studiot

Actually page 45 of the stanford link you provided (I have already thanked you for the link, paid my $10 and downloaded the pdf ) says rather more, particularly on page 45 et seq. As always the devil is in the detail.

It's a dumb photo. I'm sorry but this must be the worst ""What is this please ?" photo I have seen since I joined here. That is set in the context of maybe one such request a month on this site. I couldn't understand this one, let alone identify it. Post a half ways decent photo, or better set of photos, without the fancy editing and you might be suprised how many responses you get and how good they might be.

Problems yes, but this is the big one, even though it is a single small word. 1 The basic problem is this. Nearly all forms of 'environmental' electricity generation are a form of collection of low density energy and are inherently low voltage. This requires the parallel working of many units of generation, whether wind farms or solar or other. All this low grade supply has to be commoned up to a single output, which is technically very difficult and can be very wasteful if not done well. How would this work on a massive scale in the Sahara ? 2 Not just sand but in particular sandstorms ! 3 You are right, transmission is a difficulty, and needs to be at high voltage to avoid losses. Note my point 1 for the necessary technology to achieve this. However how do you think transmission takes place from Which are mostly offshore ? Further, you may like to know that the UK already buys (nuclear generated) electricity from France via a massive underwater cable across the English Channel. 4 So what happens when the sun isn't shining ie at night ? Yet again a storage and recovery issue

I see that you have satisfied your original request and also received some excellent advice. So I will just add a couple of extras. Firstly as you see you can always come back here and receive good quality help at any level. So if you have any specific questions, don't hesisitate to ask. Another friendly and helpful site is https://mathforums.com/ Although like all maths sites they suffer more than SF from spam. As too your subject matter: You have asked about signed numbers - a subject that many have trouble with. To fully get the most out of this you need 1) To properly understand the use of brackets (parenthesis) 2) The standard order of arithmetical operations 'BODMAS' or 'PEDMAS' Then you will be flying. This sounds fearsome but if you can correctly interpret these X = 2 + (-3) & Y = 2 - (-3) you will be well on your way. Comeback if you want more

1) That's an assumption not an answer. If this stuff is buzzing about the universe it must collide with other stuff, just as does ordinary (sub light) matter. So are you saying that the laws of conservation of momentum do not apply to such collisions either with ordinary types of matter or with more superluminal matter ? I asked why this assumption is justified. 2) I didn't ask about detecting the dark matter in question 2. I asked about detecting the emission radiation, that you say exists from superluminal matter. Or are you saying that there is none whatsoever in our part of the universe ? Again why can't /haven't we detected this ? However thank you for your answers.

Thank you so much for such a comprehensive and well thought out addition to the discussion , including the links. +1 This will take much thoughtful chewing over and investigating.

1)So what would happen when this superfast matter hit something ? Wouldn't we see evidence of this ? 2) If this superfast matter emitted light wouldn't it travel at normal lightspeed? So why couln't we measure that ?

I don't know your purpose in asking this question however a small, but important point is worth making espcially if you are an arts person. A force is a push or a pull. In the body the muscles can only pull. There is no mechanism for directly exerting a push. To obtain a push Nature causes the pulling muscle to pull on a stiff object ie a bone. This causes the other end of the bone to push against something. Muscles always work in opposing pairs and the balance between these two muscles determines which way the pull occurs. Often one half of the pair is (much) weaker than the other so for isntance a crocodile has very powerful closing muscles onhis jaw but much weaker opening ones. In relation to your question, arms hang down so they are pulling on the rest of the skeleton. So only body parts (ie muscles etc) that are involved in pulling are needed to stop them falling down. That is why there no direct connection to other bones is needed. In contrast our knees are held down by the weight of the upper body pushing down on the pelvis/thigh and eventually knee bones.

Do you think lack of change is unimportant?

Good to see you in action again, Eise. Welcome back. It is always a pleasure to have your clear thinking in a discussion. +1 and yet You various examples assume that there should/must (since the imperative is used) be one and only one capable of dealing with a given phenomenon. One of the principles of modern science, technology and general work practice is the principle of independent corroboration or check. That is arriving at the same result by different routes. Another example of differnt routes lies in the difference in the way a modern computer reaches an output versus the way a human migh do this. The computer takes lots of small simple steps but very quicklyso that the computer can arrive at a result in milliseconds that woud take a human a whole lifetime to reach by the same method. Further examples occur where a method we know to be theoretically unsound, arrives at the same result as the more complicated and long winded 'proper' method. For instance the method of virtual displacements, D'Alembert's method etc. Perhaps @Col Not Colin was getting at this sort of thing in his post ?

I have absolutely no idea how this would happen, but isn't that exactly what the word condense means? Isn't that what happens when a gas condenses to a liquid or a liquid to a solid ? A new form of PE is aquired - surface energy.

Unless the cloud can convert KE to PE somehow, since temperature is a function of KE, not PE don't you think ?

Wasn't Ok a junior member of an american religous sect ? Or did you mean the traditional scots greeting OK Hamish ?

Charmap will show you all the fonts you have available on your PC and perhaps those that are available at SF since it changes my normal font to Tahoma for the SF editor. Either way the partial is available at Unicode 2202 as in the Microsoft tutorial https://support.microsoft.com/en-us/office/insert-ascii-or-unicode-latin-based-symbols-and-characters-d13f58d3-7bcb-44a7-a4d5-972ee12e50e0 and my screenshot. Just use the sidebar to scroll through to the right part of the font you are looking at. Howver this will not help you with fractions, you need one of my methods already posted for this. Here are some samples of partials you can copy and paste the MathML code, remembering to add back the first and last square brackets I have removed for convenience. math]\frac{{\partial \Omega }}{{\partial u}}[/math [math]\frac{{\partial \Omega }}{{\partial u}}[/math] math]\frac{{{\partial ^2}\Omega }}{{\partial {v^2}}}[/math [math]\frac{{{\partial ^2}\Omega }}{{\partial {v^2}}}[/math] math]\partial x[/math [math]\partial x[/math] math]\partial y[/math [math]\partial y[/math] math]\mathop {\lim }\limits_{\delta x \to 0} [/math [math]\mathop {\lim }\limits_{\delta x \to 0} [/math] math]\frac{{dy}}{{dx}}[/math [math]\frac{{dy}}{{dx}}[/math] math]\frac{{\Delta y}}{{\Delta x}}[/math [math]\frac{{\Delta y}}{{\Delta x}}[/math] math]\frac{{\delta y}}{{\delta x}}[/math [math]\frac{{\delta y}}{{\delta x}}[/math] Don't forget to refresh your screen to get the rendering of the code. Also note that SF used to render the symbols at a reasonable size but since an undate a few months back I have to manually increase the font size (to about 16 or 18) to get viewable images on my browser. Some others don't seem to have this problem. I don't know why.

Another useful thing I forgot to mention before. If you want special characters such as greek letters, square root signs etc directly in the text you can use Windows program native charmap.exe to select, copy and paste them straight in without any LaTex etc at all. So here is Xi by this method Ξ

What you are doing reminds me of the man who said "I am trying too make a walnut into an oyster, both have a hard shell in two parts with something I want inside. Since they are 'kinda' the same I should be able to grow pearls inside a walnut"

Actually he just did, take note and learn.

Why Wilhem of course. https://en.wikipedia.org/wiki/Killing_vector_field

It was a new one on me and it means something different from a prologue which is meant to supply background information to the text, without criticism or appraisal. Prologomena (p) and prologomenon (s) include some form of appraisal or criticism. I am sure you are awae that Joigus didn't mean that, but used arbitrarily in its correct technical sense. A really good one-liner there. +1 One thing about simple principles is that we have a natural tendency to abstract a single simple principle and then try to treat it as if it were an independent variable, whereas often the variables are not (fully) independent.

Guesswork is a very inefficient method of learning at the best of times. The less solid and more hocus pocus the background you base your guesses on the more inefficient it becomes. It is no accident that the initials of Harry Potter are H.P. Who is the kid and who is teaching him ? Where do they teach magnetic cooling to kids in Physics ? Electrostatic traps work on ions not atoms. I wonder why ?

The Subtle Knife is book 2 in Phillipp Pullman's fantasy trilogy 'His Dark Materials' I expect your students can tell you all about it. https://en.wikipedia.org/wiki/His_Dark_Materials The Ockham quotes came from the prolegomena (what a word!) of Variational Principles in Dynamics and Quantum theory By Yourgrau and Mandelstam An interesting mixture of the Philisophy, and Mathematics of the Calculus of Variations. Sleep well.

This is a prime example of why you should stop guessing and listen to some very knowledgeable person who has the patience to listen to you. Alternatively you could actually read a textbook and find such things out for yourself. +1 for your patience.

Good question, how many giant's shoulders are our assumptions standing on ? +1

Not at all. You picked out a clear cut case where the 'obvious' simple explanation is incorrect. The actual reason is more complicated. In the OP I am posing a discussion question, has the razor been superceded by modern science ? My answer is obviously therefore yes, since there is at least one case where it is unreliable. But it is a good discussion and it is my hope that when (new) members produce outlandish 'theories' and say it must be true because of Ockham's Razor this thread can be pointed to as evidence of that unreliability.