Tom Mattson

OK, first of all there was a typo in my last post. I forgot to include the [imath]\frac{1}{2}[/imath] in the definition of [imath]\sinh(z)[/imath]. It's fixed now. Here are all the steps I used to solve the problem. 1.) Sub [imath]iz[/imath] for [imath]z[/imath] in [imath]\sinh(z)[/imath]. 2.) Express [imath]\sin(z)[/imath] in terms of [imath]sinh(iz)[/imath] and substitute the expression in the equation. 3.) Solve the equation for [imath]\sinh(iz)[/imath]. 4.) Take the inverse hyperbolic sine of both sides. 5.) Solve for [imath]z[/imath]. Now be advised that my first post to this thread was just the first approach that popped into my head. There is a much more direct way to solve this problem: Just take the inverse sine of both sides (use eq 1 in that link). Why did I first think of the most obtuse way to do it? Beats me, but you get the same answer either way: [imath]z=-i\ln(-1+\sqrt{2})[/imath].

The definition of z as a complex variable is implicit in the original equation. The relation [imath]f(x)=\sin(x)[/imath] is a map from [imath]\mathbb{R}[/imath] to [math][-1,1][/math] when [imath]x[/imath] is a real variable. The only way to get [imath]\sin(z)=i[/imath] is if you have [imath]z=x+iy[/imath]. So yes, it is mentioned in that the entire problem is predicated on it.

Heh. I thought I was banned.

Look this is basic physics. If you want to probe smaller length scales (which is necessary to get beyond the standard model) then you have to use a higher energy probe. You can infer that much from the deBroglie relation, [imath]\lambda=\frac{h}{p}[/imath]. If it weren't for willfully ignorant people such as yourself the repetition wouldn't be necessary. This is the same physics that was discovered by the people you hold up as heroes. Indeed they are heroes, but you wouldn't know because you've never actually studied their work. You are an *****.

What reasons do you have for thinking that those standards were ever abandoned? And please don't cite 50 years of failed attempts from the UC labs. That point has already been addressed, and I remain convinced that your tirade against the UC system is nothing more than slander based on misunderstanding. I have no idea of what you mean by "machinenexperiments" but it seems to me that your concept here is infected with not only an ignorance of what goes on in scientific research, but also a flat-out contradiction. First, on the necessity of expensive machinery to move beyond the Standard Model: The science of the last century was so overwhelmingly triumphant that that it successfully predicts physical phenomena over the highest energy domains that we are capable of generating in a laboratory setting. That means that we certainly will not move beyond the Standard Model until we solve the engineering problem of building an accelerator that is capable of generating much, much higher energies. Without data from those higher energies scientists will be unable to rule out competing theories. Literally any theory that extrapolates back to the Standard Model and/or General Relativity could be considered valid. This has nothing to do with a failure to think. And second, on the use of machines in scientific research: You seemed perfectly content to cite supercomputers in your indictment against the UC Labs. Your reason for citing them? Because they can help us think (!). So, it's OK to use computers as a substitute for analysis, but not other machines? You'll have to pardon the rest of us for not drawing the same arbitrary line in the sand that you chose to draw. Your understanding is flawed anyway. As I already pointed out, computers cannot do anything even remotely close to what you imagine they can do. I do use computers in my work, but not because they help me think. Computers aid my work because they aid in data processing, thus giving me more to think about. The more information scientists must contend with, the more patient the rest of the world must be in waiting for the next revolution.

Good grief. First of all, computers cannot think for themselves, so it is certain that they cannot help us think. A computer, no matter how sophisticated, is just a black box. Everything that goes into it and that comes out of it must be analyzed and scrutinized by a living, breathing, thinking human being. And second we have made a substantial discovery beyond quantum mechanics. It's called quantum field theory, which forms the basis of the Standard Model of particle physics. And third, it is perfectly clear to anyone who knows the subject why we haven't gone beyond that yet: More powerful machines are needed to supply the data that is needed to determine the direction that research should take. The physics of Einstein, Schrodinger, Feynman, et al uniquivocally tells us that we need those overpriced supertoys that you bemoan. See above. More powerful machines are necessary to move beyond the Standard Model. I've already answered this point. Scientific revolutions don't happen that fast. It's time to move on. I don't need your advice.

I don't take it personally, it's just that I feel that at a science forum this blathering should be put in check with extreme prejudice.

First of all, it's up to you to substantiate your claim that no fruitful scientific research goes on at the UC Labs, not simply to declare "The truth is..." And second, UC National Labs are not the only scientific institutions in this country, and they can hardly be responsible for bringing scientific progress to a screeching halt, even if your outlandish claim was true. They do work together in such collaborations, and routinely at that. I was part of one as a graduate student, and I know of many, many others. If you actually took the time to examine the facts before you concocted your theory it would look more like a well-reasoned objection to the way things are done, and less like an idiotic rant.

False facts? I wonder if those are related to true lies.

1.) It's the Poynting vector, named after the physicist John Henry Poynting. 2.) The Poynting vector is not [imath]\vec{E}\times\vec{E}[/imath]. If it were then it would be the zero vector! Rather, the Poynting vector is [imath]\vec{S}=\frac{1}{\mu_0}\vec{E}\times\vec{B}[/imath]. 3.) You should be able to work out the units yourself. You should find that it has the units of intensity. More: http://en.wikipedia.org/wiki/Poynting_vector http://scienceworld.wolfram.com/physics/PoyntingVector.html

I don't know the answer, but I know that MathWorld is your friend: http://mathworld.wolfram.com/OrdinalAddition.html Hope that helps.

Is that a promise?

Not true. In Newtonian dynamics an orbit can be any conic section. Does that change your line of questioning at all?

Don't worry!!! I won't steal it!!!

I don't know, JC MacSewell had 2 really bad ones on Page 2 of this thread: http://www.scienceforums.net/forums/showthread.php?t=9473

Compare equations (2) and (3) in the entry on Sine at MathWorld and look at what happens when you make the substitution [imath]z \longrightarrow iz[/imath] in (3). You basically get (2)' date=' up to a constant. That means that can express [imath']sin(z)[/imath] in terms of [imath]sinh(iz)[/imath]. How does that help? Look at equation (1) in the entry on Inverse Hypberbolic Sine at MathWorld. Once you make the substitution from the first paragraph you should be able to solve the equation with the result cited in this paragraph.

OK so your equation is of the form [imath]\mathcal{L}[y]=f(x)[/imath]' date=' where [imath']\mathcal{L}=\frac{d^4}{dx^4}+4[/imath]. Use the fact that [imath]\mathcal{L}[/imath] is linear to find [imath]\mathcal{L}[y_2-y_1][/imath]. You should find that the difference of two solutions to the inhomogeneous equation [imath]\mathcal{L}[y]=f(x)[/imath] is actually a solution to the homogeneous equation [imath]\mathcal{L}[y]=0[/imath]. So your answer will be independent of [imath]f(x)[/imath]. It will of course depend on 4 arbitrary constants of integration. That will work, so continue with it.

A conditional statement is not an argument at all, invalid or otherwise. It is a truth-functional statement.

There are free textbooks and lecture notes all over the place: Mathematical Logic - An Introduction Mathematical Logic A Problem Course in Mathematical Logic

Are you talking about the Banach-Tarski paradox?

taylrl, That the laws of science apply everywhere and everywhen is an assumption of science as a methodological framework. Since no formal system can explain its own axioms, there is no scientific answer as to why this must be the case. It is accepted provisionally and will continue to be accepted until something is found to be wrong with it.

When you formulate an intelligible claim, then the community here will decide for themselves whether or not it has merit. But as long as you continue to spout the same mental sewage your claims are at best undecidable.

OH MY GOD, ME TOO!