If science is based on observable, measurable data, what is the basis of science's belief of the origins of the 'Big Bang'? Even religions talk of the cataclysmic beginnings of the Universe, but they don't claim the Bang was of Nothing. Observable, mathematical data suggests nothing begets nothing.

This gets a bit beyond my expertise, but I suppose like you I find these sorts of issues irresistible. (Kant thought that part of that irresistibility was a feature of our being rational beings, by the way. Perhaps he was right.)

Anyway, I'm not exactly sure what you mean by "origins of the 'Big Bang'," but I'm unaware of any scientific theories advance any position at all on any cause or originary reason for the big bang. The bang itself, perhaps from an original singularity, is as far back as natural science goes. Indeed, in a sense, it makes no sense to speak about any time before the big bang, since as I understand it time began with the big bang, too.

Now, I have encountered speculation about the big bang being one in a 'series' of big bangs--where a bang would be followed by a period of expansion, which would be followed by a contraction back to a singularity, which would be followed by another big bang. But that still wouldn't offer an explanation about why this cycle exists in the first place. And, anyway, my understanding is that calculations of the mass and rate of expansion of the universe indicate that the universe is not expected to contract. Instead, it's expected to expand forever until entropy leads everything to decay into a kind of very low level radiation. Some have called this cold-state hell.

Perhaps some of my colleagues can offer more on this topic.

Keep this in mind, however: while it's true that atural science can only tell us about the natural order, it can make claims about things unobserved and even unobservable. Like in times past the dark side of the moon, many parts of other planets are at present unobserved, yet science makes certain claims about them. (For example, that the laws of physics apply to them; that objects there are composed of the same elements as objects here, etc.) Many sub-atomic particles (quarks, for example, perhaps even electrons) can never be observed directly. Forces are not themselves observed. What scientists observe are their effects--or anyway observable events that scientists believe are their effects. What business does natural science have in positing the existence of unobservables? Well, it's a complex story, but basically science is warranted in positing the existence of things that have never or can never been observed on the basis things that can be observed. Moreover, claims about those unobservables can be discliplined and even overthrown in science by observations of observables. That can't or anyway need not be the case in religion. In the case of religion, unobservables are posited irregardless of observation and the character and standing of those unobservables may well be (and is often) little disciplined by observation.

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