Bignose

Amazon has to carry several "introduction to java" books. Any of those would probably be a decent start. You local library probably has some, and if not, should be able to get them via interlibrary loan, too.

but, considering that it is a physics equation, the terms have units. 0 kg does not equal 0 with no units.

Predictions that can show your idea to be substantiated or not. Such as: If a body of mass x rotates at y rpm, the gravity force will be z at w meters away from that object. Or, if a body of mass x is split all the way down, it will create y number of photons at frequency z. Etc. Predictions that if an experiment would be set up, the results of the experiment would either validate or invalidate your idea. Without testable predictions, all you are doing is story telling, like that whole aside about Jules Verne and powerful computers. Without testable predictions, you certainly aren't doing science. Science requires specific predictions to be able to show in an unbiased, objective, unambiguous way that an idea is correct or not.

PI, Sometimes the why comes out and sometimes it doesn't. Is there a why [math]\pi[/math] is the value it is? Maybe, but that doesn't hamper its usefulness. The why can be an interesting question, but it doesn't ruin or invalidate the physics or math. The why isn't really the answer that physicist are looking for; physics is about making mathematical predictions of what nature will do. If I drop this block weighing 1 kg from the height of my head, what speed will it hit the ground? If a sun has a certain composition of elements, what temperature is its corona? On what date will the next solar eclipse be? Etc. Physics doesn't try to answer the why behind these questions, so the why is often out of scope. It may be that we never find out the why space-time gets warped, but we should still nonetheless be able to make predictions about what effects is has on objects. If the predictions are accurate, that is all it needs to be a success in the eyes of physics.

There are plenty of non-linear solution methods proposed, but no general one. Whereas linearization and updating is general and guaranteed to be convergent when certain rules are followed (like step size and eigenvalue restrictions). Accuracy can also be easily obtained with a good analysis of the residuals and a grid independence study. Actually, I think that one could argue that "with today's computing power" the drive to develop super-speedy solutions methods is lessened. If you use a slowly convergent method, an easy way to speed up solution is to get a bigger faster computer. I don't think that it is a great argument, but one that does hold at least some weight.

Why not write this out to that at the very least, there is one equation per line? Even better would be to use this forum's LaTeX capabilities to make it even easier to read. As it is posted above, I have zero interest in even scanning the post because it is very, very, very difficult to read it. Edited for grammar/spelling

from to you asked us to look it over and critique it. If you don't agree with what we said, you certainly don't have to take our advice, but you also don't need to be a smart-ass at those us who took some time to look it over for you. A simple "Thank you" works well in these situations.

ok, but the ad hominem attacks via name calling in the article certainly doesn't lend strength to the argument, and probably detracts from it. The aggressive tone isn't going to convince anyone who isn't already convinced. And, anyone who is anti-science will cite the name calling and (in this case justifiably) claim that scientists aren't any different than anyone else. I know it is frustrating, but I don't think that this tone helps. We've had several threads go similarly in the Speculations section. The few times (all too few) that someone has written that they will do more work, do more math, etc., a patient and respectful tact worked the best. Even if it doesn't work, at least you look like you took the high road. p.s., oh, and poking fun of the people who have a genetic disease that doesn't allow them to walk upright probably doesn't help either.

It is pretty much the equivalent of a calculator, but using a chart of values of sin would not technically be a calculator. This is essentially what's been done since the discovery of the trig functions -- tabulate their values and look up and interpolate as needed. You may be able to use the double angle or half angle formulas to get to known values, too. Also, depending on the accuracy needed, you could approximate sin by its series representation: [math]\sin x \approx x - \frac{1}{6}x^3 + \frac{1}{120}x^5 - ... [/math] though, solving a polynomial may not be significantly easier.

For tensors, I recommend Synge & Schild's Tensor Calculus. It is an older form of the subject, but I think it is significantly easier to grasp than some of the more modern treatments. S&S is still in print and a Dover book so it is a cheap own. I also like Sokolnikoff's Tensor Analysis, and it also has a chapter on fluid mechanics. I do think that this book is out of print as I bought it from a used bookseller. traditional as in Cartesian x,y,z. A lot of the books will just use generalized coordinates to develop the subject. I.e. one coordinate system will just be labeled [math]x^i[/math], and a different will just be labeled [math]y^i[/math]. What x and y are, will be specific to a problem at hand. For example, if you are converting from Cartesian to cylindrical, and you let x be the Cartesian system, then [math]x^1 \rightarrow x, x^2 \rightarrow y, x^3 \rightarrow z[/math] where I am using the right arrow to mean "corresponds to". In this case [math]y^1 \rightarrow r, y^2 \rightarrow \theta, y^3 \rightarrow z[/math] And, in fact, there isn't any particular reason you have to "go in order"... [math]x^1 \rightarrow z, x^2 \rightarrow x, x^3 \rightarrow y[/math] is perfectly fine -- you just have to keep track of the indicies correctly. The Navier-Stokes equations of fluid mechanics: [math] \rho \frac{\partial\mathbf{v}}{\partial t} + \rho \mathbf{v}\cdot\nabla\mathbf{v} = -\nabla p + \mu\nabla^2\mathbf{v} + \rho \mathbf{b}[/math] This is the equation in vector form. It is valid for all Newtonian fluids. But, to apply it in any specific coordinate system, you will have to convert the components of the equation into the coordinate system you want to work in: http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations has them all typed out for Cartesian, cylindrical, and spherical equations (about half way down, and you'll see why I didn't re-type them here)

Wow. Despite the friendly-sounding title, this book is quite the mountain. If you finish and understand this book, you will have an excellent understanding of fluids, but the learning curve of this book is unbelievably steep. This is a book over the heads of most graduate students. Are you looking for an introduction to fluids or an introduction to tensors? I can recommend much more friendly books for either, that are still challenging without being overwhelming. To answer the question, vector (which is really a tensor of rank 1) and tensor quantities follow certain rules when coordinate changes happen. These rules are in place to ensure that the principle that nature doesn't have preferred coordinate system remains in effect. This is probably best explained by an example. Consider fluid flow in a (round) pipe. Because of the geometry, this is a problem that is very nicely described using the cylindrical coordinate system. However, nature doesn't know what a cylindrical coordinate system is. Nor what a Cartesian or spherical or bipolar or any of the other coordinate systems are. In the cylindrical coordinate system, we may describe the velocity at a certain point by [math] v_r, v_{\theta}, v_z[/math]. That velocity is the same as some other set of components in the Cartesian coordinate system [math] v_x, v_y, v_z[/math]. How you convert from one set to another is based on the rules of tensors. Shear stress in a fluid is a rank 2 tensor, and has components [math] \tau_{xx}, \tau_{xy}, \tau_{xz}, \tau_{yx}, \tau_{yy}, \tau_{yz}, \tau_{zx}, \tau_{zy}, \tau_{zz}[/math]. And, these components have some other values in another coordinate system. These components change from one to another coordinate system, following the rules of tensors. They change values so that no matter what coordinate system you choose to describe the problem with, in the end you describe the same thing.

Any language can do this, really. You just need to learn the specifics on how to take input and how to increment or decrement. There isn't a reasonably mainstream language that can't do this (I suspect that there are some esoteric languages where this would be a challenge, there are some pretty weird languages out there). So, you have your choice of C, C++, C#, Visual Basic, Python, Ruby, Fortran, Java, etc. etc. etc. The only question is whether this "value" needs to be persistent or not. I.e. if it needs to be stored somewhere while the program isn't running. If so, the value will need to be written and read from a file or otherwise "pickled". If it isn't one value, but a whole mess of them, I suggest a database of some sort.

If there is any truth to this story, this is the Worst Scientist Ever. No **** the fly didn't fly away --- it had no ****ing wings!

If the mathematics is ahead of the experiment, then the math shows what experiments need to be performed to ultimately accept or reject the math. Nothing is taken just based on mathematics. Once the experiment is performed that confirms the math, then the math is accepted as a description of nature. This is why they build things like the Hubble telescope and the Large Hadron collider -- it isn't just for pretty pictures or fun. They are collecting data to confirm or reject the current models. So, until you can describe experiments that will show that your model is correct or incorrect, you are just story telling. Not performing science. Experimentation is at the very core of what science is.

It does falsify a disbelief in the possibility of limbs "falling asleep".

swansont is asking you to describe an experiment that can be done which would prove that your idea is correct or incorrect with as little ambiguity as possible. This is the concept of falsifiability. If there isn't an experiment that would show your idea is incorrect, then you don't have a scientific theory. You have a fantasy story. For example, if I believed there was no such thing as gravity -- that idea would be falsified the first time I dropped something. Please describe an experiment (or experiments) that you could do to show your idea is correct (with little or no chance that other ideas are correct) or incorrect. We need to know what testing should be done to show that your idea, and only your idea, is the correct representation of physics.

This was the 1st thought that came to my mind as well. That science uses words that normally have a very specific meaning. For example, energy has a very specific meaning. Ambiguity and impreciseness and even colloquialisms normally lead to less understanding, not more. And this forum exists largely in order to increase understanding about science.

Here in Iowa it snows enough that it isn't worth putting those down -- the plows just pry them up each winter and dig into the pavement where the reflector was. I do miss them from when I lived more in the south however, when it is nighttime and raining.

It is the instability of flow that causes turbulence. There is a whole study of fluid mechanics on stability. In short, viscous dissipation is not enough to dampen certain disturbances. Check out the absolute classic by Drazin and Reed, Hydronamic Stability They just put out a 2nd edition not too long ago. I have the first edition, and it is still the first place I consult on stability issues. There are more advanced texts out there, but this is an excellent starting point.

At least one solution exists f(n)=0. It is rather trivial, though.

for example, with the exception of this past summer's heat wave, Russia for most of its history. Mongolia is another example. Giant mirrors that lower the temperature will surely only make these areas colder and even harder for them to grow the crops they can -- I don't see how it is a net benefit to increase ag capability in one area of the world at the cost of ag capability in another. I'd much rather see the money go toward i_a's ideas of desalination plants AND money spent on the development of drought-resistant and heat-resistant crops.

md, I think that this is a pretty darn good attitude to have. I hope that you stick with the work, and continue to follow the tenants of good science at the same time. We had a good discussion on this forum a while back about whether an amateur could contribute something meaningful to the scientific community. In short, we all agreed that while it was unlikely, it wasn't impossible. The investment of time and resources to catch up to state of the art is a major cost to most people, but it isn't impossible for an amateur to accomplish. Just unlikely. I do wish you the best of luck.

I don't want to sound mean-spirited here, because it is not my intention at all, but I strongly suspect that these two quotes are related. Your having not read any other scientific papers, it is easy to understand why your paper would be of little interest to the other people who write these papers. It is also pretty bold claiming that you think you've "figured out the nature of time better than anyone ever before me" when you admit an ignorance of all the literature before you. Science is an iterative process. "On the shoulders of giants" is a typical motto. In short, it means that you learn the work that has come before you, and build upon it. Even if you are correcting or changing previous work, you are still building on it. No one person can develop all the ideas on their own, certainly not anymore, and not for quite some time. Even Einstein's papers are heavily referenced to work done before he published. So, I guess what I am suggesting is to read the previous literature -- I am sure that there are many things you can learn from it. At the very least, you need to know what current understanding is so that you can adequately explain how your idea is different.

Because science is about learning, and a goal of this forum is to help people learn for themselves, not spoon feeding answers. The question does have a homework feel to it. This forum is explicit in that it won't provide homework answers directly. It goes against much of the goals of this forum. To answer your question, I don't think that there is a way to calculate the values given. They are approximations, which means that they won't be exactly right, but may be close enough for some applications. Such as applications where you only need be within 1 or 2 orders of magnitude. You may be able to see the logic behind the approximations if you spread it out, but per the text you quoted, they aren't the exact answers to the series. There are approximations.