Bignose

Yep. 'Cause they don't make any balloons with holes in them. http://ecx.images-amazon.com/images/I/314xBg9CFFL.jpg I mean, just none at all. http://thumbs1.ebaystatic.com/d/l225/m/mlSKtTBrH7x3fJhbi-B-zSA.jpg The thought is just ludicrous, really. https://www.balloonhq.com/column/dewey/nov09/UFO6.JPG And, obviously, a balloon could never ever ever get a rip in them, ever, either. Just an unfathomable impossibility really. Nor could a balloon with one hole in it fold over itself and appear in a 2-D picture like it has two holes. Also a possibility that deserves zero consideration. (pssst. If you can't tell, I'm being pretty sarcastic.) jeremyjr, I'm still at the point where if you want to support your claim of plasma beings, extraterrestrial beings, whatever you want to call them... I still need something better than some blurry pictures.

The above is low in error for small x, because for low x, [math]\sin x \approx x[/math]. But for values of not low x, the above linearization is rather poor in accuracy. Eg. using your method to calculate sin(40.1 degrees) would have an error of about 0.05%. That may be good enough or horribly, horribly inaccurate depending on your application. I would be pretty disappointed in my calculator to have that large of an error; it was probably acceptable when calculators were first replacing slide rules, but wouldn't really be acceptable today. The above may have been true of the very first calculators, but it isn't true for modern ones. Modern calculators have errors in 1 part per million or better.

Judging from the title, I am guessing that DEs = differential equations. And, yes, most differential equations can be treated as linear over small segments of the domain; this is the basis for most numerical methods out there. There is an incredible art to figuring out exactly what is 'small' in this context. However, if there were no differential equations all together, I'm not sure what can be said, especially since they are so ubiquitous in our models today.

I think that the title question is too broad. As one example, there is no math equation that is going to 'solve' my golf game -- you can ask my regular foursome. Math can and is being used to model the game of golf. You can measure metrics like how many fairways hit, total distance hit, number of putts made, etc. In fact, there is a really neat metric developed over the last few years called shots gained based on statistically how much better or worse a player performs in a given position than the average tour player. You can also do things like model the physics of the ball and club impact, model the ball flight through the air, model the ball and turf interaction when it lands, etc. Lastly, you can model how much improvement someone should gain from practicing certain things. However, all that said, none of that actually 'solves' my game. There is no equation I can go to when I have to sink a 10 foot putt to win the hole, or to make me do the motions I know I need to do to prevent the ball from slicing off the face of the earth. In short, math is one of many tools. In science, it is used to make quantitative predictions. This is valuable because the model that makes predictions with the least error to what it measured is preferred. But, you can't just say math 'solves' everything. At least not a the level of mathematics today. There are plenty of things that occur every day that we don't have very good mathematical models for.

I must have missed that post where you presented a mathematical model, made from predictions from it, and compared it to known measurements... Without that, it's all just story telling and 'gut'.

This is why science is all about specific testable predictions. Here in an old article I remember being talked about when I was in school: http://www.colorado.edu/physics/EducationIssues/T&LPhys/PDFs/McDermott2b.pdf Basically, it shows that a large percentage of students -- even ones who got very good marks -- have no real concept of what acceleration is. In other words, their 'gut feelings' are wrong or at least miscalibrated on something that is literally physics 101. It is not hard to extrapolate that gut feelings on things more complicated than that are even less reliable. Again, science has fixed this by specific testable predictions, almost always generated from a math equation and compared to experimentally measured data. Gut feelings are great. The can be the kernel to a scientific idea. But gut feelings alone are not science, and you must also be exceptionally ready to accept that your guy feeling was wrong if the predictions don't agree with the measurements. As human beings, most of us struggle with that part of the process.

The answer is certainly less than 3. Simply because you cannot get unique answers to the variables above, x, y, z. I base this on the old "if you have A unknowns, you need to have A equations to solve" rule. There are 3 variables above, but there isn't enough information to solve all 3, so I don't think that there are 3 equations. I think that there are two. x - A = y - B and y - B = z - C. The fact that the 1st term and the 3rd term are also equal due to being equal to the middle term doesn't actually add any information.

Is that something that the thread is full of scientists who appreciate the scientific method and the process of making testable predicts and comparing them to measurement? Look, it is great to have ideas. It is great to have far off, wondrous, ponderous, incomplete, ambiguous ideas. These flights-of-fancy are often the kernel of great scientific ideas. But they, by themselves, aren't science. Because of all the reasons given above. And when you're on a science forum, people kind of, you know, expect science. Not just daydreaming. If that is what you're into, there are other forums on the internet that are more accepting. Here, we apply stricter rules to the posts in the science-based sections.

lol. Boohda, you came to this forum willingly. No one is forcing you to. If people really didn't care, they wouldn't have even bothered to ask you any questions. Do you understand that ALL science is questioned? ALL science requires supporting evidence? No one is just going to take your word that your idea is better. In answering questions, you make your idea stronger. By going out of your way to not answer questions, you just confirm that you don't have a very strong scientific idea. Basically, if you aren't going to answer questions, then this thread will be closed by the mods because it is against the rules of this forum, in no small way because you aren't participating in a scientific discussion. And if that's so, I wonder why you even bothered to come to a science forum. But we're trying to give you a chance here, man. We're reading what you're writing. We're hoping there will be some scientific discourse here. But, so far, there isn't much. To be scientific, we need predictions. That's the absolute foundation of modern science. If you can't provide that, then sorry, but this isn't science.

Apart from the criticisms above, I also wanted to add this. http://arxiv.org/abs/1403.7377You need to familiarize yourself with just how accurate GR's predictions are. The paper in the link has 100+ pages detailing them. SPOILER ALERT: GR does pretty darn well. As per the commentary above, if you want to replace GR, conceptually this is easy. Demonstrate that your idea makes even more accurate predictions than GR does. Please prepare a plot with the current measurements, the predictions made by GR, and the predictions made by your idea. The link above has many examples of this. If you really want us to accept what you say, and if you truly 'prefer to deal in predictions', then this is exactly what needs to be shown to us. Otherwise, it is all story telling and can't actually be used. Scientists are very practical people, all in all. Give us something usable, and it will be used. You need to provide us with something that makes predictions so we can compare them to measurements.

This does not have a simple yes or no answer. The details of how you calculate the finite difference matter.

uh huh. By calling them priests, you are implicitly saying they take things on faith. Can you actually cite something that is commonly believed true by physicists today that is not supported by evidence? And, you know what kills off 'the high priests'? objective evidence. Just present some objective evidence for your idea, and we'll listen. Otherwise, you asking us to accept your idea is actually YOU ACTING LIKE A PRIEST and telling us to believe something without evidence... i.e. on faith! If you're just here to rail against the establishment, *yawn*. It's been done many times before. Persecution complexes don't actually advance science.

uh huh. and this answers my request for a comparison between current best model, your model, and experimental values... how?

Well, if 'one' can, why isn't this posted in this thread? I mean, I'm not going to do it. This is work that you should do... I also don't understand why backwards is so important. It's just a sign change. This also doesn't explain dark matter or an alternative to it. If you can do this, then let's see it. Just like I asked above, please. Data, mainstream prediction, and your prediction, all on the same chart.

This is quite a broad range here. Either it correctly predicts* (please show % difference between prediction and measurement) or it doesn't. 'Looks like' is not sufficient. The moon 'looked like' green cheese for a long time. That 'prediction' failed pretty miserably. * and I've been reading this thread for quite some time now. I don't see a very good prediction, personally. I see someone claiming that some poorly defined, non-coordinate invariant, forwards and backwards velocities on the planets is somehow applicable on an intergalactic scale. Here's what I'd like to see (I ask for it often, almost never get it): show me a graph with 3 data sets plotted on it. 1st data set is the known measurements (cite very liberally so that everyone is clear where these come from). 2nd data set is the predictions made by the current mainstream ideas (also cite this liberally). 3rd data set is the predictions made by your idea; please expand on the calculations in explicit details so that we can see every assumption made. Show us this graph. And if your predictions data set is closer to the measurements than the current best predictions, then you will get plenty of attention. As above, this is how science works... show us that your ideas are more useful in that they make more accurate predictions.

Wow, what a well-thought out and thorough rebuttal. Firstly, it isn't just my concept. It is the foundation for pretty much all the successes of modern science. But secondly, I am open minded enough to listen. What objective measure would YOU use to judge the merits of ideas? The objective measure of agreement between prediction and measurement has worked wonders lately, but if you have something better, let's see it. And thirdly, as a personal suggestion, maybe work on your tact a little. If you meant to come across extremely rude, consider it successful. If you're just going to be this rude, don't bother writing me back ever.

2 reasons immediately come to mind. 1) the vast, vast majority of people who propose 'hard way' solutions, present very incomplete solutions and expect huzzahs. I want to say 'all', but I am not going to claim that I've read all of them. I personally haven't seen one. Incomplete in this case is quite simply that they have never demonstrated that their idea makes predictions that agree in any way with observations. Very often, they get 'hammered' because what is offered can be demonstrated to make predictions that are directly at odds with what is observed. If someone -- this thread included -- would show that their 'hard way' ideas make predictions that agree with what it observed, then they will not be hammered. It really is that simple. Scientifically, an idea is useful if is makes good predictions. That is all that needs to happen; yet almost no one does it. 2) Related to the above, we actually have maps of dark matter: http://www.space.com/14176-dark-matter-biggest-map-unveiled.html. I certainly have never seen a proposed 'hard way' idea that can recreate anything the looks like the dark matter map. So, yeah, they tend to get hammered. That happens in science when your idea is demonstrably not useful. There simply needs to be a demonstrate that the idea's predictions have some agreement with measurement. It really is a simply concept.

it prevents people from making sockpuppets and going to town upvoting all of their own posts. People have tried this before. Fake internet points with no value are very important to some people...

The same reason that 1st semester physics is full of frictionless surfaces, massless pulleys, and no air resistance. You tailor the message to the audience, and you establish simple concepts first before building up to the full situation.

Would your father really laugh at 113 pages the references the plethora of experiments that agree with relativity? http://arxiv.org/abs/1403.7377 because relativity has been supremely successful at making predictions that agree with what it measured. If you have something that does even better, though, I think a lot of people would be interested. When can we expect you to publish a paper that shows how the predictions made in your idea fit the measured data even better than the paper I referenced above?

So, not to be too blunt about it, but this doesn't mean much anymore. In peoples' minds, the shape of the earth was solved by being flat, the makeup of the moon was solved by green cheese, and the make up the nature of heat was solved by phlogiston. These were espoused by some of the most powerful and influential people in of their time. And all of these were demonstrated to be false, because the predictions made by these ideas turned out not to agree with what was actually measured. So, this means that we need you to turn your ideas into a model. That model can then be used to make predictions. And then those predictions can be compared to what is actually measured. Because in science, the most preferred ideas are the ones that make the most accurate predictions. Right now, pulling gravity makes the best, most accurate predictions. For us to take push gravity seriously, it needs to be demonstrated that it makes predictions at least as accurately as the current predictions. Can you provide that?

Sure. I've done a ton of these numerical methods, and I agree the nomenclature is close, but not exactly what the OP was asking. That's why hopefully he comes back with some context.

The only Google results on it is you asking this question. So you probably should give us some context to actually help you answer your question. That is, cite the work where the terms are used, please.

+1 for div, grad, curl and all that. I recommend it to many beginners to vector calculus. It certainly is not super-rigorous, but I find it to normally be a gentle introduction to the subject and good at the beginnings of building intuition on the subject.

Ant, it doesn't matter who says what. Putting more faith in a person because of their title or history or reputation is a logical fallacy called appeal to authority. http://www.nizkor.org/features/fallacies/appeal-to-authority.html I will agree that this is not the easiest one to navigate, because every one of us has to defer to experts every day. If you take your car to a repair shop, you are deferring to the mechanic's expertise. If you call a plumber, you are deferring to the plumber's expertise. When you go to your general practitioner, who then may then refer you to an internist, an so on... you are deferring to the doctors' expertise. Nevertheless, every one of these experts should gladly show you why they recommend what they recommend. A good car mechanic will show you the damaged parts, and tell you the repercussions of not fixing it, etc. A good plumber will show you the leak. A good doctor will show you the test results. Etc. This is what Strange is asking for. Not people with storied histories or titles. But, what is the actual facts? Where is the broken car part, the leak, or the blood test result? What is the actual evidence. If there isn't any, we're back the logical fallacy of trusting someone just based on their name. And on a science forum, that doesn't fly.