timo

My assumption is that there is relatively little physics involved in climatology. I would think the actual physics is very simple and that the challenges mainly lie in the field of applied math, meaning the need for efficient and stable methods to solve the equations over a large variety of scales (both time-scales from hours to years and space-scales from dunno to earth-scale). Personally, I've only met one climatologist and he is a mathematician, hence my assumptions might be biased by experience.

No, It Should Of Course Be "I Think I'm Freaking Out!!!!!" !!!!

I still only half-ways understand what you are trying to say (specifically, I still don't understand what you call "time travel" - copies of you appearing from nowhere?). It somehow sounds to me as if you were saying that a coordinate transformation t -> -t would switch past and future. This way of thinking seems to implicitely assume that future and past were defined as t>0 and t<0. Such a definition would not not be invariant under arbitrary coordinate transformations and, as I think you are trying to show, cause problems. If you define future- and past-lightcone in an invariant way, then future- and past-lightcone will remain unchanged under coordinate transformations. EDIT: I should probably state that I have not read and will not read your original post #1 (because it met the criteria for my "don't bother reading"-quickfilter). What I say is only in reply to the passage quoted in post #5, your reply and your posts #8 and #10). Thus, if what I say is redundant feel free to ignore it (or use the report post function to ask a moderator to remove this post).

Generally I don't think there is an analytical solution but it also depends on what you want to solve for: Solving for the [math]A_i[/math]: The trivial solution of course is [math]A_i = 0[/math] for all i. For arbitrary (meaning non-fixed) x ([math]x \neq -1[/math], of course), this should also be the only solution. For a fixed [math]x \neq -1[/math], you can cast the equation into the form [math]\sum_{i=0}^n A_i(1+x)^{n-i} = 0[/math] (by multiplying with (1+x)^n on both sides). Finding solutions for the [math]A_i[/math] should be possible in general (but involve some tedious combinatorics). Solving for x when the [math]A_i[/math] are known: This is equivalent to solving for y := x+1. Using the polynomial form from above, [math] \sum_{i=0}^n A_i y^{n-i} = 0 [/math], you clearly have a polynomial in the unknown y. For certain degrees of this polynomial, analytical solutions do exist. Above some degree (>3 or >4, I don't remember at the moment), no analytical way to a solution exists.

The attached image does not show an equation. btw, the LaTeX code for your image would be [math]\sum_{i=0}^n A_i (1+x)^{-i} [/math]. You might want to use and modify that (quote my post to see the source code) rather than painting a new picture.

It is an extension (admittedly the commonly-mentioned one, hence my guess).

What does this quote have to do with time travel? What is time travel?

My guess would be the gamma function.

My first idea is that three times an odd power of z plus two times an even power of z (I assume x^4 was a typo) shall equal -1 ...

It is. There is no such asymptote, but the rise of the graph goes to zero: [math] \lim _{x \rightarrow \infty} \frac{1}{2} x^{\frac{-1}{2}} = 0[/math] [math]\lim _{x \rightarrow \infty} \sqrt{x} = \infty [/math] I don't understand that. No for real-valued limits. Infinity means larger than any chosen value. That includes larger than any chosen limit (unless you accept "infinity" as a result for the limit, in which case the answer is obvious). Saying the limit is infinity actually kind-of (don't want to think about or look up a formal definition) means that the function grows beyond every boundry, so in some sense your interpretation is correct. You might see the limit being infinity as a special case of that a limit does not exsits. Note, however, that this is not an equivalence statement. The limit of sin(x) for x to infinity does not exist either. But that function does not grow beyond all borders. Don't understand that, either.

I would imagine "suspended" means "banned until the mods&admins have decided what to do", whereas a temporary ban expires automatically after some time.

Preferred by the people doing calculations, not by nature.

Ok. Yes, highest exponent (with a non-zero prefactor) counts. Yes, highest exponent (with a non-zero prefactor) counts. Not necessarily, e.g.: sin(x), exp(x), log(x), [math]\sqrt{x}[/math], [math]\Theta (x) = \left\{ \begin{array}{rcl} 0&:&x<0 \\ 1&:&x\geq 0 \end{array}\right.[/math]. I don't think so, but some scientists are rather unscrupulous approximating functions with with polynomials ("sin(x) = x" for small values of x is a common one).

There is a standard frame in cosmology. I would assume that statements about critical energies are to be understood to be meant in this frame. It's not too uncommon for physical values to be meant in a certain frame (e.g. the lifetime of the neutron).

Small remark: Strictly speaking saying that a polynomial was an equation is wrong. "x²-3x" is a polynomial (in x) but certainly not an equation (because there is no "=" sign in there). I think you should substitute "polynom" with "polynomial equation" or "polynomial function" in many sentences above.

No, the term can be simplified. Your result is not correct, either (sign error).

As you are about to find out, energy coming in discrete quanta is not a central idea in (modern) QM - it is a result that is true for some (important) scenarios. As I told you in the discussion about your QM intro, you need to have some reasons why the frequency would be restricted. For the redshift caused by relative movement and the spectral lines in your text, this is pretty simple: If you burn something that stands on your table, neither the system as a whole nor a significant amount of the individual atoms/molecules is moving with a significant fraction of c relative to you => assuming there is a reason why some burning substance could only emit certain frequencies (and that is the point your text lacks, not that you didn't consider relativistic effects), you get your spectral lines. If now the whole system was moving away with a significant fraction of c (say, in a distant star), then the whole system of spectral lines is shifted to the red (but still is discrete spectral lines), because all emitted frequencies got red-shifted equivalently. You could even use that to determine the speed that the source moves away from you. Reading tip for you (assuming you have access to some library - if you are just interested in QM, then the book is not worth buying): Atkins, "Physical Chemistry", chapters 11 (Quantum theory: Introduction and principles), 12 (QT: Techniques and application) and 13 (Atomic structure and atomic spectra). It's written for laymen (undergrad chemicists ) but probably contains a lot of valuable information for you. And don't be disappointed if you're not reading through the three chapters in a day or two - a few weeks and half a block of paper for personal notes and checking calculations is a much more realistic scale.

This is not entirely correct: - If you look at the bottom of the physics sections, you will read: "Moderators : 2 - swansont, Martin". - From the thread explaining the "<some field> expert" title (http://www.scienceforums.net/forum/showthread.php?t=11190), you can read that "Experts have some moderation abilities in forums within their area of expertise, meaning that they can bring discussions under control".

np, glad that little piece of information was enough for you. On a sidenote, because I am not sure to what extent that became clear: Solving the matrix equation I gave is exactly the same as solving a system of four linear equations. Using matrices is just the way it is done in numerics. As a simplified example: Solving [math] \left( \begin{array}{cc} a & b \\ c & d \end{array}\right) \left(\begin{array}{c} x_1 \\ x_2 \end{array} \right) = \left(\begin{array}{c} i \\ j \end{array} \right) [/math] for x1 and x2 (with all other variables given) is exactly the same as solving the system a x1 + b x2 = i c x1 + d x2 = j for x1 and x2 with all other variables given. Performing the matrix multiplication the matrix expression reads [math] \left( \begin{array}{cc} a & b \\ c & d \end{array}\right) \left(\begin{array}{c} x_1 \\ x_2 \end{array} \right) = \left(\begin{array}{c} a x_1 + b x_2 \\ c x_1 + d x_2 \end{array} \right)[/math], which is just a vector (and must be because it shall equal some vector. Therefore you have to solve [math] \left(\begin{array}{c} a x_1 + b x_2 \\ c x_1 + d x_2 \end{array} \right) = \left(\begin{array}{c} i \\ j \end{array} \right) [/math] for x1 and x2 such that the equation is true for all components of the vectors. That is equivalent to solving the system of linear equations; each of the two component of the vectors leads to one of the two linear equations.

Do you know how to solve linear systems of equations of the type Ma=b (with M being the matrix of coefficients, a being the vector looked for and b some other vector)? This case, you want to solve [math]\left( \begin{array}{cccc} x_1^3 & x_1^2 & x_1 & 1 \\ x_2^3 & x_2^2 & x_2 & 1 \\ x_3^3 & x_3^2 & x_3 & 1 \\ x_4^3 & x_4^2 & x_4 & 1 \end{array} \right) \left( \begin{array}{c} a \\ b \\ c \\ d \end{array} \right) = \left( \begin{array}{c} y_1 \\ y_2 \\ y_3 \\ y_4 \end{array} \right)[/math]

The words get smaller after renormalizing, but I don't think they unify.

My point was a little more sophisticated. Even if you fix n=1, you can still get any energy E from E=nhf=hf, by chosing f = E/h. The point is, that you need some mechanism/reason why f is not arbitrary. Actually, the reason is that f is fixed by the mode or the change of orbital. Or possibly easier: f is fixed by the wavelengths of the light. So you cannot say that light could only carry energy in discrete packages (because I can mix frequencies f to make it fit), but you can e.g. say that light with a wavelength of 600 nm can only carry discrete amounts (because you fixed the frequency with the wavelength). I'm not sure if the fixation of the frequency, its importance and the reason why it is fixed is obvious to you or not. But you didn't seem to stress the point sufficiently (I might have overread it, also). Depends. I am a physicist, not a historian. So I cannot check any of your historical claims without reading up on it. The big bang notion just looked particularly strange to me. Keep it in if you can verify that it's true. Kick it out if you can't. EDIT: Just remembered the context. From the message you want to get across: It doesn't really matter if the atoms radiate off shortly after the big bang or shortly after now (like "within the next few minutes" - but you'd better look up the actual time predicted). In fact, "shortly after now" is a much more understandable statement, because you can imagine the enviroment better. Yes. From the (in)famous uncertainty relation of position and momentum, the localization in space seems to be largly governed by the uncertainty in momentum. A realistic statement would be that for a baseball, the uncertainty in position (and momentum) is practically negligible (try calculating the uncertainty in momentum if the uncertainty in position was 1 nm). No, not really. I wouldn't even know what that means. It's really just my personal impression. Others might see that differently. I did not even realize the links when I read it. They work.

Yes. http://www.scienceforums.net/forum/showpost.php?p=66772&postcount=30. Can't remember that happening outside the internet. No. Think it was rather the fact that I disagreed with Mr. Robertson on a few of his points. Dunno the situation, perhaps they meant "emotionless borg" or something like that. I personally think that there is much more to human emotions/thinking/... than just logic. Or to complete the statement coming from the other direction: I don't think understanding human emotions/thoughts/... is not possible with logics alone. Can't logically prove that, though . Also note (or even better: accept) that not all people want to be enlightened. E.g.: I take the risk of my soul being lost for all eternity when a couple of complete strangers stands on my door wanting to talk about the bible with me. So I tell them politely that I am not interested in such a discussion and then say it a few times more because they don't seem to respect that (which puts me into the situation to re-examine the adjective "politely" in my approach to the situation). Mapping the situation onto yours, perhaps you're just getting on the nerves of your family and they can't just slam the door.

Ok, makes sense. But what is the difference between something that "really exists" in nature and something that is necessary to describe nature? Question to be understood from the standpoint of "science tries to describe nature quantitatively".

Hint: Take the 1st derivative with respect to x of the term, then take the 1st derivative of the result. Things you might need to know/use: Chain rule, product rule, derivative of e^x, derivative of 2ax^2. What exactly is your problem?