I wondern wether - in discussing the concept of 'infinity', we are actually creating a bogus discussion of.. well.. semantics.
My understanding is that the concept of infinity - in the modern sense - was merely a mathmatical tool to cope with the concept of a number being divided by zero. In the same sense that the construct "i" was created to represent the square root of a negative number.
We develop language as a tool to help us manipulate - or come to terms with - our environment. And I include mathematics as being a language, for the purposes of this discussion.
However, it is important to recognise that "the tool is not the thing itself" .. it is merely a label that may only apply in specific circumstances.
Hence to discuss a line as being infinately long is a structural/semantic error; the "infinity" tool is not intended to be used in those circumstances. It is the equivelant to asking what sound a particular colour makes, or what is the width of an odour. The question itself is synesthesic and misleading.
Stephen Hawkins touched on a varient of this in his discussion of the "big bang" singularity theory. He proposed that there COULD have been a universe in existence PRIOR to the big bang; a universe that collapsed to form the singularity from which our universe subsequently emerged. However, he pointed out that no structure or information could survive the environment of the singularity and be passed forwards, and therefore it would be impossible for us to deduce anything about the nature of that prior universe.
Hence, in practical terms, the big bang IS the starting point of our universe; it is bounded at one end. And at the other end ? Who knows; our toolkits called "length" and "duration" may not be appropriate to operate at that scale, and hence it is meaningless to attempt to apply them. Even the toolkit called "time" is only usefull for day-to-day stuff; nobody can actually state what time IS.
As for the discussion on infinate energy in a Black Hole; I am puzzled by this. A Black Hole is just a name for an object that exceeds a certain mass. Other than that, it is just a perfectly normal planet (or perhaps a sun). There is nothing inherently magical about them.
So to summarise: Infinity is a label to describe what heppens when you divide a number by zero. It has no other literal meaning. If it is used outside of this definition, then it ceases to have any real meaning and becomes .. well.. a sort of metaphor. Analysing a metaphor - especially out of its context - is rarely fruitfull or meaningfull.
Meow Purr
A cat stretches from one end of my childhood to the other.