Mapping

Sometimes I think I should start off my blog pieces with a line from Almost Famous. I have tons of strange, innocuous (and usually incoherent) thoughts racing around my head all the time, and this post will contain one of them. Here's the scene from the movie:



So here's a theory for you to disregard completely:

A few days ago I went running along the East River, and I started thinking about my face. Hey, the mind wanders. More specifically I was thinking about my resemblance to other people in my family. It's fairly obvious that I've inherited my most striking features from my maternal grandfather, Marvin. We have the same facial shape, similar bone structure, and, ah, that nose. Plus I'm starting to master his incredulous/exasperated look, though my eyebrows ain't got nothing on his:

Hardly a revelation. However, from the right angle, I think I also bear a pretty strong resemblance to my paternal grandmother, Betty. I've noticed it more and more, especially in facebook photos posted on my timeline this summer.

Which got me thinking...

One of the most useful concepts to understand in mathematics is that of a "function." There are a bajillion different ways to think about a function, but in a basic sense it takes an input and transforms it into an output. For example, a gumball machine performs the "function" of transforming a quarter into a gumball. Or with numbers, let's say your input is 2 and output is 4; input is 3 and output is 9; input is 4 and output is 16; ... The function is to take the input and square it.

You can also use functions to explain a lot of visual things that involve math. Take a projector, for example. Place your hands in front of the light of a projector, and suddenly there's a bird on the wall!

Your hands are the input, and the image on the wall is the output. Depending on how you angle your hands, different images appear on the wall. In math, stuff like this is called mapping. You're mapping an image of your hands onto the wall. The cool thing (and, yes, I'm using the word "cool" very loosely) is that the same pair of hands can make a bajillion different images, depending on how the light hits them.

...Which brings me back to my face. I was thinking that genetics are kind of like mapping. I was also probably thinking of the term "genome mapping" which doesn't exactly apply here, but, you know, word association. Certain traits from our ancestors are "mapped" onto us, only we can't see them all at once because the image depends on the angle. It's like we're a mosaic of our family tree, each feature a different projection from one of the branches.