AntiMagicMan

For me, one of them had to give way.... it was b.

Fourier series can be used to solve certain differential equations where the solution is a superposistion of an infinite number of sine or cosines. The heat equation is one example of a differential equation in which you use Fourier series to solve it.

Thankfully ancient greek philosophy has been discarded these days. A valuable lesson that sitting around and thinking is not the way to do science.

It is also possible to make it less than normal by going into free fall. Nasa trains astronauts by making a specially modified 747 go into a nose dive for a short period of time, normally about a minute.

Ah yes, that is a very good point. I shouldn't have said the limit of 1/x as x tends to 0 tends to infinity without specifying a direction. The limit at at 0 does not exist because the function is discontinuous. Basically we cannot equate 1/0 to anything.

Just be aware, I agree with what you are saying. It would be pointless trying to learn physics if you did not know maths. I was just saying that it does not follow that physics is derived from maths, which we both agree on.

Yeah, but zeno's paradox is quite wrong because I walked to the shops today.

If you keep changing the question then no one will be able to counter your argument. If you think that physics can be derived from mathematics, then you are wrong. If on the other hand you are saying maths is useful for understanding physics then I don't think anyone is going to disagree with you.

The video is so fuzzy that strings could easily have been edited out.

I read this article when it was originally published in Scientific American. You've got to admit the theory is quite nice, but I suppose it is not scientific because we could never test the hypothesis that there are alternate universes.

Basically yes. We can say quite mathematically that in the limit of x -> 0 it tends to infinity. But we cannot say it equals infinity. So the sum 1/0 is undefined, but 1/x as x goes to 0 tends to infinity. This is all due to a move in mathematics in the last century or so to remove all mention of infinity and infinitesmals and instead talk about limiting processes.

Every action has an opposite and equal reaction. When white light passes through a prism it seperates into its seperate component colours. Want any more?

You seem to misunderstand me. I could explain those concepts without using mathematics at all. Mathematics is just a tool used to express ideas. It is not fundamental to physics, it is however an incredibly useful tool.

Well mathematics elucidates physics but doesn't explain it. Mathematics is just the study of the ramifications of assuming certain axioms.

Stamp collectors like to catalogue their stamps. They may put them in order of date, in order of postmark, in order of colour, in order of reverse alphabet, but their main objective is to collect 'em all, to coin a phrase. Rutherford's derogatory use of the phrase was towards people working in such fields at the time such as geology, botany etc where there was less of a scientific culture, and more of a private hobbyist attitude. Of course these days those areas are perfectly respected scientific careers. In the time of Rutherford and before, those subjects were generally the preserve of the English nobility.

Think of the graph of 1/x, starting at 1, what happens to it as x tends to 0?

Rutherford was reffering to the fact that physics explains chemistry, chemistry explains biology etc. And the stamp collection bit was his way of making fun of scientists who just catologue stuff, like zoologists.

The light waves need to be the same frequency, but radio waves and visible light have massively different frequencies.

If someone tries to teach you that, then tell they they are wrong from me .

We do not need to prove experimentally maths. Maths is not an experimental science. In fact you are right that we shall never reach the number 1, but mathematical limits are not expressed in that way, the true definition of a limit is that you can get as close as possible to the limit to within any degree of accuracy. As for your next post, it is widely believed that eventually space time and therefore motion will be quantised, the reason we do not talk of quantised space time is because we have no working theory. As has been shown above, these "paradoxes" do not need quantised space time to be explained.

Preceded? Really, that is suprising, was that because of the refraction index of the nebula? I would have always expected the light to reach us before...

One useful way to look at what happens if you divide 1 by 0 and 1 by infinity is to consider limiting cases. If you consider the sequence 1/1, 1/(1/2), 1/(1/3) i.e the sequence 1/(1/x) which is basically x, it is clear that a sequence with a finite numerator and a denominator which tends to 0 tends to infinity. In mathematics we say [math]\[ \mathop {\lim }\limits_{x \to 0 } \frac{1}{{x}} \Leftrightarrow \mathop {\lim }\limits_{x \to \infty } x \to \infty \] [/math] Notice that we don't say that it is equal to infinity, only that it tends to infinity. It also follows that a sequence (1/1, 1/2, 1/3 ...) i.e. 1/x tends to 0 as x tends to infinity. Not minus infinity. Again, mathematically, [math] \[ \mathop {\lim }\limits_{x \to \infty } \frac{1}{x} = 0 \] [/math] This time we can say that the limit is equal to 0, because 0 is a real number, whereas infinity is not.

Ah ok. Quite an impressive feat to detect a supernovae from 19 neutrinos!

That is quite confusing, the standard input for maple and mathematica is radians... so I'm not really sure where the difference comes from.

Computerised star surveys pick them up regularly (using regularly in the sense that before computers we'd be lucky if we found 1 every 100 years ) just by scanning the sky and taking pictures and then comparing them with the previous ones. I'm not sure if we detect them using neutrinos, I would have thought neutrinos are far too weekly interacting to be able to use them to detect supernovae. Do you have a source for that, i'd be quite interested.