Bignose

Shocking or not, it works. See https://arxiv.org/abs/1403.7377 (You know, the link I posted in the 1st page of this thread that seems to have been forgotten about.) It is 113 pages of just how damn close the predictions from relativity agree with physical experiments. Until you are prepared to show us how every one of those examples is wrong and you have an idea that can make better predictions, snappy quotes and promised gifs are meaningless. This is how science works. Put up or shit up. Put up by actually showing us your theory in mathematics and how good its predictions are. If you can't, then you need to drop all these claims.

Not when you give me infinite flips. With infinite flips, a symmetric random walk on 1-D will visit every point. It doesn't matter where you start. Given infinite flips, it will visit every point.

you can think what you want, I guess, but the fact they they work as they do is validated over and over and over every second of every day. Like, airplanes take off, cars work, the electricity that is powering the device you are typing this dreck on works, the satellites that make GPS work, etc. etc. etc. Conservation of energy -- and the equations for the known different forms of energy -- are among the most validated equations we have. Maybe the single most. Your personal opinions on them are not worth the electrons it took to display that on my screen. In short, it is going to take an awful lot of extraordinary evidence for such an extraordinary claim. A helluva lot more than just a thought experiment. I shall not be holding my breath waiting for you to provide some given your history of making claims and not being able to substantiate them.

Too bad there are all these pages where it works: https://arxiv.org/abs/1403.7377 I look forward to your posting your idea that makes even more accurate predictions than relativity in every example from the paper in the above link. Also, no aether has been found to within 1 part in 10^17. See Herrmann, S.; Senger, A.; Möhle, K.; Nagel, M.; Kovalchuk, E. V.; Peters, A. (2009). "Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level". Physical Review D. 80 (100): 105011 Your idea here also needs to show us how it affects the experiments in the first paper so much yet remains hidden from the experiment in the second paper. Good luck. 1 part in 10^17 isn't much room to play with.

I'm sure my stream-of-consciousness writing there could have been made clearer. But the point has always remained: The specifics of math are going to be needed by just a tiny amount of students in their future lives, but teaching math is still important because it is teaching problem solving skills. However, I think most teachers, even most math teachers, don't get that and certainly don't emphasize it enough. The modern emphasis seems to be mostly that they need the kids to memorize enough things to pass the standardized tests, although this is true about every subject of modern education in general.

Very much so. They still learn math. They still learn quadratic formula, trig, etc. But you don't tell them that they have to learn because math. Because a syllabus says so. You tell them that you are teaching them problem solving skills, and they are learning the quadratic formula because it is another tool in the toolbox to solve math problems. Just like you teach someone what a wrench is instead of trying to loosen a nut with a pair of pliers. And eventually, they will learn what a torque wrench is, and what an impact is, etc. Learn the right tools for the right job. That is what the formulas in math are... tools to get a job done.

Sure. I think this is true for a lot of math instruction today. A lot of teachers teach math like it is just a set of rules to memorize. They should be teaching problem solving skills. And math is a very good environment for problem solving skills. Until you get to some very high levels, math has clearly right and clearly wrong answers. The tools are very well defined. The environment is set up to enable getting to the answer in a straightforward way. It is a perfect practice environment for problem solving. Compare to the real life problem solving. Often to real life problems, the tools or methods are sloppy, imperfect, or maybe don't even exist. Real world problems may have 1 answer, no answer, or many, many answers. Real world is messy. But problem solving skills are always, always, always useful. This is what the math teachers need to emphasizing. Not insisting that the kids need to know how to complete the square, know how to find lowest common denominators, or the equation of a circle. In real life, the vast majority of adults do not need that information. But those are tools used to solve problems, and solving those math problems practice problem solving skills, and we all need problem solving skills.

(my pic is at least a relevant as any of these others in terms of answering any of the questions posed in this thread, lol)

It is not empty. Apart from the obvious that you quoted some obviously non-empty text, he point is valid. The numerical representation of c changes depending on what units you use. Hence whatever specific representation you used to find that [math]\frac{c^2}{\pi^{\frac{3}{2}}}[/math] to be equal to phi (and it is not really obvious what units you used for c to do this...) for a few decimal points is coincidence. Just dumb luck. In other words, meaningless. Hence, Strange's post is exceedingly not-empty.

In other relevant news, guys, I transmuted lead into gold, won all 4 majors on the pro golf circuit, brought peace to the Middle East, and convinced Jennifer Lawrence to take me on a date (she's paying, I ain't no sugar daddy). I mean, we can just say things now, right? We don't have to actually offer any evidence of them happening. (t686, I hope you are picking up on the sarcasm, as I am laying it on just about a thickly as I can)

I call shenanigans, here. Post these, or any (really), calculations. This thread has been extremely bare of anything resembling a calculation to date.

I wish you'd work on making testable predictions instead of more hand-drawns sketches of minimal value to answering the questions asked of you so far...

You know what the link has? When you click to the actual paper that blurb your link is about? Math. Actual science. Where is yours? Deflection by grasping at straws of random links you find doesn't fix your problem, here. This is a science forum. We expect science to be attempted, even in the speculations section. Answer the direct questions posed to you, lest this thread is almost surely doomed to be closed.

No. Really, it's not. Drawings are only illustrations to your science fiction story. If you were 'in person', I'd still ask you to show me the math that it works like you say it does. We have math that describes a lot of phenomena of quantum mechanics. Why aren't you using it? We have math that describes waves really quite accurately. Why aren't you using it? And so on. This story isn't science. It is just a story. Words alone aren't going to actually explain anything. Start at the beginning. F = ma, if you have to. And derive, every single step, how you idea works. If you can't do this, then it isn't science.

t686, you've created quite a good story here. It's compelling, for sure. But 'good', 'compelling', and 'interesting' only get you so far in science. You need to provide evidence of this idea actually working. This means providing details, and almost surely computations showing us that this works. We're not just going to take your word for it, nothing personal, that's just how science works. You have to support your assertions. Otherwise, all you have is a story. Not science. Science fiction.

So, you 'prove' that this isn't u-substitution by using something different that what your 'collapse' does. You use [math]x=4\sin\theta[/math]... why not try [math]u=4\sin\theta[/math]? And maybe not make a mistake in forming the du term.... "u = 4cosθ, and du = 4cosθdθ" is obviously wrong. Lastly, is there any reason you can't use this forum's LaTeX capabilities? Your post here is very difficult to read and it doesn't have to be...

Standard texts won't use the word 'collapse', that's what was said above. But any calculus text worth the paper its printed on will delve very deeply into 'u-substitutions' quite a lot. Go to your local library and check it out.

Sure, the concept of integration as area under a curve is a picture, but show me a picture that explains trignometric integration? I'm not saying that there isn't one, I'm just rather curious if there is one... Typically, integration (as demonstrated by summing up lots of little rectangles) is done in Calc I. That's why I called Calc II integration techniques. Because it starts to detail different ways of getting that sum, not the concept of the sum itself. And I'll be really impressed if you can draw me a picture explaining the divergence theorem in 4-D. (The divergence theorem being a very important topic covered in calc III). I dont disagree that there are lots of possible pictures, but not pictures that explain some of the important topics in the classes. Some things are formulas and need to be worked with as such to get even a hint of what they are good for.

EE, almost surely not. What most typical books/courses consider calculus II could just as well be called 'integration techniques'. There really isn't much in the way of learning this via pictures. Calculus III extends I and II into multiple variables, and while there are some pictorial elements here, like a lot of other math, this is many, many times better to learn by doing than just seeing.

mikeraj, it is obvious that there is a typo somewhere. Either in your transcription, or in the original paper. Because the differentiation in the equation of constant vectors and with respect to constant vectors is meaningless. It is not defined. It doesn't exist. As zztop points out, it does appear that if you ignore the differentiation symbols, and perform some kind of tensor/element-by-element division, then you get the intended answer. It is certainly possible that the symbols were accidentally left in or added to the manuscript. Another possible avenue to seek help may be to seek out if an errata has been published to that paper, or possibly even reach out to the authors.

Not 0, but completely undefined, because differentiation with respect to constants is meaningless. But, yes, this is exactly my point. Being precise with the definitions and pointing out that something as written has no meaning is very important, in my opinion. Not creating some 'reduction' of differentiation to division. The processes here are as important as the final result. As a teacher, do you award full points where someone makes a gross process error but still gets the right answer? [math]\frac{26}{65} = \frac{2 \rlap{/}{6}}{\rlap{/}{6} 5}=\frac{2}{5}[/math] ?? I would hope this would not get full credit, despite the left and right hand sides being equal. Forgive me if I misread tone in your posts to me, then. Might I suggest thinking about your word choice a little more, because I got a lot of negative vibes. If it was unintended, my apologies.

but you do say 'reduced to' without really clearing up what reduced to is supposed to mean. I took it as replacement for (which is obviously trivially wrong): As a PhD, and as a 'teach[er] at a very famous university', you really ought to know how important it is to precisely define terms and operations, yes? Simply 'reverse engineering' the results don't actually fix grossly wrong uses of nomenclature and symbols by the OP, does it? Making sure that OP really meant differentiation there and not division would have really cleared this up... In the meantime, you had written thing like: ... which again is really poorly communicating. Because again, [latex]\frac{\partial{\vec{v_i}}}{\partial{\vec{v_j}}}[/latex] really has no meaning when the vectors are constant because differentiation of a constant is 0 and with respect to a constant isn't defined. This is all I am really arguing for, when symbols and terms are used, that we try to use them as precisely as they are defined, with their limitations and restrictions in place. That was my first objection... asking why the partial differentiation symbols were dropped for no apparent reason. If you explained that those seemed to be there in error and I missed it, I apologize. But I see OP asking for help with the partial differentiation, and I see you saying "the elements are obtained thru trivial divisions." without any real explanation why given the definition in the original pdf clearly includes differentiation symbols. Some clearer communication probably would have cleared this all up; that includes, again, the apparent tone of treating people who try to discuss things with you like idiots.

RE the downvotes to this: Lol, you can downvote any and all of my posts all you want. I really don't care about some tally of internet points. But it won't change the fact that differentiation and division are two very different operations, and one cannot be 'reduced' to another. If you disagree, why don't you show us why. I have shown why I disagree: the rules of differentiation with respect to a constant are clear and there is no definition of what it means to differentiate with respect to a constant. This is a discussion forum, let's discuss.

No. Differentiation of a constant with respect to anything is a 0. The OP's answers are not 0s. Differentiation with respect to a constant doesn't mean anything. OP's answers are something. There is something more wrong than just 'if you had made the effort to perform the calculations, you would have found...' Show me how you differentiate a constant and get something other than 0. Show me how you differentiate something with respect to a constant. There is no calculation to perform. The term as given by OP's pdf doesn't exist. I have a lot of years doing math, and I have never seen differentiation reduced to division. This isn't even wrong. This is a gross misunderstanding of what differentiation is. Whether yours or OPs, I don't really care, but it needs to be corrected.

Well then something is still grossly wrong. Derivatives of constants are 0. And there is no such thing as differentiation with respect to a constant. Either way, you don't just drop differentiation symbols and leave the original terms there. Something isn't right in the pdf or elsewhere. And, no need to be a jerk: "Had you read it, you too could have figured it out. Or maybe not." isn't really necessary. Just trying to help out.