## Saturday, October 6, 2012

### Proof by picture

Today coming to the library I took a picture of the door handles at the front entrance of the lobby,

It always came to my attention that the right handle is more faded that the left one and I decided to take a picture and run a little test on "how much more faded" it is. The direct explanation of this different could be the difference in right-handed and left-handed population at school (at least the ones that use the library), so quantifying this difference in the picture can give a rough idea of the ratio in the student population of left : right handed people.

After lowering the brightness and contrast of the picture, and adjusting the color levels, I got this image on Photoshop CS6 (the one that is at the library). Then to compare the two white regions on the handle, I ran a histogram to count how many white pixels were in each handle. The rust was 19437 pixels for the right and 9476 for the left handle. With this information we have that the ratio of left: right fading is

$\frac{9476}{19437}=0.48$

or almost 1:2. We can say that the population is split

$\frac{9476}{19437+9476}=32\%$ left-handed, $\frac{19437}{19437+9476}=68\%$ right-handed,

or nearly 3 out every 10 people are left handed. Again this is a very rough estimate since it is based only on the people that go to the library and on the fading of the handles of just one door, but I think that it reflects how much information can be obtained by simple facts, plus with almost no effort.