Cap'n Refsmmat

Are you referring to quantum entanglement experiments? Entanglement involves measuring the properties of two particles. One cannot manipulate one particle and see the changes reflected in the other particle, and so instantaneous transmission of information is impossible. With the disclaimer DrRocket makes: if it turns out that the OPERA experiment does indeed violate relativity, then superluminal information transfer may be possible. The original Newtonian version of gravity was instantaneous, and the early forms of electromagnetism were as well. You're right that most "modern" physics is not instantaneous, however.

Do you mean to imply that once consensus is reached, there is no further development, because it is a "brick wall"? I'm not sure I understand your point fully.

I'm a little late to the party, but it's worth noting: nonlocality does not work "instantly" across the entire universe. Forces previously believed to be instantaneously nonlocal, like gravity and electromagnetism, have been shown to propagate at the speed of light. There is currently no evidence to suggest it's possible to transmit information across the universe faster than light.

It proves there's no general formula to find those roots, not that they don't have roots.

You can find the exact roots of some higher degree polynomials through radicals and algebra, but there is no general formula for all polynomials.

No. No formula exists because there's no general method to use radicals and algebraic operations to get to the roots, not because one can't represent the roots with infinite accuracy.

Then I commend you on the exceptional abilities of your calculus students. In the future, however, please hold your hostility. SFN is a place for people to learn, not to have their abilities compared poorly with the average high school algebra student. The latter merely discourages people from attempting the former.

I don't see any professionals saying they had evidence that the parents unduly influenced the child -- just saying that giving the medication may be a bad idea. Did you have a specific quote in mind?

I think you vastly overestimate the capabilities of an average freshman calculus student, and hostility is certainly not going to bring anyone up to your desired standard of mathematical aptitude. If you believe replying to be an exercise in futility, please don't bother.

Which professionals say the parents unduly influenced the child? I didn't see that in the article.

That's exactly equivalent. I suspect your calculator will use a numerical algorithm to solve that as well. You should look into how common numerical algorithms work.

Yes. Why should this necessarily be true? There are a number of problems in math where solutions are easy to verify but incredibly difficult to find. The Abel-Ruffini theorem proves that one cannot create an algebraic root-finding equation for, say, seventh-order polynomials that is general to any seventh-order polynomial, like the quadratic equation is general to all quadratics. Certainly there are some seventh-order polynomials which can be factored, but there will always exist some polynomials which don't fit in your root-finding equation. A version of the proof is presented here if you're interested, although I can't vouch for its accuracy.

It seems to me that "he didn't want those particular genitals" is a hypothesis which explains the data equally well, and it's merely personal incredulity that anyone would want to do such a thing which makes you believe it to be the result of brainwashing. Given that there are, in fact, people who willingly undergo surgery to change genders, I think the incredulity is unwarranted. Now, I don't deny that it's possible that the parents' influence caused his decision, but we shouldn't jump to unwarranted conclusions and decide his parents deserve to be punched in the face. (It's also plausible that simply growing up with two inspiring and wonderful women made him want to be one, without the mothers trying to "convert" him. Most lesbians don't despise men, you know. Although I can't say whether these particular lesbians are actually inspiring or wonderful -- I'm just throwing out another hypothesis which fits the data.)

What evidence leads you to the conclusion that the child was brainwashed or unduly manipulated by the parents?

One can numerically solve for roots, but the answers will not be exact -- the calculator gives x=0 because it is able to compute an answer sufficiently close to zero. There's a number of numerical algorithms for estimating roots, one of which is used by your calculator: http://en.wikipedia.org/wiki/Root-finding_algorithm

Yes, I think it's true that: [math]\sec^2 \theta + \csc^2 \theta = \frac{1}{\cos^2 \theta} + \frac{1}{\sin^2 \theta}[/math] You can do the same thing with the other side, turning secant and cosecant into sines and cosines. From there, I think you should just try adding the fractions together.

The book's tangent equation is not defined at t=0, since the natural logarithm is only defined for positive numbers (in the reals, at least). Your tangent equation seems to be correct at t=0, although you should try making a general expression for any t just to get the hang of it.

Is it not possible to sexually abuse a child without being a pedophile? I can imagine there are a number of other reasons to commit sexual abuse, such as anger or a desire for power. One must also distinguish between pedophilia (which only applies to desire for prepubescent children) and ephebophilia.

I don't see real values when I graph a function on the imaginary line either. Why should it be a problem that graphs not designed to show a certain kind of value don't show that kind of value? I'm not sure what you're looking for. What sort of "purpose" for complex numbers would be satisfactory?

You can graph complex values in the complex plane if you'd like. I think the fundamental issue is more that nobody has ever held 3i apples.

Well, duh. Have you seen the size of horse lungs? They're clearly doing something right.

I have given a number of observable evidences of length contraction on various scales (particle accelerator to entire atmosphere to GPS satellites). Relativity has predicted the results of every experiment made to test it, most of which rely on length contraction and time dilation. You can find these in textbooks. Length contraction is a direct logical consequence of the constant speed of light. You can find this derivation in a textbook, such as Einstein's. Physics does not pretend to describe what shape Earth "actually is." It describes what values will be given when we perform a certain experiment designed to measure Earth. It may be the case that God deliberately alters our measurements to mislead us, but physics can accurately predict the altered measurements.

No, that's not what it says: You can't even have a general formula for just degree 5 polynomials, say.

What qualifies as science is what can provide a consistent and clear explanation of our experimental results. Quantum mechanics and relativity do this exceedingly well, despite their strangeness. It may be the case that space is not four-dimensional, that there is no such physical thing as a "wavefunction", or that Schrodinger's cat isn't simultaneously dead and alive. The point of science is not to argue that these theories must be absolutely true descriptions of reality. The point of science is to determine whether they are adequate models of reality, however it behaves and however it "actually" works. For example, even if the universe is powered by mischevious gnomes, it's still true that relativity and quantum mechanics provide accurate models of their behavior. If the experimental evidence suggests gnomes behave exactly like they would in a four-dimensional Minkowski spacetime, we may use that as a model of the universe, even if we really live on a seven-dimensional hypersphere powered by LSD-addled micrognomes. Physics cannot pretend to define what the universe actually is. That is the realm of metaphysics. Physics can only seek to build models which accurately represent the universe's behavior. If you cannot present experiments against theories, then you are arguing against their metaphysics, not their accuracy as a model -- and metaphysics is not relevant to a practicing physicist.

Wonder if there's any news on this from the professors that allegedly attended. A Slashdot comment claims the inventor is a fraud: http://tech.slashdot.org/comments.pl?sid=2463198&cid=37628870