studiot

I was reading a pdf paper about protons when this little fella popped up Save time be dammed. How will anyone ever learn anything serious ?

Very quickly since I'm on my way out, The Darlambertian or box operator is the four dimensional equivalent of the 3D nabla or del operator. As such it is a partial differential operator. The solution to ordinary differential equations involvesarbitrary constants of integration to be added or accounted for. The solution to partial differential equations involves arbitrary functions, not constants to be added or accounted for. A differential equation connecting space and time is an equation of motion and may also be an equation of something else such as energy. Schroedinger's equation is an example of this. Some, but not all, solutions to such equations are wave equations. A wave equation is an equation of motion - wave motion. Sorry it's only partially (pun intended) geometric, I will try to add more when time permits. Hope this helps

Quite a lot has happened in the world since the OP stopped posting in June 2009, a few years before I joined It would be nice to know how he/she got on. I note that all the advice offered involves thinking in the abstract; some people are better with tangible hands on approaches. If anyone is still interested we could look further into this, the subject used to be called practical mathematics.

1) Avoid large heavy type in capital letters. I annoys many people, who think you are shouting. 2) As a student you should be thinking for yourself. But search engines are very useful to obtain factual information eg "what is the radius of the earth in metres?" , "what is the composition of the atmosphere of Mars?". In other words it is Ok to use it to find factual data, you intend to use but you must be in charge of the calculation or other use.

What exactly do you mean by using the word emergent ? For instance do you consider the result of 1 + 1 = ? emergent and if so in what way ?

It is worth pointing out that there is a big difference between the meaning of closed in mathematics and in engineering physics.

You already have a thread about this that you seem to have abandoned ? Don't waste your (and other's ) time on a false concept of 'time'. Time and change are independent variables that are sometimes related, but not always. When they are you can sometimes deduce a subsidiary variable the time time rate of change. But you can also deduce a rate of change with regard to other non time variables. These are basic mathematical definitions and procedures. They are independent because you can have one without the other.

This 1887 presidential address (to the ICE) about renewable electricity might interest by George Barclay Bruce might interest some

Well it is said that everybody in the world is linked to everybody else by no more than 6 links Jordan Ellenberg "Shape"

A pumped storage system has two reservoirs, the ocean could be the second one. Alternatively California already has a dozen desalination plants, so the spent seawater could be desalinated. https://www.waterboards.ca.gov/water_issues/programs/ocean/desalination/docs/170105_desal_map_existing.pdf

Totally agree. The theory of Erdos-Bacon numbers applies. https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Bacon_number

I can't see that the writing in school argument ever gained any traction is British schools. From Victorian to modern times, classroom layout in relation to windows took juaat about every configuration imaginable. Many schools were built upon three or four sides of a square principle with a corridor of classrooms along each compass facing. Also schools were built all over the world encompassing many different aspects, sun entry angles, and architectural features such verandahs or shading canopies. Many factories were built with so called north light rooves to provide even non direct sunlight to the machinery inside. This very poor Wikipedia article refers. https://en.wikipedia.org/wiki/North_light_(architecture)

First and foremost your comments suggest you don't understand the difference between weight and momentum. Secondly to the west of California there is by far the largest water reservoir in the world, called the Pacific Ocean. There is no requirement for pumped storage to be freshwater. Thirdly energy extraction from flowing water for single properties has been going on since time immemorial. Nor does that energy have to be electrical. In the 15th century the city of Exeter installed a pumped water supply, driven by a water wheel pump.

Start with the molar mass. This is determined by the stoichiometry of chemical reactions. That is it depends completely on chemical composition. A different value for the molar mass may be found when another (usually physical not chemical) method is used to calculate or measure it. This different value is called the abnormal mass. The difference arises because some but not all ( eg colligative properties,) physical effects are due to the number of molecules, not their composition. Changes in composition may arise due to low abnormal molar weight (due to association) or high abnormal mass (due to dissociation). This is a clear explanation with good examples. https://www.chemistrystudent.com/ncert-class-12/1-solutions/abnormal-molar-masses.html

Lifespan would also be an important factor.