Before the Big Bang

The Big Bang has more in common with ice melting into water than anything else. I'll explain.
A property of ice is brittleness, how easily shattered it is. Water doesn't have this property at all, the property is lost in the phase transition between states.
It is a similar thing with the Big Bang and whatever Quantum Gravity physics went before. "Spacetime" is only sensical idea when things are cold enough.
The Big Bang and a black hole are the reverses of each other in the sense that in a black hole the universe returns to Quantum Gravity physics and at the Big Bang Quantum Gravity physics settled down into our universe.
The Big Bang was a "Freezing" and a black hole is a "melting".
In this analogy the singularity is 0 degrees centigrade. If an alien race only had a theory of ice they'd notice that their equations contained a singularity where brittleness became infinite and that this occurred at 0 degrees centigrade. Edited by Son Goku, : Spelling

Well it was dense and hot back then. Spacetime only exists when the energy density is low enough. High heat and high density imply high energy density. Remember that spacetime only exists on one side of the phase transition. The pre-bang "stuff" wouldn't have been compacted and crushed waiting to "burst".
Whatever that stuff is, when it gets "cold" and "calm" enough it forms a large coherent structure we call spacetime and spacetime operating under its own rules expands once it has formed.

I'm just trying to get across some of the thermodynamic analogies from the Big Bang which I think can be helpful in understanding it. Again as you know it's hard to talk about it when in certain approaches your sentence contains no target nouns (as it would with Hartle-Hawking).I'm kind of just trying to say the big bang singularity has all the hall-marks of an "effective theory" singularity (like theories of oil in the high-viscosity limit). However in some theories this approach is irrelvant, so I'd have to say it another way and emphasize other things,.......... yada yada.......I know the inaccuracy is a bit flippant and I thought you'd pick me up on it, I guess I'm just trying to avoid writing an essay.Do you think it might be better to only discuss the big bang in the context GR and stay clear of an discussion of Quantum Gravity in case one favours one approach too much?

I'll try to stick to what is known and accepted.Any theory of physics has its domains of validity and General Relativity is no exception. Mathematical theories of ice for example all have singularities at the point where temperature equal 0 degrees, the melting point of ice. This is because there are a lot of factors that come into play when ice begins to melt, that the original theory doesn't account for. However, the impressive thing is that the theories of ice announce the fact that they don't work by producing singularities. In a sense they are saying "pretending ice is all there is at this point produces nonsensical results, hence there must be something unaccounted for".When you use General Relativity to model the universe's history you basically get a huge smooth 4-D shape as the answer, these kind of smooth shapes are called manifolds. However, we get a singularity at a certain point on the manifold. Hence for regions of spacetime near this point we can't be sure General Relativity is accurate. If we move out to points on the manifold where General Relativity can still be trusted to make sense, then we'll use only those points in our theories of cosmology.
So now that we have restricted our attention to the part of the manifold where General Relativity can be trusted, what does this part of the manifold tell us?Firstly we find that the points of the manifold can be put in order, by gathering them into huge 3-D shapes, that I'll call slices. Kind of like "First slice, Second slice, Third slice......" where each of these slice's is larger than the one previous. It also turns out that these slices are completely spatial (i.e. they are only space, not spacetime).So we've gotten a smooth 4-D spacetime shape and slices it up into slices of pure space and put the slices in order of increasing size.
You might be thinking "Why slice it up?", however this is because of a stunning fact. It turns out that every observer in the universe will agree (remember this is relativity, it's hard to get observers to agree) with the way we've sliced up spacetime. Although they mightn't agree with our exact order, everyone will agree that the very small slices come before the very large slices according to their personal clock. That the very small slices occurred early on in history.Basically, the slices are the whole spatial extent of the universe at a given moment in time according to one particular observers clock. Although other observers don't quite agree with his/her/its clock, everybody agrees the universe was much smaller in the past.Beyond the very first slice, General Relativity can't be trusted so we've no idea of what happened.It is similar to inhabitants of an ice cube that froze out of a pool of water in the distant past. The inhabitants of the cube have never seen water, however their best theories of the history of their ice cube develop singularities in the distant past, near the point where the water froze and the cube formed. What they need is a general theory of H2O in all its statesYou could see String Theory, M-Theory or any Quantum Gravitational theory as being an analogue of this "general theory of H2O".Edited by Son Goku, : Spelling and grammar.

Okay, to get started I wonder if I could ask you a question ICANT.How, in your own words, would you describe a singularity. What is it?

Right, now I'll tell you what a singularity is. A singularity, in physics, is where some quantity becomes undefined or no longer makes sense.I've given this example before, but if you have a pond or live near a lake you'd have seen some ice form on the surface. That ice can be shattered so it has a certain brittleness. Very easily shattered ice has a high brittleness value, hard ice has a low brittleness value. However when the ice turns into water, brittleness no longer makes sense. You could say brittleness has a "singularity" when ice becomes water.Another example would be an electric field. Very near an electron an electric field starts having "infinite" strength. So the electric field no longer makes sense and thus has a singularity.That's what a singularity is, the point at which a physical quantity becomes undefined or nonsensical.Forgetting about the Big Bang for a moment, do you understand what I just said?

True, what is the problem between this and what I said? I might not have been clear.

No it doesn't, not always. Very close to an electron, the electric field is really a "gas" of virtual photons and ampage would be a useless concept.
(Not to mention that ampage measures current, not the electric field itself.) Really, do you actually understand the piece you quoted? In that piece Hawking is describing the standard technique used to find where singularities are located in a given solution to Einstein's Equations. No. Look, a singularity is where a specific quantity becomes nonsensical.
Physics comes with its own lingo and it makes no sense to rant on and on about it unless you specifically understand what that lingo means.The Big Bang singularity is not a "thing", it marks an early point in the universe where distance and curvature break down as sensical concepts. Hence it makes no sense to say where it came from. Replace the word singularity with "The point early in the universe's history where distance breaks down as a concept".

I'm asking about the technical terms. No. "Paths of observers" refers to the collection of points in spacetime that an observer (piece of matter) occupies. Maybe, maybe not. The standard Big Bang Theory doesn't make claims either way. I have no idea what this means. In the standard Big Bang theory there is no general "null" state or anything. This is the crux of the debate and you take a point of view that I don't understand. Your claim is that because we don't know the physics preceding this point it somehow invalidates physics afterwards?What has been said here repeatedly is that the Big Bang is a theory of the universe's evolution after a certain point. You appear to be criticising this based on the fact that we don't know where the universe as a whole comes from.
Why?Surely you don't need to understand the origins of something in order to model it from a certain point onward. For example if a fisherman asks the weather station will it be stormy later based on the weather now, he won't criticise them for not explaining where weather comes from in the first place.