Severian

It is the requirement that the symmetry should be local (i.e. that [math]\theta[/math] can depend on position) which gives charge conservation.

They have been lulling you into a false sense of security.

Electromagnetism is based on a U(1) symmetry. So the wavefunction can be shifted by an arbitrary phase [math]\psi \to e^{i\theta}\psi[/math] leaving the physics unchanged. What Feynman is refering to, is that this is exactly the symmetry we see when converting wavefunctions into probability distributions,ie. [math]P = |\psi^* \psi| \to |\psi^* e^{-i\theta} e^{i\theta} \psi | = |\psi^* \psi |[/math]

I don't know why, but somehow YT looks deeply scary. Maybe it is the suit, but he looks like he has mob connections.

Fundamental particles are point particles, but it doesn't really mean what you think. A point particle is an object whose position eigenstate is a point. So if you measure its position you get a point (in principle - clearly it is limited by experimental precision). Most of the time they are not in position eigenstates though, so they are smeared out.

Unfortunately confinement has still never been proven. Gribov claimed to have proven it but never wrote down a proof and then died. It is fairly reasonable though. For small values of the coupling constant it is pretty easy to show that the strength of the force (ie. the magnitude of the coupling constant) grows as you increase the separation (this is the proof of asymptotic freedom which won the Nobel Prize recently). However, when they get far enough apart the coupling has become so large that your proof for small coupling is not longer valid.

A scalar particle, i.e. with no spin.

I suppose it is only fair that some part of you is smart.

You are misunderstanding what happens when matter and antimatter come into contact. They 'destroy themselves' only in the sense that they are converted into something else. And this something else is usually photons. So if you hit an electron with a positron you get a photon (you could get a Z-boson as well, but that is a needless complication). Similarly two photons can 'annihilate' into one photon in much the same way. In fact, this does happen in a laser.

I have no problem with evolution (at least in some form, if not exactly Darwin's original version). What I have a problem with was your statement that science could either answer all our questions or none at all. I don't think your statement showed much 'freethinking'.

I am surprised Bush doesn't want to relable 'English' as 'American' too.

Logically it never can be. If eating the apple is wrong, then a being who never does anything wrong (because they cannot choose to do so) can never eat the apple.

I am sorry, but that is such bullshit. If you find a perfectly straight road running for hundreds of miles, you don't need to believe that it will extend in a straight line to infinity before you can make use of it. Science has been extremely useful in most of the things we have done in this planet. There is no guarantee that it has all the answers, and if we find that it doesn't we don't invalidate all of the scientific discoveries made so far.

This is the 'error function' (that is why it is called 'erf') modulo an overall factor of [math]\pi[/math]. It doesn't have a closed form but you can find an expansion for various limits (e.g. t large or t small) using integration by parts. You can find more info here: http://mathworld.wolfram.com/Erf.html

This statement in the original thread was in a context where it was presented as a possible opinion. In other words, it is legitimate for someone to make the proposition that complex structures cannot be generated by evolution. Woelen never said that this statement was a mainstream view of this site or science in general (or even his own!). He only pointed out that this hypothesis is a fair enough question to ask because it can in principle be tested. It is therefore a scientific question. (One would of course need a sandbox planet to play with and a few billion years of free time, but hey we spent $100 billion on something as useless as going to the moon...) If we are not allowed to make statements like this while being moderators or 'experts', then I will relinquish my star without hesitation.

No use denying it. We can see your piccy in your avatar, and the camera never lies...

1991 = 994 +995 but I am not sure how to prove that it is the only case (induction maybe)

English really doesn't have rules, since it is defined by what people speak and write - not by a rulebook. However, the etymology is such that words originating from French did not have their initial 'h' pronounced (e.g. hotel) but words originating from German did (e.g. hair). Whether the 'h' was pronounced or not is what determines whether we use 'a' or 'an' in modern written English. So we should have 'a hair' but 'an hotel'. Hereditary has a French origin, so it is 'an hereditary' (ie. it was originally pronounced without the 'h').

As a matter of interest (and in an attempt to bring this back on topic), what is the general view these days on punctuated equilibrium?

My personal view is that it is all tied in with sentience. We don't regard animals as sentient because they don't (we presume) have a well developed sense of self. Part of that sense of self is our morality - having an opinion about whether we (or more correctly our actions) are right or wrong. So I would say that the coming of sin to the world was really us gaining our self awareness. By eating the apple of the 'Tree of Knowledge of Good and Evil' we learn right from wrong and so when we do wrong we sin - we go against God (which is our definition of good). Now clearly if we are sentient (with morality) and animals are not, then there had to be a point in evolution where man became sentient. It is our self awareness which made Adam hide his nakedness. It is our self awareness which allows us to distinguish right from wrong and indeed which makes our actions right or wrong. We even have this distinction in our vocabulary. Someone who is immoral is a bad person, but someone who is amoral is less than human.

That is true, and notice that you are using the word 'science' here. If one disagrees with the scientific method, then even the things for which there is good evidence become uncertain.