booker

That's an interesting attempt. Is Calculus II about multivariable equations? I thought that was III. If not, that's what this problem is leading into. Your solution is about what changes happen in A when you change one variable and hold the rest constant. Then do the others, in turn, and add up the results. It's called the total derivative. In terms of differentials, which is a first approximation of the total error, in this case [math]dA = \frac{\partial A}{\partial a}da + \frac{\partial A}{\partial b}db + \frac{\partial A}{\partial \theta}d\theta[/math] Is this notation familiar to you? Maybe you're making too big a deal of this thing when the maximum calculated area is simply [math] A_{max} = (1/2)(3+0.625)(4+0.625)sin((\pi/2)+0.02)[/math] and the minumum [math] A_{min} = (1/2)(3-0.625)(4-0.625)sin((\pi/2)-0.02)[/math] So the maximum error in A would be the largest of Amax-A or A-Amin.

Then there's the exponent of a matrix http://www.sosmath.com/matrix/expo/expo.html.

I see a brazing in your future, but I've always been bad at cards.

Right, right. Now I get it: "those things which become meaningless". Excellent topic. Even thought force doesn't seem to have an equivalent, potential does as it appears in Schrodinger's equation and [math] F= \int \int \Phi [/math]

Not much works with thermoplastic. Try bridging the gap with a length of piano wire. It's even flexible. But overall, I'd definely go with the duct tape fashion statement.

Normally you'd post this in the homework folder, and you'd be required to give it a good attempt. The more work you put in, the more you get in help get, seems to be the general idea. First, what's the formula for the area of the triangle when given two sides, and their interior angle?

Hemp, the universal solvent.

Pete. I think I'd be hard-pressed to find anything that isn't lost, or redefined, really. That which is kept would include Minkowski space...

Be sure someone tells him so. You can think of f(x,y) as the height of a surface about the x-y plane. Partial derivatives are geometrically simple to envision. (If you haven't had partial derivative yet, your professor needs some additional reminding.) Slice through the surface along at some particular constant x. [math]\partial f / \partial x [/math] will be the slope of the surface along the cut. the value of [math]\partial f / \partial x [/math] is dependent on the value of y where the cut was taken. The same argument applies to [math]\partial f / \partial y [/math].

Thanks, Athiest!

Don't tell anyone, but I've thought of using it myself--just never heard 'eigen' used in this context. Shamlessly pasting out of a German-English dictionary, "eigen own {adj} fussy {adj} proper {adj} peculiar {adj} separate {adj} distinct {adj} peculiarly {adv} possessive {adj} inherent (in) {adj} appropriate (to) {adj} singular {adj} [eccentric] several {adj} [archaic: distinct, separate]" Rather a long and confusing list to correlate. Beats me, Pete. In finding extermal time, [math]\tau[/math] is independent, and the integral is over [math]dx^u / d\tau[/math]. Hello, qwe)k. I'm not sure anyone has really explained this properly to you. In physics you want to explain things, ultimately, based on how you measure or observe them--what values they take. After all, this makes it physics rather than, philosophy, or BS even. So you might ask, "how do I measure the speed of time?" If you draw a blank, maybe it's not really a question about the physical universe--not really a valid qhysics question. As far as events proceeding faster in some places than others, this is kinda what relativity is all about. Observers (that's us) in different states of velocity may notice their clocks progressing at different rates, as well as lengths having different measured values. As someone else already talked about, gravity also effects how different observers measure the time interval between events.

Never heard of it. You're referring to proper time. Is there some mathematical justification in calling it eigentime?

Fredrick- The physics is probably not as sexy as all that you've written about. The simplest example is a free Newtonian body in motion. The cause in this case, is say, a particle traveling with momentum in the x direction with coordinates (0,0,0) at time t0. The effect is the particle traveling in the x direction with coordinates (10,0,0) at time t1. If you want you can have collisions with other particles at times t0 and t1 so it has more the look and feel of cause and effect, that you might expect. One conserved quantity is momentum. The convervation law is Newton's first law (A body remains in motion unless acted upon by an exteral force). The labels of cause and effect are derived by comparing the values t0 and t1. The lesser value is cause; the greater value effect. Relabeling, like you say, by some transformation that inverts the time, can feel a little more physical than simple relabeling. There's an evolution operator for the object's position that describes how some things are not conserved--like spatial coordinates--they do not remain the same from cause to effect-- x(t) = vt + x(t0). In quantum physics the same element appear as long as one assumes wave a function corresonds to some element of physical reality--otherwise we have to speak of a potentia of some sort--or knowables--or the evolution of a calculational device.

Skeptic- Why you might find this discussion over solar cells realistic is beyond me, Skeptic. Solar FITS, of residential capacity can expect 25 years to recover capitol investment with govenment kickbacks. Large scale arrays do a bit beter, but have less kickback. Silicone is energy intensive to manufacture. Solar cell plants don't sport solar arrays on their roof for sound economic reason. They take their power off the grid. The energy returned on enery invested takes about 8 years to recoups. They take that much energy to produce. There is always a better technology around the corner, promoted to the press as the next thing about to round the bend. I believe it, when I see it, as a viable product that actually sells into the market It makes me a bit more accurate far more often than the wild-eyed, low techs.

Thank you for the reply, Fredrik. You'v obviously given this a great deal of thought! Maybe I do have a point--or a small objective. I ask, can any given law of cause and effect be states as a set of convervation laws equipped with labels that tell us which elements were cause, and which were effect. Then it's a natural question to ask if the law is invariant under relabeling--or if a new and tenable law is obtained. I don't know the drill. Could you tell me about it? There's was method to my madness in posting here. From a couple recent posts I'd read in the relativity folder, it seemed the present company was capable of thoughtful consideration. (As a benefit, I've enjoyed reading the content relating cause and effect to relativity.) -booker

What are cause and effect? Is there really anything to distinguish the two other than saying that one comes before the other? Edit: In the context of relativity you might say that there are two time-like interdependent events. According to any clock, effect would proceed cause. But is there more? Perhaps I could have posted this in the quantum mechanics folder where observation of the wavefunction could be an issue. Re: Distinguishing cause and effect using a clock. Feynman would call a clock a thermodynamic device, where the direction of advance would be determined by conditions of lower entropy in the past light cone than the future light cone. That is, the clock is advanced when in a spacetime region of lower entropy.

Hey, Pete. Re: Alcubierre’s "Warp Drive". This one premises some form of exotic energy: "...First, to create this effect, you’ll need a ring of negative energy wrapped around the ship, and lots of it too."

That sounds like it could be interesting, ajb. I take it that d^n x isn't intended to apply to the Hilbert space of quantum mechanics, right? --or thermodynamic phase space. Do you think you could maybe describe what you mean in simple terms for the rest of us?

again http://www.sepp.org/Archive/controv/ipcccont/Item05.htm again http://www.si.umich.edu/~pne/PDF/ecofables.pdf

Let’s all deny history as objective phenomena, or that rocks are hard and water wet, if it must run contrary to our desired beliefs. The religious fervor here is through the roof. I gave you a perfectly good link authored by a man who participated in these actions and writes to rationalize his actions--or justify them, if you wish. Take your pick. (And ultimately wishes you would see him as courageous. This is really a wonderful case study in self delusion, for anyone how takes interest in these sorts of things.)

Unfortunately, the archives by http://www.sepp.org detailing the fraud surrounding the 1995 IPCC report are now dead-lettered to the sepp home page. Imagine that. This .pdf covers the controvery and politicization http://www.si.umich.edu/~pne/PDF/ecofables.pdf

I won't play the word games. Would you be denying the tampering or misrepresentation?

I did that, iNow, though I was speaking of the abstract, not the study. This is not a small point. With the choice of thousands of pages vs. an abstract, the abstract was, naturally, most disseminated and read. Here's one online reference I managed to track-down. UN IPCC "The Science of Climate Change 1995," http://www.sepp.org/Archive/controv/ipcccont/Item05.htm Additionally, and something I was not previously aware of, according to the above link, the body of the report itself, was tampered with. By the way, congradulations on your contest win.

Hello, Gib. The UN is a political entity. The question at hand is what evidence would support the claim that the UN IPCC should be motivated to honest reporting of the facts. It is without doubt that the individuals within the UN have a professional intestest in promoting global issues in order to be invested with the power to solve them. I don't find an ameliorating motive. It seems to have been forgotten that the UN IPCC long ago soiled their credibility with their 1994(?) report. It was not the multi-thousand page report that was false, but the politically generated abstract of some 200 pages that infuriated the contributing scientists for it's fraudulent synopsis of their hard work. Yet subsequent reports are filed and taken as credible. -------------------------------------------------------- A lie told long enough becomes the truth. -Smilin' Joe Stalin

Does mitochondrial DNA display mutation rates consistent with flux reversal frequency?