Bignose

What does this even mean? You are using words I am familiar with, but combining them in a way I am very unfamiliar with. Please define "shearing against the time axis", please represent it mathematically, and please give me an example (several would be even better).

I'm pretty confused to. Though, the answer to the question "what units do a distance along a time axis have?" is units of time. When something moves along that axis, then that "distance" has the same units that the coordinate has. Let me give an example. Consider a population of cells that are all different ages. Let [math]f(\tau,t)[/math] be the distribution of cell ages, where [math]\tau[/math] is the cell age, and [math]t[/math] is time. Now, [math]\tau \ne t[/math]. Because, when a cell dies, it no longer ages, or when a cell splits, the two child cells have their ages reset to an age of zero ([math]\tau=0[/math]). So, in this problem, there are two time dimensions, [math]\tau[/math] and [math]t[/math]. The equation that governs this is: [math]\frac{\partial f(\tau,t)}{\partial t} + \frac{\partial \dot{T} f(\tau,t)}{\partial \tau} = R(\tau,t)[/math] where [math]R[/math] on the right hand side takes care of all the births and deaths of the cells. [math]\dot{T}[/math] in this case is a velocity along the age coordinate. It is a velocity with units of time per time. Because the "distance" along the age variable has units of time. Typically, [math]\dot{T}=1[/math] because as 1 second of real time passes, the cell should also age 1 second, but you can envision a situation where it may not be exactly a 1 to 1 ratio. Such as if you are exposing the cell to an agent that slowly kills it, you may want to define [math]\tau[/math] to be an "equivalent" age, so that when 1 second passes, it is equivalent to 10 seconds of "age" on the cell. Or, say the cell has had it's functioning messed up, like a cancer cell that reproduces like mad versus a regular cell. A cancer cell may be seen as advancing in age much more quicker than a regular cell. But, the main point is that when you measure a "distance" along an axis, that distance has the same units as the coordinate axis you traveled along. In the example I gave above, the units of distance along the age axis have units of time. And, as near as I can tell, when the OP has something that moves a distance along the time axis he is considering, that should have units of time, too. Though, like Kyrisch, I really have no idea what this thread is really asking...

The coefficient of friction would include any area effects. In many 1st and 2nd semester physics classes, this isn't covered, because it is a complication. But in general the coefficient of friction is not a constant or a piecewise function (like with static and dynamic friction) -- it is a function of all the different environmental variables. For example, it is usually at least somewhat dependent on the velocity of the obejct in motion, even if that dependence is typically weak which is why assuming a constant value isn't a terrible assumption. If the area of contact became important, then the coefficient of friction would also include that dependence. There is also an issue of remembering that force itself is area independent. That is, if I apply 20 N of force to a ball, it doesn't matter if I am grabbing the entire hemisphere or just touching it with a fingertip. 20 N is 20 N. What is dependent on area is the pressure. The pressure applied by having the ball in my palm and grabbing a hemisphere versus the pressure applied using only a fingertip would be very different, even if the force is the same 20 N in both cases.

The general conic equation can be written in Cartesian coordinates as: [math]Ax^2 + Bxy + Cy^2 + Dx +Ey + F =0[/math]. The problem is that, to identify any specific conic, you need to know the values of all six constants there, A through F. So, in general, to identify any individual conic, you will need to know 6 points that it goes through. Now, there are special cases, depending on the specific conic you want. The circle only needs three points to identify a unique circle, for example. But, in general, having only 2 points is not enough. It won't restrict the type or specific shape of the conic section going through two points. That is, you can find more than one parabola to go through any given two points, as well as find multiple hyperbolas and ellipses that will go through those two points, so two is not enough to uniquely identify any unique curve.

coke, counterexample has already been given! Look at: (I added the emphasis to the quote) Do I have to put a number in it? Ok, I will. Do the limit of [math]x^\frac{\ln 5}{\ln x}[/math]. This will go to 5. There. Counterexample.

Why do you keep skipping over D H's point that it is NOT just 0 or 1?!? It can be any value at all. Real or Complex. It could be 10.777. It could be [math]\frac{\pi}{142}[/math] it could be 7-6i. It could be 222 quadrillion. It can be anything. THAT'S why it is called "indeterminate". Because ANY value is equally valid as any other value, and none of them are "right" or "wrong".

Just because a calculator said one thing doesn't really mean anything. I can write you a program - a "calculator" - that adds two numbers together incorrectly. Does that mean that all of addition is wrong to? I mean, I have this calculator that says.... Just because the programmer who programmed that nspire calculator didn't handle [math]0^0[/math] correctly, doesn't mean that it is in fact equal to 1 or 0 or anything. There is an attitude of implicit trust that a lot of people have about their calculators and computers that they really shouldn't have. The reason we still study math by hand is because calculators and computers can be programmed wrong and make mistakes. There is operator error a great deal of the time too. We do math problems by hand because when the answer gets spat out by the calculator or computer, we have to have some intuition that checks whether it was right or wrong. Otherwise, we are just going to be slaves to whatever the computer/calculator spits out. The Simpsons had a great farcical examples of this. Mrs. Krabapple has her math text open and she asks the class "Whose calculator can tell me what 7 time 14 is?" and Milhouse is raising his hand high sayING "Oh! Oh! 'Low Battery!'". The joke is on people who just blindly accept what a calculator says. I have a few more examples from when I was a TA for a fluid mechanics class that will always stick with me. In the first, I don't remember the specific problem, but at the end the students has to multiply a 2 digit number by a 3 digit number to get the final answer. When I was grading homeworks, the students were allowed and encouraged to work in groups, so I graded them together as a group (since all the homeworks from that group were the same anyway). Well, someone had mistyped what they put into their calculator, and got a 6 digit number, copied it onto their paper and circled it and thought they were done with that problem. And, then everyone else copied that same answer. Not a single one of the 10 of them thought "hey! a 2 digit number times a 3 digit number can at most be a 5 digit number... not 6. Someone probably entered the wrong numbers in the calculator." Not a single one! And it was really, really frustrating because these were juniors in an engineering program -- they should have known better. A lot better because they should have had done a lot of math by then. The other was even more frustrating. They were supposed to calculate how much energy had to go into a pump in order to pump water from a reservoir up to the top of a water tower. And again, a group worked together, made a mistake or 3 along the way, punched some numbers into their calculator and slapped the answer on the paper. The problem? The amount of energy they put on their paper was negative! That's right, they were basically saying they would get energy out of pumping water up hill. When you think about it, everyone knows how ridiculous it was, but it is another example of implicitly trusting what the calculator spat out, and not thinking about the answer itself. At the job I do now, while Finite Element Analysis and Computational Fluid Dynamics are invaluable tools for the modern design engineer, they are far, far, far from perfect. We very often brake things in stress tests in places that were not "hot" on the FEA analysis, and the CFD is often close to the real result, but rarely is it accurate enough to design control schemes and the like. Both should be used as "ballpark" tools, not tools that can resolve the details of most any real-world situation yet. Someday in the future, maybe, but not today. And yet, there are too many people that trust those simulations a great deal, despite our being burned by them time and time again. Another example was that probe several years back that crashed into Mars because the subcontractor that built it used the English system of units instead of the metric that NASA was using. I'm sure the subcontractor's simulations seemed to be all in order, and no one said "hey! that just doesn't seem right to me... let's check that closer". Long story short here, never ever blindly accept what your computer or calculator says. Mistakes go into programming those devices, so wrong answers will be generated once in a while. It can even be as simple as multiplication -- Excel 2007 had a pretty serious bug in it for a time: http://gcn.com/articles/2007/09/25/excel-multiplication-bug-unearthed.aspx I hope I didn't come off too strong, but I really, really want to destroy that attitude of "my calculator said...", because it is a trust that is grossly misplaced. At least at this point in time. There will probably be a time when we can implicitly trust a computer's calculations, but it isn't today. ------------ Like D H wrote, depending on the way you approach the two zeros, you can make [math]0^0[/math] seem to approach any value you want. He gave a good example by having the exponent approach 0 along a logarithmic path, and getting the result of it being the constant a. There are other ways, too (an infinite number, of course). And, like D H wrote, the only "right" answer is to leave [math]0^0[/math] indeterminate. Anything else and you introduce far, far more problems than you fix. There are several other indeterminate forms, too. Math doesn't advertise itself as being able to solve everything, so there are some things it just won't have answers for, like [math]0^0[/math].

This is the step you got wrong... [math]sin^{-1}(x) = 2[/math] as tree pointed out, there is an x that solves this step -- you took the inverse of the sine function too early... [math]2\csc x -1 =0[/math] [math]2\frac{1}{\sin x} = 1 [/math] [math]\frac{1}{\sin x} = \frac{1}{2}[/math] [math]\sin x = 2[/math] and now you conclude that x has no solution because sin is limited to values between -1 and 1.

But if the buckets have any kind of shape to them, the inertia of the fluid will cause some rotation, which then will lead to centrifugal or Coriolis forces in the fluid. These things aren't really all that negligible. I might buy it if the fluid weren't water. If you had something very viscous, like glycerin or similar, then the viscosity would dampen all these disturbances out very quickly -- and virtually little to no sloshing, too! -- and I would feel that the simplifying assumptions would be more valid. But, water just isn't viscous enough for those assumptions to be valid. Eddies in water form too easily and last too long to be ignored. The non-laminar, rotating, sloshing flow that real water would experience will not fit with the simplifying assumptions that are needed to keep the problem from getting into fluid mechanics and a more detailed analysis.

I don't know (or really care) if you will come back and comment, but I still think that it is important to say: This is a beyond extraordinary claim. As I wrote above, the 2nd Law of Thermodynamics has been found to hold in every single experiment to date. From every single lab experiment, to the dynamics of suns, to the movement of single atoms and even smaller pieces like quarks, to biological entities, to every single natural occurrence ever observed to every single non-natural set of circumstances that mankind has set up. Not a single time has the 2nd Law been wrong. And, the mathematics behind many of the derivations -- while complex and as you admit over your head -- are sound. No one who has studied them has found a hole in the theory behind the 2nd Law either. No holes in the theory, no experiment that has violated it ever. EVER! Claiming it needs to be changed is going to require some of the most extraordinary evidence mankind has ever produced. May it need to be changed? Anything is possible, but you are trying to tackle what is single-handedly the most verified physical law that mankind has ever encountered. It may need to be changed, but until such a change is conclusively, objectively, and 100% verified to be genuine, the safe bet for all of science is to stick with the outcome that has happened a billion trillion quadrillion times before. That's why critics can justly cite "Your idea breaks the 2nd Law of Thermodynamics" and that is enough. There is no more needed at the moment, because the law has never, ever, ever been wrong before. If you want to try to prove the law wrong, you go ahead and try. But, the onus is on you, not anyone else. Science is completely justified in ignoring your claims until proven to the contrary. And, that is nothing personal at all -- science ignores every claim that goes against the mainstream until proven wrong. The challengers step up to the challenge and bring back more evidence. And, guess what: when good evidence is brought back, science changes its position. But, no amount of good ideas or logic or wordsmanship is a replacement for evidence. So, bring back some evidence that this Law that has been proven right every single time before is wrong, and we will listen. We will embrace your new ideas. You will be rich beyond your wildest dreams. You will win every single award possible. Heck, there will be several awards names after you if you can do it. But, there has to be evidence. Your wanting the 2nd Law to change is not enough. You have to bring back proof that the 2nd Law is wrong. Period.

No, I think you misunderstood my question. AND, you didn't actually address any of my points -- the issue of being able to observe photons leaving an emitter and impacting upon a detector pretty much defeats the concept of "light not moving" doesn't it? And, you've misunderstood my question about falsifying your idea. Because how does the twins paradox confirm or deny your idea? It fits with the current theory, so how does that discriminate between your idea and the current idea. You need to come up with an experiment that would show that your theory is clearly right or clearly wrong.

You should be able to answer this yourself. if x is the square-root of y, then by definition, x*x = y. So, what does 0.3*0.3 equal?

Not to sound too trite, but it is kind of silly to pose a reasonably complex problem but not desire a sufficiently complex analysis to try to answer the problem in a way that doesn't just make grossly inaccurate and unlikely assumptions. Like, no sloshing. Because that's not what will happen, the fluid will have an inertia either way that won't immediately dissipate and the sloshing will have a significant effect.

Yes. I firmly believe Chandrasekhar was an intellect on par with Einstein and Feynman and the other great minds of physics and math. His work is not as well known as it probably should be, but he authored many great works. He is probably best known for his work on stellar dynamics, but he also wrote a very good book on stability in hydrodynamics and magnetohydrodynamics.

As a start on the more advanced mathematics, I'd suggest you take look at Radiative Transfer by the brilliant Subrahmanyan Chandrasekhar. The book is absolutely a classic in the field of radiation.

Well, like I said, you'll need good courses in Algebra, Trigonometry, and Geometry to be ready for calculus. There are many, many books that teach these subjects. I suspect that your local library probably has a several. Check a few of them out and see if any of them click with you.

Trig and calc books, no. Differential equations and thermo and mass and energy balances, yes.

There is plenty of math that backs up the 2nd Law of Thermodynamics. As just one resource, please see Boltzmann's H-Theorem as connected to the statistical mechanics of gases (which is a purely mathematical derivation). There are similar rules that are mathematical derivations in other materials that are not gases, see some of the works by Clifford Truesdell, for example. That, and there are probably literally trillions of examples that follow this law, without a single exception ever being found. Does that mean an exception will never be found? Of course, not. But, I do think that it is very fair to say that it is exceptionally well verified -- both theoretically and empirically. And that it is going to take some very extraordinary evidence to overturn it. The onus is on you to provide that evidence. Otherwise, skepticism for any result that bend or breaks the Second Law of Thermodynamics is very, very well justified.

Well, first of all you probably need to spell it right: calculus. (I'm not trying to be snotty here, but to use Google or something similar, having the correct spelling will yield you much more meaningful results.) Secondly, I don't think that you need to rush through it. Take the advanced math classes your school offers and maybe talk with your teacher if you are looking for something more advanced. But, the classes do build on one another. Typically after Algebra 1, you are going to want to have Algebra 2, Geometry, and Trigonometry under your belt, and maybe even a Pre-Calculus class before starting Calculus. A mastery of algebra and geometry and trigonometry will make calculus go much, much smoother. If you gloss over algebra and geometry and trig, you are going to struggle mightily with calculus. So, if your goal is indeed to get to calculus as quickly as possible, working through the rest of your algebra book and a trig and a geometry book is the way to go. And you have to really work through them. Don't just read the sections, but do a great number of the homework problems and check to make sure you get them right. Don't skip over things you don't understand -- you can use the forum for that help if you need to (that's pretty much what this forum is for!). I'm sincerely not writing this to discourage you, but I think that having a good teacher go through these subjects can help a great, great deal. So, if you want to go through it on your own, I'd suggest you find a tutor or math camp or work something out with your school and its math teachers is a much better way to go than just working independently. As much as anything, a good instructor can make sure that you understand the concepts correctly rather than thinking you understand the concepts and having some wrong ideas. And, yes, there is a great deal of math higher than calculus, but the leap from Algebra 1 to Calculus is big enough for now. No need to run a decathlon before you know how to crawl.

But, light is made up of photons and we can observe photons leaving one point and impacting upon another. How can this be if "light is not moving"? I don't even know what this means. How does matter "travel" into a different dimension? Dimensions are pretty well defined mathematically, (see http://en.wikipedia.org/wiki/Dimension as a decent start). How does your use of the word dimension apply mathematically? And, finally, here is a big one: What tests could you conceive that would falsify your idea? Because for this to even be slightly scientific, there has to be tests that can falsify your idea. So, what tests can you conceive of that would falsify your idea?

You may want to consider mechanical engineering technology instead of the engineering proper. ME Technology is significantly more hands on and significantly less math-intensive. Though, make no mistake, any degree with "engineering" in it is going to require a fair amount of math and when you graduate you are going to be expected to know a fair amount of math by any potential employers. How much math is obviously going to depend on the job you take.

Why are you posting in threads that haven't been posted in for several months? The other one you gave an answer to a problem that was asked back in October! I sincerely hope that the OPs have moved on in the several months since these threads have last been active, and I don't really know what you are trying to accomplish...

YouTube videos don't seem to work too well on my computer, can't you please write it out in mathematical detail here? No, a sec/sec would be dimensionless. We measure time with units of time, not dimensionless. If you are going to use that precise of a number (three decimal zeros), it probably should be the right number. 299 792 458 m / s while close to 300 000 000, isn't the same. -------- Also, you didn't really answer my question. If it is in the video, can you please write it out here? I still want to know how something that is measured using one set of dimensions can be measured using a different dimension altogether.

Please explain this using basic units. Because as written, it is pretty much meaningless. A velocity or a speed is a distance per unit time. And the speed of light definitely has units of distance per unit time. But what exactly is a "speed of time"? Time per unit time would be dimensionless, so that cannot be equal to the velocity of light. So, what are the dimensions of "speed of time"? and what exactly does it mean?

Just like all symbols, they are there as a shorthand that virtually everyone has agreed to mean the same thing. This is virtually all symbols you run across: At the very basic you write out letters and combination of letters to 1) represent the sounds that the mouth makes and 2) the combination of letters combine to make words instead of writing out the definition of the word each and every time. Math is the same way. We write [math]\int[/math] instead of "compute the area under the curve". we write [math]\frac{d}{dx}[/math] instead of writing out "compute the rate of change with respect to x" It is no different that learning any other set of symbols. When you learn to drive, you have to learn what the set of symbols that frequently appear on road signs mean. If you learn to fly, there are usually symbols on many of the switches and gauges. If you try to read a technical blueprint, you have to learn what the symbols on the print out mean. Math is no different. As you learn the math, you will learn what the symbols mean. You just have to learn the math.