Bignose

Learning math provides a tailor-made environment to learn and practice problem solving. Math is a perfect environment because the tools are well defined, and until you get to some very high level math, there are only right and wrong answers, and every well-defined problem has an answer. Read-world problems are rarely so perfect, but the skills developed in solving problems in a good practice environment still translate.

Dimensions don't only come in 3's. Where would you get such an idea? Consider a particle described by its location in space, its velocity and its volume. That would be 7 dimensions. Some of the flavors of string theory have 13 dimensions. Any time you need to describe something that is independent of the other variables, you get another dimension. Again, going back to the particle in space example. A particle that is at space location (1,2,5) could have volume of 4 or 5 or 10 or any other non-negative value -- so the particle volume is an independent variable to the space variables. You can have any number of them, you are not just limited by multiples of 3. A zero dimensional object is a point, and it is infinitely small. Because when you specify a point, there are no other values it can take. A line is 1-D, a plane is 2-D and then above they are usually termed hyper-planes. Lastly, you need to be careful of using the word "change" because in mathematical terms, that implies a derivative of some sort. And writing things like "no change" implies that the derivative is zero. E.g. "change in Time area" would imply, to me anyway, so it would be some sort of mathematical form like: [math]\frac{d}{dt_a}[/math] Perhaps if you wrote out specifically what you mean in mathematical terms instead of words -- words have inexact and imprecise meaning whereas the math is very precise -- it would be a lot clearer.

Yep, no other person in the history of mankind has ever signed a sworn affidavit and been wrong or lying. Not ever. And, we all now Leonard Nimoy -- Spock -- is the definitive scientific authority. Unsolved Mysteries was just the icing on that cake. If it is so easy to have solved, why can't you answer any of the direct questions posted above? Why can't you reproduce it in an obviously unbiased and objective way? Maybe more to the point, why aren't you fabulously wealthy yet? Because the ability to move large amount of matter with such ease -- even if limited to just night time -- would be an exceptionally valuable service that many people would pay a great deal of money for. So, why are you wasting your time posting on a rinky-dinky Internet forum? Get out, make a fortune, then you can pay scientists to replicate all your experiments and validate your theories and sit around telling us how right you were.

Also, I'm just going to step up and say it: I think no one finds it fascinating because of the person posting it. Peron, you've shown in your other threads that you have very little interest in actually defending or discussing in any detail whatsoever any of posts you make -- your refusal to answer direct questions is what got your other threads locked -- so I think that so one is very interested in staring another discussion just to have to not actually answer any questions again. That's just my personal opinion of why no one is responding to this thread or that other new one you started.

Probably ought to explain what is meant by "movement through the fifth dimension" because Newton's Law of Gravity seems to work pretty well in 3-D.

In 2 dimensions, there is no such thing as a cross product. The resulting vector is always perpendicular to both of the two input vectors -- impossible in just 2-D.

You could graph it to get a good idea of where the roots are. But, no, in general when you start getting nonlinear, then analytical solutions are going to be rarer and rarer. That's the primary motivation behind the powerful computational techniques that we have today.

rak, I'm not ignoring your question, I just haven't had a lot of time to get back to it. My first instinct is that because your f(x) actually isn't a function (which maps a single number to a single number) but is actually a functional (which maps a function to a function), that the definition of differentiation of the function isn't the quite right. see http://mathworld.wolfram.com/FunctionalDerivative.html I need some more time to look at this, so I'll get back when I've thought about it more...

That makes a lot more sense -- I can move posts around the math section here, but I don't think they've given me enough power to move posts across forums (...yet).

Assuming all the function are well-behaved (i.e. all the derivatives exist) you just take the derivative with respect to x straight forwardly. I'm going to drop the (t) notation -- it is still in there, x is still a function of t, I'm just not going to write it all out. [math]\frac{d}{dx} f = \frac{d}{dx} \left(\frac{dx}{dt} +x\right)[/math] [math]\frac{d}{dx} f = \frac{d}{dx}\frac{dx}{dt}+\frac{d}{dx}x[/math] now, this is where the "well-behaved" comes in, the order of the differentiation with respect to x & t can be reversed: [math]\frac{d}{dx} f = \frac{d}{dt}\frac{dx}{dx}+\frac{d}{dx}x[/math] [math]\frac{d}{dx} f = \frac{d}{dt}1+1[/math] [math]\frac{d}{dx} f = 1[/math] I have no idea what Snail is talking about with matrices and the like. What matrix? where? Furthermore, what is there to "solve"? I really don't get any of Snail's reply.

The issue I have with that story is that photons are everywhere, day or night. They are the force carrier particle for all electro-magnetic forces. Heck, even if you want to just reduce this to magnetic (I am unconvinced still, but whatever) -- you still need photons to be the force carrier particle. If photons "knock off electrons", how can the carrier particles do their thing? Once the force is transmitted, using the carrier particle, wouldn't that just knock the electron off, and then there would be no force? Besides, like I wrote above, there are photons everywhere, day or night. Photons range over the entire EM spectrum. From Radio, to UV, to visible light, to IR, to gamma rays. At night, there are photons from radio and TV and satellite signals, there is cosmic background radiation. Even more simply, at night, the Earth radiates the heat the crust absorbed from the sun during the day -- these are all photons. People radiate heat, too, again photons. So, just because there aren't as many photons in the visible light spectrum at night, in no way whatsoever means that there aren't photons. Because there are plenty -- and they should be "knocking" off electrons, too. So, this whole rationale behind the story is highly, highly suspect. Visible light is only a tiny, tiny portion of the EM spectrum which is all photons! http://upload.wikimedia.org/wikipedia/commons/f/f1/EM_spectrum.svg

But you don't just "add" a water droplet. The water molecules in the air effectively "knock out" some of the other molecules in the air. If they didn't, the pressure would go up because there would be more molecules per unit volume, causing more impacts per unit area, resulting in higher pressure. But, we are assuming constant pressure and temperature when comparing the two. And, since most of the molecules in air (oxygen and nitrogen being the overwhelming majority) are heavier than water, the water results in less overall mass per unit volume for a given pressure and temperature of humid air.

I don't expect anyone to have all the answers -- but the questions I have posed are questions that will need answers should you try to advance your theory. And should be answered if you want to keep discussing your theory on this forum. More than half of my questions are simply asking you to better explain and define your terms. I don't think that this is too much to ask. Terms like "speed of time". I know what a speed it, I know what time is, but putting the together into the phrase "speed of time" doesn't mean anything to me. You are using words I am familiar with in unfamiliar ways. All I am asking if for you to explain what you mean by that better in a way that I can understand. This isn't too much to ask, especially if you want your ideas to be understood. Because right now, I don't.

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The speed of light is a known quantity, 299 792 458 m / s. There are many experiments that verify this number (that's why we know it to such accuracy). If it didn't take any time for photons to travel from point A to point B, the speed of light would be [math]\infty[/math]. It isn't. It takes time. This is known -- why the insistence on denying known facts? And, why the refusal to address any of my direct questions?

I this is all as easy as you say -- objective unbiased proof should be very, very easy to provide. So provide it already.

It is all covered by the Law of Cosines: [math]c^2 = a^2 + b^2 -2ab\cos \theta[/math]. It doesn't matter what angle is chosen, all governed by the same equation. Pythagoras' is just when [math]\cos \frac{\pi}{2} =0[/math]. That's it.

Maxwell's Equations say this is an impossibility. And they've been verified millions of times over, so what extraordinary proof is there that Maxwell's Equations are incorrect? This proof should be good enough that it should be able to be publishable in any physics journal -- at the very least it should be on something like arvix. And, just to nip it off at the forefront, I'm not going to pay to buy someone's book. If the proof is so good, it should be available for free. If the proof is convincing, it is the kind of thing that should win someone a Nobel prize, and will have to be made public anyway.

I really like this -- one sentence, straight to the point, and is exactly what I agree with.

Lan, this is more about the people who like to tell a good story and think that that story is all that is needed to be "scientific". In the P&S section, there are two very good examples -- "atoms are cubes" and "EM thread theory". Both the OPs in those threads have claimed that their ideas a completely "logical" so that means that they are right. Both fail to realize that there are many other "logical" explanations out there. "God did it" is the 800 pounds gorilla of them all, bit history is also replete with examples. It was once "logical" to know that the moon is made of cheese. It was once "logical" to know that the Earth was flat. It was once "logical" to know that the earth rode around on the back on an elephant standing on a tortoise. More recently, it was "logical" for some people to believe in N-rays, and it was "logical" to believe heat was an invisible fluid called phlogiston. The point is that logic alone is completely insufficient. Science demands evidence to back up the logic, through experimentation. And in the vast majority of experiments are going to result in precise measurements and numbers, which is why we always ask for the math when someone has a new idea. The math based on the "logic" of the idea should make quantitative predictions which can then be tested via experimentation. If the experiment and prediction agree, then you have something. If you just go with "logic" -- then all you have is a story -- just like the stories of the Earth riding on the back of an elephant and a cheese moon. You need to prove using objective, clear, unbiased evidence every single assumption before you start drawing conclusions from them. Like I wrote in the other thread, an idea based on unproven ideas is like a house built on sand -- one strong wind and it is blown away. An idea based on proven ideas is like a house build on rock or a foundation -- able to stand up to much harsher conditions. Logic alone is just sand. Logic backed up by evidence is rock.

I read the link. There are no citations to any experiments whatsoever that provide evidence that this idea is right. It all a story that assumes a few things are right at the beginning and bases things on that. But, what if those initial assumptions are wrong? It's like a house built on sand -- one good wind and it going to be blown away. Good ideas are like a house built on rock, built on a solid foundation. Those can stand up to some harsher conditions. It is the same thing with "logic". If you make a chain like if A then B; if B then C; if C then D; if D then E and if E then F -- and F is my main point. Well, if you cannot prove A in the first place, then all the other part of the chain dependent on it don't hold. So, again, I want to see a citation to an experiment that shows that the assumptions made in the beginning of that article are true. I want to know that the first things are true so that then it is worth looking at the other conclusions drawn in detail. If the first things aren't true, then there is no point in doing any work on any conclusions based on the first part.

As I wrote above -- it isn't God, it isn't QM, it's unicorns! Sheesh! Hmmmmm, if only there were some method by which such debates could be settled.... because all three sure are logical. Oh well....

Please cite the experiment that supports this statement right here. This is an incredibly strong statement, and I want to read about the extraordinary experiment and evidence that backs this statement up. Because there is an awful lot of evidence that supports the current model, so its going to take some really good evidence to overturn it. And I want to see it.

Hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha Oh wait, you're serious hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha Shoot -- I gotta catch my breath. Nope -- one more round in me hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahahahahahahahahahahahahahahahahaha Without proof, there is no such thing as science. Without proof, I can write statement like "Peron is a purple spotted jellyfish" and then get angry when you don't believe me. And, hey, since proof isn't needed anymore, I have got a great car to sell you. Only $1000. It is brand new and you have my word that it will run perfectly for the next 100 years. You should drive it over my bridge -- which I will also sell to you for only $450. You don't need anything like proof of my ownership with a deed or anything -- you can take me word at it. I also have this rock -- it's totally awesome -- it keeps bears and penguins and elephants away. I'll sell it to you for $550. That's a steal for total protection from elephants alone! But I'm going to throw in tigers and penguins for free. And in fact, if you buy all three, I'll even give you a discount. You get the car, the bridge, and the rock, all for only $1900. I also have an explanation for everything else unexplained, too. Unicorns. Unicorns wished there to be EM ropes and hence there were. Unicorns are the real reason everything is exactly as it is. ----------------------------------------------- Have I made my point yet? Proof and evidence are EVERYTHING in science. Without proof and evidence, there is no such thing as science. Without evidence that your idea is right, why should anyone believe what you write? Anyone else could write anything else and have the exact same weight. Science comes in, and cuts through all the nonsense, and picks out only the ideas that are supported by evidence. That is the whole point of science in the first place.

The more complete version of [math]\mathbf{F}=m\mathbf{a}[/math] is actually [math]\mathbf{F}=\frac{d m\mathbf{v}}{d t}[/math]. Force is the time derivative of momentum. It is usually just turned into [math]\mathbf{F}=m\mathbf{a}[/math] because most often m is just a constant, and the time derivative of velocity is acceleration. But, the second way to write it shows how intimately force and momentum are related. When momentum changes, a force occurs.