What I've Learned: Part 1 (Academics)

As of today, my classes are officially done for the semester! For me this has always been a bittersweet time - I tend to become very invested and interested in what I'm learning throughout the semester, so it can be hard when it ends. Not to mention it can be hard to leave my professors and classmates I have been spending so much time with!

In honor of the last day of classes, I wanted to share with you some of the most interesting random facts I've learned in my classes this semester. A vast majority of my time every week is taken up by classes and homework, but I feel like I don't actually talk to other people very often about what I'm learning. (I'm planning on writing another post soon about other things I've learned this semester outside of classes.) This post might be completely boring to everybody else, but here goes!

Computer Networks

• I learned that it's really not very hard to do "mail spoofing" - that is, sending email from other people's accounts. The most malicious thing I've done with it is send a friend an email from their own address, but it baffles me that after about an hour I was able to figure out how to do something that could be potentially very damaging. (That class made me kind of terrified in general about all of the security issues with the internet.)
• I'm a big fan of crime shows, and the impression I've always gotten is that an IP address is basically the permanent identification of your computer. But, did you know IP addresses change quite frequently? In fact, if you disconnect your laptop from one wireless network and connect to another, you very likely have a new IP. (So how do they always find people based on the IP address of their computer?!)

Latin 102

• The United States has 3 mottoes in Latin (if you look on a dollar bill you can see them). Probably the most well known of the three is "e pluribus unum", which means "out of many, one". The phrase has the strangest context - it is found originally in a poem written about a farmer preparing a dish of food. The quote refers to the colors of the different ingredients mixing and become one. I guess when America was called the "melting pot" they were being a bit more literal than I thought...
• When Harvard University was established, proficient knowledge of Latin (and Greek) was required for all applicants, and in fact students were not allowed to speak English on campus.

Classical Mythology

• Maybe this is old news, but I never realized that Mt. Olympus (the mythical home of the Greek gods) is a real mountain in Greece. I guess I always assumed it was made up. Wouldn't they have eventually figured out there were no gods living up there if they could climb the mountain themselves?
• You know the Disney movie Hercules? I learned all sorts of interesting things about the real story of Heracles (his original Greek name). His story wasn't so much a love story, but a horrible tragedy - because of the jealousy of one of the gods, he ended up going crazy and killing his entire family. When he does his labors and kills all the monsters, it is punishment for the murder of his family. (I don't think I'll ever be able to watch the movie again without picking apart every singe flaw in the story...)

Math (Combinatorics and Graph Theory)

• Suppose there are a group of people in a room. Assuming friendship is mutual and we only consider friendships between people in the room, it is mathematically impossibly that an odd number of people in the room each have an odd number of friends. For example, there is no possible situation in which there are exactly 3 people in a room who each have 5 friends.
• There is something called the 4 color theorem which says that any map can be colored with only 4 colors so that no two touching regions are the same color. (Even more interestingly, it can be shown that if the world were shaped like a donut instead of a sphere, 7 colors would be needed. It's actually a lot easier to figure out the case with a "donut-shaped" world.)

see - only 4 colors!