horizontal string, it will just oscillate up and down after its initial impulse. If we hang several such oscillators on the same line, like washing on a line, and just activate one as an oscillator we will find that the up and down oscillation will spread to the other weighted springs and soon they will all be going up and down together. This is resonance in action. Now we have transferred wenergy from pour initial oscillator to its neighbour and thence to its neighbour and so on. This is a form of motion (of energy in this case) sometimes called transport of energy. Wave motion is such a tranport device and it transports energy (and sometimes mass and sometimes momentum) from place to place. Wave motion can be regarded as a series of 'coupled' oscillators hand on the impuls from one to the enxt like the washing line weighted springs. Maybe this will help with what Mordred has to tell you.

You need more than one reference point. You also need a direction, at minimum. A typical example would be how we measure compass bearings. Compass bearings are measured clockwise from a chosen line called North. A second system of measurement of the same thing is the cartographers and surveyors easting and northings you get on an OS map. Bearings here are measured anticlockwise from a chosen line called East. This second system is the normal mathematical method of measuring angles in polar coordinates.

OK so this is definitely not a Calculus problem that we can solve. It is called the many body problem in Calculus gravitation. The point of traditional calculation is the we assume a system passes from on point (or state in KJW's case) to another in a smoothe continuous fashion so that each following point is somehpow close to the previous one. Such an assumption allows us to plot a path from one state, condition, place or whatever to another with infinitesimal intervening steps and never jumping. This whole centuries old assumption was shattered in the mid 20th century with the discovery of chaotic systems that do not follow such a predictable path. We do not know if a multiplanet system is long term chaotic or not but many very much simpler systems are. That is a good question. There is a difference between measuring after the event and prediction before the event.

Can you provide a bit more detail perhaps a simple example of the change ? Traditionally we use the Calculus to measure change as in velocity is rate of change of position and acceleration is rate of change velocity etc. But I am not sure if that is what you mean.

Both. Just as new tools have advance Physics, Chemistry and Maths and other sciences. But since they were already more advanced than Biology perhaps the effect was less. Other Sciences with new paradigms include Astronomy, Geology and Cosmology. Equally the successful search for the background radiation is a good example of Theory predicting something and then experiment eventually confirming it. Although not quite as expected as that has led in turn to new questions.

I owe you a big apology as I got it wrong on the plot, but correct in the text did you notice ? Fission and fusion are the wrong way round on the plot. See above for fission and fusion. Both can release energy for the right reaction, but elements from iron to beyond uranium need to break apart (fission) to release energy. Elements from Hydrogen to iron need to join together (fusion) to release energy. Conversely it take energy input to split a nucleus smaller than iron and energy to fuse together nuclei larger than iron. Don't forget that it is the nuclei which break up or fuse together. I will let Mordred tell you about the cosmology of fission and fusion. It used to be thought that only carbon could form these long chains, but recent advances in Chemistry have discovered that other elements such as sulphur and silicon can also perform in this way. No, no one could solve the problem before kekule.

Your weblink is quite good but a bit too elementary. You do not have two nearby charges in your model you have an array of infinitesimal dipoles. Furthermore if they are twisting they are not 'static'. And a moving electric field causes a magnetic field. That is how EM radiation works. ~Wiki has a good animation for movement, though it is trqanslational not rotational. https://en.wikipedia.org/wiki/Electric_dipole_moment But if you have an array of dipoles you get a surface charge. This one is not animated.

But is it proper Barista coffee ? 😀 But seriously one further point occurs to me. When I was at university they were predicting the next major 'explosion' in Science would be in the Biosciences, not the older physical ones. Well of course they were right and pqarticularly in the last 20 years or so the biosciences have changed out of all earlier recognition. Look at biophysics and biomaths to see this. Note this is not 'applications of ..' with biology as the subsidiary subject. It is now truly the other way round. https://en.wikipedia.org/wiki/Biophysics