One of my favorite intellectual pastimes is tracing branches backward until I find where they meet at the roots. Whether it is two species that evolved from a common ancestor, or two words that did, I love learning about it. When you think about it, this world is full of things that are--in a conceptual sense--tree-shaped. To see the tree, you have to look at how related things have evolved over time. For example, all the branches of the tree of life, from bread mold, to elephants, to redwoods, can be traced back to one root: a lowly single-celled organism that existed billions of years ago. All the diversity of life on earth--millions of species--also has a fundamental unity. As different as they are, redwoods and elephants have a common history, somewhere in the distant past. Because of this shared history, they have things in common: shared features they inherited from common ancestors. For example, all living things share certain genes that code for a few universal proteins, which may have been around since life began. These genes and proteins may differ very slightly between, say, E. Coli and humans, but they are basically the same, and usually still have the same function. The more recently two lineages diverged from each other, the more they will have in common. Orangutans have a lot more in common with gorillas than with seaweeds, because they shared a common ancestor with gorillas more recently.
Culture evolves too, although the process isn't directly analogous to biological evolution. Still, culture tends to unfold in tree-like patterns, where unity branches into diversity. You see this pattern with language, music, fashions, and just about anything else that people transmit to each other and modify over time. One thing that makes this interesting is that, as you look backward in time, you see unexpected connections. Here's a trivial example. A while back, I noticed the word "disaster", and for some reason thought about where it might come from. "Aster" means star, I realized, so disaster means "bad star". I looked up the history of the word, and my guess was right. Now, I could go see a bad Jerry Bruckheimer disaster movie about an asteroid threatening the earth, and lean over to the guy in the seat next to me and say "Did you know 'disaster' and 'asteroid' both come from words for stars?" When he gets up and moves, I'll have more room. See, this stuff is more useful than it looks.*
But really, what I love about noticing connections like that is that one minute you are looking at a word like "disaster" and taking it for granted. The next minute, you are looking into the word, seeing the history encoded in its structure. With disaster, you might guess (rightly) that the word comes from a time when people took astrology very seriously. Disasters were thought to happen under bad stars...disasters happened because of dis-asters. I love the fact that sometimes you can look at a word, notice the root words it's made of, and get an insight into how people thought when the word was coined.
* Just wanted to point out that "asterisk" also comes from the word for star. Just look, it even looks like one.