The universe, as we know it, is 13.75 billion years old. This is known with a pretty high degree of accuracy, plus or minus 0.13 billion years. Now hold on, stay with me.
Any scientific measurement has a margin of error. Some measurements can be done very accurately; the fine-structure constant, for example, is known to about one part in a trillion, while the gravitational constant is known to about one part in a hundred. A lot of practical science consists of working to get better and more accurate measurements of quantities like this.
Some people feel, based primarily on the Biblical accounts of the creation, that the earth is a few thousand years old, maybe a few tens of thousands, with the accepted figure varying based on who you talk to. The Irish (but Anglican) Archbishop James Ussher, for example, most famously calculated the creation to have taken place in 4004 BC, by a process often derided as "counting the begats," although that's a misrepresentation of a more sophisticated work of scholarship. More recently, disgraced doomsday preacher Harold Camping maintains that the creation occured in 11,013 BC, while other people, going through the same set of data, have come up with such dates as 12,000 BC, 6894 BC and 3947 BC. The "official" Jewish date (the Hebrew calendar counts years since the creation) corresponds to 3760 BC, but even this was not agreed upon by Jews until Maimonides settled the argument in the 12th century.
Why the disagreement? If we take the creation dates given above we get an average of 6936 BC, but the margin of error is gigantic. If the know the fine structure constant to fifteen decimal places and the gravitational constant to two, the biblically-derived dates above give us an accuracy of zero decimal places! The reason, of course, is that the Bible is not information that can be measured empirically for this purpose. It's not data in the scientific sense, and using it as such requires many gaps to be filled and assumptions to be made, gaps that are filled by the convictions and prejudices of the people making the estimate.
This kind of thing creeps into science from time to time, of course, but it gets ruthlessly stamped out when it's identified, which happens inevitably as new data comes in. These days, before most folks agree on a measurement, it needs to be taken many time, using multiple methods, and the uncertainties, in the form of a margin of error, need to be clearly stated, or minimally, the result itself needs to be stated in the number of significant figures we're sure of. So stated more formally, we know the age of the universe (as we know it) to be 13.75 ± 0.13 billion years. Since it's known with certainty to two significant figures, this often gets shortened to "13 billion years."
This illustrates one problem communicating scientific information to non-scientists. Such terms as "theory," and for that matter "age of the universe" mean something different and more precise to scientists than they do in everyday speech. When your woman on the street hears "age of the univrse," she's likely to think of it as something like "the time that's elapsed since everything first came into existence," based on the common idea of what the word "universe" means. But a cosmologist hears "the age of the Lambda-Cold Dark Matter Expansion epoch," which means something rather different — the age of some portion of everything that exists, which happens to contain the entire visible universe, but not necessarily "everything that exists."
I'm avoiding linking these scientific terms because I think it'll confuse the issue, but you're free to Google them if you're really curious. The point is that the people who accept the biblical date (more or less) and those who accept the scientific date (more or less) aren't speaking the same language, and so are talking past each other, for the most part.
This is a failure, really, of the American educational system. There's a reason, after all, why the debates between Cosmology and Creationism and Evolution and Creationism are by and large not happening in other advanced nations, and why Americans feel pressured to choose between their faith and established scientific facts. A conflict is seen where none really exists, as people who speak both languages understand, like Francis Collins and Georges LemaƮtre. Folks who speak the language of faith but not that of science, who feel forced to choose between accepting "what the Bible says" versus "what scientists say" of course stick with the Bible.
The most visible and outspoken advocates of the "new atheism," Richard Dawkins and Christopher Hitchens (both Brits, which may be no coincidence, and both of whom I have enormous respect for,) are tone-deaf when speaking to American audiences about this subject, and Dawkins was even been called on this publicly (but very politely) by Neil deGrasse Tyson. Dawkins does not, as Hitchens did not, speak the language of faith, so they pose the same kind of black-and-white conflict that Ray Comfort does from the opposite side. It's a position that may work better in far less religious Europe, but it's harder going here, and I suspect that it creates more enemies than converts.
From this standpoint, a work like Jerry's Coyne's Why Evolution Is True is much more valuable than Dawkins's brand of fiery atheism.
Framed properly, the debate should not be Christianity vs. Atheism, but whether one should accept the scientific understanding, so amply demonstrated in both theory and evidence that it's indistinguishable from colloquial "fact." Let the truth speak for itself, and educate those who don't understand that truth and how it was arrived at. This is, as history shows, considerably harder than denouncing those who don't accept the scientific version as troglodytes, but it's the right thing to do both ethically and pragmatically. The truth can carry itself, you just have to let it do the work, no matter how hard the task of explaining it to people.
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