studiot

Smart move mister. +1 I did assume nothing was meant to mean mathematical zero, though I do know the difference.

John you frequently refer to this nobody person. But you never tell us where to find him. +1 Have you read Roy Turner's book 'Relativity Physics' on this subject?

I very much doubt it, even at CERN. Do you have any idea of the difficulty of tracking a number of atoms, when that number is of the order of 1023 ? In any case that is one single experiment (or trial since I am using the word in a statistical sense) so it only produces an estimate (and not a very good one) of the probability of finding an atom in the given space. The actual probability is of course, the limit of an infinite amount of such trials. This is the experimental aspect you have failed to consider. Proper interpretation of Probability as a statistical variable follows from this as do the consequences for experimental methods. You have come here disputing both well established Physics and well established Mathematics in a most desultory manner. When we examine your claims and try to offer what we hope and consider to be helpful discussion comments do you not stop to enquire why we have said what we said ? For instance You will find the appropriate solution to Schroedinger that links it to a probability spectrum of states derived on pages 81 to 85 of Mathematical Foundations of Quantum Mechanics by G W Makey of Harvard University Published by Princeton university Press in the Mathematical Physics mongraphs series. It involves some quite advanced maths applying Stone's Theorem https://en.wikipedia.org/wiki/Stone's_theorem_on_one-parameter_unitary_groups to some very abstract algebra. Mackey also develops QM on an axiomatic basis in the book. But Born's Principle is not an axiom since it refers to an interpretation.

English is clearly difficult for you, so I will only comment that the above is a poor definition of probability and not an answer to the question I actually asked. Probability is a (mathematical) limit. And knowing what it is a limit of and what that means for experiment is crucial. It most certainly does not mean the fraction you have stated above.

You are quite right to observe that you asked for experimental verification. Unfortunately, we cannot come to that unless and until you answer the question I asked. for convenience I will restate it. Proper understanding of probability is vital to the answer. I am sorry you did not like the paper I lined to, I thought it would be of interest.

Some problems in modern maths have only been solved by super computer trial and error to exhaustion. For example the four colour problem. Not all mathematicians accept these methods.

Since this was obviously a serious question, let me wish you well in your search. As I don't know what you mathematical level is it is difficult to advise, but here are a few thoughts. An amateur would not have the resources to attack the Millenial Maths Problems, or the ones introduced by Riemann, who originated the idea a century before with his list. Further I would question if they are fun. http://www.claymath.org/millennium-problems Also I don't know if you are a reader. This route perhaps offers more fertile ground. Take heart, Napoleon was an amateur mathematician and even discoverd a minor theorem which is named after him. You will find Napoleon's theorem along with a lot of (mostly) easy to assimilate fun stuff in The Penguin Dictionary of Curious and Interesting Geometry David Wells. David has also written lesser titles - TPD of Numbers and TPD of Mathematics. Another modern book is Things to Make and Do in the Fourth Dimension Matt Parker Martin Gardner was the most famous author of Maths Puzzles and explanatory maths articles with many books to his name. You you also try some overview books from famous Mathematicians which range more sidely and interestingly than academic courses. What is mathematics? by Courant and Robbins A survey of Modern Algebra by Birkhoff and Lane Come into this category Another category lies in applied maths here From Calculus to Chaos is brialliant as is The Mathematical Mechanic by David Levi. Other than this you will need to tie things down to a much smaller area.

You might also wish to check your Physics. There is no such thing as 'suction', except as a convenient accounting fiction.

I happen to agree with you, Hilbert's Hotel is far to subtle for the mathematical knowledge and maturity of the average 5 year old. However I also think that (I certainly find this) we are constantly overestimating the capability of students, because we misremember just what we knew at their age. There were two recent threads where 16year olds were asking for essay help with mathematical subjects. I certainly offered too much depth. So I think this is too much depth for a 5 year old. Although I agree it is mathematically far superior. There is also a philosophical point about Hilbert. No definition of 'full' is offered in relation to the word infinity and it all hinges on that missing definition. Incidentally I have now received an interlibrary copy of Bell and I have mixed reactions. I find I a pretty up to date compact grand survey and it would be a useful compact source book for facts. But therin also lies its main weakness. It is disappointing in that it mostly stops tantalisingly short of detail in depth.

Have you looked at this paper? http://philsci-archive.pitt.edu/12810/1/Dikshit-Born-rule-preprint.pdf What exactly is your understanding of the meaning of the statement The probability if event, E is P ?

Any inequality effectively defines an uncertainty Here is a purely theoretical one For any closed three dimensional object The square of its volume times 36pi is less than or equal to the cube of its surface area. [math]36\pi {V^2} \le {A^3}[/math]

Have you thought about L'Hopital's rule? [math]\frac{\infty }{\infty }and\frac{0}{0}[/math]

Rocket propulsion depends on mass. A rocket is a device which separated itsself (it's mass) into two parts by ejecting one part backwards or leaving it standing. The ejected part would be the exhaust. This may be ions, gaseous matter, beta rays. The part moving 'forward' we normally think of as 'the rocket', but of course the exhaust started off as part of the rocket. So a quiescent rocket beofre it blasts off is an isolated system that has mass. Because it has mass it has a centre of mass. Since the system is isolated, not forces act on it. Therefore the system cannot change its centre of mass, which must remain in the same place as the business end progresses forward. Three things assist here. Firstly the 'rocket' can leave behind further parts than the exhaust (spent stages). Anything left behind reduces the payload mass. Secondly once the payload is beyond the reach of restraining gravity it needs no more propulsion and moves forward at constant speed in space. Thirdly the attracting gravity of another body may influence the 'rocket' further on in its flight. So in a sense the rocket does 'push against' its exhaust.

Congratulations on being the only responder who caught the main point of my topic and didn't get side tracked. +1 Apologies to evryone else for my not being clear enough. Now if I could only remember those threads I was talking about.

Well put Sir. +1

There is much wisdom to be had from a good geology book. +1

Not only do the phtons carry energy they also have momentum. So, before you ask, no, photons are not 'pure energy' despite often being accused of this in the popular press.

I think perhaps itoero is confused by specifications in instruction manuals that state for instance Voltage: +/- 1% +/- 1 digit. The digital readout will always provide a number but the spec means the last digit of the reading is uncertain in that it may be 1 higher or 1 lower. In the old days folks used to try to read greater accuracy into analog meters than was really there, estimating to 1/10 of a marked division. But really they would get it wrong a significant proportion of the time so a reading of 1.5 could be say 1.4, 1.5, 1.6 or less often 1.3 or 1.8. The correct proceedure was to read (estimate) to the nearest half division, which would return 1.5 in the example.

I am not suprised that an arithmetic connection can be made since powers and roots are linked arithmetically already both between different powers and the base of those powers.

So the proceedure has many more steps than meets the eye at first glance.

Well yes and no. But I'm not sure I like the idea of 'collecting' energy. Energy is not some sort of magic fluid (This was once a theory and the fluid was called caloric) Yes you can create a device where the input is less than the desired output. It is called a heat pump. But this is not something for nothing because no, you cannot use this heat energy to created the power to drive the device. Energy can be considered as haveing 'grades of energy'. Heat is the lowest grade and work the highest. You can expend some high grade work to drive a heat pump to extract a larger amount of low grade energy (the heat) from the air , the ground or a lake. At 20oC you can get three to four times as much heat out as electrical energy you put in to drive the machinery. Conservation of energy is not violated because you have moved some heat energy from your source to your output so the ground or lake or air is that bit colder than before. If you count the work you put in plus this loss to the environment the total is greater than the heat you get out so Thermodyamics is satisfied. We just don't 'count' the loss to the environment.

Thank you for the answer. I hadn't appreciated you were actually taking repeated square roots. What method woud you use for taking the 10 to 20 square roots of a 10 digit number on a four function calculator?

If I put n = 10 and use your V = 100000 , as well as a calculator, I get [math]\ln 100000 = {2^{10}}\left\{ {{{100000}^{\frac{1}{{{2^{10}}}}}} - 1} \right\} = 11.578[/math] So the formula is not bad even for n = 10. However how am I supposed to evaluate [math]{{{100000}^{\frac{1}{{{2^{10}}}}}}}[/math] ? I used the yx button, but how is that better than using the lnx button directly? Edit I see the formula also works for decimal fractions eg n = 10, V = 0.01 yields -4.5945 ln(0.01) yields -4.6

Is octonian arithmetic associative? Is it distributive?

Did you actually read my link ? So I thought with your first line you wanted to simplify. But then you introduced a torus. What makes you think a torus curvature is extrinsic? Let me simplify. Consider an annulus, which is a plane figure. Can you calculate the curvature of that anulus using only data from the plane? Now embed that plane in a three dimensions. What has changed? Does the addition of the third dimension allow calculation of a different curvature?