Being the inherently lazy person that I am (I swear it’s in my DNA), I put off thinking about Friday’s entry until late Thursday, then remembered that I would be out of town this weekend starting mid-Friday. I didn’t want to put off my first “regular” update, but I didn’t have the time to tackle anything ambitious for this post… so today’s post is a quick collection of thoughts (well, two) that I’ve jotted down in the past couple of weeks while spending an extraordinary amount of time waiting for buses. And they’re both bus-related.
The Bell Curve of Bus Arrival
I spent so much time worrying about math last semester that I started to think in graphs. Public buses rarely arrive exactly at the minute specified; certain everyday factors can make a bus arrive either earlier or later than anticipated. Did you know that the probable arrival of a bus forms a bell curve?
As shown in my illustration above, a bus is often most likely to arrive in the first five minutes before or after the specified arrival time. The chances that it will arrive decrease as the time on either side lengthens; the bus is less likely to arrive ten minutes before or after than five, and even less likely to arrive fifteen minutes before or after.
Example of correlation =/= causation
After a week of constructing mathematical proofs in class (why do these bus-related thoughts both have to do with math?), I was thinking a lot about symbolic logic in philosophy, which I had studied in a class back during the summer. Mathematic logic and philosophical logic are very similar… the only difference between a proof of either would be the kinds of symbols. Anyway, I was thinking about that logic course, and I remember that there was a lot of emphasis on the idea that causation does not follow from correlation. It seemed simple enough, but since then, I’ve heard it stressed in so many other areas that it made me rethink its importance. It was in my head while I was waiting for the bus, and so I came up with this example of why correlation does not imply causation:
1. Two buses, Bus A and Bus B, come by my house every hour in opposite directions.
2. Bus A always comes by one minute before Bus B.
3. There is a correlation between the arrival of Bus A and Bus B.
4. However, the arrival of Bus A does not cause the arrival of Bus B.
Therefore, correlation does not necessarily lead to causation.
I’m pretty sure I’ve missed a couple of steps necessary to make it a sound argument in formal logic, but it’s rational, anyway, and I think it’s a pretty decent example.
(As for why correlation =/= causation is so important in the first place… well, it makes sense logically when you think about it, but people assume that one thing causes another without evidence of causation all the time. It probably needs to be stressed just to aid critical thinking.)
I’ll be killing a lot of time over the weekend waiting for more buses… maybe I’ll put it to better use and try to think about something more practical, or at least one of the topics I still mean to blog about. Expect a better post on Monday!