This question came to me after reading this question on the Astronomy Page, and having a length discussion with colleagues about the 2002 movie "The Time Machine". As a result I am looking for hard-science based hypotheses about what would happen.
Setting the Background
Let's assume we as humanity, somehow damaged the moon such that it split in two (See Edit 2). This would obviously have immediate effects on our lovely blue ball we call home. What I imagine those effects would be are a drastic change in the tides, which would result in a change in weather patterns, probable large scale earthquakes as the earth and moon work out their differences and settle out a new orbit. There would probably be meteors (moon-debris) crashing through our atmosphere as well. There is probably more, but I don't know enough about geology, and what not to come up with more.
If you come up with more please note it in your answer.
Let's fast forward 500 years. What does our world, our society(ies) look like. Would we as a people advanced or would we have regressed and enter a new "Dark Ages" in terms of society and lifestyle? Here is the kicker - what would be the biggest changes we as humanity would face and how do you believe we could overcome them? Please use science to back up your hypothesis of how the lunar changes would effect us, and how these changes would impact, shape or destroy society.
It's been pointed out to me that this may be a duplicate of this question. And while, they both deal with the shattering of the moon and the effects of it on the planet. That post doesn't deal with the human aspect of it, which my question does.
Edit 2 --- How the moon was split
The year was 2049, the moon had successfully been settled with a small International group and they were researching the surface and doing minor core drilling for samples. As we discovered during the Apollo Moon Landing and since, there are a lot of moonquakes. One day, it was relatively routine, there was an asteroid impact on a portion of the moon far enough away that our settlement was left intact. However, the subsequent moonquake which was compounded by our core drilling and the new(ish) fixtures of our settlement on the planet sparked a chain reaction that resulted in the splitting of the moon - much like a windshield after getting a rock chip.
Yes, I realize that this cause is far fetched, but I wanted to go with something that would generally keep the moon in its orbit so we can focus on the human aspect of life on earth post-split.