Ghideon

Can you provide some evidence? "I dont't think so" is not a strong argument. You claim that mainstream math is incorrect and reject current proofs in links provided. Is it maybe the very definitions of the math of probabilities you question? That would make discussions about existing proofs not very fruitful. Note: The decimal comma "," should be read as a decimal point "." . It is the language setting of computer running simulation that causes confusion; for instance 0.997 is written 0,998 in that locale. You want a result based on every possible outcome instead of an outcome based large number of randomly selected samples? A discussion about random number generation in computing is better suited for a separate thread. I deliberately used secure random numbers and specified so in my note to reduce this kind of issues. csrc.nist.gov has information about certifications and research.

Ok. And the middle column? Do you claim that it does not agree with the law of large numbers? Does that make the simulation invalid? Can you explain the problem in detail so a simulation can be performed or a proof provided? Which theorem(s) of probability theory do you distrust? How is the above applicable to the discussion in this thread?

did you see the rightmost column in my result?

How? Details please.

Here are some results from a simple simulation. I’ve tried to incorporate some of the things mentioned in this thread. I think @uncool has covered many of the more theoretical aspects, hence I focus on a more experimental approach in this post. The simulation throws a coin n times, keeping track of heads and tails and finally calculates [math]|h-t| [/math] ( h=heads, t=tails) and [math] \frac{h}{t} [/math]. Initially n=10. To reduce the impact from any statistical outliers the above is repeated 20 times and the average of [math]|h-t| [/math] and [math] \frac{h}{t} [/math] is kept. Then the number of throws n is increased by a factor 10 so n=100 and the process above is run again. This is repeated for n=100, n=1000 … n=1000000000. The final result is a list of tuples containing n, average of [math] |h-t| [/math] and average of [math] \frac{h}{t} [/math] : no of throws per run average(|heads-tails|) over 20 runs average(heads/tails) over 20 runs 10 2 1,61845238095238 100 6 1,00452536506648 1000 29 0,992180661027686 10000 80 1,00101746079017 100000 263 1,00211222673523 1000000 716 1,00060018766435 10000000 2553 1,00001882460519 100000000 7893 1,00001224082561 1000000000 27652 1,00002288341028 The results supports my earlier statements as far as I can tell. If you disagree please comment in detail what additional simulations or observations you require. The descriptions provided so far is not very clear. If there is still doubt regarding validity of formulas, post a detailed description of what mathematical proof or simulations that you have performed or want help to perform. Unless specifically requested I see no reason to post long lists of source code. Note; I have limited time to investigate the specific random number implementation used but I used a random number generator intended for cryptography instead of a standard one. It should be good enough to not have impact on results. I would have preferred to run larger tests but I do not have time to improve the program.

This is still vague. Can you use mathematical symbols to show what you mean? Do you think the formulas I posted have not been proved* mathematically? Can you post a reference to observations that does not match what I said? I'll try to get some time to run a simulation (more fun than posting results from others). Where in formulas I posted is it stated that something must occur in a row or specific order? Note that earlier throws of a fair coin of course does not affect the outcome of future throws. *) Examples: http://www.columbia.edu/~ks20/stochastic-I/stochastic-I-GRP.pdf https://en.wikipedia.org/wiki/Law_of_large_numbers#Proof_of_the_weak_law

This could simply be a language* issue, @studiot could be completely right, we maybe talk about different things. Here are the full set of details behind my reasoning, all my possible mistakes and misinterpretations included, hopefully any misunderstandings can be removed. Statement: different masses means any masses; The statement is general so it must hold for any mass, not just small masses compared to some large mass. have the same gravitational acceleration means there is one acceleration that someone/something have or share with something else. different masses have the same gravitational acceleration I interpret as different bodies will, regardless of their mass, generate identical gravitational fields. This is not true according to equation [math]g= G\frac{M}{ r^{2} } [/math] So let’s try another interpretation: different bodies will, regardless of mass, accelerate identically due to gravitational acceleration generated by some other body. This seems compatible with Galileo reference. But OP state it moves identically in the field. So I interpret OP's statement as two bodies affected by acceleration in one shared gravitational field. With other words, when looking at the one gravitational field generated by two bodies they will both move towards each other. The larger mass will not be stationary. I’ll try some math: Two masses are located on the x-axis, to the right of the origin, with mass [math]m_{a}[/math] at [math]x_{a}[/math] and [math]m_{b}[/math] at [math]x_{b}[/math], with [math]x_{b} > x_{a}[/math] and positive x direction being to the right. [math]F_{ab}=G \frac{ m_{a} m_{b} }{( x_{a}- x_{b} )^{2} } = m_{a} {\ddot{x}}_{a}[/math] [math]F_{ba}=-F_{ab}=-G \frac{ m_{a} m_{b} }{( x_{a}- x_{b} )^{2} } = m_{b} {\ddot{x}}_{b}[/math] Accelerations then are [math] {\ddot{x}}_{a}=G \frac{ m_{b} }{( x_{a}- x_{b} )^{2} }[/math] [math] {\ddot{x}}_{b}=G \frac{ m_{a} }{( x_{a}- x_{b} )^{2} }[/math] Subtract [math]{\ddot{x}}_{b}-{\ddot{x}}_{a}= \frac{ d^{2}}{d t^{2} }( x_{b}- x_{a} )= -G \frac{ m_{b} }{( x_{a}- x_{b} )^{2} }-G \frac{ m_{a} }{( x_{a}- x_{b} )^{2} }=-G \frac{ m_{a}+m_{b} }{( x_{a}- x_{b} )^{2} }[/math] Change variables, let the distance r between masses be xa-xb: [math]\ddot{r}=-G \frac{ m_{a}+m_{b} }{r^{2} }[/math] Hence, looking at different masses in gravitational acceleration they do not move identically in the gravitational field. The acceleration seems to depend on both masses. Different masses seem to cause a different acceleration and different movement in the gravitational field. This may not be what OP intended. *) Or a calculation issue on my part, that is always an option.

Good points. Two more that I see as separate cases: Is it completely transparent? Is it camouflaged so that it is indistinguishable from it's surroundings?

@iNow covered most aspects. Depending on situation one could add geographic* redundancy/failover, likelihood or possibility of an insider attack, software revisions in use and how fast reported vulnerabilities are addressed. What kind of monitoring is in use? How stable is the business? Very fast growing or an economically struggling business could possibly partially neglect security policies. To what degree do you have insight in, or the possibility to monitor, that that contracts, rules and policies stated is actually followed? Will several competing cloud storages be compared, or are you assessing one specific storage? That said, there is also the information aspect; to which degree each concept applies depends on the purpose of storing and what kind of information that is stored: -How sensitive will it be when information is stolen? How sensitive is it if data is not stolen but lost? Example: completely public information may not sensitive to theft but may be valuable and must be protected against accidental or intentional deletion. Company secrets, medical records or similar should not be lost or stolen. -What are the likely parties interested in the information? Who are you protecting the information from? Casual hackers? Competitors? Intelligence agencies? So, depending on which aspects that are to be investigated, different methods for research will be applicable and different properties will be interesting to evaluate. *) A secondary site may have less strict security, be the older of two sites, having older or weaker perimeter protection, weaker fire protection or similar weaknesses.

You are discussing different small masses pulled by one large specific mass (earth). It is not a general rule that is valid for any mass. The formula I know of is [math]g= \frac{GM}{ r^{2} }[/math]. Can you show how different masses M can have the same gravitational acceleration g (for a given radius r)?

You mean that matter entering black holes is ejected through stars at some other point? If so, no that is not somerhing observations and current theories would say is physically possible.

The examples you list above are probably not research methodologies. They are more methods for management or collaboration in general. Are you looking for scientific research methodologies or more like methods for information gathering? Cloud storage is a broad area; security research methodologies could be different depending on purpose with storage and what content to store.

That discussion contains no support or evidence for your claim about anti-gravitational property. The discussion is about photons bending spacetime and contributing to gravity by some small amount. That's because photons have energy even if they have no invariant mass. But that is mainstream physics from general relativity. Side note: I liked the Hellboy movies. But I did not watch them to learn about science.

That is not correct. Or do you have a source providing some evidence?

Can you add some detail? What is the speculation?

When tossing a fair coin n times: the difference between number of heads and number of tails approaches infinity: [math] \lim_{n \rightarrow \infty } |h-t| \rightarrow \infty [/math] You claim the above to be incorrect, can you provide your alternate version? Please use math symbols. Your description is vague, can you formulate your claims in a more formal way? The math of gamblers ruin says theorem states that the game always ends when players start with a limited amount of coins. The game cannot go on forever with limited amount of pennies. But if you want the game to have the possibility to go on forever; change the game so players start with an unlimited amount of pennies. The equation above still tells you what happens. My interpretation is that you claim: [math] \lim_{n \rightarrow \infty } |h-t| =0 [/math] where n=number of tosses of a fair coin, h=number of heads, t= number of tails But the above equation is not true. The amount of heads and tails will not balance. It will deviate as I pointed out earlier.

Can you provide a mathematic reason why you believe that? You seem to claim that gamblers ruin theorem is not correct. Another way of stating what I said is: http://mathworld.wolfram.com/GamblersRuin.html That means that no matter how many pennies the players may start with, eventually one of the players will have all the pennies.

Did you understand the difference between the two equations I posted? Which one of them do you claim to be incorrect?

Show how it is false then. This could be part of the misunderstanding?

I do not get the above. "The closer and closer they would get to the same amount of them being heads or tails." That sounds like the opposite of what is known about games and probabilities*. The more times you toss a fair coin the larger the probability that there will be a large difference between number of heads and tails. Here is an attempt at using mathematic symbols** for my statement. When tossing n times: the limit for number of heads divided by number of tails is 1. [math] \lim_{n \rightarrow \infty } \big(\frac{h}{t}\big) = 1 [/math] When tossing n times: the difference between number of heads and number of tails approaches infinity is unbounded. (edit, got some help from Strange) [math] \lim_{n \rightarrow \infty } | h-t | \rightarrow \infty [/math] I remember this being taught in connection to Gamblers Ruin Theorem https://en.wikipedia.org/wiki/Gambler's_ruin#Fair_coin_flipping. *) First occurring in "On Reasoning in Games of Chance", 1657? **) Not exactly sure if "equals infinity" is the correct way to write what I intend to say.

Thanks for clarification. You seem to argue that the probability of exactly 1/2 of many and approximately 50% of many should be the same? It is not. For a large number of coin tosses there is actually a very small chance that there is exactly 1/2 heads and 1/2 tails. The only time it is probable to throw identical number of heads and tails is when the process is not fair or random. If I did a lot of tries and got 1/2 heads each time I would be suspicious. Example: Throw the coin 1000000000 times. What is the probability to throw exactly 1/2 of 1000000000 heads? Close to zero. What is the probability of throwing about 50% of them heads? Close to 1. And what is the probability of throwing heads the next time? It's 1/2

First comment, your paper says That does not sound correct. It can only be approximately valid for small masses moving in the gravitational field of a large mass. Example; a small masses will accelerate towards earth at 1g. But replace the small mass with a large mass, such as Jupiter. I do not think the result will be that Jupiter accelerates towards earth at 1g.

You might want to try the quote function in the sandbox

Thanks for the clarification! I suspected that expansion of universe was intended, that's why I stubbornly kept asking. The words have similar meaning over here as well, care must be taken so the correct physical concept is referenced. I'll read your proposed idea again using expansion wherever inflation is stated.

But if you stand on the surface of a large ball and you are not allowed to jump or dig, where can you go? To your local left, right, back, forward. Two dimensions, not three.