One of the things that I like about YouTube is the many changes to watch things that are educational. I don’t take advantage of that as often as I should, but one of the shows that I watch fairly often is Numberphile. Numberphile is as the name implies is about numbers and math and it isn’t a softball show. This is one of the few things I have ever watched that I feel like I should understand but still goes over my head the first time and there are a few of the episodes I have watched a number of times and while I believe them I’m still not sure I really understand.
Don’t let that scare you away though. Not all of the episodes are that difficult and even those that are explained from a point that doesn’t require all that much skill in math and even if you’re not all that interested in math the people doing the videos are excited enough about what they talk about that it is still interesting. It’s also a great way to learn about different mathematical concepts.
The show is a bit difficult to explain beyond simply saying that it’s very smart people talking about things that they are excited about. But I also want to try to explain one of my favorite of their videos. That is an explanation of something that seems truly bazaar, largely because it is dealing with infinity.
The video is explaining the sum of the sequence of all natural numbers. That is to say that it answers the question, if you add 1 + 2 +3 +4 … etc forever. The problem, of course, is that you can’t actually add all of them because they go on forever. But they can find the sum of some infinite sequences. For example, if you have a sequence of -1 + 1 -1 forever. The other that they use in the example is 1 -2 +3 -4 forever.
They can get the answer for the first which is 1/2 and they explain why well. Next they find the 1 -2 +3 ect. by using some very interesting math, they can find a way to change those numbers to the -1, +1 sequence. They explain it far better in the video below, but the point is that you can find the sequence of natural number is - 1/12. And if nothing else if you tell one of your friends that is true you’re going to win the argument when they say you’re insane.
There are a ton of other great videos of the Numberphile channel, including the ho to win at let’s make a deal, the problem in good will hunting and many others. But don’t take my word for it, check out their channel here or watch someone smarter than me explain the sum of the sequence of whole numbers below.